Input: Task: contrast the claim using the given text. Claim: Quantum mechanics can be completely understood through classical physics. [SEP] Text: radiation does a fairly good job predicting the ground state of Hydrogen. 4. 4. Unification of physics via Planck’s constant In conventional QM, r e + r p is expressed in terms of Planck’s constant h which is presumed to be a fundamental constant of Nature: r e + r p = h 2 4 π 2 μ e 2 E15 Here μ is the so-called ‘reduced mass’, defined by μ − 1 = m e − 1 + m p − 1 which makes μ ≈ m e. Using that approximation and equating the two expressions (13) and (14) for r e + r p implies h ≈ π e 2 c 128 m p 3 m e E16 This expression comes to a value of 6. 77 × 10 − 34 Joule-sec, about 2% high compared to the accepted value of 6. 626176 × 10 − 34 Joule-sec. This reasonable degree of closeness suggests that Planck’s constant may reasonably be considered a possible function of other fundamental constants of Nature, and so not itself an independent fundamental constant of Nature. Or the situation may reasonably be considered the other way around: that some other fundamental constant of Nature is really a function of Planck’s constant. Either way, we would have one less independent fundamental constant of Nature, and that would mean one more degree of unification among the different branches of physics. But of course, the expression for h developed here can fulfill such aspirations only if the theory being developed can do a great deal more than just match the ground state of Hydrogen. Worthy targets for additional work include: anticipating the story for isotopes of Hydrogen, anticipating from there what happens with other elements, explaining the excited states of Hydrogen and their resulting spectral lines, anticipating from there the spectral features of some other elements, and characterizing the behavior of the full database on ionization potentials of all elements, and much more. It all constitutes a developing research area that I refer to as ‘Algebraic Chemistry’. Advertisement 5. Extensions and extrapolations from hydrogen 5. 1. [SEP] Justify:

Output: The text contrasts the claim by discussing the limitations of classical physics in fully explaining phenomena in quantum mechanics, such as the significance of Planck’s constant and the need for further development beyond simply matching the behavior of Hydrogen. It emphasizes that classical physics alone cannot account for the complexities involved in quantum behaviors, highlighting that unified theories in physics go beyond classical interpretations.


Input: Task: pass the claim using the given text. Claim: Bioinformatics is crucial for analyzing genomic data. [SEP] Text: Skip to main content Explore journals Get published About BMC My account Search all BMC 1. In these cases, frequentist test statistics based on the likelihood ratio statistic have unknown distributions and are therefore not applicable. Our simulation study shows that Bayes factors favor the right model most of the time when tumor suppressor genes are present. When no tumor suppressor genes are present and background allelic-loss varies, the Bayes factors are often inconclusive, although this results in a markedly reduced false-positive rate compared to that of standard frequentist approaches. Application of our methods to three data sets of esophageal adenocarcinomas yields interesting differences from those results previously published. ConclusionsOur results indicate that Bayes factors are useful for analyzing allelic-loss data. BackgroundAllelic-loss dataThe goal of studies of allelic loss is to determine those loci in tumor tissue where genetic material has been lost. A tumor suppressor gene (TSG) is much more likely to lie on a chromosome arm where there has been significant allelic loss than elsewhere [1, 2]. The statistical challenge lies in distinguishing between "random" allelic loss that is expected in a tumor cell population and "nonrandom" loss that may be biologically meaningful. This corresponds to determining whether there is one group of arms with background allelic loss versus two groups of arms, one with background loss rates and one with elevated loss rates. Three allelic-loss data sets on esophageal adenocarcinomasEsophageal adenocarcinoma is a form of cancer involving the cells along the lining of the esophagus. The cause of esophageal adenocarcinoma is not well understood. The incidence of this cancer has been increasing rapidly. In fact, it is one of the fastest growing cancers in the over the past 20 years [1, 3, 4]. A strong association has been established between the pre-malignant condition known as Barretts esophagus and the development of adenocarcinomas of the esophagus. Barretts esophagus is a condition that develops in 10–20% of patients with chronic gastroesophageal reflux disease. The condition is characterized by the metaplastic change from normal squamous to columnar epithelium in the esophagus [1, 4]. [SEP] Justify:

Output: The text is irrelevant to the claim as it does not mention bioinformatics or its importance in analyzing genomic data. Instead, it discusses the statistical methods for analyzing allelic-loss data in esophageal adenocarcinomas without connecting these methods to bioinformatics.


Input: Task: corroborate the claim using the given text. Claim: Bioinformatics is crucial for analyzing genomic data. [SEP] Text: 2 genome browsers are incredibly helpful for the dynamic viewing of a genome and its associated annotation data (e. g. genes), most web-based genome browsers center on one or a handful of genomes, and restrict the ability to import data and perform analyses within the genome browser itself. In contrast, EPIC-CoGe allows users to take full advantage of the genomic resources and analysis tools available within the CoGe platform, including adding new data and annotation tracks, and performing comparative analyses across those tracks (Supplementary Fig. S1A and B). As described below, EPIC-CoGe includes several enhancements that allow the user to quickly integrate, visualize, search, compare, analyze and export/share their genomic data. 2. 1 Integration with CoGe’s genome management systems By integrating JBrowse within CoGe, we offer users the ability to rapidly view genomes and genome associated data for all species in the CoGe database. Users can load new genomes and perform genomic/transcriptomic analyses within CoGe using the LoadGenome and LoadExp+ suite of workflows (Grover et al. , 2017), and then easily visualize those data within EPIC-CoGe. Comparisons and analyses of data tracks (e. g. methylation overlapping SNPs) can be performed on a mixture of public and privately generated data, all while maintaining provenance and restricting access to specific users. 2. 2 Search features EPIC-CoGe offers a number of features for searching through datasets to quickly identify regions of interest. Searching within the track selector: Tracks can be searched for by name or by type (i. e. show BAM alignment). On the right side of the display the user can filter by text that pertains to either a track name or the type of data associated with that track (Supplementary Fig. S2A). For instance, the user can search through their experiments for BAM files, or search for a specific BAM file based on its name. Only tracks associated with the genome being browsed are found in the track selector, minimizing confusion. (i. e. Homo sapiens RNA-seq data is only associated with the Homo sapiens genome). Searching within the main display: Users can search features by name using the ‘Find Features’ button from the navigation bar at the top of the track viewer. Depending on the track types present, users can also search tracks within the viewer. [SEP] Justify:

Output: The text corroborates the claim by detailing the functionalities offered by EPIC-CoGe, which provide extensive tools for integrating, visualizing, searching, comparing, analyzing, and exporting genomic data. This indicates that bioinformatics tools, like EPIC-CoGe, are essential for effectively analyzing genomic information, thereby supporting the assertion that bioinformatics is crucial in this field.


Input: Task: contrast the claim using the given text. Claim: Quantum mechanics can be completely understood through classical physics. [SEP] Text: Larger nuclear mass The negative energy of the electron in the ground state of the Hydrogen is e 2 ( r e + r p ) = 3 c 2 m e 2 2 5 m p E17 This is the energy that would have to be provided to liberate the electron, or ionize the atom: the ‘ionization potential’. Eq. (16) provides the basis from which to build corresponding expressions for other entities. For example, the extension to Deuterium and/or Tritium requires that the proton mass m p be replaced with a more generic nuclear mass M and that r p be replaced by r M. Then we have for the ionization potential of this more massive system: e 2 ( r e + r M ) = 3 c 2 m e 2 2 5 M E18 5. 2. Arbitrary nuclear charge The extension of the model to a neutral atom with nuclear charge number Z involves Z electrons as well. To develop the mathematical model, we must return to the expressions for P torquing and P total radiated Eqs. (10) and (11). All the factors of e 2 change to Z 2 e 2 and the factor of m e 2 changes to Z 2 m e 2. The equality P torquing = P total radiated becomes Z 4 P torquing = ( Z 6 Z 2 ) P total radiated = Z 4 P total radiated. So nothing happens to the equality between P torquing and P total radiated Eq. (12). But for the more charged system, the energy Eq. (17) becomes Z 2 e 2 ( r e + r p ) = Z 2 3 c 2 m e 2 2 5 M E19 This scaled-up expression represents the magnitude of the total ionization potential of the system involving Z protons and Z electrons. What is then comparable to the ionization potential for removing a single electron is: Z e 2 ( r e + r M ) = Z × ( 3 c 2 m e 2 2 5 M ) ≡ ( Z M ) × ( 3 c 2 m e 2 2 5 ) E20 Thus in the math we find a Z M scaling law. What do we find in the actual data? Something much more complicated, and indeed so complicated that we would be unlikely ever to figure it out without the clue that Z M is part of the story. [SEP] Justify:

Output: The text contrasts the claim by detailing aspects of quantum mechanics that involve complex mathematical models and scaling laws which cannot be adequately explained by classical physics. It describes ionization potentials and the relationship between nuclear charge and electron behavior, indicating that understanding these phenomena requires more intricate considerations than those provided by classical physics.


Input: Task: pass the claim using the given text. Claim: Bioinformatics is crucial for analyzing genomic data. [SEP] Text: Approximately 1% of patients with Barretts esophagus progress to esophageal cancer [3]. Of those who develop the cancer about 90% will die as a result of the disease [1]. We examine three data sets of allelic-loss on esophageal adenocarcinomas that attempt to identify the tumor suppressor genes (TSGs) involved in the development of this disease. These data sets have been previously analyzed and published. We refer to each data set by the last name of the first author of the publication. Some of the data sets record allelic loss on multiple loci per chromosome arm for some of the arms. However, because the number of loci evaluated per chromosome arm is not random (i. e. , chromosome arms suspected of harboring a TSG will be assessed at more loci than others), we consider only one locus per chromosome arm. In these cases, we choose data from the most informative locus for that chromosome arm. Our approachOur general approach to analyzing allelic-loss data can be described in two main steps. The first step is to choose an appropriate model for the data using Bayes factors. The second step is to classify the chromosome arms as harboring TSGs or not according to the selected model. The details involved in these two steps are described below. Results and DiscussionProposed class of modelsA natural way to model allelic-loss data is in terms of a mixture of two distributions: one distribution corresponds to chromosome arms that harbor TSGs and the other corresponds to arms that do not. It is reasonable to expect considerable variability in the loss rates of arms that harbor TSGs due to the existence of multiple pathways leading to the same tumor type [5]. For example, deletion of a particular TSG may be in the causal pathway for 60% of tumors of a particular type while another TSG (or other TSGs) may account for the remaining 40% of the cases. In addition, it is conceivable that various factors play a role in background loss rates. For example, factors such as cell viability, fragility of the chromosome arm, and the length of telomeres are believed to influence background loss rates [6]. It is plausible that the non-TSG loci that contribute to the background loss rate are in fact composed of two biologically different groups of loci. This group includes loci that are essential for cell viability and those that are not essential. [SEP] Justify:

Output: The text is irrelevant to the claim as it focuses on the analysis of allelic-loss data related to esophageal cancer without discussing the role of bioinformatics or genomic data analysis. While it describes methodologies for analyzing certain data sets, it doesn't address the importance of bioinformatics in that context.


Input: Task: corroborate the claim using the given text. Claim: Bioinformatics is crucial for analyzing genomic data. [SEP] Text: For example, SNP tracks can be searched by type or by SNPs that overlap features (Supplementary Fig. S2B). Searching a range of values: Users can quickly identify regions within their experimental track that correspond to a particular value, or range of values. For instance, when examining a track containing expression data, it is simple to identify the transcript with the most read depth by selecting ‘Data’ from the drop-down menu next to the track label (Supplementary Fig. S2C). A pop-up window asks the user if they want to search by maximum value, minimum value, or transcripts that fall within a range of user-selected values. Values can also be selected on a histogram of all values. The results of this search are displayed in a new track. Searching data and feature tracks for overlap: The user can also identify data within a track that overlaps a particular feature based on feature type or feature name. For instance, data within a track that overlaps with a gene feature such as ‘miRNA’ can be quickly identified by clicking on the drop-down arrow next to the track label and selecting ‘that Overlaps Features’ (Supplementary Fig. S2D). A new track will be generated displaying the search results. 2. 3 On-the-fly analyses The EPIC-CoGe browser allows for multiple dynamic, on-the-fly comparison of datasets. Comparisons: Users can analyze data and feature tracks for either intersection or complement of values with any other track. Such analyses are conducted by simply dragging one experimental track on top of another while holding the command/ctrl key. A dialog window then prompts the user about which type of data to identify—unique (non-overlapping) or common (overlapping). A new track displays the results (Supplementary Fig. S3A and B). Merging tracks: Multiple tracks can be merged into a new, single track that contains all information from both. The ability to merge tracks can help alleviate ‘vertical bloat’ often encountered with genome browsers, where numerous tracks can become unwieldy. Merged track results are given a name that describes how they were generated (Supplementary Fig. S3C). Merging markers: Datasets can be simplified by merging close markers into a single contiguous marker. [SEP] Justify:

Output: The text corroborates the claim by detailing functionalities of the EPIC-CoGe browser, which allows users to perform dynamic analyses of genomic data. For example, the text mentions the ability to search for overlapping features within tracks, perform comparisons, and merge tracks, all of which are integral processes in bioinformatics that facilitate genomic data analysis.


Input: Task: contrast the claim using the given text. Claim: Quantum mechanics can be completely understood through classical physics. [SEP] Text: The involvement of M means the involvement of isotopes, and unwanted complexity. So the clue tells us to look at ionization potentials, not in raw form, but scaled by M Z to remove the Z M factor that the math anticipates. Figure 2 shows the pattern found. Seven orders of ionization are included. There is a fascinating, but lengthy, story about ionization orders 2 and up; see Whitney (2012). The part of it that will be most important for the present development is obvious from Fig. 2: the energy required to completely strip the atom scales with Z 2. Figure 2. Ionization potentials, scaled by M Z and modeled algebraically. With their M Z scaling, all of the I P ’s can be represented in terms of a baseline value equal to that of Hydrogen, I P 1 1 and an increment Δ I P 1 Z. The increment arises from interactions just between the electrons, quite apart from the nucleus. The electron-on-electron increments are very regular in their behavior. First of all, every period exhibits a general rise, and by the same factor of 7 2. Second, there is a general drop from one period to the next, for the first three periods, and all by the same factor of 7 8. Then within periods, there is a very regular pattern. There are sub-period rises keyed to the traditional ‘angular momentum’ quantum number l and to a non-traditional parameter N that goes 1 2 2 3 3 4 4 for periods 1 through 7 and gives the number of elements in a period as 2 N 2. For l ≠ 0 we have: incremental rise = total rise × fraction and fraction = [ ( 2 l + 1 ) N 2 ] [ ( N − l ) l ] The following Table details the behavior fractional rises in First-order I P ’s over all sub-periods: Table. 1. The scaled ionization potentials are called I P ’s. They are meant to be ‘population generic’; that is, the information they contain concerning one element can be applied to a calculation about another element in a different state of ionization, or excitation, by applying the Z M appropriate for the second element and its state. 5. 3. Unequal counts for electrons and protons Let us first consider ionization sates. [SEP] Justify:

Output: The text contrasts the claim by discussing ionization potential in the context of quantum mechanics and atomic behavior, implying that understanding these phenomena requires methods beyond classical physics. The existence of complexities in ionization, such as scaling with Z² and the behaviors tied to quantum numbers, suggests that quantum mechanics presents unique concepts and behaviors that cannot be fully explained by classical physics alone.


Input: Task: pass the claim using the given text. Claim: Bioinformatics is crucial for analyzing genomic data. [SEP] Text: The essential loci would be expected to exhibit loss rates considerably lower than that of the non-essential loci as their function controls the cell's survival. We propose a class of mixture models that account for the variation inherent in this type of data. Specifically, the class of models we propose is a mixture of two beta-binomial distributions. i be the number of tumors with allelic-loss for the i th chromosome arm, and let n i be the number of informative tumors for the i th chromosome arm, for i = 1, 2,. . . ,N, where N is the number of chromosome arms in the study. The density function for X i is written as follows: where θ≡ (η, π1, ω1, π0, ω0) is a vector of unknown parameters, η is the mixing probability, π j is the average loss rate, and ω j is the dispersion parameter for j = 0,1. The distribution converges to a mixture of two binomial distributions as both dispersion parameters go to 0 (ω0 → 0 and ω1 → 0). If only one of the dispersion parameters goes to 0 (ω0 → 0 or ω1 → 0), the distribution reduces to a mixture of a beta-binomial and a binomial distribution. Note that the model has only one component when the mixing parameter is zero (η = 0). Model selection using Bayes factorsBayes factors are measures used to compare the fit of two competing models. We suggest using Bayes factors to select an appropriate model for the data from the proposed class of mixture models. Let H0 and H1 represent the models under the null and alternative hypotheses, respectively. When comparing two models, it is of interest to examine the posterior odds of one model to another. It is easy to show that the posterior odds of one model to another is Equation (1) shows that the posterior odds is calculated as the product of a term known as the Bayes factor and the prior odds. factor is the marginal likelihood of the data under H1 divided by the marginal likelihood of the data under H0, or B10 ≡ Pr(X|H1)/Pr(X|H0). Thus, as Bayes factors are proportional to the posterior odds of one model to another, they are desirable measures to use for model selection. [SEP] Justify:

Output: The text does not directly address the claim regarding the importance of bioinformatics in analyzing genomic data. Instead, it focuses on statistical modeling and methods for analyzing data related to tumor genetics and does not make any claims about the broader field of bioinformatics or its role in genomic analysis.


Input: Task: corroborate the claim using the given text. Claim: Symbiotic relationships in microbiomes can influence health. [SEP] Text: What can we learn about microbiomes by studying wild mice? Published: August 25, 2022 Within every one of us, there lives a thriving community of microscopic life, known as our microbiome. Like most other vertebrates, we rely on our microbiomes to help us maintain key biological processes, such as digestion and immunity. Despite their importance, there is still a lot that we do not know about microbiomes and how they impact the health of their hosts. Knowles, from the University of Oxford in the UK, aims to change this by studying the microbiomes of wild mice — the microscopic life that lives in or on another organism, including bacteria, archaea and protists — single-celled organisms that do not have a nucleus, but are distinct from bacteria — the process of determining the order of nucleotides in a strand of DNA. This method can be used to identify which microbes are present in a sample — an experimental technique that allows a microbiome to be transferred from one individual to another — a technique used to temporarily capture wild animals designed not to harm them, that allows scientists to sample and measure them — single-celled organisms that have a nucleus, such as algae We humans often pride ourselves on our independence and self-reliance. We strive to navigate the trials and tribulations of life as resilient individuals – if we are lucky, receiving help and support from family and friends in times of need. But there is, in fact, something that is always with us, that helps to keep us functioning as we should, even though we rarely think of it – our microbiome! At this very moment, your body is home to roughly 38 trillion cells that do not belong to you, and only 30 trillion cells that do. These 38 trillion ‘foreign’ cells make up your microbiome – a collection of microscopic organisms that play an important role in keeping you alive and healthy. Much of our microbiome is found within our guts. Hundreds of species of bacteria live in our intestines, alongside a menagerie of viruses, fungi, protists and archaea. The microorganisms that make their homes in our intestines perform a range of different roles that help keep us healthy. They help us digest food, some play a role in regulating our immune system, and may even influence our moods by producing serotonin, which has antidepressant properties. Research into microbiomes has exploded over the last couple of decades. However, most microbiome studies so far have focused on humans or animals in labs. [SEP] Justify:

Output: The text corroborates the claim by explaining the essential roles of microorganisms in our microbiome, which contribute to key biological processes such as digestion, immunity regulation, and even mood influences through serotonin production. It emphasizes that the microbiome is composed of trillions of cells that interact with our body, illustrating the significant impact of these symbiotic relationships on health.


Input: Task: contrast the claim using the given text. Claim: Quantum mechanics can be completely understood through classical physics. [SEP] Text: It is the stuff of special-purpose laboratory or field investigation. By contrast, total stripping one-at-a-time is a gentle process. The one-at-a-time process is an example of the stuff of ordinary production Chemistry. 5. 4. Excited states - hydrogen Now let us begin to consider excitation states. These are key for understanding emission or absorption spectra, a fabulously rich source of data about atoms. But atomic spectra are complicated. The standard way to begin to understand them is mathematically, from the family of solutions provided by the differential equation that Schrödinger postulated for the abstract wave function characterizing the electron in the Hydrogen atom. The standard QM view is that the Hydrogen atom has multiple ‘stable states’, each with negative energy, − E determined largely by a principle quantum number n = 1 2 3. . . ∞ according to − E n ≈ − E 1 n 2. The idea is that the electron can reside in an upper state ( n 1 ), but only rather precariously, and when it teeters and falls back to the ground state ( n = 1 ), a photon is emitted. But the Hydrogen atom has only two constituent p5. 5. Beyond both hydrogen and ground states: spectroscopy, we observe light created when an atomic system relaxes in some way. For elements beyond Hydrogen, the spectral lines that occur are often characterized in part by the so-called Rydberg factor: R ∞ = 2 π 2 m e e 4 c h 3 Z 2 1 + m e M E41 ∞ is traditionally interpreted as the energy needed for total removal of one electron from the ground state to infinity, leaving an ion. The energy needed for an electron to get from a state labeled n 1 to a higher state labeled n 2 n 1 and conversely the energy released when it goes back to n 1 is then modeled as Δ E = R ∞ [ 1 ( n 1 ) 2 − 1 ( n 2 ) 2 ] E42 Observe that R ∞ contains a factor of Z 2 just like the I P ’s for total ionization, I P Z Z of Eq. (25) do. That means R ∞ is referring to the absolutely largest photon energy that the system could ever possibly be imagined deliver: starting from a state of total ionization, i. e. [SEP] Justify:

Output: The text contrasts the claim by explaining concepts in quantum mechanics, such as the behavior of the hydrogen atom's electron and the mathematical underpinnings of quantum states, which cannot be completely described by classical physics. The mention of Schrödinger's differential equation highlights the need for a quantum framework to explain phenomena that classical physics does not adequately cover.


Input: Task: pass the claim using the given text. Claim: Bioinformatics is crucial for analyzing genomic data. [SEP] Text: Note that if the prior odds are assumed to be 1, then the Bayes factor is equivalent to the posterior odds. One can think of the Bayes factor as a Bayesian likelihood ratio statistic. Like the likelihood ratio statistic, the Bayes factor is a ratio of likelihoods under two models being considered. However, while the likelihood ratio statistic is the ratio of two maximized likelihoods for two competing, nested models, the Bayes factor is the ratio of two likelihoods integrated or averaged over the entire parameter space and the models need not be nested. An important consideration with a Bayesian approach is that a prior distribution is assumed for all of the parameters in the model. The advantage to this is that one can incorporate prior information into determining which model is more appropriate. This is a disadvantage, however, if the Bayes factor is sensitive to the prior and if the prior has been chosen incorrectly. factors are evidence in favor of the alternative hypothesis. Kass and Raftery (1995) discuss guidelines for interpreting the measure [7]. Following the authors' suggestion, we transform the Bayes factor to the same scale as that of the likelihood ratio statistic and use the criterion that 2lnB10 > 2 implies positive evidence in favor of the alternative model. Comparing a uni-component model to a two-component model would address the question of whether there is one versus two groups of chromosome arms. Further, comparing a two-component beta-binomial model to a two-component binomial model would address whether there is overdispersion in either group. The advantage of this is that it provides insight into the number of chromosome arm groups, whereas standard applicable frequentist tests will only indicate whether there is one or more groups [8, 9]. ClassificationProvided there is sufficient evidence to indicate that there are two groups of chromosome arms, it is desirable to identify which chromosome arms belong in which group. Classification of the chromosome arms can be done by calculating the conditional probability of group membership of each arm under a given model. [SEP] Justify:

Output: The text does not directly discuss bioinformatics or its role in analyzing genomic data. Instead, it describes concepts regarding the Bayes factor and likelihood ratios in a statistical context, which are relevant in data analysis but do not specifically address the importance of bioinformatics in genomic data analysis. Therefore, it is deemed irrelevant to the claim.


Input: Task: corroborate the claim using the given text. Claim: Symbiotic relationships in microbiomes can influence health. [SEP] Text: Knowles, of the Department of Biology at the University of Oxford, believes that more research should be conducted on wild animals. She says, “My view is that if we want to gain a deep understanding of how microbes affect animals, we need to study microbiomes across as broad a range of animals as possible, and in wild settings, not just in the lab. ” The ways in which an animal behaves and interacts with its environment can have an impact on its microbiome and how this influences its health. Laboratory settings are, by definition, controlled and artificial. Therefore, any studies conducted under these conditions may have limited relevance to animals in the real world. Lab animals are not exposed to the same microbes that wild animals are, and the ways in which this exposure happens can be very different. In lab studies, animals are also not free to behave as they normally would and are kept secure and well-fed by humans. On the other hand, wild animals are subject to the forces of natural selection and must fend for themselves. Mice, for example, behave very differently in the wild than they do when confined to laboratories. In the wild, they spend much of their time foraging for food, are constantly on the look-out for danger, and need to find a mate to reproduce. In labs, all their food is provided, they are safe from natural predators, and can only reproduce when humans allow. ’S WORK? Mice make great test subjects because they are common, easy to find in large numbers and relatively comfortable being handled by humans. A lot of Sarah’s work involves marking individual wild mice so that they can be monitored in their natural habitat throughout their lives. Mice rarely travel very far, and they will often return to live traps, which means that Sarah’s team can study the same individuals and their microbiomes repeatedly over time. “This is important as their microbiomes are not static but constantly changing, in ways that could alter their effects,” she explains. Another advantage of studying wild mice is that mice have been studied extensively in lab settings. This means that there is already a wealth of literature and research techniques for mice and their microbiomes that Sarah can use to inform her own studies. “This makes the research I do more insightful and powerful than it might be if I focused on a more obscure species,” explains Sarah. ? [SEP] Justify:

Output: The text corroborates the claim by discussing how an animal's behavior and interactions with its environment impact its microbiome, which subsequently influences its health. It emphasizes the importance of studying microbiomes in wild animals to understand how these factors play a role in health outcomes, stating that 'the ways in which an animal behaves and interacts with its environment can have an impact on its microbiome and how this influences its health.' This supports the idea that symbiotic relationships within microbiomes are crucial to health.


Input: Task: contrast the claim using the given text. Claim: Quantum mechanics can be completely understood through classical physics. [SEP] Text: a naked nucleus, and having the entire electron population return in one fell swoop, with the emission of just one photon for the whole job. That scenario could never actually happen. One-at-a-time electron return is the only plausible return scenario. The inverse square integers in the square bracket bring Δ E down to values appropriate for one-at-a-time scenarios. Observe that the Rydberg model for spectral lines already conflicts with an older model for the atom developed from the PT; i. e. , electron ‘shells’ enclosing the nucleus, inner shells filled, and at most one outer shell unfilled; partially filled for most elements, and completely filled for noble gasses. The older PT-based model suggests shielding of the nucleus by the filled inner shells of electrons. But the occurrence of a Z 2 in R ∞ even for large n 1 and n 2 in Δ E means there is no shielding of the nucleus. So electrons must be in tight clusters, rather than nucleus-enclosing shells. Observe that R ∞ does not contain any Z M factor like the I P model contains. Instead, it has a factor 1 ( 1 + m e M ) = M ( M + m e ) E43 which is essentially unity. At the time when R ∞ was formulated, most of the known trans-Hydrogenic elements had M ≈ 2 Z and the factor of Z M ≈ 1 2 could be absorbed into an external constant factor, the 2 π 2 m e e 4 c h 3 in R ∞. That is no longer the case today. We know about heavy elements for which M → 2. 5 Z or Z M → 2 5. So now it would be better to use the function Z M instead of the number 1 2. An extra bonus would be that Hydrogen, with Z M = 1 would be included. Now consider that spectral lines might not to arise from de-ionizing one ion of one atom, but rather from de-exciting a system involving multiple neutral atoms. In this description, the n 1 and n 2 are not identifiers of different states of one atom, but rather numbers of atoms organized into super atoms. Otherwise, nothing really changes. However we interpret their meaning, the predicted spectral lines remain the same. Advertisement 6. Unification between Newton and last technical Section of this 6. 1. [SEP] Justify:

Output: The text contrasts the claim by discussing models of electron behavior that highlight the inadequacies of classical physics in explaining quantum phenomena. It explains issues such as the shielding of the nucleus and the organization of atoms, which suggests that the complexities of quantum mechanics cannot be fully captured by classical models. Terms such as 'Z^2 in R ∞' and discussions about spectral lines emphasize the failures of classical explanations and underscore that a deeper understanding is needed beyond classical physics.


Input: Task: pass the claim using the given text. Claim: Bioinformatics is crucial for analyzing genomic data. [SEP] Text: i ~ η f1(x i n i θ1) + (1 - η)f0(x i n i θ0), then it can be shown using Bayes' rule that where is the maximum likelihood estimate (MLE) of θ, Z i is the group membership of the i th chromosome arm and Z i = 1 implies that the i th chromosome arm is in the TSG group. For the analyses here, chromosome arms with conditional probabilities exceeding 0. 5 are classified in the TSG group. Also note that MLEs are computed using the nlminb function in S-Plus. Performance of the Bayes factorsTable 1 presents a description of simulated data sets used to evaluate the performance of the Bayes factors. One hundred data sets are generated under each scenario. All parameters chosen to generate the data are based on the Barrett esophageal cancer data set discussed later [1]. Under the first scenario, data are generated from a two-component binomial mixture model, where each group has a constant loss rate. The two groups are fairly well-separated with the TSG group's loss rate considerably higher than the background loss rate. We specify only five chromosome arms to harbor TSGs, which is believed to be typical. The second scenario is one where there are no TSGs and the background loss rate follows a beta distribution. The distributional parameters are chosen by examining the Barrett data set after removal of the five chromosome arms with the highest rates of allelic loss (these arms are implicated by Barrett et al. (1996) [1] as potentially harboring TSGs). This gives an expected loss rate of 0. 26 and a dispersion parameter of 0. 07. Under the third scenario there are two groups of chromosome arms with one group exhibiting a constant background loss rate of 0. 22 and the second group of five chromosome arms exhibiting varying and higher rates of allelic loss. In the last scenario, both groups of chromosome arms have varying loss rates. The TSG loss rate distribution follows that of Scenario 3 and the non-TSG loss rate distribution follows that of Scenario 2. Table 1 Description of scenarios used in simulation studyFull size tableTable 2 presents the percentage of time one model is favored over the other based on 2ln(Bayes factor) for data generated under each of the scenarios described in Table 1. [SEP] Justify:

Output: The text does not directly address the importance of bioinformatics in analyzing genomic data. Instead, it discusses the application of statistical methods, such as Bayes' rule and maximum likelihood estimation, in the context of analyzing specifics related to chromosome arms and loss rates, without explicitly linking these methods to the broader claim about bioinformatics.


Input: Task: corroborate the claim using the given text. Claim: Symbiotic relationships in microbiomes can influence health. [SEP] Text: Sarah’s research involves a lot of fieldwork, with teams of two to six researchers setting out into the wild to sample mice. Some fieldwork is conducted locally in Oxford University’s research woodland, Wytham Woods, although sometimes the team also travels further afield. One current study is being conducted on the remote island of Skokholm, off the coast of Wales in the UK, where small teams of researchers stay for several weeks at a time. “It involves a lot of early mornings and hard work, but it is also great fun and wonderful to be in the great outdoors; there’s great team spirit and camaraderie on fieldwork,” Sarah explains. Sarah often uses a technique known as ‘capture-mark-recapture’ when conducting fieldwork. This involves catching mice in live traps, marking them and then releasing them back into the wild so that they can be caught again at a later date. Sarah’s team sprays a little sesame oil outside the trap door to attract the mice and, when the mice are captured, the team takes measurements and collects data on characteristics such as their weight, sex and age. The team also collects a faecal sample. Back in the lab, Sarah’s team makes use of molecular biology to analyse the samples. The researchers extract DNA from each faecal sample and sequence it to get a profile of the mouse’s entire community of microbes. “That gives us a window into which microbes are present within the gut, and in what numbers,” says Sarah. The team then uses statistical tests to analyse this microbiome data alongside information about the mice themselves, to answer questions about what affects the microbiome and how. ’? When mice come into contact with each other, they often exchange microbes. Therefore, the social networks they form have a big impact on the composition of their gut microbiome. Sarah and her team study the influence of social contact by tracking mice with passive integrated transponder (PIT) tags. Sarah explains, “These are the same sort of tag some people use to identify their pet cats and dogs, only much smaller. ” Comparing the patterns of social contact among mice with their microbiome profiles has taught Sarah a lot about how microbes are exchanged in wild settings. Diet can also influence a mouse’s microbiome. [SEP] Justify:

Output: The text corroborates the claim by discussing how Sarah's research on mice demonstrates that social interactions among mice affect their gut microbiome composition. It explains that when mice come into contact with each other, they often exchange microbes, and the social networks they form significantly influence the gut microbiome. This shows a direct connection between the microbiome, the interactions (symbiotic relationships) among the mice, and the potential implications for their health.


Input: Task: contrast the claim using the given text. Claim: Quantum mechanics can be completely understood through classical physics. [SEP] Text: The opportunity offered by tensor notation The display of four transformation behaviors requires the use of four tensor index positions. So in addition to the usual contravariant (index up-right) and covariant (index down-right) positions on the right side of a tensor symbol, we need to us the positions available on the left side: index up-left and index down-left. Since left-side index positions have not been in used in this new way before, they need new names designed for the purpose. To recall the move from right to left, let us use the prefix ‘trans’. So let the up-left index position be called ‘transcontravariant’, and let the down-left index position be called ‘transcovariant’). All the transformations are describing what happens to tensor merates when the frame of reference changes; i. e. when the basis unit vectors defining the frame of 6. 2. Transformation of a contravariant object The most familiar transformation is the contravariant one. The prefix ‘contra’ means these tensor merates change opposite to the way the basis unit vectors of the reference frame change. For an arbitrary input vector X α the transformation reads X ¯ β = [ ∂ x ¯ β ∂ x α ] X α where we see the transformation as partial derivatives of coordinates, new with respect to old. ¯ β = T α β X α where we see the transformation written as the tensor T α β. Also equivalently, we have [ X ¯ 0 X ¯ 1 ] = [ T 0 0 T 1 0 T 0 1 T 1 1 ] [ X 0 X 1 ] where we see everything, the input and output vectors and the transformation, in matrix format. Or equivalently, we have X ¯ 0 = T 0 0 X 0 + T 1 0 X 1 and X ¯ 1 = T 0 1 X 0 + T 1 1 X 1 as two separate linear equations. For the contravariant transformation matrix [ T 0 0 T 1 0 T 0 1 T 1 1 ] one can define a reverse transformation matrix [ R 0 0 R 1 0 R 0 1 R 1 1 ] wherein R 0 0 = T 0 0 and R 1 1 = T 1 1 but R 1 0 = − T 1 0 and R 0 1 = − T 0 1. [SEP] Justify:

Output: The text contrasts the claim by discussing concepts in tensor notation and transformations that are inherently rooted in advanced mathematical frameworks. These discussions indicate that understanding transformations involving tensors—an area that requires knowledge beyond classical physics—implies that quantum mechanics cannot be fully comprehended solely through classical physics.


Input: Task: pass the claim using the given text. Claim: Bioinformatics is crucial for analyzing genomic data. [SEP] Text: For each scenario, a 5 × 5 matrix of pairwise comparisons is presented. The rows of the matrix correspond to models considered under H1 (models appearing in the numerator of the Bayes factor). The columns of the matrix correspond to models considered under H0 (models appearing in the denominator of the Bayes factor). Table 2 Percentage of time model under H1 is favored over model under H0 for different scenarios For a given scenario, the rows indicate the model under H1 while the columns indicate the model under H0. The (i, j)th element in the matrix represents the percentage of time the model in the i th row is favored over that in the j th column. Full size tableFor data generated from a two-component binomial model (Scenario 1), the true model is mostly favored over the uni-component models. In fact, when comparing the true model to a uni-component beta-binomial model, the latter model is only favored 5% of the time. This can be viewed as a false-negative rate. Note that the Bayes factors never provide evidence in favor of a uni-component model in comparisons with either of the other two-component models for data from this scenario. Furthermore, the true model is selected 75% of the time over the two-component beta-binomial model. factors are ambiguous, however, when comparing the true model to a two-component beta-binomial/binomial model, where neither is favored 69% of the time. For data that follow a uni-component beta-binomial distribution (Scenario 2), the results are inconclusive 62% of the time when comparing the true model to the two-component binomial model. For twenty-two percent of the data sets the right model is favored, but 16% of the time, the two-component model is selected. Thus, this comparison results in a 16% false-positive rate. Similar results are found when comparing the true model to a two-component beta-binomial/binomial model. factors favor the correct model over the two-component beta-binomial model roughly half the time and favor neither model the other half. Comparisons between the two-component models and the one-component binomial model not surprisingly show a strong preference for the two-component models, as they better accommodate the variability of the data. [SEP] Justify:

Output: The text does not directly address or provide evidence for the claim about the importance of bioinformatics in analyzing genomic data. Instead, it discusses various scenarios involving model comparisons and Bayes factors, which are specific statistical analyses not explicitly linked to bioinformatics or genomic analysis.


Input: Task: corroborate the claim using the given text. Claim: Symbiotic relationships in microbiomes can influence health. [SEP] Text: Although it is hard to observe what mice eat, as they are nocturnal and like to stay hidden, Sarah’s team can analyse the faecal samples to get an idea of what each mouse has been eating. The researchers can then compare each mouse’s diet to their microbiome profile to understand how diet shapes this important microbial community. ? “One key thing we’ve learnt, so far,” says Sarah, “is that each wild mouse’s microbiome is rather unique – a bit like a fingerprint. The microbiomes are highly responsive to each mouse’s external environment. A mouse’s microbiome is influenced by the other mice they encounter, including their mother in early life and social contacts, and by what they eat. For example, the microbiome of wild mice changes with the seasons as different food sources become available. ” Download the 10. 33424/289 Link to the activity sheet 0 +1 Pinterest 0 LinkedIn 0 wild house mouse (Mus musculus domesticus) waiting to be released Setting a live trap on to capture wild house mice Sarah’s PhD student setting out traps near the cliffs on logger used to measure the movements and social networks of wild mice Sarah’s student Eveliina extracting DNA from mouse faecal samples in the lab (photo credit: Will Smith) PhD student Kirsty processing mice on fieldwork at © Unless stated otherwise, all photos by Sarah aims to understand the significance of natural variation in the microbiome – how it affects physiology and the ability of mice to survive and reproduce. Sarah plans to carry out experiments involving faecal microbiome transplants to see how different microbiomes affect processes such as thermoregulation (how animals regulate their body temperature), weight gain and behaviour. Understanding the influence that microbiome variation has on wild mice may yield insights into how we humans are affected by our microbial companions. Sarah’s work, along with other research in the field of microbiome science, has the potential to influence important sectors such as medicine, agriculture and conservation. of : : Studying the gut microbiomes of wild mice to understand how they impact physiology and behaviour : (NERC), part of UK Research and Innovation (UKRI), Council (ERC) This 1. Follow your curiosity and interests. 2. There is no one type of person that can be a biologist, so don’t believe you are not good enough, or not from the right background. 3. [SEP] Justify:

Output: The text corroborates the claim by discussing how the microbiome of wild mice is influenced by their diet and social interactions, stating that each mouse's microbiome is unique and responsive to their external environment. It emphasizes the aim of understanding how natural variation in the microbiome affects physiology and health-related processes such as thermoregulation, weight gain, and behavior. Furthermore, Sarah's research into microbiome variation and its implications suggests that similar dynamics could affect human health, supporting the idea of symbiotic relationships in microbiomes influencing health.


Input: Task: contrast the claim using the given text. Claim: Quantum mechanics can be completely understood through classical physics. [SEP] Text: Applied to X ¯ β the reverse transformation R β α takes X ¯ β back to X α : X α = R β α X ¯ β. That is to say: X 0 = R 0 0 X ¯ 0 + R 1 0 X ¯ 1 and X 1 = R 0 1 X ¯ 0 + R 1 1 X ¯ 1. Expressed in matrix form, the reverse transformation is the inverse transformation: [ X 0 X 1 ] = [ R 0 0 R 1 0 R 0 1 R 1 1 ] [ X ¯ 0 X ¯ 1 ] or [ R 0 0 R 1 0 R 0 1 R 1 1 ] [ T 0 0 T 1 0 T 0 1 T 1 1 ] = [ 1 0 0 1 ]. The distinction between the words reverse and inverse is nil in the contravariant context. But it becomes important in the next context. 6. 3. Transformation of a covariant object The prefix ‘contra’ means reverse to the prefix ‘co’. The covariant transformation goes the same way the basis unit vectors change. So the covariant transformation X ¯ β = C β α X α in matrix format [ X ¯ 0 X ¯ 1 ] = [ C 0 0 C 0 1 C 1 0 C 1 1 ] [ X 0 X 1 ] uses transformation matrix C equal to the reverse contravariant transformation matrix R : [ X ¯ 0 X ¯ 1 ] = [ R 0 0 R 1 0 R 0 1 R 1 1 ] [ X 0 X 1 ] or equivalently X ¯ 0 = R 0 0 X 0 + R 1 0 X 1 and X ¯ 1 = R 0 1 X 0 + R 1 1 X 1. It is generally assumed that this is the same as saying the covariant transformation is the inverse to the contravariant transformation. Notice however that the off-diagonal merates C 0 1 = R 1 0 and C 1 0 = R 0 1 have indices switched around. This is because C operates on a covariant object, whereas, in its original definition, R operated on a contravariant object. The index switching makes no difference if we limit attention to transformations that are space-time symmetric, i. e. Lorentz transformations. But if we wish to investigate any other type of transformation, we have to investigate whether the switch makes a difference. Consider the inner product X ¯ β X ¯ β. [SEP] Justify:

Output: The text contrasts the claim by describing the complexities of transformations in mathematical physics, including the distinctions between covariant and contravariant transformations. This suggests that understanding quantum mechanics requires more than just classical physics concepts, as it delves into the unique mathematical structures that underpin quantum theory, indicating that classical physics alone is insufficient for a complete understanding.


Input: Task: pass the claim using the given text. Claim: Bioinformatics is crucial for analyzing genomic data. [SEP] Text: The third quarter of Table 2 presents results for data generated under Scenario 3. The two-component beta-binomial/binomial model is favored in the majority of the cases over the other models within the class, which makes sense as this model is most similar to the data-generated model. Only once is an alternative hypothesis favored when compared to this model and this is the two-component beta-binomial model. When comparing the two-component beta-binomial/binomial model to the other two-component models, the Bayes factors do not favor either of the models being compared about 20 percent of the time. In general, the two-component models were mostly favored over the one-component models. For data generated under Scenario 4, we expect the two-component beta-binomial model to be chosen over the other models in the class as this model is closest to the truth. The results show that when this model is compared to the two-component binomial or the one-component beta-binomial, it is mostly favored, and these models are never selected. As the two-component beta-binomial model is fairly similar to the two-component beta-binomial/binomial model, however, most of the time neither model is chosen over the other. The two-component beta-binomial is favored only 35% of the time, while the two-component beta-binomial/binomial is favored 9% of the time. Interestingly, when comparing the one-component beta-binomial to the two-component binomial, the one-component model is chosen 72% of the time and the two-component binomial model is chosen only 5% of the time. This suggests that the measure is fairly sensitive to the overdispersion in the two groups. Another example of this is a comparison between the two-component beta-binomial/binomial model and the one-component beta-binomial model. In this case, the two-component model is only favored 54% of the time, where the uni-component model is a better fit to 5% of the data sets, and both models are equally good fits to the data 41% of the time. This simulation study demonstrates that the Bayes factors are an appropriate method of model selection. They perform particularly well for data generated from the two-component models. [SEP] Justify:

Output: The text does not address the importance of bioinformatics in analyzing genomic data. Instead, it discusses various statistical models and their performance comparisons for specific data scenarios without any mention of bioinformatics or genomics.


Input: Task: corroborate the claim using the given text. Claim: Symbiotic relationships in microbiomes can influence health. [SEP] Text: IntroductionArchaea are prokaryotes belonging to the third domain of life, first classified separately from bacteria in 1977 by. Fox based on their ribosomal RNA genes [1••, 2]. Although the classification of archaea is a rapidly progressing field, current classifications categorize this domain into four large clades, namely the Euryarchaeota, the TACK superphylum (Thaumarchaeota, Aigarchaeota, Crenarchaeota, Korarchaeota), the Asgard archaea, and the DPANN clade (Diapherotrites, Parvarchaeota, Aenigmarchaeota, Nanoarchaeota) [3, 4] (Fig. 1). Euryarchaeota represents the most extensively studied phylum as it includes the methanogens, which play an essential role in (syntrophic) anaerobic degradation processes [5] (Fig. 1). Besides this complex phylogeny, archaea harbor characteristics distinct from the other domains of life [6]. These unique characteristics are the lack of peptidoglycans in their cell wall and ether-linked lipids in their cell membrane. Archaea also show higher diversity in cell wall structures, e. g. , surface layer proteins and heteroglycans [6]. Comparative analyses of archaeal genomes have identified several molecular conserved signatures uniquely present in archaea (l groups). One unique feature of archaea is the metabolic production of methane (methanogenesis) [6]. During the last decades, these exclusive properties were mainly regarded as unique adaptions to various extreme environments inhabited by archaea [7]. However, several studies have since discovered that archaea also live in moderate habitats, including soil and ocean [8]. They have been reported to be stable commensals of multicellular host organisms (plants and animals), where they participate in functions such as growth promotion, nutrient supply, protection against abiotic stress, methanogenesis, transformation of heavy metals, trimethylamine metabolism, and immune modulation (reviewed in [5]). Studies have confirmed the presence of archaea in various human body sites, such as the gut, skin, nose, mouth, lungs, and vagina [9,10,11]. [SEP] Justify:

Output: The text corroborates the claim by discussing how archaea, as stable commensals in various multicellular host organisms, take part in beneficial functions such as growth promotion, nutrient supply, protection against abiotic stress, and immune modulation. These interactions highlight the influence of microbial symbiotic relationships on health.


Input: Task: contrast the claim using the given text. Claim: Quantum mechanics can be completely understood through classical physics. [SEP] Text: transformation, it is preserved, equal to X ¯ β X ¯ β = X α X α. But if we do not have space-time symmetry, is it still preserved? This question has to be answered by testing. Laying out the problem in matrix format, we have to make one of the vectors, say the covariant one, a row vector, and then we have to test: [ X ¯ 0 X ¯ 1 ] [ X ¯ 0 X ¯ 1 ] = [ X 0 X 1 ] [ R 0 0 R 0 1 R 1 0 R 1 1 ] [ T 0 0 T 1 0 T 0 1 T 1 1 ] [ X 0 X 1 ] = = [ X 0 X 1 ] [ X 0 X 1 ] E44 Observe that the R matrix is transposed from what it would need to be to make the R T matrix product collapse to the identity. So the inner product X α X α is generally not preserved if we do not have space-time symmetry. 6. 4. Transformations for objects of four types In order to recover the general availability of preserved inner products, the two additional transformation behaviors are defined. The transcovariant transformation is defined as the transposed inverse of the contravariant one. The transcontravariant transformation is defined as the transposed inverse of the covariant one. Recall that this discussion began with the contravariant transformation written in the tensor notation X ¯ β = [ ∂ x ¯ β ∂ x α ] X α. The discussion soon became complicated enough to merit introduction of more detailed notation that can clearly distinguish the four cases. The following Table illustrates the expanded tensor notation: Table. 2. is organized for user convenience, with the position of information corresponding to the index position: upper right for contravariant, lower right for covariant, lower left for transcovariant, and upper left for transcontravariant. The index position assigned to an object determines the transformation law that it follows. Now let two arbitrary numbers with magnitude less than unity be represented by the letters A and B (chosen from the word ‘arbitrary’! ). Let the arbitrary numbers represent in turn the off-diagonal elements of transformation matrices. The following table shows the corresponding matrix notation: Table. 3. [SEP] Justify:

Output: The text contrasts the claim by discussing complex mathematical transformations and concepts inherent to quantum mechanics, implying that understanding these aspects cannot be achieved through classical physics alone. The mention of 'space-time symmetry' and the need for matrix transformations highlights quantum mechanics' complexity beyond classical explanations.


Input: Task: pass the claim using the given text. Claim: Bioinformatics is crucial for analyzing genomic data. [SEP] Text: In particular, most of the time, the correct model is chosen, and furthermore, reasonable false-negative rates are observed for comparisons made on data generated from the two-component binomial model as well as the two-component beta-binomial/binomial model. Data generated from a one-component beta-binomial model produces interesting results. Although the false-positive rates are reasonable when comparing the one-component beta-binomial model to the other two-component models (16%, 7% and 0% for the two-component binomial, two-component beta-binomial/binomial, and two-component beta-binomial, respectively), there is a large percentage of time, when neither model is favored (62%, 69% and 50%). Since both models are often good fits to the data, it would be difficult to decide with confidence whether or not there is a second group of arms in these cases. Application of methods to data setsIn this section, we apply the methods discussed to three allelic-loss data sets. Specifically, we use Bayes factors to choose a reasonable model or set of models for the data in order to address whether TSGs exist on any of the chromosome arms, and we classify the chromosome arms as harboring TSGs or not based on the selected model(s). Table 3 presents a summary of the results for the three data sets. The set of models chosen by the Bayes factors is provided along with the individual chromosome arms that were identified as having TSGs based on these models. The set of chosen models was comprised of those with 2ln(Bayes factors) exceeding 2 when compared to models outside the set and with 2ln(Bayes factors) less than 2 when compared to models within the set. Details of the analysis for each data set are described below, with slightly more emphasis placed on the first data set. Table 3 Summary of results after applying methods to three data sets For each data set, the selected model(s) with the chromosome arms classified in the tumor suppressor gene group and corresponding conditional probabilities of harboring a tumor suppressor gene are provided. A set of models was chosen such that models in the set had 2ln(Bayes factors) exceeding 2 when compared to models outside the set and 2ln(Bayes factors) less than 2 when compared to models within the set. A chromosome arm is in bold print if it has been identified in more than one data set. [SEP] Justify:

Output: The text does not address the importance of bioinformatics in analyzing genomic data or provide evidence supporting the claim. Instead, it discusses the application of statistical models to data sets without explicitly linking this to bioinformatics or its importance in the analysis of genomic data.


Input: Task: corroborate the claim using the given text. Claim: Symbiotic relationships in microbiomes can influence health. [SEP] Text: Although enormous progress has already been made in archaeal research [12•], their unique physiological, structural, and molecular properties complicate further investigations, particularly in the context of microbiome research [13•, 14••]. This review aims to summarize the current knowledge about archaea as components within microbiomes and focuses on their interactions with their bacterial neighbors and the archaeal communication types used for these interactions. Fig. 1Archaeal phylogeny. Schematic representation of a phylogenetic tree based on 16S rRNA sequences from Archaea and Bacteria, adapted from [3]Full size imagein Natural EcosystemsResearchers only recently became aware of how archaea interact with each other and organisms of other domains. For instance, methanogens are involved in essential steps of the global methane cycle, partially conducted in a symbiotic interaction with herbivorous animals or sulfate-reducing bacteria [15]. Many syntrophic associations have been described for hydrogenotrophic methanogens, such as fermentative Acetobacterium and Syntrophobacter, Desulfovibrio, Thermoanaerobacter, Desulfotomaculum, and Pelotomaculum (reviewed in [15]). Besides microbial assemblages, archaea further interact with multicellular eukaryotes. Recent next-generation sequencing studies revealed highly abundant and diverse archaeal signatures in plant-associated microbiomes [16]. Particularly, plant roots and rhizospheres provide anoxic or oxygen-depleted micro-niches for methanogens and ammonium-oxidizing archaea [17]. Notably, plant genotypes affected the composition and structure of these archaeal communities [18]. The interaction could be based on syntrophic nitrogen cycling, and archaea are suggested to affect the nutrient exchange and coping with environmental stress [19]. Although there is initial evidence of specific interactions among archaea and between archaea and other domains of life, their mechanisms and ecological roles often remain unclear. Archaea in AnimalsAnimals have been shown to be inhabited not only by trillions of bacteria and fungi but also by archaea, more precisely primarily Euryarchaeota, with a high abundance of anaerobically growing methanogens found within their digestive tracts [7]. Only a few studies have reported Crenarchaeota and Thaumarchaeota within animal microbiomes [20, 21]. [SEP] Justify:

Output: The text corroborates the claim by discussing the interactions between archaea and other organisms, particularly focusing on symbiotic relationships such as those involving methanogens and herbivorous animals, as well as the interactions between archaea and multicellular eukaryotes. It emphasizes that these interactions, including nutrient exchange and communication among microbial communities, play a significant role in the dynamics of microbiomes, thus impacting health.


Input: Task: contrast the claim using the given text. Claim: Quantum mechanics can be completely understood through classical physics. [SEP] Text: Observe that this Table uses negative signs on the arbitrary A and B in the contravariant and transcontravariant cases, positive signs in the covariant and transcovariant cases. This sign choice is used to help recall the prefixes ‘contra’ and ‘co’. Observe too that if B = A we have space-time symmetry, which is the case of Lorentz transformations. And observe finally that if B = 0 we have universal time, which is the case of Galilean transformations. and B are arbitrary, and so can also represent other transformations as yet unnamed. 6. 5. Transformations for invariant objects The underlying purpose of tensor calculus is to focus on mathematical objects that are ‘coordinate free’, or ‘frame independent’, or ‘invariant’ (whether in form or in numerical value), – all expressions meaning that coordinate transformation does not change anything fundamental about an object so-described: values of scalars, or relationships expressed as equations involving tensors. The user of tensor calculus expects certain behaviors. There should be number invariant inner products of vectors and of higher-order tensors. The ‘unity’, or ‘Kronecker delta’ is not presently regarded as a real tensor, but can be accepted as one if it can be demonstrated number invariant. Finally, the user will certainly expect a number invariant ‘metric tensor’, the essential tool for manipulating index positions to develop tensor equations. Displaying that all these expectations can be met in the case of arbitrary transformations, not just Lorentz transformations, is the objective of this Sub-Section. The matrix notation is useful in checking out the transformation of all these entities. [SEP] Justify:

Output: The text contrasts the claim by detailing the importance of tensor calculus and transformations that highlight 'coordinate free' or 'frame independent' mathematical objects. This suggests a complexity that classical physics alone cannot address. It implies that understanding the intricacies of transformations in quantum mechanics requires concepts that extend beyond classical physics, reinforcing that quantum mechanics involves principles that cannot be fully explained through classical frameworks alone.


Input: Task: pass the claim using the given text. Claim: Bioinformatics is crucial for analyzing genomic data. [SEP] Text: Full size tabledata setdata set records allelic loss on 20 esophageal adenocarcinomas and two high-grade dysplasias. Figure 1 presents a histogram of the proportion of tumors with allelic loss for each of the forty chromosome arms studied (markers were not placed on the short arms of chromosomes 13, 14, 15 and 22 as these are too small to study). Two of the chromosome arms examined do not exhibit allelic loss (arms 20q and 21p) for any of the tumors observed. The mean allelic-loss rate for all arms exhibiting loss is 0. 27 and the median allelic-loss rate is 0. 24. From the figure, three chromosome arms appear to stand apart from the others in exhibiting considerably higher allelic-loss rates: 9p, 5q, and 17p. Figure 1Histogram of allelic loss for the Barrett data setFull size imageTable 4 presents 2ln(Bayes factors) for the pairwise comparisons of the models for each of the three data sets. In addition, the posterior probability of each model is presented assuming a prior probability for the models such thatTable 4 2ln(Bayes Factors) and posterior probabilities of each model considered for the three data sets For a given data set, the first five rows of data correspond to the model under H1 while the first five columns correspond to the model under H0. The (i, j)th element in the matrix represents the value of 2ln(Bayes Factors) for the model corresponding to the i th row versus the model corresponding to the j th column. Values of 2ln(Bayes Factors) are in bold print if they exceed 2. The last column provides values of the posterior probability of the model in the i th row. Those values corresponding to selected models are in bold print. Full size tableP(2 Component Model) = P(1 Component Model) = 1/2This givesP(2 bb) = P(2 bb/bin) = P(2 bin) = 1/6P(1 bb) = P(1 bin) = 1/4. For the Barrett data set, the two-component models are strongly favored over the one-component models, clearly indicating a group of arms that exhibit higher than background loss rates. [SEP] Justify:

Output: The text discusses specific data and statistical models related to allelic loss in tumors but does not address bioinformatics or its role in analyzing genomic data. Hence, it is irrelevant to the claim.


Input: Task: corroborate the claim using the given text. Claim: Symbiotic relationships in microbiomes can influence health. [SEP] Text: The presence of archaea has been confirmed in sponges, mollusks, corals, arthropods, vertebrates, and humans (reviewed in [5, 15]). Investigations using Axinella sponge species associations with Cenarchaeum symbiosum or other filamentous Crenarchaeota [22], and the symbiosis of the demosponge Tentorium semisuberites with Cren- and Euryarchaeota [23], pointed to an archaeal contribution to the sponge nitrogen metabolism. A role within nitrogen cycling has also been identified in marine mollusks for Thaumarchaeota phylogenetically related to Nitrosopumilus maritimus [24]. Among arthropods, the largest animal phylum, exclusively methane-producing archaea were detected in millipedes, cockroaches, termites, and scarab beetles [25]. Here, the methanogens were primarily found in the hindguts of these animals [26]. In these interactions, archaea utilize hydrogen, carbon dioxide, and acetate resulting from the anaerobic degradation of lignocellulose [27]. Within the methanogenic archaea, particularly Methanobrevibacter species are extraordinarily well-adapted to interact with animal hosts and microbial neighbors [28••]. Consequently, Methanobrevibacter species are the predominant archaea in the gastrointestinal tracts (GITs) of various ruminants and non-ruminants, including cattle, sheep, reindeer, goats, buffalo, pigs, rhinoceroses, and chickens, among others (reviewed in [5, 28••]). In ruminants, archaea-bacteria consortia produce more than one-third of the methane [29]. Systematic analyses of methane production in the guts of over 250 vertebrates revealed that methane production and, thus, the presence of methanogens depends on the phylogenetic lineage [25]. Methanobrevibacter were shown to be flexible exponents of syntrophic interactions that enhance the efficiency of bacterial polysaccharide fermentation through methanogenesis since they can consume various fermentation products of primary and secondary fermenters, such as methanol, hydrogen, and carbon dioxide [30]. Methanobrevibacter smithii is known as a partner in a syntrophic interaction with Bacteroides thetaiotaomicron [31]. [SEP] Justify:

Output: The text corroborates the claim by discussing the significant role that archaea play in the interactions with animal hosts and their microbial neighbors, specifically mentioning that Methanobrevibacter species, which are well-adapted to symbiotic relationships, enhance the efficiency of bacterial fermentation. It emphasizes that these interactions are crucial for methane production and nitrogen metabolism in various species, directly linking symbiotic relationships in microbiomes to biological processes critical for health.


Input: Task: contrast the claim using the given text. Claim: Quantum mechanics can be completely understood through classical physics. [SEP] Text: For example, the preserved inner product of a vector X with itself looks like (note the transpositions for operating on row vectors): X ¯ β X ¯ β = [ X ¯ 0 X ¯ 1 ] [ X ¯ 0 X ¯ 1 ] = [ X 0 X 1 ] 1 1 − A B [ 1 + B + A 1 ] [ X 0 X 1 ] [ 1 − B − A 1 ] [ X 0 X 1 ] = [ X 0 X 1 ] [ X 0 X 1 ] = X α X α E45 or X ¯ β X ¯ β = [ X ¯ 0 X ¯ 1 ] [ X ¯ 0 X ¯ 1 ] = [ X 0 X 1 ] 1 1 − A B [ 1 − B − A 1 ] [ 1 + B + A 1 ] [ X 0 X 1 ] = [ X 0 X 1 ] [ X 0 X 1 ] = X α X α E46 The more familiar inner product X α X α is preserved with Lorentz transformations, but not with arbitrary transformations. So it shouldn’t be considered any kind of ‘invariant’. The same is true of the unfamiliar ( X α ) ( X α ). With the extended tensor notation, we can identify the index positions that definitely make a number invariant Kronecker delta. It looks like (note the transpositions for operating on row vectors): δ ¯ δ γ = 1 1 − A B [ 1 + A + B 1 ] [ 1 0 0 1 ] [ 1 − A − B 1 ] = [ 1 0 0 1 ] = δ β α E47 or δ ¯ δ γ = 1 1 − A B [ 1 − A − B 1 ] [ 1 0 0 1 ] [ 1 + A + B 1 ] = [ 1 0 0 1 ] = δ β α E48 The more familiar δ β α is preserved with Lorentz transformations, but not with arbitrary transformations. That is why it does not qualify as a tensor. The same is true of the unfamiliar δ β α. Some readers will be surprised to see the present argument using the Lorentz metric, [ 1 0 0 − 1 ] without accepting a limitation to Loentz transformations. It is widely supposed that the Lorentz metric requires Lorentz transformations, and/or Lorentz transformations require the Lorentz metric. [SEP] Justify:

Output: The text contrasts the claim by discussing aspects of quantum mechanics and tensor notation that indicate the limitations of classical physics in accurately describing quantum phenomena. It highlights that certain properties, such as the invariance of the inner product under Lorentz transformations, cannot be accounted for by classical physics, suggesting that a complete understanding of quantum mechanics cannot be achieved through classical concepts alone.


Input: Task: pass the claim using the given text. Claim: Bioinformatics is crucial for analyzing genomic data. [SEP] Text: In particular, the Bayes factors demonstrate that the two-component beta-binomial/binomial model provides the best fit. Note that the posterior probability of this model is considerably higher than that of the others, providing further evidence of its superiority. Table 5 presents the MLEs of the parameters for the two-component models listed in order of posterior probability (largest to smallest). First note that = 0, reducing the two-component beta-binomial model to a two-component beta-binomial/binomial model. The parameter estimates for these two models are identical and imply that the beta-binomial distribution corresponds to the TSG loss and the binomial distribution corresponds to the background loss. The estimate of the probability that a chromosome arm is in the TSG group is 0. 097. The estimated background loss rate is 0. 228, and the expected background loss rate for arms with TSGs is estimated at 0. 708 with a loss rate variance of 0. 07. The fit from the two-component binomial model gives a slightly lower mixing parameter estimate and a slightly higher estimate of the TSG loss rate. Table 5 Results from fitting two-component models to the Barrett data set Maximum likelihood estimates along with selected chromosome arms and corresponding conditional probabilities of harboring a tumor suppressor gene for the two-component models for the Barrett data set. Full size tableThe conditional probabilities of group membership based on the two-component beta-binomial/binomial model yield the same classification rule as that based on the other two-component models. Chromosome arms 5q, 9p, and 17p are classified in the TSG group. The conditional probabilities of group membership for these chromosome arms are quite similar across the three models. data setdata set consists of 38 esophageal adenocarcinomas. Allelic-loss data were recorded on 39 chromosome arms (as in the Barrett data set, the short arms of chromosomes 13, 14, 15, 21, and 22 were not included in the study). A histogram of the proportion of tumors with allelic loss is presented in Figure 2. The mean allelic-loss rate is 0. 36 and the median allelic-loss rate is 0. 32. By simply viewing the histogram, four of the chromosome arms have been identified as having suspiciously high allelic-loss rates. These are chromosome arms 4q, 9p, 18q, and 17p. [SEP] Justify:

Output: The text is irrelevant to the claim as it focuses on statistical models and parameter estimates related to specific genomic data without discussing the role or importance of bioinformatics in the analysis process.


Input: Task: corroborate the claim using the given text. Claim: Symbiotic relationships in microbiomes can influence health. [SEP] Text: Here, the archaeon affected the expression of Bacteroides enzymes responsible for producing formate and acetate, which the archaeon utilizes. In gnotobiotic mice, the consortium was assumed to affect the energy balance of the host [32]. Furthermore, other methanogenic archaea, like Methanosphaera, Methanosarcina, Methanomassiliicoccus, and Methanimicrococcus, have been identified in the gut of various animals despite their low abundance [5]. Besides the archaeal colonization of the GIT, various animals also carry methanogens, Haloarchaea and Thaumarchaeota on the skin [33]. Also, those archaeal groups consume metabolic end products from the host and the microbiome and are supposed to affect the host [34••]. Although the archaeal community, also called archaeome, is now increasingly recognized as an essential component of (host-associated) microbiomes, contributing to methane production and potentially involved in disease-relevant processes, the underlying interaction mechanisms are still largely unknown [28••]. Role of Archaea in HumansThe human microbiome contains numerous archaea, particularly on the skin, in the respiratory tract, and in the GIT [10] (Fig. 2). Several studies estimated that approx. 500–1000 different microbial species are present within the human body at any time, accounting for 4 × 1013 cells. Archaea are predicted to account for around 1% of the total microbial cell count [35]. The human archeaome includes many lineages, including (Nitrososphaeria), and members of the DPANN clade [28••](Fig. 1, 2). The oral cavity harbors various methanogenic strains of the genera Methanobrevibacter and Methanomassiliicoccus, often enriched in patients with periodontal disease [36]. Recent studies even identified halophilic and thermophilic Euryarchaeota and Thaumarchaeota in the human mouth [37] (Figs. 1, 2). The human skin is inhabited by Thaumarchaeota (Nitrososphaera), assumed to be responsible for ammonium turnover, and associated with odor reduction and skin improvement [33] (Fig. 2). Further, age and skin physiology affect the human skin archaeome [38]. [SEP] Justify:

Output: The text corroborates the claim by detailing how archaeal communities within various microbiomes, including the human microbiome, can influence the health of the host. It describes how archaeons interact with other microbial species and the host's metabolism, mentioning their role in producing methane and consuming metabolic end products which can impact the energy balance of the host. The text emphasizes that while the interaction mechanisms are not fully understood, the recognition of archaea as an important component of microbiomes indicates their potential influence on health, thus aligns with the claim.


Input: Task: contrast the claim using the given text. Claim: Quantum mechanics can be completely understood through classical physics. [SEP] Text: But such a connection is not in fact mandatory. The generally preserved forms of the Lorentz metric tensor look like (note the transpositions for operating on row vectors): g ¯ δ γ = 1 1 − A B [ 1 − A − B 1 ] [ 1 0 0 − 1 ] [ 1 − A − B 1 ] = 1 1 − A B [ 1 − A − B 1 ] [ 1 − A + B − 1 ] = [ 1 0 0 − 1 ] = g β α E49 and g ¯ δ γ = 1 1 − A B [ 1 + A + B 1 ] [ 1 0 0 − 1 ] [ 1 + A + B 1 ] = 1 1 − A B [ 1 + A + B 1 ] [ 1 + A − B − 1 ] = [ 1 0 0 − 1 ] = g β α E50 The more familiar g β α and g β α are preserved with Lorentz transformations, but not with arbitrary transformations. They shouldn’t be considered any kind of ‘invariant’. The same is true of the unfamiliar g β α and g β α. The number invariant g α β and g α β can function to raise and lower indices on objects. For example, X β = ( g α β ) X α and X β = ( g α β ) X α or X α = ( g α β ) ( X β ) and X a = ( g a b ) ( X b ). One can also write additional index assignments for g. Altogether, there are 10 possible assignments, as there are 4 × 3 2 = 6 with indices in different corners, and 4 with indices in the same corner. Two of the additional index assignments look like g β α and g β α. These two entities cannot do anything to an index except change its name. For example, X α = X β ( g β α ) and X α = X β ( g β α ) or X β = ( g β α ) ( X α ) and X β = ( g β α ) ( X α ). So g β α and g β α are just equivalent to the number invariant δ β α and δ β α already noted above. Further additional index assignments on g create entities that can serve to convert a regular index into a trans one, or a trans one into a regular one. [SEP] Justify:

Output: The text contrasts the claim by discussing complexities of the Lorentz metric tensor and transformations, indicating that classical physics does not suffice to understand the nuances of quantum mechanics. It suggests that while there are certain familiar forms preserved in physics, the underlying principles differ significantly, which implies a limitation of classical physics in fully explaining quantum mechanics.


Input: Task: pass the claim using the given text. Claim: Bioinformatics is crucial for analyzing genomic data. [SEP] Text: Figure 2Histogram of allelic loss for the Gleeson data setFull size imageFor the Gleeson data set, the two-component beta-binomial/binomial model, the two-component binomial model and the uni-component beta-binomial model are all favored over the two-component beta-binomial model and the uni-component binomial model (4). Because two of the two-component models as well as the uni-component beta-binomial model are comparable fits to the data, this may imply there is not strong enough evidence of more than one group of chromosome arms. However, while the uni-component beta-binomial model and the two-component beta-binomial/binomial model appear to fit similarly, the two-component binomial model appears to be a slightly better fit than these two as shown by the corresponding posterior probabilities. Maximum likelihood estimates obtained from fitting both the two-component beta-binomial and the beta-binomial/binomial model imply both components follow a binomial distribution as the dispersion parameter estimates are 0. Fits of all three two-component models yield identical parameter estimates, and therefore the rule obtained from the two-component binomial model which has the highest posterior probability is equivalent to that obtained from the other two-component models. Classification using this model places six chromosome arms in the TSG group. These are identified as chromosome arms 4q, 9p, 9q, 12q, 17p, and 18q. Note that three of these chromosome arms (4q, 9q and 12q) exhibit lower than the average background loss rate in the Barrett data set. However, 9p and 17p are categorized along with 5q in the TSG group. Furthermore, although not classified in the TSG group, chromosome arm 18q exhibits the fourth highest allelic-loss rate in the Barrett data set. data setdata set consists of 30 esophageal adenocarcinomas on 39 chromosome arms (the same arms included in the Gleeson data set). A histogram of the Hammoud data set is presented in Figure 3. Chromosome arms 4q and 17p have been identified on the plot as they appear to stand out from the others as having relatively high allelic-loss rates. The mean allelic-loss rate is 0. 20 and the median allelic-loss rate is 0. 18. [SEP] Justify:

Output: The text primarily discusses statistical models used in analyzing data from specific genomic studies, particularly focusing on allelic loss in cancer. It does not provide a direct relation to bioinformatics or explicitly state its importance in the analysis of genomic data, making the text largely irrelevant to the claim.


Input: Task: corroborate the claim using the given text. Claim: Symbiotic relationships in microbiomes can influence health. [SEP] Text: Few studies describe the presence of archaea in human nasal, lung, and vaginal microbiomes [39••] (Fig. 2). As mentioned for animals, the vast majority of human-associated archaea is found in the intestine, accounting for up to 10% of the anaerobic community [40] (Fig. 2). The abundance of methanogenic archaea in the human gut is highly variable and represented by two physiological types of humans regarding gas exhalation (methane emitters and non-emitters) [41•]. While the specific role of non-methanogenic archaea in the human body remains to be explored, methanogens maintain numerous syntrophic relationships with resident bacteria by being involved in fermentation processes through hydrogen removal [28••]. M. smithii was the first archaeon isolated from human feces and is the most abundant archaeon found in the intestine [42]. M. smithii genomes displayed genomic adaptations to the human gut, such as producing surface glycans and adhesion-like proteins [30]. These adaptations are considered to originate from bacteria through lateral gene transfer [43]. Besides M. smithii, other methanogens such as Methanosphaera stadtmanae, and Methanomassiliicoccus luminyensis have been detected in human stool samples [44]. The use of modern high-throughput sequencing techniques revealed the presence of additional community members from the Eury- and Crenarchaeota, such as and Thermoplasmatales within the human intestine [45]. Fig. 2Human archaeome. Archaea identified in different body sites of humans. Created in BioRender. comFull size imageAlthough archaea can generally be considered commensal or beneficial organisms, and no archaeal pathogen is currently known, reports of archaeal involvement in human diseases are accumulating, particularly in immunocompromised individuals [46••]. Archaea have been found to have immunomodulatory abilities. For example, certain species of archaea can stimulate the immune system, increasing the production of cytokines and other immune cells [28••, 42, 47]. Other studies have suggested that archaea can exert anti-inflammatory effects by reducing the production of pro-inflammatory cytokines, such as methanogenic archaea, or increasing the production of anti-inflammatory cytokines [42, 48]. [SEP] Justify:

Output: The text corroborates the claim by discussing the interactions between archaea and bacteria in the human microbiome, particularly emphasizing the symbiotic relationships that are formed. It mentions that methanogens, a type of archaea, maintain syntrophic relationships with resident bacteria through fermentation processes, indicating that these relationships are beneficial. Additionally, it highlights the immunomodulatory abilities of certain archaea, such as their role in stimulating the immune system and potentially exerting anti-inflammatory effects, which further supports the assertion that these symbiotic relationships influence health.


Input: Task: contrast the claim using the given text. Claim: Quantum mechanics can be completely understood through classical physics. [SEP] Text: None of these entities are number invariant, but in practice, that does not matter. The user does not convert just a single object; the user converts a whole tensor equation. The index-converting g entities typically occur in pairs, and the pairs contract to number invariant objects. When they don’t occur in pairs, they do occur on both sides of an equation, and cannot affect the issue of equation form invariance. Another two of these of g ’s are g β α and g α β. They function to do X β = ( g α β ) X α and X α = ( g α β ) X β or X β = g β α ( X α ) and X α = g β α ( X β ). As a pair, they contract to ( g β γ ) ( g γ α ) = g β α or to ( g γ β ) ( g α γ ) = g β α both of which are number invariant. The final four indexed g ’s are g α β g α β g α β and g α β. They can all function to change a regular index into a trans one, or a trans one into a regular one, but with a twist: ‘co’ goes to ‘contra’, or ‘contra’ goes to ‘co’. That is, X ′ α = ( g α β ) X β X α = ( g α β )  X β g α β ( X α ) = X β and g α β ( X α ) = X β. As noted above, the contractions ( g β γ ) ( g γ α ) = g β α and ( g β γ ) ( g γ α ) = g β α are number invariant. The bottom line is this: to be sure of invariance under arbitrary transformation, not just Lorentz transformation, always contract a regular index with a trans index. 6. 6. General invariance for Maxwell’s equations Maxwell’s equations in current tensor notation read: ∂ α F α β = 4 π c J β E51 and ∂ α D α β = 0 β E52 The two-index F α β and D α β tensors refer to the electromagnetic field and the ‘dual’ thereof. [SEP] Justify:

Output: The text contrasts the claim by discussing complex mathematical concepts used in tensor equations and invariance, indicating that a complete understanding of certain physical phenomena requires specialized knowledge beyond classical physics. Specifically, the text mentions 'invariance under arbitrary transformation' and tensor notation applications, which are distinct from classical concepts, suggesting limitations in fully comprehending quantum mechanics through classical physics alone.


Input: Task: pass the claim using the given text. Claim: Bioinformatics is crucial for analyzing genomic data. [SEP] Text: Figure 3Histogram of allelic loss for the Hammoud data setFull size imageThe pairwise comparisons using the Bayes factors for the Hammoud data set (4) demonstrate that both the two-component beta-binomial/binomial model and the two-component binomial model give the best fits to the data. Note that the posterior probabilities of these models are practically the same indicating these models are equally good fits to the data. As only two-component models are selected from the class, there is strong evidence to suggest that a second group of chromosome arms with TSGs exists. Classification using both the two-component beta-binomial/binomlal model and the two-component binomial model places chromosome arms 4q and 17p in the TSG group. Both models yield similar conditional probabilities of group membership for the arms, and as in the other data sets, both models yield the same classification rule. Note that chromosome arm 4q is implicated by our analysis of the Gleeson data set and 17p is implicated by our analyses of all three previous data sets. ConclusionsTesting of one versus two components in a mixture model is problematic as the likelihood ratio test is not applicable. Bayes factors provide a natural solution to this problem. Although we make only crude comparisons using the Bayes factors, the results favor the right model most of the time for data arising from a two-component model. More importantly, when comparing a two-component model versus a one-component model for these data, the two-component model is generally chosen. For data that arise from a one-component beta-binomial model, the Bayes factors were not able to choose as well between the true model and a two-component model. Specifically, when comparing the true model to the two-component binomial, the false-positive rate was 16%. On the other hand, the Bayes factors are inconclusive for 62% of the data sets when making this comparison. This is actually encouraging when considering some frequentist options. Standard applicable frequentist methods such as an exact test and the dispersion score test are limited to testing for one versus more than one group of chromosome arms [8, 9]. Simulation studies examining these methods for these data reject the hypothesis of one group 93 and 89 percent of the time, respectively [10]. Based on this, one might conclude that a model with two (or more) groups would be appropriate. [SEP] Justify:

Output: The text does not directly address the importance of bioinformatics in analyzing genomic data. Instead, it focuses on statistical modeling and inference techniques applied to specific genomic datasets, discussing methods like Bayes factors and the performance of different models without explicitly tying this analysis to the role of bioinformatics as a whole.


Input: Task: corroborate the claim using the given text. Claim: Symbiotic relationships in microbiomes can influence health. [SEP] Text: The exact mechanisms by which archaea exert their immunomodulatory effects are not yet fully understood, but it is thought that they may act through interactions with the gut microbiome and the gut epithelial cells [28••]. Other studies have proposed that archaea may interact with Toll-like receptors (TLRs) on immune cells, activating immune responses [49]. It is assumed that M. smithii may contribute to developing autoimmune diseases through various mechanisms, including producing metabolites, like methane, that activate immune cells and stimulate inflammation [34••]. In addition to its direct effects on the immune system, M. smithii may also indirectly contribute to autoimmune disease development by altering the gut microbiome and disrupting the balance of commensal microorganisms [50, 51]. Dysbiosis has been implicated in the development of various autoimmune diseases (reviewed in [28••]). Furthermore, M. stadtmanae was more abundant in the gut microbiome of patients with inflammatory bowel disease (IBD) [52] and may be associated with an increased risk of other autoimmune diseases, such as type 1 diabetes [53]. However, the effects of these interactions are not yet fully understood, and more research is needed to determine the precise ways archaea may affect the human immune system. It is also possible that different species of archaea may have different effects on the immune system and that the effects may depend on the context in which the interaction occurs. Increasing evidence suggests that archaea may play a role in the development and progression of cancer in humans through various mechanisms, including the production of carcinogenic metabolites, modulation of immune responses, and alteration of the tumor microenvironment [54, 55]. Further, alterations in the abundance and diversity of archaeal populations may be associated with an increased risk of colorectal cancer [55]. For example, certain species of archaea, such as M. smithii, may be more abundant in the gut microbiome of individuals with colorectal cancer than in healthy individuals [56]. Similarly, hydrogen sulfide-producing archaea have been implicated in the development of gastric cancer due to the ability of hydrogen sulfide to cause DNA damage and inhibit apoptosis [57]. Other studies have suggested that archaea may be involved in oral infections and periodontitis [36, 58]. In particular, Methanobrevibacter oralis has been identified in the oral microbiomes of patients with periodontitis [59]. [SEP] Justify:

Output: The text corroborates the claim by discussing the interactions of archaea with the gut microbiome and their potential effects on immune responses and autoimmune diseases. It provides evidence that alterations in the gut microbiome associated with archaea may influence health outcomes, including the development of autoimmune diseases and cancer, indicating that the microbiome plays a crucial role in health under certain conditions.


Input: Task: contrast the claim using the given text. Claim: Quantum mechanics can be completely understood through classical physics. [SEP] Text: The electromagnetic field tensor F α β has merates that are components of the three-dimensional electric and magnetic field vectors, E and B. α β is the dual to F α β whose merates are components of B and − E. The one-index tensors J β and ∂ α refer to the source charge-current density vector and the differential operator vector. The indices α and β take the four values 0 1 2 3. The seeming limitation of Maxwell’s equations to invariance only under Lorentz transformation arises entirely from the differential operator being written as a covariant vector. In the extended tensor algebra, this operator is identified as transcovariant, and then Maxwell’s equations look like: ( ∂ α ) F α β = 4 π c J β E53 and ( ∂ α ) D α β = 0 β E54 Written this way, Maxwell’s equations are manifestly form invariant, not only under Lorentz transformation, but also under any arbitrary (just well-behaved) transformation, including Galilean transformation. Advertisement 7. Maxwell’s equations and photons: Photons have a life history that begins with emission as an electromagnetic pulse pulse, proceeds with development into a waveform, then changes into regression back to a pulse, and ends with absorption by a receiver. This life history of the photon can be modeled by imagining some mirrors that apply boundary conditions corresponding to the desired scenario, feeding a Gaussian pulse at the source to Maxwell’s equations, watching Hermite polynomials then emerge, and then finally pile up at the receiver. About EM signals and photons: The life history of the photon suggests that the assumption upon which Einstein’s SRT is founded is over-simplified. If we will make the founding assumption more realistic, then we will get more believable results. The more believable results can help us reconcile SRT with the QM of atoms. We can understand why Planck’s constant occurs. It represents the balance between competing phenomena: on the one hand, energy loss due to radiation from accelerating charges; on the other hand, energy gain due to internal torquing within the atomic system due to finite speed of signal propagation. About Atoms: Viewed in the right way, chemical and spectroscopic data reveal a tremendous amount of regularity. [SEP] Justify:

Output: The text contrasts the claim by discussing the limitations of classical physics in explaining quantum phenomena. It mentions that 'the assumption upon which Einstein’s SRT is founded is over-simplified' and suggests that a more realistic assumption might reconcile Special Relativity with Quantum Mechanics, indicating that classical physics alone is insufficient to fully understand quantum mechanics.