arXiv research

In this paper, we propose multi-variable LSTM capable of accurate forecasting and variable importance interpretation for time series with exogenous variables. Current attention mechanism in recurrent neural networks mostly focuses on the temporal aspect of data and falls short of characterizing variable importance. To …

In this paper, we propose an interpretable LSTM recurrent neural network, i.e., multi-variable LSTM for time series with exogenous variables. Currently, widely used attention mechanism in recurrent neural networks mostly focuses on the temporal aspect of data and falls short of characterizing variable importance. To th…

We define a multi-variable version of the Affine Index Polynomial for virtual links. This invariant reduces to the original Affine Index Polynomial in the case of virtual knots, and also generalizes the version for compatible virtual links recently developed by L. Kauffman. We prove that this invariant is a Vassiliev i…

We will prove that, for a $2$ or $3$ component $L$-space link, $HFL^-$ is completely determined by the multi-variable Alexander polynomial of all the sub-links of $L$, as well as the pairwise linking numbers of all the components of $L$. We will also give some restrictions on the multi-variable Alexander polynomial of …

For recurrent neural networks trained on time series with target and exogenous variables, in addition to accurate prediction, it is also desired to provide interpretable insights into the data. In this paper, we explore the structure of LSTM recurrent neural networks to learn variable-wise hidden states, with the aim t…

Updated polynomial for virtual tangles, compatible with decompositions.

New Alexander polynomial defined for transverse graphs.

The Conway potential function (CPF) for colored links is a convenient version of the multi-variable Alexander-Conway polynomial. We give a skein characterization of CPF, much simpler than the one by Murakami. In particular, Conway's `smoothing of crossings' is not in the axioms. The proof uses a reduction scheme in a t…

Precisely forecasting wind speed is essential for wind power producers and grid operators. However, this task is challenging due to the stochasticity of wind speed. To accurately predict short-term wind speed under uncertainties, this paper proposed a multi-variable stacked LSTMs model (MSLSTM). The proposed method uti…

MCP extends conformal prediction to vector-valued score functions without data splitting.

UCB algorithms estimate uplifts in multi-variable reward systems.

In recent years, twisted Alexander polynomial has been playing an important role in low-dimensional topology. For Montesinos links, we develop an efficient method to compute the twisted Alexander polynomial associated to any linear representation. In particular, formulas for multi-variable Alexander polynomials of thes…

We show that link Floer homology detects the Thurston norm of a link complement. As an application, we show that the Thurston polytope of an alternating link is dual to the Newton polytope of its multi-variable Alexander polynomial. To illustrate these techniques, we also compute the Thurston polytopes of several speci…

The paper extends Pearson correlation to multi-variables, useful for noise measurement and feature selection.

We construct the Einstein equation for an invariant Riemannian metric on the exceptional full flag manifold $M=G_2/T$. By computing a Gröbner basis for a system of polynomials of multi-variables we prove that this manifold admits exactly two non-Kähler invariant Einstein metrics. Thus $G_2/T$ turns out to be the first …

This paper speeds up OCSSVM training using SMO.

In many regular cases, there exists a (properly defined) limit of iterations of a function in several real variables, and this limit satisfies the functional equation (1-z)f(x)=f(f(xz)(1-z)/z); here z is a scalar and x is a vector. This is a special case of a well-known translation equation. In this paper we present a …

A mathematical paradox shows secant planes don't always form a tangent plane, but some analogies hold with a specific vector product.

Physical activity levels are an important predictor of cardiovascular health and increasingly being measured by sensors, like accelerometers. Accelerometers produce rich multivariate data that can inform important clinical decisions related to individual patients and public health. The CHAMPION study, a study of youth …

The paper analyzes online learning of smooth functions in both single and multi-variable settings.

An $L$-space link is a link in $S^3$ on which all large surgeries are $L$-spaces. In this paper, we initiate a general study of the definitions, properties, and examples of $L$-space links. In particular, we find many hyperbolic $L$-space links, including some chain links and two-bridge links; from them, we obtain many…

In systems biomedicine, an experimenter encounters different potential sources of variation in data such as individual samples, multiple experimental conditions, and multi-variable network-level responses. In multiparametric cytometry, which is often used for analyzing patient samples, such issues are critical. While c…

It has been a central open problem in Heegaard Floer theory whether cobordisms of links induce homomorphisms on the associated link Floer homology groups. We provide an affirmative answer by introducing a natural notion of cobordism between sutured manifolds, and showing that such a cobordism induces a map on sutured F…

We give a criterion to detect whether the derivatives of the HOMFLY polynomial at a point is a Vassiliev invariant or not. In particular, for a complex number b we show that the derivative P_K^{(m,n)}(b,0)=d^m/da^m d^n/dx^n P_K(a,x)|(a, x) = (b, 0) of the HOMFLY polynomial of a knot K at (b,0) is a Vassiliev invariant …

There are more than eight hundred interest rates published in China bond market every day. Which are the benchmark interest rates that have broad influences on most interest rates is a major concern for economists. In this paper, multi-variable Granger causality test is developed and applied to construct a directed net…

Geometric interpretations of some virtual knot invariants are given in terms of invariants of links in $\mathbb{S}^3$. Alexander polynomials of almost classical knots are shown to be specializations of the multi-variable Alexander polynomial of certain two-component boundary links of the form $J \sqcup K$ with $J$ a fi…

This paper defines and proves properties of Floer homology for sutured manifolds.

Zh-construction links virtual links to classical ones, simplifying knot invariants.

IGANI uses iterative GANs to improve traffic data imputation.

Knitted and woven textile structures are examples of doubly periodic structures in a thickened plane made out of intertwining strands of yarn. Factoring out the group of translation symmetries of such a structure gives rise to a link diagram in a thickened torus. Such a diagram on a standard torus is converted into a c…

Paper compares ML models for fast power system contingency case identification.

Learn true model from metastable samples of discrete distributions.

Television is an ever-evolving multi billion dollar industry. The success of a television show in an increasingly technological society is a vast multi-variable formula. The art of success is not just something that happens, but is studied, replicated, and applied. Hollywood can be unpredictable regarding success, as m…

Study uses Bayesian Optimization to analyze noise effects in materials research.