cssi/SciSciGPT-SciSciNet huggingface dataset:
Dehn’s algorithm for simple diagrams

Dehn gave an algorithm for deciding if two cyclic words in the standard presentation of the fundamental group of a closed oriented surface of positive genus represent the same conjugacy class. A simple diagram on a surface is a disjoint union of simple closed curves none of which bound a disk. If F is a once punctured closed surface of negative Euler characteristic, simple diagrams are classified up to isotopy by their geometric intersection numbers with the edges of an ideal triangulation of F. Simple diagrams on the unpunctured surface F can be represented by simple diagrams on F. The weight of a simple diagram is the sum of its geometric intersection numbers with the edges of the triangulation. We show that you can pass from any representative to a least weight representative via a sequence of elementary moves, that monotonically decrease weights. This leads to a geometric analog of Dehn’s algorithm for simple diagrams.
The expected codimension of a matroid variety

Matroid varieties are the closures in the Grassmannian of sets of points defined by specifying which Plucker coordinates vanish and which do not. In general these varieties are very ill-behaved, but in many cases one can estimate their codimension by keeping careful track of the conditions imposed by the vanishing of each Plucker coordinates on the columns of the matrix representing a point of the Grassmannian. This paper presents a way to make this procedure precise, producing a number for each matroid variety called its expected codimension that can be computed combinatorially solely from the list of Plucker coordinates that are prescribed to vanish. We prove that for a special, well-studied class of matroid varieties called positroid varieties, the expected codimension coincides with the actual codimension.
Using a new zero forcing process to guarantee the Strong Arnold Property

Abstract The maximum nullity M ( G ) and the Colin de Verdiere type parameter ξ ( G ) both consider the largest possible nullity over matrices in S ( G ) , which is the family of real symmetric matrices whose i , j -entry, i ≠ j , is nonzero if i is adjacent to j, and zero otherwise; however, ξ ( G ) restricts to those matrices A in S ( G ) with the Strong Arnold Property, which means X = O is the only symmetric matrix that satisfies A ∘ X = O , I ∘ X = O , and A X = O . This paper introduces zero forcing parameters Z SAP ( G ) and Z vc ( G ) , and proves that Z SAP ( G ) = 0 implies every matrix A ∈ S ( G ) has the Strong Arnold Property and that the inequality M ( G ) − Z vc ( G ) ≤ ξ ( G ) holds for every graph G. Finally, the values of ξ ( G ) are computed for all graphs up to 7 vertices, establishing ξ ( G ) = ⌊ Z ⌋ ( G ) for these graphs.
Operator scaling with specified marginals

The completely positive maps, a generalization of the nonnegative matrices, are a well-studied class of maps from n× n matrices to m× m matrices. The existence of the operator analogues of doubly stochastic scalings of matrices, the study of which is known as operator scaling, is equivalent to a multitude of problems in computer science and mathematics such rational identity testing in non-commuting variables, noncommutative rank of symbolic matrices, and a basic problem in invariant theory (Garg et. al., 2016).We study operator scaling with specified marginals, which is the operator analogue of scaling matrices to specified row and column sums (or marginals). We characterize the operators which can be scaled to given marginals, much in the spirit of the Gurvits’ algorithmic characterization of the operators that can be scaled to doubly stochastic (Gurvits, 2004). Our algorithm, which is a modified version of Gurvits’ algorithm, produces approximate scalings in time poly(n,m) whenever scalings exist. A central ingredient in our analysis is a reduction from operator scaling with specified marginals to operator scaling in the doubly stochastic setting.Instances of operator scaling with specified marginals arise in diverse areas of study such as the Brascamp-Lieb inequalities, communication complexity, eigenvalues of sums of Hermitian matrices, and quantum information theory. Some of the known theorems in these areas, several of which had no algorithmic proof, are straightforward consequences of our characterization theorem. For instance, we obtain a simple algorithm to find, when it exists, a tuple of Hermitian matrices with given spectra whose sum has a given spectrum. We also prove new theorems such as a generalization of Forster’s theorem (Forster, 2002) concerning radial isotropic position.
Obstructing pseudoconvex embeddings and contractible Stein fillings for Brieskorn spheres

Abstract A question in low-dimensional symplectic topology asks whether every compact contractible 4-manifold admits the structure of a Stein domain. A related conjecture due to Gompf asserts that no nontrivial Brieskorn homology sphere admits a pseudoconvex embedding in C 2 , with either orientation. We give the first known example of a contractible, boundary-irreducible 4-manifold that admits no Stein structure with either orientation, though its boundary has Stein fillings with both orientations. We also verify Gompf's conjecture, with one orientation, for a family of Brieskorn spheres of which some are known to admit a smooth embedding in C 2 . A byproduct of our example is the construction of a cork that does not admit a Stein structure with either orientation.
Visual Progression Analysis of Student Records Data

University curriculum, both on a campus level and on a per-major level, are affected in a complex way by many decisions of many administrators and faculty over time. As universities across the United States share an urgency to significantly improve student success and success retention, there is a pressing need to better understand how the student population is progressing through the curriculum, and how to provide better supporting infrastructure and refine the curriculum for the purpose of improving student outcomes. This work has developed a visual knowledge discovery system called eCamp that pulls together a variety of population-scale data products, including student grades, major descriptions, and graduation records. These datasets were previously disconnected and only available to and maintained by independent campus offices. The framework models and analyzes the multi-level relationships hidden within these data products, and visualizes the student flow patterns through individual majors as well as through a hierarchy of majors. These results support analytical tasks involving student outcomes, student retention, and curriculum design. It is shown how eCamp has revealed student progression information that was previously unavailable.
Median-Truncated Nonconvex Approach for Phase Retrieval With Outliers

This paper investigates the phase retrieval problem, which aims to recover a signal from the magnitudes of its linear measurements. We develop statistically and computationally efficient algorithms for the situation when the measurements are corrupted by sparse outliers that can take arbitrary values. We propose a novel approach to robustify the gradient descent algorithm by using the sample median as a guide for pruning spurious samples in initialization and local search. Adopting a Poisson loss and a reshaped quadratic loss, respectively, we obtain two algorithms termed median-truncated Wirtinger flow and median-reshaped Wirtinger flow , both of which provably recover the signal from a near-optimal number of measurements when the measurement vectors are composed of independent and identically distributed Gaussian entries, up to a logarithmic factor, even when a constant fraction of the measurements is adversarially corrupted. We further show that both algorithms are stable in the presence of additional dense bounded noise. Our analysis is accomplished by developing non-trivial concentration results of median-related quantities, which may be of independent interest. We provide numerical experiments to demonstrate the effectiveness of our approach.
Dynamical localization in molecular alignment of kicked quantum rotors

The periodically $\ensuremath{\delta}$-kicked quantum linear rotor is known to experience nonclassical bounded energy growth due to quantum dynamical localization in angular momentum space. We study the effect of random deviations of the kick period in simulations and experiments. This breaks the energy and angular momentum localization and increases the rotational alignment, which is the analog of the onset of Anderson localization in one-dimensional chains.
Regular Incidence Complexes, Polytopes, and C-Groups

Regular incidence complexes are combinatorial incidence structures generalizing regular convex polytopes, regular complex polytopes, various types of incidence geometries, and many other highly symmetric objects. The special case of abstract regular polytopes has been well-studied. The paper describes the combinatorial structure of a regular incidence complex in terms of a system of distinguished generating subgroups of its automorphism group or a flag-transitive subgroup. Then the groups admitting a flag-transitive action on an incidence complex are characterized as generalized string C-groups. Further, extensions of regular incidence complexes are studied, and certain incidence complexes particularly close to abstract polytopes, called abstract polytope complexes, are investigated.
Higher Galois theory

Abstract We generalize toposic Galois theory to higher topoi. We show that locally constant sheaves in a locally ( n − 1 ) -connected n -topos are equivalent to representations of its fundamental pro- n -groupoid, and that the latter can be described in terms of Galois torsors. We also show that finite locally constant sheaves in an arbitrary ∞-topos are equivalent to finite representations of its fundamental pro-∞-groupoid. Finally, we relate the fundamental pro-∞-groupoid of 1-topoi to the construction of Artin and Mazur and, in the case of the etale topos of a scheme, to its refinement by Friedlander.
CONGRUENCES FOR PARTITION PAIRS WITH CONDITIONS

We prove congruences for the number of partition pairs $(\pi_1,\pi_2)$ such that $\pi_1$ is non-empty, $s(\pi_1)\le s(\pi_2)$, and $\ell(\pi_2)< 2s(\pi_1)$ where $s(\pi)$ is the smallest part and $\ell(\pi)$ is the largest part of a partition. The proofs use Bailey's Lemma and a generalized Lambert series identity of Chan. We also discuss how a partition pair crank gives combinatorial refinements of these congruences.
Analysis of a model microswimmer with applications to blebbing cells and mini-robots

Recent research has shown that motile cells can adapt their mode of propulsion depending on the environment in which they find themselves. One mode is swimming by blebbing or other shape changes, and in this paper we analyze a class of models for movement of cells by blebbing and of nano-robots in a viscous fluid at low Reynolds number. At the level of individuals, the shape changes comprise volume exchanges between connected spheres that can control their separation, which are simple enough that significant analytical results can be obtained. Our goal is to understand how the efficiency of movement depends on the amplitude and period of the volume exchanges when the spheres approach closely during a cycle. Previous analyses were predicated on wide separation, and we show that the speed increases significantly as the separation decreases due to the strong hydrodynamic interactions between spheres in close proximity. The scallop theorem asserts that at least two degrees of freedom are needed to produce net motion in a cyclic sequence of shape changes, and we show that these degrees can reside in different swimmers whose collective motion is studied. We also show that different combinations of mode sharing can lead to significant differences in the translation and performance of pairs of swimmers.
A Discriminative View of MRF Pre-processing Algorithms

While Markov Random Fields (MRFs) are widely used in computer vision, they present a quite challenging inference problem. MRF inference can be accelerated by preprocessing techniques like Dead End Elimination (DEE) [8] or QPBO-based approaches [18, 24, 25] which compute the optimal labeling of a subset of variables. These techniques are guaranteed to never wrongly label a variable but they often leave a large number of variables unlabeled. We address this shortcoming by interpreting pre-processing as a classification problem, which allows us to trade off false positives (i.e., giving a variable an incorrect label) versus false negatives (i.e., failing to label a variable). We describe an efficient discriminative rule that finds optimal solutions for a subset of variables. Our technique provides both per-instance and worst-case guarantees concerning the quality of the solution. Empirical studies were conducted over several benchmark datasets. We obtain a speedup factor of 2 to 12 over expansion moves [4] without preprocessing, and on difficult non-submodular energy functions produce slightly lower energy.
The “Riemann Hypothesis” is true for period polynomials of almost all newforms

The period polynomial \(r_f(z)\) for a weight \(k \ge 3\) and level N newform \(f \in S_k(\varGamma _0(N),\chi )\) is the generating function for special values of L(s, f). The functional equation for L(s, f) induces a functional equation on \(r_f(z)\). Jin, Ma, Ono, and Soundararajan proved that for all newforms f of even weight \(k \ge 4\) and trivial nebentypus, the “Riemann Hypothesis” holds for \(r_f(z)\): that is, all roots of \(r_f(z)\) lie on the circle of symmetry \(|z| =1/\sqrt{N}\). We generalize their methods to prove that this phenomenon holds for all but possibly finitely many newforms f of weight \(k \ge 3\) with any nebentypus. We also show that the roots of \(r_f(z)\) are equidistributed if N or k is sufficiently large.
Fast Moment Estimation for Generalized Latent Dirichlet Models

ABSTRACTWe develop a generalized method of moments (GMM) approach for fast parameter estimation in a new class of Dirichlet latent variable models with mixed data types. Parameter estimation via GMM has computational and statistical advantages over alternative methods, such as expectation maximization, variational inference, and Markov chain Monte Carlo. A key computational advantage of our method, Moment Estimation for latent Dirichlet models (MELD), is that parameter estimation does not require instantiation of the latent variables. Moreover, performance is agnostic to distributional assumptions of the observations. We derive population moment conditions after marginalizing out the sample-specific Dirichlet latent variables. The moment conditions only depend on component mean parameters. We illustrate the utility of our approach on simulated data, comparing results from MELD to alternative methods, and we show the promise of our approach through the application to several datasets. Supplementary materia...
Meshfree finite difference approximations for functions of the eigenvalues of the Hessian

We introduce meshfree finite difference methods for approximating nonlinear elliptic operators that depend on second directional derivatives or the eigenvalues of the Hessian. Approximations are defined on unstructured point clouds, which allows for very complicated domains and a non-uniform distribution of discretisation points. The schemes are monotone, which ensures that they converge to the viscosity solution of the underlying PDE as long as the equation has a comparison principle. Numerical experiments demonstrate convergence for a variety of equations including problems posed on random point clouds, complex domains, degenerate equations, and singular solutions.
Improved calculation of vibrational mode lifetimes in anharmonic solids – Part II: Numerical results

In a two-part publication, we propose and analyze a formal foundation for practical calculations of vibrational mode lifetimes in solids. The approach is based on a recursion method analysis of the Liouvillian. In the first part, we derived the lifetime of vibrational modes in terms of moments of the power spectrum of the Liouvillian as projected onto the relevant subspace of phase space. In practical terms, the moments are evaluated as ensemble averages of well-defined operators, meaning that the entire calculation is to be done with Monte Carlo. In this second part, we present a numerical analysis of a simple anharmonic model of lattice vibrations which exhibits two regimes of behavior, at low temperature and at high temperature. Our results show that, for this simple model, the mode lifetime as a function of temperature and wavevector can be simply approximated as a function of the shift in frequency from the harmonic limit. We next compare these calculations, obtained using both Monte Carlo and computationally intensive molecular dynamics, with those using the lowest order moment formalism from the Part I. We show that, in the high temperature regime, the lowest order approximation gives a reliable approximation to the calculated lifetimes. The results also show that extension to at least fourth moment is required to obtain reliable results over a full range of temperatures.
Generalizations of the image conjecture and the Mathieu conjecture

Abstract We first propose a generalization of the image conjecture Zhao (submitted for publication) [31] for the commuting differential operators related with classical orthogonal polynomials. We then show that the non-trivial case of this generalized image conjecture is equivalent to a variation of the Mathieu conjecture Mathieu (1997) [21] from integrals of G -finite functions over reductive Lie groups G to integrals of polynomials over open subsets of R n with any positive measures. Via this equivalence, the generalized image conjecture can also be viewed as a natural variation of the Duistermaat and van der Kallen theorem Duistermaat and van der Kallen (1998) [14] on Laurent polynomials with no constant terms. To put all the conjectures above in a common setting, we introduce what we call the Mathieu subspaces of associative algebras. We also discuss some examples of Mathieu subspaces from other sources and derive some general results on this newly introduced notion.
A Deeper Look at 3D Shape Classifiers

We investigate the role of representations and architectures for classifying 3D shapes in terms of their computational efficiency, generalization, and robustness to adversarial transformations. By varying the number of training examples and employing cross-modal transfer learning we study the role of initialization of existing deep architectures for 3D shape classification. Our analysis shows that multiview methods continue to offer the best generalization even without pretraining on large labeled image datasets, and even when trained on simplified inputs such as binary silhouettes. Furthermore, the performance of voxel-based 3D convolutional networks and point-based architectures can be improved via cross-modal transfer from image representations. Finally, we analyze the robustness of 3D shape classifiers to adversarial transformations and present a novel approach for generating adversarial perturbations of a 3D shape for multiview classifiers using a differentiable renderer. We find that point-based networks are more robust to point position perturbations while voxel-based and multiview networks are easily fooled with the addition of imperceptible noise to the input.
Single-scattering optical tomography

We consider the problem of optical tomographic imaging in the mesoscopic regime where the photon mean-free path is on the order of the system size. It is shown that a tomographic imaging technique can be devised which is based on the assumption of single scattering and utilizes a generalization of the Radon transform which we refer to as the broken-ray transform. The technique can be used to recover the extinction coefficient of an inhomogeneous medium from angularly resolved measurements and is illustrated with numerical simulations. The forward data for these simulations were obtained by numerically solving the radiative transport equation without any approximations. Tomographic imaging in slabs of different widths was considered and it was shown that the technique can tolerate a maximum width that corresponds to approximately six scattering events. It is also shown that the use of broken rays does not result in additional ill posedness of the inverse problem in comparison to the classical problem of inverting the Radon transform. Applications to biomedical imaging are described.
Secure Degrees of Freedom for the MIMO Wire-Tap Channel With a Multi-Antenna Cooperative Jammer

In this paper, a multiple antenna wire-tap channel in the presence of a multi-antenna cooperative jammer is studied. In particular, the secure degrees of freedom (s.d.o.f.) of this channel is established, with $N_{t}$ antennas at the transmitter, $N_{r}$ antennas at the legitimate receiver, and $N_{e}$ antennas at the eavesdropper, for all possible values of the number of antennas, $N_{c}$ , at the cooperative jammer. In establishing the result, several different ranges of $N_{c}$ need to be considered separately. The lower and upper bounds for these ranges of $N_{c}$ are derived, and are shown to be tight. The achievability techniques developed rely on a variety of signaling, beamforming, and alignment techniques, which vary according to the (relative) number of antennas at each terminal and whether the s.d.o.f. is integer valued. Specifically, it is shown that, whenever the s.d.o.f. is integer valued, Gaussian signaling for both transmission and cooperative jamming, linear precoding at the transmitter and the cooperative jammer, and linear processing at the legitimate receiver, are sufficient for achieving the s.d.o.f. of the channel. By contrast, when the s.d.o.f. is not an integer, the achievable schemes need to rely on structured signaling at the transmitter and the cooperative jammer, and joint signal space and signal scale alignment. The converse is established by combining an upper bound, which allows for full cooperation between the transmitter and the cooperative jammer, with another upper bound which exploits the secrecy and reliability constraints.
Eigenvalue clustering, control energy, and logarithmic capacity

Abstract We prove two bounds showing that if the eigenvalues of a matrix are clustered in a region of the complex plane then the corresponding discrete-time linear system requires significant energy to control. A curious feature of one of our bounds is that the dependence on the region is via its logarithmic capacity, which is a measure of how well a unit of mass may be spread out over the region to minimize a logarithmic potential.
The value of timing information in event-triggered control: The scalar case

The problem of event-triggered control with rate-limited communication is considered. For continuous-time scalar systems without disturbances, a phase transition behavior of the transmission rate required for stabilization as a function of the communication delay is revealed. It is shown that for low values of the delay the timing information carried by the triggering events is large and the system can be stabilized with any positive rate. On the other hand, when the delay exceeds a certain threshold that depends on the given triggering strategy, the timing information alone is not enough to achieve stabilization and the rate must begin to grow, eventually becoming larger than what required by the classic data-rate theorem. The critical point where the transmission rate equals the one imposed by the data-rate theorem occurs when the delay equals the inverse of the entropy rate of the plant, representing the intrinsic rate at which the system generates information. At this critical point, the timing information supplied by event triggering is completely balanced by the information loss due to the communication delay. Exponential convergence guarantees are also discussed, and an explicit construction providing a sufficient condition for stabilization is given.
Gaps of Smallest Possible Order between Primes in an Arithmetic Progression

Let $t \in \mathbb{N}$, $\eta >0$. Suppose that $x$ is a sufficiently large real number and $q$ is a natural number with $q \leq x^{5/12-\eta}$, $q$ not a multiple of the conductor of the exceptional character $\chi^*$ (if it exists). Suppose further that, \[ \max \{p : p | q \} < \exp (\frac{\log x}{C \log \log x}) \; \; {and} \; \; \prod_{p | q} p < x^{\delta}, \] where $C$ and $\delta$ are suitable positive constants depending on $t$ and $\eta$. Let $a \in \mathbb{Z}$, $(a,q)=1$ and \[ \mathcal{A} = \{n \in (x/2, x]: n \equiv a \pmod{q} \} . \] We prove that there are primes $p_1 < p_2 < ... < p_t$ in $\mathcal{A}$ with \[ p_t - p_1 \ll qt \exp (\frac{40 t}{9-20 \theta}) . \] Here $\theta = (\log q) / \log x$.
Strong mixed-integer formulations for the floor layout problem

The floor layout problem (FLP) tasks a designer with positioning a collection of rectangular boxes on a fixed floor in such a way that minimizes total communication costs between the components. Wh...
Generalized Earley Parser: Bridging Symbolic Grammars and Sequence Data for Future Prediction

Future predictions on sequence data (e.g., videos or audios) require the algorithms to capture non-Markovian and compositional properties of high-level semantics. Context-free grammars are natural choices to capture such properties, but traditional grammar parsers (e.g., Earley parser) only take symbolic sentences as inputs. In this paper, we generalize the Earley parser to parse sequence data which is neither segmented nor labeled. This generalized Earley parser integrates a grammar parser with a classifier to find the optimal segmentation and labels, and makes top-down future predictions. Experiments show that our method significantly outperforms other approaches for future human activity prediction.
Naturality of Heegaard Floer invariants under positive rational contact surgery

For a nullhomologous Legendrian knot in a closed contact $3$-manifold $Y$ we consider a contact structure obtained by positive rational contact surgery. We prove that in this situation the Heegaard Floer contact invariant of $Y$ is mapped by a surgery cobordism to the contact invariant of the result of contact surgery, and we characterize the $\mathrm{spin}^c$ structure on the cobordism that induces the relevant map. As a consequence we determine necessary and sufficient conditions for the nonvanishing of the contact invariant after rational surgery on a Legendrian knot in the standard $3$-sphere, generalizing previous results of Lisca–Stipsicz and Golla. In fact, our methods allow direct calculation of the contact invariant in terms of the rational surgery mapping cone of Ozsvath and Szabo. The proof involves a construction called reducible open book surgery, which reduces in special cases to the capping-off construction studied by Baldwin.
Distributed Hierarchical Control for State Estimation With Robotic Sensor Networks

This paper addresses active state estimation with a team of robotic sensors. The states to be estimated are represented by spatially distributed, uncorrelated, stationary vectors. Given a prior belief on the geographic locations of the states, we cluster the states in moderately sized groups and propose a new hierarchical dynamic programming framework to compute optimal sensing policies for each cluster that mitigates the computational cost of planning optimal policies in the combined belief space. Then, we develop a decentralized assignment algorithm that dynamically allocates clusters to robots based on the precomputed optimal policies at each cluster. The integrated distributed state estimation framework is optimal at the cluster level but also scales very well to large numbers of states and robot sensors. We demonstrate efficiency of the proposed method in both simulations and real-world experiments using stereoscopic vision sensors.
Square-Contact Representations of Partial 2-Trees and Triconnected Simply-Nested Graphs

A square-contact representation of a planar graph $G=(V,E)$ maps vertices in $V$ to interior-disjoint axis-aligned squares in the plane and edges in $E$ to adjacencies between the sides of the corresponding squares. In this paper, we study proper square-contact representations of planar graphs, in which any two squares are either disjoint or share infinitely many points. We characterize the partial $2$-trees and the triconnected cycle-trees allowing for such representations. For partial $2$-trees our characterization uses a simple forbidden subgraph whose structure forces a separating triangle in any embedding. For the triconnected cycle-trees, a subclass of the triconnected simply-nested graphs, we use a new structural decomposition for the graphs in this family, which may be of independent interest. Finally, we study square-contact representations of general triconnected simply-nested graphs with respect to their outerplanarity index.
Conic Scan-and-Cover algorithms for nonparametric topic modeling

We propose new algorithms for topic modeling when the number of topics is unknown. Our approach relies on an analysis of the concentration of mass and angular geometry of the topic simplex, a convex polytope constructed by taking the convex hull of vertices representing the latent topics. Our algorithms are shown in practice to have accuracy comparable to a Gibbs sampler in terms of topic estimation, which requires the number of topics be given. Moreover, they are one of the fastest among several state of the art parametric techniques. Statistical consistency of our estimator is established under some conditions.
Transport of a dilute active suspension in pressure-driven channel flow

Confined suspensions of active particles show peculiar dynamics characterized by wall accumulation, as well as upstream swimming, centreline depletion and shear trapping when a pressure-driven flow is imposed. We use theory and numerical simulations to investigate the effects of confinement and non-uniform shear on the dynamics of a dilute suspension of Brownian active swimmers by incorporating a detailed treatment of boundary conditions within a simple kinetic model where the configuration of the suspension is described using a conservation equation for the probability distribution function of particle positions and orientations, and where particle–particle and particle–wall hydrodynamic interactions are neglected. Based on this model, we first investigate the effects of confinement in the absence of flow, in which case the dynamics is governed by a swimming Peclet number, or ratio of the persistence length of particle trajectories over the channel width, and a second swimmer-specific parameter whose inverse measures the strength of propulsion. In the limit of weak and strong propulsion, asymptotic expressions for the full distribution function are derived. For finite propulsion, analytical expressions for the concentration and polarization profiles are also obtained using a truncated moment expansion of the distribution function. In agreement with experimental observations, the existence of a concentration/polarization boundary layer in wide channels is reported and characterized, suggesting that wall accumulation in active suspensions is primarily a kinematic effect that does not require hydrodynamic interactions. Next, we show that application of a pressure-driven Poiseuille flow leads to net upstream swimming of the particles relative to the flow, and an analytical expression for the mean upstream velocity is derived in the weak-flow limit. In stronger imposed flows, we also predict the formation of a depletion layer near the channel centreline, due to cross-streamline migration of the swimming particles towards high-shear regions where they become trapped, and an asymptotic analysis in the strong-flow limit is used to obtain a scale for the depletion layer thickness and to rationalize the non-monotonic dependence of the intensity of depletion upon flow rate. Our theoretical predictions are all shown to be in excellent agreement with finite-volume numerical simulations of the kinetic model, and are also supported by recent experiments on bacterial suspensions in microfluidic devices.
Importance Sampling with Unequal Support.

Importance sampling is often used in machine learning when training and testing data come from different distributions. In this paper we propose a new variant of importance sampling that can reduce the variance of importance samplingbased estimates by orders of magnitude when the supports of the training and testing distributions differ. After motivating and presenting our new importance sampling estimator, we provide a detailed theoretical analysis that characterizes both its bias and variance relative to the ordinary importance sampling estimator (in various settings, which include cases where ordinary importance sampling is biased, while our new estimator is not, and vice versa). We conclude with an example of how our new importance sampling estimator can be used to improve estimates of how well a new treatment policy for diabetes will work for an individual, using only data from when the individual used a previous treatment policy.
Topological forcing semantics with settling

Abstract It was realized early on that topologies can model constructive systems, as the open sets form a Heyting algebra. After the development of forcing, in the form of Boolean-valued models, it became clear that, just as over ZF any Boolean-valued model also satisfies ZF, Heyting-valued models satisfy IZF, which stands for Intuitionistic ZF, the most direct constructive re-working of the ZF axioms. In this paper, we return to topologies, and introduce a variant model, along with a correspondingly revised forcing or satisfaction relation. The purpose is to prove independence results related to weakenings of the Power Set axiom. The original motivation is the second model of [9] , based on R , which shows that Exponentiation, in the context of CZF minus Subset Collection, does not suffice to prove that the Dedekind reals form a set. The current semantics is the generalization of that model from R to an arbitrary topological space. It is investigated which set-theoretic principles hold in such models in general. In addition, natural properties of the underlying topological space are shown to imply the validity of stronger such principles.
Mean field analysis of neural networks: A central limit theorem

Abstract We rigorously prove a central limit theorem for neural network models with a single hidden layer. The central limit theorem is proven in the asymptotic regime of simultaneously (A) large numbers of hidden units and (B) large numbers of stochastic gradient descent training iterations. Our result describes the neural network’s fluctuations around its mean-field limit. The fluctuations have a Gaussian distribution and satisfy a stochastic partial differential equation. The proof relies upon weak convergence methods from stochastic analysis. In particular, we prove relative compactness for the sequence of processes and uniqueness of the limiting process in a suitable Sobolev space.
f -GAN: training generative neural samplers using variational divergence minimization

Generative neural samplers are probabilistic models that implement sampling using feedforward neural networks: they take a random input vector and produce a sample from a probability distribution defined by the network weights. These models are expressive and allow efficient computation of samples and derivatives, but cannot be used for computing likelihoods or for marginalization. The generative-adversarial training method allows to train such models through the use of an auxiliary discriminative neural network. We show that the generative-adversarial approach is a special case of an existing more general variational divergence estimation approach. We show that any f-divergence can be used for training generative neural samplers. We discuss the benefits of various choices of divergence functions on training complexity and the quality of the obtained generative models.
Entropy-Isomap: Manifold Learning for High-dimensional Dynamic Processes

Scientific and engineering processes deliver massive high-dimensional data sets that are generated as non-linear transformations of an initial state and few process parameters. Mapping such data to a low-dimensional manifold facilitates better understanding of the underlying processes, and enables their optimization. In this paper, we first show that off-theshelf non-linear spectral dimensionality reduction methods, e.g., Isomap, fail for such data, primarily due to the presence of strong temporal correlations. Then, we propose a novel method, Entropy-Isomap, to address the issue. The proposed method is successfully applied to large data describing a fabrication process of organic materials. The resulting low-dimensional representation correctly captures process control variables, allows for low-dimensional visualization of the material morphology evolution, and provides key insights to improve the process.
Continuous control with deep reinforcement learning

Abstract: We adapt the ideas underlying the success of Deep Q-Learning to the continuous action domain. We present an actor-critic, model-free algorithm based on the deterministic policy gradient that can operate over continuous action spaces. Using the same learning algorithm, network architecture and hyper-parameters, our algorithm robustly solves more than 20 simulated physics tasks, including classic problems such as cartpole swing-up, dexterous manipulation, legged locomotion and car driving. Our algorithm is able to find policies whose performance is competitive with those found by a planning algorithm with full access to the dynamics of the domain and its derivatives. We further demonstrate that for many of the tasks the algorithm can learn policies end-to-end: directly from raw pixel inputs.
Exponential Energy Decay for Kerr–de Sitter Black Holes Beyond Event Horizons

We establish an exponential decay estimate for linear waves on the Kerr-de Sitter slowly rotating black hole. Combining the cutoff resolvent estimate of arXiv:1003.6128 with the red-shift effect and a parametrix near the event horizons, we obtain exponential decay on the whole space.
OSLO: Automatic Cell Counting and Segmentation for Oligodendrocyte Progenitor Cells

Reliable cell counting and segmentation of oligodendrocyte progenitor cells (OPCs) are critical image analysis steps that could potentially unlock mysteries regarding OPC function during pathology. We propose a saliency-based method to detect OPCS and use a marker-controlled watershed algorithm to segment the OPCS This method first implements frequency-tuned saliency detection on separate channels to obtain regions of cell candidates. Final detection results and internal markers can be computed by combining information from separate saliency maps. An optimal saliency level for OPCS (OSLO) is highlighted in this work. Here, watershed segmentation is performed efficiently with effective internal markers. Experiments show that our method outperforms existing methods in terms of accuracy.
Joint Embedding of Words and Labels for Text Classification

Word embeddings are effective intermediate representations for capturing semantic regularities between words, when learning the representations of text sequences. We propose to view text classification as a label-word joint embedding problem: each label is embedded in the same space with the word vectors. We introduce an attention framework that measures the compatibility of embeddings between text sequences and labels. The attention is learned on a training set of labeled samples to ensure that, given a text sequence, the relevant words are weighted higher than the irrelevant ones. Our method maintains the interpretability of word embeddings, and enjoys a built-in ability to leverage alternative sources of information, in addition to input text sequences. Extensive results on the several large text datasets show that the proposed framework outperforms the state-of-the-art methods by a large margin, in terms of both accuracy and speed.
Dueling Bandits with Weak Regret

We consider online content recommendation with implicit feedback through pairwise comparisons, formalized as the so-called dueling bandit problem. We study the dueling bandit problem in the Condorcet winner setting, and consider two notions of regret: the more well-studied strong regret, which is 0 only when both arms pulled are the Condorcet winner; and the less well-studied weak regret, which is 0 if either arm pulled is the Condorcet winner. We propose a new algorithm for this problem, Winner Stays (WS), with variations for each kind of regret: WS for weak regret (WS-W) has expected cumulative weak regret that is $O(N^2)$, and $O(N\log(N))$ if arms have a total order; WS for strong regret (WS-S) has expected cumulative strong regret of $O(N^2 + N \log(T))$, and $O(N\log(N)+N\log(T))$ if arms have a total order. WS-W is the first dueling bandit algorithm with weak regret that is constant in time. WS is simple to compute, even for problems with many arms, and we demonstrate through numerical experiments on simulated and real data that WS has significantly smaller regret than existing algorithms in both the weak- and strong-regret settings.
The Graphical Horseshoe Estimator for Inverse Covariance Matrices

We develop a new estimator of the inverse covariance matrix for high-dimensional multivariate normal data using the horseshoe prior. The proposed graphical horseshoe estimator has attractive proper...
ON WEYL MODULES OVER AFFINE LIE ALGEBRAS IN PRIME CHARACTERISTIC

We construct a family of homomorphisms between Weyl modules for affine Lie algebras in characteristic p, which supports our conjecture on the strong linkage principle in this context. We also exhibit a large class of reducible Weyl modules beyond level one, for p not necessarily small.
AdaNet: adaptive structural learning of artificial neural networks

We present new algorithms for adaptively learning artificial neural networks. Our algorithms (ADA NET) adaptively learn both the structure of the network and its weights. They are based on a solid theoretical analysis, including data-dependent generalization guarantees that we prove and discuss in detail. We report the results of large-scale experiments with one of our algorithms on several binary classification tasks extracted from the CIFAR-10 dataset and on the Criteo dataset. The results demonstrate that our algorithm can automatically learn network structures with very competitive performance accuracies when compared with those achieved by neural networks found by standard approaches.
Post-Inference Prior Swapping

While Bayesian methods are praised for their ability to incorporate useful prior knowledge, in practice, convenient priors that allow for computationally cheap or tractable inference are commonly used. In this paper, we investigate the following question: for a given model, is it possible to compute an inference result with any convenient false prior, and afterwards, given any target prior of interest, quickly transform this result into the target posterior? A potential solution is to use importance sampling (IS). However, we demonstrate that IS will fail for many choices of the target prior, depending on its parametric form and similarity to the false prior. Instead, we propose prior swapping, a method that leverages the pre-inferred false posterior to efficiently generate accurate posterior samples under arbitrary target priors. Prior swapping lets us apply less-costly inference algorithms to certain models, and incorporate new or updated prior information "post-inference". We give theoretical guarantees about our method, and demonstrate it empirically on a number of models and priors.
A sharp quantitative version of Hales' isoperimetric honeycomb theorem

Abstract We prove a sharp quantitative version of Hales' isoperimetric honeycomb theorem by exploiting a quantitative isoperimetric inequality for polygons and an improved convergence theorem for planar bubble clusters. Further applications include the description of isoperimetric tilings of the torus with respect to almost unit-area constraints or with respect to almost flat Riemannian metrics.
On the Sobolev-Poincare inequality of CR-manifolds

The purpose is to study the CR-manifold with a contact structure conformal to the Heisenberg group. In our previous work \cite{WY}, we have proved that if the $Q'$-curvature is nonnegative, and the integral of $Q'$-curvature is below the dimensional bound $c_1'$, then we have the isoperimetric inequality. In this paper, we manage to drop the condition on the nonnegativity of the $Q'$-curvature. We prove that the volume form $e^{4u}$ is a strong $A_\infty$ weight. As a corollary, we prove the Sobolev-Poincar\'e inequality on a class of CR-manifolds with integrable $Q'$-curvature.
Trading-off cost of deployment versus accuracy in learning predictive models

Predictive models are finding an increasing number of applications in many industries. As a result, a practical means for trading-off the cost of deploying a model versus its effectiveness is needed. Our work is motivated by risk prediction problems in healthcare. Cost-structures in domains such as healthcare are quite complex, posing a significant challenge to existing approaches. We propose a novel framework for designing cost-sensitive structured regularizers that is suitable for problems with complex cost dependencies. We draw upon a surprising connection to boolean circuits. In particular, we represent the problem costs as a multi-layer boolean circuit, and then use properties of boolean circuits to define an extended feature vector and a group regularizer that exactly captures the underlying cost structure. The resulting regularizer may then be combined with a fidelity function to perform model prediction, for example. For the challenging real-world application of risk prediction for sepsis in intensive care units, the use of our regularizer leads to models that are in harmony with the underlying cost structure and thus provide an excellent prediction accuracy versus cost tradeoff.
STARK: Structured dictionary learning through rank-one tensor recovery

In recent years, a class of dictionaries have been proposed for multidimensional (tensor) data representation that exploit the structure of tensor data by imposing a Kronecker structure on the dictionary underlying the data. In this work, a novel algorithm called “STARK” is provided to learn Kronecker structured dictionaries that can represent tensors of any order. By establishing that the Kronecker product of any number of matrices can be rearranged to form a rank-1 tensor, we show that Kronecker structure can be enforced on the dictionary by solving a rank-1 tensor recovery problem. Because rank-1 tensor recovery is a challenging nonconvex problem, we resort to solving a convex relaxation of this problem. Empirical experiments on synthetic and real data show promising results for our proposed algorithm.