arXiv research

Self-training improves generalization by fitting to reliable pseudo-labels or gradually improving the classification plane.

Spatio-temporal (ST) data for urban applications, such as taxi demand, traffic flow, regional rainfall is inherently stochastic and unpredictable. Recently, deep learning based ST prediction models are proposed to learn the ST characteristics of data. However, it is still very challenging (1) to adequately learn the co…

In this paper, we introduce an equivalence relation on the set of local moves and classify local moves, called the extended $ST$-moves, up to the equivalence. Moreover, by inducing a binary relation on the set of equivalence classes of local moves, we show that an extended $ST$-move realizes the crossing change or the …

We show that two Alexander biquandles M and M' are isomorphic iff there is an isomorphism of Z[s,1/s,t,1/t]-modules h:(1-st)M --> (1-st)M' and a bijection g:O_s(A) --> O_s(A') between the s-orbits of sets of coset representatives of M/(1-st)M and M'/(1-st)M' respectively satisfying certain compatibility conditions.

We study the problem of subspace tracking in the presence of missing data (ST-miss). In recent work, we studied a related problem called robust ST. In this work, we show that a simple modification of our robust ST solution also provably solves ST-miss and robust ST-miss. To our knowledge, our result is the first `compl…

Let $G$ be a connected complex semisimple Lie group, equipped with a standard multiplicative Poisson structure $π_{\rm st}$ determined by a pair of opposite Borel subgroups $(B, B_-)$. We prove that for each $v$ in the Weyl group $W$ of $G$, the double Bruhat cell $G^{v,v} = BvB \cap B_-vB_-$ in $G$, together with the …

Arnold introduced invariants $J^+$, $J^-$ and $St$ for generic planar curves. It is known that both $J^+ /2 + St$ and $J^- /2 + St$ are invariants for generic spherical curves. Applying these invariants to underlying curves of knot diagrams, we can obtain lower bounds for the number of Reidemeister moves for uknotting.…

ST-MAML tackles task ambiguity in meta-learning by encoding tasks with stochastic representations.

The Straight-Through (ST) estimator is a widely used technique for back-propagating gradients through discrete random variables. However, this effective method lacks theoretical justification. In this paper, we show that ST can be interpreted as the simulation of the projected Wasserstein gradient flow (pWGF). Based on…

This paper presents a decomposition of the 3-strand Singular Braid Group.

QC-ST and CoCo methods correct batch effects in metabolomics data.

In this paper we present recent results toward the computation of the HOMFLYPT skein module of the lens spaces $L(p,1)$, $\mathcal{S}\left(L(p,1) \right)$, via braids. Our starting point is the knot theory of the solid torus ST and the Lambropoulou invariant, $X$, for knots and links in ST, the universal analogue of th…

In this paper we give an alternative basis, $\mathcal{B}_{\rm ST}$, for the Kauffman bracket skein module of the solid torus, ${\rm KBSM}\left({\rm ST}\right)$. The basis $\mathcal{B}_{\rm ST}$ is obtained with the use of the Tempereley--Lieb algebra of type B and it is appropriate for computing the Kauffman bracket sk…

Surface mount technology (SMT) is a process for producing printed circuit boards. Solder paste printer (SPP), package mounter, and solder reflow oven are used for SMT. The board on which the solder paste is deposited from the SPP is monitored by solder paste inspector (SPI). If SPP malfunctions due to the printer defec…

Karl Menger's 1934 paper on the St. Petersburg paradox contains mathematical errors that invalidate his conclusion that unbounded utility functions, specifically Bernoulli's logarithmic utility, fail to resolve modified versions of the St. Petersburg paradox.

We introduce and study a notion of `Sasaki with torsion structure' (ST) as an odd-dimensional analogue of Kähler with torsion geometry (KT). These are normal almost contact metric manifolds that admit a unique compatible connection with 3-form torsion. Any odd-dimensional compact Lie group is shown to admit such a stru…

In this paper we work toward the Homflypt skein module of the lens spaces $L(p,1)$, $\mathcal{S}(L(p,1))$, using braids. In particular, we establish the connection between $\mathcal{S}({\rm ST})$, the Homflypt skein module of the solid torus ST, and $\mathcal{S}(L(p,1))$ and arrive at an infinite system, whose solution…

New pricing theory solves St. Petersburg paradox.

Explicitly found generators of cohomology for SL_n(Z) using sharbly cycles and cosharbly cocycles.

Proposes a method to forecast spatial-temporal data with limited training data.

The problem of local feedback equivalence for 1-dimensional control systems of the 1-st order is considered. The algebra of differential invariants and criteria for the feedback equivalence for regular control systems are found.

The paper studies pseudo and singular links in a solid torus, developing invariants and algebraic structures.

We prove a Chekanov-type theorem for the spherization of the cotangent bundle $ST^*B$ of a closed manifold $B$. It claims that for Legendrian submanifolds in $ST^*B$ the property "to be given by a generating family quadratic at infinity" persists under Legendrian isotopies.

The structure set $\ST^{TOP}(M)$ of an $n$-dimensional topological manifold $M$ for $n \geqslant 5$ has a homotopy invariant functorial abelian group structure, by the algebraic version of the Browder-Novikov-Sullivan-Wall surgery theory. An element $(N,f) \in \ST^{TOP}(M)$ is an equivalence class of $n$-dimensional ma…

StreamEnsemble dynamically selects ML models for ST data streams to improve predictive accuracy.

Contact round surgeries on $(\mathbb{S}^3,ξ_{st})$ help in constructing and understanding contact 3-manifolds.

ST-MTM models complex time series by decomposing and masking seasonal and trend components.

Improved Thompson Sampling outperforms existing Bayesian optimization methods.

In building intelligent transportation systems such as taxi or rideshare services, accurate prediction of travel time and distance is crucial for customer experience and resource management. Using the NYC taxi dataset, which contains taxi trips data collected from GPS-enabled taxis [23], this paper investigates the use…

Paper proposes a new method to assess default risk using CEV process in KMV model.

Reintroduces straight-through estimators for binary neural networks.

Researchers develop a new basis to simplify solving infinite systems for HOMFLYPT skein module of lens spaces.

For an $(m+1)$-dimensional space-time $(X^{m+1}, g),$ define a mapped null hypersurface to be a smooth map $ν:N^{m}\to X^{m+1}$ (that is not necessarily an immersion) such that there exists a smooth field of null lines along $ν$ that are both tangent and $g$-orthogonal to $ν.$ We study relations between mapped null hyp…

We present a generic framework for spatio-temporal (ST) data modeling, analysis, and forecasting, with a special focus on data that is sparse in both space and time. Our multi-scaled framework is a seamless coupling of two major components: a self-exciting point process that models the macroscale statistical behaviors …

In this paper, by modifying the arguments in \cite{WY}, we get some rigidity theorems on compact manifolds with nonempty boundary. The results in this paper are similar with those in \cite{ST} and \cite{WY}. Like \cite{ST} and \cite{WY}, we still use quasi-spherical metrics introduced by \cite{Ba} to get monotonicity o…

Unified framework for Arnold-type invariants via dual complexes and finite-difference structures.

Rokhlin's work simplified signature theorems for mathematicians.

A resolution of the St. Petersburg paradox is presented. In contrast to the standard resolution, utility is not required. Instead, the time-average performance of the lottery is computed. The final result can be phrased mathematically identically to Daniel Bernoulli's resolution, which uses logarithmic utility, but is …

We establish an $h$-principle for exact Lagrangian immersions with transverse self-intersections and the minimal, or near-minimal number of double points. One corollary of our result is that any orientable closed 3-manifold admits an exact Lagrangian immersion into standard symplectic 6-space $\R^6_\st$ with exactly on…

An elementary stabilization of a Legendrian link $L$ in the spherical cotangent bundle $ST^*M$ of a surface $M$ is a surgery that results in attaching a handle to $M$ along two discs away from the image in $M$ of the projection of the link $L$. A virtual Legendrian isotopy is a composition of stabilizations, destabiliz…

This article is an expanded version of talks given by the authors in Oberwolfach, Bochum, and at the Fano Conference in Torino. Some new results (e. g. the material concerning flag varieties, Quot spaces over $¶^1$, and the generalized quiver representations) were included. The main goal is the construction of gauge th…

Random square-tiled surfaces have normal genus distribution and cover all integer vectors.

In this paper, we develop a reinforcement learning (RL) based system to learn an effective policy for carpooling that maximizes transportation efficiency so that fewer cars are required to fulfill the given amount of trip demand. For this purpose, first, we develop a deep neural network model, called ST-NN (Spatio-Temp…

ST-GCN improves rs-fMRI prediction accuracy by modeling spatio-temporal graph connectivity.

The spatio-temporal graph learning is becoming an increasingly important object of graph study. Many application domains involve highly dynamic graphs where temporal information is crucial, e.g. traffic networks and financial transaction graphs. Despite the constant progress made on learning structured data, there is s…

New invariant measures doubly slice links, disproving previous bounds.

A major challenge in computed tomography (CT) is to reduce X-ray dose to a low or even ultra-low level while maintaining the high quality of reconstructed images. We propose a new method for CT reconstruction that combines penalized weighted-least squares reconstruction (PWLS) with regularization based on a sparsifying…

As big spatial data becomes increasingly prevalent, classical spatiotemporal (ST) methods often do not scale well. While methods have been developed to account for high-dimensional spatial objects, the setting where there are exceedingly large samples of spatial observations has had less attention. The variational auto…