Invariant generation for P-solvable loops with assignments

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It is well-known that for any integral domain R, the Serre conjecture ring R(X), i.e., the localization of the univariate polynomial ring R[X] at monic polynomials, is a Bezout domain of Krull dimension

Self-attention mechanisms and non-local blocks have become crucial building blocks for state-of-the-art neural architectures thanks to their unparalleled ability in capturing long-range dependencies in the input. However their cost is quadratic with the nu ...

We propose and analyse randomized cubature formulae for the numerical integration of functions with respect to a given probability measure μ defined on a domain Γ⊆ℝ^d, in any dimension d. Each cubature formula is conceived to be exact on a given finite dim ...

The celebrated PCP Theorem states that any language in NP can be decided via a verifier that reads O(1) bits from a polynomially long proof. Interactive oracle proofs (IOP), a generalization of PCPs, allow the verifier to interact with the prover for multi ...

The diffusion strategy for distributed learning from streaming data employs local stochastic gradient updates along with exchange of iterates over neighborhoods. In Part I [3] of this work we established that agents cluster around a network centroid and pr ...

Programming with monads can be advantageous even in imperative languages with builtin support for side effects. However, in these languages composing monadic programs is different from composing side effecting imperative programs. This does not need to be ...

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We show that Cutting Planes (CP) proofs are hard to find: Given an unsatisfiable formula F, It is -hard to find a CP refutation of F in time polynomial in the length of the shortest such refutation; and unless Gap-Hitting-Set admits a nontrivial algorithm, ...

We study discretizations of polynomial processes using finite state Markov processes satisfying suitable moment matching conditions. The states of these Markov processes together with their transition probabilities can be interpreted as Markov cubature rul ...

An integer program (IP) is a problem of the form

\min \{f(x) : \, Ax = b, \ l \leq x \leq u, \ x \in \Z^n\}

, where

A \in \Z^{m \times n}

b \in \Z^m

l,u \in \Z^n

, and

f: \Z^n \rightarrow \Z

is a separable convex objective function. The problem o ...

We characterize the irreducible polynomials that occur as the characteristic polynomial of an automorphism of an even unimodular lattice of a given signature, generalizing a theorem of Gross and McMullen. As part of the proof, we give a general criterion i ...

In a seminal work, Micciancio and Voulgaris (SIAM J Comput 42(3):1364-1391, 2013) described a deterministic single-exponential time algorithm for the closest vector problem (CVP) on lattices. It is based on the computation of the Voronoi cell of the given ...

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The diffusion strategy for distributed learning from streaming data employs local stochastic gradient updates along with exchange of iterates over neighborhoods. In this work we establish that agents cluster around a network centroid in the mean-fourth sen ...

In a number of cases the minimal polynomials of the images of unipotent elements of non-prime order in irreducible representations of the exceptional algebraic groups in good characteristics are found. It is proved that if p > 5 for a group of type E-8 and ...

We devise a Hybrid High-Order (HHO) method for highly oscillatory elliptic problems that is capable of handling general meshes. The method hinges on discrete unknowns that are polynomials attached to the faces and cells of a coarse mesh; those attached to ...

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Let F-p be a prime field of order p > 2, and let A be a set in F-p with very small size in terms of p. In this note, we show that the number of distinct cubic distances determined by points in A x A satisfies vertical bar(A - A)(3) + (A - A)(3 vertical bar ...

Optimization is a fundamental tool in modern science. Numerous important tasks in biology, economy, physics and computer science can be cast as optimization problems. Consider the example of machine learning: recent advances have shown that even the most s ...

Invariant generation for P-solvable loops with assignments

Chat with Graph Search

The multivariate Serre conjecture ring

Linear Complexity Self-Attention With 3rd Order Polynomials

Stable high-order randomized cubature formulae in arbitrary dimension

A PCP Theorem for Interactive Proofs and Applications

Distributed Learning in Non-Convex Environments-Part II: Polynomial Escape From Saddle-Points

Representing Monads with Capabilities

Distributed Learning in Non-Convex Environments-Part I: Agreement at a Linear Rate

Admissibility of Uncertain Injections in Quadratic Algebraic Systems

Automating cutting planes is NP-hard

Markov cubature rules for polynomial processes

New Results in Integer and Lattice Programming

Automorphisms of even unimodular lattices and equivariant Witt groups

On compact representations of Voronoi cells of lattices

Polynomial Jump-Diffusion Models

Polynomial Escape-Time From Saddle Points In Distributed Non-Convex Optimization

Minimal Polynomials Of Unipotent Elements Of Non-Prime Order In Irreducible Representations Of The Exceptional Algebraic Groups In Some Good Characteristics

A Hybrid High-Order Method for Highly Oscillatory Elliptic Problems

Coupling non-conforming discretizations of PDEs by spectral approximation of the Lagrange multiplier space

Four-Variable Expanders Over The Prime Fields

New Algorithmic Paradigms for Discrete Problems using Dynamical Systems and Polynomials