Related papers: Weak convergence of the periodic multiplicative Se…
We introduce the notion of weakly associative algebra and its relations with the notion of nonassociative Poisson algebras.
We prove that the inverse of a positive-definite matrix can be approximated by a weighted-sum of a small number of matrix exponentials. Combining this with a previous result [OSV12], we establish an equivalence between matrix inversion and…
We consider a weak adversarial network approach to numerically solve a class of inverse problems, including electrical impedance tomography and dynamic electrical impedance tomography problems. We leverage the weak formulation of PDE in the…
We prove some variational analysis of regularity and weak convergence of nonlocal variational principle.
Bipartite quantum entangled systems can exhibit measurement correlations that violate Bell inequalities, revealing the profoundly counter-intuitive nature of the physical universe. These correlations reflect the impossibility of…
We present a recursive minimal polynomial theorem for finite sequences over a commutative integral domain $D$. This theorem is relative to any element of $D$. The ingredients are: the arithmetic of Laurent polynomials over $D$, a recursive…
The running weak mixing angle is used as a convenient tool to keep control of dominating logarithmic corrections in the Standard Model of the electroweak interactions connecting measurements at largely differing energy scales. To relate the…
In this paper we investigate weak polynomial identities for the Weyl algebra $\mathsf{A}_1$ over an infinite field of arbitrary characteristic. Namely, we describe weak polynomial identities of the minimal degree, which is three, and of…
The Nystr\"om method is a popular choice for finding a low-rank approximation to a symmetric positive semi-definite matrix. The method can fail when applied to symmetric indefinite matrices, for which the error can be unboundedly large. In…
We examine the linear convergence rates of variants of the proximal point method for finding zeros of maximal monotone operators. We begin by showing how metric subregularity is sufficient for linear convergence to a zero of a maximal…
We explore an algorithm for approximating roots of integers, discuss its motivation and derivation, and analyze its convergence rates with varying parameters and inputs. We also perform comparisons with established methods for approximating…
Many practical optimization problems lack strong convexity. Fortunately, recent studies have revealed that first-order algorithms also enjoy linear convergences under various weaker regularity conditions. While the relationship among…
This paper considers the approximation of the continuous time filtering equation for the case of a multiple timescale (slow-intermediate, and fast scales) that may have correlation between the slow-intermediate process and the observation…
We investigate convergence of the expectation maximization algorithm by representing it as a generalized proximal method. Convergence of iterates and not just in value is investigated under natural hypotheses such as definability of the…
Sequential Monte Carlo methods are typically not straightforward to implement on parallel architectures. This is because standard resampling schemes involve communication between all particles. The $\alpha$-sequential Monte Carlo method was…
A classical counterexample due to E. De Giorgi, shows that the weak maximum principle does not remain true for general linear elliptic differential systems. After that, there are some efforts to establish the weak maximum principle for…
We experimentally determine weak values for a single photon's polarization, obtained via a weak measurement that employs a two-photon entangling operation, and postselection. The weak values cannot be explained by a semiclassical wave…
We show that using only weak hyperbolicity (no smoothness, compactness or exponential rates) the Hopf argument produces multiple mixing in an elementary way. While this recovers classical results with far simpler proofs, the point is the…
We present a sufficient condition that a pseudointegrable system has weak mixing property. The result is derived from Veech's weak mixing theorem for interval exhange [Veech, W.A. Amer.J.Math. {\bf 106}, 1331 (1984)]. We also present an…
The method for the recursive calculation of the effective potential is applied successfully in case of weak coupling limit (g tend to zero) to a multidimensional complex cubic potential. In strong-coupling limit (g tend to infinity), the…