cssi/SciSciGPT-SciSciNet huggingface dataset:
Synthesis of Porphyrins Bearing trans-Thiols

A route to porphyrins bearing trans-thiols is described using a thioacetyl-containing aldehyde or a thioacetyl-containing dipyrromethane in the presence of catalytic BF3·OEt2 followed by oxidation....
An automated, machine learning–based detection algorithm for spike‐wave discharges (SWDs) in a mouse model of absence epilepsy

Objective Manual detection of spike-wave discharges (SWDs) from electroencephalography (EEG) records is time intensive, costly, and subject to inconsistencies/biases. In addition, manual scoring often omits information on SWD confidence/intensity, which may be important for the investigation of mechanistic-based research questions. Our objective is to develop an automated method for the detection of SWDs in a mouse model of absence epilepsy that is focused on the characteristics of human scoring of preselected events to establish a confidence-based, continuous-valued scoring. Methods We develop a support vector machine (SVM)-based algorithm for the automated detection of SWDs in the γ2R43Q mouse model of absence epilepsy. The algorithm first identifies putative SWD events using frequency- and amplitude-based peak detection. Four humans scored a set of 2500 putative events identified by the algorithm. Then, using predictors calculated from the wavelet transform of each event and the labels from human scoring, we trained an SVM to classify (SWD/nonSWD) and assign confidence scores to each event identified from 60, 24-hour EEG records. We provide a detailed assessment of intra- and interrater scoring that demonstrates advantages of automated scoring. Results The algorithm scored SWDs along a continuum that is highly correlated with human confidence and that allows us to more effectively characterize ambiguous events. We demonstrate that events along our scoring continuum are temporally and proportionately correlated with abrupt changes in spectral power bands relevant to normal behavioral states including sleep. Significance Although there are automated and semi-automated methods for the detection of SWDs in humans and rats, we contribute to the need for continued development of SWD detection in mice. Our results demonstrate the value of viewing detection of SWDs as a continuous classification problem to better understand "ground truth" in SWD detection (ie, the most reliable features agreed upon by humans that also correlate with objective physiologic measures).
Ab initio chemical kinetics for ClO reactions with HOx, ClOx and NOx (x = 1, 2): A review

Abstract Six reaction systems relevant to the atmosphere and the ammonium perchlorate combustion chemistry have been studied. The systems include the bimolecular reactions of ClO with HO, HO 2 , ClO, OClO, NO and NO 2 and some of their reverse processes. The geometries of the reactants, intermediates, transition states and products involved in these reactions were optimized at the B3LYP/6-311+G(3df, 2p) level and final energies were refined at the modified Gaussian – 2 (G2M) or CCSD(T)/6-311+G(3df, 2p) level. Temperature/pressure-dependent rate constants for major product channels have been predicted and compared with the available experimental data. Detailed mechanisms for these reactions have been discussed on the basis of predicted potential energy surfaces. The calculated geometrical parameters, heats of formation and rate constants are quite satisfactory and in good agreement with available experimental data. For practical applications, the heats of formation of the key species, and the rate constants for all the major reactions discussed under different conditions have been recommended.
Accelerating Learning in Active Management: The Alpha-Brier Process

Forecasting tournaments have shown it is possible to improve the accuracy of forecasts of real-world events that sophisticated observers often supposed are too idiosyncratic to be pinned down by numerical probabilities. Building on this research program, the authors propose the Alpha-Brier process to help firms improve forecasts guiding investment decisions. Alpha-Brier offers four major benefits: (1) It reduces the noisiness of vague-verbiage forecasts, such as X “might” or “could” happen, that are open to varying interpretations; (2) it makes it easier to distinguish skill from luck as drivers of portfolio performance; (3) it gives investors faster feedback on the accuracy of their probability judgments; and (4) it lets managers test which methods of training, incentivizing, and aggregating judgments deliver the biggest boosts to accuracy. Paradoxically, the more pervasive the skepticism toward the core premise of Alpha-Brier that probability judgments can be extended to superficially unique events, the more opportunities there will be for firms to exploit market inefficiencies linked to overreliance on vague-verbiage forecasts. TOPICS:Statistical methods, portfolio construction, performance measurement
Scalable Bayesian Variable Selection Using Nonlocal Prior Densities in Ultrahigh-Dimensional Settings

Bayesian model selection procedures based on nonlocal alternative prior densities are extended to ultrahigh dimensional settings and compared to other variable selection procedures using precision-recall curves. Variable selection procedures included in these comparisons include methods based on g-priors, reciprocal lasso, adaptive lasso, scad, and minimax concave penalty criteria. The use of precision-recall curves eliminates the sensitivity of our conclusions to the choice of tuning parameters. We find that Bayesian variable selection procedures based on nonlocal priors are competitive to all other procedures in a range of simulation scenarios, and we subsequently explain this favorable performance through a theoretical examination of their consistency properties. When certain regularity conditions apply, we demonstrate that the nonlocal procedures are consistent for linear models even when the number of covariates p increases sub-exponentially with the sample size n. A model selection procedure based on Zellner's g-prior is also found to be competitive with penalized likelihood methods in identifying the true model, but the posterior distribution on the model space induced by this method is much more dispersed than the posterior distribution induced on the model space by the nonlocal prior methods. We investigate the asymptotic form of the marginal likelihood based on the nonlocal priors and show that it attains a unique term that cannot be derived from the other Bayesian model selection procedures. We also propose a scalable and efficient algorithm called Simplified Shotgun Stochastic Search with Screening (S5) to explore the enormous model space, and we show that S5 dramatically reduces the computing time without losing the capacity to search the interesting region in the model space, at least in the simulation settings considered. The S5 algorithm is available in an R package BayesS5 on CRAN.
Millimeter-Wave Human Blockage at 73 GHz with a Simple Double Knife-Edge Diffraction Model and Extension for Directional Antennas

This paper presents 73 GHz human blockage measurements for a point-to-point link with a 5 m transmitter-receiver separation distance in an indoor environment, with a human that walked at a speed of approximately 1 m/s at a perpendicular orientation to the line between the transmitter and receiver, at various distances between them. The experiment measures the shadowing effect of a moving human body when using directional antennas at the transmitter and receiver for millimeter- wave radio communications. The measurements were conducted using a 500 Megachips-per-second wideband correlator channel sounder with a 1 GHz first null-to-null RF bandwidth. Results indicate high shadowing attenuation is not just due to the human blocker but also is due to the static directional nature of the antennas used, leading to the need for phased-array antennas to switch beam directions in the presence of obstructions and blockages at millimeter-waves. A simple model for human blockage is provided based on the double knife-edge diffraction (DKED) model where humans are approximated by a rectangular screen with infinite vertical height, similar to the human blockage model given by the METIS project.
Three stories on a two-sided coin: Index coding, locally recoverable distributed storage, and guessing games on graphs

Three science and engineering problems of recent interests—index coding, locally recoverable distributed storage, and guessing games on graphs—are discussed and the connection between their optimal solutions is elucidated. By generalizing recent results by Shanmugam and Dimakis and by Mazumdar on the complementarity between the optimal broadcast rate of an index coding problem on a directed graph and the normalized rate of a locally recoverable distributed storage problem on the same graph, it is shown that the capacity region and the optimal rate region of these two problems are complementary. The main ingredients in establishing this result are the notion of confusion graph introduced by Alon et al. (2008), the vertex transitivity of a confusion graph, the characterization of the index coding capacity region via the fractional chromatic number of confusion graphs, and the characterization of the optimal rate region of the locally recoverable distributed storage via the independence number of confusion graphs. As the third and final facet of the complementarity, guessing games on graphs by Riis are discussed as special cases of the locally recoverable distributed storage problem, and it is shown that the winning probability of the optimal strategy for a guessing game and the ratio between the winning probabilities of the optimal strategy and a random guess can be characterized, respectively, by the capacity region for index coding and the optimal rate region for distributed storage.
Near-Optimal Representation Learning for Hierarchical Reinforcement Learning

We study the problem of representation learning in goal-conditioned hierarchical reinforcement learning. In such hierarchical structures, a higher-level controller solves tasks by iteratively communicating goals which a lower-level policy is trained to reach. Accordingly, the choice of representation -- the mapping of observation space to goal space -- is crucial. To study this problem, we develop a notion of sub-optimality of a representation, defined in terms of expected reward of the optimal hierarchical policy using this representation. We derive expressions which bound the sub-optimality and show how these expressions can be translated to representation learning objectives which may be optimized in practice. Results on a number of difficult continuous-control tasks show that our approach to representation learning yields qualitatively better representations as well as quantitatively better hierarchical policies, compared to existing methods (see videos at this https URL).
Damping Effect on PageRank Distribution

We extend the personalized PageRank model invented by Brin and Page to a model family, endowing each model with a characteristic damping scheme. On social bio-physical networks of today, actions, reactions and counteractions vary or unfold more than ever. It is imperative to advance modeling methodology and enrich model repertoire in order to capture or uncover, differentiate and recognize various network phenomenons and propagation patterns. We investigate the response in PageRank distribution to inter- and intra-model variation in damping. Our investigation leads to new theoretical and empirical findings. In empirical study, we use quantitative measures to assess damping effect of 3 particular models on 6 large realworld link graphs. It is found that the patterns of PageRank vectors vary more distinctively among the 3 models on each graph than among the 6 graphs with each model. This suggests the utility of model variety for differentiating network activities and propagation patterns. Our quantitative analysis of damping effect, over many model and parameter changes, is facilitated by a highly efficient algorithm, which calculates all PageRank vectors at once via a commonly shared, spectrally invariant subspace. The spectral space is found to be of low dimension with each of the real-world link graphs.
Ladder Networks for Emotion Recognition: Using Unsupervised Auxiliary Tasks to Improve Predictions of Emotional Attributes.

Recognizing emotions using few attribute dimensions such as arousal, valence and dominance provides the flexibility to effectively represent complex range of emotional behaviors. Conventional methods to learn these emotional descriptors primarily focus on separate models to recognize each of these attributes. Recent work has shown that learning these attributes together regularizes the models, leading to better feature representations. This study explores new forms of regularization by adding unsupervised auxiliary tasks to reconstruct hidden layer representations. This auxiliary task requires the denoising of hidden representations at every layer of an auto-encoder. The framework relies on ladder networks that utilize skip connections between encoder and decoder layers to learn powerful representations of emotional dimensions. The results show that ladder networks improve the performance of the system compared to baselines that individually learn each attribute, and conventional denoising autoencoders. Furthermore, the unsupervised auxiliary tasks have promising potential to be used in a semi-supervised setting, where few labeled sentences are available.
Estimates for character sums with various convolutions

We provide estimates for sums of the form \[\left|\sum_{a\in A}\sum_{b\in B}\sum_{c\in C}\chi(a+b+c)\right|\] and \[\left|\sum_{a\in A}\sum_{b\in B}\sum_{c\in C}\sum_{d\in D}\chi(a+b+cd)\right|\] when $A,B,C,D\subset \mathbb F_p$, the field with $p$ elements and $\chi$ is a non-trivial multiplicative character modulo $p$.
The Consequences of Student Loan Credit Expansions: Evidence From Three Decades of Default Cycles

Abstract This paper studies the link between credit availability and student loan repayment using administrative federal student loan data. We demonstrate that policy-driven changes in credit available to high-default institutions explains almost all of the historical time-series variation in defaults. Between 1981 and 1988, eligibility for federal loans was expanded, leading to the entry of institutions with borrowers more likely to default. From 1988 to 1992, credit access was tightened, leading to the exit of many institutions with high default rates. After 1992, the cycle was repeated, with credit access gradually loosened by unwinding many of the pre-1992 reforms.
Chiral algebras in Landau-Ginzburg models

Chiral algebras in the cohomology of the $$ {\overline{Q}}_{+} $$ supercharge of two-dimensional $$ \mathcal{N}=\left(0,2\right) $$ theories on flat spacetime are discussed. Using the supercurrent multiplet, we show that the answer is renormalization group invariant for theories with an R-symmetry. For $$ \mathcal{N}=\left(0,2\right) $$ Landau-Ginzburg models, the chiral algebra is determined by the operator equations of motion, which preserve their classical form, and quantum renormalization of composite operators. We study these theories and then specialize to the $$ \mathcal{N}=\left(2,2\right) $$ models and consider some examples.
Balancing Communication and Computation in Distributed Optimization

Methods for distributed optimization have received significant attention in recent years owing to their wide applicability in various domains including machine learning, robotics, and sensor networks. A distributed optimization method typically consists of two key components: communication and computation. More specifically, at every iteration (or every several iterations) of a distributed algorithm, each node in the network requires some form of information exchange with its neighboring nodes (communication) and the computation step related to a (sub)-gradient (computation). The standard way of judging an algorithm via only the number of iterations overlooks the complexity associated with each iteration. Moreover, various applications deploying distributed methods may prefer a different composition of communication and computation. Motivated by this discrepancy, in this paper, we propose an adaptive cost framework that adjusts the cost measure depending on the features of various applications. We present a flexible algorithmic framework, where communication and computation steps are explicitly decomposed to enable algorithm customization for various applications. We apply this framework to the well-known distributed gradient descent (DGD) method, and show that the resulting customized algorithms, which we call DGD $^t$ , NEAR-DGD $^t$ , and NEAR-DGD $^+$ , compare favorably to their base algorithms, both theoretically and empirically. The proposed NEAR-DGD $^+$ algorithm is an exact first-order method where the communication and computation steps are nested, and when the number of communication steps is adaptively increased, the method converges to the optimal solution. We test the performance and illustrate the flexibility of the methods, as well as practical variants, on quadratic functions and classification problems that arise in machine learning, in terms of iterations, gradient evaluations, communications, and the proposed cost framework.
Simple certificate of solvability of power flow equations for distribution systems

Power flow solvable boundary plays an important role in contingency analysis, security assessment, and planning processes. However, to construct the real solvable boundary in multidimensional parameter space is burdensome and time consuming. In this paper, we develop a new technique to approximate the solvable boundary of distribution systems based on Banach fixed point theorem. Not only the new technique is fast and non-iterative, but also the approximated boundary is more valuable to system operators in the sense that it is closer to the feasible region. Moreover, a simple solvable criterion is also introduced that can serve as a security constraint in various planning and operational problems.
Embeddedness of least area minimal hypersurfaces

In “Simple closed geodesics on convex surfaces” [J. Differential Geom., 36(3):517–549, 1992], E. Calabi and J. Cao showed that a closed geodesic of least length in a two-sphere with nonnegative curvature is always simple. Using min-max theory, we prove that for some higher dimensions, this result holds without assumptions on the curvature. More precisely, in a closed $(n+1)$-manifold with $2 \leq n \leq 6$, a least area closed minimal hypersurface exists and any such hypersurface is embedded. As an application, we give a short proof of the fact that if a closed three-manifold $M$ has scalar curvature at least $6$ and is not isometric to the round three-sphere, then $M$ contains an embedded closed minimal surface of area less than $4 \pi$. This confirms a conjecture of F. C. Marques and A. Neves.
Scattering resonances as viscosity limits

Using the method of complex scaling we show that scattering resonances of \( - \Delta + V \), \( V \in L^\infty _\mathrm{{c}} ( {\mathbb {R}}^n ) \), are limits of eigenvalues of \( - \Delta + V - i \varepsilon x^2 \) as \( \varepsilon \rightarrow 0+\). That justifies a method proposed in computational chemistry and reflects a general principle for resonances in other settings.
Adaptive sampling for rapidly matching histograms

In exploratory data analysis, analysts often have a need to identify histograms that possess a specific distribution, among a large class of candidate histograms, e.g., find countries whose income distribution is most similar to that of Greece. This distribution could be a new one that the user is curious about, or a known distribution from an existing histogram visualization. At present, this process of identification is brute-force, requiring the manual generation and evaluation of a large number of histograms. We present FastMatch: an end-to-end approach for interactively retrieving the histogram visualizations most similar to a user-specified target, from a large collection of histograms. The primary technical contribution underlying FastMatch is a probabilistic algorithm, HistSim, a theoretically sound sampling-based approach to identify the top-k closest histograms under e1 distance. While HistSim can be used independently, within FastMatch we couple HistSim with a novel system architecture that is aware of practical considerations, employing asynchronous block-based sampling policies. FastMatch obtains near-perfect accuracy with up to 35× speedup over approaches that do not use sampling on several real-world datasets.
A unifying formalism for shortest path problems with expensive edge evaluations via lazy best-first search over paths with edge selectors

While the shortest path problem has myriad applications, the computational efficiency of suitable algorithms depends intimately on the underlying problem domain. In this paper, we focus on domains where evaluating the edge weight function dominates algorithm running time. Inspired by approaches in robotic motion planning, we define and investigate the Lazy Shortest Path class of algorithms which is differentiated by the choice of an edge selector function. We show that several algorithms in the literature are equivalent to this lazy algorithm for appropriate choice of this selector. Further, we propose various novel selectors inspired by sampling and statistical mechanics, and find that these selectors outperform existing algorithms on a set of example problems.
The LORACs Prior for VAEs: Letting the Trees Speak for the Data

In variational autoencoders, the prior on the latent codes $z$ is often treated as an afterthought, but the prior shapes the kind of latent representation that the model learns. If the goal is to learn a representation that is interpretable and useful, then the prior should reflect the ways in which the high-level factors that describe the data vary. The ``default'' prior is a standard normal, but if the natural factors of variation in the dataset exhibit discrete structure or are not independent, then the isotropic-normal prior will actually encourage learning representations that \emph{mask} this structure. To alleviate this problem, we propose using a flexible Bayesian nonparametric hierarchical clustering prior based on the time-marginalized coalescent (TMC). To scale learning to large datasets, we develop a new inducing-point approximation and inference algorithm. We then apply the method without supervision to several datasets and examine the interpretability and practical performance of the inferred hierarchies and learned latent space.
Integral of two-loop modular graph functions

The integral of an arbitrary two-loop modular graph function over the fundamental domain for SL(2, ℤ) in the upper half plane is evaluated using recent results on the Poincare series for these functions.
Neural network gradient Hamiltonian Monte Carlo

Hamiltonian Monte Carlo is a widely used algorithm for sampling from posterior distributions of complex Bayesian models. It can efficiently explore high-dimensional parameter spaces guided by simulated Hamiltonian flows. However, the algorithm requires repeated gradient calculations, and these computations become increasingly burdensome as data sets scale. We present a method to substantially reduce the computation burden by using a neural network to approximate the gradient. First, we prove that the proposed method still maintains convergence to the true distribution though the approximated gradient no longer comes from a Hamiltonian system. Second, we conduct experiments on synthetic examples and real data to validate the proposed method.
A Deep Unsupervised Learning Approach Toward MTBI Identification Using Diffusion MRI

Mild traumatic brain injury is a growing public health problem with an estimated incidence of over 1.7 million people annually in US. Diagnosis is based on clinical history and symptoms, and accurate, concrete measures of injury are lacking. This work aims to directly use diffusion MR images obtained within one month of trauma to detect injury, by incorporating deep learning techniques. To overcome the challenge due to limited training data, we describe each brain region using the bag of word representation, which specifies the distribution of representative patch patterns. We apply a convolutional auto-encoder to learn the patch-level features, from overlapping image patches extracted from the MR images, to learn features from diffusion MR images of brain using an unsupervised approach. Our experimental results show that the bag of word representation using patch level features learnt by the auto encoder provides similar performance as that using the raw patch patterns, both significantly outperform earlier work relying on the mean values of MR metrics in selected brain regions.
Long rainbow cycles and Hamiltonian cycles using many colors in properly edge-colored complete graphs

Abstract We prove two results regarding cycles in properly edge-colored graphs. First, we make a small improvement to the recent breakthrough work of Alon, Pokrovskiy and Sudakov who showed that every properly edge-colored complete graph G on n vertices has a rainbow cycle on at least n − O ( n 3 ∕ 4 ) vertices, by showing that G has a rainbow cycle on at least n − O ( log n n ) vertices. Second, by modifying the argument of Hatami and Shor which gives a lower bound for the length of a partial transversal in a Latin Square, we prove that every properly colored complete graph has a Hamiltonian cycle in which at least n − O ( ( log n ) 2 ) different colors appear. For large n , this is an improvement of the previous best known lower bound of n − 2 n of Andersen.
Complex varieties with infinite Chow groups modulo 2

For a very general principally polarized complex abelian 3-fold, the Chow group of algebraic cycles is innite modulo every prime number. In particular, this gives the
Analyzing the Robustness of Nearest Neighbors to Adversarial Examples

Motivated by safety-critical applications, test-time attacks on classifiers via adversarial examples has recently received a great deal of attention. However, there is a general lack of understanding on why adversarial examples arise; whether they originate due to inherent properties of data or due to lack of training samples remains ill-understood. In this work, we introduce a theoretical framework analogous to bias-variance theory for understanding these effects. We use our framework to analyze the robustness of a canonical non-parametric classifier - the k-nearest neighbors. Our analysis shows that its robustness properties depend critically on the value of k - the classifier may be inherently non-robust for small k, but its robustness approaches that of the Bayes Optimal classifier for fast-growing k. We propose a novel modified 1-nearest neighbor classifier, and guarantee its robustness in the large sample limit. Our experiments suggest that this classifier may have good robustness properties even for reasonable data set sizes.
The Frobenius complexity of a local ring of prime characteristic

Abstract We introduce a new invariant for local rings of prime characteristic, called Frobenius complexity, that measures the abundance of Frobenius actions on the injective hull of the residue field of a local ring. We present an important case where the Frobenius complexity is finite, and prove that complete, normal rings of dimension two or less have Frobenius complexity less than or equal to zero. Moreover, we compute the Frobenius complexity for the determinantal ring obtained by modding out the 2 × 2 minors of a 2 × 3 matrix of indeterminates, showing that this number can be positive, irrational and depends upon the characteristic. We also settle a conjecture of Katzman, Schwede, Singh and Zhang on the infinite generation of the ring of Frobenius operators of a local normal complete Q -Gorenstein ring.
On the rate of convergence of strong Euler approximation for SDEs driven by Levy processes

A SDE driven by an -stable process, with a Lipshitz continuous coefficient and a -Holder drift is considered. The existence and uniqueness of a strong solution is proved when by showing that it is the -limit of Euler approximations. The -error (rate of convergence) is obtained for a nondegenerate truncated and nontruncated driving process. The rate in the case of Lipshitz continuous coefficients is derived as well.
Biphoton statistic of quantum light generated on a silicon chip

We demonstrate a silicon-chip biphoton source with an unprecedented quantum cross-correlation up to gsi(2)(0) = (2.58 ± 0.16) × 104. The emitted photons are within single whispering gallery mode with self-correlations of gss(2)(0) = 1.90 ± 0.05 and gii(2)(0) = 1.87 ± 0.06 for signal and idler photons, respectively. We observe the waveform asymmetry of cross-correlation between signal and idler photons and reveal the identical and nonexponential nature of self-correlations of individual signal and idler photon modes, which is the nature of cavity-enhanced nonlinear optical processes. The high efficiency and high purity of the biphoton source allow us to herald single photons with a conditional self-correlation gc(2)(0) as low as 0.0059 ± 0.0014 at a pair flux of 1.95 × 105 pairs/s, which remains below 0.026 ± 0.001 for a biphoton flux up to 2.93 × 106 pairs/s with a tunable photon preparation efficiency in the single-mode fiber up to 51% and a raw heralding efficiency up to 3.4%. Our work unambiguously dem...
Stable absorbing boundary conditions for molecular dynamics in general domains

A systematic strategy of absorbing boundary conditions for molecular dynamics simulations are presented. The exact boundary conditions for crystalline solids with harmonic approximation are expressed as a dynamic Dirichlet-to-Neumann (DtN) map. It connects the displacement of the atoms at the boundary to the traction on these atoms. The DtN map is valid for a domain with general geometry. To avoid evaluating the time convolution of the dynamic DtN map, we approximate the associated kernel function by rational functions in the Laplace domain. The parameters in the approximations are determined by interpolations. The explicit forms of the zeroth, first, and second order approximations will be presented. The stability of the molecular dynamics model, supplemented with these absorbing boundary conditions is established. Two numerical simulations are performed to demonstrate the effectiveness of the methods.
Multi-agent constrained optimization of a strongly convex function over time-varying directed networks

We consider cooperative multi-agent consensus optimization problems over undirected and directed time-varying communication networks, where only local communications are allowed. The objective is to minimize the sum of agent-specific possibly non-smooth composite convex functions over agent-specific private conic constraint sets; hence, the optimal consensus decision should lie in the intersection of these private sets. Assuming the sum function is strongly convex, we provide convergence rates in sub-optimality, infeasibility and consensus violation; examine the effect of underlying network topology on the convergence rates of the proposed decentralized algorithm.
Exponential Growth in Two-Dimensional Topological Fluid Dynamics

Abstract This paper describes topological kinematics associated with the stirring by rods of a two-dimensional fluid. The main tool is theThurston-Nielsen (TN) theory which implies that depending on the stirring protocol the essential topological length of material lines grows either exponentially or linearly. We give an application to the growth of the gradient of a passively advected scalar, the Helmholtz-Kelvin Theorem then yields applications to Euler flows. The main theorem shows that there are periodic stirring protocols for which generic initial vorticity yields a solution to Euler's equations which is not periodic and further, the L ∞ and L 1 -norms of the gradient of its vorticity grow exponentially in time.
Restricted Boltzmann Machine for Classification with Hierarchical Correlated Prior.

Restricted Boltzmann machines (RBM) and its variants have become hot research topics recently, and widely applied to many classification problems, such as character recognition and document categorization. Often, classification RBM ignores the interclass relationship or prior knowledge of sharing information among classes. In this paper, we are interested in RBM with the hierarchical prior over classes. We assume parameters for nearby nodes are correlated in the hierarchical tree, and further the parameters at each node of the tree be orthogonal to those at its ancestors. We propose a hierarchical correlated RBM for classification problem, which generalizes the classification RBM with sharing information among different classes. In order to reduce the redundancy between node parameters in the hierarchy, we also introduce orthogonal restrictions to our objective function. We test our method on challenge datasets, and show promising results compared to competitive baselines.
Model-Independent Analytic Nonlinear Blind Source Separation

Consider a time series of signal measurements, x(t), where x has two or more components. This paper shows how to perform nonlinear blind source separation; i.e., how to determine if these signals are equal to linear or nonlinear mixtures of the state variables of two or more statistically independent subsystems. First, the local distributions of measurement velocities are processed in order to derive vectors at each point in x-space. If the data are separable, each of these vectors must be directed along a subspace of \(x \text{-space }\) that is traversed by varying the state variable of one subsystem, while all other subsystems are kept constant. Because of this property, these vectors can be used to construct a small set of mappings, which must contain the “unmixing” function, if it exists. Therefore, nonlinear blind source separation can be performed by examining the separability of the data after they have been transformed by each of these mappings. The method is analytic, constructive, and model-independent. It is illustrated by blindly recovering the separate utterances of two speakers from nonlinear combinations of their audio waveforms.
Prescribing the behavior of Weil–Petersson geodesics in the moduli space of Riemann surfaces

We study Weil–Petersson (WP) geodesics with narrow end invariant and develop techniques to control length-functions and twist parameters along them and prescribe their itinerary in the moduli space of Riemann surfaces. This class of geodesics is rich enough to provide for examples of closed WP geodesics in the thin part of the moduli space, as well as divergent WP geodesic rays with minimal filling ending lamination. Some ingredients of independent interest are the following: A strength version of Wolpert's Geodesic Limit Theorem proved in Sec. 4. The stability of hierarchy resolution paths between narrow pairs of partial markings or laminations in the pants graph proved in Sec. 5. A kind of symbolic coding for laminations in terms of subsurface coefficients presented in Sec. 7.
A provable approach for double-sparse coding

Sparse coding is a crucial subroutine in algorithms for various signal processing, deep learning, and other machine learning applications. The central goal is to learn an overcomplete dictionary that can sparsely represent a given dataset. However, storage, transmission, and processing of the learned dictionary can be untenably high if the data dimension is high. In this paper, we consider the double-sparsity model introduced by Rubinstein, Zibulevsky, and Elad (2010) where the dictionary itself is the product of a fixed, known basis and a data-adaptive sparse component. First, we introduce a simple algorithm for double-sparse coding that can be amenable to efficient implementation via neural architectures. Second, we theoretically analyze its performance and demonstrate asymptotic sample complexity and running time benefits over existing (provable) approaches for sparse coding. To our knowledge, our work introduces the first computationally efficient algorithm for double-sparse coding that enjoys rigorous statistical guarantees. Finally, we support our analysis via several numerical experiments on simulated data, confirming that our method can indeed be useful in problem sizes encountered in practical applications.
Free resolutions and sparse determinantal ideals

A sparse generic matrix is a matrix whose entries are distinct variables and zeros. Such matrices were studied by Giusti and Merle who computed some invariants of their ideals of maximal minors. In this paper we extend these results by computing a minimal free resolution for all such sparse determinantal ideals. We do so by introducing a technique for pruning minimal free resolutions when a subset of the variables is set to zero. Our technique correctly computes a minimal free resolution in two cases of interest: resolutions of monomial ideals, and ideals resolved by the Eagon-Northcott Complex. As a consequence we can show that sparse determinantal ideals have a linear resolution over the integers, and that the projective dimension depends only on the number of columns of the matrix which are identically zero. Finally, we show that all such ideals have the property that regardless of the term order chosen, the Betti numbers of the ideal and its initial ideal are the same. In particular the nonzero generators of these ideals form a universal Grobner basis.
Tight chiral polyhedra

A chiral polyhedron with Schlafli symbol {p,q} is called tight if it has 2pq flags, which is the minimum possible. In this paper, we fully characterize the Schlafli symbols of tight chiral polyhedra. We also provide presentations for the automorphism groups of several families of tight chiral polyhedra.
Privacy Verification in POMDPs via Barrier Certificates

Privacy is an increasing concern in cyber-physical systems that operates over a shared network. In this paper, we propose a method for privacy verification of cyber-physical systems modeled by Markov decision processes (MDPs) and partially-observable Markov decision processes (POMDPs) based on barrier certificates. To this end, we consider an opacity-based notion of privacy, which is characterized by the beliefs in system states. We show that the belief update equations can be represented as discrete-time switched systems, for which we propose a set of conditions for privacy verification in terms of barrier certificates. We further demonstrate that, for MDPs and for POMDPs, privacy verification can be computationally implemented by solving a set of semi-definite programs and sum-of-squares programs, respectively. The method is illustrated by an application to privacy verification of an inventory management system.
Equivariant sl.n/-link homology

For every positive integer $n$ we construct a bigraded homology theory for links, such that the corresponding invariant of the unknot is closely related to the U(n)-equivariant cohomology ring of $\mathbb{CP}^{n-1}$; our construction specializes to the Khovanov-Rozansky $sl_n$-homology. We are motivated by the "universal" rank two Frobenius extension studied by M. Khovanov in \cite{Kh3} for $sl_2$-homology.
Backprop KF: learning discriminative deterministic state estimators

Generative state estimators based on probabilistic filters and smoothers are one of the most popular classes of state estimators for robots and autonomous vehicles. However, generative models have limited capacity to handle rich sensory observations, such as camera images, since they must model the entire distribution over sensor readings. Discriminative models do not suffer from this limitation, but are typically more complex to train as latent variable models for state estimation. We present an alternative approach where the parameters of the latent state distribution are directly optimized as a deterministic computation graph, resulting in a simple and effective gradient descent algorithm for training discriminative state estimators. We show that this procedure can be used to train state estimators that use complex input, such as raw camera images, which must be processed using expressive nonlinear function approximators such as convolutional neural networks. Our model can be viewed as a type of recurrent neural network, and the connection to probabilistic filtering allows us to design a network architecture that is particularly well suited for state estimation. We evaluate our approach on synthetic tracking task with raw image inputs and on the visual odometry task in the KITTI dataset. The results show significant improvement over both standard generative approaches and regular recurrent neural networks.
Canonical estimation in a rare-events regime

We propose a general methodology for performing statistical inference within a ‘rare-events regime’ that was recently suggested by Wagner, Viswanath and Kulkarni. Our approach allows one to easily establish consistent estimators for a very large class of canonical estimation problems, in a large alphabet setting. These include the problems studied in the original paper, such as entropy and probability estimation, in addition to many other interesting ones. We particularly illustrate this approach by consistently estimating the size of the alphabet and the range of the probabilities. We start by proposing an abstract methodology based on constructing a probability measure with the desired asymptotic properties. We then demonstrate two concrete constructions by casting the Good-Turing estimator as a pseudo-empirical measure, and by using the theory of mixture model estimation.
On a remarkable formula of Jerison and Lee in CR geometry

We discuss a remarkable formula discovered by Jerison and Lee to classify constant scalar curvature pseudohermitian structures on the sphere. We show that the formula is valid in the wider context of Einstein pseudohermitian manifolds. As an application we prove a uniqueness result that generalizes the theorem of Jerison and Lee.
Coboundary categories and local rules

First we develop the theory of local rules for coboundary categories. Then we describe the local rules in two main cases. First for the quantum groups in general and in the seminormal representations of the Hecke algebras. Then for crystals in general and specifically for crystals of minuscule representations. Finally we show how growth diagrams can be extended to construct the action of the cactus group on highest weight words.
A unified framework for polycrystal plasticity with grain boundary evolution

Abstract Plastic deformation in polycrystals is governed by the interplay between intra-granular slip and grain boundary-mediated plasticity. However, while the role played by bulk dislocations is relatively well-understood, the contribution of grain boundaries (GBs) has only recently begun to be studied. GB plasticity is known to play a key role along with bulk plasticity under a wide range of conditions, such as dynamic recovery, superplasticity, severe plastic deformation, etc., and developing models capable of simultaneously capturing GB and bulk plasticity has become a topic of high relevance. In this paper we develop a thermodynamically-consistent polycrystal plasticity model capable of simulating a variety of grain boundary-mediated plastic processes in conjunction with bulk dislocation slip. The model starts from the description of a single crystal and creates lattice strain-free polycrystalline configurations by using a specially-designed multiplicative decomposition developed by the authors. This leads to the introduction of a particular class of geometrically necessary dislocations (GND) that define fundamental GB features such as misorientation and inclination. The evolution of the system is based on an energy functional that uses a non-standard function of the GND tensor to account for the grain boundary energy, as well as for the standard elastic energy. Our implementation builds on smooth descriptions of GBs inspired on diffuse-interface models of grain evolution for numerical convenience. We demonstrate the generality and potential of the methodology by simulating a wide variety of phenomena such as shear-induced GB sliding, coupled GB motion, curvature-induced grain rotation and shrinkage, and polygonization via dislocation sub-grain formation.
FLUCTUATIONS OF MATRIX ENTRIES OF ANALYTIC FUNCTIONS OF NON-HERMITIAN RANDOM MATRICES

Consider an n × n non-Hermitian random matrix Mn whose entries are independent real random variables. Under suitable conditions on the entries, we study the fluctuations of the entries of f(Mn) as n tends to infinity, where f is analytic on an appropriate domain. This extends the results in [19, 20, 23] from symmetric random matrices to the non-Hermitian case.
A rate-distortion based secrecy system with side information at the decoders

A secrecy system with side information at the decoders is studied in the context of lossy source compression over a noiseless broadcast channel. The decoders have access to different side information sequences that are correlated with the source. The fidelity of the communication to the legitimate receiver is measured by a distortion metric, as is traditionally done in the Wyner-Ziv problem. The secrecy performance of the system is also evaluated under a distortion metric. An achievable rate-distortion region is derived for the general case of arbitrarily correlated side information. Exact bounds are obtained for several special cases in which the side information satisfies certain constraints. An example is considered in which the side information sequences come from a binary erasure channel and a binary symmetric channel.
Active Learning of Dynamics for Data-Driven Control Using Koopman Operators

This paper presents an active learning strategy for robotic systems that takes into account task information, enables fast learning, and allows control to be readily synthesized by taking advantage of the Koopman operator representation. We first motivate the use of representing nonlinear systems as linear Koopman operator systems by illustrating the improved model-based control performance with an actuated Van der Pol system. Information-theoretic methods are then applied to the Koopman operator formulation of dynamical systems where we derive a controller for active learning of robot dynamics. The active learning controller is shown to increase the rate of information about the Koopman operator. In addition, our active learning controller can readily incorporate policies built on the Koopman dynamics, enabling the benefits of fast active learning and improved control. Results using a quadcopter illustrate single-execution active learning and stabilization capabilities during free fall. The results for active learning are extended for automating Koopman observables and we implement our method on real robotic systems.
Lifting GIS maps into strong geometric context for scene understanding

Contextual information can have a substantial impact on the performance of visual tasks such as semantic segmentation, object detection, and geometric estimation. Data stored in Geographic Information Systems (GIS) offers a rich source of contextual information that has been largely untapped by computer vision. We propose to leverage such information for scene understanding by combining GIS resources with large sets of unorganized photographs using Structure from Motion (SfM) techniques. We present a pipeline to quickly generate strong 3D geometric priors from 2D GIS data using SfM models aligned with minimal user input. Given an image resectioned against this model, we generate robust predictions of depth, surface normals, and semantic labels. Despite the lack of detail in the model, we show that the precision of the predicted geometry is substantially more accurate than other single-image depth estimation methods. We then demonstrate the utility of these contextual constraints for re-scoring pedestrian detections, and use these GIS contextual features alongside object detection score maps to improve a CRF-based semantic segmentation framework, boosting accuracy over baseline models.