cssi/SciSciGPT-SciSciNet huggingface dataset:
Data-driven spectral decomposition and forecasting of ergodic dynamical systems

Abstract We develop a framework for dimension reduction, mode decomposition, and nonparametric forecasting of data generated by ergodic dynamical systems. This framework is based on a representation of the Koopman and Perron–Frobenius groups of unitary operators in a smooth orthonormal basis of the L 2 space of the dynamical system, acquired from time-ordered data through the diffusion maps algorithm. Using this representation, we compute Koopman eigenfunctions through a regularized advection–diffusion operator, and employ these eigenfunctions in dimension reduction maps with projectible dynamics and high smoothness for the given observation modality. In systems with pure point spectra, we construct a decomposition of the generator of the Koopman group into mutually commuting vector fields that transform naturally under changes of observation modality, which we reconstruct in data space through a representation of the pushforward map in the Koopman eigenfunction basis. We also establish a correspondence between Koopman operators and Laplace–Beltrami operators constructed from data in Takens delay-coordinate space, and use this correspondence to provide an interpretation of diffusion-mapped delay coordinates for this class of systems. Moreover, we take advantage of a special property of the Koopman eigenfunction basis, namely that the basis elements evolve as simple harmonic oscillators, to build nonparametric forecast models for probability densities and observables. In systems with more complex spectral behavior, including mixing systems, we develop a method inspired from time change in dynamical systems to transform the generator to a new operator with potentially improved spectral properties, and use that operator for vector field decomposition and nonparametric forecasting.
Solubilization kinetics determines the pulsatory dynamics of lipid vesicles exposed to surfactant.

Abstract We establish a biophysical model for the dynamics of lipid vesicles exposed to surfactants. The solubilization of the lipid membrane due to the insertion of surfactant molecules induces a reduction of membrane surface area at almost constant vesicle volume. This results in a rate-dependent increase of membrane tension and leads to the opening of a micron-sized pore. We show that solubilization kinetics due to surfactants can determine the regime of pore dynamics: either the pores open and reseal within a second (short-lived pore), or the pore stays open up to a few minutes (long-lived pore). First, we validate our model with previously published experimental measurements of pore dynamics. Then, we investigate how the solubilization kinetics and membrane properties affect the dynamics of the pore and construct a phase diagram for short and long-lived pores. Finally, we examine the dynamics of sequential pore openings and show that cyclic short-lived pores occur with a period inversely proportional to the solubilization rate. By deriving a theoretical expression for the cycle period, we provide an analytical tool to estimate the solubilization rate of lipid vesicles by surfactants. Our findings shed light on some fundamental biophysical mechanisms that allow simple cell-like structures to sustain their integrity against environmental stresses, and have the potential to aid the design of vesicle-based drug delivery systems. This article is part of a Special Issue entitled: Emergence of Complex Behavior in Biomembranes edited by Marjorie Longo.
The role of conditional independence in the evolution of intelligent systems

Systems are typically made from simple components regardless of their complexity. While the function of each part is easily understood, higher order functions are emergent properties and are notoriously difficult to explain. In networked systems, both digital and biological, each component receives inputs, performs a simple computation, and creates an output. When these components have multiple outputs, we intuitively assume that the outputs are causally dependent on the inputs but are themselves independent of each other given the state of their shared input [11]. However, this intuition can be violated for components with probabilistic logic, as these typically cannot be decomposed into separate logic gates with one output each. This violation of conditional independence on the past system state is equivalent to instantaneous interaction --- the idea is that some information between the outputs is not coming from the inputs and thus must have been created instantaneously. Here we compare evolved artificial neural systems with and without instantaneous interaction across several task environments. We show that systems without instantaneous interactions evolve faster, to higher final levels of performance, and require fewer logic components to create a densely connected cognitive machinery.
A Longitudinal Study of Google Play

The difficulty of large-scale monitoring of app markets affects our understanding of their dynamics. This is particularly true for dimensions such as app update frequency, control and pricing, the impact of developer actions on app popularity, as well as coveted membership in top app lists. In this paper, we perform a detailed temporal analysis on two datasets we have collected from the Google Play Store, one consisting of 160 000 apps and the other of 87 223 newly released apps. We have monitored and collected data about these apps over more than six months. Our results show that a high number of these apps have not been updated over the monitoring interval. Moreover, these apps are controlled by a few developers that dominate the total number of app downloads. We observe that infrequently updated apps significantly impact the median app price. However, a changing app price does not correlate with the download count. Furthermore, we show that apps that attain higher ranks have better stability in top app lists. We show that app market analytics can help detect emerging threat vectors, and identify search rank fraud and even malware. Further, we discuss the research implications of app market analytics on improving developer and user experiences.
Data-Driven Diagnostics of Mechanism and Source of Sustained Oscillations

Sustained oscillations observed in power systems can damage equipment, degrade the power quality and increase the risks of cascading blackouts. There are several mechanisms that can give rise to oscillations, each requiring different countermeasure to suppress or eliminate the oscillation. This work develops mathematical framework for analysis of sustained oscillations and identifies statistical signatures of each mechanism, based on which a novel oscillation diagnosis method is developed via real-time processing of phasor measurement units (PMUs) data. Case studies show that the proposed method can accurately identify the exact mechanism for sustained oscillation, and meanwhile provide insightful information to locate the oscillation sources.
Learning Fast Algorithms for Linear Transforms Using Butterfly Factorizations

Fast linear transforms are ubiquitous in machine learning, including the discrete Fourier transform, discrete cosine transform, and other structured transformations such as convolutions. All of these transforms can be represented by dense matrix-vector multiplication, yet each has a specialized and highly efficient (subquadratic) algorithm. We ask to what extent hand-crafting these algorithms and implementations is necessary, what structural priors they encode, and how much knowledge is required to automatically learn a fast algorithm for a provided structured transform. Motivated by a characterization of fast matrix-vector multiplication as products of sparse matrices, we introduce a parameterization of divide-and-conquer methods that is capable of representing a large class of transforms. This generic formulation can automatically learn an efficient algorithm for many important transforms; for example, it recovers the O(N log N) Cooley-Tukey FFT algorithm to machine precision, for dimensions N up to 1024. Furthermore, our method can be incorporated as a lightweight replacement of generic matrices in machine learning pipelines to learn efficient and compressible transformations. On a standard task of compressing a single hidden-layer network, our method exceeds the classification accuracy of unconstrained matrices on CIFAR-10 by 3.9 points-the first time a structured approach has done so-with 4× faster inference speed and 40× fewer parameters.
Structured Low-Rank Matrix Factorization: Global Optimality, Algorithms, and Applications

Convex formulations of low-rank matrix factorization problems have received considerable attention in machine learning. However, such formulations often require solving for a matrix of the size of the data matrix, making it challenging to apply them to large scale datasets. Moreover, in many applications the data can display structures beyond simply being low-rank, e.g., images and videos present complex spatio-temporal structures that are largely ignored by standard low-rank methods. In this paper we study a matrix factorization technique that is suitable for large datasets and captures additional structure in the factors by using a particular form of regularization that includes well-known regularizers such as total variation and the nuclear norm as particular cases. Although the resulting optimization problem is non-convex, we show that if the size of the factors is large enough, under certain conditions, any local minimizer for the factors yields a global minimizer. A few practical algorithms are also provided to solve the matrix factorization problem, and bounds on the distance from a given approximate solution of the optimization problem to the global optimum are derived. Examples in neural calcium imaging video segmentation and hyperspectral compressed recovery show the advantages of our approach on high-dimensional datasets.
Development of Safety Performance Functions: Incorporating Unobserved Heterogeneity and Functional Form Analysis:

To improve transportation safety, this study applies Highway Safety Manual (HSM) procedures to roadways while accounting for unobserved heterogeneity and exploring alternative functional forms for ...
Joint inference of user community and interest patterns in social interaction networks

Online social media have become an integral part of our social beings. Analyzing conversations in social media platforms can lead to complex probabilistic models to understand social interaction networks. In this paper, we present a modeling approach for characterizing social interaction networks by jointly inferring user communities and interests based on social media interactions. We present several pattern inference models: (1) interest pattern model (IPM) captures population level interaction topics, (2) user interest pattern model (UIPM) captures user specific interaction topics, and (3) community interest pattern model (CIPM) captures both community structures and user interests. We test our methods on Twitter data collected from Purdue University community. From our model results, we observe the interaction topics and communities related to two big events within Purdue University community, namely Purdue Day of Giving and Senator Bernie Sanders’ visit to Purdue University as part of Indiana Primary Election 2016. Constructing social interaction networks based on user interactions accounts for the similarity of users’ interactions on various topics of interest and indicates their community belonging further beyond connectivity. We observed that the degree-distributions of such networks follow power-law that is indicative of the existence of fewer nodes in the network with higher levels of interactions, and many other nodes with less interaction. We also discuss the application of such networks as a useful tool to effectively disseminate specific information to the target audience towards planning any large-scale events and demonstrate how to single out specific nodes in a given community by running network algorithms.
Gerbal Representations of Double Loop Groups

A crucial role in representation theory of loop groups of reductive Lie groups and their Lie algebras is played by their nontrivial second cohomology classes, which give rise to their central extensions (the affine Kac–Moody groups and Lie algebras). Loop groups embed into the group GL∞ of continuous automorphisms of C((t)), and these classes come from a second cohomology class of GL∞. In a similar way, double loop groups embed into a group of automorphisms of C((t))((s)), denoted by GL∞,∞, which has a nontrivial third cohomology. In this paper, we explain how to realize a third cohomology class in representation theory of a group: it naturally arises when we consider representations on categories rather than vector spaces. We call them “gerbal representations”. We then construct a gerbal representation of GL∞,∞ (and hence of double loop groups), realizing its nontrivial third cohomology class, on a category of modules over an infinite-dimensional Clifford algebra. This is a two-dimensional analog of the fermionic Fock representations of the ordinary loop groups.
Perturbations of local maxima and comparison principles for boundary-degenerate linear differential equations

We develop strong and weak maximum principles for boundary-degenerate elliptic and parabolic linear second-order partial differential operators, $Au := -\mathrm{tr}(aD^2u)- + cu$, with partial Dirichlet boundary conditions. The coefficient, $a(x)$, is assumed to vanish along a non-empty open subset, $\partial_0\mathscr{O}$, called the \emph{degenerate boundary portion}, of the boundary, $\partial\mathscr{O}$, of the domain $\mathscr{O}\subset\mathbb{R}^d$, while $a(x)$ is non-zero at any point of the \emph{non-degenerate boundary portion}, $\partial_1\mathscr{O} := \partial\mathscr{O}\setminus\overline{\partial_0\mathscr{O}}$. If an $A$-subharmonic function, $u$ in $C^2(\mathscr{O})$ or $W^{2,d}_{\mathrm{loc}}(\mathscr{O})$, is $C^1$ up to $\partial_0\mathscr{O}$ and has a strict local maximum at a point in $\partial_0\mathscr{O}$, we show that $u$ can be perturbed, by the addition of a suitable function $w\in C^2(\mathscr{O})\cap C^1(\mathbb{R}^d)$, to a strictly $A$-subharmonic function $v=u+w$ having a local maximum in the interior of $\mathscr{O}$. Consequently, we obtain strong and weak maximum principles for $A$-subharmonic functions in $C^2(\mathscr{O})$ and $W^{2,d}_{\mathrm{loc}}(\mathscr{O})$ which are $C^1$ up to $\partial_0\mathscr{O}$. Only the non-degenerate boundary portion, $\partial_1\mathscr{O}$, is required for boundary comparisons. Our results extend those in Daskalopoulos and Hamilton (1998), Epstein and Mazzeo [arXiv:1110.0032], and the author [arXiv:1204.6613, 1306.5197], where $\mathrm{tr}(aD^2u)$ is in addition assumed to be continuous up to and vanish along $\partial_0\mathscr{O}$ in order to yield comparable maximum principles for $A$-subharmonic functions in $C^2(\mathscr{O})$, while the results developed here for $A$-subharmonic functions in $W^{2,d}_{\mathrm{loc}}(\mathscr{O})$ are entirely new.
On the attractor for the semi-dissipative Boussinesq equations

Abstract In this article, we study the long time behavior of solutions of a variant of the Boussinesq system in which the equation for the velocity is parabolic while the equation for the temperature is hyperbolic. We prove that the system has a global attractor which retains some of the properties of the global attractors for the 2D and 3D Navier–Stokes equations. Moreover, this attractor contains infinitely many invariant manifolds in which several universal properties of the Batchelor, Kraichnan, Leith theory of turbulence are potentially present.
Boolean formulae, hypergraphs and combinatorial topology

Abstract With a view toward studying the homotopy type of spaces of Boolean formulae, we introduce a simplicial complex, called the theta complex, associated to any hypergraph, which is the Alexander dual of the more well-known independence complex. In particular, the set of satisfiable formulae in k-conjunctive normal form with ⩽n variables has the homotopy type of Θ ( Cube ( n , n − k ) ) , where Cube ( n , n − k ) is a hypergraph associated to the ( n − k ) -skeleton of an n-cube. We make partial progress in calculating the homotopy type of theta for these cubical hypergraphs, and we also give calculations and examples for other hypergraphs as well. Indeed studying the theta complex of hypergraphs is an interesting problem in its own right.
Smoluchowski–Kramers approximation for the damped stochastic wave equation with multiplicative noise in any spatial dimension

We show that the solutions to the damped stochastic wave equation converge pathwise to the solution of a stochastic heat equation. This is called the Smoluchowski–Kramers approximation. Cerrai and Freidlin have previously demonstrated that this result holds in the cases where the system is exposed to additive noise in any spatial dimension or when the system is exposed to multiplicative noise and the spatial dimension is one. The current paper proves that the Smoluchowski–Kramers approximation is valid in any spatial dimension when the system is exposed to multiplicative noise.
Globalization with probabilistic convexity

We introduce a notion of probabilistic convexity and generalize some classical globalization theorems in Alexandrov geometry. A weighted Alexandrov's lemma is developed as a basic tool.
Game theory with translucent players

A traditional assumption in game theory is that players are opaque to one another—if a player changes strategies, then this change in strategies does not affect the choice of other players’ strategies. In many situations this is an unrealistic assumption. We develop a framework for reasoning about games where the players may be translucent to one another; in particular, a player may believe that if she were to change strategies, then the other player would also change strategies. Translucent players may achieve significantly more efficient outcomes than opaque ones. Our main result is a characterization of strategies consistent with appropriate analogues of common belief of rationality. Common Counterfactual Belief of Rationality (CCBR) holds if (1) everyone is rational, (2) everyone counterfactually believes that everyone else is rational (i.e., all players i believe that everyone else would still be rational even if i were to switch strategies), (3) everyone counterfactually believes that everyone else is rational, and counterfactually believes that everyone else is rational, and so on. CCBR characterizes the set of strategies surviving iterated removal of minimax-dominated strategies, where a strategy $$\sigma $$ for player i is minimax dominated by $$\sigma '$$ if the worst-case payoff for i using $$\sigma '$$ is better than the best possible payoff using $$\sigma $$ .
Generic extensions and generic polynomials for multiplicative groups

Let A A be a finite-dimensional algebra over a finite field F q F q and let G=A × G = A × be the multiplicative group of A A . In this paper, we construct explicitly a generic Galois G -extension S/R S / R , where R is a localized polynomial ring over F q F q , and an explicit generic polynomial for G in dim F q ⁡(A) dim F q ⁡ ( A ) parameters.
A note on one-dimensional time fractional ODEs

Abstract In this note, we prove or re-prove several important results regarding one dimensional time fractional ODEs following our previous work Feng et al. [ 15 ]. Here we use the definition of Caputo derivative proposed in Li and Liu (2017) [ [5] , [7] ] based on a convolution group. In particular, we establish generalized comparison principles consistent with the new definition of Caputo derivatives. In addition, we establish the full asymptotic behaviors of the solutions for D c γ u = A u p . Lastly, we provide a simplified proof for the strict monotonicity and stability in initial values for the time fractional differential equations with weak assumptions.
A Tight 4/3 Approximation for Capacitated Vehicle Routing in Trees

Given a set of clients with demands, the Capacitated Vehicle Routing problem is to find a set of tours that collectively cover all client demand, such that the capacity of each vehicle is not exceeded and such that the sum of the tour lengths is minimized. In this paper, we provide a 4/3-approximation algorithm for Capacitated Vehicle Routing on trees, improving over the previous best-known approximation ratio of $(\sqrt{41}-1)/4$ by Asano et al., while using the same lower bound. Asano et al. show that there exist instances whose optimal cost is 4/3 times this lower bound. Notably, our 4/3 approximation ratio is therefore tight for this lower bound, achieving the best-possible performance.
Comparing the Max and Noisy-Or Pooling Functions in Multiple Instance Learning for Weakly Supervised Sequence Learning Tasks.

Many sequence learning tasks require the localization of certain events in sequences. Because it can be expensive to obtain strong labeling that specifies the starting and ending times of the events, modern systems are often trained with weak labeling without explicit timing information. Multiple instance learning (MIL) is a popular framework for learning from weak labeling. In a common scenario of MIL, it is necessary to choose a pooling function to aggregate the predictions for the individual steps of the sequences. In this paper, we compare the "max" and "noisy-or" pooling functions on a speech recognition task and a sound event detection task. We find that max pooling is able to localize phonemes and sound events, while noisy-or pooling fails. We provide a theoretical explanation of the different behavior of the two pooling functions on sequence learning tasks.
Key-Rate Bound of a Semi-Quantum Protocol Using an Entropic Uncertainty Relation

In this paper we present a new proof technique for semi-quantum key distribution (SQKD) protocols which makes use of a quantum entropic uncertainty relation to bound an adversary's information. We develop several new techniques for analyzing SQKD protocols; furthermore, our new proof may hold application in the security analysis of other semi-quantum protocols or protocols relying on two-way quantum communication.
Iris Presentation Attack Detection Based on Photometric Stereo Features

We propose a new iris presentation attack detection method using three-dimensional features of an observed iris region estimated by photometric stereo. Our implementation uses a pair of iris images acquired by a common commercial iris sensor (LG 4000). No hardware modifications of any kind are required. Our approach should be applicable to any iris sensor that can illuminate the eye from two different directions. Each iris image in the pair is captured under near-infrared illumination at a different angle relative to the eye. Photometric stereo is used to estimate surface normal vectors in the non-occluded portions of the iris region. The variability of the normal vectors is used as the presentation attack detection score. This score is larger for a texture that is irregularly opaque and printed on a convex contact lens, and is smaller for an authentic iris texture. Thus the problem is formulated as binary classification into (a) an eye wearing textured contact lens and (b) the texture of an actual iris surface (possibly seen through a clear contact lens). Experiments were carried out on a database of approx. 2,900 iris image pairs acquired from approx. 100 subjects. Our method was able to correctly classify over 95% of samples when tested on contact lens brands unseen in training, and over 98% of samples when the contact lens brand was seen during training. The source codes of the method are made available to other researchers.
Measuring Catastrophic Forgetting in Neural Networks

Deep neural networks are used in many state-of-the-art systems for machine perception. Once a network is trained to do a specific task, e.g., bird classification, it cannot easily be trained to do new tasks, e.g., incrementally learning to recognize additional bird species or learning an entirely different task such as flower recognition. When new tasks are added, typical deep neural networks are prone to catastrophically forgetting previous tasks. Networks that are capable of assimilating new information incrementally, much like how humans form new memories over time, will be more efficient than re-training the model from scratch each time a new task needs to be learned. There have been multiple attempts to develop schemes that mitigate catastrophic forgetting, but these methods have not been directly compared, the tests used to evaluate them vary considerably, and these methods have only been evaluated on small-scale problems (e.g., MNIST). In this paper, we introduce new metrics and benchmarks for directly comparing five different mechanisms designed to mitigate catastrophic forgetting in neural networks: regularization, ensembling, rehearsal, dual-memory, and sparse-coding. Our experiments on real-world images and sounds show that the mechanism(s) that are critical for optimal performance vary based on the incremental training paradigm and type of data being used, but they all demonstrate that the catastrophic forgetting problem is not yet solved.
The weak Lefschetz property and powers of linear forms in K[x,y,z]

We show that an Artinian quotient of an ideal I ⊆ K[x, y, z] generated by powers of linear forms has the Weak Lefschetz Property. If the syzygy bundle of I is semistable, the property follows from results of Brenner-Kaid. Our proof works without this hypothesis, which typically does not hold.
Rate of Convergence of the Bundle Method

The number of iterations needed by the bundle method for nonsmooth optimization to achieve a specified solution accuracy can be bounded by the product of the inverse of the accuracy and its logarithm, if the function is strongly convex. The result is true for the versions of the method with multiple cuts and with cut aggregation.
Simple Sensitivity Analysis for Differential Measurement Error

Sensitivity analysis results are given for differential measurement error of either the exposure or outcome. In the case of differential measurement error of the outcome, it is shown that the true effect of the exposure on the outcome on the risk ratio scale must be at least as large as the observed association between the exposure and the mismeasured outcome divided by the maximum strength of differential measurement error. This maximum strength of differential measurement error is itself assessed as the risk ratio of the controlled direct effect of the exposure on the mismeasured outcome not through the true outcome. In the case of differential measurement error of the exposure, under certain assumptions concerning classification probabilities, the true effect on the odds ratio scale of the exposure on the outcome must be at least as large as the observed odds ratio between the mismeasured exposure and the outcome divided by the maximum odds ratio of the effect of the outcome on mismeasured exposure conditional on the true exposure. The results can be immediately used to indicate the minimum strength of differential measurement error that would be needed to explain away an observed association between an exposure measurement and an outcome measurement for this to be solely due to measurement error.
New restriction estimates for the 3-d paraboloid over finite fields

Abstract We improve the range of exponents for the restriction problem for the 3-d paraboloid over finite fields. The key new ingredient is a variant of the Bourgain–Katz–Tao finite field incidence theorem derived from sum-product estimates. In prime order fields, we give an explicit relationship between the exponent in this incidence theorem and restriction estimates for the paraboloid.
Fourier series of modular graph functions

Abstract Modular graph functions associate to a graph an S L ( 2 , Z ) -invariant function on the upper half plane. We obtain the Fourier series of modular graph functions of arbitrary weight w and two-loop order. The motivation for this work is to develop a deeper understanding of the origin of the algebraic identities between modular graph functions which have been discovered recently, and of the relation between the existence of these identities and the occurrence of cusp forms. We show that the constant Fourier mode, as a function of the modulus τ, consists of a Laurent polynomial in y = π Im τ of degree ( w , 1 − w ) , plus a contribution which decays exponentially as y → ∞ . The Laurent polynomial is a linear combination with rational coefficients of the top term y w , and lower order terms ζ ( 2 k + 1 ) y w − 2 k − 1 for 1 ≤ k ≤ w − 1 , as well as terms ζ ( 2 w − 2 l − 3 ) ζ ( 2 l + 1 ) y 2 − w for 1 ≤ l ≤ w − 3 . The exponential contribution is a linear combination of exponentials of y and incomplete Γ-functions whose coefficients are Laurent polynomials in y with rational coefficients.
Gradient descent aligns the layers of deep linear networks

This paper establishes risk convergence and asymptotic weight matrix alignment --- a form of implicit regularization --- of gradient flow and gradient descent when applied to deep linear networks on linearly separable data. In more detail, for gradient flow applied to strictly decreasing loss functions (with similar results for gradient descent with particular decreasing step sizes): (i) the risk converges to 0; (ii) the normalized i-th weight matrix asymptotically equals its rank-1 approximation $u_iv_i^{\top}$; (iii) these rank-1 matrices are aligned across layers, meaning $|v_{i+1}^{\top}u_i|\to1$. In the case of the logistic loss (binary cross entropy), more can be said: the linear function induced by the network --- the product of its weight matrices --- converges to the same direction as the maximum margin solution. This last property was identified in prior work, but only under assumptions on gradient descent which here are implied by the alignment phenomenon.
Nonparametric infinite horizon Kullback-Leibler stochastic control

We present two nonparametric approaches to Kullback-Leibler (KL) control, or linearly-solvable Markov decision problem (LMDP) based on Gaussian processes (GP) and Nystrom approximation. Compared to recently developed parametric methods, the proposed data-driven frameworks feature accurate function approximation and efficient on-line operations. Theoretically, we derive the mathematical connection of KL control based on dynamic programming with earlier work in control theory which relies on information theoretic dualities for the infinite time horizon case. Algorithmically, we give explicit optimal control policies in nonparametric forms, and propose on-line update schemes with budgeted computational costs. Numerical results demonstrate the effectiveness and usefulness of the proposed frameworks.
The role of an integration identity in the analysis of the Cauchy-Leray transform

The purpose of this paper is to complement the results by Lanzani and Stein (2017) by showing the dense definability of the Cauchy-Leray transform for the domains that give the counterexamples of Lanzani and Stein (2017), where L p -boundedness is shown to fail when either the “near” C 2 boundary regularity, or the strong ℂ-linear convexity assumption is dropped.
Variational policy for guiding point processes

Temporal point processes have been widely applied to model event sequence data generated by online users. In this paper, we consider the problem of how to design the optimal control policy for point processes, such that the stochastic system driven by the point process is steered to a target state. In particular, we exploit the key insight to view the stochastic optimal control problem from the perspective of optimal measure and variational inference. We further propose a convex optimization framework and an efficient algorithm to update the policy adaptively to the current system state. Experiments on synthetic and real-world data show that our algorithm can steer the user activities much more accurately and efficiently than other stochastic control methods.
A Hiking Trip Through the Orders of Magnitude: Deriving Efficient Generators for Closed Simply-Typed Lambda Terms and Normal Forms

Contrary to several other families of lambda terms, no closed formula or generating function is known and none of the sophisticated techniques devised in analytic combinatorics can currently help with counting or generating the set of simply-typed closed lambda terms of a given size.
Focused Crawl of Web Archives to Build Event Collections

Event collections are frequently built by crawling the live web on the basis of seed URIs nominated by human experts. Focused web crawling is a technique where the crawler is guided by reference content pertaining to the event. Given the dynamic nature of the web and the pace with which topics evolve, the timing of the crawl is a concern for both approaches. We investigate the feasibility of performing focused crawls on the archived web. By utilizing the Memento infrastructure, we obtain resources from 22 web archives that contribute to building event collections. We create collections on four events and compare the relevance of their resources to collections built from crawling the live web as well as from a manually curated collection. Our results show that focused crawling on the archived web can be done and indeed results in highly relevant collections, especially for events that happened further in the past
The Hoffman–Rossi Theorem for Operator Algebras

We study possible noncommutative (operator algebra) variants of the classical Hoffman–Rossi theorem from the theory of function algebras. In particular we give a condition on the range of a contractive weak* continuous homomorphism defined on an operator algebra A, which is necessary and sufficient (in the setting we explain) for a positive weak* continuous extension to any von Neumann algebra containing A.
On the cyclic torsion of elliptic curves over cubic number fields

Abstract Let E be an elliptic curve defined over a number field K . Then its Mordell–Weil group E ( K ) is finitely generated: E ( K ) ≅ E ( K ) t o r × Z r . In this paper, we discuss the cyclic torsion subgroup of elliptic curves over cubic number fields. For N = 169 , 143 , 91 , 65 , 77 or 55, we show that Z / N Z is not a subgroup of E ( K ) t o r for any elliptic curve E over a cubic number field K .
Occupation times of discrete-time fractional Brownian motion

We prove a conditional local limit theorem for discrete-time fractional Brownian motions (dfBm) with Hurst parameter 3 4 < H < 1. Using results from infinite ergodic theory, it is then shown that t...
On-the-Fly Adaptive ${k}$ -Space Sampling for Linear MRI Reconstruction Using Moment-Based Spectral Analysis

In high-dimensional magnetic resonance imaging applications, time-consuming, sequential acquisition of data samples in the spatial frequency domain ( ${k}$ -space) can often be accelerated by accounting for dependencies in linear reconstruction, at the cost of noise amplification that depends on the sampling pattern. Common examples are support-constrained, parallel, and dynamic MRI, and ${k}$ -space sampling strategies are primarily driven by image-domain metrics that are expensive to compute for arbitrary sampling patterns. It remains challenging to provide systematic and computationally efficient automatic designs of arbitrary multidimensional Cartesian sampling patterns that mitigate noise amplification, given the subspace to which the object is confined. To address this problem, this paper introduces a theoretical framework that describes local geometric properties of the sampling pattern and relates them to the spread in the eigenvalues of the information matrix described by its first two spectral moments. This new criterion is then used for very efficient optimization of complex multidimensional sampling patterns that does not require reconstructing images or explicitly mapping noise amplification. Experiments with in vivo data show strong agreement between this criterion and traditional, comprehensive image-domain- and ${k}$ -space-based metrics, indicating the potential of the approach for computationally efficient (on-the-fly), automatic, and adaptive design of sampling patterns.
Interference Avoidance Position Planning in UAV-Assisted Wireless Communication

We consider unmanned aerial vehicle (UAV)-assisted wireless communication employing UAVs as relay nodes to increase the throughput between a pair of transmitter and receiver. We focus on developing effective methods to position the UAV(s) in the sky in the presence of a major source of interference, the existence of which makes the problem non-trivial. First, we consider utilizing a single UAV, for which we develop a theoretical framework to determine its optimal position aiming to maximize the SIR of the system. To this end, we investigate the problem for three practical scenarios, in which the position of the UAV is: (i) vertically fixed, horizontally adjustable; (ii) horizontally fixed, vertically adjustable; (iii) both horizontally and vertically adjustable. Afterward, we consider employing multiple UAVs, for which we propose a cost-effective method that simultaneously minimizes the number of required UAVs and determines their optimal positions so as to guarantee a certain SIR of the system. We further develop a distributed placement algorithm, which can increase the SIR of the system given an arbitrary number of UAVs. Numerical simulations are provided to evaluate the performance of our proposed methods.
A Microstates Approach to Relative Free Entropy

We introduce a microstates-based notion of relative free entropy. This quantity is a microstates analog of Voiculescu's microstates-free relative entropy χ*(X1,…,Xn:B), and coinsides with his microstates entropy in the case that the algebra B consists of just mulitplies of identity. More generally, there is a formula relating the two in the case that B is a matrix algebra. We discuss several properties of our relative entropy, including maximization results and an infinitesimal change of variables formula.
Brute-Force Facial Landmark Analysis With A 140,000-Way Classifier

We propose a simple approach to visual alignment, focusing on the illustrative task of facial landmark estimation. While most prior work treats this as a regression problem, we instead formulate it as a discrete $K$-way classification task, where a classifier is trained to return one of $K$ discrete alignments. One crucial benefit of a classifier is the ability to report back a (softmax) distribution over putative alignments. We demonstrate that this distribution is a rich representation that can be marginalized (to generate uncertainty estimates over groups of landmarks) and conditioned on (to incorporate top-down context, provided by temporal constraints in a video stream or an interactive human user). Such capabilities are difficult to integrate into classic regression-based approaches. We study performance as a function of the number of classes $K$, including the extreme "exemplar class" setting where $K$ is equal to the number of training examples (140K in our setting). Perhaps surprisingly, we show that classifiers can still be learned in this setting. When compared to prior work in classification, our $K$ is unprecedentedly large, including many "fine-grained" classes that are very similar. We address these issues by using a multi-label loss function that allows for training examples to be non-uniformly shared across discrete classes. We perform a comprehensive experimental analysis of our method on standard benchmarks, demonstrating state-of-the-art results for facial alignment in videos.
On quadratic rational maps with prescribed good reduction

Given a number field $K$ and a finite set $S$ of places of $K$, the first main result of this paper shows that the quadratic rational maps $\phi:{\mathbb P}^1\to{\mathbb P}^1$ defined over $K$ which have good reduction at all places outside $S$ comprise a Zariski-dense subset of the moduli space ${\mathcal M}_2$ parametrizing all isomorphism classes of quadratic rational maps. We then consider quadratic rational maps with double unramified fixed-point structure, and our second main result establishes a geometric Shafarevich-type non-Zariski-density result for the set of such maps with good reduction outside $S$. We also prove a variation of this result for quadratic rational maps with unramified 2-cycle structure.
Schur Number Five.

We present the solution of a century-old problem known as Schur Number Five: What is the largest (natural) number $n$ such that there exists a five-coloring of the positive numbers up to $n$ without a monochromatic solution of the equation $a + b = c$? We obtained the solution, $n = 160$, by encoding the problem into propositional logic and applying massively parallel satisfiability solving techniques on the resulting formula. We constructed and validated a proof of the solution to increase trust in the correctness of the multi-CPU-year computations. The proof is two petabytes in size and was certified using a formally verified proof checker, demonstrating that any result by satisfiability solvers---no matter how large---can now be validated using highly trustworthy systems.
UNCOUNTABLE REAL CLOSED FIELDS WITH PA INTEGER PARTS

D’Aquino, Knight, and Starchenko classified the countable real closed fields with integer parts that are nonstandard models of Peano Arithmetic. We rule out some possibilities for extending their results to the uncountable and study real closures of ɷ1-like models of PA.
Machine learning models for the lattice thermal conductivity prediction of inorganic materials

Abstract The lattice thermal conductivity ( κ L ) is a critical property of thermoelectrics, thermal barrier coating materials and semiconductors. While accurate empirical measurements of κ L are extremely challenging, it is usually approximated through computational approaches, such as semi-empirical models, Green-Kubo formalism coupled with molecular dynamics simulations, and first-principles based methods. However, these theoretical methods are not only limited in terms of their accuracy, but sometimes become computationally intractable owing to their cost. Thus, in this work, we build a machine learning (ML)-based model to accurately and instantly predict κ L of inorganic materials, using a benchmark data set of experimentally measured κ L of about 100 inorganic materials. We use advanced and universal feature engineering techniques along with the Gaussian process regression algorithm, and compare the performance of our ML model with past theoretical works. The trained ML model is not only helpful for rational design and screening of novel materials, but we also identify key features governing the thermal transport behavior in non-metals.
Stable Bin Packing of Non-convex 3D Objects with a Robot Manipulator

Recent progress in the field of robotic manipulation has generated interest in fully automatic object packing in warehouses. This paper proposes a formulation of the packing problem that is tailored to the automated warehousing domain. Besides minimizing waste space inside a container, the problem requires stability of the object pile during packing and the feasibility of the robot motion executing the placement plans. To address this problem, a set of constraints are formulated, and a constructive packing pipeline is proposed to solve these constraints. The pipeline is able to pack geometrically complex, non-convex objects while satisfying stability and robot packability constraints. In particular, a new 3D positioning heuristic called Heightmap-Minimization heuristic is proposed, and heightmaps are used to speed up the search. Experimental evaluation of the method is conducted with a realistic physical simulator on a dataset of scanned real-world items, demonstrating stable and high-quality packing plans compared with other 3D packing methods.
Interactive Effects of Seagrass and the Microphytobenthos on Sediment Suspension Within Shallow Coastal Bays

The suspension and transport of sediments in coastal environments influences water column clarity, and also affects the growth of photosynthetic organisms. The presence of benthic vegetation, such as seagrass, can attenuate wave and tidal energy, thereby altering suspended sediment concentrations (SSC) and microphytobenthos (MPB) biomass that secrete biogenic compounds that can increase sediment cohesion. The dual role of seagrass and MPB in altering the seasonal critical bed shear stress, τc, necessary to suspend sediment was studied within a Zostera marina seagrass meadow and an adjacent unvegetated region within a shallow coastal bay in Virginia, USA. Hydrodynamics and MPB biomass were recorded seasonally to determine the critical bed shear stress and subsequent SSC response. Results show that seagrasses reduced mean currents and waves, thus lowering SSC within the meadow. In addition, seagrass created favorable conditions for MPB growth, with annual mean sediment carbohydrate concentrations, a proxy for MPB activity, to be double within the seagrass compared to the unvegetated site. Sediment carbohydrate concentrations within the seagrass bed were higher during winter than summer due to enhanced light penetration, which coincided with an increase in τc to 0.056 Pa compared to 0.024 Pa. τc was found to be 0.021 Pa at the unvegetated site, with bed shear exceeding this threshold > 85% of the time. These findings suggest both MPB and seagrass play an important and interactive role in regulating seasonal sediment resuspension, and constant reworking of the bed sediments in high shear regions prevented the establishment of MPB.
Characterizing the Exact Behaviors of Temporal Difference Learning Algorithms Using Markov Jump Linear System Theory

In this paper, we provide a unified analysis of temporal difference learning algorithms with linear function approximators by exploiting their connections to Markov jump linear systems (MJLS). We tailor the MJLS theory developed in the control community to characterize the exact behaviors of the first and second order moments of a large family of temporal difference learning algorithms. For both the IID and Markov noise cases, we show that the evolution of some augmented versions of the mean and covariance matrix of the TD estimation error exactly follows the trajectory of a deterministic linear time-invariant (LTI) dynamical system. Applying the well-known LTI system theory, we obtain closed-form expressions for the mean and covariance matrix of the TD estimation error at any time step. We provide a tight matrix spectral radius condition to guarantee the convergence of the covariance matrix of the TD estimation error, and perform a perturbation analysis to characterize the dependence of the TD behaviors on learning rate. For the IID case, we provide an exact formula characterizing how the mean and covariance matrix of the TD estimation error converge to the steady state values at a linear rate. For the Markov case, we use our formulas to explain how the behaviors of TD learning algorithms are affected by learning rate and the underlying Markov chain. For both cases, upper and lower bounds for the mean square TD error are provided. The mean square TD error is shown to converge linearly to an exact limit.