相关论文: Analytic trajectory bootstrap for matrix models

In this paper we describe two bootstrap methods for massive data sets. Naive applications of common resampling methodology are often impractical for massive data sets due to computational burden and due to complex patterns of inhomogeneity.…

Despite the existence of different error metrics for trajectory evaluation in SLAM, their theoretical justifications and connections are rarely studied, and few methods handle temporal association properly. In this work, we propose to…

Large Language Models achieve next-token prediction by transporting a vectorized piece of text (prompt) across an accompanying embedding space under the action of successive transformer layers. The resulting high-dimensional trajectories…

A core problem in statistical network analysis is to develop network analogues of classical techniques. The problem of bootstrapping network data stands out as especially challenging, since typically one observes only a single network,…

This thesis addresses two persistent and closely related challenges in modern deep learning, reliability and efficiency, through a unified framework grounded in Spectral Geometry and Random Matrix Theory (RMT). As deep networks and large…

In this paper, we introduce a powerful technique based on Leave-one-out analysis to the study of low-rank matrix completion problems. Using this technique, we develop a general approach for obtaining fine-grained, entrywise bounds for…

We present a new approach to bootstrapping string-like theories by exploiting a local crossing symmetric dispersion relation and field redefinition ambiguities. This approach enables us to use mass-level truncation and to go beyond the dual…

Using recently developed methods of character expansions we solve exactly in the large N limit a new two-matrix model of hermitean matrices A and B with the action S={1\over 2}(\tr A^2+\tr B^2)-{\alpha\over 4}(\tr A^4+\tr B^4) -{\beta\over…

We study linear-time temporal logics interpreted over data words with multiple attributes. We restrict the atomic formulas to equalities of attribute values in successive positions and to repetitions of attribute values in the future or…

Analyzing the urban trajectory in cities has become an important topic in data mining. How can we model the human mobility consisting of stay and travel from the raw trajectory data? How can we infer such a mobility model from the single…

We present an "algebraic treatment" of the analytical Bethe Ansatz. For this purpose, we introduce abstract monodromy and transfer matrices which provide an algebraic framework for the analytical Bethe Ansatz. It allows us to deal with a…

The eigenvalues of matrices representing the structure of large-scale complex networks present a wide range of applications, from the analysis of dynamical processes taking place in the network to spectral techniques aiming to rank the…

We study the $2\rightarrow2$ $S$-matrix element of a generic, gapped and Lorentz invariant QFT in $d=1+1$ space time dimensions. We derive an analytical bound on the coupling of the asymptotic states to unstable particles (a.k.a.…

Applications of the bootstrap program to superconformal field theories promise unique new insights into their landscape and could even lead to the discovery of new models. Most existing results of the superconformal bootstrap were obtained…

The transfer matrix and matrix multiplication ansatz, when applied to nonequilibrium steady states in asymmetric exclusion processed and traffic models, has given many exact results for phase diagrams, bulk densities and fluxes, as well as…

Rough sets are efficient for data pre-processing in data mining. As a generalization of the linear independence in vector spaces, matroids provide well-established platforms for greedy algorithms. In this paper, we apply rough sets to…

Recent analyses highlight challenges in autonomous vehicle technologies, particularly failures in decision-making under dynamic or emergency conditions. Traditional automated driving systems recalculate the entire trajectory in a changing…

In this paper, based on results of exact learning and test theory, we study arbitrary infinite binary information systems each of which consists of an infinite set of elements and an infinite set of two-valued functions (attributes) defined…

Bundles of strings which interact via short-ranged pair potentials are studied in two dimensions. The corresponding transfer matrix problem is solved analytically for arbitrary string number N by Bethe ansatz methods. Bundles consisting of…

A two--parameter family of asymmetric exclusion processes for particles on a one-dimensional lattice is defined. The two parameters of the model control the driving force and an effect which we call pushing, due to the fact that particles…