相关论文: Localization and projections on bi-parameter BMO

We introduce a Bayesian perspective for the structured matrix factorization problem. The proposed framework provides a probabilistic interpretation for existing geometric methods based on determinant minimization. We model input data…

We consider discrete one-dimensional Schr\"odinger operators with random potentials obtained via a block code applied to an i.i.d. sequence of random variables. It is shown that, almost surely, these operators exhibit spectral and dynamical…

Matrix factorization is a key tool in data analysis; its applications include recommender systems, correlation analysis, signal processing, among others. Binary matrices are a particular case which has received significant attention for…

We construct phase space localizing operators in all dimensions. These are frequency localized variants of the conditional expectation operator related to a dyadic stopping time. Our construction is an improvement over the so-called phase…

Person re-identification is an important technique towards automatic search of a person's presence in a surveillance video. Two fundamental problems are critical for person re-identification, feature representation and metric learning. An…

Bayesian Optimisation (BO) is a technique used in optimising a $D$-dimensional function which is typically expensive to evaluate. While there have been many successes for BO in low dimensions, scaling it to high dimensions has been…

In this paper, we present an approach to integer factorization using distributed representations formed with Vector Symbolic Architectures. The approach formulates integer factorization in a manner such that it can be solved using neural…

An algorithm for irreducible decomposition of representations of finite groups over fields of characteristic zero is described. The algorithm uses the fact that the decomposition induces a partition of the invariant inner product into a…

Parametric factorizations of linear partial operators on the plane are considered for operators of orders two, three and four. The operators are assumed to have a completely factorable symbol. It is proved that ``irreducible'' parametric…

We investigate conditions under which the identity matrix $I_n$ can be continuously factorized through a continuous $N\times N$ matrix function $A$ with domain in $\mathbb{R}$. We study the relationship of the dimension $N$, the diagonal…

An appearance-based robot self-localization problem is considered in the machine learning framework. The appearance space is composed of all possible images, which can be captured by a robot's visual system under all robot localizations.…

We revisit the localization tensor (LT) from geometric and probabilistic perspectives and construct extensions that are naturally compatible with periodic boundary conditions (PBC), without redefining the position operator. In open boundary…

Bayesian Optimization (BO) methods are useful for optimizing functions that are expen- sive to evaluate, lack an analytical expression and whose evaluations can be contaminated by noise. These methods rely on a probabilistic model of the…

Given a quiver with potential associated to a toric Calabi-Yau threefold, the numerical Donaldson-Thomas invariants for the moduli space of framed representations can be computed by using toric localization, which reduces the problem to the…

In my thesis, I present one particular example of the formalism capable of describing the propagation of a family of light rays in a curved spacetime. It is based on the resolvent operator of the geodesic deviation equation for null…

Sparse matrix factorization is the problem of approximating a matrix $\mathbf{Z}$ by a product of $J$ sparse factors $\mathbf{X}^{(J)} \mathbf{X}^{(J-1)} \ldots \mathbf{X}^{(1)}$. This paper focuses on identifiability issues that appear in…

In this paper, we study properties of the bilinear multiplier space. We give a necessary condition for a continuous integrable function to be a bilinear multiplier on variable exponent Lebesgue spaces. And we prove the localization theorem…

We provide bicategorical analogs of several aspects of the notion of geometry in the sense of the theory of spectrum. We first introduce a notion of local right biadjoint, and prove it to be equivalent to a notion of bistable pseudofunctor,…

We prove a dyadic representation theorem for bi-parameter singular integrals. That is, we represent certain bi-parameter operators as rapidly decaying averages of what we call bi-parameter shifts. A new version of the product space T1…

A promising approach to accurate positioning of robots is ground texture based localization. It is based on the observation that visual features of ground images enable fingerprint-like place recognition. We tackle the issue of efficient…