Related papers: Kedlaya's algorithm in larger characteristic

The design of general purpose processors relies heavily on a workload gathering step in which representative programs are collected from various application domains. Processor performance, when running the workload set, is profiled using…

Schoening in 1999 presented a simple randomized algorithm for k-SAT with running time O(a^n * poly(n)) for a = 2(k-1)/k. We give a deterministic version of this algorithm running in time O((a+epsilon)^n * poly(n)), where epsilon > 0 can be…

Saddle-point or primal-dual methods have recently attracted renewed interest as a systematic technique to design distributed algorithms which solve convex optimization problems. When implemented online for streaming data or as dynamic…

We prove a linear bound on the average total curvature of the central path of linear programming theory in terms on the number of independent variables of the primal problem, and independent on the number of constraints.

This paper considers the problem of canonical-correlation analysis (CCA) (Hotelling, 1936) and, more broadly, the generalized eigenvector problem for a pair of symmetric matrices. These are two fundamental problems in data analysis and…

This work develops a class of probabilistic algorithms for the numerical solution of nonlinear, time-dependent partial differential equations (PDEs). Current state-of-the-art PDE solvers treat the space- and time-dimensions separately,…

We give a semidefinite programming characterization of the Crawford number. We show that the computation of the Crawford number within $\varepsilon$ precision is computable in polynomial time in the data and $|\log \varepsilon |$.

We prove time-dependent versions of Kingman's subadditive ergodic theorem, which can be used to study stochastic processes as well as propagation of solutions to PDE in time-dependent environments.

An experimental comparison of two or more optimization algorithms requires the same computational resources to be assigned to each algorithm. When a maximum runtime is set as the stopping criterion, all algorithms need to be executed in the…

We address the problem of enumerating all temporal k-cores given a query time range and a temporal graph, which suffers from poor efficiency and scalability in the state-of-the-art solution. Motivated by an existing concept called core…

We design an algorithm for computing the $p$-curvature of a differential system in positive characteristic $p$. For a system of dimension $r$ with coefficients of degree at most $d$, its complexity is $\softO (p d r^\omega)$ operations in…

We propose automated techniques for the verification and control of probabilistic real-time systems that are only partially observable. To formally model such systems, we define an extension of probabilistic timed automata in which local…

In this paper we consider symmetric, positive semidefinite (SPSD) matrix $A$ and present two algorithms for computing the $p$-Schatten norm $\|A\|_p$. The first algorithm works for any SPSD matrix $A$. The second algorithm works for…

Through a straightforward Bayesian approach we show that under some general conditions a maximum running time, namely the number of discrete steps performed by a computer program during its execution, can be defined such that the…

We show that a subclass of infinite-state probabilistic programs that can be modeled by probabilistic one-counter automata (pOC) admits an efficient quantitative analysis. In particular, we show that the expected termination time can be…

We consider the weak-type inequality for Littlewood-Paley square functions on A_p weighted Lebesgue spaces. Of interest is the sharp in the A_p characteristic estimate. The case of 1<p<2 is subcritical, and the sharp power of 1/p is…

With qubits encoded into atomic ground and Rydberg states and situated on the vertexes of a graph, the conditional quantum dynamics of Rydberg blockade, which inhibits simultaneous excitation of nearby atoms, has been employed recently to…

We show that the two-stage minimum description length (MDL) criterion widely used to estimate linear change-point (CP) models corresponds to the marginal likelihood of a Bayesian model with a specific class of prior distributions. This…

Changepoint detection is a central problem in time series and genomic data. For some applications, it is natural to impose constraints on the directions of changes. One example is ChIP-seq data, for which adding an up-down constraint…

A complete p-adic Khintchine type theorem for approximation by p-adic algebraic numbers is established.