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Research ArticleMicrobiome

# Sinus Microbiome Diversity Depletion and Corynebacterium tuberculostearicum Enrichment Mediates Rhinosinusitis

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Science Translational Medicine  12 Sep 2012:
Vol. 4, Issue 151, pp. 151ra124
DOI: 10.1126/scitranslmed.3003783

## Abstract

Persistent mucosal inflammation and microbial infection are characteristics of chronic rhinosinusitis (CRS). Mucosal microbiota dysbiosis is found in other chronic inflammatory diseases; however, the relationship between sinus microbiota composition and CRS is unknown. Using comparative microbiome profiling of a cohort of CRS patients and healthy subjects, we demonstrate that the sinus microbiota of CRS patients exhibits significantly reduced bacterial diversity compared with that of healthy controls. In our cohort of CRS patients, multiple, phylogenetically distinct lactic acid bacteria were depleted concomitant with an increase in the relative abundance of a single species, Corynebacterium tuberculostearicum. We recapitulated the conditions observed in our human cohort in a murine model and confirmed the pathogenic potential of C. tuberculostearicum and the critical necessity for a replete mucosal microbiota to protect against this species. Moreover, Lactobacillus sakei, which was identified from our comparative microbiome analyses as a potentially protective species, defended against C. tuberculostearicum sinus infection, even in the context of a depleted sinus bacterial community. These studies demonstrate that sinus mucosal health is highly dependent on the composition of the resident microbiota as well as identify both a new sino-pathogen and a strong bacterial candidate for therapeutic intervention.

## Introduction

Bacterial rhinosinusitis (sinusitis), which affects more than 15% of the U.S. population annually, is one of the most common problems presented to the primary care practitioner in the ambulatory setting and results in more than $5.8 billion in direct health care expenditures (1). Typically classified by duration of symptoms, sinusitis may be acute (less than 4 weeks in duration), sub-acute (4 to 12 weeks), or chronic (>12 weeks with or without acute exacerbations) (2). Chronic rhinosinusitis (CRS) alone represents a large portion of sinusitis cases, affecting more than 30 million Americans (3) and resulting in an annual economic health care burden in excess of$2.4 billion. Culture-based studies have demonstrated chronic bacterial colonization of CRS patient sinus cavities and implicated these species in the pathophysiology of the disease (4, 5). Despite these findings, the microbiology and immunology underlying CRS remain poorly described and controversial, and to date, no clear etiology has been described (6).

Confounding the field are recent findings demonstrating that known bacterial pathogens, such as Staphylococcus and Streptococcus species isolated from CRS sinuses and implicated in the disease (4, 5, 7, 8), have also been detected in the nasopharynx of healthy individuals with no sinus symptomatology (9). Thus, the composition of the microbiota at discrete mucosal sites may define the abundance and pathogenic behavior of specific members of the assemblage. Indeed, perturbation of the native gastrointestinal microbiota of mice, before Clostridium difficile instillation, results in increased fecal abundance of this species and enhanced murine susceptibility to infection (10). Similarly, disruption of the hindgut microbiota of the mosquito (Anopheles gambiae), the natural vector for Plasmodium falciparum, results in altered vectoral capacity characterized by increased host susceptibility to P. falciparum infection (11). Collectively, these observations suggest that microbiota composition plays a key role in the protection against pathogen overgrowth and virulence gene expression and that perturbations to these assemblages must be considered as potential contributing factors to infectious and inflammatory disease etiology.

Although the sinuses are primarily lined with respiratory epithelia, which readily supports colonization by a diverse microbiome at other upper respiratory sites such as the oropharynx (9, 12), to date little is known of the composition of the resident microbiome of the paranasal sinuses and the contribution of these assemblages to sinus mucosal health. Most microbiological studies of this niche are based on culture-based approaches, which underestimate the diversity of species present. The application of culture-independent approaches offers the opportunity to provide a broader picture of sinus microbiome composition and identify both gross community characteristics and discrete species associated with health status that contribute to or protect against disease development.

Here, we present findings from a high-resolution culture-independent comparative analysis of the sinus microbiota of CRS patients and healthy subjects without CRS, undergoing open nasal or sinus surgery. Surgical patients were preferred because they typically exhibit severe disease, and surgery provides access to affected sinus mucosal surfaces that are otherwise inaccessible. Specifically, efforts aimed to determine whether specific features of the sinus mucosal microbiota were associated with disease state and severity and to identify both pathogenic and protective species in this niche.

## Results

### Comparative sinus microbiota analysis

Maxillary sinus samples from 20 subjects (10 CRS and 10 healthy individuals) were used for this study. Patient details are provided in Table 1. Mucin hypersecretion is a hallmark of sinus disease (13, 14). Therefore, to confirm that the CRS patients exhibited a phenotype consistent with disease, we performed quantitative polymerase chain reaction (qPCR) analysis of Muc5A gene [encoding mucin primarily secreted from surface epithelium goblet cells in humans (15, 16)] expression. This analysis confirmed significant (P < 0.007, Student’s t test) up-regulation of this gene in CRS patients compared to healthy control subjects (fig. S1), thus validating the presence of sinus disease in our CRS cohort. qPCR analysis of bacterial burden by total 16S ribosomal RNA (rRNA) copy number demonstrated that perioperative CRS patients and healthy subjects exhibited no significant difference in sinus bacterial burden (2.10 × 106 ± 1.01 × 106 versus 2.92 × 106 ± 2.17 × 106 copies of 16S rRNA gene per microgram of total DNA in CRS and healthy control subjects, respectively; t = 0.93; P = 0.37, Student’s t test). These data suggest that the sinus niche supports a defined bacterial load and that microbiota composition and relative taxonomic distribution, rather than the number of bacteria present, are related to disease state.

Table 1

Patient information. TMP/SMX, trimethoprim/sulfamethoxazole; AMP/SUL, ampicillin/sulbactam; AMO/CLU, amoxicillin/clavulanate.

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A standardized phylogenetic microarray, the 16S rRNA PhyloChip, was used to compare the presence and relative abundance of about 8500 bacterial taxa, representing broad membership of all known bacterial phyla (Hugenholtz phylogenetic classification). Because the primary aim of this study was to generate and compare a high-resolution profile of the microbiota present in healthy subjects and CRS patients, a phylogenetic microarray approach was used in favor of shotgun sequencing with limited read depth, which primarily identifies the higher-abundance species in a given community. We specifically sought to include lower-abundance microbiome members in this comparative analysis because recent evidence has demonstrated that such species can contribute considerably to microbiome function (17) and act as keystone species that shape microbial community composition (18). Using this tool, we profiled bacterial communities present in 14 subjects (7 healthy and 7 CRS) with sufficient amplified 16S rRNA product to be analyzed. Comparative analyses of gross bacterial community metrics between the CRS and the healthy groups demonstrated that compared to healthy individuals, CRS patients exhibited substantial microbiota perturbation characterized by significantly reduced bacterial richness (number of bacterial types detected; P ≤ 0.005, Welch’s t test; Fig. 1A), evenness (relative distribution of bacterial types; P ≤ 0.04, Welch’s t test; Fig. 1B), and Shannon’s diversity (metric calculated using richness and evenness indices; P ≤ 0.01, Welch’s t test; Fig. 1C). These observations were further supported by hierarchical cluster analysis (HCA), which demonstrated that most healthy subjects clustered in a single tightly knit group. The bacterial communities from healthy subjects were compositionally distinct from CRS patients, whose bacterial communities clustered into two distinct groups (Fig. 1D). Healthy subject CRS 14 clustered with CRS patients; however, it was subsequently determined that this individual had historically suffered from chronic nasal allergies. This analysis confirmed that the sinus microbiota composition of healthy subjects is distinct from that of CRS patients and that, within the CRS population, discrete subgroups with distinct microbial community profiles exist.

Although the numbers in this study were insufficient to comprehensively assess factors responsible for the observed clustering pattern, antibiotic use was examined because of its well-defined influence on microbiota composition. As is standard surgical procedure, all study subjects (CRS and healthy) received prophylactic antibiotics immediately (1 hour) before surgery and sample collection. Long-term preoperative antibiotic administration was absent for most healthy subjects and variable in the CRS patient group (Table 1). However, patients with disparate long-term antimicrobial administration histories (for example, CRS 4, 6, and 2; group II; Table 1) clustered closely together. Moreover, this group, which included two patients who had not received long-term antibiotics, exhibited significantly lower (P < 0.006, Student’s t test) sinus community diversity compared to microbiota from patients in group I, all of whom had received long-term prophylactic antibiotic administration. These data suggest that although it may be a contributory factor in shaping the sinus mucosal microbiome, antimicrobial therapy is not the sole selective pressure defining bacterial community composition and loss of diversity in this niche.

### Discriminatory taxa characteristic of healthy and CRS sinuses

Using the 20-question Sino-Nasal Outcome Test (SNOT-20) survey as a metric to score sinus symptomatology, we confirmed that compared to healthy controls, CRS patients reported significantly higher scores, indicating more severe sinus symptomatology (P ≤ 0.003, Student’s t test), and, subsequently, that the observed microbiota clustering patterns were consistent with patient-reported sinus symptomatology (Fig. 1D). Because of this level of independent validation of disease activity, we next characterized at the taxon level (at least 97% 16S rRNA sequence identity) the specific community members that differentiated healthy subjects and CRS patients. Known pathogenic members of the Pseudomonadaceae, Lachnospiraceae, Ralstoniaceae, Mycobacteriaceae, and Helicobacteriaceae were detected in both CRS with and healthy subjects without sinonasal symptoms (table S1). Thus, the mere detection of a suspected or known pathogen in a given niche is not necessarily associated with pathogenicity; these data suggest that the microbiota composition at that site may play a large role in defining the activity of community members. After correction for false discovery (P ≤ 0.05, q ≤ 0.05), a total of 1482 taxa were detected in significantly lower relative abundance in CRS patient sinuses (table S2), which underscores the extent of sinus microbiota collapse in our CRS patient population. A large number of taxa exhibiting the most significant reductions in relative abundance in the CRS patients belonged to the order Lactobacillales; these species included known probiotic species such as Lactobacillus sakei as well as other phylogenetically distinct lactic acid bacteria such as Carnobacterium alterfunditum, Enterococcus mundtii, and Pediococcus pentosaceus. In contrast, only a single taxon with the representative species, Corynebacterium tuberculostearicum, exhibited a significant increase in abundance in CRS patients (P ≤ 0.03, q ≤ 0.003, Welch’s t test).

To further underscore the clinical significance of these findings, we examined the microbiota data to identify those species that correlated with SNOT-20 symptom severity scores. Two hundred twenty-eight taxa were significantly (P < 0.05, Welch’s t test) correlated with lower SNOT-20 scores (indicative of healthy sinuses; Fig. 2 and table S3). Among these taxa were members of the Lactobacillaceae, Enterococcaceae, Aerococcaceae, and Streptococcaceae, which supports the hypothesis that members of these families represent key protective groups in healthy sinuses. In contrast, the relative abundance of only two taxa was positively correlated with increased symptom severity; both belonged to the Corynebacteriaceae (table S3). Of these two, the taxon most positively correlated with symptom severity was again represented by C. tuberculostearicum (r = 0.62; P ≤ 0.02). To validate these findings, we performed qPCR analysis with primers designed to specifically amplify C. tuberculostearicum. Linear regression of C. tuberculostearicum qPCR-derived copy number against both array-reported fluorescence intensity and SNOT-20 score demonstrated good concordance (r = 0.66; P ≤ 0.01 and r = 0.68; P ≤ 0.01, respectively), corroborating the array-based findings and confirming that a strong relationship between the abundance of this species and sinus symptom severity existed (fig. S2).

### Murine model of sinusitis

To determine whether C. tuberculostearicum, which is typically considered a skin commensal, exhibited any pathogenic potential and whether this may be influenced by resident microbiota in the sinus cavity, we developed a murine model of sinus infection and used goblet cell hyperplasia and mucin hypersecretion, characteristic indicators of pathology in human populations (13), as the outcome measures to define pathogenic activity in the sinuses. Four groups of mice (n = 5 animals per group) representing (i) untreated control, (ii) antibiotic-treated (to elicit microbiome depletion), (iii) C. tuberculostearicum [American Type Culture Collection (ATCC) 35694]–inoculated, and (iv) antibiotic-treated and C. tuberculostearicum–inoculated animals were used (fig. S3). qPCR analyses of total 16S rRNA copy number from the sinuses of these animals confirmed that the burden of bacteria in the antibiotic-treated groups was significantly lower (P < 0.03, Student’s t test) than that of untreated animals, confirming acute antimicrobial depletion of bacterial burden and presumably mucosal sinus microbiota diversity in antibiotic-treated groups of animals. Histological examination of the sinus mucosa from each group of animals demonstrated that the untreated control and the antibiotic-treated animals did not exhibit aberrant epithelial physiology (Fig. 3A, i and ii), whereas instillation of large numbers of C. tuberculostearicum in the presence of a replete sinus microbiota elicited a modest increase in the number of mucin-secreting goblet cells (Fig. 3Aiii). However, animals treated with both an antimicrobial and C. tuberculostearicum exhibited profound goblet cell hyperplasia (Fig. 3, Aiv and B, and table S6) that was significantly greater than that observed in any other group (table S4). Because mucin hypersecretion is a hallmark of respiratory infection (19) and chronic sinusitis (13, 14), these data confirm that C. tuberculostearicum is capable of inducing a characteristic host response to pathogenic microbes and that this phenotype is significantly augmented under conditions of depleted sinus microbiota.

To demonstrate that goblet cell hyperplasia and mucin hypersecretion were induced specifically by C. tuberculostearicum and that this is not simply a host response to instillation of large numbers of any bacterial species into the sinus niche, we repeated the above experiment and included an additional group of animals who were treated with antibiotics before instillation of L. sakei (ATCC 15521; fig. S3). We specifically chose L. sakei because this bacterium was present in high abundance in healthy mucosal samples and was among those taxa exhibiting the most significant depletion in CRS patients. Thus, we postulated that it may represent a protective sinus mucosal colonizer and, as such, should not induce mucosal responses characteristic of infection of this niche.

qPCR was performed on all treatment groups to confirm that animals receiving bacterial inocula exhibited the presence of these species (fig. S4). Histological imaging of the maxillary sinuses (Fig. 4A) demonstrated that the antibiotic-treated and C. tuberculostearicum–inoculated group exhibited significant increases in goblet cell hyperplasia and mucin hypersecretion (Fig. 4Aiii). However, mice that received identical numbers of L. sakei demonstrated epithelial physiology comparable to that of control animals (no significant differences in goblet cell numbers; table S5; (Fig. 4Aiv), thus confirming that the observed sinus histopathology was specifically due to C. tuberculostearicum instillation and that potentially protective species such as L. sakei do not induce this host response. Enumeration of goblet cell numbers in each treatment group confirmed these observations (Fig. 4B and table S5).

Because the collective data generated in this study suggested that L. sakei may represent a putative protective species of sinus mucosa, we also determined whether co-instillation of L. sakei with C. tuberculostearicum could abrogate the goblet cell hyperplasia and mucin hypersecretion phenotype induced by the pathogenic species, even in the context of a depleted native microbiota. After treatment with antibiotics, equal numbers of both species were instilled into the sinuses of mice. Histological examination revealed sinus epithelia comparable to that of animals in the control groups (Fig. 4Av), with no significant differences in goblet cell numbers observed across these groups (Fig. 4B and table S5). qPCR analyses demonstrated significantly (P < 0.02, Student’s t test) reduced C. tuberculostearicum abundance in the co-instilled animals when compared to animals infected with C. tuberculostearicum alone (fig. S4); however, L. sakei numbers in these animals were similar to those in animals treated with this species alone (fig. S4). This finding indicates that L. sakei protects the sinus epithelium, putatively through competitive inhibition of C. tuberculostearicum, and may represent a novel therapeutic option for amelioration or prevention of sinus pathology, even in patients with severe sinus microbiome depletion.

## Discussion

It is becoming increasingly apparent that human health status is highly dependent on the diverse microbial assemblages that inhabit discrete host niches, particularly mucosal-associated surfaces. Recent advances in culture-independent technologies have increased our ability to describe the diversity of microbial species that colonize specific host sites (2025), the compositional and functional changes that occur in disease states (26), and the specific community members that are highly correlated with clinical symptom severity (21) or induction of specific immune responses (27). Because of extensive use of conventional laboratory culture approaches to detect microbial species, we have been conditioned to view chronic or acute infections as exclusively due to a single pathogenic species. However, recent studies have demonstrated that the composition of the resident microbiota in a given niche can strongly influence the behavior of specific species, particularly pathogens (10, 11, 28), and, as such, represents an important contributory factor to disease etiology.

To date, culture-based approaches to characterize the etiological agent of CRS have provided a reductionist and somewhat discordant view of the microbiology associated with this disease. In an attempt to better define this aspect, we examined whether sinus microbiota composition was altered with this chronic inflammatory disease. Despite our relatively small number of subjects, a clear signal emerged, demonstrating that the sinus microbiota of our patient cohort was characterized by both grossly depleted communities and a significant increase in relative abundance of a single organism, C. tuberculostearicum. Although phylogenetically its closest bacterial relatives include Mycobacteria and Nocardia, genera synonymous with pathogenesis, C. tuberculostearicum is customarily considered an innocuous member of the healthy skin microbiota and an unlikely etiological agent of CRS. Therefore, we developed a murine model of sinusitis to recreate the observed microbiological features of CRS and confirmed both the pathogenic potential of this species and that its impact on sinus epithelial responses, associated with pathogenesis, was significantly enhanced in the absence of a replete sinus microbiota.

The critical role of the microbiome in modulating the impact of C. tuberculostearicum on sinus mucosal responses likely explains why it (and putatively multiple other microbial species) has not previously been considered a pathogen. The observed necessary combination of microbiota depletion and C. tuberculostearicum outgrowth to elicit a pathophenotype confirms that microbiome composition plays a key role in defining the behavior of specific species in the consortium. Several lines of evidence in the recent literature support this. For example, perturbation of the gastrointestinal microbiota of mice results in proliferation of C. difficile and induces a supershedder phenotype (10), demonstrating the role a diverse microbiota plays in suppressing outgrowth of specific pathogenic species. This phenomenon may also explain why, despite detection of known pathogens in healthy sinus microbiota, these individuals exhibit no symptomatology and, more broadly, provide an explanation as to why seemingly similar patients, exhibiting comparable quantities of known pathogenic species, may exhibit markedly different clinical outcomes. These studies highlight the critical role microbiome composition plays in defining microbial behavior and underscore the need to better understand the complex microbe-microbiome-host interplay that governs microbial-host responses and undoubtedly defines disparate clinical outcomes in patient populations.

One limitation of this study is the small sample size and the inclusion of only surgical chronic sinusitis patients with severe disease. It is entirely plausible that subgroups of sinusitis patients with distinct pathophenotypes because of overgrowth of other microbial species such as fungal pathogens exist. Nonetheless, we believe that a depleted mucosal microbiome forms the universal context for proliferation of such species. These observations have obvious implications for other sinonasal pathogens such as Staphylococcus aureus as well as for inflammatory diseases in distinct niches in which gross perturbations to the microbiota have been described, such as inflammatory bowel disease (29), necrotizing enterocolitis (30), and asthma (31, 32).

One advantage to this comparative study design is the ability to identify those species associated with healthy sinuses that, presumably, provide mucosal protection. The murine model developed in this study provided an opportunity to determine whether such species may afford protection against the pathophysiology induced by a combination of depleted microbiota and C. tuberculostearicum. From these efforts, it is clear that L. sakei, a probiotic species that has demonstrated efficacy in human studies of children with atopic eczema-dermatitis syndrome (33), represents a potentially novel therapeutic for the treatment of sinusitis subtypes, including CRS. The observation that several members of the Lactobacillaceae, including L. sakei, as well as other known lactic acid–producing members of the Firmicutes, were significantly depleted suggests that characteristic physiological features of these species, such as bacteriocin or lactic acid production (34, 35), may serve to outcompete pathogenic species. This competition may plausibly shape the sinus mucosal microbiota and protect this niche from pathogen overgrowth, although these hypotheses require further study.

Because of the crucial role microbiome composition plays in CRS, it is tempting to speculate that key events that disturb the sinus microbial ecosystem such as viral infection may serve to initiate disease. Indeed, viral infection commonly precedes development of CRS (36) and is implicated in the genesis of other chronic inflammatory diseases (3739). Our findings also have significant implications for clinical practice, particularly for the excessive use of antimicrobials, which contribute to microbiota depletion, in the treatment of viral sinusitis and other upper respiratory infections. Our data suggest that a more appropriate strategy may involve microbial supplementation during periods of acute sinusitis with one or a combination of species identified in this study. Certainly, restoration ecology has proven effective and received much media attention in other host niches such as the lower gastrointestinal tract where fecal transplant has been shown to resolve recalcitrant C. difficile infection with a high rate of success (40). Although further studies are necessary to determine the efficacy of using a multispecies sinus supplementation approach, there is precedence for this concept. A double-blind placebo-controlled trial of more than 300 children demonstrated significant decreases in fever incidence, coughing, and rhinorrhea in probiotic-supplemented children relative to the control group. This impact was even more significant in those children receiving a combination of probiotic strains (Lactobacillus and Bifidobacterium species), thus providing strong supporting evidence for the protective effect of combinations of such species against upper respiratory pathogens (41).

Demonstration that a bacterial species that commonly inhabits human skin is an etiological agent of CRS invites a change in how we perceive pathogens. Our data suggest that apparently commensal species in one setting may produce disease in another, based at least in part on the local microbial composition. The study also illustrates why the etiology of CRS, and likely other chronic inflammatory diseases, has been so difficult to define. CRS pathophysiology is multifactorial and, at least in our patient population, co-dependent on microbiota composition and increased relative abundance of C. tuberculostearicum. Simply investigating either aspect in isolation is insufficient. However, the advanced technologies we now have for profiling microbiota composition and function provide us with an unprecedented opportunity to consider microbiota composition as a contributor to disease state, to identify novel etiological agents, and to better determine the congruence of mechanisms underlying chronic inflammatory diseases.

## Materials and Methods

### Patient sample collection

Patient and disease stratification was performed on the basis of recent clinical history, nasal endoscopy, computed tomography sinus review, and a validated quality-of-life instrument, the disease-specific SNOT-20 survey (42). Sinus brushings were obtained during functional endoscopic sinus surgery of CRS patients or surgery for non-CRS complaints (for example, obstructive sleep apnea or post-traumatic malocclusion) in healthy subjects. Endoscopically guided brush samples of mucosal surfaces of the lateral, central, and medial portions of the maxillary sinus were obtained and pooled together in 1 ml of RNAlater and placed at 4°C for 24 hours before storage at −80°C until processed for analysis.

### DNA extraction and PhyloChip analysis

Mucosal brushings were transferred to Lysis Matrix B (MP Biomedicals) tubes containing 600 μl of RLT buffer (Qiagen). Samples were subjected to 30 s of bead beating at 5.5 m/s followed by centrifugation for 1 min at 2000 rpm. Supernatant was transferred to the AllPrep DNA spin column, and nucleic acid purification (DNA and RNA) was carried out according to the manufacturer’s instructions (Qiagen) as previously described (43). Nucleic acid concentrations were determined with a NanoDrop spectrophotometer (Thermo Scientific). PhyloChip analysis was performed as previously described (44) with 250 ng of purified pooled 16S rRNA amplicon per sample generated using 27F and 1492R universal primers (45). Data sets were conservatively filtered (44), and probe set fluorescence intensity was normalized and log-transformed before analysis with packages in the R statistical environment. HCA was performed on Canberra dissimilarities calculated with the ‘vegdist’ function in the ‘vegan’ R package. Canberra dissimilarities have been demonstrated to perform well in cluster detection (46). HCA of the Canberra dissimilarity matrix was performed with averaging linkage, and significant clusters were determined with approximately unbiased P values and bootstrap values by a multiscale bootstrap resampling approach implemented in the R package pvclust (47). The 16S rRNA sequences of significant taxa were used to construct a neighbor-joining with nearest-neighbor interchange tree with FastTree (48), which was annotated with the Interactive Tree of Life [http://itol.embl.de/; (49)].

### Murine sinus studies

Female 4- to 5-week-old C57BL6/J mice weighing 16 to 18 g were purchased from The Jackson Laboratory and housed in microisolator cages in the Parnassus Services Building at the University of California, San Francisco, Parnassus Campus. All protocols performed were approved by the Animal Care and Use Committee of the University of California, San Francisco. Animals were permitted to acclimatize for 2 weeks with food and water ad libitum before study. Mice were orally administered amoxicillin/clavulanate at a dose of 100 mg/kg once a day for 5 days before bacterial instillation. Before intranasal inoculation with C. tuberculostearicum (ATCC 35694), L. sakei (ATCC 15521), or combination of both species, mice were anesthetized by intraperitoneal injection with avertin (250 mg/kg). ATCC strains were used to confirm that the phenotypes elicited by these species were not exclusive to clinical isolates of these organisms. Inoculation was performed once a day for 3 days by applying 25 μl of either C. tuberculostearicum [1.0 × 1011 colony-forming units (CFU)/ml] or L. sakei (1.0 × 1011 CFU/ml), or combination of both microbes in equal ratios (total 2.0 × 1011 CFU/ml), in phosphate-buffered saline (PBS) onto the external nares and inhalation by the animals. This concentration was based on previously described murine sinusitis studies (50, 51). Mice were monitored during the entire process until fully recovered from anesthesia. Twenty-four hours after the final bacterial inoculation, mice were euthanized by CO2 asphyxiation followed by induced pneumothorax. The heads were decapitated, and sinuses were dissected for histological (n = 2 animals per treatment group) and molecular analysis (n = 3 animals per treatment group). Dissected sinuses used for molecular analyses were placed in RNAlater (Ambion) and stored at 4°C until processed the following day in the same manner as described above for human samples.

### Sinus histology

Sinuses were fixed overnight in 4% paraformaldehyde, followed by overnight decalcification in Decalcifying Solution A (Fisher). Samples were then dehydrated, rinsed with PBS (1 hour), soaked in 30% ethanol (1 hour) and 50% ethanol (1 hour), transferred to 70% ethanol, and stored at 4°C until subsequent preparation. Samples were sectioned to 5-μm thickness and mounted onto glass microscope slides. Hematoxylin and eosin and PAS staining were performed as previously described (52). PAS-stained sections prepared from four groups of mice (CTAB, CTAB+, CT+AB, and CT+AB) were imaged at ×20 and ×60 magnifications, and PAS-positive cells were counted for three different sections per mice (two mice in each group). The number of goblet cells was expressed as the total number of PAS-positive cells per micrometer length of epithelium.

### Quantitative polymerase chain reaction

Bacterial burden was determined with extracted DNA (10 ng per sample, triplicate reactions) and universal 16S rRNA qPCR primers [338F, 5′-ACTCCTACGGGAGGCAGCAG-3′ (45); 518R, 5′-ATTACCGCGGCTGCTGG-3′; (53)]. QuantiTect SYBR Green (Qiagen) was used according to the manufacturer’s instructions. Reaction mixtures (25 μl total) contained 12.5 μl of 2× QuantiTect SYBR Green (Qiagen), 2.5 μl each of 3 μM forward and reverse primers, and 6.5 μl of H2O. Reactions were amplified with the Mx3000P Real-Time PCR System (Stratagene) and the following cycling conditions: 95°C for 10 min followed by 40 cycles of 95°C for 30 s, 55°C for 1 min, and 72°C for 30 s with data acquisition at 55°C. C. tuberculostearicum abundance was determined by qPCR with CT-F (5′-GAACGGAAAGGCCCTGCTTGCA-3′) and CT-R (5′-GGCTCCTATCCGGTATTAGACC-3′); L. sakei abundance was determined with the primer pair LS-F (5′-GGTAAAGGCTCACCAAGACCGTGAT-3′) and LS-R (5′-TCACGCGGCGTTGCTCCATC-3′). Reaction mixtures and PCR conditions were as described above.

For Muc5A expression analysis, confirmed DNA-free total RNA (1 μg) was reverse-transcribed at 42°C for 50 min in a 20-μl reaction mixture with 1 μl of SuperScript II (Invitrogen). Complementary DNA (cDNA) was diluted 1:5 in molecular-grade water. qPCRs were performed in a 25-μl final volume with 12.5 μl of SYBR Green PCR master mix; 10 μM each of primers Muc5AF (5′-TGTGGCGGGAAAGACAGC-3′), Muc5AR (5′-CCTTCCTATGGCTTAGCTTCAGC-3′), β-actinF (5′-CACCACACCTTCTACAATGAGCTGC-3′), and β-actinR (5′-ACACCCTGGATAGCAACGTACATGC-3′); 4 μl of diluted cDNA; and 6 μl of molecular-grade water. Reactions were amplified under the following conditions: 94°C for 10 min followed by 40 cycles of 94°C for 30 s, 58°C for 1 min, and 72°C for 30 s.

## Supplementary Materials

www.sciencetranslationalmedicine.org/cgi/content/full/4/151/151ra124/DC1

Fig. S1. Muc5A mRNA expression (normalized to β-actin) is significantly increased in CRS patient samples compared to healthy subjects.

Fig. S2. Linear regression of qPCR-derived C. tuberculostearicum abundance with array-reported florescence intensity and SNOT-20 score indicates strong concordance between qPCR and array-generated findings and confirms a strong positive relationship between C. tuberculostearicum abundance and symptom severity.

Fig. S3. Murine experimental design.

Fig. S4. qPCR quantification of C. tuberculostearicum and L. sakei load in murine sinus tissue.

Table S1. Bacterial taxa detected in study samples.

Table S2. Bacterial taxa detected in significantly altered abundance in CRS patient versus healthy subject sinuses.

Table S3. Bacterial taxa significantly correlated with sinus symptom severity.

Table S4. Significance values for comparative goblet cell number per micrometer of epithelial cell surface across mouse treatment groups.

Table S5. Significance values for comparative goblet cell number per micrometer of epithelial cell surface across mouse treatment groups that include animals instilled with L. sakei.

Table S6. Kolmogorov-Smirnov assessment of data distribution.

## References and Notes

1. Acknowledgments: We thank the patients who provided samples for this study, H. Boushey for initiating this collaboration, and his and K. Norman’s critical assessment of the manuscript. We are grateful for microbiome analyses assistance provided by E. Brodie, M. Cox, and K. Fujimura; technical assistance from D. Mandal; and sample collection by W. Ma. Funding: This study was supported by an American Rhinological Society grant awarded to F.C.R. and S.V.L. S.V.L. is also funded by the Rainin Foundation and through a National Institute of Allergy and Infectious Disease award AI097172. N.A.N. is also funded through a National Institute of Allergy and Infectious Diseases award AI097172. N.A.A. is funded through the Minority Biomedical Research Support–Research Initiative for Scientific Enhancement grant 5R25-GM059298 and California Institute for Regenerative Medicine grant TB1-01194 at San Francisco State University, and A.N.G. and W. Ma are funded, in part, by the Rebecca Susan Buffett Foundation. Author contributions: N.A.A., Y.S., and N.A.N. contributed to experimental design, performed the experiments, and contributed to manuscript preparation. F.C.R., S.D.P., and A.N.G. provided clinical samples and contributed to human study design and manuscript preparation. S.V.L. designed the study, conceived the experiments, and prepared the manuscript. Competing interests: S.V.L. is a member of the Scientific Advisory Board of Second Genome. S.V.L., A.N.G., and S.D.P. are authors on patent application no. 61/624,105, “Sinusitis diagnostics and treatments.” None of the other authors declare any competing interests. Data and materials availability: PhyloChip data used in this study are available at the Gene Expression Omnibus Web site (https://www.ncbi.nlm.nih.gov/geo/) under accession number GSE37850.
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# Set x-ray of two objects inside another object

I have a mesh 'Suzanne' parented to an armature 'Armature'. Both are located inside another mesh 'Cube'. I want both 'Suzanne' and it's armature 'Armature' to be visible in the 3D view through 'Cube'. I tried setting the x-ray of 'Suzanne' and it's armature 'Armature' to True in Python, but then 'Suzanne'only appears through 'Cube'. I wonder how I can make both 'Suzanne' and it's armature 'Armature' appear through 'Cube'.

The .blend file can be found here in this Link

• Considering this is just for display anyways, could you get rid of the xray on Suzanne and instead add transparency to the cube? Jul 6 '18 at 16:24

format: plain


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• ### The wind and the magnetospheric accretion onto the T Tauri star S Coronae Australis at sub-au resolution(1709.01348)

Sept. 5, 2017 astro-ph.SR
To investigate the inner regions of protoplanetary disks, we performed near-infrared interferometric observations of the classical TTauri binary system S CrA. We present the first VLTI-GRAVITY high spectral resolution ($R\sim$4000) observations of a classical TTauri binary, S CrA (composed of S CrA N and S CrA S and separated by $\sim$1.4"), combining the four 8-m telescopes in dual-field mode. Our observations in the near-infrared K-band continuum reveal a disk around each binary component, with similar half-flux radii of about 0.1 au at d$\sim$130 pc, inclinations ($i=$28$\pm$3$^o$\ and $i=$22$\pm$6$^o$), and position angles (PA=0$^o\pm$6$^o$ and PA=-2$^o\pm$12$^o$), suggesting that they formed from the fragmentation of a common disk. The S CrA N spectrum shows bright HeI and Br$\gamma$ line emission exhibiting inverse P-Cygni profiles, typically associated with infalling gas. The continuum-compensated Br$\gamma$ line visibilities of S CrA N show the presence of a compact Br$\gamma$ emitting region the radius of which is about $\sim$0.06 au, which is twice as big as the truncation radius. This component is mostly tracing a wind. Moreover, a slight radius change between the blue- and red-shifted Br$\gamma$ line components is marginally detected. The presence of an inverse P-Cygni profile in the HeI and Br$\gamma$ lines, along with the tentative detection of a slightly larger size of the blue-shifted Br$\gamma$ line component, hint at the simultaneous presence of a wind and magnetospheric accretion in S CrA N.
• ### Distinguishing black-hole spin-orbit resonances by their gravitational wave signatures. II: Full parameter estimation(1507.05587)

Feb. 15, 2016 gr-qc, astro-ph.HE
Gravitational waves from coalescing binary black holes encode the evolution of their spins prior to merger. In the post-Newtonian regime and on the precession timescale, this evolution has one of three morphologies, with the spins either librating around one of two fixed points ("resonances") or circulating freely. In this work we perform full parameter estimation on resonant binaries with fixed masses and spin magnitudes, changing three parameters: a conserved "projected effective spin" $\xi$ and resonant family $\Delta\Phi=0,\pi$ (which uniquely label the source), the inclination $\theta_{JN}$ of the binary's total angular momentum with respect to the line of sight (which determines the strength of precessional effects in the waveform), and the signal amplitude. We demonstrate that resonances can be distinguished for a wide range of binaries, except for highly symmetric configurations where precessional effects are suppressed. Motivated by new insight into double-spin evolution, we introduce new variables to characterize precessing black hole binaries which naturally reflects the timescale separation of the system and therefore better encode the dynamical information carried by gravitational waves.
• SNO+ is a large liquid scintillator-based experiment located 2km underground at SNOLAB, Sudbury, Canada. It reuses the Sudbury Neutrino Observatory detector, consisting of a 12m diameter acrylic vessel which will be filled with about 780 tonnes of ultra-pure liquid scintillator. Designed as a multipurpose neutrino experiment, the primary goal of SNO+ is a search for the neutrinoless double-beta decay (0$\nu\beta\beta$) of 130Te. In Phase I, the detector will be loaded with 0.3% natural tellurium, corresponding to nearly 800 kg of 130Te, with an expected effective Majorana neutrino mass sensitivity in the region of 55-133 meV, just above the inverted mass hierarchy. Recently, the possibility of deploying up to ten times more natural tellurium has been investigated, which would enable SNO+ to achieve sensitivity deep into the parameter space for the inverted neutrino mass hierarchy in the future. Additionally, SNO+ aims to measure reactor antineutrino oscillations, low-energy solar neutrinos, and geoneutrinos, to be sensitive to supernova neutrinos, and to search for exotic physics. A first phase with the detector filled with water will begin soon, with the scintillator phase expected to start after a few months of water data taking. The 0$\nu\beta\beta$ Phase I is foreseen for 2017.
• ### Localized starbursts in dwarf galaxies produced by impact of low metallicity cosmic gas clouds(1509.00180)

Sept. 1, 2015 astro-ph.GA
Models of galaxy formation predict that gas accretion from the cosmic web is a primary driver of star formation over cosmic history. Except in very dense environments where galaxy mergers are also important, model galaxies feed from cold streams of gas from the web that penetrate their dark matter haloes. Although these predictions are unambiguous, the observational support has been indirect so far. Here we report spectroscopic evidence for this process in extremely metal-poor galaxies (XMPs) of the local Universe, taking the form of localized starbursts associated with gas having low metallicity. Detailed abundance analyses based on Gran Telescopio Canarias (GTC) optical spectra of ten XMPs show that the galaxy hosts have metallicities around 60 % solar on average, while the large star-forming regions that dominate their integrated light have low metallicities of some 6 % solar. Because gas mixes azimuthally in a rotation timescale (a few hundred Myr), the observed metallicity inhomogeneities are only possible if the metal-poor gas fell onto the disk recently. We analyze several possibilities for the origin of the metal-poor gas, favoring the metal-poor gas infall predicted by numerical models. If this interpretation is correct, XMPs trace the cosmic web gas in their surroundings, making them probes to examine its properties.
• ### The calibration system for the photomultiplier array of the SNO+ experiment(1411.4830)

Jan. 16, 2015 hep-ex, physics.ins-det
A light injection system using LEDs and optical fibres was designed for the calibration and monitoring of the photomultiplier array of the SNO+ experiment at SNOLAB. Large volume, non-segmented, low-background detectors for rare event physics, such as the multi-purpose SNO+ experiment, need a calibration system that allow an accurate and regular measurement of the performance parameters of their photomultiplier arrays, while minimising the risk of radioactivity ingress. The design implemented for SNO+ uses a set of optical fibres to inject light pulses from external LEDs into the detector. The design, fabrication and installation of this light injection system, as well as the first commissioning tests, are described in this paper. Monte Carlo simulations were compared with the commissioning test results, confirming that the system meets the performance requirements.
• ### The long bar as seen by the VVV survey: I. Colour-magnitude diagrams(1209.4370)

Sept. 27, 2012 astro-ph.GA
The VISTA Variable Survey (VVV) is able to map the Galaxy at l<0 with an unpaired depth (at least 3 mag deeper than 2MASS), opening new possibilities for studying the inner structure of the Milky Way. In this paper we concentrate on the exploitation of these data to better understand the spatial disposition and distribution of the structures present in the inner Milky Way, particularly the Long Bar and its interaction with the inner disc. The observations show the presence of a clear overdensity of stars with associated recent stellar formation that we interpret as the traces of the Long Bar, and we derive an angle for it of 41+/-5 with the Sun-Galactic centre line, touching the disc near l=27 and l=-12. The colour-magnitude diagrams presented here also show a lack of disc stars in several lines of sight, a fact that we associate with the truncation of the disc by the potential of this bar for Galactocentric radius less than 5kpc.
• ### Effect of the frequency chirp on laser wakefield acceleration(1112.4380)

The role of laser frequency chirps in the laser wakefield accelerator is examined. We show that in the linear regime, the evolution of the laser pulse length is affected by the frequency chirp, and that positive (negative) chirp compresses (stretches) the laser pulse, thereby increasing (decreasing) the peak vector potential and wakefield amplitude. In the blowout regime, the frequency chirp can be used to fine tune the localized etching rates at the front of the laser. In our simulations, chirped laser pulses can lead to 15% higher self-trapped electrons, and 10% higher peak energies as compare to the transform-limited pulse. Chirps may be used to control the phase velocity of the wake, and to relax the self-guiding conditions at the front of the laser. Our predictions are confirmed by multi-dimensional particle-in-cell simulations with OSIRIS.
• Ensuring the radiation hardness of PbWO4 crystals was one of the main priorities during the construction of the electromagnetic calorimeter of the CMS experiment at CERN. The production on an industrial scale of radiation hard crystals and their certification over a period of several years represented a difficult challenge both for CMS and for the crystal suppliers. The present article reviews the related scientific and technological problems encountered.
• ### Images IV: Strong evolution of the oxygen abundance in gaseous phases of intermediate mass galaxies since z=0.8(0810.0272)

Oct. 2, 2008 astro-ph
Intermediate mass galaxies (logM(Msun)>10) at z~0.6 are the likeliest progenitors of the present-day numerous population of spirals. There is growing evidence that they have evolved rapidly since the last 6 to 8 Gyr ago, and likely have formed a significant fraction of their stellar mass, often showing perturbed morphologies and kinematics. We have gathered a representative sample of 88 such galaxies and have provided robust estimates of their gas phase metallicity. For doing so, we have used moderate spectral resolution spectroscopy at VLT/FORS2 with unprecedented high S/N allowing to remove biases coming from interstellar absorption lines and extinction to establish robust values of R23=([OII]3727 + [OIII]4959,5007)/Hbeta. We definitively confirm that the predominant population of z~0.6 starbursts and luminous IR galaxies (LIRGs) are on average, two times less metal rich than the local galaxies at a given stellar mass. We do find that the metal abundance of the gaseous phase of galaxies is evolving linearly with time, from z=1 to z=0 and after comparing with other studies, from z=3 to z=0. Combining our results with the reported evolution of the Tully Fisher relation, we do find that such an evolution requires that ~30% of the stellar mass of local galaxies have been formed through an external supply of gas, thus excluding the close box model. Distant starbursts & LIRGs have properties (metal abundance, star formation efficiency & morphologies) similar to those of local LIRGs. Their underlying physics is likely dominated by gas infall probably through merging or interactions. Our study further supports the rapid evolution of z~0.4-1 galaxies. Gas exchanges between galaxies is likely the main cause of this evolution.
• ### Characterization of the hot Neptune GJ 436b with Spitzer and ground-based observations(0707.3809)

Sept. 14, 2007 astro-ph
We present Spitzer Space Telescope infrared photometry of a secondary eclipse of the hot Neptune GJ436b. The observations were obtained using the 8-micron band of the InfraRed Array Camera (IRAC). The data spanning the predicted time of secondary eclipse show a clear flux decrement with the expected shape and duration. The observed eclipse depth of 0.58 mmag allows us to estimate a blackbody brightness temperature of T_p = 717 +- 35 K at 8 microns. We compare this infrared flux measurement to a model of the planetary thermal emission, and show that this model reproduces properly the observed flux decrement. The timing of the secondary eclipse confirms the non-zero orbital eccentricity of the planet, while also increasing its precision (e = 0.14 +- 0.01). Additional new spectroscopic and photometric observations allow us to estimate the rotational period of the star and to assess the potential presence of another planet.
• ### Accurate Spitzer infrared radius measurement for the hot Neptune GJ 436b(0707.2261)

July 24, 2007 astro-ph
We present Spitzer Space Telescope infrared photometry of a primary transit of the hot Neptune GJ 436b. The observations were obtained using the 8 microns band of the InfraRed Array Camera (IRAC). The high accuracy of the transit data and the weak limb-darkening in the 8 microns IRAC band allow us to derive (assuming M = 0.44 +- 0.04 Msun for the primary) a precise value for the planetary radius (4.19 +0.21-0.16 Rearth), the stellar radius (0.463 +0.022-0.017 Rsun), the orbital inclination (85.90 +0.19-0.18 degrees) and transit timing (2454280.78186 +0.00015-0.00008 HJD). Assuming current planet models, an internal structure similar to that of Neptune with a small H/He envelope is necessary to account for the measured radius of GJ 436b.
• ### Generating multi-GeV electron bunches using single stage laser wakefield acceleration in a 3D nonlinear regime(physics/0612227)

The extraordinary ability of space-charge waves in plasmas to accelerate charged particles at gradients that are orders of magnitude greater than in current accelerators has been well documented. We develop a phenomenological framework for Laser WakeField Acceleration (LWFA) in the 3D nonlinear regime, in which the plasma electrons are expelled by the radiation pressure of a short pulse laser, leading to nearly complete blowout. Our theory provides a recipe for designing a LWFA for given laser and plasma parameters and estimates the number and the energy of the accelerated electrons whether self-injected or externally injected. These formulas apply for self-guided as well as externally guided pulses (e.g. by plasma channels). We demonstrate our results by presenting a sample Particle-In-Cell (PIC) simulation of a 30f sec, 200T W laser interacting with a 0.75cm long plasma with density 1.5*10^18 cm^-3 to produce an ultra-short (10f s) mono-energetic bunch of self-injected electrons at 1.5 GeV with 0.3nC of charge. For future higher-energy accelerator applications we propose a parameter space, that is distinct from that described by Gordienko and Pukhov [Physics of Plasmas 12, 043109 (2005)] in that it involves lower densities and wider spot sizes while keeping the intensity relatively constant. We find that this helps increase the output electron beam energy while keeping the efficiency high.
• ### Multiwavelength analysis of the young open cluster NGC 2362(astro-ph/0602487)

Feb. 22, 2006 astro-ph
We present a multiwavelength analysis of the young open cluster NGC 2362. UBVRcIc CCD photometric observations, together with available data in the Chandra data base, near infrared data from the Two Micron All Sky Survey (2MASS), and recently published Halpha spectroscopy were used to get information about the evolutionary stage of the cluster and the main physical properties of its stellar content. Cluster membership is estimated for every individual star by means of ZAMS and isochrone fitting. The cluster is confirmed to host a richly populated pre-main sequence (PMS), and to contain a large amount of X-ray emitting stars, which reach from the PMS members of GK spectral type, up to the most luminous OB type main sequence (MS) members. The PMS cluster members show no significant age spread, and the comparison to both PMS and post-MS isochrones suggests a younger age for the more massive MS than for lower mass PMS members. The analysis allows to asses the validity of currently used pre-main sequence evolutionary models, and supports the suggestion of a well defined positive correlation of the X-ray emission from PMS stars with their bolometric luminosity. Clear differences are found on the other hand, between the X-ray activity properties of MS and PMS cluster members, both in the relation between X-ray luminosity and bolometric luminosity, and in spectral properties as well.
• ### Size distribution of circumstellar disks in the Trapezium cluster(astro-ph/0506585)

June 24, 2005 astro-ph
In this paper we present results on the size distribution of circumstellar disks in the Trapezium cluster as measured from HST/WFPC2 data. Direct diameter measurements of a sample of 135 bright proplyds and 14 silhouettes disks suggest that there is a single population of disks well characterized by a power-law distribution with an exponent of -1.9 +- 0.3 between disk diameters 100-400 AU. For the stellar mass sampled (from late G to late M stars) we find no obvious correlation between disk diameter and stellar mass. We also find that there is no obvious correlation between disk diameter and the projected distance to the ionizing Trapezium OB stars. We estimate that about 40% of the disks in the Trapezium have radius larger than 50 AU. We suggest that the origin of the Solar system's (Kuiper belt) outer edge is likely to be due to the star formation environment and disk destruction processes (photoevaporation, collisions) present in the stellar cluster on which the Sun was probably formed. Finally, we identified a previously unknown proplyd and named it 266-557, following convention.
• ### The CORALIE survey for southern extra-solar planets. XII. Orbital solutions for 16 extra-solar planets discovered with CORALIE(astro-ph/0310316)

Nov. 10, 2003 astro-ph
This paper summarizes the information gathered for 16 still unpublished exoplanet candidates discovered with the CORALIE echelle spectrograph mounted on the Euler Swiss telescope at La Silla Observatory. Amongst these new candidates, 10 are typical extrasolar Jupiter-like planets on intermediate- or long-period (100<P<1350d) and fairly eccentric (0.2<e<0.5) orbits (HD19994, HD65216, HD92788, HD111232, HD114386, HD142415, HD147513, HD196050, HD216437, HD216770). Two of these stars are in binary systems. The next 3 candidates are shorter-period planets (HD6434, HD121504) with lower eccentricities among which a hot Jupiter (HD83443). More interesting cases are finally given by the multiple-planet systems HD82943 and HD169830. The former is a resonant P_2/P_1=2/1 system in which planet-planet interactions are influencing the system evolution. The latter is more hierarchically structured.
• ### Soliton generation of two-component Bose-Einstein condensates in optical lattices(cond-mat/0307156)

July 8, 2003 cond-mat.soft
Coupled nonlinear Schrodinger equations (CNLS) with an external elliptic function potential model a quasi one--dimensional interacting two-component Bose-Einstein condensate trapped in a standing light wave. New families of stationary solutions of the CNLS with a periodic potential are presented and their stability studied by direct numerical simulations. Some of these solutions allow reduction to Manakov system. From a physical point of view these solutions can be interpreted as exact Bloch states at the edge of the Brillouin zone. Some of them are stable while others are found to be unstable against modulations of long wavelength. The solutions which are modulationally unstable are shown to lead to the formation of localized ground states of the coupled BEC system.
• ### Scalar Mesons within a model for all non-exotic mesons(hep-ph/0201006)

Jan. 2, 2002 hep-ph
We describe a four-parameter model for non-exotic meson-meson scattering, which accommodates all non-exotic mesons, hence also the light scalar mesons, as resonances and bound states characterised by complex singularities of the scattering amplitude as a function of the total invariant mass. The majority of the full $S$-matrix mesonic poles stem from an underlying confinement spectrum. However, the light scalar mesons K0*(830), a0(980), f0(400-1200), and f0(980) do not, but instead originate in 3P0-barrier semi-bound states. In the case of bound states, wave functions can be determined. For ccbar and bbbar, radiative transitions have been calculated. Here we compare the results to the data.
• ### Probing the pc- and kpc-scale environment of the powerful radio galaxy Hercules A(astro-ph/0111607)

Nov. 30, 2001 astro-ph
We present the kpc-scale behaviour of the powerful extragalactic radio source Hercules A and the behaviour of the intracluster gas in which the radio source is situated. We have found that Hercules A exhibits a strong Laing-Garrington effect. The X-ray observations have revealed an extended X-ray emission elongated along the radio galaxy axis. The estimated temperature of the cluster is kT = 2.45 keV and the central electron density is no~7.8 x 10^(-3) cm^(-3) which reveals a hot, dense environment in which Hercules A is situated. From the combined study of the radio and X-ray data we have estimated a central value of 3<Bo (muG)<9. We also present the most recent results from the analysis of the radio data on the pc-scale structure of the radio galaxy, observed at 18 cm by the EVN-MERLIN array. A faint but compact radio source, coincident with the optical centre of Hercules A was detected by the EVN at 18 mas resolution. The total flux density of the EVN core is 14.6 mJy. Its angular size is 18 x 7 mas with a position angle of ~139 degrees. There is also evidence for extended emission in the NW-SE direction, most probably from the eastern pc-scale jet. If this is true then there is a misalignment between the direction of the pc-eastern and the aligned kpc-scale jets of ~35 degrees.
• ### Quasiparticle spectrum of a type-II superconductor in a high magnetic field with randomly pinned vortices(cond-mat/9905180)

May 13, 1999 cond-mat.supr-con
We show that gapless superconductivity of a strongly type-II superconductor in a high magnetic field prevails in the presence of disorder, suggesting a topological nature. We calculate the density of states of the Bogoliubov-de Gennes quasiparticles for a two-dimensional inhomogeneous system in both cases of weak and strong disorder. In the limit of very weak disorder, the effect is very small and the density of states is not appreciably changed. As the disorder increases, the density of states at low energies increases and the ratio of the low-energy density of states to its maximum increases significantly.
• ### Hall conductance of a pinned vortex lattice in a high magnetic field(cond-mat/9905181)

May 13, 1999 cond-mat.supr-con
We calculate the quasiparticle contribution to the zero temperature Hall conductance of two-dimensional extreme type-II superconductors in a high magnetic field, using the Landau basis. As one enters the superconducting phase the Hall conductance is renormalized to smaller values, with respect to the normal state result, until a quantum level-crossing transition is reached. At high values of the order parameter, where the quasiparticles are bound to the vortex cores, the Hall conductance is expected to tend to zero due to a theorem of Thouless.
• ### Neutrino Magnetic Moment Upper Bound From Solar Neutrino Observations(hep-ph/9712462)

Dec. 19, 1997 hep-ph
Using the data from SuperKamiokande, Kamiokande and Homestake solar neutrino experiments we derive an upper bound on the magnetic moment of the neutrino and find $\mu_{\nu_e}\leq(2.2-2.3)\times 10^{-10}\mu_{B}$, within four different standard solar models. We assume equal magnetic moments for all neutrino flavours. This limit is obtained when neutrinos do not undergo any "disappearence" mechanism other than the magnetic moment conversion due to the solar magnetic field and for a total or nearly total suppression of the intermediate energy neutrinos. In our work we consider an energy dependent suppression of solar neutrinos. We also point out that the limit may be further reduced if the detector threshold energy in $\nu_{e,x}e^{-}$ scattering with solar neutrinos is decreased.
• ### Characteristic functions and process identification by neural networks(physics/9712035)

Dec. 17, 1997 physics.data-an
Principal component analysis (PCA) algorithms use neural networks to extract the eigenvectors of the correlation matrix from the data. However, if the process is non-Gaussian, PCA algorithms or their higher order generalisations provide only incomplete or misleading information on the statistical properties of the data. To handle such situations we propose neural network algorithms, with an hybrid (supervised and unsupervised) learning scheme, which constructs the characteristic function of the probability distribution and the transition functions of the stochastic process. Illustrative examples are presented, which include Cauchy and Levy-type processes
• ### Non-commutative time-frequency tomography(physics/9712022)

Dec. 12, 1997 physics.data-an
The characterization of non-stationary signals requires joint time and frequency information. However, time (t) and frequency (omega) being non-commuting variables there cannot be a joint probability density in the (t,omega) plane and the time-frequency distributions, that have been proposed, have difficult interpretation problems arising from negative or complex values and spurious components. As an alternative we propose to obtain time-frequency information by looking at the marginal distributions along rotated directions in the (t,omega) plane. The rigorous probability interpretation of the marginal distributions avoids all interpretation ambiguities. Applications to signal analysis and signal detection are discussed as well as an extension of the method to other pairs of non-commuting variables.
• ### On the computation of quantum characteristic exponents(quant-ph/9711068)

Nov. 26, 1997 quant-ph
A quantum characteristic exponent may be defined, with the same operational meaning as the classical Lyapunov exponent when the latter is expressed as a functional of densities. Existence conditions and supporting measure properties are discussed as well as the problems encountered in the numerical computation of the quantum exponents. Although an example of true quantum chaos may be exhibited, the taming effect of quantum mechanics on chaos is quite apparent in the computation of the quantum exponents. However, even when the exponents vanish, the functionals used for their definition may still provide a characterization of distinct complexity classes for quantum behavior.
• ### Boundary-layer control by electric fields: A feasibility study(physics/9705020)

May 15, 1997 physics.flu-dyn
A problem of great concern in aviation and submarine propulsion is the control of the boundary layer and, in particular, the methods to extend the laminar region as a means to decrease noise and fuel consumption. In this paper we study the flow of air along an airfoil when a layer of ionized gas and a longitudinal electric field are created in the boundary layer region. By deriving scaling solutions and more accurate numerical solutions we discuss the possibility of achieving significant boundary layer control for realistic physical parameters. Practical design formulas and criteria are obtained. We also discuss the perspectives for active control of the laminar-to-turbulent transition fluctuations by electromagnetic field modulation.


text:
# Adding a New Package to the Build¶

New packages intended for distribution to end users should generally be added as a dependency of a “top level product”: these are the roots of the LSST package hierarchy. They include lsst_apps, lsst_distrib, qserv_distrib and lsst_sims.

Before adding a new dependency to any of these products, it must be approved through the usual Discussion and Decision Making Process (RFC, RFD): consensus must be reached regarding both the name and the suitability of the new package. Before adopting the RFC, implementation tickets should be created to cover package creation.

After approval, code written internally by Data Management should be packaged following the template in the lsst/templates repository. DM packaging of third party code should proceed as described in Distributing Third-Party Packages with EUPS.

New packages must be added to the LSST organization on GitHub and access must be granted to appropriate teams. For DM written code, these include “Data Management” and “Overlords”; for third party code, “DM Externals” and “Overlords” (but not Data Management).

The new package must be added to the etc/repos.yaml file in the lsstsw package along with its corresponding GitHub URL. This file is governed by a “self-merge” policy: upon opening a pull request, it will be checked by the Travis CI system, and developers may merge without further review on success. Refer to RFC-75 for background.

The new package then needs to be added to the ups/*.table file (and possibly the ups/*.cfg file) of one or more other packages in the stack where it is used.

## Handling Git LFS backed repos¶

New Git LFS (see Using Git Large File Storage (LFS) for Data Repositories) backed repos (or existing repos being converted to lfs) require additional configuration.

• The repos.yaml entry must declare that the repository is LFS backed.

afwdata:
url: https://github.com/lsst/afwdata.git
lfs: true

See the comment block at the top of repos.yaml for additional details.

• At present, the EUPS distrib packaging mechanism does not support lfs backed repos. These products must not be added to any top level meta-package or as a mandatory (non-optional) recursive dependency of a top level package.

• Optional dependencies must be added to manifest.remap to prevent the creation of broken EUPS distrib packages. Please note that the “self-merge” policy of RFC-75 does not apply to manifest.remap.

Unlike changes merged into repos.yaml, modifications to manifest.remap do not take immediate affect

recommend procedure is to attach the modification PR to a DM Jira issue on the Continuous Integration component.


text:
# Variance Component Estimation

Hi everyone! I am new to Stan, and I am trying to estimate variance components in a hierarchical linear model. I have some example data, and I have the outputs of two different statistical software packages, the results of which I am trying to match. So far, I have been terribly unsuccessful.

I am trying to fit the model y_{ijk} \sim \mu + \alpha_i + \beta_j + \alpha\beta_{i,j} + \epsilon, where \alpha_i \sim \mathcal{N}(0,\sigma^2_\alpha), \beta_i \sim \mathcal{N}(0,\sigma^2_\beta), \alpha \beta _i \sim \mathcal{N}(0,\sigma^2_{\alpha\beta}), \epsilon_{ijk} \sim \mathcal{N}(0,\sigma^2_e)

Both of the other statistical packages I am using give both REML and “Bayesian” estimates of these parameters, as shown below. I am attempting to recreate – or at least get close to – the Bayesian estimates. (However, getting the REML estimates would be very beneficial to my understanding)

Software 1:
REML:
sig1 = .0514553
sig2 = 1.0864466
sig3 = 0.0000000
sig4 = .0399733

Bayesian:
sig1 = .024646
sig2 = .884780
sig3 = .00201177
sig4 = .0382738

Software 2:
REML:
sig1 = .05146
sig2 = 1.0864
sig3 = 0
sig4 = .03997

Bayesian:
sig1 = .024795
sig2 = .89201
sig3 = .002013
sig4 = .03867

I have seen some documentation about how to use covariance matrices, but it appears that such matrices must be positive definite, and the software I am trying to replicate reports that “The Estimated G Matrix is not positive definite.”

How can I estimate these components of variance?

Stan Code:

data {
int LENGTH;
vector[LENGTH] x1;
vector[LENGTH] x2;
vector[LENGTH] Y;
}

parameters {
real mu;
real a;
real b;
real ab;
real eps;

real<lower=0> sig_a;
real<lower=0> sig_b;
real<lower=0> sig_ab;
real<lower=0> sig_e;
}

model {
Y ~ normal(mu + a*x1 + b*x2 + ab * (x1 .* x2) + eps, sig_a + sig_b + sig_ab + sig_e);
a ~ normal(0,sig_a);
b ~ normal(0,sig_b);
ab ~ normal(0,sig_ab);
eps ~ normal(0,sig_e);
}

Data:
x1,x2,y
1,1,0.29
1,1,0.41
1,1,0.64
2,1,0.08
2,1,0.25
2,1,0.07
3,1,0.04
3,1,-0.11
3,1,-0.15
1,2,-0.56
1,2,-0.68
1,2,-0.58
2,2,-0.47
2,2,-1.22
2,2,-0.68
3,2,-1.38
3,2,-1.13
3,2,-0.96
1,3,1.34
1,3,1.17
1,3,1.27
2,3,1.19
2,3,0.94
2,3,1.34
3,3,0.88
3,3,1.09
3,3,0.67
1,4,0.47
1,4,0.5
1,4,0.64
2,4,0.01
2,4,1.03
2,4,0.2
3,4,0.14
3,4,0.2
3,4,0.11
1,5,-0.8
1,5,-0.92
1,5,-0.84
2,5,-0.56
2,5,-1.2
2,5,-1.28
3,5,-1.46
3,5,-1.07
3,5,-1.45
1,6,0.02
1,6,-0.11
1,6,-0.21
2,6,-0.2
2,6,0.22
2,6,0.06
3,6,-0.29
3,6,-0.67
3,6,-0.49
1,7,0.59
1,7,0.75
1,7,0.66
2,7,0.47
2,7,0.55
2,7,0.83
3,7,0.02
3,7,0.01
3,7,0.21
1,8,-0.31
1,8,-0.2
1,8,-0.17
2,8,-0.63
2,8,0.08
2,8,-0.34
3,8,-0.46
3,8,-0.56
3,8,-0.49
1,9,2.26
1,9,1.99
1,9,2.01
2,9,1.8
2,9,2.12
2,9,2.19
3,9,1.77
3,9,1.45
3,9,1.87
1,10,-1.36
1,10,-1.25
1,10,-1.31
2,10,-1.68
2,10,-1.62
2,10,-1.5
3,10,-1.49
3,10,-1.77
3,10,-2.16


text:
# Deleting duplicates from matrix

I have a 4x4 symmetric matrix that is obtained by solving some equations. I tried deleting duplicates with DeleteDuplicates, but that's not working with nested lists (elements of those lists that are the same).

So I have this

$$\begin{pmatrix} a_{11} & a_{12} & a_{13} & a_{14} \\ a_{21} & a_{22} & a_{23} & a_{24} \\ a_{31} & a_{32} & a_{33} & a_{34} \\ a_{41} & a_{42} & a_{43} & a_{44} \\ \end{pmatrix}\to a_{nm}=a_{mn}\to \begin{pmatrix} a_{11} & a_{12} & a_{13} & a_{14} \\ 0 & a_{22} & a_{23} & a_{24} \\ 0 & 0 & a_{33} & a_{34} \\ 0 & 0 & 0 & a_{44} \\ \end{pmatrix}$$

I'd like to be able to remove lower triangle of a matrix but only if they are the same. How to do that?

-
I noticed the UpperTriangularize function, which is what I need, it's just that I would like to be sure first if the matrix in question is symmetric. Should I make an If statement? –  dingo_d Oct 14 '13 at 16:12
You can use SymmetricMatrixQ –  rm -rf Oct 14 '13 at 16:22

Let mat be your matrix:

func[mat_?SymmetricMatrixQ] := UpperTriangularize[mat];
func[mat_?(Not@SymmetricMatrixQ[#] &)] := mat;

If the matrix is symmetric the above will convert to upper triangular matrix including diagonal,else it will return original matrix, e.g.

m = {{a, b, c}, {b, d, e}, {c, e, f}};
m//MatrixForm
func[m]//MatrixForm

yields:

-
Thanks :) That does the trick :) –  dingo_d Oct 15 '13 at 12:49

I don't think this applies specifically to the OPs situation, but I thought I'd contribute just in case it's useful. As mentioned in the comments, using UpperTriangularize with a conditional statement to check for symmetry is the appropriate route; however if the matrix elements are, for example, coordinates, then SymmetricMatrixQ won't recognize the matrix as symmetric. A circuitous route to a 4x4 matrix of x,y coordinates:

m1 =  RandomInteger[{1, 10}, {4, 4}];
m2 =  RandomInteger[{1, 10}, {4, 4}];
sm1 = m1 + Transpose[m1];
sm2 = m2 + Transpose[m2];

SymmetricMatrixQ[sm3] returns False, but sm3 == Tranpose[sm3] returns True. Additionally, UpperTriangularize doesn't like this matrix, so I make my own function:
newUpperTriangularize[x_] := UpperTriangularize[x /. {_, _} -> 1]*x;


text:
# America’s “Freedom’?

By Murray Bourne, 20 Mar 2005

Dubya loved to crow about the "freedom" and "peace" that he brought to the "Iraqi people", since the "victory" in Iraq. The USATODAY poll of April 2004 showed that the majority thought of the Americans as occupiers (71%), not liberators (19%) and that the invasion brought more harm (46%) than good (33%). While they are glad to be rid of Saddam (80% have an unfavorable view towards him) their view of Bush is not so hot (55% have an unfavourable view).

Not surprisingly, there were differences in the views of the occupation by the Sunnis (not happy, as they lost most), Shiites (somewhere in the middle) and Kurds (overwhelmingly happy). Source: USATODAY.com - Apr 2004 Poll: Iraqis out of patience

One year on, I am wondering how they feel now as the occupation drags on and the difficulties of withdrawing become greater.

Be the first to comment below.

### Comment Preview

HTML: You can use simple tags like <b>, <a href="...">, etc.

To enter math, you can can either:

1. Use simple calculator-like input in the following format (surround your math in backticks, or qq on tablet or phone):
a^2 = sqrt(b^2 + c^2)
(See more on ASCIIMath syntax); or
2. Use simple LaTeX in the following format. Surround your math with $$ and $$.
$$\int g dx = \sqrt{\frac{a}{b}}$$
(This is standard simple LaTeX.)

NOTE: You can mix both types of math entry in your comment.

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text:
# Why do all SSH-RSA Keys begin with “AAAAB3NzaC1yc”?

My Friend and I have been generating a few ssh2-rsa keys and noticed that all the public keys began with "AAAAB3NzaC1yc". The similarity extended to "AAAAB3NzaC1yc2EAAAABIwAAAQEA" between two keys I generated on the same machine on two successive attempts. I can even google "AAAAB3Nz" and end up getting a few hits.

Is this normal? Or are we doing something wrong while generating? Suffering from insufficient randomness?

-
What are you using to generate them? Openssl, openssh, pgp? It is probably an encoding. –  mikeazo Jan 8 '13 at 17:39
We used puTTYgen on two different windows machine and ssh-keygen on a linux machine. –  Lord Loh. Jan 8 '13 at 18:23

The public key blob doesn't consist of just the numbers that make up the public key: it begins with a header that says “this is an SSH public key”. The repeated prefix encodes this header.

RFC 4254 specifies the encoding of public key in SSH key format.

The "ssh-rsa" key format has the following specific encoding:

 string    "ssh-rsa"
mpint     e
mpint     n

Here the 'e' and 'n' parameters form the signature key blob.

The string is encoded as 32-bit big endian length followed by the literal string:

0,0,0,7,'s','s','h','-','r','s','a'

Encoding this sequence of bytes in Base64 gives:

AAAAB3NzaC1yc2E

The public exponent is also usually the same, so the common prefix is even longer. The bulk of the key is the public modulus, and that is completely different in different keys.

-


text:
# Implement strStr() in Python

PythonServer Side ProgrammingProgramming

Suppose we have two strings str and sub_str. We have to find the first occurrence of sub_str in the str. So if the string str is “helloworld”, and substring is “lo”, then the result will be 3.

This can be done using the strstr() function in C. We have to design another function that is similar to the strstr() in C.

To solve this, follow these steps −

• i := 0, j := 0, m := length of sub_str and n := length of str
• if m = 0, then return 0
• while i < n and n – i + 1 = m, do
• if str[i] = sub_str[j], then
• temp := j
• while j < m and i < n and sub_str[j] == str[j], do
• increase i and j by 1
• if j = m, then return temp
• i := temp + 1
• j := 0
• else increase i by 1
• return -1

Let us see the implementation to get better understanding

## Example (Python)

Live Demo

class Solution(object):
def strStr(self, haystack, needle):
"""
:type haystack: str
:type needle: str
:rtype: int
"""
i = 0
j = 0
m = len(needle)
n = len(haystack)
if m ==0:
return 0
while i<n and n-i+1>=m:
if haystack[i] == needle[j]:
temp = i
while j<m and i<n and needle[j]==haystack[i]:
i+=1
j+=1
if j == m:
return temp
i= temp+1
j = 0
else:
i+=1
return -1
haystack = "helloworld"
needle = "lo"
ob1 = Solution()
print(ob1.strStr(haystack, needle))

## Input

haystack = "helloworld"
needle = "lo"

## Output

3
Published on 08-Jan-2020 10:42:57


text:
How the rate of convergence of a sequence relates to the convergence its summation (the series).

I am currently writing my IB HL Math Internal Assessment. I was researching why "$\sum_{n=1}^\infty \frac{1}{n}$" diverges , but "$\sum_{n=1}^\infty \frac{1}{n^2}$" converges. My research brought me to the p-Series convergence test: $$\sum_{n=1}^\infty \frac{1}{n^x}$$ which converges when x>1.

The convergence of this type of infinite series does not only depend on IF the values of the sequence converge to zero. The convergence of this type of infinite series actually depends on the RATE AT WHICH the values of the sequence converge to zero (Why does the harmonic series diverge but the p-harmonic series converge). I want to further explore the correlation between the rate at which the sequence converges to zero and the convergence of the series. For example, I tried to create a function to examine the trend of the the rates at which $\sum_{n=1}^\infty \frac{1} {n^x}$ converge to zero, but realized that the rates of the graphs are not one value (i.e. 4).. Each rate of $\frac{1}{n^x}$ are infinite values, such as $y=\frac{-0.5}{n^2}$ (the rate of convergence of the sequence of the harmonic series).

The problem I am having is that I cannot find research online that tells me more than "the convergence of the series "1/n^x" is dependent on the rate at which the values converge to 0. I want to further explore the "rigorous proofs" that were mentioned in "Why does the harmonic series diverge but the p-harmonic series converge".

I tried to explain this topic as best I could. Thank you for your time.

EDIT: the SEQUENCE of 1/n would be: 1, 1/2, 1/3, etc... The SERIES of 1/n would be 1 + (1/2) + (1/3) + ... + (1/n) Here is an example of what I am looking for: The terms of the harmonic series (1/n) converge to zero, but the summation of all these terms, called the series, DOES NOT converge to a number. This is because the sequence does not converge to zero fast enough. I am trying to gain a deeper mathematical understanding of this idea.

• I think this is a really good question, so +1. – Simply Beautiful Art Jan 15 '17 at 1:55
• To be clear: you seem to be asking for more than just a proof that $\sum_{n=1}^\infty \frac{1}{n^p}$ converges for $p > 1$, you seem to be asking about how fast that happens? – Chris Jan 15 '17 at 1:58
• @Chris No, I get out of it that the OP wants even more specifically the answer to the question in general, as in, beyond just that series. I think that would make this very interesting. – Simply Beautiful Art Jan 15 '17 at 2:01
• Why not just compare with the integral of $1/t^p$? Assuming $p>0$, you can draw a picture to see that $$\sum_{n=1}^{\infty} \frac{1}{n^p} \geq \int_1^{\infty} \frac{1}{t^p}dt \geq \sum_{n=2}^{\infty} \frac{1}{n^p}$$ – Michael Jan 15 '17 at 2:12
• @Michael It does not tell you how fast it converges though, and how "fast-ness" relates to convergence. – Simply Beautiful Art Jan 15 '17 at 2:13


text:
help

Image text transcribed for accessibility: For an RL circuit with R= 1.0 kOhm and L=100 mH calculated the time constant for when the inductor is charging Sketch (in the space below) what you would expect the voltage across the inductor to look like if the source used is running on a square wave pattern (shown in red below) For a circuit consisting of a Resistor, an Inductor and a Capacitor in series we can define the total impedance in the following manner: We can minimize the impedance by picking a frequency such that omega L = 1/omega C Calculate what the frequency, f in hertz, to minimize the impedance: when R=1.0 kOhm. L=100mH. and C=0.01 muF.


text:
## If $$y=(x-5)^2+(x+1)^2-6,$$ then $$y$$ is least when $$x =$$

##### This topic has expert replies
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Posts: 2058
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### If $$y=(x-5)^2+(x+1)^2-6,$$ then $$y$$ is least when $$x =$$

by M7MBA » Sun Jan 16, 2022 12:06 pm

00:00

A

B

C

D

E

## Global Stats

If $$y=(x-5)^2+(x+1)^2-6,$$ then $$y$$ is least when $$x =$$

A. -2
B. -1
C. 0
D. 2
E. None of the above


text:
# General Instructions for Creating Graphs and Figures

Examples below can be generated by plot_example.m script in Tools repository.

• Use subfig to place your figures reasonably. Note that a new figure is created each time, so don't forget to close your figures. Preferably close all at the beginning of your script.
• Each figure should a have descriptive title.
• When necessary, a legend describing lines of different colors/styles should be added, preferably inside the plot, if possible.

### Figures with Bitmap Image Superimposed

• Do not use imshow Matlab command for displaying bitmaps. Use image (or imagesc for grayscale bitmaps), then axes are kept shown.
• Ensure square pixels: axis image (this hides area outside the image) or axis equal.

### 2D and 3D Euclidean Plots

• Ensure equal axis scale: axis equal
• Use labels for axes, e.g. xlabel( 'x' ), zlabel( 'z' )

### Plotting vectors

• Use quiver and quiver3 to plot bound vectors in 2D/3D.
• Use as quiver(X,Y,U,V,0) where X,Y is the origin and U,V the vector. The scaling argument 0 ensures the arrow is of the proper length.

### Other Graphs

• Use labels for axes, e.g. xlabel( 'time [s]' ), ylabel( 'voltage [mV]' ). Don't forget units.
• Use axis tight to set axis limits tightly to data.


text:
# Re: Paper and slides on indefiniteness of CH

Dear John,

On Mon, 11 Aug 2014, John Steel wrote:

If certain technical conjectures areproved, then “V=ultimate L” is an attractive axiom. The paper “Godel’s program“, available on my webpage, gives an argument for that.

Many thanks for mentioning this paper of yours, which I read with great interest. It would be very helpful if you could clarify a few points made in that paper, especially with regard to interpretative power, practical completeness, your multiverse discussion and Woodin’s new axiom. I also have a few more minor questions which I’ll stick at the end.

Page 6

Footnote 10: I think it’s worth mentioning that for reflexive theories, S is interpretable in T iff S proves the consistency of T’s finite subtheories. So in fact for “natural” theories there really is no difference between consistency strength and interpretative power. This comes up again later in the paper.

You state:

If T, U are natural theories of consistency strength at least that of ‘there are infinitely many Woodin cardinals’ then the consequences of T in 2nd order arithmetic are contained in those of U, or vice-versa.

I don’t agree. First recall a milestone of inner model theory:

If the singular cardinal hypothesis fails then there is an inner model with a measurable cardinal.

From this it is clear that ZFC + “there is an inner model with a measurable cardinal” is a natural theory. Similarly for any large cardinal axiom LCA the theory ZFC + “There is an inner model satisfying LCA” is a natural theory. But this theory has the same consistency strength as ZFC + LCA yet fails to prove $\Pi^1_3$ sentences which are provable in ZFC + LCA. (By Shoenfield it does prove any $\Sigma^1_3$ sentence provable in ZFC + LCA.) Nor does it prove even $\Pi_1^1$ determinacy.

So what definition of natural do you have in mind here? The fact is, and this comes up later in your paper, there are many theories equiconsistent with theories of the form ZFC + LCA which do not prove the existence of large cardinals.

Footnote 11: Another issue with natural. Consider the theories PA + The least $n$ at which the Paris-Harrington function is not defined is even, and the same theory with “even” replaced by “odd”. These theories are equiconsistent with PA yet contradict each other.

Page 8

Theorem 3.2: Given arbitrarily large Woodin cardinals, set-generic extensions satisfy the same sentences about $L(\mathbb R)$.

It is easy to see that if one drops “set-generic” then the result is false and even if one replaces “set-generic extensions” with “extensions with arbitrarily large Woodin cardinals” it is still false (in general). I mention this as you claim that “large cardinal axioms are complete for sentences about $L(\mathbb R)$“; what notion of “complete” do you have in mind? Surely the requirement of set-genericity is a very strong requirement!

Page 10

There may be consistency strengths beyond those we have reached to date that cannot be reached in any natural way without deciding CH.

This is a fascinating comment! I never imagined this possibility. Do you have any suggestions as to what these could be?

Page 11

Here you talk about the set-generic multiverse. This is where you lose me almost completely; I don’t seem to grasp the point. Here are some comments and questions.

You have explained, and I agree, that natural theories under the equivalence relation of equiconsistency fall into a wellordered hierarchy with theories of the form ZFC + LCA as representatives of the equivalence classes. I would go further and say that equiconsistency is the same as mutual interpretability for natural theories. But as I said there are many natural theories not of the form ZFC + LCA; yet you claim the following:

The way we interpret set theories today is to think of them as theories of inner models of generic extensions of models satisfying some large cardinal hypothesis … We don’t seem to lose any meaning this way.

Of course by “generic” you mean “set-generic” as you are trying to motivate the set-generic multiverse. Now what happened to the theories (which may deny large cardinal existence) associated to Easton’s model where GCH fails at all regular cardinals, or more dramatically a model where $\kappa^+$ is greater than $(\kappa^+)^\text{HOD}$ for every cardinal $latex \kappa$? These don’t seem to fit into your rather restricted framework. In other words, for reasons not provided, you choose to focus only on theories which describe models obtained by starting with a model of some large cardinal hypothesis and then massaging it slightly using set-generic extensions and ground models. Otherwise said you have taken our nice equivalence relation under mutual interpretability and cut it down to a very restricted subdomain of theories which respect large cardinal existence. What happened to the other natural theories?

On Page 13 you give some explanation as to why you choose just the set-generic multiverse and claim:

“Our multiverse is an equivalence class of worlds under ‘has the same information’.”

But this can’t be right: Suppose that $G_0$, $G_1$ are mutually generic for an Easton class-product; the $V[G_0]$ and $V[G_1]$ lie in different set-generic multiverses but have the same information.

It is a bit cumbersome but surely one could build a suitable and larger multiverse using some iterated class-forcing instead of the Levy collapses you use. But as you know I’m not much of a fan of any use of forcing in foundational investigations and moreover I’d first like to better understand what it is you want a multiverse foundation to achieve.

Page 14

Here you introduce 3 theses about the set-generic multiverse. I don’t understand the first one (“Every proposition”? What about CH?) or the second one (What does “makes sense” mean?). The third one, asserting the existence of a “core” is clear enough, but for the uninitiated it should be made clear that this is miles away from what a “core” in the sense of core model theory is like: Easton products kill “cores” and reverse Easton iterations produce them! So being a “core” of one’s set-generic multiverse is a rather flimsy notion. Can you explain why on Page 15 you say that the “role [of 'core' existence] in our search for a universal framework theory seems crucial”?

You then advertise Hugh’s new axiom as having 3 properties:

1. It implies core existence.
2. It suggests a way of developing fine-structure theory for the core.
3. It may be consistent with all large cardinals.

Surely there is something missing here! Look at my paper with Peter Holy: “A quasi-lower bound on the consistency strength of PFA, to appear, Transactions American Mathematical Society“. (I spoke about it at the 1st European Set Theory meeting in 2007.)

We use a “formidable” argument to show that condensation with acceptability is consistent with essentially all large cardinals. As we use a reverse Easton iteration the models we build are the “cores” in your sense of their own set-generic multiverses. And condensation plus acceptability is a big step towards a fine-structure theory. It isn’t hard to put all of this into an axiom so our work fulfills the description you have above of Hugh’s axiom.

Is it possible that what is missing is some kind of absoluteness property that you left out, which Hugh’s axiom guarantees but my work with Holy does not?

OK, those are my main comments and questions. I’ll end with some lesser points.

Page 3

Defn 2.1: Probably you want to restrict to 1st order theories.

Adding Con(T) to T can destroy consistency unless you are talking about “true” theories.

“Reflection principles”: It is wrong to take these to go past axioms consistent with $V = L$. Reflection has a meaning which should be respected.

Page 5

Conjecture at the top about well-ordered consistency strengths: It is vague because of “natural extension of ZFC” and “large cardinal hypothesis”. But at least the first vagueness can be removed by just saying that the axioms Con(ZFC + LCA) are cofinal in all Con(T)’s, natural or otherwise. A dream result would be to show that the minimal ordinal heights of well-founded models of “LCA’s” are cofinal in those of arbitrary sentences with well-founded models. It is not totally out of the question that one could prove something like that but I don’t know how to do it (with some suitable definition of “LCA”).

In your discussion of consistency lower bounds it is very much worthwhile to consider “quasi” lower bounds. Indeed core model theory doesn’t get more than Woodin cardinals from PFA but the Viale-Weiß work and my work with Holy cited above show that there are quasi lower bounds in the supercompact range. For me this is important evidence for the consistency of supercompacts.

Page 12

The Laver-Woodin result: Are you sure you’ve got this right? I see that the ground model $W$ is definable in the $P$-generic extension with parameter $P(\kappa)^W$ where $\kappa = |P|^+$ of the extension, but not from $P$ and the $P$-generic.

Best,
Sy

PS: How do you use the concept of “truth” in set theory? Is it governed by “good math” and “mathematical depth”, or do you see it as more than that? Your answer will help me understand your paper better.


text:
Question

# Unlike phenol, 2,4-dinitrophenol is soluble in sodium carbonate solution in water because?A. presence of two - $N{{O}_{2}}$groups in the ring makes 2, 4 – dinitrophenol a stronger acid than phenol.B. presence of two - $N{{O}_{2}}$groups in the ring makes 2, 4 – dinitrophenol a weaker acid than phenol.C. presence of two - $N{{O}_{2}}$groups make the hydrogen bonding easier, making 2,4-dinitrophenol soluble.D. nitro group reacts with $N{{a}_{2}}C{{O}_{3}}$while the -OH group does not.

Hint: To solve this question you should have a basic idea regarding the structures of phenol and 2,4-dinitrophenol and about electron withdrawing groups and its effect after adding to any compound. Phenol has a benzene ring with one hydroxyl group and 2,4-dinitrophenol has two nitrogen oxide molecules more than phenol.

Structures of phenol and 2,4-dinitrophenol are drawn below.

(2,4 – dinitrophenol) (phenol)
In 2,4 – dinitrophenol two - $N{{O}_{2}}$ groups are present. $N{{O}_{2}}$ has a strong electron withdrawing nature which increases acidity of the compound.
Electron withdrawing group (EWG): An atom or group that draws electron density from neighboring atoms towards itself, usually by resonance or inductive effects.
Therefore, presence of two electron withdrawing - $N{{O}_{2}}$groups in the ring makes 2,4- dinitrophenol a stronger acid than phenol.
Sodium Carbonate solution is basic in nature. Hence, Stronger the acid it is easily soluble in the basic solution.
Therefore, it reacts with $N{{a}_{2}}C{{O}_{3}}$solution to form sodium salt with the evolution of $C{{O}_{2}}$, thus making it soluble in$N{{a}_{2}}C{{O}_{3}}$.
Hence, unlike phenol, 2,4-dinitrophenol is soluble in sodium carbonate solution in water because presence of two - $N{{O}_{2}}$groups in the ring makes 2, 4 – dinitrophenol a stronger acid than phenol.

Hence, option A is the right answer.
Note:
Always remember, 2,4,6 – trinitrophenol > 2,4 – dinitrophenol > phenol, order of acidic nature of the compounds.
Orders of electron withdrawing group is -$N{{O}_{2}}$, -$CN$,-$CHO$,-$COR$,-$COOH$,-$COOR$, -$CON{{H}_{2}}$(strongest to weakest)


text:
# Complex Domains and Paths

$\int_{\gamma } \frac{1}{1+z^2}dz$ where $\gamma$ is some path joining 0 to 1 which is in the domain of $f(z) = \frac{1}{1+z^2}$.


text:
# How do I make the 'such that' symbol from Set Theory?

I am looking for the 'such that' symbol in set theory. I don't know what it's called so I'm not sure how to look for it. For the moment, I am just using this '|'. What is the appropriate symbol?

-

\mid, as it has the spacing of a binary relation. If you want it to resize, see “How to automatically resize the vertical bar in a set comprehension?”.
If you want the vertical bar to resize, it's better, spacing-wise, to use (inside a macro, to avoid unnecessary typing) \left\{ x \in X \mathrel{}\middle|\mathrel{} x > \frac{1}{2}\right\} as mentioned in tex.stackexchange.com/questions/5502 – Philippe Goutet Dec 1 '10 at 9:42
Actually it is probably best to use the bracket package suggested by Will in the link above. – Caramdir Dec 2 '10 at 3:23
The problem with the bracket package is that it fiddles with the spacing in ways that may not be wanted. For example, it inserts medium space on the inside as if you typed \{\: and \:\}. This will not look good in a context like \{ x \mid x \neq 0 \}/\{x > 0\}. – Philippe Goutet Dec 3 '10 at 17:44


text:
# On the degree of cyclotomic fields extension.

Let $F$ be a field and $n$ be any integer satisfying $(n,\text{char}(F))=1$ when $\text{char}(F)\ne 0$.

Let $\xi$ be a primitive $n$-th root of unity. I know that $\text{Gal}(F(\xi)/F)$ is isomorphic to a subgroup of $(\mathbb{Z}_n)^{\times}$ and it is isomorphic when $F=\mathbb{Q}$. (In this case, deg (irr($\xi$,$\mathbb{Q}$))=$\phi(n)$ where $\phi$ is Euler Phi-function.)

The reason (I think) why this does not hold in general is that $F$ may contain $\xi$. So if $\xi\notin F$, can we assure $|F(\xi)/F|=\phi(n)$?

In other words, is the polynomial $\prod_{1\le k \le n, \ (n,k)=1} (t-\xi^k)\in F[t]$ irreducible?

If not, please let me know some counter example.

• A sneaky one is $\mathbb Q(\zeta_5)$ over $\mathbb Q(\sqrt 5)$. – user208649 Apr 23 '16 at 7:28

No, it is still not sufficient to assume that $\xi\notin F$. For example, if $F=\mathbb{Q}(i)$ and $$\xi=e^{2\pi i / 8}=\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{2}}i$$ then $[F(\xi):F]=2$ but $\xi\notin F$. Observe that $\varphi(8)=4$, and $$\underbrace{[F(\xi):\mathbb{Q}]}_{4}=\underbrace{[F(\xi):F]}_{2}\underbrace{[F:\mathbb{Q}]}_{2}$$

The Galois group of the $n$th cyclotomic field is $\mathrm{Gal}(\mathbb{Q}(\xi)/\mathbb{Q}))\cong(\mathbb{Z}/n)^\times$. If (and only if) $\varphi(n)=|(\mathbb{Z}/n)^{\times}|$ is a composite number, there will be a non-trivial subgroup of $(\mathbb{Z}/n)^\times$, and hence (by the Fundamental Theorem of Galois Theory) a field $F$ with $\mathbb{Q}(\xi)\supsetneq F\supsetneq \mathbb{Q}$, which will have the property that $1<[F(\xi):F]<\varphi(n)$.

• +1 Another small counterexample is with $F=\Bbb{Q}(\sqrt5)$ and $n=5$. The number $\xi+\overline{\xi}=2\cos(2\pi/5)$, and the formula $2\cos(2\pi/5)=(1+\sqrt5)/2$ shows that $\xi$ is of degree $2$ over $F$. – Jyrki Lahtonen Apr 23 '16 at 7:25
• @Zev Chonoles, Thank you for letting me know this good example. It helped me very much! – user29422 Apr 23 '16 at 8:51
• @Jyrki Lahtonen, How did you get the formula $2\cos(\frac{2\pi }{5})=\frac{1+\sqrt{5}}{2}$? – user29422 Apr 23 '16 at 9:01
• @Jyrki Lahtonen, Oh, I see. Thank you!^^ – user29422 Apr 23 '16 at 9:08