arXiv research

Explains connections between monopoles and modules on elliptic curves.

Introduces modular $q$-holonomic modules to solve $q$-difference equations.

Correspondence found between Askey-Wilson polynomials and genus-two handlebody skein module.

An interesting theme in complex differential geometry is to find a correspondence between algebraic objects and differential geometric objects. One of the most attractive is the non-abelian Hodge theory of Simpson. In this paper, pursuing an analogue of the non-abelian Hodge theory in the context of $q$-difference modu…

Minor typographical errors fixed. Cochran constructed many links with Alexander module that of the unlink and some nonvanishing Milnor invariants, using as input commutators in a free group and as an invariant the longitudes of the links. We present a different and conjecturally complete construction, that uses element…

Spatio-temporal (ST) data, which represent multiple time series data corresponding to different spatial locations, are ubiquitous in real-world dynamic systems, such as air quality readings. Forecasting over ST data is of great importance but challenging as it is affected by many complex factors, including spatial char…

Study of 2d gauged linear sigma models to derive difference equations and spectral data.

Enhanced bikei modules distinguish unoriented and non-orientable surface-links.

We study periodic monopoles satisfying some mild conditions, called of GCK type. Particularly, we give a classification of periodic monopoles of GCK type in terms of difference modules with parabolic structure, which is a kind of Kobayashi-Hitchin correspondence between differential geometric objects and algebraic obje…

Paper proposes a method to control robots of different shapes efficiently.

Many prediction problems, such as those that arise in the context of robotics, have a simplifying underlying structure that, if known, could accelerate learning. In this paper, we present a strategy for learning a set of neural network modules that can be combined in different ways. We train different modular structure…

MixFT re-partitions data into sub-domains for better TSFM fine-tuning.

GNN-FiLM uses feature-wise linear modulation to improve graph neural networks.

Improves speaker verification for variable-duration utterances using a feature pyramid module.

Study Berry connections for 2d GLSMs, linking to cohomology theories.

We establish a relationship between two different generalizations of Lie algebroid representations: representation up to homotopy and Vaintrob's Lie algebroid modules. Specifically, we show that there is a noncanonical way to obtain a representation up to homotopy from a given Lie algebroid module, and that any two rep…

Extends Kauffman's formula to 3-manifolds with markings.

Motivation: The rapid growth of diverse biological data allows us to consider interactions between a variety of objects, such as genes, chemicals, molecular signatures, diseases, pathways and environmental exposures. Often, any pair of objects--such as a gene and a disease--can be related in different ways, for example…

Paper defends deep learning classifiers against channel-aware adversarial attacks.

Model proteins with bonds using Kauffman bracket skein module.

The classical abelian invariants of a knot are the Alexander module, which is the first homology group of the the unique infinite cyclic covering space of S^3-K, considered as a module over the (commutative) Laurent polynomial ring, and the Blanchfield linking pairing defined on this module. From the perspective of the…

Learn to automatically plug domain-specific modules into a common network.

Study connects knot contact homology to Chern-Simons theory's large N limit.

Improves Bayesian optimization efficiency for mixed variable spaces.

Let ${\cal D}^k$ be the space of $k$-th order linear differential operators on ${\bf R}$: $A=a_k(x)\frac{d^k}{dx^k}+\cdots+a_0(x)$. We study a natural 1-parameter family of $\Diff(\bf R)$- (and $\Vect(\bf R)$)-modules on ${\cal D}^k$. (To define this family, one considers arguments of differential operators as tensor-d…

Proposes GPCA module for channel attention in CNNs using Gaussian processes.

PICLE uses probabilistic models to efficiently evaluate and compose modules for continual learning.

Three definitions of graded vector bundles are shown to be equivalent.

We propose a finite difference scheme to simulate solutions to a certain type of hyperbolic stochastic partial differential equation (HSPDE). These solutions can in turn estimate so called volatility modulated Volterra (VMV) processes and Lévy semistationary (LSS) processes, which is a class of processes that have been…

Shared workspace improves neural module coordination in deep learning.

Combines Hebbian and DQN for better POMDP problem solving.

Training Generative Adversarial Networks (GANs) is notoriously challenging. We propose and study an architectural modification, self-modulation, which improves GAN performance across different data sets, architectures, losses, regularizers, and hyperparameter settings. Intuitively, self-modulation allows the intermedia…

Dynamic information balancing reduces catastrophic forgetting in modular neural networks.

Two solutions for multi-modal record linkage using Deep Learning inspired by Visual Question Answering.

A framework evaluates the impact of different modules in graph contrastive learning.

Python module for RL trading in limit order books.

In this paper the properties of the Kauffman bracket skein module of $L(p,q)$ are investigated. Links in lens spaces are represented both through band and disk diagrams. The possibility to transform between the diagrams enables us to compute the Kauffman bracket skein module on an interesting class of examples consisti…

Study skein modules via gauge theory, finding non-TQFT dimensions.

This paper presents a novel and flexible solution for fault prediction based on data collected from SCADA system. Fault prediction is offered at two different levels based on a data-driven approach: (a) generic fault/status prediction and (b) specific fault class prediction, implemented by means of two different machin…

CardiacGen generates realistic ECG signals for training deep learning models.

This paper presents a Semantic Attribute Modulation (SAM) for language modeling and style variation. The semantic attribute modulation includes various document attributes, such as titles, authors, and document categories. We consider two types of attributes, (title attributes and category attributes), and a flexible a…

Paper proposes a time-frequency analysis method for blind modulation classification in MIMO systems.

Current deep learning models are mostly build upon neural networks, i.e., multiple layers of parameterized differentiable nonlinear modules that can be trained by backpropagation. In this paper, we explore the possibility of building deep models based on non-differentiable modules. We conjecture that the mystery behind…

Improved recurrent neural networks learn long-term dependencies through multi-scale memory.

The paper constructs tilting modules for knots using algebraic structures.

In this paper, a generalized multivariate Student-t mixture model is developed for classification and clustering of Low Probability of Intercept radar waveforms. A Low Probability of Intercept radar signal is characterized by a pulse compression waveform which is either frequency-modulated or phase-modulated. The propo…

The linking genotype to phenotype is the fundamental aim of modern genetics. We focus on study of links between gene expression data and phenotype data through integrative analysis. We propose three approaches. 1) The inherent complexity of phenotypes makes high-throughput phenotype profiling a very difficult and labor…

We construct Heegaard Floer theory for 3-manifolds with connected boundary. The theory associates to an oriented, parametrized two-manifold a differential graded algebra. For a three-manifold with parametrized boundary, the invariant comes in two different versions, one of which (type D) is a module over the algebra an…