Related papers: Strong approximation and descent

We propose the use of two point Pade approximants to find expressions valid uniformly in coupling constant for theories with both weak and strong coupling expansions. In particular, one can use these approximants in models with a…

We construct an infinite family of imaginary bicyclic biquadratic number fields $k$ with the 2-ranks of their 2-class groups are $\geq3$, whose strongly ambiguous classes of $k/Q(i)$ capitulate in the absolute genus field $k^{(*)}$, which…

The Dirichlet forms methods, in order to represent errors and their propagation, are particularly powerful in infinite dimensional problems such as models involving stochastic analysis encountered in finance or physics, cf. [5]. Now, coming…

In this paper, we propose an inexact proximal Newton-type method for nonconvex composite problems. We establish the global convergence rate of the order $\mathcal{O}(k^{-1/2})$ in terms of the minimal norm of the KKT residual mapping and…

We propose a gradient descent method for solving optimization problems arising in settings of tropical geometry - a variant of algebraic geometry that has attracted growing interest in applications such as computational biology, economics,…

This paper introduces a new derivative parsing algorithm for recognition of parsing expression grammars. Derivative parsing is shown to have a polynomial worst-case time bound, an improvement on the exponential bound of the recursive…

The proximal inertial gradient descent is efficient for the composite minimization and applicable for broad of machine learning problems. In this paper, we revisit the computational complexity of this algorithm and present other novel…

We revisit two NP-hard geometric partitioning problems - convex decomposition and surface approximation. Building on recent developments in geometric separators, we present quasi-polynomial time algorithms for these problems with improved…

Finding the product of two polynomials is an essential and basic problem in computer algebra. While most previous results have focused on the worst-case complexity, we instead employ the technique of adaptive analysis to give an improvement…

Stochastic Gradient Descent (SGD) methods see many uses in optimization problems. Modifications to the algorithm, such as momentum-based SGD methods have been known to produce better results in certain cases. Much of this, however, is due…

We obtain the strong asymptotics of multiple orthogonal polynomials which arise in a mixed type Hermite-Pad\'e approximation problem defined on a Nikishin system of functions. The results obtained allow to give exact estimates of the rate…

We prove limit equalities between the sharp constants in weighted Nikolskii-type inequalities for multivariate polynomials on an $m$-dimensional cube and ball and the corresponding constants for entire functions of exponential type.

In this paper, we study weak approximation with Brauer--Manin obstruction with respect to extensions of number fields. For any nontrivial extension $L/K,$ assuming a conjecture of M. Stoll, we prove that there exists a $K$-threefold…

We study the approximability of predicates on $k$ variables from a domain $[q]$, and give a new sufficient condition for such predicates to be approximation resistant under the Unique Games Conjecture. Specifically, we show that a predicate…

Let $k$ be a field, $V$ a $k$-vector space and $X$ be a subset of $V $. A function $f:X\to k$ is weakly polynomial of degree $\leq a$, if the restriction of $f$ on any affine subspace $L\subset X$ is a polynomial of degree $\leq a$. In this…

Variational approximation methods have proven to be useful for scaling Bayesian computations to large data sets and highly parametrized models. Applying variational methods involves solving an optimization problem, and recent research in…

Let k be an algebraically closed field. Given an extension A : B of finite-dimensional k- algebras, we establish criteria ensuring that the representation-theoretic notion of polynomial growth is preserved under ascent and descent. These…

Surveying some of the recent developments on approximate subgroups and super-strong approximation for thin groups, we describe the Bourgain-Gamburd method for establishing spectral gaps for finite groups and the proof of the classification…

This work focuses on approximation and generation for the derived category of complexes with quasi-coherent cohomology on algebraic stacks. Our methods establish that approximation by compact objects descends along covers that are…

We develop a new, unified approach to the following two classical questions on elliptic PDE: the strong maximum principle for equations with non-Lipschitz nonlinearities, and the at most exponential decay of solutions in the whole space or…