相关论文: Optimal Ramp Schemes and Related Combinatorial Obj…

The matrix completion problem consists of finding or approximating a low-rank matrix based on a few samples of this matrix. We propose a new algorithm for matrix completion that minimizes the least-square distance on the sampling set over…

We consider finitary approximations of the (embedding) Ramsey property. Using a class of homogeneous reducts of random ordered hypergraphs, we prove that these properties form a strict hierarchy. We also show that every class of finite…

This paper proposes a novel orthogonal-by-construction parametrization for augmenting physics-based input-output models with a learning component in an additive sense. The parametrization allows to jointly optimize the parameters of the…

We identify a link between regular matroids and torus representations all of whose isotropy groups have an odd number of components. Applying Seymour's 1980 classification of the former objects, we obtain a classification of the latter. In…

A grid poset -- or grid for short -- is a product of chains. We ask, what does a random linear extension of a grid look like? In particular, we show that the average "jump number," i.e., the number of times that two consecutive elements in…

Motion planning problems have been studied by both the robotics and the controls research communities for a long time, and many algorithms have been developed for their solution. Among them, incremental sampling-based motion planning…

Let $R$ be a commutative ring with identity. The co-maximal ideal graph of $R$, denoted by $\Gamma(R)$, is a simple graph whose vertices are proper ideals of $R$ which are not contained in the Jacobson radical of $R$ and two distinct…

Two ideal polygons, $(p_1,\ldots,p_n)$ and $(q_1,\ldots,q_n)$, in the hyperbolic plane or in hyperbolic space are said to be $\alpha$-related if the cross-ratio $[p_i,p_{i+1},q_i,q_{i+1}] = \alpha$ for all $i$ (the vertices lie on the…

We consider the line planning problem in public transport in the Parametric City, an idealized model that captures typical scenarios by a (small) number of parameters. The Parametric City is rotation symmetric, but optimal line plans are…

Random features are a powerful technique for rewriting positive-definite kernels as linear products. They bring linear tools to bear in important nonlinear domains like KNNs and attention. Unfortunately, practical implementations require…

It is shown that (1) if a good set has finitely many related components, then they are full, (2) loops correspond one-to-one to extreme points of a convex set. Some other properties of good sets are discussed.

Optimal transport maps define a one-to-one correspondence between probability distributions, and as such have grown popular for machine learning applications. However, these maps are generally defined on empirical observations and cannot be…

In this paper, we study the rigidity of uniform Roe algebras via the ideal structures. We showed that for given metric spaces X and Y with bounded geometry, if their uniform Roe algebras are isomorphic, then they are coarse equivalent.

Motion planning under differential constraints is a classic problem in robotics. To date, the state of the art is represented by sampling-based techniques, with the Rapidly-exploring Random Tree algorithm as a leading example. Yet, the…

Convergence guarantees for optimization over bounded-rank matrices are delicate to obtain because the feasible set is a non-smooth and non-convex algebraic variety. Existing techniques include projected gradient descent, fixed-rank…

Relying on recent advances in statistical estimation of covariance distances based on random matrix theory, this article proposes an improved covariance and precision matrix estimation for a wide family of metrics. The method is shown to…

We study a well known machine learning model -the perceptron- as a simple model of jamming of hard objects. We exhibit two regimes: 1) a convex optimisation regime where jamming is hypostatic and non-critical. 2) a non convex optimisation…

We consider the problem of correct motion planning for T-intersection merge-ins of arbitrary geometry and vehicle density. A merge-in support system has to estimate the chances that a gap between two consecutive vehicles can be taken…

In this paper, we investigate stochastic comparisons of parallel systems, and obtain two characterization results in this regard. First, we compare a parallel system with independent heterogeneous components to a parallel system with…

The restricted strong convexity is an effective tool for deriving globally linear convergence rates of descent methods in convex minimization. Recently, the global error bound and quadratic growth properties appeared as new competitors. In…