arXiv research

Paper optimizes change-point detection using learned distributions from training sequences.

Develops a new point process model for detecting neural spike sequences.

The paper extends sequences while preserving statistical properties using a mixture model.

We construct infinite sequences of pseudo-Anosov homeomorphisms without fixed points and leaving invariant a sequence of orientable measured foliations on the same topological surface and the same stratum of the space of abelian differentials. The existence of such sequences show that all pseudo-Anosov homeomorphisms f…

Paper proposes semi-supervised learning using change points for sequence classification.

Meta-learning improves event prediction from short sequences.

The paper establishes conditions for optimal sampling configurations on complex manifolds.

The paper studies splitting maps in link Floer homology using skein exact sequences.

Corrects earlier work on surface orbifold pure braid groups.

Study Palais-Smale sequences for Ricci curvature on homogeneous spaces.

In this article, we extend Huisken's theorem that convex surfaces flow to round points by mean curvature flow. We construct certain classes of mean convex and non-mean convex hypersurfaces that shrink to round points and use these constructions to create pathological examples of flows. We find a sequence of flows that …

Combinatorial proof of grid homology properties.

This paper proposes a new meta-learning method -- named HARMLESS (HAwkes Relational Meta LEarning method for Short Sequences) for learning heterogeneous point process models from short event sequence data along with a relational network. Specifically, we propose a hierarchical Bayesian mixture Hawkes process model, whi…

This paper introduces CloudLSTM, a new branch of recurrent neural models tailored to forecasting over data streams generated by geospatial point-cloud sources. We design a Dynamic Point-cloud Convolution (DConv) operator as the core component of CloudLSTMs, which performs convolution directly over point-clouds and extr…

Temporal point process is an expressive tool for modeling event sequences over time. In this paper, we take a reinforcement learning view whereby the observed sequences are assumed to be generated from a mixture of latent policies. The purpose is to cluster the sequences with different temporal patterns into the underl…

Framework handles both exchangeable and non-exchangeable event sequences without tuning.

Elliptic curves and braid groups linked through configuration spaces.

Survey on modeling event sequences through temporal processes.

We present a recurrent encoder-decoder deep neural network architecture that directly translates speech in one language into text in another. The model does not explicitly transcribe the speech into text in the source language, nor does it require supervision from the ground truth source language transcription during t…

A 2-manifold's group structure is deduced from orbit configuration spaces.

We construct a spectral sequence associated to a stratified space, which computes the compactly supported cohomology groups of an open stratum in terms of the compactly supported cohomology groups of closed strata and the reduced cohomology groups of the poset of strata. Several familiar spectral sequences arise as spe…

Open problem seeks an online learning algorithm for binary classification.

We present a homogenization theorem for isotropically-distributed point defects, by considering a sequence of manifolds with increasingly dense point defects. The loci of the defects are chosen randomly according to a weighted Poisson point process, making it a continuous version of the first passage percolation model.…

Event sequences can be modeled by temporal point processes (TPPs) to capture their asynchronous and probabilistic nature. We propose an intensity-free framework that directly models the point process distribution by utilizing normalizing flows. This approach is capable of capturing highly complex temporal distributions…

We suggest a novel method of clustering and exploratory analysis of temporal event sequences data (also known as categorical time series) based on three-dimensional data grid models. A data set of temporal event sequences can be represented as a data set of three-dimensional points, each point is defined by three varia…

The paper proves stability of critical points for conformally invariant Lagrangians.

CAUSE learns Granger causality from event sequences, outperforming existing methods.

S2P2 model improves predictive likelihoods for MTPPs.

Paper tackles adaptive deletion of data points from trained models.

A convolutional sequence to sequence non-intrusive load monitoring model is proposed in this paper. Gated linear unit convolutional layers are used to extract information from the sequences of aggregate electricity consumption. Residual blocks are also introduced to refine the output of the neural network. The partiall…

Latent Block-Diffusion Temporal Point Processes (LBDTPP) is a semi-autoregressive framework for generating asynchronous event sequences.

Recently, a new embedding/compactness theorem for integral currents in a sequence of metric spaces has been established by the second author. We present a version of this result for locally integral currents in a sequence of pointed metric spaces. To this end we introduce another variant of the Ambrosio--Kirchheim theo…

Study smooth convergence of metric flows from $\mathbb{F}$-limits.

For collapsing sequences of Riemannian manifolds which satisfy a uniform lower Ricci curvature bound it is shown that there is a sequence of scales such that for a set of good base points of large measure the pointed rescaled manifolds subconverge to a product of a Euclidean and a compact space. All Euclidean factors h…

EventFlow forecasts event sequences without autoregression, improving accuracy.

Online detection of instantaneous changes in the generative process of a data sequence generally focuses on retrospective inference of such change points without considering their future occurrences. We extend the Bayesian Online Change Point Detection algorithm to also infer the number of time steps until the next cha…

We prove that the Yang-Mills $α$-functional satisfies the Palais-Smale condition. This guarantees the existence of critical points, which are called Yang-Mills $α$-connections. It was shown by Hong, Tian and Yin in [10] (to appear in Comm. Math. Helv.) that as $α\to 1$, a sequence of Yang-Mills $α$-connections converge…

Study on the structure of classifier boundaries in DNA sequencing.

The paper solves the isoperimetric problem on noncompact metric spaces with lower Ricci bounds.

Continuous-time event sequences represent discrete events occurring in continuous time. Such sequences arise frequently in real-life. Usually we expect the sequences to follow some regular pattern over time. However, sometimes these patterns may be interrupted by unexpected absence or occurrences of events. Identificat…

We study discrete conjugate nets whose Laplace sequence is of period four. Corresponding points of opposite nets in this cyclic sequence have equal osculating planes in different net directions, that is, they correspond in an asymptotic transformation. We show that this implies that the connecting lines of correspondin…

A topological groupoid G is K-pointed, if it is equipped with a homomorphism from a topological group K to G. We describe the homotopy groups of such K-pointed topological groupoids and relate these groups to the ordinary homotopy groups in terms of a long exact sequence. As an application, we give an obstruction to pr…

We introduce two invariants called sl(3) Khovanov module and pointed sl(3) Khovanov homology for spatial webs (bipartite trivalent graphs). Those invariants are related to Kronheimer-Mrowka's instanton invariants $J^\sharp$ and $I^\sharp$ for spatial webs by two spectral sequences. As an application of the spectral seq…

Let T be a torus. We present an exact sequence relating the relative equivariant cohomologies of the skeletons of an equivariantly formal T-space. This sequence, which goes back to Atiyah and Bredon, generalizes the so-called Chang-Skjelbred lemma. As coefficients, we allow prime fields and subrings of the rationals, i…

The paper studies how neural networks evolve representations, finding a unique fixed point for nonlinear activations.

ADD-THIN improves TPP forecasting by handling long-term data sequences.

We construct a sequence of compact embedded minimal disks in the unit ball in Euclidean 3-space whose boundaries are in the boundary of the ball and where the curvatures blow up at every point of a line segment of the vertical axis, extending from the origin. We further study the transversal structure of the minimal li…

We study the Birman exact sequence for compact 3-manifolds.