相关论文: Modifying the Time-Convolutionless Master Equation…

In this work, we obtain performance guarantees for modified-CS and for its improved version, modified-CS-Add-LS-Del, for recursive reconstruction of a time sequence of sparse signals from a reduced set of noisy measurements available at…

Time-Reversal-Invariance non-conservation has for the first time been unequivocally demonstrated in a direct measurement, one of the results of the CPLEAR experiment. What is the situation then with regard to time-reversal-invariance…

Classical computability theory tells us that self-modifying code (SMC) on a deterministic universal Turing machine can be simulated by non-SMC code on the same model. That abstraction, however, omits the external timing inputs, concurrency,…

The Moore-Penrose inverse is a genuine extension of the matrix inverse. Given a complex matrix, there uniquely exists another complex matrix satisfying the four Moore-Penrose conditions, and if the original matrix is nonsingular, it is…

The final goal of this paper is to prove existence of local (strong) solutions to a (fully nonlinear) porous medium equation with blow-up term and nondecreasing constraint. To this end, the equation, arising in the context of Damage…

We propose and test an iterative technique for improving the temporal focusing of a time reversal mirror. A single amplification parameter is introduced to tune the convergence of the iteration. The tunable iterative technique is validated…

A fundamental pursuit of microwave metrology is the determination of the characteristic impedance profile of microwave systems. Among other methods, this can be practically achieved by means of time-domain reflectometry (TDR) that measures…

Multi-energy computed tomography (ME-CT) is an x-ray transmission imaging technique that uses the energy dependence of x-ray photon attenuation to determine the elemental composition of an object of interest. Mathematically, forward ME-CT…

A common optimization problem is the minimization of a symmetric positive definite quadratic form $< x,Tx >$ under linear constrains. The solution to this problem may be given using the Moore-Penrose inverse matrix. In this work we extend…

The stability of an initially one-dimensional electron hole to perturbations varying sinusoidally transverse to its trapping direction is analysed in detail. It is shown that the expected low-frequency eigenmode of the linearized…

A new generalized matrix inverse is derived which is consistent with respect to arbitrary nonsingular diagonal transformations, e.g., it preserves units associated with variables under state space transformations, thus providing a general…

Standard optimal control methods perform optimization in the time domain. However, many experimental settings demand the expression of the control signal as a superposition of given waveforms, a case that cannot easily be accommodated using…

We analyze in full mathematical rigor the most general quartically perturbed invariant probability measure for a random tensor. Using a version of the Loop Vertex Expansion (which we call the mixed expansion) we show that the cumulants…

A lattice model of critical dense polymers is solved exactly for arbitrary system size on the torus. More generally, an infinite family of lattice loop models is studied on the torus and related to the corresponding Fortuin-Kasteleyn random…

Generalized inverses of tensors play increasingly important roles in computational mathematics and numerical analysis. It is appropriate to develop the theory of generalized inverses of tensors within the algebraic structure of a ring. In…

In exploring Predictive Health Management (PHM) strategies for Proton Exchange Membrane Fuel Cells (PEMFC), the Transformer model, widely used in data-driven approaches, excels in many fields but struggles with time series analysis due to…

Contrastive learning (CL) continuously achieves significant breakthroughs across multiple domains. However, the most common InfoNCE-based methods suffer from some dilemmas, such as \textit{uniformity-tolerance dilemma} (UTD) and…

In this article two new algorithms are presented that convert a given data tensor train into either a Tucker decomposition with orthogonal matrix factors or a multi-scale entanglement renormalization ansatz (MERA). The Tucker core tensor is…

This work introduces new results in continuous-time reinforcement learning (CT-RL) control of affine nonlinear systems to address a major algorithmic challenge due to a lack of persistence of excitation (PE). This PE design limitation has…

Machine Reading Comprehension with Unanswerable Questions is a difficult NLP task, challenged by the questions which can not be answered from passages. It is observed that subtle literal changes often make an answerable question…