arXiv research

A spring-block chain placed on a running conveyor belt is considered for modeling stylized facts observed in the dynamics of stock indexes. Individual stocks are modeled by the blocks, while the stock-stock correlations are introduced via simple elastic forces acting in the springs. The dragging effect of the moving be…

BS-NAS broadens and shrinks search space for optimal neural architectures.

Theory explains how deep nets learn features from data.

We propose a link prediction algorithm that is based on spring-electrical models. The idea to study these models came from the fact that spring-electrical models have been successfully used for networks visualization. A good network visualization usually implies that nodes similar in terms of network topology, e.g., co…

We establish an analogy between the motion of spring whose mass increases linearly with time and volatile stock markets dynamics within an economic model based on simple temporal demand and supply functions [J. Phys. A: Math. Gen. 33, 3637 (2000)]. The total system energy E_t is shown to be proportional to a decreasing…

We develop a progressive training approach for neural networks which adaptively grows the network structure by splitting existing neurons to multiple off-springs. By leveraging a functional steepest descent idea, we derive a simple criterion for deciding the best subset of neurons to split and a splitting gradient for …

In this paper, we study the system identification problem for sparse linear time-invariant systems. We propose a sparsity promoting block-regularized estimator to identify the dynamics of the system with only a limited number of input-state data samples. We characterize the properties of this estimator under high-dimen…

These are lecture notes that are based on the lectures from a class I taught on the topic of Spectral Graph Methods at UC Berkeley during the Spring 2015 semester.

Notes for a one semester course. The notes contain a description of compact three dimensional Seifert fibered spaces and a classification up to homeomorphism of compact three dimensional Seifert fibered spaces with non-empty boundary.

Proposes TFCL to mitigate negative transfer in MTL by collaborating across features and tasks.

Deep neural networks improve free energy calculations for peptide conformations.

In this lecture notes, we aim at giving an introduction to the Kähler-Ricci flow (KRF) on Fano manifolds. It covers some of the developments of the KRF in its first twenty years (1984-2003), especially an essentially self-contained exposition of Perelman's uniform estimates on the scalar curvature, the diameter, and th…

We introduce a microscopic model which describes the dynamics of each dealer in multiple foreign exchange markets, taking account of the triangular arbitrage transaction. The model reproduces the interaction among the markets well. We explore the relation between the parameters of the present microscopic model and the …

Model predicts increased social unrest during COVID-19 using social media data.

Lecture notes on geodesics in differential geometry.

In this survey paper, we outline the proofs of the rigidity results for simple, thick, hyperbolic P-manifolds found in our three earlier papers math.GR/0506518, math.GT/0410476, and math.GR/0409586. We discuss how the arguments change in the two, three, and higher dimensional settings. This paper was written for the 22…

Expands Bayesian experiment design framework to account for model discrepancies.

Notes describe geometric interpretations of cohomology in trisected 4-manifolds.

Study reveals holiday effect on China's time-honored brands, especially alcoholic beverages.

COSMIC identifies LTV systems from large data sets efficiently.

Diffusion models simulate molecular dynamics with adjustable accuracy.

Bayesian method for multivariate autoregressive models with exogenous inputs.

These are the lecture notes for an advanced Ph.D. level course I taught in Spring'02 at the C.N. Yang Institute for Theoretical Physics at Stony Brook. The course primarily focused on an introduction to stochastic calculus and derivative pricing with various stochastic computations recast in the language of path integr…

Since the events of the Arab Spring, there has been increased interest in using social media to anticipate social unrest. While efforts have been made toward automated unrest prediction, we focus on filtering the vast volume of tweets to identify tweets relevant to unrest, which can be provided to downstream users for …

These notes were inspired by the course ''Quantum Field Theory from a Functional Integral Point of View'' given at the University of Zurich in Spring 2017 by Santosh Kandel. We describe Feynman's path integral approach to quantum mechanics and quantum field theory from a functional integral point of view, where the mai…

A neural network method estimates entropy production from system trajectories.

This paper presents a novel Block Iterative Bayesian Algorithm (Block-IBA) for reconstructing block-sparse signals with unknown block structures. Unlike the existing algorithms for block sparse signal recovery which assume the cluster structure of the nonzero elements of the unknown signal to be independent and identic…

This letter presents a novel Block Bayesian Hypothesis Testing Algorithm (Block-BHTA) for reconstructing block sparse signals with unknown block structures. The Block-BHTA comprises the detection and recovery of the supports, and the estimation of the amplitudes of the block sparse signal. The support detection and rec…

Develops a new non-abelian framework for Riemann surfaces and differential equations.

Agents learn and control complex mechanical systems through shared memories.

We examine the recovery of block sparse signals and extend the framework in two important directions; one by exploiting signals' intra-block correlation and the other by generalizing signals' block structure. We propose two families of algorithms based on the framework of block sparse Bayesian learning (BSBL). One fami…

This survey is based on a series of lectures that we gave at MSRI in Spring 2015 and on a series of papers, mostly written jointly with Joan Porti. Our goal here is to: 1. Describe a class of discrete subgroups $Γ<G$ of higher rank semisimple Lie groups, which exhibit some "rank 1 behavior". 2. Give different character…

We theoretically investigate the convergence rate and support consistency (i.e., correctly identifying the subset of non-zero coefficients in the large sample limit) of multiple kernel learning (MKL). We focus on MKL with block-l1 regularization (inducing sparse kernel combination), block-l2 regularization (inducing un…

There exist various types of network block models such as the Stochastic Block Model (SBM), the Degree Corrected Block Model (DCBM), and the Popularity Adjusted Block Model (PABM). While this leads to a variety of choices, the block models do not have a nested structure. In addition, there is a substantial jump in the …

SympFormer accelerates attention blocks using inertial dynamics on density spaces.

We introduce block-tree graphs as a framework for deriving efficient algorithms on graphical models. We define block-tree graphs as a tree-structured graph where each node is a cluster of nodes such that the clusters in the graph are disjoint. This differs from junction-trees, where two clusters connected by an edge al…

We simplify matrix computations for block matrices, especially useful for covariance and correlation matrices.

Attention mechanism is a hot spot in deep learning field. Using channel attention model is an effective method for improving the performance of the convolutional neural network. Squeeze-and-Excitation block takes advantage of the channel dependence, selectively emphasizing the important channels and compressing the rel…

Proposes BMME for optimizing nonsmooth nonconvex problems with block structure.

Alternating Direction Method of Multipliers (ADMM) has become a widely used optimization method for convex problems, particularly in the context of data mining in which large optimization problems are often encountered. ADMM has several desirable properties, including the ability to decompose large problems into smalle…

Paper proposes ABDR for convex subspace clustering with adaptive block diagonal representation.

The workshop focuses on AI principles for structured data.

We introduce an approach for imposing physically motivated inductive biases on graph networks to learn interpretable representations and improved zero-shot generalization. Our experiments show that our graph network models, which implement this inductive bias, can learn message representations equivalent to the true fo…

(Original version of PhD thesis, submitted in Spring 2009 to Harvard University. Provides a solution of the $p > k^2$ case, corresponding to Berge families I-VI, of the "Lens space realization problem" later solved in entirety by Greene.) In the 1980's, Berge proved that a certain collection of knots in $S^3$ admitted …

Witten- Helffer-Sjöstrand theory is a considerable addition to the De Rham- Hodge theory for Riemannian manifolds and can serve as a general tool to prove results about comparison of numerical invariants associated to compact manifolds analytically, i.e. by using a Riemannian metric, or combinatorially, i.e by using a …

We consider practical data characteristics underlying federated learning, where unbalanced and non-i.i.d. data from clients have a block-cyclic structure: each cycle contains several blocks, and each client's training data follow block-specific and non-i.i.d. distributions. Such a data structure would introduce client …

In the present paper we study a sparse stochastic network enabled with a block structure. The popular Stochastic Block Model (SBM) and the Degree Corrected Block Model (DCBM) address sparsity by placing an upper bound on the maximum probability of connections between any pair of nodes. As a result, sparsity describes o…

Incorporating deep neural networks in image compressive sensing (CS) receives intensive attentions in multimedia technology and applications recently. As deep network approaches learn the inverse mapping directly from the CS measurements, the reconstruction speed is significantly faster than the conventional CS algorit…