cssi/SciSciGPT-SciSciNet huggingface dataset:
Prediction with missing data via Bayesian Additive Regression Trees

We present a method for incorporating missing data into general prediction problems which use nonparametric statistical learning. We focus on a tree-based method, Bayesian Additive Regression Trees (BART), enhanced with “Missingness Incorporated in Attributes,” a recently proposed approach for incorporating missingness into decision trees. This procedure extends the native partitioning mechanisms found in tree-based models and does not require imputation. Simulations on generated models and real data indicate that our procedure offers promise for both selection model and pattern-mixture frameworks as measured by out-of-sample predictive accuracy. We also illustrate BART's abilities to incorporate missingness into uncertainty intervals. Our implementation is readily available in the R package bartMachine. The Canadian Journal of Statistics 43: 224–239; 2015 © 2015 Statistical Society of Canada Resume Les auteurs presentent une methode qui permet d'inclure les donnees manquantes dans des problemes generaux de prevision a l'aide de l'apprentissage statistique non parametrique. Ils se concentrent sur les arbres de regression additifs bayesiens auxquels ils appliquent une approche recemment suggeree qui consiste a incorporer les valeurs manquantes aux attributs dans un modele d'arbre. Cette approche, qui ne necessite pas d'imputation, generalise le mecanisme de partitionnement utilise dans la construction de l'arbre. Grâce a des simulations et a l'analyse de donnees reelles, les auteurs constatent que leur methode offre des performances prometteuses en termes de taux de bonne classification mesure sur un echantillon test, autant dans un cadre de selection de variables que pour la reconnaissance de motifs. Ils illustrent egalement la capacite des arbres de regression additifs bayesiens a inclure les donnees manquantes dans les intervalles d'incertitude. Les auteurs fournissent une implementation de leur methode dans la bibliotheque de fonctions R qui s'intitule bartMachine. La revue canadienne de statistique 43: 224–239; 2015 © 2015 Societe statistique du Canada
Discriminative probabilistic models for relational data

In many supervised learning tasks, the entities to be labeled are related to each other in complex ways and their labels are not independent. For example, in hypertext classification, the labels of linked pages are highly correlated. A standard approach is to classify each entity independently, ignoring the correlations between them. Recently, Probabilistic Relational Models, a relational version of Bayesian networks, were used to define a joint probabilistic model for a collection of related entities. In this paper, we present an alternative framework that builds on (conditional) Markov networks and addresses two limitations of the previous approach. First, undirected models do not impose the acyclicity constraint that hinders representation of many important relational dependencies in directed models. Second, undirected models are well suited for discriminative training, where we optimize the conditional likelihood of the labels given the features, which generally improves classification accuracy. We show how to train these models effectively, and how to use approximate probabilistic inference over the learned model for collective classification of multiple related entities. We provide experimental results on a webpage classification task, showing that accuracy can be significantly improved by modeling relational dependencies.
Volume analysis of supercooled water under high pressure

Motivated by an experimental finding on the density of supercooled water at high pressure [O. Mishima, J. Chem. Phys. 133, 144503 (2010)] we performed atomistic molecular dynamics simulations study of bulk water in the isothermal-isobaric ensemble. Cooling and heating cycles at different isobars and isothermal compression at different temperatures are performed on the water sample with pressures that range from 0 to 1.0 GPa. The cooling simulations are done at temperatures that range from 40 K to 380 K using two different cooling rates, 10 K/ns and 10 K/5 ns. For the heating simulations we used the slowest heating rate (10 K/5 ns) by applying the same range of isobars. Our analysis of the variation of the volume of the bulk water sample with temperature at different pressures from both isobaric cooling/heating and isothermal compression cycles indicates a concave-downward curvature at high pressures that is consistent with the experiment for emulsified water. In particular, a strong concave down curvature is observed between the temperatures 180 K and 220 K. Below the glass transition temperature, which is around 180 K at 1GPa, the volume turns to concave upward curvature. No crystallization of the supercooled liquid state was observed below 180 K even after running the system for an additional microsecond.
Applied machine learning to predict stress hotspots II: Hexagonal close packed materials

Abstract Stress hotspots are regions of stress concentrations that form under deformation in polycrystalline materials. We use a machine learning approach to study the effect of preferred slip systems and microstructural features that reflect local crystallography, geometry, and connectivity on stress hotspot formation in hexagonal close packed materials under uniaxial tensile stress. We consider two cases: a hypothetical HCP material without any preferred slip systems with a critically resolved shear stress (CRSS) ratio of 1:1:1, and a second with CRSS ratio 0.1:1:3 for basal: prismatic: pyramidal slip systems. Random forest based machine learning models predict hotspot formation with an AUC (area under curve) score of 0.82 for the Equal CRSS and 0.81 for the Unequal CRSS cases. The results show how data driven techniques can be utilized to predict hotspots as well as pinpoint the microstructural features causing stress hotspot formation in polycrystalline microstructures.
Characterizing bounded orthogonally additive polynomials on vector lattices

We derive formulas for characterizing bounded orthogonally additive polynomials in two ways. Firstly, we prove that certain formulas for orthogonally additive polynomials derived in Kusraeva (Vladikavkaz Math J 16(4):49–53, 2014) actually characterize them. Secondly, by employing complexifications of the unique symmetric multilinear maps associated with orthogonally additive polynomials, we derive new characterizing formulas.
Finitistic Dimensions And Piecewise Hereditary Property Of Skew Group Algebras

Let Λ be a finite-dimensional algebra and G be a finite group whose elements act on Λ as algebra automorphisms. Assume that Λ has a complete set E of primitive orthogonal idempotents, closed under the action of a Sylow p-subgroup S ≤ G. If the action of S on E is free, we show that the skew group algebra Λ G and Λ have the same finitistic dimension, and have the same strong global dimension if the fixed algebra ΛS is a direct summand of the ΛS-bimodule Λ. Using a homological characterization of piecewise hereditary algebras proved by Happel and Zacharia, we deduce a criterion for Λ G to be piecewise hereditary.
Monte Carlo on Manifolds: Sampling Densities and Integrating Functions

We describe and analyze some Monte Carlo methods for manifolds in Euclidean space defined by equality and inequality constraints. First, we give an MCMC sampler for probability distributions defined by un-normalized densities on such manifolds. The sampler uses a specific orthogonal projection to the surface that requires only information about the tangent space to the manifold, obtainable from first derivatives of the constraint functions, hence avoiding the need for curvature information or second derivatives. Second, we use the sampler to develop a multi-stage algorithm to compute integrals over such manifolds. We provide single-run error estimates that avoid the need for multiple independent runs. Computational experiments on various test problems show that the algorithms and error estimates work in practice. The method is applied to compute the entropies of different sticky hard sphere systems. These predict the temperature or interaction energy at which loops of hard sticky spheres become preferable to chains.
Instability of nonlinear dispersive solitary waves

We consider linear instability of solitary waves of several classes of dispersive long wave models. They include generalizations of KDV, BBM, regularized Boussinesq equations, with general dispersive operators and nonlinear terms. We obtain criteria for the existence of exponentially growing solutions to the linearized problem. The novelty is that we dealt with models with nonlocal dispersive terms, for which the spectra problem is out of reach by the Evans function technique. For the proof, we reduce the linearized problem to study a family of nonlocal operators, which are closely related to properties of solitary waves. A continuation argument with a moving kernel formula is used to find the instability criteria. These techniques have also been extended to study instability of periodic waves and of the full water wave problem.
Recover and RELAX: concern-oriented software architecture recovery for systems development and maintenance

The stakeholders of a system are legitimately interested in whether and how its architecture reflects their respective concerns at each point of its development and maintenance processes. Having such knowledge available at all times would enable them to continually adjust their systems structure at each juncture and reduce the buildup of technical debt that can be hard to reduce once it has persisted over many iterations. Unfortunately, software systems often lack reliable and current documentation about their architecture. In order to remedy this situation, researchers have conceived a number of architectural recovery methods, some of them concern-oriented. However, the design choices forming the bases of most existing recovery methods make it so none of them have a complete set of desirable qualities for the purpose stated above. Tailoring a recovery to a system is either not possible or only through iterative experiments with numeric parameters. Furthermore, limitations in the scalability of the employed recovery algorithms make it prohibitive to apply the existing techniques to large systems. Finally, since several current recovery methods employ non-deterministic sampling, their inconsistent results do not lend themselves well to tracking a systems course over several versions, as needed by its stakeholders. RELAX (RELiable Architecture EXtraction), a new concern-based recovery method that uses text classification, addresses these issues efficiently (1) by assembling the overall recovery result from smaller, independent parts, (2) basing it on an algorithm with linear time complexity and (3) being tailorable to the recovery of a single system or a sequence thereof through the selection of meaningfully named, semantic topics. An intuitive and informative architectural visualization rounds out RELAX's contributions. RELAX is illustrated on a number of existing open-source systems and compared to other recovery methods.
The Douglas property for multiplier algebras of operators

Abstract For a collection of reproducing kernels k which includes those for the Hardy space of the polydisk and the ball and for the Bergman space, k is a complete Pick kernel if and only if the multiplier algebra of H 2 ( k ) has the Douglas property. Consequences for solving the operator equation A X = Y are examined.
Coordination using implicit communication

We explore a basic noise-free signaling scenario where coordination and communication are naturally merged. A random signal X 1 , …, X n is processed to produce a control signal or action sequence A 1 , …, A n , which is observed and further processed (without access to X 1 , …, X n ) to produce a third sequence B 1 , …, B n . The object of interest is the set of empirical joint distributions p(x, a, b) that can be achieved in this setting. We show that H(A) ≥ I(X;A,B) is the necessary and sufficient condition for achieving p(x, a, b) when no causality constraints are enforced on the encoders. We also give results for various causality constraints. This setting sheds light on the embedding of digital information in analog signals, a concept that is exploited in digital watermarking, steganography, cooperative communication, and strategic play in team games such as bridge.
Active diagnosis via AUC maximization: an efficient approach for multiple fault identification in large scale, noisy networks

The problem of active diagnosis arises in several applications such as disease diagnosis, and fault diagnosis in computer networks, where the goal is to rapidly identify the binary states of a set of objects (e.g., faulty or working) by sequentially selecting, and observing, (noisy) responses to binary valued queries. Current algorithms in this area rely on loopy belief propagation for active query selection. These algorithms have an exponential time complexity, making them slow and even intractable in large networks. We propose a rank-based greedy algorithm that sequentially chooses queries such that the area under the ROC curve of the rank-based output is maximized. The AUC criterion allows us to make a simplifying assumption that significantly reduces the complexity of active query selection (from exponential to near quadratic), with little or no compromise on the performance quality.
Robust tracking and behavioral modeling of movements of biological collectives from ordinary video recordings

We propose a novel computational method to extract information about interactions among individuals with different behavioral states in a biological collective from ordinary video recordings. Assuming that individuals are acting as finite state machines, our method first detects discrete behavioral states of those individuals and then constructs a model of their state transitions, taking into account the positions and states of other individuals in the vicinity. We have tested the proposed method through applications to two real-world biological collectives: termites in an experimental setting and human pedestrians in a university campus. For each application, a robust tracking system was developed in-house, utilizing interactive human intervention (for termite tracking) or online agent-based simulation (for pedestrian tracking). In both cases, significant interactions were detected between nearby individuals with different states, demonstrating the effectiveness of the proposed method.
Gauge Theory in Two Dimensions: Topological, Geometric and Probabilistic Aspects

Two dimensional Yang-Mills theory has proved to be a surprisingly rich model, despite, or possibly because of, its simplicity and tractability both in classical and quantum forms. The purpose of this article is to give a largely self-contained introduction to classical and quantum Yang-Mills theory on the plane and on compact surfaces, along with its relationship to ChernSimons theory, illustrating some of the directions of current and recent research activity.
A Bayesian Perspective on Generalization and Stochastic Gradient Descent

We consider two questions at the heart of machine learning; how can we predict if a minimum will generalize to the test set, and why does stochastic gradient descent find minima that generalize well? Our work responds to Zhang et al. (2016), who showed deep neural networks can easily memorize randomly labeled training data, despite generalizing well on real labels of the same inputs. We show that the same phenomenon occurs in small linear models. These observations are explained by the Bayesian evidence, which penalizes sharp minima but is invariant to model parameterization. We also demonstrate that, when one holds the learning rate fixed, there is an optimum batch size which maximizes the test set accuracy. We propose that the noise introduced by small mini-batches drives the parameters towards minima whose evidence is large. Interpreting stochastic gradient descent as a stochastic differential equation, we identify the "noise scale" $g = \epsilon (\frac{N}{B} - 1) \approx \epsilon N/B$, where $\epsilon$ is the learning rate, $N$ the training set size and $B$ the batch size. Consequently the optimum batch size is proportional to both the learning rate and the size of the training set, $B_{opt} \propto \epsilon N$. We verify these predictions empirically.
The Bergman Analytic Content of Planar Domains

Given a planar domain $$\Omega $$ , the Bergman analytic content measures the $$L^{2}(\Omega )$$ -distance between $$\bar{z}$$ and the Bergman space $$A^{2}(\Omega )$$ . We compute the Bergman analytic content of simply connected quadrature domains with quadrature formula supported at one point, and we also determine the function $$f \in A^2(\Omega )$$ that best approximates $$\bar{z}$$ . We show that, for simply connected domains, the square of the Bergman analytic content is equivalent to torsional rigidity from classical elasticity theory, while for multiply connected domains these two domain constants are not equivalent in general.
Reuters tracer: Toward automated news production using large scale social media data

To deal with the sheer volume of information and gain competitive advantage, the news industry has started to explore and invest in news automation. In this paper, we present Reuters Tracer, a system that automates end-to-end news production using Twitter data. It is capable of detecting, classifying, annotating, and disseminating news in real time for Reuters journalists without manual intervention. In contrast to other similar systems, Tracer is topic and domain agnostic. It has a bottom-up approach to news detection, and does not rely on a predefined set of sources or subjects. Instead, it identifies emerging conversations from 12+ million tweets per day and selects those that are news-like. Then, it contextualizes each story by adding a summary and a topic to it, estimating its newsworthiness, veracity, novelty, and scope, and geotags it. Designing algorithms to generate news that meets the standards of Reuters journalists in accuracy and timeliness is quite challenging. But Tracer is able to achieve competitive precision, recall, timeliness, and veracity on news detection and delivery. In this paper, we reveal our key algorithm designs and evaluations that helped us achieve this goal, and lessons learned along the way.
A Morse-bott Approach to Monopole Floer Homology and the Triangulation Conjecture

In the present work we generalize the construction of monopole Floer homology due to Kronheimer and Mrowka to the case of a gradient flow with Morse-Bott singularities. Focusing then on the special case of a three-manifold equipped with a spin$^c$ structure isomorphic to its conjugate, we define the counterpart in this context of Manolescu's recent $\mathrm{Pin}(2)$-equivariant Seiberg-Witten-Floer homology. In particular, we provide an alternative approach to his disproof of the celebrated Triangulation conjecture.
Vehicle Speed Prediction Using Deep Learning

Global optimization of the energy consumption of dual power source vehicles such as hybrid electric vehicles, plug-in hybrid electric vehicles, and plug in fuel cell electric vehicles requires knowledge of the complete route characteristics at the beginning of the trip. One of the main characteristics is the vehicle speed profile across the route. The profile will translate directly into energy requirements for a given vehicle. However, the vehicle speed that a given driver chooses will vary from driver to driver and from time to time, and may be slower, equal to, or faster than the average traffic flow. If the specific driver speed profile can be predicted, the energy usage can be optimized across the route chosen. The purpose of this paper is to research the application of Deep Learning techniques to this problem to identify at the beginning of a drive cycle the driver specific vehicle speed profile for an individual driver repeated drive cycle, which can be used in an optimization algorithm to minimize the amount of fossil fuel energy used during the trip.
Normal subgroups of invertibles and of unitaries in a C*-algebra

We investigate the normal subgroups of the groups of invertibles and unitaries in the connected component of the identity. By relating normal subgroups to closed two-sided ideals we obtain a "sandwich condition" describing all the closed normal subgroups both in the invertible and in the the unitary case. We use this to prove a conjecture by Elliott and Rordam: in a simple C*-algebra, the group of approximately inner automorphisms induced by unitaries in the connected component of the identity is topologically simple. Turning to non-closed subgroups, we show, among other things, that in simple unital C*-algebra the commutator subgroup of the group of invertibles in the connected component of the identity is a simple group modulo its center. A similar result holds for unitaries under a mild extra assumption.
A survey on Heegaard Floer homology and concordance

In this survey paper, we discuss several different knot concordance invariants coming from the Heegaard Floer homology package of Ozsvath and Szabo. Along the way, we prove that if two knots are concordant, then their knot Floer complexes satisfy a certain type of stable equivalence.
A Hardy-type result on the average of the lattice point error term over long intervals

Suppose $D$ is a suitably admissible compact subset of $\mathbb{R}^k$ having a smooth boundary with possible zones of zero curvature. Let \mbox{$R(T,\theta,x)= N(T,\theta,x) - T^{k}\mathrm{vol}(D)$,} where $N(T,\theta,x)$ is the number of integral lattice points contained in an $x$-translation of $T\theta(D)$, with $T >0$ a dilation parameter and $\theta \in SO(k)$. Then $R(T,\theta,x)$ can be regarded as a function with parameter $T$ on the space $E_{*}^{+}(k)$, where $E_{*}^{+}(k)$ is the quotient of the direct Euclidean group by the subgroup of integral translations, and $E_{*}^{+}(k)$ has a normalized invariant measure which is the product of normalized measures on $SO(k)$ and the $k$-torus. We derive an integral estimate, valid for almost all $(\theta,x) \in E_{*}^{+}(k)$, one consequence of which in two dimensions is that for almost all $(\theta,x) \in E_{*}^{+}(2)$, a counterpart of the Hardy circle estimate \mbox{$(1/T)\int_{1}^{T} |R(t,\theta,x)\,dt| \ll T^{\frac{1}{4} +\epsilon}\;$}is valid with an improved estimate. We conclude with an account of hyperbolic versions for which, drawing on previous work of Hill and Parnovski \cite{hill-parnovski}, we give counterparts in all dimensions, for both the compact and non-compact finite volume cases.
Fourier bases and a distance problem of Erd\H os

We prove that no ball admits a non-harmonic orthogonal basis of exponentials. We use a combinatorial result, originally studied by Erdý os, which says that the number of distances determined by n points in R d is at least Cdn 1 d +ǫd, ǫd > 0.
List Approximation for Increasing Kolmogorov Complexity.

It is impossible to effectively modify a string in order to increase its Kolmogorov complexity. But is it possible to construct a few strings, not longer than the input string, so that most of them have larger complexity? We show that the answer is yes. We present an algorithm that on input a string x of length n returns a list with O(n^2) many strings, all of length n, such that 99% of them are more complex than x, provided the complexity of x is less than n. We obtain similar results for other parameters, including a polynomial-time construction.
Spatial Channel Covariance Estimation for the Hybrid MIMO Architecture: A Compressive Sensing-Based Approach

Spatial channel covariance information can replace full knowledge of the entire channel matrix for designing analog precoders in hybrid multiple-input-multiple-output (MIMO) architecture. Spatial channel covariance estimation, however, is challenging for the hybrid MIMO architecture because the estimator operating at baseband can only obtain a lower dimensional pre-combined signal through fewer radio frequency chains than antennas. In this paper, we propose two approaches to covariance estimation based on compressive sensing techniques. One is to apply a time-varying sensing matrix, and the other is to exploit the prior knowledge that the covariance matrix is Hermitian. We present the rationale behind the two ideas and validate the superiority of the proposed methods by theoretical analysis and numerical simulations. We conclude the paper by extending the proposed algorithms from narrowband MIMO systems with a single receive antenna to wideband systems with multiple receive antennas.
Capacitated kinetic clustering in mobile networks by optimal transportation theory

We consider the problem of capacitated kinetic clustering in which n mobile terminals and k base stations with respective operating capacities are given. The task is to assign the mobile terminals to the base stations such that the total squared distance from each terminal to its assigned base station is minimized and the capacity constraints are satisfied. This paper focuses on the development of distributed and computationally efficient algorithms that adapt to the motion of both terminals and base stations. Suggested by the optimal transportation theory, we exploit the structural property of the optimal solution, which can be represented by a power diagram on the base stations such that the total usage of nodes within each power cell equals the capacity of the corresponding base station. We show by using the kinetic data structure framework the first analytical upper bound on the number of changes in the optimal solution, i.e., its stability. On the algorithm side, using the power diagram formulation we show that the solution can be represented in size proportional to the number of base stations and can be solved by an iterative, local algorithm. In particular, this algorithm can naturally exploit the continuity of motion and has orders of magnitude faster than existing solutions using min-cost matching and linear programming, and thus is able to handle large scale data under mobility.
Sparse PCA via bipartite matchings

We consider the following multi-component sparse PCA problem: given a set of data points, we seek to extract a small number of sparse components with disjoint supports that jointly capture the maximum possible variance. Such components can be computed one by one, repeatedly solving the single-component problem and deflating the input data matrix, but this greedy procedure is suboptimal. We present a novel algorithm for sparse PCA that jointly optimizes multiple disjoint components. The extracted features capture variance that lies within a multiplicative factor arbitrarily close to 1 from the optimal. Our algorithm is combinatorial and computes the desired components by solving multiple instances of the bipartite maximum weight matching problem. Its complexity grows as a low order polynomial in the ambient dimension of the input data, but exponentially in its rank. However, it can be effectively applied on a low-dimensional sketch of the input data. We evaluate our algorithm on real datasets and empirically demonstrate that in many cases it outperforms existing, deflation-based approaches.
Fourier coefficients of three-dimensional vector-valued modular forms

A thorough analysis is made of the Fourier coefficients for vector-valued modular forms associated to three-dimensional irreducible representations of the modular group. In particular, the following statement is verified for all but a finite number of equivalence classes: if a vector-valued modular form associated to such a representation has rational Fourier coefficients, then these coefficients have "unbounded denominators", i.e. there is a prime number p, depending on the representation, which occurs to an arbitrarily high power in the denominators of the coefficients. This provides a verification in the three-dimensional setting of a generalization of a long-standing conjecture about noncongruence modular forms.
Robust semi-cooperative multi-agent coordination in the presence of stochastic disturbances

This paper presents a robust distributed coordination protocol that achieves generation of collision-free trajectories for multiple unicycle agents in the presence of stochastic uncertainties. We build upon our earlier work on semi-cooperative coordination and we redesign the coordination controllers so that the agents counteract a class of state (wind) disturbances and measurement noise. Safety and convergence is proved analytically, while simulation results demonstrate the efficacy of the proposed solution.
Expected Patterns in Permutation Classes

Each length $k$ pattern occurs equally often in the set $S_n$ of all permutations of length $n$, but the same is not true in general for a proper subset of $S_n$. Miklos Bona recently proved that if we consider the set of $n$-permutations avoiding the pattern 132, all other non-monotone patterns of length 3 are equally common. In this paper we focus on the set $\operatorname{Av}_n (123)$ of $n$-permutations avoiding $123$, and give exact formulae for the occurrences of each length 3 pattern. While this set does not have the same symmetries as $\operatorname{Av}_n (132)$, we find several similarities between the two and prove that the number of 231 patterns is the same in each.
Approximation algorithms for route planning with nonlinear objectives

We consider optimal route planning when the objective function is a general nonlinear and non-monotonic function. Such an objective models user behavior more accurately, for example, when a user is risk-averse, or the utility function needs to capture a penalty for early arrival. It is known that as nonlinearity arises, the problem becomes NP-hard and little is known about computing optimal solutions when in addition there is no monotonicity guarantee. We show that an approximately optimal non-simple path can be efficiently computed under some natural constraints. In particular, we provide a fully polynomial approximation scheme under hop constraints. Our approximation algorithm can extend to run in pseudo-polynomial time under a more general linear constraint that sometimes is useful. As a by-product, we show that our algorithm can be applied to the problem of finding a path that is most likely to be on time for a given deadline.
Mining the Relationship between Emoji Usage Patterns and Personality

Emojis have been widely used in textual communications as a new way to convey nonverbal cues. An interesting observation is the various emoji usage patterns among different users. In this paper, we investigate the correlation between user personality traits and their emoji usage patterns, particularly on overall amounts and specific preferences. To achieve this goal, we build a large Twitter dataset which includes 352,245 users and over 1.13 billion tweets associated with calculated personality traits and emoji usage patterns. Our correlation and emoji prediction results provide insights into the power of diverse personalities that lead to varies emoji usage patterns as well as its potential in emoji recommendation tasks.
Asymptotic formulae for mixed congruence stacks

Much like the important work of Hardy and Ramanujan (Proc Lond Math Soc 2(17):75–115, 1919) proving the asymptotic formula for the partition function, Auluck (Math Proc Camb Philos Soc 47:679–686, 1951) and Wright (Quart J Math (Oxf) 22:107–116, 1971) gave similar formulas for unimodal sequences. Following the circle method of Wright, we provide the asymptotic expansion for unimodal sequences on a two-parameter family of mixed congruence relations, with parts on one side up to the peak satisfying $$r \pmod {m}$$ and parts on the other side $$-r\pmod {m}$$ . Techniques used in the proofs include Wright’s circle method, modular transformations, and bounding of complex integrals.
Robust hierarchical density estimation and regression for re-stained histological whole slide image co-registration.

For many disease conditions, tissue samples are colored with multiple dyes and stains to add contrast and location information for specific proteins to accurately identify and diagnose disease. This presents a computational challenge for digital pathology, as whole-slide images (WSIs) need to be properly overlaid (i.e. registered) to identify co-localized features. Traditional image registration methods sometimes fail due to the high variation of cell density and insufficient texture information in WSIs–particularly at high magnifications. In this paper, we proposed a robust image registration strategy to align re-stained WSIs precisely and efficiently. This method is applied to 30 pairs of immunohistochemical (IHC) stains and their hematoxylin and eosin (H&E) counterparts. Our approach advances the existing methods in three key ways. First, we introduce refinements to existing image registration methods. Second, we present an effective weighting strategy using kernel density estimation to mitigate registration errors. Third, we account for the linear relationship across WSI levels to improve accuracy. Our experiments show significant decreases in registration errors when matching IHC and H&E pairs, enabling subcellular-level analysis on stained and re-stained histological images. We also provide a tool to allow users to develop their own registration benchmarking experiments.
Learning Deep Structure-Preserving Image-Text Embeddings

This paper proposes a method for learning joint embeddings of images and text using a two-branch neural network with multiple layers of linear projections followed by nonlinearities. The network is trained using a largemargin objective that combines cross-view ranking constraints with within-view neighborhood structure preservation constraints inspired by metric learning literature. Extensive experiments show that our approach gains significant improvements in accuracy for image-to-text and textto-image retrieval. Our method achieves new state-of-theart results on the Flickr30K and MSCOCO image-sentence datasets and shows promise on the new task of phrase localization on the Flickr30K Entities dataset.
De Giorgi techniques applied to Hamilton–Jacobi equations with unbounded right-hand side

In this article we obtain Holder estimates for solutions to second-order Hamilton-Jacobi equations with super-quadratic growth in the gradient and unbounded source term. The estimates are uniform with respect to the smallness of the diffusion and the smoothness of the Hamiltonian. Our work is in the spirit of a result by P. Cardaliaguet and L. Silvestre [5]. We utilize De Giorgi's method, which was introduced to this class of equations in [6].
Sensor Management: Past, Present, and Future

Sensor systems typically operate under resource constraints that prevent the simultaneous use of all resources all of the time. Sensor management becomes relevant when the sensing system has the capability of actively managing these resources; i.e., changing its operating configuration during deployment in reaction to previous measurements. Examples of systems in which sensor management is currently used or is likely to be used in the near future include autonomous robots, surveillance and reconnaissance networks, and waveform-agile radars. This paper provides an overview of the theory, algorithms, and applications of sensor management as it has developed over the past decades and as it stands today.
On the algebraicity of generalized power series

Let K be an algebraically closed field of characteristic p. We exhibit a counterexample against a theorem asserted in one of our earlier papers, which claims to characterize the integral closure of K((t)) within the field of Hahn–Mal’cev–Neumann generalized power series. We then give a corrected characterization, generalizing our earlier description in terms of finite automata in the case where K is the algebraic closure of a finite field. We also characterize the integral closure of K(t), thus generalizing a well-known theorem of Christol and suggesting a possible framework for computing in this integral closure. We recover various corollaries on the structure of algebraic generalized power series; one of these is an extension of Derksen’s theorem on the zero sets of linear recurrent sequences in characteristic p.
Faster Gaussian summation: theory and experiment

We provide faster algorithms for the problem of Gaussian summation, which occurs in many machine learning methods. We develop two new extensions - an O(Dp) Taylor expansion for the Gaussian kernel with rigorous error bounds and a new error control scheme integrating any arbitrary approximation method - within the best discrete-algorithmic framework using adaptive hierarchical data structures. We rigorously evaluate these techniques empirically in the context of optimal bandwidth selection in kernel density estimation, revealing the strengths and weaknesses of current state-of-the-art approaches for the first time. Our results demonstrate that the new error control scheme yields improved performance, whereas the series expansion approach is only effective in low dimensions (five or less).
Towards Deep Learning based Hand Keypoints Detection for Rapid Sequential Movements from RGB Images

Hand keypoints detection and pose estimation has numerous applications in computer vision, but it is still an unsolved problem in many aspects. An application of hand keypoints detection is in performing cognitive assessments of a subject by observing the performance of that subject in physical tasks involving rapid finger motion. As a part of this work, we introduce a novel hand keypoints benchmark dataset that consists of hand gestures recorded specifically for cognitive behavior monitoring. We explore the state of the art methods in hand keypoint detection and we provide quantitative evaluations for the performance of these methods on our dataset. In future, these results and our dataset can serve as a useful benchmark for hand keypoint recognition for rapid finger movements.
Toward the Schur Expansion of Macdonald Polynomials

We give an explicit combinatorial formula for the Schur expansion of Macdonald polynomials indexed by partitions with second part at most two. This gives a uniform formula for both hook and two column partitions. The proof comes as a corollary to the result that generalized dual equivalence classes of permutations are in explicit bijection with unions of standard dual equivalence classes of permutations for certain cases, establishing an earlier conjecture of the author, and suggesting that this result might be generalized to arbitrary partitions.
Intrinsic random functions on the sphere

Abstract Spatial stochastic processes that are modeled over the entire Earth’s surface require statistical approaches that directly consider the spherical domain. In practice, such processes rarely are second-order stationary — that is, they do not have constant mean values or the covariance function that depends only on their angular distance. Here, in order to model non-stationary processes on the sphere, we extend the notion of intrinsic random functions and show that low-frequency truncation plays an essential role. We show that these developments can be presented through the theory of reproducing kernel Hilbert space. In addition, the link between universal kriging and splines is carefully investigated, whereby we show that thin-plate splines are non-applicable for surface fitting on the sphere.
Auditing for Distributed Storage Systems

Distributed storage codes have recently received a lot of attention in the community. Independently, another body of work has proposed integrity-checking schemes for cloud storage, none of which, however, is customized for coding-based storage or can efficiently support repair. In this work, we bridge the gap between these two currently disconnected bodies of work. We propose $ {\ssr NC {\mathchar"702D }Audit}$ , a novel cryptography-based remote data integrity-checking scheme, designed specifically for network-coding-based distributed storage systems. $ {\ssr NC {\mathchar"702D }Audit}$ combines, for the first time, the following desired properties: 1) efficient checking of data integrity; 2) efficient support for repairing failed nodes; and 3) protection against information leakage when checking is performed by a third party. The key ingredient of the design of $ {\ssr NC {\mathchar"702D }Audit}$ is a novel combination of $ {\ssr SpaceMac}$ , a homomorphic message authentication code (MAC) scheme for network coding, and $ {\ssr NCrypt}$ , a novel chosen-plaintext attack (CPA) secure encryption scheme that preserves the correctness of $ {\ssr SpaceMac}$ . Our evaluation of $ {\ssr NC {\mathchar"702D }Audit}$ based on a real Java implementation shows that the proposed scheme has significantly lower overhead compared to the state-of-the-art schemes for both auditing and repairing of failed nodes.
A GENERAL 'BANG-BANG' PRINCIPLE FOR PREDICTING THE MAXIMUM OF A RANDOM WALK

Let ( B t ) 0≤ t ≤ T be either a Bernoulli random walk or a Brownian motion with drift, and let M t := max{ B s : 0 ≤ s ≤ t }, 0 ≤ t ≤ T . In this paper we solve the general optimal prediction problem sup 0≤τ≤ T E[ f ( M T − B τ ], where the supremum is over all stopping times τ adapted to the natural filtration of ( B t ) and f is a nonincreasing convex function. The optimal stopping time τ * is shown to be of ‘bang-bang’ type: τ * ≡ 0 if the drift of the underlying process ( B t ) is negative and τ * ≡ T if the drift is positive. This result generalizes recent findings of Toit and Peskir (2009) and Yam, Yung and Zhou (2009), and provides additional mathematical justification for the dictum in finance that one should sell bad stocks immediately, but keep good stocks as long as possible.
Circular Networks from Distorted Metrics

Trees have long been used as a graphical representation of species relationships. However complex evolutionary events, such as genetic reassortments or hybrid speciations which occur commonly in viruses, bacteria and plants, do not fit into this elementary framework. Alternatively, various network representations have been developed. Circular networks are a natural generalization of leaf-labeled trees interpreted as split systems, that is, collections of bipartitions over leaf labels corresponding to current species. Although such networks do not explicitly model specific evolutionary events of interest, their straightforward visualization and fast reconstruction have made them a popular exploratory tool to detect network-like evolution in genetic datasets. Standard reconstruction methods for circular networks, such as Neighbor-Net, rely on an associated metric on the species set. Such a metric is first estimated from DNA sequences, which leads to a key difficulty: distantly related sequences produce statistically unreliable estimates. This is problematic for Neighbor-Net as it is based on the popular tree reconstruction method Neighbor-Joining, whose sensitivity to distance estimation errors is well established theoretically. In the tree case, more robust reconstruction methods have been developed using the notion of a distorted metric, which captures the dependence of the error in the distance through a radius of accuracy. Here we design the first circular network reconstruction method based on distorted metrics. Our method is computationally efficient. Moreover, the analysis of its radius of accuracy highlights the important role played by the maximum incompatibility, a measure of the extent to which the network differs from a tree.
Entry Times Distribution for Dynamical Balls on Metric Spaces

We show that the entry and return times for dynamical balls (Bowen balls) is exponential for systems that have an $$\alpha $$ -mixing invariant measure with certain regularities. We also show that systems modeled by Young’s tower has exponential entry time distribution for dynamical balls. We also apply the results to conformal maps and expanding maps on the interval.
signSGD: Compressed Optimisation for Non-Convex Problems

Training large neural networks requires distributing learning across multiple workers, where the cost of communicating gradients can be a significant bottleneck. signSGD alleviates this problem by transmitting just the sign of each minibatch stochastic gradient. We prove that it can get the best of both worlds: compressed gradients and SGD-level convergence rate. The relative l_1/l_2 geometry of gradients, noise and curvature informs whether signSGD or SGD is theoretically better suited to a particular problem. On the practical side we find that the momentum counterpart of signSGD is able to match the accuracy and convergence speed of Adam on deep Imagenet models. We extend our theory to the distributed setting, where the parameter server uses majority vote to aggregate gradient signs from each worker enabling 1-bit compression of worker-server communication in both directions. Using a theorem by Gauss we prove that majority vote can achieve the same reduction in variance as full precision distributed SGD. Thus, there is great promise for sign-based optimisation schemes to achieve fast communication and fast convergence. Code to reproduce experiments is to be found at https://github.com/jxbz/signSGD.
Entropy of an autoequivalence on Calabi–Yau manifolds

We prove that the categorical entropy of the autoequivalence $T_{\mathcal{O}}\circ(-\otimes\mathcal{O}(-1))$ on a Calabi-Yau manifold is the unique positive real number $\lambda$ satisfying $$ \sum_{k\geq 1}\frac{\chi(\mathcal{O}(k))}{e^{k\lambda}}=e^{(d-1)t}. $$ We then use this result to construct the first counterexamples of a conjecture on categorical entropy by Kikuta and Takahashi.
Communication Efficient Distributed Agnostic Boosting

We consider the problem of learning from distributed data in the agnostic setting, i.e., in the presence of arbitrary forms of noise. Our main contribution is a general distributed boosting-based procedure for learning an arbitrary concept space, that is simultaneously noise tolerant, communication efficient, and computationally efficient. This improves significantly over prior works that were either communication efficient only in noise-free scenarios or computationally prohibitive. Empirical results on large synthetic and real-world datasets demonstrate the effectiveness and scalability of the proposed approach.
Predicting Gender From Iris Texture May Be Harder Than It Seems

Predicting gender from iris images has been reported by several researchers as an application of machine learning in biometrics. Recent works on this topic have suggested that the preponderance of the gender cues is located in the periocular region rather than in the iris texture itself. This paper focuses on teasing out whether the information for gender prediction is in the texture of the iris stroma, the periocular region, or both. We present a larger dataset for gender from iris, and evaluate gender prediction accuracy using linear SVM and CNN, comparing hand-crafted and deep features. We use probabilistic occlusion masking to gain insight on the problem. Results suggest the discriminative power of the iris texture for gender is weaker than previously thought, and that the gender-related information is primarily in the periocular region.
Thermally Tunable Hybrid Photonic Architecture for Nonlinear Optical Circuits

Integrated photonic systems are a leading solution for fast and energy-efficient information processing. We develop a thermally tunable hybrid photonic platform for implementation of coherent optical networks applicable to dedicated computing and machine learning. The hybrid architecture comprises gallium arsenide (GaAs) photonic crystal cavities, silicon nitride (SiNx) grating couplers and waveguides, and chromium (Cr) microheaters on an integrated photonic chip. We utilize the band-edge nonlinearity in GaAs photonic crystal cavity for switching at 6 ps time scale. The cavities are evanescently connected to a common bus waveguide, separating the computation and communication layers. To synchronize the operating frequency, we design metal microheaters that locally, continuously, and reversibly tune photonic crystal cavities to a common resonance. We demonstrate 7 nm tunability range with no significant quality factor deterioration. By coupling the free-space light to the photonic chip, we demonstrate the ...