cssi/SciSciGPT-SciSciNet huggingface dataset:
DeepLigand: accurate prediction of MHC class I ligands using peptide embedding

Motivation The computational modeling of peptide display by class I major histocompatibility complexes (MHCs) is essential for peptide-based therapeutics design. Existing computational methods for peptide-display focus on modeling the peptide-MHC-binding affinity. However, such models are not able to characterize the sequence features for the other cellular processes in the peptide display pathway that determines MHC ligand selection. Results We introduce a semi-supervised model, DeepLigand that outperforms the state-of-the-art models in MHC Class I ligand prediction. DeepLigand combines a peptide language model and peptide binding affinity prediction to score MHC class I peptide presentation. The peptide language model characterizes sequence features that correspond to secondary factors in MHC ligand selection other than binding affinity. The peptide embedding is learned by pre-training on natural ligands, and can discriminate between ligands and non-ligands in the absence of binding affinity prediction. Although conventional affinity-based models fail to classify peptides with moderate affinities, DeepLigand discriminates ligands from non-ligands with consistently high accuracy. Availability and implementation We make DeepLigand available at https://github.com/gifford-lab/DeepLigand. Supplementary information Supplementary data are available at Bioinformatics online.
Paired-end mappability of transposable elements in the human genome

Though transposable elements make up around half of the human genome, the repetitive nature of their sequences makes it difficult to accurately align conventional sequencing reads. However, in light of new advances in sequencing technology, such as increased read length and paired-end libraries, these repetitive regions are now becoming easier to align to. This study investigates the mappability of transposable elements with 50 bp, 76 bp and 100 bp paired-end read libraries. With respect to those read lengths and allowing for 3 mismatches during alignment, over 68, 85, and 88% of all transposable elements in the RepeatMasker database are uniquely mappable, suggesting that accurate locus-specific mapping of older transposable elements is well within reach.
The Effect of Franchising on Store Performance: Evidence from an Ownership Change

Although many franchisors choose to own some stores and franchise others, attempts to estimate the effect of franchising on store performance are hampered by an important selection issue: The franc...
Recent Advances in Cosmological Hydrogen Reionization

I discuss recent advances in the study of hydrogen reionization, focusing on progress that was achieved during the years 2010–2011. First, I discuss recent measurements of the progress of reionization. Next, I discuss recent observational constraints on the nature and abundance of the dominant ionizing sources. Finally, I discuss recent progress in modeling reionization. This review is written for an audience of astronomers who do not specialize in the high-redshift Universe.
Functor is to Lens as Applicative is to Biplate: Introducing Multiplate

This paper gives two new categorical characterisations of lenses: one as a coalgebra of the store comonad, and the other as a monoidal natural transformation on a category of a certain class of coalgebras. The store comonad of the first characterisation can be generalized to a Cartesian store comonad, and the coalgebras of this Cartesian store comonad turn out to be exactly the Biplates of the Uniplate generic programming library. On the other hand, the monoidal natural transformations on functors can be generalized to work on a category of more specific coalgebras. This generalization turns out to be the type of compos from the Compos generic programming library. A theorem, originally conjectured by van Laarhoven, proves that these two generalizations are isomorphic, thus the core data types of the Uniplate and Compos libraries supporting generic program on single recursive types are the same. Both the Uniplate and Compos libraries generalize this core functionality to support mutually recursive types in different ways. This paper proposes a third extension to support mutually recursive data types that is as powerful as Compos and as easy to use as Uniplate. This proposal, called Multiplate, only requires rank 3 polymorphism in addition to the normal type class mechanism of Haskell.
Construction of normal numbers with respect to the $Q$-Cantor series expansion for certain $Q$

A. Renyi \cite{Renyi} made a definition that gives one generalization of simple normality in the context of $Q$-Cantor series. Similarly, in this paper we give a definition which generalizes the notion of normality in the context of $Q$-Cantor series. We will prove a theorem that allows us to concatenate sequences of digits that have a special property to give us the digits of a $Q$-normal number for certain $Q$. We will then use this theorem to construct a Q and a real number $x$ that is $Q$-normal.
Reconstructing Neuronal Anatomy from Whole-Brain Images

Reconstructing multiple molecularly defined neurons from individual brains and across multiple brain regions can reveal organizational principles of the nervous system. However, high resolution imaging of the whole brain is a technically challenging and slow process. Recently, oblique light sheet microscopy has emerged as a rapid imaging method that can provide whole brain fluorescence microscopy at a voxel size of $0.4\times 0.4\times 2.5\mu \mathrm{m}^{3}$. On the other hand, complex image artifacts due to whole-brain coverage produce apparent discontinuities in neuronal arbors. Here, we present connectivity-preserving methods and data augmentation strategies for supervised learning of neuroanatomy from light microscopy using neural networks. We quantify the merit of our approach by implementing an end-to-end automated tracing pipeline. Lastly, we demonstrate a scalable, distributed implementation that can reconstruct the large datasets that sub-micron whole-brain images produce.
Derived Azumaya algebras and twisted K-theory

Abstract We construct a relative version of topological K-theory, in the sense of [11] , over an arbitrary quasi-compact, quasi-separated C -scheme X. This has as input a Perf ( X ) -linear stable ∞-category and output a sheaf of spectra on X ( C ) , the space of complex points of X. We then characterize the values of this functor on inputs of the form Perf ( X , A ) , for A a derived Azumaya algebra over X. In such cases we show that this coincides with the α-twisted topological K-theory of X ( C ) for some appropriately defined twist of K-theory. We use this to provide a topological analogue of a classical result of Quillen's on the algebraic K-theory of Severi-Brauer varieties.
Bayesian multitask learning with latent hierarchies

We learn multiple hypotheses for related tasks under a latent hierarchical relationship between tasks. We exploit the intuition that for domain adaptation, we wish to share classifier structure, but for multitask learning, we wish to share covariance structure. Our hierarchical model is seen to subsume several previously proposed multitask learning models and performs well on three distinct real-world data sets.
Revisiting Unreasonable Effectiveness of Data in Deep Learning Era

The success of deep learning in vision can be attributed to: (a) models with high capacity; (b) increased computational power; and (c) availability of large-scale labeled data. Since 2012, there have been significant advances in representation capabilities of the models and computational capabilities of GPUs. But the size of the biggest dataset has surprisingly remained constant. What will happen if we increase the dataset size by 10 × or 100 × ? This paper takes a step towards clearing the clouds of mystery surrounding the relationship between ‘enormous data’ and visual deep learning. By exploiting the JFT-300M dataset which has more than 375M noisy labels for 300M images, we investigate how the performance of current vision tasks would change if this data was used for representation learning. Our paper delivers some surprising (and some expected) findings. First, we find that the performance on vision tasks increases logarithmically based on volume of training data size. Second, we show that representation learning (or pre-training) still holds a lot of promise. One can improve performance on many vision tasks by just training a better base model. Finally, as expected, we present new state-of-the-art results for different vision tasks including image classification, object detection, semantic segmentation and human pose estimation. Our sincere hope is that this inspires vision community to not undervalue the data and develop collective efforts in building larger datasets.
Data Representation and Compression Using Linear-Programming Approximations

Abstract: We propose `Dracula', a new framework for unsupervised feature selection from sequential data such as text. Dracula learns a dictionary of $n$-grams that efficiently compresses a given corpus and recursively compresses its own dictionary; in effect, Dracula is a `deep' extension of Compressive Feature Learning. It requires solving a binary linear program that may be relaxed to a linear program. Both problems exhibit considerable structure, their solution paths are well behaved, and we identify parameters which control the depth and diversity of the dictionary. We also discuss how to derive features from the compressed documents and show that while certain unregularized linear models are invariant to the structure of the compressed dictionary, this structure may be used to regularize learning. Experiments are presented that demonstrate the efficacy of Dracula's features.
Quantum Key Distribution (QKD) and Commodity Security Protocols: Introduction and Integration

We present an overview of quantum key distribution (QKD), a secure key exchange method based on the quantum laws of physics rather than computational complexity. We also provide an overview of the two most widely used commodity security protocols, IPsec and TLS. Pursuing a key exchange model, we propose how QKD could be integrated into these security applications. For such a QKD integration we propose a support layer that provides a set of common QKD services between the QKD protocol and the security applications.
Mining temporal patterns from iTRAQ mass spectrometry(LC-MS/MS) data

Large-scale proteomic analysis is emerging as a powerful technique in biology and relies heavily on data acquired by state-of-the-art mass spectrometers. As with any other field in Systems Biology, computational tools are required to deal with this ocean of data. iTRAQ (isobaric Tags for Relative and Absolute quantification) is a technique that allows simultaneous quantification of proteins from multiple samples. Although iTRAQ data gives useful insights to the biologist, it is more complex to perform analysis and draw biological conclusions because of its multi-plexed design. One such problem is to find proteins that behave in a similar way (i.e. change in abundance) among various time points since the temporal variations in the proteomics data reveal important biological information. Distance based methods such as Euclidian distance or Pearson coefficient, and clustering techniques such as k-mean etc, are not able to take into account the temporal information of the series. In this paper, we present an linear-time algorithm for clustering similar patterns among various iTRAQ time course data irrespective of their absolute values. The algorithm, referred to as Temporal Pattern Mining(TPM), maps the data from a Cartesian plane to a discrete binary plane. After the mapping a dynamic programming technique allows mining of similar data elements that are temporally closer to each other. The proposed algorithm accurately clusters iTRAQ data that are temporally closer to each other with more than 99% accuracy. Experimental results for different problem sizes are analyzed in terms of quality of clusters, execution time and scalability for large data sets. An example from our proteomics data is provided at the end to demonstrate the performance of the algorithm and its abil∗* Corresponding author: National Institutes of Health, Building 10, Room 6N312, 10 Center Drive, MSC 1603, Bethesda, MD 208921603. E-mail address: fahad.saeed@nih.gov ity to cluster temporal series irrespective of their distance from each other.
An integro-differential equation without continuous solutions

We show an example of a non-symmetric integro-differential equation of order $\alpha$, for $\alpha \in (0,1)$, for which H\"older estimates do not hold even though the kernels are comparable to the fractional Laplacian.
Attention-Based Models for Text-Dependent Speaker Verification

Attention-based models have recently shown great performance on a range of tasks, such as speech recognition, machine translation, and image captioning due to their ability to summarize relevant information that expands through the entire length of an input sequence. In this paper, we analyze the usage of attention mechanisms to the problem of sequence summarization in our end-to-end text-dependent speaker recognition system. We explore different topologies and their variants of the attention layer, and compare different pooling methods on the attention weights. Ultimately, we show that attention-based models can improves the Equal Error Rate (EER) of our speaker verification system by relatively 14% compared to our non-attention LSTM baseline model.
Inter-Operator Feedback in Data Stream Management Systems via Punctuation

high-speed data streams may overwhelm the capabilities of stream processing systems; techniques such as data prioritization, avoidance of unnecessary processing and on- demand result production may be necessary to reduce processing requirements. However, the dynamic nature of data streams, in terms of both rate and content, makes the application of such techniques challenging. Such techniques have been addressed in the context of static and centralized query optimization; however, they have not been fully addressed for data-stream management systems. In this work, we present a comprehensive framework designed to support prioritization, avoidance of unnecessary work, and on-demand result production over distributed, unreliable, bursty, disordered data sources, typical of many streams. We propose a form of inter-operator feedback, which flows against the stream direction, to communicate the information needed to enable execution of these techniques. This feedback leverages punctuations to describe the subsets of interest. We identify potential sources of feedback information, characterize new types of punctuation to support feedback, and describe the roles of producers, exploiters, and relayers of feedback that query operators may implement. We also present initial experimental observations using the NiagaraST data-stream system.
BIOS ORAM: Improved Privacy-Preserving Data Access for Parameterized Outsourced Storage

Algorithms for oblivious random access machine (ORAM) simulation allow a client, Alice, to obfuscate a pattern of data accesses with a server, Bob, who is maintaining Alice's outsourced data while trying to learn information about her data. We present a novel ORAM scheme that improves the asymptotic I/O overhead of previous schemes for a wide range of size parameters for clientside private memory and message blocks, from logarithmic to polynomial. Our method achieves statistical security for hiding Alice's access pattern and, with high probability, achieves an I/O overhead that ranges from O(1) to O(log2 n/(log logn)2), depending on these size parameters, where n is the size of Alice's outsourced memory. Our scheme, which we call BIOS ORAM, combines multiple uses of B-trees with a reduction of ORAM simulation to isogrammic access sequences.
How Important Is a Neuron

The problem of attributing a deep network's prediction to its \emph{input/base} features is well-studied. We introduce the notion of \emph{conductance} to extend the notion of attribution to the understanding the importance of \emph{hidden} units. Informally, the conductance of a hidden unit of a deep network is the \emph{flow} of attribution via this hidden unit. We use conductance to understand the importance of a hidden unit to the prediction for a specific input, or over a set of inputs. We evaluate the effectiveness of conductance in multiple ways, including theoretical properties, ablation studies, and a feature selection task. The empirical evaluations are done using the Inception network over ImageNet data, and a sentiment analysis network over reviews. In both cases, we demonstrate the effectiveness of conductance in identifying interesting insights about the internal workings of these networks.
On the numerical solution of the far field refractor problem

Abstract The far field refractor problem with a discrete target is solved with a numerical scheme that uses and simplify ideas from Caffarelli et al. (1999). A numerical implementation is carried out and examples are shown.
Heat content and horizontal mean curvature on the Heisenberg group

We identify the short time asymptotics of the sub-Riemannian heat content for a smoothly bounded domain in the first Heisenberg group. Our asymptotic formula generalizes prior work by van den Berg–...
An Application of Mirror Extensions

In this paper we apply our previous results of mirror extensions to obtain realizations of three modular invariants constructed by A. N. Schellekens by holomorphic conformal nets with central charge equal to 24.
NORMAL NUMBERS AND COMPLETENESS RESULTS FOR DIFFERENCE SETS

We consider some natural sets of real numbers arising in ergodic theory and show that they are, respectively, complete in the classes and , that is, the class of sets which are 2-differences (respectively, ω-differences) of sets.
On the relation between very weak and Leray–Hopf solutions to Navier–Stokes equations

We prove a general result that implies that very weak solutions to the Cauchy problem for the Navier-Stokes equations must be, in fact, Leray-Hopf solutions if only their initial data are (solenoidal) with finite kinetic energy.
Ignoring extreme opinions in complex networks: The impact of heterogeneous thresholds

We consider a class of opinion dynamics on networks where at each time-step, each node in the network disregards the opinions of a certain number of its most extreme neighbors and updates its own opinion as a weighted average of the remaining opinions. When all nodes disregard the same number of extreme neighbors, previous work has shown that consensus will be reached if and only if the network satisfies certain topological properties. In this paper, we consider the implications of allowing each node to have a personal threshold for the number of extreme neighbors to ignore. We provide graph conditions under which consensus is guaranteed for such dynamics. We then study random networks where each node's threshold is drawn from a certain distribution, and provide conditions on that distribution, together with conditions on the edge formation probability, that guarantee that consensus will be reached asymptotically almost surely.
Designing Incentive Schemes for Privacy-Sensitive Users

Businesses (retailers) often wish to offer personalized advertisements (coupons) to individuals (consumers), but run the risk of strong reactions from consumers who want a customized shopping experience but feel their privacy has been violated. Existing models for privacy such as differential privacy or information theory try to quantify privacy risk but do not capture the subjective experience and heterogeneous expression of privacy-sensitivity. We propose a Markov decision process (MDP) model to capture (i) different consumer privacy sensitivities via a time-varying state; (ii) different coupon types (action set) for the retailer; and (iii) the action-and-state-dependent cost for perceived privacy violations. For the simple case with two states ("Normal" and "Alerted"), two coupons (targeted and untargeted) model, and consumer behavior statistics known to the retailer, we show that a stationary threshold-based policy is the optimal coupon-offering strategy for a retailer that wishes to minimize its expected discounted cost. The threshold is a function of all model parameters; the retailer offers a targeted coupon if its belief that the consumer is in the "Alerted" state is below the threshold. We extend this two-state model to consumers with multiple privacy-sensitivity states as well as coupon-dependent state transition probabilities. Furthermore, we study the case with imperfect (noisy) cost feedback from consumers and uncertain initial belief state.
Robust superhedging with jumps and diffusion

Abstract We establish a nondominated version of the optional decomposition theorem in a setting that includes jump processes with nonvanishing diffusion as well as general continuous processes. This result is used to derive a robust superhedging duality and the existence of an optimal superhedging strategy for general contingent claims. We illustrate the main results in the framework of nonlinear Levy processes.
Quantum entanglement phenomena in photosynthetic light harvesting complexes

Abstract We review recent theoretical calculations of quantum entanglement in photosynthetic light harvesting complexes. These works establish, for the first time, a manifestation of this characteristically quantum mechanical phenomenon in biologically functional structures. We begin by summarizing calculations on model biomolecular systems that aim to reveal non-trivial characteristics of quantum entanglement in non-equilibrium biological environments. We then discuss and compare several calculations performed recently of excitonic dynamics in the Fenna-Matthews-Olson light harvesting complex and of the electronic entanglement present in this widely studied pigment-protein structure. We point out the commonalities between the derived results and also identify and explain the differences. We also discuss recent work that examines entanglement in the structurally more intricate light harvesting complex II (LHCII). During this overview, we take the opportunity to clarify several subtle issues relating to entanglement in such biomolecular systems, including the role of entanglement in biological function, the complexity of dynamical modeling that is required to capture the salient features of entanglement in such biomolecular systems, and the relationship between entanglement and other quantum mechanical features that are observed and predicted in light harvesting complexes. Finally, we suggest possible extensions of the current work and also review the options for experimental confirmation of the predicted entanglement phenomena in light harvesting complexes.
ON SUPPORT VARIETIES AND THE HUMPHREYS CONJECTURE IN TYPE A

Abstract Let G be a reductive algebraic group scheme defined over F p and let G 1 denote the Frobenius kernel of G. To each finite-dimensional G-module M, one can define the support variety V G 1 ( M ) , which can be regarded as a G-stable closed subvariety of the nilpotent cone. A G-module is called a tilting module if it has both good and Weyl filtrations. In 1997, it was conjectured by J.E. Humphreys that when p ≥ h , the support varieties of the indecomposable tilting modules align with the nilpotent orbits given by the Lusztig bijection. In this paper, we shall verify this conjecture when G = S L n + 1 and p > n + 1 .
A Unified Theory of Early Visual Representations from Retina to Cortex through Anatomically Constrained Deep CNNs

The vertebrate visual system is hierarchically organized to process visual information in successive stages. Neural representations vary drastically across the first stages of visual processing: at the output of the retina, ganglion cell receptive fields (RFs) exhibit a clear antagonistic center-surround structure, whereas in the primary visual cortex (V1), typical RFs are sharply tuned to a precise orientation. There is currently no unified theory explaining these differences in representations across layers. Here, using a deep convolutional neural network trained on image recognition as a model of the visual system, we show that such differences in representation can emerge as a direct consequence of different neural resource constraints on the retinal and cortical networks, and for the first time we find a single model from which both geometries spontaneously emerge at the appropriate stages of visual processing. The key constraint is a reduced number of neurons at the retinal output, consistent with the anatomy of the optic nerve as a stringent bottleneck. Second, we find that, for simple downstream cortical networks, visual representations at the retinal output emerge as nonlinear and lossy feature detectors, whereas they emerge as linear and faithful encoders of the visual scene for more complex cortical networks. This result predicts that the retinas of small vertebrates (e.g. salamander, frog) should perform sophisticated nonlinear computations, extracting features directly relevant to behavior, whereas retinas of large animals such as primates should mostly encode the visual scene linearly and respond to a much broader range of stimuli. These predictions could reconcile the two seemingly incompatible views of the retina as either performing feature extraction or efficient coding of natural scenes, by suggesting that all vertebrates lie on a spectrum between these two objectives, depending on the degree of neural resources allocated to their visual system.
CALIPER: Continuous Authentication Layered with Integrated PKI Encoding Recognition

Architectures relying on continuous authentication require a secure way to challenge the user's identity without trusting that the Continuous Authentication Subsystem (CAS) has not been compromised, i.e., that the response to the layer which manages service/application access is not fake. In this paper, we introduce the CALIPER protocol, in which a separate Continuous Access Verification Entity (CAVE) directly challenges the user's identity in a continuous authentication regime. Instead of simply returning authentication probabilities or confidence scores, CALIPER's CAS uses live hard and soft biometric samples from the user to extract a cryptographic private key embedded in a challenge posed by the CAVE. The CAS then uses this key to sign a response to the CAVE. CALIPER supports multiple modalities, key lengths, and security levels and can be applied in two scenarios: One where the CAS must authenticate its user to a CAVE running on a remote server (device-server) for access to remote application data, and another where the CAS must authenticate its user to a locally running trusted computing module (TCM) for access to local application data (device-TCM). We further demonstrate that CALIPER can leverage device hardware resources to enable privacy and security even when the device's kernel is compromised, and we show how this authentication protocol can even be expanded to obfuscate direct kernel object manipulation (DKOM) malwares.
Leveraging Intra-User and Inter-User Representation Learning for Automated Hate Speech Detection

Hate speech detection is a critical, yet challenging problem in Natural Language Processing (NLP). Despite the existence of numerous studies dedicated to the development of NLP hate speech detection approaches, the accuracy is still poor. The central problem is that social media posts are short and noisy, and most existing hate speech detection solutions take each post as an isolated input instance, which is likely to yield high false positive and negative rates. In this paper, we radically improve automated hate speech detection by presenting a novel model that leverages intra-user and inter-user representation learning for robust hate speech detection on Twitter. In addition to the target Tweet, we collect and analyze the user’s historical posts to model intra-user Tweet representations. To suppress the noise in a single Tweet, we also model the similar Tweets posted by all other users with reinforced inter-user representation learning techniques. Experimentally, we show that leveraging these two representations can significantly improve the f-score of a strong bidirectional LSTM baseline model by 10.1%.
Power laws in preferential attachment graphs and Stein's method for the negative binomial distribution

For a family of linear preferential attachment graphs, we provide rates of convergence for the total variation distance between the degree of a randomly chosen vertex and an appropriate power law distribution as the number of vertices tends to ∞. Our proof uses a new formulation of Stein's method for the negative binomial distribution, which stems from a distributional transformation that has the negative binomial distributions as the only fixed points.
Improving Neural Parsing by Disentangling Model Combination and Reranking Effects

Recent work has proposed several generative neural models for constituency parsing that achieve state-of-the-art results. Since direct search in these generative models is difficult, they have primarily been used to rescore candidate outputs from base parsers in which decoding is more straightforward. We first present an algorithm for direct search in these generative models. We then demonstrate that the rescoring results are at least partly due to implicit model combination rather than reranking effects. Finally, we show that explicit model combination can improve performance even further, resulting in new state-of-the-art numbers on the PTB of 94.25 F1 when training only on gold data and 94.66 F1 when using external data.
Measuring Political Gerrymandering

In 2018, a Pennsylvania court struck down the state’s congressional map due to unconstitutional partisan gerrymandering, and a new map was established in time for the midterm elections. Recent laws...
Unique information via dependency constraints

Author(s): James, RG; Emenheiser, J; Crutchfield, JP | Abstract: The partial information decomposition (PID) is perhaps the leading proposal for resolving information shared between a set of sources and a target into redundant, synergistic, and unique constituents. Unfortunately, the PID framework has been hindered by a lack of a generally agreed-upon, multivariate method of quantifying the constituents. Here, we take a step toward rectifying this by developing a decomposition based on a new method that quantifies unique information. We first develop a broadly applicable method - the dependency decomposition - that delineates how statistical dependencies influence the structure of a joint distribution. The dependency decomposition then allows us to define a measure of the information about a target that can be uniquely attributed to a particular source as the least amount which the source-target statistical dependency can influence the information shared between the sources and the target. The result is the first measure that satisfies the core axioms of the PID framework while not satisfying the Blackwell relation, which depends on a particular interpretation of how the variables are related. This makes a key step forward to a practical PID.
Penrose-type inequalities with a Euclidean background

The Riemannian Penrose inequality (RPI) bounds from below the ADM mass of asymptotically flat manifolds of nonnegative scalar curvature in terms of the total area of all outermost compact minimal surfaces. The general form of the RPI is currently known for manifolds of dimension up to seven. In the present work, we prove a Penrose-like inequality that is valid in all dimensions, for conformally flat manifolds. Our inequality treats the area contributions of the minimal surfaces in a more favorable way than the RPI, at the expense of using the smaller Euclidean area (rather than the intrinsic area). We give an example in which our estimate is sharper than the RPI when many minimal surfaces are present. We do not require the minimal surfaces to be outermost. We also generalize the technique to allow for metrics conformal to a scalar-flat (not necessarily Euclidean) background and prove a Penrose-type inequality without an assumption on the sign of scalar curvature. Finally, we derive a new lower bound for the ADM mass of a conformally flat, asymptotically flat manifold containing any number of zero area singularities.
Optimization over structured subsets of positive semidefinite matrices via column generation

We develop algorithms to construct inner approximations of the cone of positive semidefinite matrices via linear programming and second order cone programming. Starting with an initial linear algebraic approximation suggested recently by Ahmadi and Majumdar, we describe an iterative process through which our approximation is improved at every step. This is done using ideas from column generation in large-scale linear programming. We then apply these techniques to approximate the sum of squares cone in a nonconvex polynomial optimization setting, and the copositive cone for a discrete optimization problem.
Smart, Responsible, and Upper Caste Only: Measuring Caste Attitudes through Large-Scale Analysis of Matrimonial Profiles.

Discriminatory caste attitudes currently stigmatize millions of Indians, subjecting individuals to prejudice in all aspects of life. Governmental incentives and societal movements have attempted to counter these attitudes, yet accurate measurements of public opinions on caste are not yet available for understanding whether progress is being made. Here, we introduce a novel approach to measure public attitudes of caste through an indicator variable: openness to intercaste marriage. Using a massive dataset of over 313K profiles from a major Indian matrimonial site, we precisely quantify public attitudes, along with differences between generations and between Indian residents and diaspora. We show that younger generations are more open to intercaste marriage, yet attitudes are based on a complex function of social status beyond their own caste. In examining the desired qualities in a spouse, we find that individuals open to intercaste marriage are more individualistic in the qualities they desire, rather than favoring family-related qualities, which mirrors larger societal trends away from collectivism. Finally, we show that attitudes in diaspora are significantly less open, suggesting a bi-cultural model of integration. Our research provides the first empirical evidence identifying how various intersections of identity shape attitudes toward intercaste marriage in India and among the Indian diaspora in the US.
Interdependence of Transmission Branch Parameters on the Voltage Levels

Transformers and transmission lines are critical components of a grid network. This paper analyzes the statistical properties of the electrical parameters of transmission branches and especially examines their interdependence on the voltage levels. Some interesting findings include: (a) with appropriate conversion of MVA rating, a transformers per unit reactance exhibits consistent statistical pattern independent of voltage levels and capacity; (b) the distributed reactance (ohms/km) of transmission lines also has some consistent patterns regardless of voltage levels; (c) other parameters such as the branch resistance, the MVA ratings, the transmission line length, etc, manifest strong interdependence on the voltage levels which can be approximated by a power function with different power constants. The results will be useful in both creation of synthetic power grid test cases and validation of existing grid models.
Metric Foliations of Homogeneous Three-Spheres

A smooth foliation of a Riemannian manifold is metric when its leaves are locally equidistant and is homogeneous when its leaves are locally orbits of a Lie group acting by isometries. Homogeneous foliations are metric foliations, but metric foliations need not be homogeneous foliations. We prove that a homogeneous three-sphere is naturally reductive if and only if all of its metric foliations are homogeneous.
The Language Features and Architecture of B-Prolog

B-Prolog is a high-performance implementation of the standard Prolog language with several extensions including matching clauses, action rules for event handling, finite-domain constraint solving, arrays and hash tables, declarative loop constructs, and tabling. The B-Prolog system is based on the Tree-Oriented Abstract Machine (TOAM) architecture which differs from the Warren Abstract Machine (WAM) mainly in that (1) arguments are passed old fashionedly through the stack, (2) only one frame is used for each predicate call, and (3) instructions are provided for encoding matching trees. The most recent architecture, called TOAM Jr., departs further from the WAM in that it employs no registers for arguments or temporary variables, and provides variable-size instructions for encoding predicate calls. This paper gives an overview of the language features and a detailed description of the TOAM Jr. architecture, including architectural support for action rules and tabling.
Normally elliptic singular perturbations and persistence of homoclinic orbits

Abstract We consider a dynamical system, possibly infinite dimensional or non-autonomous, with fast and slow time scales which is oscillatory with high frequencies in the fast directions. We first derive and justify the limit system of the slow variables. Assuming a steady state persists, we construct the stable, unstable, center-stable, center-unstable, and center manifolds of the steady state of a size of order O ( 1 ) and give their leading order approximations. Finally, using these tools, we study the persistence of homoclinic solutions in this type of normally elliptic singular perturbation problems.
Neural Speed Reading via Skim-RNN.

Inspired by the principles of speed reading, we introduce Skim-RNN, a recurrent neural network (RNN) that dynamically decides to update only a small fraction of the hidden state for relatively unimportant input tokens. Skim-RNN gives computational advantage over an RNN that always updates the entire hidden state. Skim-RNN uses the same input and output interfaces as a standard RNN and can be easily used instead of RNNs in existing models. In our experiments, we show that Skim-RNN can achieve significantly reduced computational cost without losing accuracy compared to standard RNNs across five different natural language tasks. In addition, we demonstrate that the trade-off between accuracy and speed of Skim-RNN can be dynamically controlled during inference time in a stable manner. Our analysis also shows that Skim-RNN running on a single CPU offers lower latency compared to standard RNNs on GPUs.
SINGLE INDEX LATENT VARIABLE MODELS FOR NETWORK TOPOLOGY INFERENCE

A semi-parametric, non-linear regression model in the presence of latent variables is applied towards learning network graph structure. These latent variables can correspond to un-modeled phenomena or unmeasured agents in a complex system of interacting entities. This formulation jointly estimates non-linearities in the underlying data generation, the direct interactions between measured entities, and the indirect effects of unmeasured processes on the observed data. The learning is posed as regularized empirical risk minimization. Details of the algorithm for learning the model are outlined. Experiments demonstrate the performance of the learned model on real data.
An Analysis of Active Learning With Uniform Feature Noise

In active learning, the user sequentially chooses values for feature X and an oracle returns the corresponding label Y . In this paper, we consider the eect of feature noise in active learning, which could arise either because X itself is being measured, or it is corrupted in transmission to the oracle, or the oracle returns the label of a noisy version of the query point. In statistics, feature noise is known as \errors in variables" and has been studied extensively in non-active settings. However, the eect of feature noise in active learning has not been studied before. We consider the well-known Berkson errors-in-variables model with additive uniform noise of width .
Ehrhart Series of Polytopes Related to Symmetric Doubly-Stochastic Matrices

In Ehrhart theory, the $h^*$-vector of a rational polytope often provides insights into properties of the polytope that may be otherwise obscured. As an example, the Birkhoff polytope, also known as the polytope of real doubly-stochastic matrices, has a unimodal $h^*$-vector, but when even small modifications are made to the polytope, the same property can be very difficult to prove. In this paper, we examine the $h^*$-vectors of a class of polytopes containing real doubly-stochastic symmetric matrices.
Dynamical properties of a two-gene network with hysteresis

Motivated by the recent development of advanced experimental techniques in molecular biology, this paper focuses on the study of the dynamical properties of a two-gene regulatory network. A mathematical model for a two-gene regulatory network is derived and several of their properties are analyzed. Due to the presence of mixed continuous/discrete dynamics and hysteresis, we employ hybrid systems models to capture the dynamics of the system. The proposed model incorporates binary hysteresis with different thresholds capturing the interaction between the genes. We analyze properties of the solutions and asymptotic stability of equilibria in the system as a function of their parameters. As a difference to previous efforts employing piecewise-linear models, the analysis of our hybrid system model reveals the presence of limit cycles for a certain range of parameters, a behavior that is associated with the presence of hysteresis. The set of points defining the limit cycle is characterized and its asymptotic stability properties are studied. Furthermore, we determine conditions under which the stability properties of the limit cycle are robust to changes of parameters. Numerical simulations are presented to illustrate the findings.
Simplicial energy and simplicial harmonic maps

We introduce a combinatorial energy for maps of triangulated surfaces with simplicial metrics and analyze the existence and uniqueness properties of the corresponding harmonic maps. We show that some important applications of smooth harmonic maps can be obtained in this setting.
Joint Caching, Routing, and Channel Assignment for Collaborative Small-Cell Cellular Networks

We consider joint caching, routing, and channel assignment for video delivery over coordinated small-cell cellular systems of the future Internet. We formulate the problem of maximizing the throughput of the system as a linear program, in which the number of variables is very large. To address channel interference, our formulation incorporates the conflict graph that arises when wireless links interfere with each other due to simultaneous transmission. We utilize the column generation method to solve the problem by breaking it into a restricted master subproblem that involves a select subset of variables and a collection of pricing subproblems that select the new variable to be introduced into the restricted master problem, if that leads to a better objective function value. To control the complexity of the column generation optimization further, due to the exponential number of independent sets that arise from the conflict graph, we introduce an approximation algorithm that computes a solution that is within $\epsilon $ to optimality, at much lower complexity. Our framework demonstrates considerable gains in average transmission rate at which the video data can be delivered to the users, over the state-of-the-art Femtocaching system, of up to 46%. These operational gains in system performance map to analogous gains in video application quality, thereby enhancing the user experience considerably.
Homogenization in perforated domains and interior Lipschitz estimates

Abstract We establish interior Lipschitz estimates at the macroscopic scale for solutions to systems of linear elasticity with rapidly oscillating periodic coefficients and mixed boundary conditions in domains periodically perforated at a microscopic scale e by establishing H 1 -convergence rates for such solutions. The interior estimates are derived directly without the use of compactness via an argument presented in [3] that was adapted for elliptic equations in [2] and [11] . As a consequence, we derive a Liouville type estimate for solutions to the systems of linear elasticity in unbounded periodically perforated domains.
CHARACTERIZING GORENSTEIN RINGS USING CONTRACTING ENDOMORPHISMS

Abstract We prove several characterizations of Gorenstein rings in terms of vanishings of derived functors of certain modules or complexes whose scalars are restricted via contracting endomorphisms. These results can be viewed as analogues of results of Kunz (in the case of the Frobenius) and Avramov–Hochster–Iyengar–Yao (in the case of general contracting endomorphisms).
The Problem of Analogical Inference in Inductive Logic.

We consider one problem that was largely left open by Rudolf Carnap in his work on inductive logic, the problem of analogical inference. After discussing some previous attempts to solve this problem, we propose a new solution that is based on the ideas of Bruno de Finetti on probabilistic symmetries. We explain how our new inductive logic can be developed within the Carnapian paradigm of inductive logic-deriving an inductive rule from a set of simple postulates about the observational process-and discuss some of its properties.
Hilbert series and degree bounds for matrix (semi-)invariants

Abstract We study the ring R ( n , m ) of invariants for the left–right action of SL n × SL n on m-tuples of n × n complex matrices. We show that R ( 3 , m ) is generated by invariants of degree ≤309 for all m. Then, we use a combinatorial description of the invariants to show that R ( n , m ) cannot be generated by invariants of degree n 2 for large m. We also compute the Hilbert series for several cases.
On the ability of neural nets to express distributions

Deep neural nets have caused a revolution in many classification tasks. A related ongoing revolution -- also theoretically not understood -- concerns their ability to serve as generative models for complicated types of data such as images and texts. These models are trained using ideas like variational autoencoders and Generative Adversarial Networks. We take a first cut at explaining the expressivity of multilayer nets by giving a sufficient criterion for a function to be approximable by a neural network with $n$ hidden layers. A key ingredient is Barron's Theorem \cite{Barron1993}, which gives a Fourier criterion for approximability of a function by a neural network with 1 hidden layer. We show that a composition of $n$ functions which satisfy certain Fourier conditions ("Barron functions") can be approximated by a $n+1$-layer neural network. For probability distributions, this translates into a criterion for a probability distribution to be approximable in Wasserstein distance -- a natural metric on probability distributions -- by a neural network applied to a fixed base distribution (e.g., multivariate gaussian). Building up recent lower bound work, we also give an example function that shows that composition of Barron functions is more expressive than Barron functions alone.
A characterization of bi-Lipschitz embeddable metric spaces in terms of local bi-Lipschitz embeddability

We characterize uniformly perfect, complete, doubling metric spaces which embed bi- Lipschitzly into Euclidean space. Our result applies in particular to spaces of Grushin type equipped with Carnot-Carath\'eodory distance. Hence we obtain the first example of a sub-Riemannian mani- fold admitting such a bi-Lipschitz embedding. Our techniques involve a passage from local to global information, building on work of Christ and McShane. A new feature of our proof is the verification of the co-Lipschitz condition. This verification splits into a large scale case and a local case. These cases are distinguished by a relative distance map which is associated to a Whitney-type decom- position of an open subset {\Omega} of the space. We prove that if the Whitney cubes embed uniformly bi-Lipschitzly into a fixed Euclidean space, and if the complement of {\Omega} also embeds, then so does the full space.