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This tutorial explains Linear Discriminant Analysis (LDA) and Quadratic Discriminant Analysis (QDA) as two fundamental classification methods in statistical and probabilistic learning. We start with the optimization of decision boundary on which the posteriors are equal. Then, LDA and QDA are derived for binary and multiple classes. The estimation of parameters in LDA and QDA are also covered. Then, we explain how LDA and QDA are related to metric learning, kernel principal component analysis, Mahalanobis distance, logistic regression, Bayes optimal classifier, Gaussian naive Bayes, and likelihood ratio test. We also prove that LDA and Fisher discriminant analysis are equivalent. We finally clarify some of the theoretical concepts with simulations we provide.
The advantages offered by the presence of a schema are numerous. However, many XML documents in practice are not accompanied by a (valid) schema, making schema inference an attractive research problem. The fundamental task in XML schema learning is inferring restricted subclasses of regular expressions. Most previous work either lacks support for interleaving or only has limited support for interleaving. In this paper, we first propose a new subclass Single Occurrence Regular Expressions with Interleaving (SOIRE), which has unrestricted support for interleaving. Then, based on single occurrence automaton and maximum independent set, we propose an algorithm iSOIRE to infer SOIREs. Finally, we further conduct a series of experiments on real datasets to evaluate the effectiveness of our work, comparing with both ongoing learning algorithms in academia and industrial tools in real-world. The results reveal the practicability of SOIRE and the effectiveness of iSOIRE, showing the high preciseness and conciseness of our work.
Researchers illustrate improvements in contextual encoding strategies via resultant performance on a battery of shared Natural Language Understanding (NLU) tasks. Many of these tasks are of a categorical prediction variety: given a conditioning context (e.g., an NLI premise), provide a label based on an associated prompt (e.g., an NLI hypothesis). The categorical nature of these tasks has led to common use of a cross entropy log-loss objective during training. We suggest this loss is intuitively wrong when applied to plausibility tasks, where the prompt by design is neither categorically entailed nor contradictory given the context. Log-loss naturally drives models to assign scores near 0.0 or 1.0, in contrast to our proposed use of a margin-based loss. Following a discussion of our intuition, we describe a confirmation study based on an extreme, synthetically curated task derived from MultiNLI. We find that a margin-based loss leads to a more plausible model of plausibility. Finally, we illustrate improvements on the Choice Of Plausible Alternative (COPA) task through this change in loss.
According to common relevance-judgments regimes, such as TREC’s, a document can be deemed relevant to a query even if it contains a very short passage of text with pertinent information. This fact has motivated work on passage-based document retrieval: document ranking methods that induce information from the document’s passages. However, the main source of passage-based information utilized was passage-query similarities. We address the challenge of utilizing richer sources of passage-based information to improve document retrieval effectiveness. Specifically, we devise a suite of learning-to-rank-based document retrieval methods that utilize an effective ranking of passages produced in response to the query; the passage ranking is also induced using a learning-to-rank approach. Some of the methods quantify the ranking of the passages of a document. Others utilize the feature-based representation of passages used for learning a passage ranker. Empirical evaluation attests to the clear merits of our methods with respect to highly effective baselines. Our best performing method is based on learning a document ranking function using document-query features and passage-query features of the document’s passage most highly ranked.
We present a novel framework based on optimal transport for the challenging problem of comparing graphs. Specifically, we exploit the probabilistic distribution of smooth graph signals defined with respect to the graph topology. This allows us to derive an explicit expression of the Wasserstein distance between graph signal distributions in terms of the graph Laplacian matrices. This leads to a structurally meaningful measure for comparing graphs, which is able to take into account the global structure of graphs, while most other measures merely observe local changes independently. Our measure is then used for formulating a new graph alignment problem, whose objective is to estimate the permutation that minimizes the distance between two graphs. We further propose an efficient stochastic algorithm based on Bayesian exploration to accommodate for the non-convexity of the graph alignment problem. We finally demonstrate the performance of our novel framework on different tasks like graph alignment, graph classification and graph signal prediction, and we show that our method leads to significant improvement with respect to the-state-of-art algorithms.
The idea of Artificial Intelligence (AI) has a long history. It turned out, however, that reaching intelligence at human levels is more complicated than originally anticipated. Currently we are experiencing a renewed interest in AI, fueled by an enormous increase in computing power and an even larger increase in data, in combination with improved AI technologies like deep learning. Healthcare is considered the next domain to be revolutionized by Artificial Intelligence. While AI approaches are excellently suited to develop certain algorithms, for biomedical applications there are specific challenges. We propose recommendations to improve AI projects in the biomedical space and especially clinical healthcare.
In this work, we introduce \emph{interactive structure search}, a generic framework that encompasses many interactive learning settings, both explored and unexplored. We show that a recently developed active learning algorithm of~\citet{TD17} can be adapted for interactive structure search, that it can be made noise-tolerant, and that it enjoys favorable convergence rates.
Deep learning is increasingly used as a basic building block of security systems. Unfortunately, deep neural networks are hard to interpret, and their decision process is opaque to the practitioner. Recent work has started to address this problem by considering black-box explanations for deep learning in computer security (CCS’18). The underlying explanation methods, however, ignore the structure of neural networks and thus omit crucial information for analyzing the decision process. In this paper, we investigate white-box explanations and systematically compare them with current black-box approaches. In an extensive evaluation with learning-based systems for malware detection and vulnerability discovery, we demonstrate that white-box explanations are more concise, sparse, complete and efficient than black-box approaches. As a consequence, we generally recommend the use of white-box explanations if access to the employed neural network is available, which usually is the case for stand-alone systems for malware detection, binary analysis, and vulnerability discovery.
Effectively combining logic reasoning and probabilistic inference has been a long-standing goal of machine learning: the former has the ability to generalize with small training data, while the latter provides a principled framework for dealing with noisy data. However, existing methods for combining the best of both worlds are typically computationally intensive. In this paper, we focus on Markov Logic Networks and explore the use of graph neural networks (GNNs) for representing probabilistic logic inference. It is revealed from our analysis that the representation power of GNN alone is not enough for such a task. We instead propose a more expressive variant, called ExpressGNN, which can perform effective probabilistic logic inference while being able to scale to a large number of entities. We demonstrate by several benchmark datasets that ExpressGNN has the potential to advance probabilistic logic reasoning to the next stage.
Centuries of development in natural sciences and mathematical modeling provide valuable domain expert knowledge that has yet to be explored for the development of machine learning models. When modeling complex physical systems, both domain knowledge and data contribute important information about the system. In this paper, we present a data-driven model that takes advantage of partial domain knowledge in order to improve generalization and interpretability. The presented model, which we call EVGP (Explicit Variational Gaussian Process), uses an explicit linear prior to incorporate partial domain knowledge while using data to fill in the gaps in knowledge. Variational inference was used to obtain a sparse approximation that scales well to large datasets. The advantages include: 1) using partial domain knowledge to improve inductive bias (assumptions of the model), 2) scalability to large datasets, 3) improved interpretability. We show how the EVGP model can be used to learn system dynamics using basic Newtonian mechanics as prior knowledge. We demonstrate that using simple priors from partially defined physics models considerably improves performance when compared to fully data-driven models.
One reason for the emergence of bias in AI systems is biased data — datasets that may not be true representations of the underlying distributions — and may over or under-represent groups with respect to protected attributes such as gender or race. We consider the problem of correcting such biases and learning distributions that are ‘fair’, with respect to measures such as proportional representation and statistical parity, from the given samples. Our approach is based on a novel formulation of the problem of learning a fair distribution as a maximum entropy optimization problem with a given expectation vector and a prior distribution. Technically, our main contributions are: (1) a new second-order method to compute the (dual of the) maximum entropy distribution over an exponentially-sized discrete domain that turns out to be faster than previous methods, and (2) methods to construct prior distributions and expectation vectors that provably guarantee that the learned distributions satisfy a wide class of fairness criteria. Our results also come with quantitative bounds on the total variation distance between the empirical distribution obtained from the samples and the learned fair distribution. Our experimental results include testing our approach on the COMPAS dataset and showing that the fair distributions not only improve disparate impact values but when used to train classifiers only incur a small loss of accuracy.
We introduce VAMPIRE, a lightweight pretraining framework for effective text classification when data and computing resources are limited. We pretrain a unigram document model as a variational autoencoder on in-domain, unlabeled data and use its internal states as features in a downstream classifier. Empirically, we show the relative strength of VAMPIRE against computationally expensive contextual embeddings and other popular semi-supervised baselines under low resource settings. We also find that fine-tuning to in-domain data is crucial to achieving decent performance from contextual embeddings when working with limited supervision. We accompany this paper with code to pretrain and use VAMPIRE embeddings in downstream tasks.
Robust real-time monitoring of high-dimensional data streams has many important real-world applications such as industrial quality control, signal detection, biosurveillance, but unfortunately it is highly non-trivial to develop efficient schemes due to two challenges: (1) the unknown sparse number or subset of affected data streams and (2) the uncertainty of model specification for high-dimensional data. In this article, motivated by the detection of smaller persistent changes in the presence of larger transient outliers, we develop a family of efficient real-time robust detection schemes for high-dimensional data streams through monitoring feature spaces such as PCA or wavelet coefficients when the feature coefficients are from Tukey-Huber’s gross error models with outliers. We propose to construct a new local detection statistic for each feature called $L_{\alpha}$-CUSUM statistic that can reduce the effect of outliers by using the Box-Cox transformation of the likelihood function, and then raise a global alarm based upon the sum of the soft-thresholding transformation of these local $L_{\alpha}$-CUSUM statistics so that to filter out unaffected features. In addition, we propose a new concept called false alarm breakdown point to measure the robustness of online monitoring schemes, and also characterize the breakdown point of our proposed schemes. Asymptotic analysis, extensive numerical simulations and case study of nonlinear profile monitoring are conducted to illustrate the robustness and usefulness of our proposed schemes.
We present a method to generate directed acyclic graphs (DAGs) using deep reinforcement learning, specifically deep Q-learning. Generating graphs with specified structures is an important and challenging task in various application fields, however most current graph generation methods produce graphs with undirected edges. We demonstrate that this method is capable of generating DAGs with topology and node types satisfying specified criteria in highly sparse reward environments.
We present SParC, a dataset for cross-domainSemanticParsing inContext that consists of 4,298 coherent question sequences (12k+ individual questions annotated with SQL queries). It is obtained from controlled user interactions with 200 complex databases over 138 domains. We provide an in-depth analysis of SParC and show that it introduces new challenges compared to existing datasets. SParC demonstrates complex contextual dependencies, (2) has greater semantic diversity, and (3) requires generalization to unseen domains due to its cross-domain nature and the unseen databases at test time. We experiment with two state-of-the-art text-to-SQL models adapted to the context-dependent, cross-domain setup. The best model obtains an exact match accuracy of 20.2% over all questions and less than10% over all interaction sequences, indicating that the cross-domain setting and the con-textual phenomena of the dataset present significant challenges for future research. The dataset, baselines, and leaderboard are released at https://…/sparc.
With the continuous and vast increase in the amount of data in our digital world, it has been acknowledged that the number of knowledgeable data scientists can not scale to address these challenges. Thus, there was a crucial need for automating the process of building good machine learning models. In the last few years, several techniques and frameworks have been introduced to tackle the challenge of automating the process of Combined Algorithm Selection and Hyper-parameter tuning (CASH) in the machine learning domain. The main aim of these techniques is to reduce the role of the human in the loop and fill the gap for non-expert machine learning users by playing the role of the domain expert. In this paper, we present a comprehensive survey for the state-of-the-art efforts in tackling the CASH problem. In addition, we highlight the research work of automating the other steps of the full complex machine learning pipeline (AutoML) from data understanding till model deployment. Furthermore, we provide comprehensive coverage for the various tools and frameworks that have been introduced in this domain. Finally, we discuss some of the research directions and open challenges that need to be addressed in order to achieve the vision and goals of the AutoML process.
The Progressive-X algorithm, Prog-X in short, is proposed for geometric multi-model fitting. The method interleaves sampling and consolidation of the current data interpretation via repetitive hypothesis proposal, fast rejection, and integration of the new hypothesis into the kept instance set by labeling energy minimization. Due to exploring the data progressively, the method has several beneficial properties compared with the state-of-the-art. First, a clear criterion, adopted from RANSAC, controls the termination and stops the algorithm when the probability of finding a new model with a reasonable number of inliers falls below a threshold. Second, Prog-X is an any-time algorithm. Thus, whenever is interrupted, e.g. due to a time limit, the returned instances cover real and, likely, the most dominant ones. The method is superior to the state-of-the-art in terms of accuracy in both synthetic experiments and on publicly available real-world datasets for homography, two-view motion, and motion segmentation.
We incorporate self activation into influence propagation and propose the self-activation independent cascade (SAIC) model: nodes may be self activated besides being selected as seeds, and influence propagates from both selected seeds and self activated nodes. Self activation reflects the real-world scenarios such as people naturally share product recommendations with their friends even without marketing intervention. It also leads to two new forms of optimization problems: (a) {\em preemptive influence maximization (PIM)}, which aims to find $k$ nodes that, if self-activated, can reach the most number of nodes before other self-activated nodes; and (b) {\em boosted preemptive influence maximization (BPIM)}, which aims to select $k$ seeds that are guaranteed to be activated and can reach the most number of nodes before other self-activated nodes. We propose scalable algorithms for PIM and BPIM and prove that they achieve $1-\varepsilon$ approximation for PIM and $1-1/e-\varepsilon$ approximation for BPIM, for any $\varepsilon > 0$. Through extensive tests on real-world graphs, we demonstrate that our algorithms outperform the baseline algorithms significantly for the PIM problem in solution quality, and also outperform the baselines for BPIM when self-activation behaviors are non-uniform across nodes.
Using machine learning in high-stakes applications often requires predictions to be accompanied by explanations comprehensible to the domain user, who has ultimate responsibility for decisions and outcomes. Recently, a new framework for providing explanations, called TED, has been proposed to provide meaningful explanations for predictions. This framework augments training data to include explanations elicited from domain users, in addition to features and labels. This approach ensures that explanations for predictions are tailored to the complexity expectations and domain knowledge of the consumer. In this paper, we build on this foundational work, by exploring more sophisticated instantiations of the TED framework and empirically evaluate their effectiveness in two diverse domains, chemical odor and skin cancer prediction. Results demonstrate that meaningful explanations can be reliably taught to machine learning algorithms, and in some cases, improving modeling accuracy.
Privacy-preserving deep learning is crucial for deploying deep neural network based solutions, especially when the model works on data that contains sensitive information. Most privacy-preserving methods lead to undesirable performance degradation. Ensemble learning is an effective way to improve model performance. In this work, we propose a new method for teacher ensembles that uses more informative network outputs under differential private stochastic gradient descent and provide provable privacy guarantees. Out method employs knowledge distillation and hint learning on intermediate representations to facilitate the training of student model. Additionally, we propose a simple weighted ensemble scheme that works more robustly across different teaching settings. Experimental results on three common image datasets benchmark (i.e., CIFAR10, MINST, and SVHN) demonstrate that our approach outperforms previous state-of-the-art methods on both performance and privacy-budget.
Recently, a parametrized class of loss functions called $\alpha$-loss, $\alpha \in [1,\infty]$, has been introduced for classification. This family, which includes the log-loss and the 0-1 loss as special cases, comes with compelling properties including an equivalent margin-based form which is classification-calibrated for all $\alpha$. We introduce a generalization of this family to the entire range of $\alpha \in (0,\infty]$ and establish how the parameter $\alpha$ enables the practitioner to choose among a host of operating conditions that are important in modern machine learning tasks. We prove that smaller $\alpha$ values are more conducive to faster optimization; in fact, $\alpha$-loss is convex for $\alpha \le 1$ and quasi-convex for $\alpha >1$. Moreover, we establish bounds to quantify the degradation of the local-quasi-convexity of the optimization landscape as $\alpha$ increases; we show that this directly translates to a computational slow down. On the other hand, our theoretical results also suggest that larger $\alpha$ values lead to better generalization performance. This is a consequence of the ability of the $\alpha$-loss to limit the effect of less likely data as $\alpha$ increases from 1, thereby facilitating robustness to outliers and noise in the training data. We provide strong evidence supporting this assertion with several experiments on benchmark datasets that establish the efficacy of $\alpha$-loss for $\alpha > 1$ in robustness to errors in the training data. Of equal interest is the fact that, for $\alpha < 1$, our experiments show that the decreased robustness seems to counteract class imbalances in training data.
Residual networks (ResNet) and weight normalization play an important role in various deep learning applications. However, parameter initialization strategies have not been studied previously for weight normalized networks and, in practice, initialization methods designed for un-normalized networks are used as a proxy. Similarly, initialization for ResNets have also been studied for un-normalized networks and often under simplified settings ignoring the shortcut connection. To address these issues, we propose a novel parameter initialization strategy that avoids explosion/vanishment of information across layers for weight normalized networks with and without residual connections. The proposed strategy is based on a theoretical analysis using mean field approximation. We run over 2,500 experiments and evaluate our proposal on image datasets showing that the proposed initialization outperforms existing initialization methods in terms of generalization performance, robustness to hyper-parameter values and variance between seeds, especially when networks get deeper in which case existing methods fail to even start training. Finally, we show that using our initialization in conjunction with learning rate warmup is able to reduce the gap between the performance of weight normalized and batch normalized networks.
Measuring graph clustering quality remains an open problem. To address it, we introduce quality measures based on comparisons of intra- and inter-cluster densities, an accompanying statistical test of the significance of their differences and a step-by-step routine for clustering quality assessment. Our null hypothesis does not rely on any generative model for the graph, unlike modularity which uses the configuration model as a null model. Our measures are shown to meet the axioms of a good clustering quality function, unlike the very commonly used modularity measure. They also have an intuitive graph-theoretic interpretation, a formal statistical interpretation and can be easily tested for significance. Our work is centered on the idea that well clustered graphs will display a significantly larger intra-cluster density than inter-cluster density. We develop tests to validate the existence of such a cluster structure. We empirically explore the behavior of our measures under a number of stress test scenarios and compare their behavior to the commonly used modularity and conductance measures. Empirical stress test results confirm that our measures compare very favorably to the established ones. In particular, they are shown to be more responsive to graph structure and less sensitive to sample size and breakdowns during numerical implementation and less sensitive to uncertainty in connectivity. These features are especially important in the context of larger data sets or when the data may contain errors in the connectivity patterns.
This study proposes an end-to-end framework for solving multi-objective optimization problems (MOPs) using Deep Reinforcement Learning (DRL), termed DRL-MOA. The idea of decomposition is adopted to decompose a MOP into a set of scalar optimization subproblems. The subproblems are then optimized cooperatively by a neighbourhood-based parameter transfer strategy which significantly accelerates the training procedure and makes the realization of DRL-MOA possible. The subproblems are modelled as neural networks and the RL method is used to optimize them. In specific, the multi-objective travelling salesman problem (MOTSP) is solved in this work using the DRL-MOA framework by modelling the subproblem as the Pointer Network. It is found that, once the trained model is available, it can scale to MOTSPs of any number of cities, e.g., 70-city, 100-city, even the 200-city MOTSP, without re-training the model. The Pareto Front can be directly obtained by a simple feed-forward of the network; thereby, no iteration is required and the MOP can be always solved in a reasonable time. Experimental results indicate a strong convergence ability of the DRL-MOA, especially for large-scale MOTSPs, e.g., 200-city MOTSP, for which evolutionary algorithms such as NSGA-II and MOEA/D are pretty hard to converge even implemented for a large number of iterations. The DRL-MOA can also obtain a much wider spread of the PF than the two competitors. Moreover, the DRL-MOA has a high level of modularity and can be easily generalized to other MOPs by replacing the modelling of the subproblem.
Multi-model inference covers a wide range of modern statistical applications such as variable selection, model confidence set, model averaging and variable importance. The performance of multi-model inference depends on the availability of candidate models, whose quality has been rarely studied in literature. In this paper, we study genetic algorithm (GA) in order to obtain high-quality candidate models. Inspired by the process of natural selection, GA performs genetic operations such as selection, crossover and mutation iteratively to update a collection of potential solutions (models) until convergence. The convergence properties are studied based on the Markov chain theory and used to design an adaptive termination criterion that vastly reduces the computational cost. In addition, a new schema theory is established to characterize how the current model set is improved through evolutionary process. Extensive numerical experiments are carried out to verify our theory and demonstrate the empirical power of GA, and new findings are obtained for two real data examples.
We study the problem of embedding-based entity alignment between knowledge graphs (KGs). Previous works mainly focus on the relational structure of entities. Some further incorporate another type of features, such as attributes, for refinement. However, a vast of entity features are still unexplored or not equally treated together, which impairs the accuracy and robustness of embedding-based entity alignment. In this paper, we propose a novel framework that unifies multiple views of entities to learn embeddings for entity alignment. Specifically, we embed entities based on the views of entity names, relations and attributes, with several combination strategies. Furthermore, we design some cross-KG inference methods to enhance the alignment between two KGs. Our experiments on real-world datasets show that the proposed framework significantly outperforms the state-of-the-art embedding-based entity alignment methods. The selected views, cross-KG inference and combination strategies all contribute to the performance improvement.
Recently, several adversarial attack methods to black-box deep neural networks have been proposed and they serve as an excellent testing bed for investigating safety issues with DNNs. These methods generally take in the query and corresponding feedback from the targeted DNN model and infer suitable attack patterns accordingly. However, due to lacking prior and inefficiency in leveraging the query information, these methods are mostly query-intensive. In this work, we propose a meta attack strategy which is capable of attacking the target black-box model with much fewer queries. Its high query-efficiency comes from prior abstraction on training a meta attacker which can speed up the search for adversarial examples significantly. Extensive experiments on MNIST, CIFAR10 and tiny-Imagenet demonstrate that, our meta-attack method can remarkably reduce the number of model queries without sacrificing the attack performance. Moreover, the obtained meta attacker is not restricted to a particular model but can be reused easily with fast adaptive ability to attack a variety of models.
Continual learning aims to learn new tasks without forgetting previously learned ones. This is especially challenging when one cannot access data from previous tasks and when the model has a fixed capacity. Current regularization-based continual learning algorithms need an external representation and extra computation to measure the parameters’ importance. In contrast, we propose Uncertainty-guided Continual Bayesian Neural Networks (UCB), where the learning rate adapts according to the uncertainty defined in the probability distribution of the weights in networks. Uncertainty is a natural way to identify what to remember and what to change as we continually learn, allowing to mitigate catastrophic forgetting. We also show a variant of our model, which uses uncertainty for weight pruning and retains task performance after pruning by saving binary masks per tasks. We evaluate our UCB approach extensively on diverse object classification datasets with short and long sequences of tasks and report superior or on-par performance compared to existing approaches. Additionally, we show that our model does not necessarily need task information at test time, i.e. it does not presume knowledge of which task a sample belongs to.
Exploration strategy design is one of the challenging problems in reinforcement learning~(RL), especially when the environment contains a large state space or sparse rewards. During exploration, the agent tries to discover novel areas or high reward~(quality) areas. In most existing methods, the novelty and quality in the neighboring area of the current state are not well utilized to guide the exploration of the agent. To tackle this problem, we propose a novel RL framework, called \underline{c}lustered \underline{r}einforcement \underline{l}earning~(CRL), for efficient exploration in RL. CRL adopts clustering to divide the collected states into several clusters, based on which a bonus reward reflecting both novelty and quality in the neighboring area~(cluster) of the current state is given to the agent. Experiments on a continuous control task and several \emph{Atari 2600} games show that CRL can outperform other state-of-the-art methods to achieve the best performance in most cases.
In this paper we propose a new method to assist in labeling data arriving from fast running processes using anomaly detection. A result is the possibility to manually classify data arriving at a high rates to train machine learning models. To circumvent the problem of not having a real ground truth we propose specific metrics for model selection and validation of the results. The use case is taken from the food packaging industry, where processes are affected by regular but short breakdowns causing interruptions in the production process. Fast production rates make it hard for machine operators to identify the source and thus the cause of the breakdown. Self learning assistance systems can help them finding the root cause of the problem and assist the machine operator in applying lasting solutions. These learning systems need to be trained to identify reoccurring problems using data analytics. Training is not easy as the process is too fast to be manually monitored to add specific classifications on the single data points.
Matrix completion based on low-rank models is very popular and comes with powerful algorithms and theoretical guarantees. However, existing methods do not consider the case of values missing not at random (MNAR) which are widely encountered in practice. Considering a data matrix generated from a probabilistic principal component analysis (PPCA) model containing several MNAR variables, we propose estimators for the means, variances and covariances related to the MNAR missing variables and study their consistency. The proposed estimators present the advantage of being computed without explicitly modeling the MNAR mechanism and by only using observed data. In addition, we propose an imputation method of the data matrix and an estimation of the PPCA loading matrix. We compare our proposal with the classical methods used in low-rank models, as iterative methods based on singular value decomposition.
Inspired by recent work in attention models for image captioning and question answering, we present a soft attention model for the reinforcement learning domain. This model uses a soft, top-down attention mechanism to create a bottleneck in the agent, forcing it to focus on task-relevant information by sequentially querying its view of the environment. The output of the attention mechanism allows direct observation of the information used by the agent to select its actions, enabling easier interpretation of this model than of traditional models. We analyze different strategies that the agents learn and show that a handful of strategies arise repeatedly across different games. We also show that the model learns to query separately about space and content (where’ vs. what’). We demonstrate that an agent using this mechanism can achieve performance competitive with state-of-the-art models on ATARI tasks while still being interpretable.
In this article, we introduce an entropy based on the formal power series expansion of the Ihara Zeta function. We find a number of inequalities based on the values of the Ihara zeta function. These new entropies are applicable in symbolic dynamics and the dynamics of billiards.
We propose a simple and efficient method to combine semi-supervised learning with weakly-supervised learning for deep neural networks. Designing deep neural networks for weakly-supervised learning is always accompanied by a tradeoff between fine-information and coarse-level classification accuracy. While using unlabeled data for semi-supervised learning, in contrast to seeking for this tradeoff, we design two extremely different models for different targets, one of which just pursues finer information for the final target. Another one is more professional to achieve higher coarse-level classification accuracy so that it is regarded as a more professional teacher to teach the former model using unlabeled data. We present an end-to-end semi-supervised learning process termed guiding learning for these two different models so that improve the training efficiency. Our approach improves the $1^{st}$ place result on Task4 of the DCASE2018 challenge from $32.4\%$ to $38.3\%$, achieving start-of-art performance.
With the increasing adoption of Deep Neural Network (DNN) models as integral parts of software systems, efficient operational testing of DNNs is much in demand to ensure these models’ actual performance in field conditions. A challenge is that the testing often needs to produce precise results with a very limited budget for labeling data collected in field. Viewing software testing as a practice of reliability estimation through statistical sampling, we re-interpret the idea behind conventional structural coverages as conditioning for variance reduction. With this insight we propose an efficient DNN testing method based on the conditioning on the representation learned by the DNN model under testing. The representation is defined by the probabilistic distribution of the output of neurons in the last hidden layer of the model. To sampling from this high dimensional distribution in which the operational data are sparsely distributed, we design an algorithm leveraging cross entropy minimization. Experiments with various DNN models and datasets were conducted to evaluate the general efficiency of the approach. The results show that, compared with simple random sampling, this approach requires only about a half of labeled inputs to achieve the same level of precision.
Lean processes focus on doing only necessery things in an efficient way. Artificial intelligence and Machine Learning offer new opportunities to optimizing processes. The presented approach demonstrates an improvement of the test process by using Machine Learning as a support tool for test management. The scope is the semi-automation of the selection of regression tests. The proposed lean testing process uses Machine Learning as a supporting machine, while keeping the human test manager in charge of the adequate test case selection. 1 Introduction Many established long running projects and programs are execute regression tests during the release tests. The regression tests are the part of the release test to ensure that functionality from past releases still works fine in the new release. In many projects, a significant part of these regression tests are not automated and therefore executed manually. Manual tests are expensive and time intensive [1], which is why often only a relevant subset of all possible regression tests are executed in order to safe time and money. Depending on the software process, different approaches can be used to identify the right set of regression tests. The source code file level is a frequent entry point for this identification [2]. Advanced approaches combine different file level methods [3]. To handle black-box tests, methods like [4] or [5] can be used for test case prioritiza-tion. To decide which tests can be skipped, a relevance ranking of the tests in a regression test suite is needed. Based on the relevance a test is in or out of the regression test set for a specific release. This decision is a task of the test manager supported by experts. The task can be time-consuming in case of big (often a 4-to 5-digit number) regression test suites because the selection is specific to each release. Trends are going to continuous prioritization [6], which this work wants to support with the presented ML based approach for black box regression test case prioritization. Any regression test selection is made upon release specific changes. Changes can be new or deleted code based on refactoring or implementation of new features. But also changes on externals systems which are connected by interfaces have to be considered


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# American Institute of Mathematical Sciences

February  2016, 10(1): 151-162. doi: 10.3934/amc.2016.10.151

## Further results on fibre products of Kummer covers and curves with many points over finite fields

 1 Department of Mathematics and Institute of Applied Mathematics, Middle East Technical University, Dumlupnar Bulvar, 06800, Ankara, Turkey 2 Department of Mathematics, Atlm University, Incek, Golbas, 06836, Ankara, Turkey 3 Department of Mathematics, Hacettepe University, Beytepe, 06800, Ankara, Turkey

Received  December 2014 Revised  December 2015 Published  March 2016

We study fibre products of an arbitrary number of Kummer covers of the projective line over $\mathbb{F}_q$ under suitable weak assumptions. If $q-1 = r^a$ for some prime $r$, then we completely determine the number of rational points over a rational point of the projective line. Using this result we obtain explicit examples of fibre products of three Kummer covers supplying new entries for the current table of curves with many points (http://www.manypoints.org, October 31 2015).
Citation: Ferruh Özbudak, Burcu Gülmez Temür, Oǧuz Yayla. Further results on fibre products of Kummer covers and curves with many points over finite fields. Advances in Mathematics of Communications, 2016, 10 (1) : 151-162. doi: 10.3934/amc.2016.10.151
##### References:
 [1] A. Garcia and A. Garzon, On Kummer covers with many rational points over finite fields,, J. Pure Appl. Algebra, 185 (2003), 177. doi: 10.1016/S0022-4049(03)00110-5. [2] G. van der Geer and M. van der Vlugt, Tables of curves with many points,, Math. Comput., 69 (2000), 797. doi: 10.1090/S0025-5718-99-01143-6. [3] J. W. P. Hirschfeld, Projective Geometries over Finite Fields,, 2nd edition, (1998). [4] J. W. P. Hirschfeld, G. Korchmáros and F. Torres, Algebraic Curves over a Finite Field,, Princeton Univ. Press, (2008). [5] B. Huppert and N. Blackburn, Finite Groups II, Springer-Verlag, (1981). [6] M. Q. Kawakita, Kummer curves and their fibre products with many rational points,, Appl. Algebra Engrg. Comm. Comput., 14 (2003), 55. [7] H. Niederreiter and C. Xing, Rational Points on Curves over Finite Fields,, Cambridge Univ. Press, (2001). doi: 10.1017/CBO9781107325951. [8] H. Niederreiter and C. Xing, Algebraic Geometry in Coding Theory and Cryptography,, Princeton Univ. Press, (2009). [9] F. Özbudak and H. Stichtenoth, Curves with many points and configurations of hyperplanes over finite fields,, Finite Fields Appl., 5 (1999), 436. doi: 10.1006/ffta.1999.0262. [10] F. Özbudak and B. G. Temür, Finite number of fibre products of Kummer covers and curves with many points over finite fields,, Des. Codes Crypt., 70 (2014), 385. doi: 10.1007/s10623-012-9706-2. [11] H. Stichtenoth, Algebraic Function Fields and Codes,, Springer, (1993). [12] M. A. Tsfasman, S. G. Vlădut and D. Nogin, Algebraic Geometric Codes: Basic Notions,, Amer. Math. Soc., (2007). doi: 10.1090/surv/139. [13] , Manypoints-Table of Curves with Many Points,, available online at , ().

show all references

##### References:
 [1] A. Garcia and A. Garzon, On Kummer covers with many rational points over finite fields,, J. Pure Appl. Algebra, 185 (2003), 177. doi: 10.1016/S0022-4049(03)00110-5. [2] G. van der Geer and M. van der Vlugt, Tables of curves with many points,, Math. Comput., 69 (2000), 797. doi: 10.1090/S0025-5718-99-01143-6. [3] J. W. P. Hirschfeld, Projective Geometries over Finite Fields,, 2nd edition, (1998). [4] J. W. P. Hirschfeld, G. Korchmáros and F. Torres, Algebraic Curves over a Finite Field,, Princeton Univ. Press, (2008). [5] B. Huppert and N. Blackburn, Finite Groups II, Springer-Verlag, (1981). [6] M. Q. Kawakita, Kummer curves and their fibre products with many rational points,, Appl. Algebra Engrg. Comm. Comput., 14 (2003), 55. [7] H. Niederreiter and C. Xing, Rational Points on Curves over Finite Fields,, Cambridge Univ. Press, (2001). doi: 10.1017/CBO9781107325951. [8] H. Niederreiter and C. Xing, Algebraic Geometry in Coding Theory and Cryptography,, Princeton Univ. Press, (2009). [9] F. Özbudak and H. Stichtenoth, Curves with many points and configurations of hyperplanes over finite fields,, Finite Fields Appl., 5 (1999), 436. doi: 10.1006/ffta.1999.0262. [10] F. Özbudak and B. G. Temür, Finite number of fibre products of Kummer covers and curves with many points over finite fields,, Des. Codes Crypt., 70 (2014), 385. doi: 10.1007/s10623-012-9706-2. [11] H. Stichtenoth, Algebraic Function Fields and Codes,, Springer, (1993). [12] M. A. Tsfasman, S. G. Vlădut and D. Nogin, Algebraic Geometric Codes: Basic Notions,, Amer. Math. Soc., (2007). doi: 10.1090/surv/139. [13] , Manypoints-Table of Curves with Many Points,, available online at , ().

2018 Impact Factor: 0.879

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# How to update BibLatex and biber manually on Windows?

How can I update my `bibLatex` and `biber` on my Windows 7. I currently have `biber 2.3` and `biblatex 3.0`

I have a file called "thesis.tex" and a reference file called "ThesisRef.bib" I am using the command prompt with following order of commands:

1. pdflatex thesis
2. biber thesis
3. pdflatex thesis

First command i get some warning regarding the reference to figures and labels but when i run the command "biber thesis". I get following log

``````    INFO - This is Biber 2.3
INFO - Logfile is 'thesis.blg'
WARN - Warning: Found biblatex control file version 3.0, expected version 2.9
INFO - Found 1 citekeys in bib section 0
INFO - Processing section 0
INFO - Looking for bibtex format file 'ThesisRef.bib' for section 0
INFO - Decoding LaTeX character macros into UTF-8
INFO - Found BibTeX data source 'ThesisRef.bib'
INFO - Overriding locale 'en-US' defaults 'variable = shifted' with 'variable =non-ignorable'
INFO - Overriding locale 'en-US' defaults 'normalization = NFD' with 'normalization = prenormalized'
INFO - Sorting list 'nyt/global' of type 'entry' with scheme 'nyt' and locale 'en-US'
INFO - No sort tailoring available for locale 'en-US'
INFO - Overriding locale 'en-US' defaults 'normalization = NFD' with 'normalization = prenormalized'
INFO - Overriding locale 'en-US' defaults 'variable = shifted' with 'variable =non-ignorable'
INFO - Sorting list 'nyt' of type 'entry' with scheme 'nyt' and locale 'en-US'
INFO - No sort tailoring available for locale 'en-US'
INFO - Writing 'thesis.bbl' with encoding 'ascii'
INFO - Output to thesis.bbl
INFO - WARNINGS: 1
``````

When I run the third command I get the following error

``````    Package biblatex Warning: File 'thesis.bbl' is wrong format version - expected 2.6.
<thesis.bbl
!Use of \sortlist doesn't match its definition
1.21 \sortlist {
nyt}{nyt}
``````

From other similar question, I figured that I need to make my biber and biblatex version compatible. However I don't know how to do that on Windows. I tried downloading the biber.exe 2.4 file and replaced it with existing file in `C:\Users\\$Name\AppData\Local\MiKTeX\2.9\miktex\` and also `C:\Program Files\MiKTeX 2.9\miktex\bin\x64` and then `Refresh FNDB` It doesn't work.

Can someone please tell me, how I can update the `biblatex` and `biber` on Windows 7(64 bit)?

• @Johannes_B: Thanks for the reply. However this answer doesn't mention which folders should I replace in the windows directory. The automatic update mentioned doesn't work for me. – Aseem May 20 '16 at 9:23
• Simply launch `MiKTeX Update Manager` (both in administrator an user modes). Current versions are `biber 2.5` and `biblatex 3.4`. – Bernard May 20 '16 at 11:49

You should not update `biblatex` and Biber manually. It is almost always better to let your TeX distribution sort that out.
In MikTeX you need to run the Updater in both User and Admin mode (maybe you have to run each version twice) to update your packages. See also the very detailed How should one maintain and update a MiKTeX installation?. In TeX live you use `tlmgr` for updates.
If you have any manual installations of `biblatex` and Biber you need to remove those, so they don't get picked up instead of the proper ones placed by your distribution.


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## Friday, May 26, 2017

### Physics World insults me, simultaneously promotes climate alarmism and crackpottery in HEP

The writer's cognitive dissonance is amazing

Most readers of news outlets about science have begun to notice that most of the conventional semipopular news sources about physics – but also most other topics – are fading away.

They haven't been sufficiently financially rewarded for the quality of their writing so they reduced the quality of the writing and focused on cheap things that were enough for the undemanding readers. That decreased their attractiveness among the demanding readers as well as their revenue which led to a further, forced decrease of the quality because it's increasingly obvious that almost anyone can produce similar low-quality texts.

The actual, especially big shot, professional physicists know that The Reference Frame is arguably the highest-quality medium discussing current events in physics – especially those whose status is being misinterpreted elsewhere – and while they are sometimes cowardly and don't want to associate themselves with your humble correspondent too tightly, most people have noticed that this weblog actually is the spokesman of the world's scientific elite which is a little bit under attack from a coalition of aggressive simpletons.

So the simpletons and their mouthpieces increasingly frequently react to my texts. Well, there are many inkspillers on their side but they're missing a detail: The truth is not on their side.

Less than two weeks ago, I discussed a 43-page-long preprint by Christopher Fuchs who reacted to my texts explaining why QBism doesn't bring any new beef relatively to the orthodox, "Copenhagen" interpretation of quantum mechanics. His long tirade basically claims that the "wonderful added value" of QBism is that Nature issues normative statements and one of them is that you shall or you are obliged to gamble.

Sorry, natural sciences can't recognize normative statements – science cannot answer moral questions – and gambling is in no way a preferred or recommended let alone obligatory way to use the probabilities calculated from quantum mechanics. The bookmakers' jargon has nothing to do with the fundamental laws of physics and its addition to papers about the "interpretations" of quantum mechanics cannot improve the physicists' understanding of Nature by one iota.

Yesterday, several people sent me an article
Going against the grain
in the April 2017 issue of the Physics World. The author, Benjamin Skuse, seemingly criticizes the consensus and celebrates those who are brave to challenge it. Except that in reality, he does something totally different. He wants to introduce the consensus that bad science must be embraced by everybody and everyone must celebrate the new consensus where all the junk is placed on the pedestal. Some clique in the Physics World decided to convert a part of the journal to an "anti-reference-frame". But will mediocre activists such as Skuse – in combination with the powerful institutions behind the journal – be enough to defeat me?

He starts by mentioning Kepler, Avogadro, and Boltzmann – and a point of the article is that the likes of Lee Smolin and Tim Palmer are in the same league. So the evil establishment should finally celebrate Smolins and Palmers. Skuse apparently thinks that if he omits the comparison of his crackpot pals to Galileo, he won't get the 40 points to his crackpot index according to the rule #35. Well, I am afraid that Kapler, Avogadro, and Boltzmann are enough for those 40 points. You can easily see that Skuse has basically tried to negate several blog posts of mine – he has mentioned my name, with an insulting description of my occupation. Sometimes, my views were attributed to "the string theory majority in quantum gravity". But the text makes it obvious that this guy has only read a few texts like mine, not actual full-blown research articles, let alone the string theoretical ones.

It's also crazy to describe the likes of Smolin and Palmer as brave warriors against the establishment and consensus when these and similar far left activists pretending to be scientists basically control all the relevant scientific space in the old media.

Another amazing fact about the article that immediately stuns you is that the following paragraphs of this "assault on the concept of consensus" is actually a celebration of the ludicrous claim that there is a consensus about the dangerous man-made climate change. He uncritically mentions John Cook's claim that 97.1% of the scientists support these bogus claims.

The number 97% first appeared in a worthless poll among some cherry-picked 77 people, 75 of which agreed with some alarmist assertion. Dropout John Cook's own version of the number came from counting comments on his crackpot server. 97% of the time, he signed his comments with his own name, 3% of the time, he signed as Luboš Motl. By counting the comments, he decided that 97% of the people support the ideology of the dangerous man-made climate change. There is absolutely nothing serious about any of the claims about the 97% consensus and everyone who takes any comment of this kind seriously is a hopelessly brainwashed moron.

Whether it's this episode or others, every sane person knows that the claim about the 97% consensus is rubbish. The number of researchers who think that there is a danger of climate change in the next century is comparable to 1/2 and has already been distorted by the political influence in the discipline, currently the most politicized discipline of natural science. So the percentages just don't say anything about the validity of the claims, anyway. Skuse doesn't understand these basic things – in spite of his pretending that he understands what's wrong with using the consensus as a weapon.

Skuse's low-quality piece ends up being a hit piece on your humble correspondent in particular and string theorists in general while it celebrates several crackpots – and wrong work by several otherwise credible physicists. Aside from Smolin, the most celebrated person in Skuse's rant is Tim Palmer whose ludicrous talk about the climate Armageddon was discussed last year. I had to laugh out loud when I read:
In contrast to his climate-science research, Palmer’s work in fundamental physics challenges conventional wisdom in its field.
So Skuse is persuading us that Palmer lives a double life, like Superman. In one-half of his scientific life, he is the physically strong Superman. In the other, he's a physically weak journalist Clark Kent. This story about a split personality is surely cute but the truth is much more prosaic. Tim Palmer is simply a crackpot and a stupid peabrain in all fields related to science that he tried to touch. The actual difference is the difference between theoretical physics on one side and the climate science on the other side. Theoretical physics still internally respects meritocracy most of the time while the institutionalized climate science has been largely hijacked by junk pseudoscientists such as Palmer.

This is the actual reason why Palmer is taken more seriously by the "community of climate scientists" than by the "community of theoretical physicists". Most of the people counted as the "climate science community" in 2017 are just garbage as scientists. But the value of Palmer's work in both disciplines is pretty much exactly the same – it is zero.

Skuse sketches some weird claims by Palmer about physics. He wants a theory of quantum gravity but he also wants to promote the weather-related sciences so he wants the spacetime to look like a fractal tornado. If there were some justifiable room for fractals in quantum gravity, it would be cool and important, except that no such evidence is included in Palmer's papers. Palmer's papers are on par with Leo Vuyk's comments about the raspberry universe. It's ludicrous for an inkspiller like Skuse to "demand" that physicists take a hack such as Palmer seriously.

Is consensus important in science? It depends on the precise statement you make about the consensus.

Some consensus may be the result of actual evidence that became available and has persuaded most scientists in a field that a certain statement or theory is correct. For example, an overwhelming majority of the scientists has been persuaded that the Earth is not flat. But the consensus may also be the result of political pressures, intimidation, or physical elimination of those who are inconvenient. For this reason, consensus cannot be considered evidence of any statement and whoever uses such soft social criteria instead of the technical ones automatically reduces himself to a non-scientist. A scientist simply cannot decide about his own field by counting the colleagues who have one opinion or another.

On the other hand, if some consensus emerges about a scientific question, it's not necessarily a proof of a pathology. There exists an active community of successful workers in quantum gravity whose majority agrees with the statement that "string theory is the only game in town" when it comes to the theories of quantum gravity and the unification of all forces.

What does this "consensus" actually mean? It means that if you localize a group of some 1,000 or so people who work on successful papers addressing similar questions, most of them agree that "string theory is the only game in town". But this number 1,000 must be compared to millions of scientists or seven billion people on Earth. The people agreeing with the statement about string theory were cherry-picked pretty much tautologically. Those who have the abilities and other intellectual strengths to work on string theory are also those who generally think that it's a uniquely valuable framework in physics.

This is not too surprising. It's really almost a tautology. If you aren't capable of grasping string theory, you will probably underestimate its value and validity. A human may only "really" appreciate things that he understands, at least to some extent. On the other hand, if you have done enough to actually write research papers on string theory, it's probably because you found the theory important. Why would you otherwise do all the hard work – learning, thinking, writing – that is needed to do research in string theory?

So the observation about the consensus in stringy quantum gravity is basically an empty statement. It is almost exactly on par with the statement that most researchers doing the "loop quantum gravity" kind of stuff are in consensus that "loop quantum gravity" is a top promising path towards a theory of quantum gravity. The actual reason why these two "consensuses" aren't viewed as equivalent is that everyone can see that the average as well as total amount of brilliance among the string theorists exceeds that of the "loop quantum gravitists" by many orders of magnitude.

What the Skuses and Smolins actually want is for the brilliant scientists to embrace the cheap, wrong, and junk ideas, and work on them. But without the help of a flamethrower, that is pretty much impossible. They're brilliant exactly because their thinking is sharper than that of the less brilliant ones. So you can't achieve that goal: it is logically self-contradictory. Idiots will generally advocate idiotic ideas and brilliant people will work on brilliant ideas. There are thousands of defenders of loop quantum gravity – a much greater number than the number of string theorists – but their impact in physics is tiny simply because they're not as good as the string theorists.

String theorists don't influence theoretical physics so much because they have hijacked some "powerful tools" such as magazines, political offices etc.: almost all of those belong to the likes of Skuse. String theorists have the influence because they produce actual results and evidence and their brilliance is often self-evident to every impartial, intelligent enough observer. String theorists are generally brighter than loop quantum gravitists. It's a fact that you can't change. And it's not an accidental fact: string theorists are more brilliant because it's their brilliance that has led them to learn, study, and appreciate string theory. If you're brilliant enough, you may become a string theorist. If you're not, you may end up being a champion of loop quantum gravity. It's that simple. For similar reasons, The Reference Frame has a bigger impact on the thinking of the physics community about potentially controversial research questions than Physics World – despite the much better funding etc. of the Physics World – simply because I am right, I know what I am actually saying, and every competent physicist (especially professor etc.) simply sees that. I – and the string theorists – are the David who can beat the Goliath because we're much smarter and because we're right.

Skuse also tries to praise the nonsensical work of Gerard 't Hooft attempting to revise the foundations of quantum mechanics; and Erik Verlinde's wrong statement that gravity is an entropic force. Again, it makes no sense to argue about those things in 2017. Who hasn't been able to see that and why 't Hooft has lost it is simply in a lower league that doesn't meaningfully interact with the cream of the theoretical physics community. In the same way, who can't understand in 2017 that the entropy can't oscillate along with the gravitational potential energy of two bodies (because of irreversibility or the second law) and that the number of microstates can't depend on the distance (because that would cripple the factorization of the Hilbert space and destroyed e.g. the neutron interferometry in gravitational fields), he simply belongs to the broader public but not to the elite of the physics research community. Entropy may be defined in gravitating systems and plays a lot of roles. But Verlinde had made a much more specific statement – that the gravitational force may be presented as an entropic one – and that statement is simply wrong.

To summarize:

Consensus may emerge because of legitimate reasons but also because of illegitimate reasons. The more politicized a discipline is, the more likely it is for the actual reason behind some consensus to be scientifically illegitimate. No actual scientist deciding about his healthy discipline will ever mention consensus as an argument. Inkspillers and activists such as Skuse and Smolin do so all the time. They are trying to distort science by political demagogy all the time. "You have to embrace this idea or another" because "the number of the people who believe it is already very high or it is too low" etc.

What's remarkable about the likes of Skuse and Smolin is that they manifestly use these unacceptable political arguments in both directions – they constantly contradict themselves. Sometimes, they are using consensus as a "proof" that a claim is right and a reason why the consensus should be even stronger; sometimes, they are using consensus as a "proof" that something is wrong and there should be much more diversity. You simply can't have it in both ways. And actual scientists can't have it in either way. Whether there is consensus or not must be absolutely irrelevant for an actual scientist's decision whether he believes a statement or another. A person may sometimes decide according to sociological criteria and even scientists do so – but whenever they do so, it simply means that they're outsiders in that discipline and their opinion shouldn't be counted in any scientifically meaningful poll trying to find the truth.

When a whole discipline becomes dominated by the people whose behavior is affected by such things, the discipline is on a downward trend. That was the case of the climate science 30 years ago when the catastrophicists were still a fringe minority who claimed that their percentage must grow. But the discipline remained profoundly sick when these pseudoscientists represent a majority of that politicized field: the usage of the political arguments is sick in both directions.

Professional high-energy physics linked to quantum gravity hasn't been crippled in this way yet which is why basically every employable person and student knows that the papers by Palmer, Smolin, 't Hooft, Verlinde etc. promoted by Skuse are wrong or at least not very good. For the likes of Skuse to change the situation would mean to destroy this field, too. I hope it will never happen and Skuse's and similar propaganda pieces will only matter for an irrelevant community of brainwashed laymen whose number should keep on decreasing as the old, deteriorating journals lose their impact.


text:
# How to raise the output of \genfrac?

I want to write rational numbers in mixed-numeral notation. To do so, I currently use \tfrac (AmSLaTeX):

\frac{5}{4} = 1\tfrac{1}{4}

But the fractional part is still too big for my taste. Therefore I defined \ttfrac with respect to genfrac as suggested in the "User's Guide for the amsmath Package" [amsldoc] (subsection 4.11.3):

\newcommand{\ttfrac}[2]{\genfrac{}{}{}{2}{#1}{#2}}

The above code then becomes:

\frac{5}{4} = 1\ttfrac{1}{4}

It fits better my taste, but now the fractional part is shifted down. What is the best way to raise it up a bit ?

You shouldn't write numbers that way, because it's ambiguous. Anyway, for raising the scriptsize fraction you can use \vcenter:

\documentclass{article}
\usepackage{amsmath}

\newcommand{\ttfrac}[2]{\vcenter{\hbox{$\genfrac{}{}{}{2}{#1}{#2}$}}}

\begin{document}

$1\ttfrac{1}{4}$ versus $1\tfrac{1}{4}$

\end{document}


text:
# Z=f(x,y), x=function, y=function. dz/dx=

## Homework Statement

Consider z=f(x,y), where x=rcosθ and y=rsinθ

Show that $\frac{\partial z}{\partial x}=\cos\theta\frac{\partial z}{\partial r}-\frac{1}{r}\sin\theta\frac{\partial z}{\partial\theta}$

## The Attempt at a Solution

Z
Connects to X and Y
X Connects to r and θ, Y Connects to r and θ

Is dz/dx not then equal to dx/dr + dx/dθ? because that is equivalent to dz/dx = r -rsinθ.
What am I doing wrong here?

Simon Bridge
Homework Helper
Evaluate ##\frac{\partial z}{\partial r}##

$\frac{\partial z}{\partial r}=\cos\theta\frac{\partial z}{\partial x}+\sin\theta\frac{\partial z}{\partial y}$

then rearranging this $\frac{\partial z}{\partial x}=\sec\theta\frac{\partial z}{\partial r}-\tan\theta\frac{\partial z}{\partial y}$

I'm not doing something right or not understanding some underlying concept here. Why was my dz/dx derivation wrong?

Simon Bridge
Homework Helper
Don't rearrange yet. Do the other partial - the one with theta.

$\frac{\partial z}{\partial\theta}=-r\sin\theta\frac{\partial z}{\partial x}+\frac{1}{r}\cos\theta\frac{\partial z}{\partial y}$

I've re-arranged this and get $\frac{\partial z}{\partial x}=-\frac{1}{r}\csc\frac{\partial z}{\partial\theta}+\frac{1}{r^{2}}\cot\theta\frac{\partial z}{\partial y}$

which should be the same as $\frac{\partial z}{\partial x}=\sec\theta\frac{\partial z}{\partial r}-\tan\theta\frac{\partial z}{\partial y}$

Now I'm more confused...

Isn't it just $r-r\sin\theta$?

Simon Bridge
Homework Helper
- you want ∂z/∂x in terms of ∂z/∂r and ∂z/dθ.

You don't need any terms in ∂z/∂y ... but the above relations each have such a term.
This should suggest a course of action to you.

Hey Simon, I got it!

I isolated $\frac{\partial z}{\partial y}$ for both equations of $\frac{\partial z}{\partial r}$ and $\frac{\partial z}{\partial \theta}$ and then equated the two and re-arranged a little to get $\frac{\partial z}{\partial x}=\cos\theta\frac{\partial z}{\partial r}-\frac{1}{r}\sin\theta\frac{\partial z}{\partial\theta}$.

However, I still don't get why the solution is simply not $\frac{\partial z}{\partial x}= \frac{\partial x}{\partial r}+ \frac{\partial x}{\partial \theta}=\cos\theta - r\sin\theta$

Simon Bridge
However, I still don't get why the solution is simply not $$\frac{\partial z}{\partial x}= \frac{\partial x}{\partial r}+ \frac{\partial x}{\partial \theta}=\cos\theta - r\sin\theta$$