cssi/SciSciGPT-SciSciNet huggingface dataset:
Testing for Conditional Mean Independence with Covariates through Martingale Difference Divergence.

As a crucial problem in statistics is to decide whether additional variables are needed in a regression model. We propose a new multivariate test to investigate the conditional mean independence of Y given X conditioning on some known effect Z, i.e., E(Y|X, Z) = E(Y|Z). Assuming that E(Y|Z) and Z are linearly related, we reformulate an equivalent notion of conditional mean independence through transformation, which is approximated in practice. We apply the martingale difference divergence (Shao and Zhang, 2014) to measure conditional mean dependence, and show that the estimation error from approximation is negligible, as it has no impact on the asymptotic distribution of the test statistic under some regularity assumptions. The implementation of our test is demonstrated by both simulations and a financial data example.
Robust Hypothesis Test for Nonlinear Effect with Gaussian Processes

This work constructs a hypothesis test for detecting whether an data-generating function $h: \real^p \rightarrow \real$ belongs to a specific reproducing kernel Hilbert space $\mathcal{H}_0$, where the structure of $\mathcal{H}_0$ is only partially known. Utilizing the theory of reproducing kernels, we reduce this hypothesis to a simple one-sided score test for a scalar parameter, develop a testing procedure that is robust against the mis-specification of kernel functions, and also propose an ensemble-based estimator for the null model to guarantee test performance in small samples. To demonstrate the utility of the proposed method, we apply our test to the problem of detecting nonlinear interaction between groups of continuous features. We evaluate the finite-sample performance of our test under different data-generating functions and estimation strategies for the null model. Our results revealed interesting connection between notions in machine learning (model underfit/overfit) and those in statistical inference (i.e. Type I error/power of hypothesis test), and also highlighted unexpected consequences of common model estimating strategies (e.g. estimating kernel hyperparameters using maximum likelihood estimation) on model inference.
Extrinsic Diophantine approximation on manifolds and fractals

Fix d∈N, and let S⊆Rd be either a real-analytic manifold or the limit set of an iterated function system (for example, S could be the Cantor set or the von Koch snowflake). An extrinsic Diophantine approximation to a point x∈S is a rational point p/q close to x which lies outside of S. These approximations correspond to a question asked by K. Mahler (1984) regarding the Cantor set. Our main result is an extrinsic analogue of Dirichlet's theorem. Specifically, we prove that if S does not contain a line segment, then for every x∈S∖Qd, there exists C>0 such that infinitely many vectors p/q∈Qd∖S satisfy ‖x−p/q‖<C/q(d+1)/d. As this formula agrees with Dirichlet's theorem in Rd up to a multiplicative constant, one concludes that the set of rational approximants to points in S which lie outside of S is large. Furthermore, we deduce extrinsic analogues of the Jarnik–Schmidt and Khinchin theorems from known results.
Endoscopic Classification of Representations of Quasi-split Unitary Groups

Introduction Statement of the main theorems Local character identities and the intertwining relation Trace formulas and their stabilization The Standard model Study of critical cases Local classification Nontempered representations Global classification Addendum Bibliography
Drift mode accelerometry for spaceborne gravity measurements

A drift mode accelerometer is a precision instrument for spacecraft that overcomes much of the acceleration noise and readout dynamic range limitations of traditional electrostatic accelerometers. It has the potential of achieving acceleration noise performance similar to that of drag-free systems over a restricted frequency band without the need for external drag-free control or continuous spacecraft propulsion. Like traditional accelerometers, the drift mode accelerometer contains a high-density test mass surrounded by an electrode housing, which can control and sense all six degrees of freedom of the test mass. Unlike traditional accelerometers, the suspension system is operated with a low duty cycle so that the limiting suspension force noise only acts over brief, known time intervals, which can be neglected in the data analysis. The readout is performed using a laser interferometer which is immune to the dynamic range limitations of even the best voltage references typically used to determine the inertial acceleration of electrostatic accelerometers. The drift mode accelerometer is a novel offshoot of the like-named operational mode of the LISA Pathfinder spacecraft, in which its test mass suspension system is cycled on and off to estimate the acceleration noise associated with the front-end electronics. This paper presents the concept of a drift mode accelerometer, describes the operation of such a device, develops models for its performance with respect to non-drag-free satellite geodesy and gravitational wave missions, and discusses plans for testing the performance of a prototype sensor in the laboratory using torsion pendula.
Catcher-evader games

Algorithms for computing game-theoretic solutions have recently been applied to a number of security domains. However, many of the techniques developed for compact representations of security games do not extend to Bayesian security games, which allow us to model uncertainty about the attacker's type. In this paper, we introduce a general framework of catcher-evader games that can capture Bayesian security games as well as other game families of interest. We show that computing Stackelberg strategies is NP-hard, but give an algorithm for computing a Nash equilibrium that performs well in experiments. We also prove that the Nash equilibria of these games satisfy the interchangeability property, so that equilibrium selection is not an issue.
Planar cycle covering graphs

We describe a new variational lower-bound on the minimum energy configuration of a planar binary Markov Random Field (MRF). Our method is based on adding auxiliary nodes to every face of a planar embedding of the graph in order to capture the effect of unary potentials. A ground state of the resulting approximation can be computed efficiently by reduction to minimum-weight perfect matching. We show that optimization of variational parameters achieves the same lower-bound as dual-decomposition into the set of all cycles of the original graph. We demonstrate that our variational optimization converges quickly and provides high-quality solutions to hard combinatorial problems 10-100x faster than competing algorithms that optimize the same bound.
Robust manipulation of light using topologically protected plasmonic modes.

We propose using a topological plasmonic crystal structure composed of an array of nearly parallel nanowires with unequal spacing for manipulating light. In the paraxial approximation, the Helmholtz equation that describes the propagation of light along the nanowires maps onto the Schrodinger equation of the Su-Schrieffer-Heeger (SSH) model. Using a full three-dimensional finite difference time domain solution of the Maxwell equations, we verify the existence of topological defect modes, with sub-wavelength localization, bound to domain walls of the plasmonic crystal. We show that by manipulating domain walls we can construct spatial mode filters that couple bulk modes to topological defect modes, and topological beam-splitters that couple two topological defect modes. Finally, we show that the structures are tolerant to fabrication errors with an inverse length-scale smaller than the topological band gap.
Why All Rings Should Have a 1

Should the definition of ring require the existence of a multiplicative identity 1?Emmy Noether, when giving the modern axiomatic definition of a commutative ring, in 1921, did not include such an ...
Modeling and optimization of complex building energy systems with deep neural networks

Modern buildings encompass complex dynamics of multiple electrical, mechanical, and control systems. One of the biggest hurdles in applying conventional model-based optimization and control methods to building energy management is the huge cost and effort of capturing diverse and temporally correlated dynamics. Here we propose an alternative approach which is model-free and data-driven. By utilizing high volume of data coming from advanced sensors, we train a deep Recurrent Neural Networks (RNN) which could accurately represent the operation's temporal dynamics of building complexes. The trained network is then directly fitted into a constrained optimization problem with finite horizons. By reformulating the constrained optimization as an unconstrained optimization problem, we use iterative gradient descents method with momentum to find optimal control inputs. Simulation results demonstrate proposed method's improved performances over model-based approach on both building system modeling and control.
The Strength of Abstraction with Predicative Comprehension

Frege's theorem says that second-order Peano arithmetic is interpretable in Hume's Principle and full impredicative comprehension. Hume's Principle is one example of an abstraction principle, while another paradigmatic example is Basic Law V from Frege's Grundgesetze. In this paper we study the strength of abstraction principles in the presence of predicative restrictions on the comprehension schema, and in particular we study a predicative Fregean theory which contains all the abstraction principles whose underlying equivalence relations can be proven to be equivalence relations in a weak background second-order logic. We show that this predicative Fregean theory interprets second-order Peano arithmetic (cf. Theorem 3.2).
Characterizing projective spaces on deformations of Hilbert schemes of K3 surfaces

We seek to characterize homology classes of Lagrangian projective spaces embedded in irreducible holomorphic-symplectic manifolds, up to the action of the monodromy group. This paper addresses the case of manifolds deformation-equivalent to the Hilbert scheme of length-3 subschemes of a K3 surface. The class of the projective space in the cohomology ring has prescribed intersection properties, which translate into Diophantine equations. Possible homology classes correspond to integral points on an explicit elliptic curve; our proof entails showing that the only such point is two-torsion. © 2011 Wiley Periodicals, Inc.
The intermediate disorder regime for a directed polymer model on a hierarchical lattice

Abstract We study a directed polymer model defined on a hierarchical diamond lattice, where the lattice is constructed recursively through a recipe depending on a branching number b ∈ N and a segment number s ∈ N . When b ≤ s it is known that the model exhibits strong disorder for all positive values of the inverse temperature β , and thus weak disorder reigns only for β = 0 (infinite temperature). Our focus is on the so-called intermediate disorder regime in which the inverse temperature β ≡ β n vanishes at an appropriate rate as the size n of the system grows. Our analysis requires separate treatment for the cases b s and b = s . In the case b s we prove that when the inverse temperature is taken to be of the form β n = β ( b / s ) n / 2 for β > 0 , the normalized partition function of the system converges weakly as n → ∞ to a distribution L ( β ) and does so universally with respect to the initial weight distribution. We prove the convergence using renormalization group type ideas rather than the standard Wiener chaos analysis. In the case b = s we find a critical point in the behavior of the model when the inverse temperature is scaled as β n = β / n ; for an explicitly computable critical value κ b > 0 the variance of the normalized partition function converges to zero with large n when β ≤ κ b and grows without bound when β > κ b . Finally, we prove a central limit theorem for the normalized partition function when β ≤ κ b .
Spherical Latent Spaces for Stable Variational Autoencoders

A hallmark of variational autoencoders (VAEs) for text processing is their combination of powerful encoder-decoder models, such as LSTMs, with simple latent distributions, typically multivariate Gaussians. These models pose a difficult optimization problem: there is an especially bad local optimum where the variational posterior always equals the prior and the model does not use the latent variable at all, a kind of “collapse” which is encouraged by the KL divergence term of the objective. In this work, we experiment with another choice of latent distribution, namely the von Mises-Fisher (vMF) distribution, which places mass on the surface of the unit hypersphere. With this choice of prior and posterior, the KL divergence term now only depends on the variance of the vMF distribution, giving us the ability to treat it as a fixed hyperparameter. We show that doing so not only averts the KL collapse, but consistently gives better likelihoods than Gaussians across a range of modeling conditions, including recurrent language modeling and bag-of-words document modeling. An analysis of the properties of our vMF representations shows that they learn richer and more nuanced structures in their latent representations than their Gaussian counterparts.
Forcing with adequate sets of models as side conditions

We present a general framework for forcing on ω2 with finite conditions using countable models as side conditions. This framework is based on a method of comparing countable models as being membership related up to a large initial segment. We give several examples of this type of forcing, including adding a function on ω2, adding a nonreflecting stationary subset of ω2∩ cof (ω), and adding an ω1-Kurepa tree.
Aggregate Hazes in Exoplanet Atmospheres

Photochemical hazes have been frequently used to interpret exoplanet transmission spectra that show an upward slope towards shorter wavelengths and weak molecular features. While previous studies have only considered spherical haze particles, photochemical hazes composed of hydrocarbon aggregate particles are common throughout the solar system. We use an aerosol microphysics model to investigate the effect of aggregate photochemical haze particles on transmission spectra of warm exoplanets. We find that the wavelength dependence of the optical depth of aggregate particle hazes is flatter than for spheres since aggregates grow to larger radii. As a result, while spherical haze opacity displays a scattering slope towards shorter wavelengths, aggregate haze opacity can be gray in the optical and NIR, similar to those assumed for condensate cloud decks. We further find that haze opacity increases with increasing production rate, decreasing eddy diffusivity, and increasing monomer size, though the magnitude of the latter effect is dependent on production rate and the atmospheric pressure levels probed. We generate synthetic exoplanet transmission spectra to investigate the effect of these hazes on spectral features. For high haze opacity cases, aggregate hazes lead to flat, nearly featureless spectra, while spherical hazes produce sloped spectra with clear spectral features at long wavelengths. Finally, we generate synthetic transmission spectra of GJ 1214b for aggregate and spherical hazes and compare them to space-based observations. We find that aggregate hazes can reproduce the data significantly better than spherical hazes, assuming a production rate limited by delivery of methane to the upper atmosphere.
Probabilistic Record Linkage and Deduplication after Indexing, Blocking, and Filtering

Probabilistic record linkage, the task of merging two or more databases in the absence of a unique identifier, is a perennial and challenging problem. It is closely related to the problem of deduplicating a single database, which can be cast as linking a single database against itself. In both cases the number of possible links grows rapidly in the size of the databases under consideration, and in most applications it is necessary to first reduce the number of record pairs that will be compared. Spurred by practical considerations, a range of methods have been developed for this task. These methods go under a variety of names, including indexing and blocking, and have seen significant development. However, methods for inferring linkage structure that account for indexing, blocking, and additional filtering steps have not seen commensurate development. In this paper we review the implications of indexing, blocking and filtering within the popular Fellegi-Sunter framework, and propose a new model to account for particular forms of indexing and filtering.
Towards Conceptual Compression

We introduce convolutional DRAW, a homogeneous deep generative model achieving state-of-the-art performance in latent variable image modeling. The algorithm naturally stratifies information into higher and lower level details, creating abstract features and as such addressing one of the fundamentally desired properties of representation learning. Furthermore, the hierarchical ordering of its latents creates the opportunity to selectively store global information about an image, yielding a high quality 'conceptual compression' framework.
High-dimensional quantum key distribution using dispersive optics

We propose a high-dimensional quantum key distribution (QKD) protocol that employs temporal correlations of entangled photons. The security of the protocol relies on measurements by Alice and Bob in one of two conjugate bases, implemented using dispersive optics. We show that this dispersion-based approach is secure against collective attacks. The protocol, which represents a QKD analog of pulse position modulation, is compatible with standard fiber telecommunications channels and wavelength division multiplexers. We describe several physical implementations to enhance the transmission rate and describe a heralded qudit source that is easy to implement and enables secret-key generation at $g4$ bits per character of distilled key across over 200 km of fiber.
Convex relaxation regression: black-box optimization of smooth functions by learning their convex envelopes

Finding efficient and provable methods to solve non-convex optimization problems is an outstanding challenge in machine learning and optimization theory. A popular approach used to tackle non-convex problems is to use convex relaxation techniques to find a convex surrogate for the problem. Unfortunately, convex relaxations typically must be found on a problem-by-problem basis. Thus, providing a general-purpose strategy to estimate a convex relaxation would have a wide reaching impact. Here, we introduce Convex Relaxation Regression (CoRR), an approach for learning convex relaxations for a class of smooth functions. The idea behind our approach is to estimate the convex envelope of a function f by evaluating f at a set of T random points and then fitting a convex function to these function evaluations. We prove that with probability greater than 1 - δ, the solution of our algorithm converges to the global optimizer of f with error O((log(1/δ/T)α) for some α > 0. Our approach enables the use of convex optimization tools to solve non-convex optimization problems.
A Modified SEIR Model for the Spread of Ebola in Western Africa and Metrics for Resource Allocation

Abstract A modified, deterministic SEIR model is developed for the 2014 Ebola epidemic occurring in the West African nations of Guinea, Liberia, and Sierra Leone. The model describes the dynamical interaction of susceptible and infected populations, while accounting for the effects of hospitalization and the spread of disease through interactions with deceased, but infectious, individuals. Using data from the World Health Organization (WHO), parameters within the model are fit to recent estimates of infected and deceased cases from each nation. The model is then analyzed using these parameter values. Finally, several metrics are proposed to determine which of these nations is in greatest need of additional resources to combat the spread of infection. These include local and global sensitivity metrics of both the infected population and the basic reproduction number with respect to rates of hospitalization and proper burial.
Rate optimal estimation and confidence intervals for high-dimensional regression with missing covariates

Abstract We consider the problems of estimation and of constructing component-wise confidence intervals in a sparse high-dimensional linear regression model when some covariates of the design matrix are missing completely at random. We analyze a variant of the Dantzig selector for estimating the regression model and we use a de-biasing argument to construct component-wise confidence intervals. We also complement our mathematical study in the supplementary materials with extensive simulations on synthetic and semi-synthetic data that show the accuracy of our asymptotic predictions for finite sample sizes.
Matching networks for one shot learning

Learning from a few examples remains a key challenge in machine learning. Despite recent advances in important domains such as vision and language, the standard supervised deep learning paradigm does not offer a satisfactory solution for learning new concepts rapidly from little data. In this work, we employ ideas from metric learning based on deep neural features and from recent advances that augment neural networks with external memories. Our framework learns a network that maps a small labelled support set and an unlabelled example to its label, obviating the need for fine-tuning to adapt to new class types. We then define one-shot learning problems on vision (using Omniglot, ImageNet) and language tasks. Our algorithm improves one-shot accuracy on ImageNet from 87.6% to 93.2% and from 88.0% to 93.8% on Omniglot compared to competing approaches. We also demonstrate the usefulness of the same model on language modeling by introducing a one-shot task on the Penn Treebank.
The Exon Junction Complex Undergoes a Compositional Switch that Alters mRNP Structure and Nonsense-Mediated mRNA Decay Activity.

The exon junction complex (EJC) deposited upstream of mRNA exon junctions shapes structure, composition, and fate of spliced mRNA ribonucleoprotein particles (mRNPs). To achieve this, the EJC core nucleates assembly of a dynamic shell of peripheral proteins that function in diverse post-transcriptional processes. To illuminate consequences of EJC composition change, we purified EJCs from human cells via peripheral proteins RNPS1 and CASC3. We show that the EJC originates as an SR-rich mega-dalton-sized RNP that contains RNPS1 but lacks CASC3. Sometime before or during translation, the EJC undergoes compositional and structural remodeling into an SR-devoid monomeric complex that contains CASC3. Surprisingly, RNPS1 is important for nonsense-mediated mRNA decay (NMD) in general, whereas CASC3 is needed for NMD of only select mRNAs. The switch to CASC3-EJC slows down NMD. Overall, the EJC compositional switch dramatically alters mRNP structure and specifies two distinct phases of EJC-dependent NMD.
Exceptional representations of Weyl groups

Abstract We consider various consequences of the existence of exceptional representations of an irreducible Weyl group.
Can 3D Pose Be Learned from 2D Projections Alone

3D pose estimation from a single image is a challenging task in computer vision. We present a weakly supervised approach to estimate 3D pose points, given only 2D pose landmarks. Our method does not require correspondences between 2D and 3D points to build explicit 3D priors. We utilize an adversarial framework to impose a prior on the 3D structure, learned solely from their random 2D projections. Given a set of 2D pose landmarks, the generator network hypothesizes their depths to obtain a 3D skeleton. We propose a novel Random Projection layer, which randomly projects the generated 3D skeleton and sends the resulting 2D pose to the discriminator. The discriminator improves by discriminating between the generated poses and pose samples from a real distribution of 2D poses. Training does not require correspondence between the 2D inputs to either the generator or the discriminator. We apply our approach to the task of 3D human pose estimation. Results on Human3.6M dataset demonstrates that our approach outperforms many previous supervised and weakly supervised approaches.
The Laplacian in RL: Learning Representations with Efficient Approximations.

The smallest eigenvectors of the graph Laplacian are well-known to provide a succinct representation of the geometry of a weighted graph. In reinforcement learning (RL), where the weighted graph may be interpreted as the state transition process induced by a behavior policy acting on the environment, approximating the eigenvectors of the Laplacian provides a promising approach to state representation learning. However, existing methods for performing this approximation are ill-suited in general RL settings for two main reasons: First, they are computationally expensive, often requiring operations on large matrices. Second, these methods lack adequate justification beyond simple, tabular, finite-state settings. In this paper, we present a fully general and scalable method for approximating the eigenvectors of the Laplacian in a model-free RL context. We systematically evaluate our approach and empirically show that it generalizes beyond the tabular, finite-state setting. Even in tabular, finite-state settings, its ability to approximate the eigenvectors outperforms previous proposals. Finally, we show the potential benefits of using a Laplacian representation learned using our method in goal-achieving RL tasks, providing evidence that our technique can be used to significantly improve the performance of an RL agent.
Linear and quadratic ranges in representation stability

Abstract We prove two general results concerning spectral sequences of FI-modules. These results can be used to significantly improve stable ranges in a large portion of the stability theorems for FI-modules currently in the literature. We work this out in detail for the cohomology of configuration spaces where we prove a linear stable range and the homology of congruence subgroups of general linear groups where we prove a quadratic stable range. Previously, the best stable ranges known in these examples were exponential. Up to an additive constant, our work on congruence subgroups verifies a conjecture of Djament.
Step Size Matters in Deep Learning

Training a neural network with the gradient descent algorithm gives rise to a discrete-time nonlinear dynamical system. Consequently, behaviors that are typically observed in these systems emerge during training, such as convergence to an orbit but not to a fixed point or dependence of convergence on the initialization. Step size of the algorithm plays a critical role in these behaviors: it determines the subset of the local optima that the algorithm can converge to, and it specifies the magnitude of the oscillations if the algorithm converges to an orbit. To elucidate the effects of the step size on training of neural networks, we study the gradient descent algorithm as a discrete-time dynamical system, and by analyzing the Lyapunov stability of different solutions, we show the relationship between the step size of the algorithm and the solutions that can be obtained with this algorithm. The results provide an explanation for several phenomena observed in practice, including the deterioration in the training error with increased depth, the hardness of estimating linear mappings with large singular values, and the distinct performance of deep residual networks.
Preprojective analogue of the cone construction

We formulate a relative, representation theoretic, notion of the algebraic cone construction. This motivates a generalization of the cone corresponding to a preprojective algebra.
A Mathematical Formalization of Hierarchical Temporal Memory’s Spatial Pooler

Hierarchical temporal memory~(HTM) is an emerging machine learning algorithm, with the potential to provide a means to perform predictions on spatiotemporal data. The algorithm, inspired by the neocortex, currently does not have a comprehensive mathematical framework. This work brings together all aspects of the spatial pooler~(SP), a critical learning component in HTM, under a single unifying framework. The primary learning mechanism is explored, where a maximum likelihood estimator for determining the degree of permanence update is proposed. The boosting mechanisms are studied and found to be a secondary learning mechanism. The SP is demonstrated in both spatial and categorical multi-class classification, where the SP is found to perform exceptionally well on categorical data. Observations are made relating HTM to well-known algorithms such as competitive learning and attribute bagging. Methods are provided for using the SP for classification as well as dimensionality reduction. Empirical evidence verifies that given the proper parameterizations, the SP may be used for feature learning.
Default Bayesian analysis with global-local shrinkage priors

We provide a framework for assessing the default nature of a prior distribution using the property of regular variation, which we study for global-local shrinkage priors. In particular, we show that the horseshoe priors, originally designed to handle sparsity, are regularly varying and thus are appropriate for default Bayesian analysis. To illustrate our methodology, we discuss four problems of noninformative priors that have been shown to be highly informative for nonlinear functions. In each case, we show that global-local horseshoe priors perform as required. Global-local shrinkage priors can separate a low-dimensional signal from high-dimensional noise even for nonlinear functions.
The detour problem in a stochastic environment: Tolman revisited.

Abstract We designed a grid world task to study human planning and re-planning behavior in an unknown stochastic environment. In our grid world, participants were asked to travel from a random starting point to a random goal position while maximizing their reward. Because they were not familiar with the environment, they needed to learn its characteristics from experience to plan optimally. Later in the task, we randomly blocked the optimal path to investigate whether and how people adjust their original plans to find a detour. To this end, we developed and compared 12 different models. These models were different on how they learned and represented the environment and how they planned to catch the goal. The majority of our participants were able to plan optimally. We also showed that people were capable of revising their plans when an unexpected event occurred. The result from the model comparison showed that the model-based reinforcement learning approach provided the best account for the data and outperformed heuristics in explaining the behavioral data in the re-planning trials.
Robust Subgraph Generation Improves Abstract Meaning Representation Parsing

The Abstract Meaning Representation (AMR) is a representation for opendomain rich semantics, with potential use in fields like event extraction and machine translation. Node generation, typically done using a simple dictionary lookup, is currently an important limiting factor in AMR parsing. We propose a small set of actions that derive AMR subgraphs by transformations on spans of text, which allows for more robust learning of this stage. Our set of construction actions generalize better than the previous approach, and can be learned with a simple classifier. We improve on the previous state-of-the-art result for AMR parsing, boosting end-to-end performance by 3 F1 on both the LDC2013E117 and LDC2014T12 datasets.
Stable systolic category of manifolds and the cup-length

It follows from a theorem of Gromov that the stable systolic category \({\rm cat}_{\rm stsys} M\) of a closed manifold M is bounded from below by \({\rm cl}_{\mathbb{Q}} M\), the rational cup-length of M [Ka07]. We study the inequality in the opposite direction. In particular, combining our results with Gromov’s theorem, we prove the equality \({\rm cat}_{\rm stsys} M = {\rm cl}_{\mathbb{Q}} M\) for simply connected manifolds of dimension ≤ 7.
Power grid simulation using matrix exponential method with rational Krylov subspaces

One well-adopted power grid simulation methodology is to factorize matrix once and perform only backward/forward substitution with a deliberately chosen step size along the simulation. Since the required simulation time is usually long for the power grid design, the costly factorization is amortized. However, such fixed step size cannot exploit larger step size for the low frequency response in the power grid to speedup the simulation. In this work, we utilize the matrix exponential method with the rational Krylov subspace approximation to enable adaptive step size in the power grid simulation. The kernel operation in our method only demands one factorization and backward/forward substitutions. Moreover, the rational Krylov subspace approximation can relax the stiffness constraint of the previous works [12][13]. The cheap computation of adaptivity in our method could exploit the long low-frequency response in a power grid and significantly accelerate the simulation. The experimental results show that our method achieves up to 18X speedup over the trapezoidal method with fixed step size.
Crowd Counting Through Walls Using WiFi

Counting the number of people inside a building, from outside and without entering the building, is crucial for many applications. In this paper, we are interested in counting the total number of people walking inside a building (or in general behind walls), using readily-deployable WiFi transceivers that are installed outside the building, and only based on WiFi RSSI measurements. The key observation of the paper is that the inter-event times, corresponding to the dip events of the received signal, are fairly robust to the attenuation through walls (for instance as compared to the exact dip values). We then propose a methodology that can extract the total number of people from the inter-event times. More specifically, we first show how to characterize the wireless received power measurements as a superposition of renewal-type processes. By borrowing theories from the renewal-process literature, we then show how the probability mass function of the inter-event times carries vital information on the number of people. We validate our framework with 44 experiments in five different areas on our campus (3 classrooms, a conference room, and a hallway), using only one WiFi transmitter and receiver installed outside of the building, and for up to and including 20 people. Our experiments further include areas with different wall materials, such as concrete, plaster, and wood, to validate the robustness of the proposed approach. Overall, our results show that our approach can estimate the total number of people behind the walls with a high accuracy while minimizing the need for prior calibrations.
Large-scale heterogeneous service systems with general packing constraints

A service system with multiple types of customers, arriving according to Poisson processes, is considered. The system is heterogeneous in that the servers can also be of multiple types. Each customer has an independent, exponentially distributed service time, with the mean determined by its type. Multiple customers (possibly of different types) can be placed for service into one server, subject to `packing' constraints, which depend on the server type. Service times of different customers are independent, even if served simultaneously by the same server. The large-scale asymptotic regime is considered such that the customer arrival rates grow to ∞. We consider two variants of the model. For the infinite-server model, we prove asymptotic optimality of the greedy random (GRAND) algorithm in the sense of minimizing the weighted (by type) number of occupied servers in steady state. (This version of GRAND generalizes that introduced by Stolyar and Zhong (2015) for homogeneous systems, with all servers of the same type.) We then introduce a natural extension of the GRAND algorithm for finite-server systems with blocking. Assuming subcritical system load, we prove existence, uniqueness, and local stability of the large-scale system equilibrium point such that no blocking occurs. This result strongly suggests a conjecture that the steady-state blocking probability under the algorithm vanishes in the large-scale limit.
A modulation invariant Carleson embedding theorem outside local L 2

Yen Do and Christoph Thiele developed a theory of Carleson embeddings in outer Lp spaces for the wave packet transform $${F_\phi }(f)(u,t,\eta ) = \int {f(x){e^{i\eta (u - x)}}\phi \left( {\frac{{u - x}}{t}} \right)} \frac{{dx}}{t},(u,t,\eta ) \in R \times (0,\infty ) \times R$$ of functions f ∈ Lp(R) in the range 2 ≤ p ≤ ∞, referred to as local L2. In this article, we formulate a suitable extension of this theory to exponents 1 < p < 2, answering a question posed by Do and Thiele. The proof of our main embedding theorem involves a refined multi-frequency Calderon-Zygmund decomposition in the vein of work by Di Plinio and Thiele and by Nazarov, Oberlin, and Thiele. We apply our embedding theorem to recover the full known range of Lp estimates for the bilinear Hilbert transforms without reducing to discrete model sums or appealing to generalized restricted weak-type interpolation.
SMOOTH METRIC MEASURE SPACES AND QUASI-EINSTEIN METRICS

Smooth metric measure spaces have been studied from the two different perspectives of Bakry–Emery and Chang–Gursky–Yang, both of which are closely related to work of Perelman on the Ricci flow. These perspectives include a generalization of the Ricci curvature and the associated quasi-Einstein metrics, which include Einstein metrics, conformally Einstein metrics, gradient Ricci solitons and static metrics. In this paper, we describe a natural perspective on smooth metric measure spaces from the point of view of conformal geometry and show how it unites these earlier perspectives within a unified framework. We offer many results and interpretations which illustrate the unifying nature of this perspective, including a natural variational characterization of quasi-Einstein metrics as well as some interesting families of examples of such metrics.
Nonuniform Reductions and NP-Completeness

Nonuniformity is a central concept in computational complexity with powerful connections to circuit complexity and randomness. Nonuniform reductions have been used to study the isomorphism conjecture for NP and completeness for larger complexity classes. We study the power of nonuniform reductions for NP0completeness, obtaining both separations and upper bounds for nonuniform completeness vs uniform complessness in NP. Under various hypotheses, we obtain the following separations: 1. There is a set complete for NP under nonuniform many-one reductions, but not under uniform many-one reductions. This is true even with a single bit of nonuniform advice. 2. There is a set complete for NP under nonuniform many-one reductions with polynomial-size advice, but not under uniform Turing reductions. That is, polynomial nonuniformity is stronger than a polynomial number of queries. 3. For any fixed polynomial p(n), there is a set complete for NP under uniform 2-truth-table reductions, but not under nonuniform many-one reductions that use p(n) advice. That is, giving a uniform reduction a second query makes it more powerful than a nonuniform reduction with fixed polynomial advice. 4. There is a set complete for NP under nonuniform many-one reductions with polynomial ad- vice, but not under nonuniform many-one reductions with logarithmic advice. This hierarchy theorem also holds for other reducibilities, such as truth-table and Turing. We also consider uniform upper bounds on nonuniform completeness. Hirahara (2015) showed that unconditionally every set that is complete for NP under nonuniform truth-table reductions that use logarithmic advice is also uniformly Turing-complete. We show that under a derandomization hypothesis, the same statement for truth-table reductions and truth-table completeness also holds.
Extractive Summarization: Limits, Compression, Generalized Model and Heuristics

Due to its promise to alleviate information overload, text summarization has attracted the attention of many researchers. However, it has remained a serious challenge. Here, we ﬁrst prove empirical limits on the recall (and F1-scores) of extractive summarizers on the DUC datasets under ROUGE evaluation for both the single-document and multi-document summarization tasks. Next we deﬁne the concept of compressibility of a document and present a new model of summarization, which generalizes existing models in the literature and integrates several dimensions of the summarization problem, viz., abstractive versus extractive, single versus multi-document, and syntactic versus semantic. Finally, we examine some new and some existing single-document summarization algorithms in a single framework and compare with state of the art summarizers on DUC data.
Residually finite actions and crossed products

We study a notion of residual finiteness for continuous actions of discrete groups on compact Hausdorff spaces and how it relates to the existence of norm microstates for the reduced crossed product. Our main result asserts that an action of a free group on a zero-dimensional compact metrizable space is residually finite if and only if its reduced crossed product admits norm microstates, i.e., is an MF algebra.
Flat surfaces, Bratteli diagrams and unique ergodicity à la Masur

Recalling the construction of a flat surface from a Bratteli diagram, this paper considers the dynamics of the shift map on the space of all bi-infinite Bratteli diagrams as the renormalizing dynamics on a moduli space of flat surfaces of finite area. A criterion of unique ergodicity similar to that of Masur’s for flat surface holds: if there is a subsequence of the renormalizing dynamical system which has a good accumulation point, the translation flow or Bratteli–Vershik transformation is uniquely ergodic. Related questions are explored.
Attend, infer, repeat: fast scene understanding with generative models

We present a framework for efficient inference in structured image models that explicitly reason about objects. We achieve this by performing probabilistic inference using a recurrent neural network that attends to scene elements and processes them one at a time. Crucially, the model itself learns to choose the appropriate number of inference steps. We use this scheme to learn to perform inference in partially specified 2D models (variable-sized variational auto-encoders) and fully specified 3D models (probabilistic renderers). We show that such models learn to identify multiple objects - counting, locating and classifying the elements of a scene -without any supervision, e.g., decomposing 3D images with various numbers of objects in a single forward pass of a neural network at unprecedented speed. We further show that the networks produce accurate inferences when compared to supervised counterparts, and that their structure leads to improved generalization.
Polynomial Cunningham chains

A sequence of prime numbers p1,p2,p3,…, such that pi=2pi−1+ϵ for all i, is called a Cunningham chain of the first or second kind, depending on whether ϵ=1 or −1 respectively. If k is the smallest positive integer such that 2pk+ϵ is composite, then we say the chain has length k. It is conjectured that there are infinitely many Cunningham chains of length k for every positive integer k. A sequence of polynomials f1(x),f2(x),… in Z[x], such that f1(x) has positive leading coefficient, each fi(x) is irreducible in Q[x] and fi(x)=xfi−1(x)+ϵ for all i, is defined to be a polynomial Cunningham chain of the first or second kind, depending on whether ϵ=1 or −1 respectively. If k is the least positive integer such that fk+1(x) is reducible in Q[x], then we say the chain has length k. In this article, for polynomial Cunningham chains of both kinds, we prove that there are infinitely many chains of length k and, unlike the situation in the integers, that there are infinitely many chains of infinite length, by explicitly giving infinitely many polynomials f1(x), such that fk+1(x) is the only term in the sequence {fi(x)}i=1∞ that is reducible.
Stochastic gradient MCMC methods for hidden Markov models

Stochastic gradient MCMC (SG-MCMC) algorithms have proven useful in scaling Bayesian inference to large datasets under an assumption of i.i.d data. We instead develop an SG-MCMC algorithm to learn the parameters of hidden Markov models (HMMs) for time-dependent data. There are two challenges to applying SG-MCMC in this setting: The latent discrete states, and needing to break dependencies when considering minibatches. We consider a marginal likelihood representation of the HMM and propose an algorithm that harnesses the inherent memory decay of the process. We demonstrate the effectiveness of our algorithm on synthetic experiments and an ion channel recording data, with runtimes significantly outperforming batch MCMC.
Learning continuous control policies by stochastic value gradients

We present a unified framework for learning continuous control policies using backpropagation. It supports stochastic control by treating stochasticity in the Bellman equation as a deterministic function of exogenous noise. The product is a spectrum of general policy gradient algorithms that range from model-free methods with value functions to model-based methods without value functions. We use learned models but only require observations from the environment instead of observations from model-predicted trajectories, minimizing the impact of compounded model errors. We apply these algorithms first to a toy stochastic control problem and then to several physics-based control problems in simulation. One of these variants, SVG(1), shows the effectiveness of learning models, value functions, and policies simultaneously in continuous domains.
The projective dimension of three cubics is at most 5

Abstract Let R be a polynomial ring over a field and I an ideal generated by three forms of degree three. Motivated by Stillman's question, Engheta proved that the projective dimension pd ( R / I ) of R / I is at most 36, although the example with largest projective dimension he constructed has pd ( R / I ) = 5 . Based on computational evidence, it had been conjectured that pd ( R / I ) ≤ 5 . In the present paper we prove this conjectured sharp bound.
An alternate description of equivariant connections

Abstract In this note, we consider a Lie group G acting on a manifold M. We prove that the category of principal bundles with connection on the differential quotient stack is equivalent to the category of G-equivariant principal bundles on M with G-invariant connection.
Improved Training for Online End-to-end Speech Recognition Systems.

Achieving high accuracy with end-to-end speech recognizers requires careful parameter initialization prior to training. Otherwise, the networks may fail to find a good local optimum. This is particularly true for online networks, such as unidirectional LSTMs. Currently, the best strategy to train such systems is to bootstrap the training from a tied-triphone system. However, this is time consuming, and more importantly, is impossible for languages without a high-quality pronunciation lexicon. In this work, we propose an initialization strategy that uses teacher-student learning to transfer knowledge from a large, well-trained, offline end-to-end speech recognition model to an online end-to-end model, eliminating the need for a lexicon or any other linguistic resources. We also explore curriculum learning and label smoothing and show how they can be combined with the proposed teacher-student learning for further improvements. We evaluate our methods on a Microsoft Cortana personal assistant task and show that the proposed method results in a 19% relative improvement in word error rate compared to a randomly-initialized baseline system.