arXiv research

Proves existence of longest paths in sub-Lorentzian problems.

A new graph kernel uses LCS and Wasserstein distance for better graph comparisons.

Unified algorithm for optimizing rewards in stochastic path problems.

Researchers found the longest arcs for specific sub-Lorentzian structures.

We consider the problem of packing node-disjoint directed paths in a directed graph. We consider a variant of this problem where each path starts within a fixed subset of root nodes, subject to a given bound on the length of paths. This problem is motivated by the so-called kidney exchange problem, but has potential ot…

We consider the problem of clustering with the longest-leg path distance (LLPD) metric, which is informative for elongated and irregularly shaped clusters. We prove finite-sample guarantees on the performance of clustering with respect to this metric when random samples are drawn from multiple intrinsically low-dimensi…

Study of longest arcs and cut loci in deformed anti de-Sitter spaces.

If a hyperbolic 3-manifold admits an exceptional Dehn filling, then the length of the slope of that Dehn filling is known to be at most six. However, the bound of six appears to be sharp only in the toroidal case. In this paper, we investigate slope lengths of other exceptional fillings. We construct hyperbolic 3-manif…

For finite reflection groups of types A and B, we determine the diameter of the graph whose vertices are reduced words for the longest element and whose edges are braid relations. This is deduced from a more general theorem that applies to supersolvable hyperplane arrangements.

In this work we classify the stable regions (second order minima of perimeter under an area constraint) in tori of revolution with piecewise continuous decreasing Gauss curvature from the longest parallel and with a horizontal symmetry. Some applications to isoperimetric problems are also given.

Deep autoregressive sequence-to-sequence models have demonstrated impressive performance across a wide variety of tasks in recent years. While common architecture classes such as recurrent, convolutional, and self-attention networks make different trade-offs between the amount of computation needed per layer and the le…

In the presence of certain topological conditions, we provide lower bounds for the infimum of the length function associated to a collection of curves on Teichmüller space that depend on the dual cube complex associated to the collection, a concept due to Sageev. As an application of our bounds, we obtain estimates for…

On a hyperbolic Riemann surface, given two simple closed geodesics that intersect $n$ times, we address the question of a sharp lower bound $L_n$ on the length attained by the longest of the two geodesics. We show the existence of a surface $S_n$ on which there exists two simple closed geodesics of length $L_n$ interse…

We formulate and prove that there are "abundant" in nilpotent orbits in real semisimple Lie algebras, in the following sense. If S denotes the collection of hyperbolic elements corresponding the weighted Dynkin diagrams coming from nilpotent orbits, then S span the maximally expected space, namely, the (-1)-eigenspace …

What is the longest rope on the unit sphere? Intuition tells us that the answer to this packing problem depends on the rope's thickness. For a countably infinite number of prescribed thickness values we construct and classify all solution curves. The simplest ones are similar to the seamlines of a tennis ball, others e…

A smart method predicts and optimizes decisions online with resource constraints.

Given a Finsler space, we introduce a system of partial differential equations, called the Landsberg equation. Based on a careful analysis of the Landsberg equation and the observation that the solution space is invariant under the linear isometries of the tangent Minkowski spaces, we prove that an $(α_1, α_2)$-metric …

The study of record statistics of correlated series is gaining momentum. In this work, we study the records statistics of the time series of select stock market data and the geometric random walk, primarily through simulations. We show that the distribution of the age of records is a power law with the exponent $α$ lyi…

While designing the state space of an MDP, it is common to include states that are transient or not reachable by any policy (e.g., in mountain car, the product space of speed and position contains configurations that are not physically reachable). This leads to defining weakly-communicating or multi-chain MDPs. In this…

We consider the problem of hedging a European interest rate contingent claim with a portfolio of zero-coupon bonds and show that an HJM type Markovian model driven by an infinite number of sources of randomness does not have some of the shortcomings found in the classical finite-factor models. Indeed, under natural con…

Neural networks solve Knapsack problems with provable guarantees.

For a Riemannian metric $g$ on the two-sphere, let $\ell_{\min}(g)$ be the length of the shortest closed geodesic and $\ell_{\max}(g)$ be the length of the longest simple closed geodesic. We prove that if the curvature of $g$ is positive and sufficiently pinched, then the sharp systolic inequalities \[ \ell_{\rm min}(g…

This study assesses the influence of the forecast horizon on the forecasting performance of several machine learning techniques. We compare the fo recast accuracy of Support Vector Regression (SVR) to Neural Network (NN) models, using a linear model as a benchmark. We focus on international tourism demand to all sevent…

The paper tackles causal bandits with unknown SCMs and soft interventions, providing upper and lower bounds on regret.

Study on length distribution of random multicurves on large genus surfaces converging to Poisson-Dirichlet distribution.

The paper tackles causal bandits for SEMs, proposing algorithms that avoid estimating $2^N$ reward distributions.

Study of a series of Lorentzian structures on SL(2,R) with SO(1,1) symmetry.

We address the problem of computing a single linkage dendrogram. A possible approach is to: (i) Form an edge weighted graph $G$ over the data, with edge weights reflecting dissimilarities. (ii) Calculate the MST $T$ of $G$. (iii) Break the longest edge of $T$ thereby splitting it into subtrees $T_L$, $T_R$. (iv) Apply …

This paper is devoted to the first systematic investigation of manifolds that are Einstein for a connection with skew symmetric torsion. We derive the Einstein equation from a variational principle and prove that, for parallel torsion, any Einstein manifold with skew torsion has constant scalar curvature; and if it is …

New solutions to 3D integrability equations using quantum cluster algebras.

Researchers found sub-Lorentzian geodesics on a specific Lie subgroup.

This paper addresses robust CBs for linear SEMs with model fluctuations.

Researchers show a complex structure is not a counterexample to a topological problem.

There is an increasing interest in the development of new data-driven models useful to assess the performance of communication networks. For many applications, like network monitoring and troubleshooting, a data model is of little use if it cannot be interpreted by a human operator. In this paper, we present an extensi…

Model compares altruism and individualism in wealth dynamics.

Users in social networks whose posts stay at the top of their followers'{} feeds the longest time are more likely to be noticed. Can we design an online algorithm to help them decide when to post to stay at the top? In this paper, we address this question as a novel optimal control problem for jump stochastic different…

The paper develops methods to price and hedge options in path-dependent stock models.

Extend classical theory of affine processes to path-dependent setting

Simpler method derived for path geometries on surfaces, characterizing projective path geometries.

Recently, path norm was proposed as a new capacity measure for neural networks with Rectified Linear Unit (ReLU) activation function, which takes the rescaling-invariant property of ReLU into account. It has been shown that the generalization error bound in terms of the path norm explains the empirical generalization b…

We consider the problem of path inference: given a path prefix, i.e., a partially observed sequence of nodes in a graph, we want to predict which nodes are in the missing suffix. In particular, we focus on natural paths occurring as a by-product of the interaction of an agent with a network---a driver on the transporta…

Proposes a novel path generation and evaluation method for video games.

Introduces q-paths for generalizing geometric annealing paths in machine learning.

ETGL-DDPG improves DDPG for sparse reward control with new exploration and replay techniques.

This paper improves tail dependence analysis by introducing a path-based approach.

This paper considers possible price paths of a financial security in an idealized market. Its main result is that the variation index of typical price paths is at most 2, in this sense, typical price paths are not rougher than typical paths of Brownian motion. We do not make any stochastic assumptions and only assume t…

One-shot path planning for multiple agents using neural networks.

Foundation for robust finance using rough path theory.