cssi/SciSciGPT-SciSciNet huggingface dataset:
Depth2Action: Exploring Embedded Depth for Large-Scale Action Recognition

This paper performs the first investigation into depth for large-scale human action recognition in video where the depth cues are estimated from the videos themselves. We develop a new framework called depth2action and experiment thoroughly into how best to incorporate the depth information. We introduce spatio-temporal depth normalization (STDN) to enforce temporal consistency in our estimated depth sequences. We also propose modified depth motion maps (MDMM) to capture the subtle temporal changes in depth. These two components significantly improve the action recognition performance. We evaluate our depth2action framework on three large-scale action recognition video benchmarks. Our model achieves state-of-the-art performance when combined with appearance and motion information thus demonstrating that depth2action is indeed complementary to existing approaches.
On n-tardy sets

Abstract Harrington and Soare introduced the notion of an n -tardy set. They showed that there is a nonempty E property Q ( A ) such that if Q ( A ) then A is 2 -tardy. Since they also showed no 2 -tardy set is complete, Harrington and Soare showed that there exists an orbit of computably enumerable sets such that every set in that orbit is incomplete. Our study of n -tardy sets takes off from where Harrington and Soare left off. We answer all the open questions asked by Harrington and Soare about n -tardy sets. We show there is a 3 -tardy set A that is not computed by any 2 -tardy set B . We also show that there are nonempty E properties Q n ( A ) such that if Q n ( A ) then A is properly n -tardy.
Design of improved quasi-cyclic protograph-based Raptor-like LDPC codes for short block-lengths

Protograph-based Raptor-like low-density parity-check codes (PBRL codes) are a recently proposed family of easily encodable and decodable rate-compatible LDPC (RC-LDPC) codes. These codes have an excellent iterative decoding threshold and performance across all design rates. PBRL codes designed thus far, for both long and short block-lengths, have been based on optimizing the iterative decoding threshold of the protograph of the RC code family at various design rates. In this work, we propose a design method to obtain better quasi-cyclic (QC) RC-LDPC codes with PBRL structure for short block-lengths (of a few hundred bits). We achieve this by maximizing an upper bound on the minimum distance of any QC-LDPC code that can be obtained from the protograph of a PBRL ensemble. The obtained codes outperform the original PBRL codes at short block-lengths by significantly improving the error floor behavior at all design rates. Furthermore, we identify a reduction in complexity of the design procedure, facilitated by the general structure of a PBRL ensemble.
Real-time 2D Multi-Person Pose Estimation on CPU: Lightweight OpenPose.

In this work we adapt multi-person pose estimation architecture to use it on edge devices. We follow the bottom-up approach from OpenPose, the winner of COCO 2016 Keypoints Challenge, because of its decent quality and robustness to number of people inside the frame. With proposed network design and optimized post-processing code the full solution runs at 28 frames per second (fps) on Intel$\unicode{xAE}$ NUC 6i7KYB mini PC and 26 fps on Core$^{TM}$ i7-6850K CPU. The network model has 4.1M parameters and 9 billions floating-point operations (GFLOPs) complexity, which is just ~15% of the baseline 2-stage OpenPose with almost the same quality. The code and model are available as a part of Intel$\unicode{xAE}$ OpenVINO$^{TM}$ Toolkit.
Input Convex Neural Networks

This paper presents the input convex neural network architecture. These are scalar-valued (potentially deep) neural networks with constraints on the network parameters such that the output of the network is a convex function of (some of) the inputs. The networks allow for efficient inference via optimization over some inputs to the network given others, and can be applied to settings including structured prediction, data imputation, reinforcement learning, and others. In this paper we lay the basic groundwork for these models, proposing methods for inference, optimization and learning, and analyze their representational power. We show that many existing neural network architectures can be made input-convex with a minor modification, and develop specialized optimization algorithms tailored to this setting. Finally, we highlight the performance of the methods on multi-label prediction, image completion, and reinforcement learning problems, where we show improvement over the existing state of the art in many cases.
Asymptotic expansion for solutions of the Navier–Stokes equations with non-potential body forces

Abstract We study the long-time behavior of spatially periodic solutions of the Navier–Stokes equations in the three-dimensional space. The body force is assumed to possess an asymptotic expansion or, resp., finite asymptotic approximation, in Sobolev–Gevrey spaces, as time tends to infinity, in terms of polynomial and decaying exponential functions of time. We establish an asymptotic expansion, or resp., finite asymptotic approximation, of the same type for the Leray–Hopf weak solutions. This extends previous results that were obtained in the case of potential forces, to the non-potential force case, where the body force may have different levels of regularity and asymptotic approximation. This expansion or approximation, in fact, reveals precisely how the structure of the force influences the asymptotic behavior of the solutions.
SUPERCLOSENESS OF ORTHOGONAL PROJECTIONS ONTO NEARBY FINITE ELEMENT SPACES

We derive upper bounds on the difference between the orthogonal projections of a smooth function u onto two finite element spaces that are nearby, in the sense that the support of every shape function belonging to one but not both of the spaces is contained in a common region whose measure tends to zero under mesh refinement. The bounds apply, in particular, to the setting in which the two finite element spaces consist of continuous functions that are elementwise polynomials over shape-regular, quasi-uniform meshes that coincide except on a region of measure O(h γ ), where γ is a nonnegative scalar and h is the mesh spacing. The projector may be, for example, the orthogonal projector with respect to the L 2 -o rH 1 -inner product. In these and other circumstances, the bounds are superconvergent under a few mild regularity assumptions. That is, under mesh refinement, the two projections differ in norm by an amount that decays to zero at a faster rate than the amounts by which each projection differs from u. We present numerical examples to illustrate these superconvergent estimates and verify the necessity of the regularity assumptions on u.
Note: Variational encoding of protein dynamics benefits from maximizing latent autocorrelation.

As deep Variational Auto-Encoder (VAE) frameworks become more widely used for modeling biomolecular simulation data, we emphasize the capability of the VAE architecture to concurrently maximize the time scale of the latent space while inferring a reduced coordinate, which assists in finding slow processes as according to the variational approach to conformational dynamics. We provide evidence that the VDE framework [Hernandez et al., Phys. Rev. E 97, 062412 (2018)], which uses this autocorrelation loss along with a time-lagged reconstruction loss, obtains a variationally optimized latent coordinate in comparison with related loss functions. We thus recommend leveraging the autocorrelation of the latent space while training neural network models of biomolecular simulation data to better represent slow processes.
A new approach to low-distortion embeddings of finite metric spaces into non-superreflexive Banach spaces

Abstract The main goal of this paper is to develop a new embedding method which we use to show that some finite metric spaces admit low-distortion embeddings into all non-superreflexive spaces. This method is based on the theory of equal-signs-additive sequences developed by Brunel and Sucheston (1975–1976). We also show that some of the low-distortion embeddability results obtained using this method cannot be obtained using the method based on the factorization between the summing basis and the unit vector basis of l 1 , which was used by Bourgain (1986) and Johnson and Schechtman (2009).
Unsupervised active learning in large domains

Active learning is a powerful approach to analyzing data effectively. We show that the feasibility of active learning depends crucially on the choice of measure with respect to which the query is being optimized. The standard information gain, for example, does not permit an accurate evaluation with a small committee, a representative subset of the model space. We propose a surrogate measure requiring only a small committec and discuss the properties of this new measure. We devise, in addition, a bootstrap approach for committee selection. The advantages of this approach are illustrated in the context of recovering (regulatory) network models.
Entropic optimal transport is maximum-likelihood deconvolution

Abstract We give a statistical interpretation of entropic optimal transport by showing that performing maximum-likelihood estimation for Gaussian deconvolution corresponds to calculating a projection with respect to the entropic optimal transport distance. This structural result gives theoretical support for the wide adoption of these tools in the machine learning community.
Graph-based Security and Privacy Analytics via Collective Classification with Joint Weight Learning and Propagation.

Many security and privacy problems can be modeled as a graph classification problem, where nodes in the graph are classified by collective classification simultaneously. State-of-the-art collective classification methods for such graph-based security and privacy analytics follow the following paradigm: assign weights to edges of the graph, iteratively propagate reputation scores of nodes among the weighted graph, and use the final reputation scores to classify nodes in the graph. The key challenge is to assign edge weights such that an edge has a large weight if the two corresponding nodes have the same label, and a small weight otherwise. Although collective classification has been studied and applied for security and privacy problems for more than a decade, how to address this challenge is still an open question. In this work, we propose a novel collective classification framework to address this long-standing challenge. We first formulate learning edge weights as an optimization problem, which quantifies the goals about the final reputation scores that we aim to achieve. However, it is computationally hard to solve the optimization problem because the final reputation scores depend on the edge weights in a very complex way. To address the computational challenge, we propose to jointly learn the edge weights and propagate the reputation scores, which is essentially an approximate solution to the optimization problem. We compare our framework with state-of-the-art methods for graph-based security and privacy analytics using four large-scale real-world datasets from various application scenarios such as Sybil detection in social networks, fake review detection in Yelp, and attribute inference attacks. Our results demonstrate that our framework achieves higher accuracies than state-of-the-art methods with an acceptable computational overhead.
Weighted local estimates for singular integral operators

A local median decomposition is used to prove that a weighted local mean of a function is controlled by a weighted local mean of its local sharp maximal function. Together with (a local version of) the estimate $M^{\sharp}_{0,s}(Tf)(x) \le c\,Mf(x)$ for Calderon-Zygmund singular integral operators, this allows us to express the local weighted integral control of $Tf$ by $Mf$. Similar estimates hold for $T$ replaced by singular integrals with kernels satisfying Hormander-type conditions or integral operators with homogeneous kernels, and $M$ replaced by an appropriate maximal function $M_T$. Using sharper bounds in the local median decomposition we prove two-weight, $L^p_v$-$L^q_w$ estimates for singular integral operators for $1<p\le q<\infty$. In all cases, the results include weights that are not necessarily $A_{\infty}$. The local nature of these estimates leads to results involving weighted generalized Orlicz-Campanato and Orlicz-Morrey spaces.
Equivariant "K"-theory and the Chern character for discrete groups

Let X be a compact Hausdorff space, let Γ be a discrete group that acts continuously on X from the right, define X = {(x, γ) ∈ X×Γ : x ·γ = x}, and let Γ act on X via the formula (x, γ) · α = (x · α,α−1γα). Results of P. Baum and A. Connes, along with facts about the Chern character, imply that Ki Γ(X) and K i( X/Γ) are isomorphic up to torsion for i = 0, 1. In this paper, we present an example where the groups Ki Γ(X) and K i( X/Γ) are not isomorphic. Let Γ be a finite discrete group acting continuously on a compact Hausdorff space X from the right. Define X = {(x, γ) ∈ X × Γ : x · γ = x} and endow X with the subspace topology that it inherits from X × Γ. The group Γ acts on X via the formula (x, γ) ·α = (x ·α, αγα), and we can consider the orbit space X/Γ. Theorem 1.19 in [1] states that there exist isomorphisms K Γ(X)⊗ C ∼= ∞ ∑
Singular knots and involutive quandles

The aim of this paper is to define certain algebraic structures coming from generalized Reidemeister moves of singular knot theory. We give examples, show that the set of colorings by these algebra...
Homological mirror symmetry is T-duality for $\mathbb{P}^n$

In this paper, we apply the idea of T-duality to projective spaces. From a connection on a line bundle on $\mathbb P^n$, a Lagrangian in the mirror Landau-Ginzburg model is constructed. Under this correspondence, the full strong exceptional collection $\mathcal O_{\mathbb P^n}(-n-1),...,\mathcal O_{\mathbb P^n}(-1)$ is mapped to standard Lagrangians in the sense of \cite{nz}. Passing to constructible sheaves, we explicitly compute the quiver structure of these Lagrangians, and find that they match the quiver structure of this exceptional collection of $\mathbb P^n$. In this way, T-duality provides quasi-equivalence of the Fukaya category generated by these Lagrangians and the category of coherent sheaves on $\mathbb P^n$, which is a kind of homological mirror symmetry.
Isoparametric hypersurfaces with four principal curvatures, IV

The classification work Isoparametric hypersurfaces with four principal curvatures, and Isoparametric hypersurfaces with four principal curvatures, II, left unsettled only those anomalous isoparametric hypersurfaces with four principal curvatures and multiplicity pair $\{4, 5\}$, $\{6, 9\}$, or $\{7, 8\}$ in the sphere. By systematically exploring the ideal theory in commutative algebra in conjunction with the geometry of isoparametric hypersurfaces, we show that an isoparametric hypersurface with four principal curvatures and multiplicities $\{4, 5\}$ in $S^{19}$ is homogeneous, and, moreover, an isoparametric hypersurface with four principal curvatures and multiplicities $\{6, 9\}$ in $S^{31}$ is either the inhomogeneous one constructed by Ferus, Karcher, and Munzner, or the one that is homogeneous. This classification reveals the striking resemblance between these two rather different types of isoparametric hypersurfaces in the homogeneous category, even though the one with multiplicities $\{6, 9\}$ is of the type constructed by Ferus, Karcher, and Munzner and the one with multiplicities $\{4, 5\}$ stands alone. The quaternion and the octonion algebras play a fundamental role in their geometric structures. A unifying theme in Isoparametric hypersurfaces with four principal curvatures, and Isoparametric hypersurfaces with four principal curvatures, II, and the present sequel to them is Serre’s criterion of normal varieties. Its technical side pertinent to our situation that we developed in Isoparametric hypersurfaces with four principal curvatures, and Isoparametric hypersurfaces with four principal curvatures, II and extend in this sequel is instrumental. The classification leaves only the case of multiplicity pair $\{7, 8\}$ open.
Tight query complexity lower bounds for PCA via finite sample deformed wigner law

We prove a query complexity lower bound for approximating the top r dimensional eigenspace of a matrix. We consider an oracle model where, given a symmetric matrix M ∈ ℝd × d, an algorithm Alg is allowed to make T exact queries of the form w(i) = M v(i) for i in {1,...,T}, where v(i) is drawn from a distribution which depends arbitrarily on the past queries and measurements {v(j),w(i)}1 ≤ j ≤ i−1. We show that for every gap ∈ (0,1/2], there exists a distribution over matrices M for which 1) gapr(M) = Ω(gap) (where gapr(M) is the normalized gap between the r and r+1-st largest-magnitude eigenvector of M), and 2) any Alg which takes fewer than const × r logd/√gap queries fails (with overwhelming probability) to identity a matrix V ∈ ℝd × r with orthonormal columns for which ⟨ V, M V⟩ ≥ (1 − const × gap)∑i=1r λi(M). Our bound requires only that d is a small polynomial in 1/gap and r, and matches the upper bounds of Musco and Musco ’15. Moreover, it establishes a strict separation between convex optimization and “strict-saddle” non-convex optimization of which PCA is a canonical example: in the former, first-order methods can have dimension-free iteration complexity, whereas in PCA, the iteration complexity of gradient-based methods must necessarily grow with the dimension. Our argument proceeds via a reduction to estimating a rank-r spike in a deformed Wigner model M =W + λ U U⊤, where W is from the Gaussian Orthogonal Ensemble, U is uniform on the d × r-Stieffel manifold and λ > 1 governs the size of the perturbation. Surprisingly, this ubiquitous random matrix model witnesses the worst-case rate for eigenspace approximation, and the ‘accelerated’ gap−1/2 in the rate follows as a consequence of the correspendence between the asymptotic eigengap and the size of the perturbation λ, when λ is near the “phase transition” λ = 1. To verify that d need only be polynomial in gap−1 and r, we prove a finite sample convergence theorem for top eigenvalues of a deformed Wigner matrix, which may be of independent interest. We then lower bound the above estimation problem with a novel technique based on Fano-style data-processing inequalities with truncated likelihoods; the technique generalizes the Bayes-risk lower bound of Chen et al. ’16, and we believe it is particularly suited to lower bounds in adaptive settings like the one considered in this paper.
Multi-Segment Reconstruction Using Invariant Features

Multi-segment reconstruction (MSR) problem consists of recovering a signal from noisy segments with unknown positions of the observation windows. One example arises in DNA sequence assembly, which is typically solved by matching short reads to form longer sequences. Instead of trying to locate the segment within the sequence through pair-wise matching, we propose a new approach that uses shift-invariant features to estimate both the underlying signal and the distribution of the positions of the segments. Using the invariant features, we formulate the problem as a constrained nonlinear least-squares. The non-convexity of the problem leads to its sensitivity to the initialization. However, with clean data, we show empirically that for longer segment lengths, random initialization achieves exact recovery. Furthermore, we compare the performance of our approach to the results of expectation maximization and demonstrate that the new approach is robust to noise and computationally more efficient.
On Integrable Generalizations of the Pentagram Map

In this paper we prove that the generalization to $\mathbb{RP}^n$ of the pentagram map defined in \cite{KS} is invariant under certain scalings for any $n$. This property allows the definition of a Lax representation for the map, to be used to establish its integrability.
Random ball-polyhedra and inequalities for intrinsic volumes

We prove a randomized version of the generalized Urysohn inequality relating mean width to the other intrinsic volumes. To do this, we introduce a stochastic approximation procedure that sees each convex body K as the limit of intersections of Euclidean balls of large radii and centered at randomly chosen points. The proof depends on a new isoperimetric inequality for the intrinsic volumes of such intersections. If the centers are i.i.d. and sampled according to a bounded continuous distribution, then the extremizing measure is uniform on a Euclidean ball. If one additionally assumes that the centers have i.i.d. coordinates, then the uniform measure on a cube is the extremizer. We also discuss connections to a randomized version of the extended isoperimetric inequality and symmetrization techniques.
Exact Byzantine Consensus on Undirected Graphs under Local Broadcast Model

This paper considers the Byzantine consensus problem for nodes with binary inputs. The nodes are interconnected by a network represented as an undirected graph, and the system is assumed to be synchronous. Under the classical point-to-point communication model, it is well-known that the following two conditions are both necessary and sufficient to achieve Byzantine consensus among n nodes in the presence of up to ƒ Byzantine faulty nodes: n & 3 #8805; 3 ≥ ƒ+ 1 and vertex connectivity at least 2 ƒ + 1. In the classical point-to-point communication model, it is possible for a faulty node to equivocate, i.e., transmit conflicting information to different neighbors. Such equivocation is possible because messages sent by a node to one of its neighbors are not overheard by other neighbors.This paper considers the local broadcast model. In contrast to the point-to-point communication model, in the local broadcast model, messages sent by a node are received identically by all of its neighbors. Thus, under the local broadcast model, attempts by a node to send conflicting information can be detected by its neighbors. Under this model, we show that the following two conditions are both necessary and sufficient for Byzantine consensus: vertex connectivity at least ⌋ 3 fƒ / 2 ⌊ + 1 and minimum node degree at least 2 ƒ. Observe that the local broadcast model results in a lower requirement for connectivity and the number of nodes n, as compared to the point-to-point communication model.We extend the above results to a hybrid model that allows some of the Byzantine faulty nodes to equivocate. The hybrid model bridges the gap between the point-to-point and local broadcast models, and helps to precisely characterize the trade-off between equivocation and network requirements.
Learning Activation Functions to Improve Deep Neural Networks

Artificial neural networks typically have a fixed, non-linear activation function at each neuron. We have designed a novel form of piecewise linear activation function that is learned independently for each neuron using gradient descent. With this adaptive activation function, we are able to improve upon deep neural network architectures composed of static rectified linear units, achieving state-of-the-art performance on CIFAR-10 (7.51%), CIFAR-100 (30.83%), and a benchmark from high-energy physics involving Higgs boson decay modes.
Mobile beamforming & spatially controlled relay communications

We consider stochastic motion planning in single-source singledestination robotic relay networks, under a cooperative beamforming framework. Assuming that the communication medium constitutes a spatiotemporal stochastic field, we propose a 2-stage stochastic programming formulation of the problem of specifying the positions of the relays, such that the expected reciprocal of their total beamforming power is maximized. Stochastic decision making is made on the basis of random causal CSI. Recognizing the intractability of the original problem, we propose a lower bound relaxation, resulting to a nontrivial optimization problem with respect to the relay locations, which is equivalent to a small set of simple, tractable subproblems. Our formulation results in spatial controllers with a predictive character; at each time slot, the new relay positions should be such that the expected power reciprocal at the next time slot is maximized. Quite remarkably, the optimal control policy to the relaxed problem is purely selective; under a certain sense, only the best relay should move.
Memory Consistency Conditions for Self-Assembly Programming

Perhaps the two most significant theoretical questions about the programming of self-assembling agents are: (1) necessary and sufficient conditions to produce a unique terminal assembly, and (2) error correc- tion. We address both questions, by reducing two well-studied models of tile assembly to models of distributed shared memory (DSM), in order to obtain results from the memory consistency conditions induced by tile assem- bly systems when simulated in the DSM setting. The Abstract Tile Assembly Model (aTAM) can be simulated by a DSM system that obeys causal consistency, and the locally deterministic tile assembly systems in the aTAM correspond exactly to the concurrent-write free programs that simulate tile assembly in such a model. Thus, the detection of the failure of local determinism (which had formerly been an open problem) reduces to the detection of data races in simulating programs. Further, the Kinetic Tile Assembly Model can be simulated by a DSM system that obeys GWO, a memory consistency condition defined by Steinke and Nutt. (To our knowledge, this is the first natural example of a DSM system that obeys GWO, but no stronger consistency condition.) We combine these results with the observation that self-assembly algorithms are local algorithms, and there exists a fast conversion of deterministic local algorithms into deterministic self-stabilizing algorithms. This provides an "immediate" generalization of a theorem by Soloveichik et al. about the existence of tile as- sembly systems that simultaneously perform two forms of self-stabilization: proofreading and self-healing. Our reductions and proof techniques can be extended to the programming of self-assembling agents in a variety of media, not just DNA tiles, and not just two-dimensional surfaces.
Representations of rank two affine Hecke algebras at roots of unity

Abstract In this paper, we will fully describe the irreducible representations of the crystallographic rank two affine Hecke algebras using algebraic and combinatorial methods, for all possible values of q . The focus is on the case when q is a root of unity of small order.
Identifiability and testability in GRT with individual differences

Abstract Silbert and Thomas (2013) showed that failures of decisional separability are not, in general, identifiable in fully parameterized 2 × 2 Gaussian GRT models. A recent extension of 2 × 2 GRT models (GRTwIND) was developed to solve this problem and a conceptually similar problem with the simultaneous identifiability of means and marginal variances in GRT models. Central to the ability of GRTwIND to solve these problems is the assumption of universal perception , which consists of shared perceptual distributions modified by attentional and global scaling parameters (Soto et al., 2015). If universal perception is valid, GRTwIND solves both issues. In this paper, we show that GRTwIND with universal perception and subject-specific failures of decisional separability is mathematically, and thereby empirically, equivalent to a model with decisional separability and failure of universal perception. We then provide a formal proof of the fact that means and marginal variances are not, in general, simultaneously identifiable in 2 × 2 GRT models, including GRTwIND. These results can be taken to delineate precisely what the assumption of universal perception must consist of. Based on these results and related recent mathematical developments in the GRT framework, we propose that, in addition to requiring a fixed subset of parameters to determine the location and scale of any given GRT model, some subset of parameters must be set in GRT models to fix the orthogonality of the modeled perceptual dimensions, a central conceptual underpinning of the GRT framework. We conclude with a discussion of perceptual primacy and its relationship to universal perception.
Bytes Are All You Need: End-to-end Multilingual Speech Recognition and Synthesis with Bytes

We present two end-to-end models: Audio-to-Byte (A2B) and Byte-to-Audio (B2A), for multilingual speech recognition and synthesis. Prior work has predominantly used characters, sub-words or words as the unit of choice to model text. These units are difficult to scale to languages with large vocabularies, particularly in the case of multilingual processing. In this work, we model text via a sequence of Unicode bytes, specifically, the UTF-8 variable length byte sequence for each character. Bytes allow us to avoid large softmaxes in languages with large vocabularies, and share representations in multilingual models. We show that bytes are superior to grapheme characters over a wide variety of languages in monolingual end-to-end speech recognition. Additionally, our multilingual byte model outperform each respective single language baseline on average by 4.4% relatively. In Japanese-English code-switching speech, our multilingual byte model outperform our monolingual baseline by 38.6% relatively. Finally, we present an end-to-end multilingual speech synthesis model using byte representations which matches the performance of our monolingual baselines.
Large-Scale Approximate Kernel Canonical Correlation Analysis

Abstract: Kernel canonical correlation analysis (KCCA) is a nonlinear multi-view representation learning technique with broad applicability in statistics and machine learning. Although there is a closed-form solution for the KCCA objective, it involves solving an $N\times N$ eigenvalue system where $N$ is the training set size, making its computational requirements in both memory and time prohibitive for large-scale problems. Various approximation techniques have been developed for KCCA. A commonly used approach is to first transform the original inputs to an $M$-dimensional random feature space so that inner products in the feature space approximate kernel evaluations, and then apply linear CCA to the transformed inputs. In many applications, however, the dimensionality $M$ of the random feature space may need to be very large in order to obtain a sufficiently good approximation; it then becomes challenging to perform the linear CCA step on the resulting very high-dimensional data matrices. We show how to use a stochastic optimization algorithm, recently proposed for linear CCA and its neural-network extension, to further alleviate the computation requirements of approximate KCCA. This approach allows us to run approximate KCCA on a speech dataset with $1.4$ million training samples and a random feature space of dimensionality $M=100000$ on a typical workstation.
Hilbert function spaces and the Nevanlinna-Pick problem on the polydisc

Abstract In [4] , Agler and McCarthy (2005) used Hilbert function spaces to study the uniqueness properties of the Nevanlinna–Pick problem on the bidisc. In this work we give a geometric procedure for constructing a Nevanlinna–Pick problem on D n with a specified set of uniqueness. On the way to establishing this procedure, we prove a result about Hilbert function spaces and partially answer a question posed by Agler and McCarthy.
Low-Resolution Fault Localization Using Phasor Measurement Units with Community Detection

A significant portion of the literature on fault localization assumes (more or less explicitly) that there are sufficient reliable measurements to guarantee that the system is observable. While several heuristics exist to break the observability barrier, they mostly rely on recognizing spatio-temporal patterns, without giving insights on how the performance are tied with the system features and the sensor deployment. In this paper, we try to fill this gap and investigate the limitations and performance limits of fault localization using Phasor Measurement Units (PMUs), in the low measurements regime, i.e., when the system is unobservable with the measurements available. Our main contribution is to show how one can leverage the scarce measurements to localize different type of distribution line faults (three-phase, single-phase to ground, …) at the level of sub-graph, rather than with the resolution of a line. We show that the resolution we obtain is strongly tied with the graph clustering notion in network science.
The Integrable Bootstrap Program at Large N and Its Applications in Gauge Theory

We present results for the large-N limit of the (1+1)-dimensional principal chiral sigma model. This is an asymptotically-free N N matrix-valued field with massive excitations. All the form factors and the exact correlation functions of the Noether-current operator and the energy-momentum tensor are found, from Smirnov’s form-factor axioms. We consider (2+1)dimensional SU(¥) Yang-Mills theory as an array of principal chiral models with a currentcurrent interaction. We discuss how to use our new form factors to calculate physical quantities in this gauge theory.
Identification of Critical Nodes in Large-Scale Spatial Networks

The notion of network connectivity is used to characterize the robustness and failure tolerance of networks, with high connectivity being a desirable feature. In this paper, we develop a novel gradient flow-based approach to the problem of identifying critical nodes in large-scale networks, with algebraic connectivity (the second smallest eigenvalue of the graph Laplacian) as the chosen metric. Employing a graph-embedding technique, we reduce the class of considered weight-balanced graphs to spatial networks with uniformly distributed nodes and nearest-neighbors communication topologies. Through a continuum approximation, we consider the Laplace operator on a manifold (with the Neumann boundary condition) as the limiting case of the graph Laplacian. We then reduce the critical node set identification problem to that of finding a ball of fixed radius, whose removal minimizes the second (Neumann) eigenvalue of the Laplace operator on the residual domain. This leads us to consider two functional and nested optimization problems. Resorting to the min–max theorem, we first treat the problem of determining the second smallest eigenvalue for a fixed domain by minimizing an energy functional. We then obtain a closed-form expression for a projected gradient flow that converges to the set of eigenfunctions of the Laplace operator and prove that the only locally asymptotically stable critical point is the second eigenfunction. Building on these results, we consider the critical ball identification problem and define novel dynamics to converge asymptotically to these points. Finally, we provide a characterization of the location of critical nodes (for infinitesimally small balls) as those points that belong to the nodal set of the second eigenfunction of the Laplacian operator.
Structured Signal Recovery From Quadratic Measurements: Breaking Sample Complexity Barriers via Nonconvex Optimization

This paper concerns the problem of recovering an unknown but structured signal ${x}\in \mathbb {R} ^{n}$ from $m$ -quadratic measurements of the form ${y}_{r}= \left |{\langle {a}_{r}, {x}\rangle }\right |^{{2}}$ for ${r}={1},{2},\ldots, {m}$ . We focus on the under-determined setting where the number of measurements is significantly smaller than the dimension of the signal ( ${m} ). We formulate the recovery problem as a nonconvex optimization problem where prior structural information about the signal is enforced through constrains on the optimization variables. We prove the projected gradient descent, when initialized in a neighborhood of the desired signal, converges to the unknown signal at a linear rate. These results hold for any closed constraint set (convex or non-convex) providing convergence guarantees to the global optimum even when the objective function and constraint set are nonconvex. Furthermore, these results hold with a number of measurements that are only a constant factor away from the minimal number of measurements required to uniquely identify the unknown signal. Our results provide the first provably tractable algorithm for this data-poor regime, breaking local sample complexity barriers that have emerged in this paper. In this paper, we utilize and further develop powerful tools for uniform convergence of empirical processes that may have broader implications for rigorous understanding of constrained nonconvex optimization heuristics.
Distributed transient frequency control for power networks with stability and performance guarantees

Abstract This paper proposes a distributed strategy regulated on a subset of individual buses in a power network described by the swing equations to achieve transient frequency control while preserving asymptotic stability. Transient frequency control refers to the ability to maintain the transient frequency of each bus of interest in a given safe region, provided (i) it is initially in it, and (ii) if it is initially not, then drive the frequency to converge to this region within a finite time, with a guaranteed convergence rate. Building on Lyapunov stability and set invariance theory, we formulate the stability and the transient frequency requirements as two separate constraints for the control input. Our design synthesizes a controller that satisfies both constraints simultaneously. The controller is distributed and Lipschitz, guaranteeing the existence and uniqueness of the trajectories of the closed-loop system. We further bound its magnitude and demonstrate its robustness against measurement inaccuracies. Simulations on the IEEE 39-bus power network illustrate our results.
Invariant subspaces of the shift plus complex Volterra operator

Abstract The lattice of closed invariant subspaces of the Volterra operator acting on L 2 ( 0 , 1 ) was completely described by Sarason [8] . On the other hand, he explicitly found the lattice of closed invariant subspaces of the shift plus Volterra operator on L 2 ( 0 , 1 ) in [9] . Inspired by Sarason's results, we find the lattice of closed invariant subspaces of the shift plus complex Volterra operator acting on the Hardy space.
Normal Truncated Toeplitz Operators

The characterization of normal truncated Toepltiz operators is first given by Chalendar and Timotin. We give an elementary proof of their result without using the algebraic properties of truncated Toeplitz operators.
Analogues of a transformation formula of Ramanujan

We derive two new analogues of a transformation formula of Ramanujan involving the Gamma function and Riemann zeta function present in his Lost Notebook. Both involve infinite series consisting of Hurwitz zeta functions and yield modular-type relations. As a special case of the first formula, we obtain an identity involving polygamma functions given by A. P. Guinand and as a limiting case of the second formula, we derive the transformation formula of Ramanujan.
The 1729 K3 surface

We revisit the mathematics that Ramanujan developed in connection with the famous “taxi-cab” number 1729. A study of his writings reveals that he had been studying Euler’s diophantine equation $$\begin{aligned} a^3+b^3=c^3+d^3. \end{aligned}$$ a 3 + b 3 = c 3 + d 3 . It turns out that Ramanujan’s work anticipated deep structures and phenomena which have become fundamental objects in arithmetic geometry and number theory. We find that he discovered a K3 surface with Picard number 18, one which can be used to obtain infinitely many cubic twists over $$\mathbb {Q}$$ Q with rank $$\ge 2$$ ≥ 2 .
High-Dimensional Adaptive Minimax Sparse Estimation With Interactions

High-dimensional linear regression with interaction effects is broadly applied in research fields such as bioinformatics and social science. In this paper, first, we investigate the minimax rate of convergence for regression estimation in high-dimensional sparse linear models with two-way interactions. Here, we derive matching upper and lower bounds under three types of heredity conditions: strong heredity, weak heredity, and no heredity. From the results: 1) A stronger heredity condition may or may not drastically improve the minimax rate of convergence. In fact, in some situations, the minimax rates of convergence are the same under all three heredity conditions; 2) The minimax rate of convergence is determined by the maximum of the total price of estimating the main effects and that of estimating the interaction effects, which goes beyond purely comparing the order of the number of non-zero main effects $r_{1}$ and non-zero interaction effects $r_{2}$ ; and 3) Under any of the three heredity conditions, the estimation of the interaction terms may be the dominant part in determining the rate of convergence. This is due to either the dominant number of interaction effects over main effects or the higher interaction estimation price induced by a large ambient dimension. Second, we construct an adaptive estimator that achieves the minimax rate of convergence regardless of the true heredity condition and the sparsity indices $r_{1}, r_{2}$ .
A duality formalism in the spirit of Grothendieck and Verdier

We study monoidal categories that enjoy a certain weakening of the rigidity property, namely, the existence of a dualizing object in the sense of Grothendieck and Verdier. We call them Grothendieck-Verdier categories. Notable examples include the derived category of constructible sheaves on a scheme (with respect to tensor product) as well as the derived and equivariant derived categories of constructible sheaves on an algebraic group (with respect to convolution). We show that the notions of pivotal category and ribbon category, which are well known in the setting of rigid monoidal categories, as well as certain standard results associated with these notions, have natural analogues in the world of Grothendieck-Verdier categories.
Unsupervised learning in neuromemristive systems

Neuromemristive systems (NMSs) currently represent the most promising platform to achieve energy efficient neuro-inspired computation. However, since the research field is less than a decade old, there are still countless algorithms and design paradigms to be explored within these systems. One particular domain that remains to be fully investigated within NMSs is unsupervised learning. In this work, we explore the design of an NMS for unsupervised clustering, which is a critical element of several machine learning algorithms. Using a simple memristor crossbar architecture and learning rule, we are able to achieve performance which is on par with MATLAB's k-means clustering.
Thick subcategories of the bounded derived category of a finite group

A new proof of the classification for tensor ideal thick subcategories of the bounded derived category, and the stable category, of modular representations of a finite group is obtained. The arguments apply more generally to yield a classification of thick subcategories of the bounded derived category of an artinian complete intersection ring. One of the salient features of this work is that it takes no recourse to infinite constructions, unlike the previous proofs of these results.
Bootstrapping Conversational Agents with Weak Supervision

Many conversational agents in the market today follow a standard bot development framework which requires training intent classifiers to recognize user input. The need to create a proper set of training examples is often the bottleneck in the development process. In many occasions agent developers have access to historical chat logs that can provide a good quantity as well as coverage of training examples. However, the cost of labeling them with tens to hundreds of intents often prohibits taking full advantage of these chat logs. In this paper, we present a framework called search, label, and propagate (SLP) for bootstrapping intents from existing chat logs using weak supervision. The framework reduces hours to days of labeling effort down to minutes of work by using a search engine to find examples, then relies on a data programming approach to automatically expand the labels. We report on a user study that shows positive user feedback for this new approach to build conversational agents, and demonstrates the effectiveness of using data programming for autolabeling. While the system is developed for training conversational agents, the framework has broader application in significantly reducing labeling effort for training text classifiers.
Shared feelings: understanding facebook reactions to scholarly articles

Research on social-media platforms has tended to rely on textual analysis to perform research tasks. While text-based approaches have significantly increased our understanding of online behavior and social dynamics, they overlook features on these platforms that have grown in prominence in the past few years: click-based responses to content. In this paper, we present a new dataset of Facebook Reactions to scholarly content. We give an overview of its structure, analyze some of the statistical trends in the data, and use it to train and test two supervised learning algorithms. Our preliminary tests suggest the presence of stratification in the number of users following pages, divisions that seem to fall in line with distinctions in the subject matter of those pages.
Learning Extreme Hummingbird Maneuvers on Flapping Wing Robots

Biological studies show that hummingbirds can perform extreme aerobatic maneuvers during fast escape. Given a sudden looming visual stimulus at hover, a hummingbird initiates a fast backward translation coupled with a 180-degree yaw turn, which is followed by instant posture stabilization in just under 10 wingbeats. Consider the wingbeat frequency of 40Hz, this aggressive maneuver is carried out in just 0.2 seconds. Inspired by the hummingbirds’ near-maximal performance during such extreme maneuvers, we developed a flight control strategy and experimentally demonstrated that such maneuverability can be achieved by an at-scale 12-gram hummingbird robot equipped with just two actuators driving a pair of flapping wings up to 40Hz. The proposed hybrid control policy combines model-based nonlinear control with model-free reinforcement learning. We used the model-based nonlinear control for nominal flight conditions where dynamic models are relatively accurate. During extreme maneuvers when the modeling error becomes unmanageable, we use a model-free reinforcement learning policy trained and optimized in simulation to ’destabilize’ the system for peak performance during maneuvering. The hybrid policy manifests a maneuver that is close to that observed in hummingbirds. Direct simulation-to-real transfer is achieved, demonstrating the hummingbird-like fast evasive maneuvers on the at-scale hummingbird robot.