cssi/SciSciGPT-SciSciNet huggingface dataset:
Discrete Structure of the Brain Rhythms.

Neuronal activity in the brain generates synchronous oscillations of the Local Field Potential (LFP). The traditional analyses of the LFPs are based on decomposing the signal into simpler components, such as sinusoidal harmonics. However, a common drawback of such methods is that the decomposition primitives are usually presumed from the onset, which may bias our understanding of the signal’s structure. Here, we introduce an alternative approach that allows an impartial, high resolution, hands-off decomposition of the brain waves into a small number of discrete, frequency-modulated oscillatory processes, which we call oscillons. In particular, we demonstrate that mouse hippocampal LFP contain a single oscillon that occupies the θ-frequency band and a couple of γ-oscillons that correspond, respectively, to slow and fast γ-waves. Since the oscillons were identified empirically, they may represent the actual, physical structure of synchronous oscillations in neuronal ensembles, whereas Fourier-defined “brain waves” are nothing but poorly resolved oscillons.
A unifying framework for Linearly Solvable control

Recent work has led to the development of an elegant theory of Linearly Solvable Markov Decision Processes (LMDPs) and related Path-Integral Control Problems. Traditionally, LMDPs have been formulated using stochastic policies and a control cost based on the KL divergence. In this paper, we extend this framework to a more general class of divergences: the Renyi divergences. These are a more general class of divergences parameterized by a continuous parameter α that include the KL divergence as a special case. The resulting control problems can be interpreted as solving a risk-sensitive version of the LMDP problem. For α > 0, we get risk-averse behavior (the degree of risk-aversion increases with a) and for α < 0, we get risk-seeking behavior. We recover LMDPs in the limit as α → 0. This work generalizes the recently developed risk-sensitive path-integral control formalism which can be seen as the continuous-time limit of results obtained in this paper. To the best of our knowledge, this is a general theory of linearly solvable control and includes all previous work as a special case. We also present an alternative interpretation of these results as solving a 2-player (cooperative or competitive) Markov Game. From the linearity follow a number of nice properties including compositionality of control laws and a path-integral representation of the value function. We demonstrate the usefulness of the framework on control problems with noise where different values of α lead to qualitatively different control behaviors.
An algorithmic approach to the Polydegree Conjecture for plane polynomial automorphisms

Abstract We study the interaction between two structures on the group of polynomial automorphisms of the affine plane: its structure as an amalgamated free product and as an infinite-dimensional algebraic variety. We introduce a new conjecture, and show how it implies the Polydegree Conjecture. As the new conjecture is an ideal membership question, this shows that the Polydegree Conjecture is algorithmically decidable. We further describe how this approach provides a unified and shorter method of recovering existing results of Edo and Furter.
Phase transition on the convergence rate of parameter estimation under an Ornstein–Uhlenbeck diffusion on a tree

Diffusion processes on trees are commonly used in evolutionary biology to model the joint distribution of continuous traits, such as body mass, across species. Estimating the parameters of such processes from tip values presents challenges because of the intrinsic correlation between the observations produced by the shared evolutionary history, thus violating the standard independence assumption of large-sample theory. For instance (Ho and Ane, Ann Stat 41:957–981, 2013) recently proved that the mean (also known in this context as selection optimum) of an Ornstein–Uhlenbeck process on a tree cannot be estimated consistently from an increasing number of tip observations if the tree height is bounded. Here, using a fruitful connection to the so-called reconstruction problem in probability theory, we study the convergence rate of parameter estimation in the unbounded height case. For the mean of the process, we provide a necessary and sufficient condition for the consistency of the maximum likelihood estimator (MLE) and establish a phase transition on its convergence rate in terms of the growth of the tree. In particular we show that a loss of $$\sqrt{n}$$ -consistency (i.e., the variance of the MLE becomes $$\varOmega (n^{-1})$$ , where n is the number of tips) occurs when the tree growth is larger than a threshold related to the phase transition of the reconstruction problem. For the covariance parameters, we give a novel, efficient estimation method which achieves $$\sqrt{n}$$ -consistency under natural assumptions on the tree. Our theoretical results provide practical suggestions for the design of comparative data collection.
Learning Latent Representations in Neural Networks for Clustering through Pseudo Supervision and Graph-based Activity Regularization

In this paper, we propose a novel unsupervised clustering approach exploiting the hidden information that is indirectly introduced through a pseudo classification objective. Specifically, we randomly assign a pseudo parent-class label to each observation which is then modified by applying the domain specific transformation associated with the assigned label. Generated pseudo observation-label pairs are subsequently used to train a neural network with Auto-clustering Output Layer (ACOL) that introduces multiple softmax nodes for each pseudo parent-class. Due to the unsupervised objective based on Graph-based Activity Regularization (GAR) terms, softmax duplicates of each parent-class are specialized as the hidden information captured through the help of domain specific transformations is propagated during training. Ultimately we obtain a k-means friendly latent representation. Furthermore, we demonstrate how the chosen transformation type impacts performance and helps propagate the latent information that is useful in revealing unknown clusters. Our results show state-of-the-art performance for unsupervised clustering tasks on MNIST, SVHN and USPS datasets, with the highest accuracies reported to date in the literature.
A variational Barban–Davenport–Halberstam Theorem

Abstract We prove variational forms of the Barban–Davenport–Halberstam Theorem and the large sieve inequality. We apply our result to prove an estimate for the sum of the squares of prime differences, averaged over arithmetic progressions.
Growing controllable networks via whiskering and submodular optimization

The topology of a network directly influences the behaviour and controllability of dynamical processes on that network. Therefore, the design of network topologies is an important area of research when examining the control of distributed systems. We discuss a method for growing networks known as whiskering, as well as generalizations of this process, and prove that they preserve controllability. We then use techniques from submodular optimization to analyze optimization algorithms for adding new nodes to a network to optimize certain objectives, such as graph connectivity.
Rational certificates of positivity on compact semialgebraic sets

Let ℝ[X] denote the real polynomial ring ℝ[X 1 , ..., X n ] and write Σ ℝ[X] 2 for the set of sums of squares in ℝ[X]. Given g 1 , ... , g s ∈ ℝ[X] such that the semialgebraic set K := {x ∈ ℝ n | g i (x) ≥ 0 for all i) is compact, Schmud-gen's theorem says that if f ∈ ℝ[X] such that f > 0 on K, then f is in the preordering in ℝ[X] generated by the g i 's, i.e., f can be written as a finite sum of elements σ g e 1 1 ... g e s s , where σ is a sum of squares in ℝ[X] and each e i ∈ {0, 1}. Putinar's theorem says that under a condition on the set of generators {g 1 , ..., g s } (which is a stronger condition than the compactness of K), any f > 0 on K can be written f = σ 0 + σ 1 g 1 + ··· + σ s g s , where σ i ∈ Σ ℝ[X] 2 . Both of these theorems can be viewed as statements about the existence of certificates of positivity on compact semialgebraic sets. In this note we show that if the defining polynomials g 1 , ..., g s and polynomial f have coefficients in ℚ, then in Schmudgen's theorem we can find a representation in which the σ's are sums of squares of polynomials over ℚ. We prove a similar result for Putinar's theorem assuming that the set of generators contains N ― Σ X 2 i for some N ∈ ℕ.
Explicit Salem sets and applications to metrical Diophantine approximation

Let $Q$ be an infinite subset of $\mathbb{Z}$, let $\Psi: \mathbb{Z} \rightarrow [0,\infty)$ be positive on $Q$, and let $\theta \in \mathbb{R}$. Define $$ E(Q,\Psi,\theta) = \{ x \in \mathbb{R} : \| q x - \theta \| \leq \Psi(q) \text{ for infinitely many $q \in Q$} \}. $$ We prove a lower bound on the Fourier dimension of $E(Q,\Psi,\theta)$. This generalizes theorems of Kaufman and Bluhm and yields new explicit examples of Salem sets. We give applications to metrical Diophantine approximation, including determining the Hausdorff dimension of $E(Q,\Psi,\theta)$ in new cases. We also prove a higher-dimensional analog of our result.
Lossy compression with privacy constraints: Optimality of polar codes

A lossy source coding problem with privacy constraint is studied in which two correlated discrete sources X and Y are compressed into a reconstruction X with some prescribed distortion D. In addition, a privacy constraint is specified as the equivocation between the lossy reconstruction X and Y. This models the situation where a certain amount of source information from one user is provided as utility (given by the fidelity of its reconstruction) to another user or the public, while some other correlated part of the source information Y must be kept private. In this work, we show that polar codes are able, possibly with the aid of time sharing, to achieve any point in the optimal rate-distortion-equivocation region identified by Yamamoto, thus providing a constructive scheme that obtains the optimal tradeoff between utility and privacy in this framework.
Tensor vs. Matrix Methods: Robust Tensor Decomposition under Block Sparse Perturbations

Author(s): Anandkumar, Animashree; Jain, Prateek; Shi, Yang; Niranjan, UN | Abstract: Robust tensor CP decomposition involves decomposing a tensor into low rank and sparse components. We propose a novel non-convex iterative algorithm with guaranteed recovery. It alternates between low-rank CP decomposition through gradient ascent (a variant of the tensor power method), and hard thresholding of the residual. We prove convergence to the globally optimal solution under natural incoherence conditions on the low rank component, and bounded level of sparse perturbations. We compare our method with natural baselines which apply robust matrix PCA either to the {\em flattened} tensor, or to the matrix slices of the tensor. Our method can provably handle a far greater level of perturbation when the sparse tensor is block-structured. This naturally occurs in many applications such as the activity detection task in videos. Our experiments validate these findings. Thus, we establish that tensor methods can tolerate a higher level of gross corruptions compared to matrix methods.
Reducible surgeries and Heegaard Floer homology

In this paper, we use Heegaard Floer homology to study reducible surgeries. In particular, suppose K is a non-cable knot in the three-sphere with an L-space surgery. If p-surgery on K is reducible, we show that p equals 2g(K)-1. This implies that any knot with an L-space surgery has at most one reducible surgery, a fact that we show additionally for any knot of genus at most two.
Plane Gossip: Approximating rumor spread in planar graphs

We study the design of schedules for multi-commodity multicast. In this problem, we are given an undirected graph G and a collection of source-destination pairs, and the goal is to schedule a minimum-length sequence of matchings that connects every source with its respective destination. The primary communication constraint of the multi-commodity multicast model is the number of connections that a given node can make, not link bandwidth. Multi-commodity multicast and its special cases, (single-commodity) broadcast and multicast, are all NP-complete. Multi-commodity multicast is closely related to the problem of finding a subgraph of optimal poise, where the poise is defined as the sum of the maximum degree and the maximum distance between any source-destination pair. We show that for any instance of the multicast problem, the minimum poise subgraph can be approximated to within a factor of \(O(\log k)\) with respect to the value of a natural LP relaxation in a graph with k source-destination pairs. This is the first upper bound on the integrality gap of the natural LP; all previous algorithms yielded approximations with respect to the integer optimum. Using this integrality gap upper bound and shortest-path separators in planar graphs, we obtain our main result: an \(O(\log ^3 k \frac{\log n}{\log \log n})\)-approximation for multi-commodity multicast for planar graphs which improves on the \(2^{\widetilde{O}(\sqrt{\log n})}\)-approximation for general graphs.
Gradient Sparsification for Communication-Efficient Distributed Optimization

Modern large-scale machine learning applications require stochastic optimization algorithms to be implemented on distributed computational architectures. A key bottleneck is the communication overhead for exchanging information such as stochastic gradients among different workers. In this paper, to reduce the communication cost, we propose a convex optimization formulation to minimize the coding length of stochastic gradients. The key idea is to randomly drop out coordinates of the stochastic gradient vectors and amplify the remaining coordinates appropriately to ensure the sparsified gradient to be unbiased. To solve the optimal sparsification efficiently, several simple and fast algorithms are proposed for an approximate solution, with a theoretical guarantee for sparseness. Experiments on $\ell_2$ regularized logistic regression, support vector machines, and convolutional neural networks validate our sparsification approaches.
Polynomial-Time Approximation Schemes for Knapsack and Related Counting Problems using Branching Programs

We give a deterministic, polynomial-time algorithm for approximately counting the number of {0, 1}-solutions to any instance of the knapsack problem. On an instance of length n with total weight W and accuracy parameter e, our algorithm produces a (1 + e)-multiplicative approximation in time poly(n, logW, 1/e). We also give algorithms with identical guarantees for general integer knapsack, the multidimensional knapsack problem (with a constant number of constraints) and for contingency tables (with a constant number of rows). Previously, only randomized approximation schemes were known for these problems due to work by Morris and Sinclair and work by Dyer. Our algorithms work by constructing small-width, read-once branching programs for approximating the underlying solution space under a carefully chosen distribution. As a byproduct of this approach, we obtain new query algorithms for learning functions of k halfspaces with respect to the uniform distribution on {0, 1}. The running time of our algorithm is polynomial in the accuracy parameter e. Previously even for the case of k = 2, only algorithms with an exponential dependence on e were known. ∗Mail: parik@microsoft.com †Mail: klivans@cs.utexas.edu. Work done while visiting Microsoft Research, Silicon Valley. ‡Mail: raghu@cs.utexas.edu. Work done as an intern at Microsoft Research, Silicon Valley.
BMO Solvability and Absolute Continuity of Harmonic Measure

We show that for a uniformly elliptic divergence form operator L, defined in an open set \(\Omega \) with Ahlfors–David regular boundary, BMO solvability implies scale-invariant quantitative absolute continuity (the weak-\(A_\infty \) property) of elliptic-harmonic measure with respect to surface measure on \(\partial \Omega \). We do not impose any connectivity hypothesis, qualitative, or quantitative; in particular, we do not assume the Harnack Chain condition, even within individual connected components of \(\Omega \). In this generality, our results are new even for the Laplacian. Moreover, we obtain a partial converse, assuming in addition that \(\Omega \) satisfies an interior Corkscrew condition, in the special case that L is the Laplacian.
MidiNet: A Convolutional Generative Adversarial Network for Symbolic-Domain Music Generation.

Most existing neural network models for music generation use recurrent neural networks. However, the recent WaveNet model proposed by DeepMind shows that convolutional neural networks (CNNs) can also generate realistic musical waveforms in the audio domain. Following this light, we investigate using CNNs for generating melody (a series of MIDI notes) one bar after another in the symbolic domain. In addition to the generator, we use a discriminator to learn the distributions of melodies, making it a generative adversarial network (GAN). Moreover, we propose a novel conditional mechanism to exploit available prior knowledge, so that the model can generate melodies either from scratch, by following a chord sequence, or by conditioning on the melody of previous bars (e.g. a priming melody), among other possibilities. The resulting model, named MidiNet, can be expanded to generate music with multiple MIDI channels (i.e. tracks). We conduct a user study to compare the melody of eight-bar long generated by MidiNet and by Google's MelodyRNN models, each time using the same priming melody. Result shows that MidiNet performs comparably with MelodyRNN models in being realistic and pleasant to listen to, yet MidiNet's melodies are reported to be much more interesting.
All hyperbolic Coxeter n-cubes

Abstract Beside simplices, n-cubes form an important class of simple polyhedra. Unlike hyperbolic Coxeter simplices, hyperbolic Coxeter n-cubes are not classified. We show that there is no hyperbolic Coxeter n-cube for n ≥ 6 , and provide a full classification for n ≤ 5 . Our methods, which are essentially of combinatorial and algebraic nature, can be (and have been successfully) implemented in a symbolic computation software such as Mathematica ®.
Road Segmentation using CNN and Distributed LSTM

In automated driving systems (ADS) and advanced driver-assistance systems (ADAS), an efficient road segmentation is necessary to perceive the drivable region and build an occupancy map for path planning. The existing algorithms implement gigantic convolutional neural networks (CNNs) that are computationally expensive and time consuming. In this paper, we introduced distributed LSTM, a neural network widely used in audio and video processing, to process rows and columns in images and feature maps. We then propose a new network combining the convolutional and distributed LSTM layers to solve the road segmentation problem. In the end, the network is trained and tested in KITTI road benchmark. The result shows that the combined structure enhances the feature extraction and processing but takes less processing time than pure CNN structure.
Smoothed Action Value Functions for Learning Gaussian Policies

State-action value functions (i.e., Q-values) are ubiquitous in reinforcement learning (RL), giving rise to popular algorithms such as SARSA and Q-learning. We propose a new notion of action value defined by a Gaussian smoothed version of the expected Q-value. We show that such smoothed Q-values still satisfy a Bellman equation, making them learnable from experience sampled from an environment. Moreover, the gradients of expected reward with respect to the mean and covariance of a parameterized Gaussian policy can be recovered from the gradient and Hessian of the smoothed Q-value function. Based on these relationships, we develop new algorithms for training a Gaussian policy directly from a learned smoothed Q-value approximator. The approach is additionally amenable to proximal optimization by augmenting the objective with a penalty on KL-divergence from a previous policy. We find that the ability to learn both a mean and covariance during training leads to significantly improved results on standard continuous control benchmarks.
A Statistical Learning Theory Framework for Supervised Pattern Discovery.

This paper formalizes a latent variable inference problem we call supervised pattern discovery, the goal of which is to find sets of observations that belong to a single “pattern.” We discuss two versions of the problem and prove uniform risk bounds for both. In the first version, collections of patterns can be generated in an arbitrary manner and the data consist of multiple labeled collections. In the second version, the patterns are assumed to be generated independently by identically distributed processes. These processes are allowed to take an arbitrary form, so observations within a pattern are not in general independent of each other. The bounds for the second version of the problem are stated in terms of a new complexity measure, the quasi-Rademacher complexity.
Modeling Microscopic Chemical Sensors in Capillaries

Nanotechnology-based microscopic robots could provide accurate in vivo measurement of chemicals in the bloodstream for detailed biological research and as an aid to medical treatment. Quantitative performance estimates of such devices require models of how chemicals in the blood diffuse to the devices. This paper models microscopic robots and red blood cells (erythrocytes) in capillaries using realistic distorted cell shapes. The models evaluate two sensing scenarios: robots moving with the cells past a chemical source on the vessel wall, and robots attached to the wall for longer-term chemical monitoring of chemicals released into the bloodstream. Using axial symmetric geometry with realistic flow speeds and diffusion coefficients, we compare detection performance with a simpler model that does not include the cells. The average chemical absorption is quantitatively similar in both models, indicating the simpler model is an adequate design guide to sensor performance in capillaries. However, determining the variation in forces and absorption as cells move requires the full model.
Random fusion frames are nearly equiangular and tight

Abstract This paper demonstrates that random, independently chosen equi-dimensional subspaces with a unitarily invariant distribution in a real Hilbert space provide nearly tight, nearly equiangular fusion frames. The angle between a pair of subspaces is measured in terms of the Hilbert–Schmidt inner product of the corresponding orthogonal projections. If the subspaces are selected at random, then a measure concentration argument shows that these inner products concentrate near an average value. Overwhelming success probability for near tightness and equiangularity is guaranteed if the dimension of the subspaces is sufficiently small compared to that of the Hilbert space and if the dimension of the Hilbert space is small compared to the sum of all subspace dimensions.
Highlights from STAR

Selected results from the STAR collaboration are presented. We focus on recent results on jet-like correlations, nuclear modification factors of identified hadrons, elliptic flow of multi-strange baryons {Xi} and {Omega} and resonance yields. First measurements of open charm production at RHIC are presented.
Laurent phenomenon algebras

We generalize Fomin and Zelevinsky's cluster algebras by allowing exchange polynomials to be arbitrary irreducible polynomials, rather than binomials.
Throwing a Ball as Far as Possible, Revisited

What initial trajectory angle maximizes the arc length of an ideal projectile? We show the optimal angle, which depends neither on the initial speed nor on the acceleration of gravity, is the solut...
Local smoothing for the quantum Liouville equation

Abstract We analyze in this work the regularity properties of the density operator solution to the quantum Liouville equation. As was recently done for the Strichartz inequalities, we extend to systems of orthonormal functions the local smoothing estimates satisfied by the solutions to the Schrodinger equation. We show in particular that the local density associated to the solution to the free, linear, quantum Liouville equation admits locally fractional derivatives of given order provided the data belong to some Schatten spaces.
Natasha 2: Faster Non-Convex Optimization Than SGD

(this is a theory paper) We design a stochastic algorithm to find e -approximate local minima of any smooth nonconvex function in rate O(e−3.25) , with only oracle access to stochastic gradients. The best result was essentially O(e−4) by stochastic gradient descent (SGD).
Collections of Hypersurfaces Containing a Curve

We consider the closed locus of $r$-tuples of hypersurfaces in $\mathbb{P}^r$ with positive dimensional intersection, and show in a large range of degrees that its largest component is the locus of $r$-tuples of hypersurfaces whose intersection contains a line. We then apply our methods to obtain new results on the largest components of the locus of hypersurfaces with positive dimensional singular loci and the locus of smooth hypersurfaces with a higher dimensional family of lines through a point than expected.
Fuchs' problem for indecomposable abelian groups

Abstract More than 50 years ago, Laszlo Fuchs asked which abelian groups can be the group of units of a commutative ring. Though progress has been made, the question remains open. We provide an answer to this question in the case of indecomposable abelian groups by classifying the indecomposable abelian groups that are realizable as the group of units of a ring of any given characteristic.
On the Complexity of Learning Neural Networks

The stunning empirical successes of neural networks currently lack rigorous theoretical explanation. What form would such an explanation take, in the face of existing complexity-theoretic lower bounds? A first step might be to show that data generated by neural networks with a single hidden layer, smooth activation functions and benign input distributions can be learned efficiently. We demonstrate here a comprehensive lower bound ruling out this possibility: for a wide class of activation functions (including all currently used), and inputs drawn from any logconcave distribution, there is a family of one-hidden-layer functions whose output is a sum gate that are hard to learn in a precise sense: any statistical query algorithm (which includes all known variants of stochastic gradient descent with any loss function) needs an exponential number of queries even using tolerance inversely proportional to the input dimensionality. Moreover, this hard family of functions is realizable with a small (sublinear in dimension) number of activation units in the single hidden layer. The lower bound is also robust to small perturbations of the true weights. Systematic experiments illustrate a phase transition in the training error as predicted by the analysis.
On Switching Stabilizability for Continuous-Time Switched Linear Systems

This technical note studies switching stabilization problems for continuous-time switched linear systems. We consider four types of switching stabilizability defined under different assumptions on the switching control input. The most general switching stabilizability is defined as the existence of a measurable switching signal under which the resulting time-varying system is asymptotically stable. Discrete switching stabilizability is defined similarly but requires the switching signal to be piecewise constant on intervals of uniform length. In addition, we define feedback stabilizability in Filippov sense (respectively, sample-and-hold sense) as the existence of a feedback law under which closed-loop Filippov solution (respectively, sample-and-hold solution) is asymptotically stable. It is proved that the four switching stabilizability notions are equivalent and their sufficient and necessary condition is the existence of a piecewise quadratic control-Lyapunov function that can be expressed as the pointwise minimum of a finite number of quadratic functions.
The Perils of Exploration under Competition: A Computational Modeling Approach

We empirically study the interplay between exploration and competition. Systems that learn from interactions with users often engage in exploration: making potentially suboptimal decisions in order to acquire new information for future decisions. However, when multiple systems are competing for the same market of users, exploration may hurt a system's reputation in the near term, with adverse competitive effects. In particular, a system may enter a "death spiral", when the short-term reputation cost decreases the number of users for the system to learn from, which degrades the system's performance relative to competition and further decreases the market share. We ask whether better exploration algorithms are incentivized under competition. We run extensive numerical experiments in a stylized duopoly model in which two firms deploy multi-armed bandit algorithms and compete for myopic users. We find that duopoly and monopoly tend to favor a primitive "greedy algorithm" that does not explore and leads to low consumer welfare, whereas a temporary monopoly (a duopoly with an early entrant) may incentivize better bandit algorithms and lead to higher consumer welfare. Our findings shed light on the first-mover advantage in the digital economy by exploring the role that data can play as a barrier to entry in online markets.
Object-Based Reasoning in VQA

Visual Question Answering (VQA) is a novel problem domain where multi-modal inputs must be processed in order to solve the task given in the form of a natural language. As the solutions inherently require to combine visual and natural language processing with abstract reasoning, the problem is considered as AI-complete. Recent advances indicate that using high-level, abstract facts extracted from the inputs might facilitate reasoning. Following that direction we decided to develop a solution combining state-of-the-art object detection and reasoning modules. The results, achieved on the well-balanced CLEVR dataset, confirm the promises and show significant, few percent improvements of accuracy on the complex "counting" task.
Membrane-dependent neuromorphic learning rule for unsupervised spike pattern detection

Several learning rules for synaptic plasticity, that depend on either spike timing or internal state variables, have been proposed in the past imparting varying computational capabilities to Spiking Neural Networkss (SNNs). Due to design complications these learning rules are typically not implemented on neuromorphic devices leaving the devices to be only capable of inference. In this work we propose a unidirectional post-synaptic potential dependent learning rule that is only triggered by pre-synaptic spikes, and easy to implement on hardware. We demonstrate that such a learning rule is functionally capable of replicating computational capabilities of pairwise STDP. Further more, we demonstrate that this learning rule can be used to learn and classify spatio-temporal spike patterns in an unsupervised manner using individual neurons. We argue that this learning rule is computationally powerful and also ideal for hardware implementations due to its unidirectional memory access.
Equivariant Slices for Symplectic Cones

The Darboux-Weinstein decomposition is a central result in the theory of Poisson (degenerate symplectic) varieties, which gives a local decomposition at a point as a product of the formal neighborhood of the symplectic leaf through the point and a formal slice. Recently, conical symplectic resolutions, and more generally, Poisson cones, have been very actively studied in representation theory and algebraic geometry. This motivates asking for a C*-equivariant version of the Darboux-Weinstein decomposition. In this paper, we develop such a theory, prove basic results on their existence and uniqueness, study examples (quotient singularities and hypertoric varieties), and applications to noncommutative algebra (their quantization). We also pose some natural questions on existence and quantization of C*-actions on slices to conical symplectic leaves.
Location- and Time-Dependent VPD for Privacy-Preserving Wireless Accesses to Cloud Services

The advent of smartphones in recent years has changed the wireless landscape. Smartphones have become a platform for online user interface to cloud databases. Cloud databases may provide a large set of user-private and sensitive data (i.e., objects), while smartphone users (i.e., subjects) provide location-sensitive information. Secure and private services in wireless accessing to cloud databases have been discussed actively for the past recent years. However, the previous techniques are unsatisfactory for dynamism of moving subjects' wireless accesses. In this paper, we propose a novel technique to dynamically generate virtual private databases (VPD) for each access by taking subjects' location and time information into account. The contribution of this paper includes a privacy-preserving access control mechanism for dynamism of wireless access.
A logarithmic additive integrality gap for bin packing

For bin packing, the input consists of n items with sizes s1,...,sn ∈ [0,1] which have to be assigned to a minimum number of bins of size 1. Recently, the second author gave an LP-based polynomial time algorithm that employed techniques from discrepancy theory to find a solution using at most OPT + O(logOPT·loglogOPT) bins. In this paper, we build on the techniques of Rothvoss to present an approximation algorithm that has an additive gap of only O(logOPT) bins. This gap matches certain combinatorial lower bounds, and any further improvement would have to use more algebraic structure.
Thermodynamic free energy methods to investigate shape transitions in bilayer membranes

The conformational free energy landscape of a system is a fundamental thermodynamic quantity of importance particularly in the study of soft matter and biological systems, in which the entropic contributions play a dominant role. While computational methods to delineate the free energy landscape are routinely used to analyze the relative stability of conformational states, to determine phase boundaries, and to compute ligand-receptor binding energies its use in problems involving the cell membrane is limited. Here, we present an overview of four different free energy methods to study morphological transitions in bilayer membranes, induced either by the action of curvature remodeling proteins or due to the application of external forces. Using a triangulated surface as a model for the cell membrane and using the framework of dynamical triangulation Monte Carlo, we have focused on the methods of Widom insertion, thermodynamic integration, Bennett acceptance scheme, and umbrella sampling and weighted histogram analysis. We have demonstrated how these methods can be employed in a variety of problems involving the cell membrane. Specifically, we have shown that the chemical potential, computed using Widom insertion, and the relative free energies, computed using thermodynamic integration and Bennett acceptance method, are excellent measures to study the transition from curvature sensing to curvature inducing behavior of membrane associated proteins. The umbrella sampling and WHAM analysis has been used to study the thermodynamics of tether formation in cell membranes and the quantitative predictions of the computational model are in excellent agreement with experimental measurements. Furthermore, we also present a method based on WHAM and thermodynamic integration to handle problems related to end-point-catastrophe that are common in most free energy methods.
Linear Coupling: An Ultimate Unification of Gradient and Mirror Descent

First-order methods play a central role in large-scale machine learning. Even though many variations exist, each suited to a particular problem, almost all such methods fundamentally rely on two types of algorithmic steps: gradient descent, which yields primal progress, and mirror descent, which yields dual progress. We observe that the performances of gradient and mirror descent are complementary, so that faster algorithms can be designed by "linearly coupling" the two. We show how to reconstruct Nesterov's accelerated gradient methods using linear coupling, which gives a cleaner interpretation than Nesterov's original proofs. We also discuss the power of linear coupling by extending it to many other settings that Nesterov's methods cannot apply to.
Randomized Clustered Nystrom for Large-Scale Kernel Machines

The Nystrom method has been popular for generating the low-rank approximation of kernel matrices that arise in many machine learning problems. The approximation quality of the Nystrom method depends crucially on the number of selected landmark points and the selection procedure. In this paper, we present a novel algorithm to compute the optimal Nystrom low-approximation when the number of landmark points exceed the target rank. Moreover, we introduce a randomized algorithm for generating landmark points that is scalable to large-scale data sets. The proposed method performs K-means clustering on low-dimensional random projections of a data set and, thus, leads to significant savings for high-dimensional data sets. Our theoretical results characterize the tradeoffs between the accuracy and efficiency of our proposed method. Extensive experiments demonstrate the competitive performance as well as the efficiency of our proposed method.
Two-Sided Infinite Systems of Competing Brownian Particles

Two-sided infinite systems of Brownian particles with rank-dependent dynamics, indexed by all integers, exhibit different properties from their one-sided infinite counterparts, indexed by positive integers, and from finite systems. Consider the gap process, which is formed by spacings between adjacent particles. In stark contrast with finite and one-sided infinite systems, two-sided infinite systems can have one- or two-parameter family of stationary gap distributions, or the gap process weakly converging to zero as time goes to infinity.
Enabling Fine-Grain Restricted Coset Coding Through Word-Level Compression for PCM

Phase change memory (PCM) has recently emerged as a promising technology to meet the fast growing demand for large capacity memory in computer systems, replacing DRAM that is impeded by physical limitations. Multi-level cell (MLC) PCM offers high density with low per-byte fabrication cost. However, despite many advantages, such as scalability and low leakage, the energy for programming intermediate states is considerably larger than programing single-level cell PCM. In this paper, we study encoding techniques to reduce write energy for MLC PCM when the encoding granularity is lowered below the typical cache line size. We observe that encoding data blocks at small granularity to reduce write energy actually increases the write energy because of the auxiliary encoding bits. We mitigate this adverse effect by 1) designing suitable codeword mappings that use fewer auxiliary bits and 2) proposing a new Word-Level Compression (WLC) which compresses more than 91% of the memory lines and provides enough room to store the auxiliary data using a novel restricted coset encoding applied at small data block granularities. Experimental results show that the proposed encoding at 16-bit data granularity reduces the write energy by 39%, on average, versus the leading encoding approach for write energy reduction. Furthermore, it improves endurance by 20% and is more reliable than the leading approach. Hardware synthesis evaluation shows that the proposed encoding can be implemented on-chip with only a nominal area overhead.
Two-point Correlation Function and Feynman-Kac Formula for the Stochastic Heat Equation

In this paper, we obtain an explicit formula for the two-point correlation function for the solutions to the stochastic heat equation on \(\mathbb {R}\). The bounds for p-th moments proved in Chen and Dalang (Ann. Probab. 2015) are simplified. We validate the Feynman-Kac formula for the p-point correlation function of the solutions to this equation with measure-valued initial data.
AmazonQA: A Review-Based Question Answering Task

Every day, thousands of customers post questions on Amazon product pages. After some time, if they are fortunate, a knowledgeable customer might answer their question. Observing that many questions can be answered based upon the available product reviews, we propose the task of review-based QA. Given a corpus of reviews and a question, the QA system synthesizes an answer. To this end, we introduce a new dataset and propose a method that combines information retrieval techniques for selecting relevant reviews (given a question) and "reading comprehension" models for synthesizing an answer (given a question and review). Our dataset consists of 923k questions, 3.6M answers and 14M reviews across 156k products. Building on the well-known Amazon dataset, we collect additional annotations, marking each question as either answerable or unanswerable based on the available reviews. A deployed system could first classify a question as answerable and then attempt to generate an answer. Notably, unlike many popular QA datasets, here, the questions, passages, and answers are all extracted from real human interactions. We evaluate numerous models for answer generation and propose strong baselines, demonstrating the challenging nature of this new task.
Hadamard equiangular tight frames

Abstract An equiangular tight frame (ETF) is a type of optimal packing of lines. They are often represented as the columns of a short, fat matrix. In certain applications we want this matrix to be flat, that is, have unimodular entries. In particular, real flat ETFs are equivalent to self-complementary binary codes that achieve the Grey-Rankin bound. Some flat ETFs are (complex) Hadamard ETFs, meaning they arise by extracting rows from a (complex) Hadamard matrix. In this paper, we give some new results about flat ETFs. We give an explicit Naimark complement for all Steiner ETFs, which in turn implies that all Kirkman ETFs are possibly-complex Hadamard ETFs. This in particular produces a new infinite family of real flat ETFs. Another result establishes an equivalence between real flat ETFs and certain types of quasi-symmetric designs, resulting in a new infinite family of such designs.
Provable Gradient Variance Guarantees for Black-Box Variational Inference

Recent variational inference methods use stochastic gradient estimators whose variance is not well understood. Theoretical guarantees for these estimators are important to understand when these methods will or will not work. This paper gives bounds for the common “reparameterization” estimators when the target is smooth and the variational family is a location-scale distribution. These bounds are unimprovable and thus provide the best possible guarantees under the stated assumptions.
Annotating Student Talk in Text-based Classroom Discussions

Classroom discussions in English Language Arts have a positive effect on students’ reading, writing and reasoning skills. Although prior work has largely focused on teacher talk and student-teacher interactions, we focus on three theoretically-motivated aspects of high-quality student talk: argumentation, specificity, and knowledge domain. We introduce an annotation scheme, then show that the scheme can be used to produce reliable annotations and that the annotations are predictive of discussion quality. We also highlight opportunities provided by our scheme for education and natural language processing research.
A criterion for Kolchin subgroups of Out(Fr)

This paper provides a decidable criterion for when a subgroup of Out(Fr) generated by two Dehn twists consists entirely of polynomially growing elements, answering an earlier question of the author.
Hierarchical Distributed Voltage Regulation in Networked Autonomous Grids

We propose a novel algorithm to solve optimal power flow (OPF) that aims at dispatching controllable distributed energy resources (DERs) for voltage regulation at minimum cost. The proposed algorithm features unprecedented scalability to large distribution networks by utilizing an information structure based on networked autonomous grids (AGs). Specifically, each AG is a subtree of a large distribution network that has a tree topology. The topology and line parameters of each AG are known only to a regional coordinator (RC) that is responsible for communicating with and dispatching the DERs within this AG. The reduced network, where each AG is treated as a node, is managed by a central coordinator (CC), which knows the topology and line parameters of the reduced network only and communicates with all the RCs. We jointly explore this information structure and the structure of the linearized distribution power flow (LinDistFlow) model to derive a hierarchical, distributed implementation of the primal-dual gradient algorithm that solves the OPF. The proposed implementation significantly reduces the computation burden compared to the centrally coordinated implementation of the primal-dual algorithm. Numerical results on a 4,521-node test feeder show that the proposed hierarchical distributed algorithm can achieve an improvement of more than tenfold in the speed of convergence compared to the centrally coordinated primal-dual algorithm.
Metal Abundances and Star Formation Rates of Emission-line Galaxies in and around the Boötes Void

We explore the possible dependencies of galaxy metal abundance and star-formation rate (SFR) on local environment, focusing on the volume of space in and around the Bootes Void. Our sample of star-forming galaxies comes from the second catalog of the H-alpha-selected KPNO International Spectroscopic Survey (KISS) which overlaps the void. This sample represents a statistically complete, line-flux-limited ensemble of 820 star-forming galaxies, all of which possess metallicity and SFR estimates. We carry out two distinct analyses of the KISS galaxies: one which probes the properties of the entire sample as a function of local density, and a second which details the properties of 33 KISS star-forming galaxies located within the Bootes Void. In both cases we find no evidence that either the metallicity of the KISS galaxies or their SFRs depend on the environments within which the galaxies are located. Our global analysis does show weak trends for decreasing stellar mass, decreasing metallicity, and decreasing SFRs with decreasing local densities. However, we argue that the metallicity and SFR trends are artifacts of the stellar mass - local density trend. In particular, the change in metallicity with density is precisely what one would predict from the mass-metallicity relation given the observed drop in stellar mass with decreasing metallicity. Likewise, the SFR trend with density disappears when one instead considers the mass-normalized specific SFR. The KISS galaxies dwelling in the Bootes Void are found to have nearly identical metallicity and SFR properties to a matched comparison sample, despite the fact that the former are located in density environments that are, on average, more than 16 times lower.