arXiv research

Maps can be embedded in higher dimensions if they lift to embeddings in product spaces.

Study symplectic embeddings of 4-manifolds using Lefschetz fibrations.

Study embedding of achiral Lefschetz fibrations in 6D manifolds.

Meta-learning for Koopman spectral analysis with short time-series data.

Framework for dynamic node embeddings from graph streams.

Study of codimension-1 embeddings in 3-manifolds using twist maps and push maps.

Knowledge Graph (KG) embedding has attracted more attention in recent years. Most KG embedding models learn from time-unaware triples. However, the inclusion of temporal information beside triples would further improve the performance of a KGE model. In this regard, we propose ATiSE, a temporal KG embedding model which…

We present a probabilistic language model for time-stamped text data which tracks the semantic evolution of individual words over time. The model represents words and contexts by latent trajectories in an embedding space. At each moment in time, the embedding vectors are inferred from a probabilistic version of word2ve…

Existence of balanced embedding proved for complex manifold into infinite-dimensional space.

AUASE embeds dynamic networks with stability guarantees for node comparison.

LaT-PFN model predicts time series with zero-shot capability.

This paper proposes an out-of-sample extension framework for a global manifold learning algorithm (Isomap) that uses temporal information in out-of-sample points in order to make the embedding more robust to noise and artifacts. Given a set of noise-free training data and its embedding, the proposed framework extends t…

In this work we prove the fact that, for a short time, it is possible to construct a smooth parametrized family of isometric embeddings of an arbitrary smooth parametrized family of Riemannian metrics on a smooth closed manifold into an Euclidean space. In order to prove this statement we work out stability estimates w…

Classifies smooth isotopy of a specific Lagrangian embedding.

Measures time-delay embedding for noisy, sparse data.

Efficiently computes embeddings for large graphs using coarsening.

ULES embeds dynamic networks with stability guarantees.

Framework predicts patient risk progression over time.

Sparse OSEs achieve optimal embedding dimension of O(d).

New method preserves distances in time series data.

Network representation learning in low dimensional vector space has attracted considerable attention in both academic and industrial domains. Most real-world networks are dynamic with addition/deletion of nodes and edges. The existing graph embedding methods are designed for static networks and they cannot capture evol…

An embedding of the m-times punctured disc into the n-times punctured disc, for n>m, yields an embedding of the braid group on m strands B_m into the braid group on n strands B_n, called a geometric embedding. The main example consists of adding n-m trivial strands to the right of each braid on m strands. We show that …

Boosted embeddings improve time series forecasting models.

We work entirely in the smooth category. An embedding $f:(S^2\times S^1)\sqcup S^3\rightarrow {\mathbb R}^6$ is {\it Brunnian}, if the restriction of $f$ to each component is isotopic to the standard embedding. For each triple of integers $k,m,n$ such that $m\equiv n \pmod{2}$, we explicitly construct a Brunnian embedd…

Paper uses DMD to embed time in spatiotemporal forecasting.

Time-delayed embeddings avoid self-intersections for high enough delay.

A new method for embedding temporal relationships in graphs.

In this note, we discuss embeddings of $3$--manifolds via open books. First we show that every open book of every closed orientable $3$--manifold admits an open book embedding in any open book decompistion of $S^2 \times S^3$ and $S^2 \widetilde{\times} S^3$ with the page a disk bundle over $S^2$ and monodromy the iden…

The paper embeds 4-manifolds into CP^2 x CP^1 using Lefschetz fibrations.

We show that any metric on $S^2$ with Gauss curvature $K \geq -κ$ admits a $C^{1,1}$-isometric embedding into the hyperbolic space with sectional curvature $-κ$. We also give a sufficient condition for a metric on $S^2$ to be isometrically embedded into anti-de Sitter spacetime with the prescribed cosmological time fun…

We give an algorithm to decide which elements of pi_2(S^2\times S^1#...#S^2\times S^1) can be represented by embedded spheres. Such spheres correspond to splittings of the free group on k generators. Equivalently our algorithm decides whether, for a handlebody N, an element in pi_2(N,\partial N) can be represented by a…

Study geodesic properties of time series data using Wasserstein metric.

OracleAD detects multivariate time series anomalies without labels.

Study of metrics on spheres and their complex structure properties.

Production recommendation systems rely on embedding methods to represent various features. An impeding challenge in practice is that the large embedding matrix incurs substantial memory footprint in serving as the number of features grows over time. We propose a similarity-aware embedding matrix compression method call…

In this paper, we provide some results on Skorokhod embedding with local time and its applications to the robust hedging problem in finance. First we investigate the robust hedging of options depending on the local time by using the recently introduced stochastic control approach, in order to identify the optimal hedgi…

Phase2vec learns embeddings of dynamical systems without supervision.

Graph embedding provides an efficient solution for graph analysis by converting the graph into a low-dimensional space which preserves the structure information. In contrast to the graph structure data, the i.i.d. node embedding can be processed efficiently in terms of both time and space. Current semi-supervised graph…

Topic modeling analyzes documents to learn meaningful patterns of words. For documents collected in sequence, dynamic topic models capture how these patterns vary over time. We develop the dynamic embedded topic model (D-ETM), a generative model of documents that combines dynamic latent Dirichlet allocation (D-LDA) and…

Study on fundamental groups of framed circle embeddings in 4-manifolds.

Networks evolve continuously over time with the addition, deletion, and changing of links and nodes. Such temporal networks (or edge streams) consist of a sequence of timestamped edges and are seemingly ubiquitous. Despite the importance of accurately modeling the temporal information, most embedding methods ignore it …

Word evolution refers to the changing meanings and associations of words throughout time, as a byproduct of human language evolution. By studying word evolution, we can infer social trends and language constructs over different periods of human history. However, traditional techniques such as word representation learni…

Alternative approach to regularize time-dependent singular Lagrangian systems.

HyFAD improves time series imputation by combining time and frequency diffusion.

Authors construct hypertori with constant negative mean curvature in a sphere.

Word embeddings are a powerful approach for unsupervised analysis of language. Recently, Rudolph et al. (2016) developed exponential family embeddings, which cast word embeddings in a probabilistic framework. Here, we develop dynamic embeddings, building on exponential family embeddings to capture how the meanings of w…

New method for computing terminal embeddings in sublinear time.

EPNE models evolving network patterns for better predictions.