This paper describes the probabilistic behaviour of a random Sturmian word. It performs the probabilistic analysis of the recurrence function which can be viewed as a waiting time to discover all the factors of length n of the Sturmian word. This parameter is central to combinatorics of words. Having fixed a possible length n for the factors, we let α to be drawn uniformly from the unit interva...

Automatic verification by means of extended static checking (ESC) has seen some success in industry and academia due to its lightweight and easy-to-use nature. Unfortunately, ESC comes at a cost: a host of logical and practical completeness and soundness issues. Interactive verification technology, on the other hand, is usually complete and sound, but requires a large amount of mathematical and...

We describe the design, semantics, and implementation of a probabilistic programming language where programs are spreadsheet queries. Given an input database consisting of tables held in a spreadsheet, a query constructs a probabilistic model conditioned by the spreadsheet data, and returns an output database determined by inference. This work extends probabilistic programming systems in three ...

In this paper we develop a novel probabilistic generalization bound for learning the kernel problem. First, we show that the generalization analysis of the regularized kernel learning system reduces to investigation of the suprema of the Rademacher chaos process of order two over candidate kernels, which we refer to as Rademacher chaos complexity. Next, we show how to estimate the empirical Rad...

In this paper we develop a novel probabilistic generalization bound for regularized kernel learning algorithms. First, we show that generalization analysis of kernel learning algorithms reduces to investigation of the suprema of homogeneous Rademacher chaos process of order two over candidate kernels, which we refer to it as Rademacher chaos complexity. Our new methodology is based on the princ...

In this paper we develop a novel probabilistic generalization bound for learning the kernel problem. First, we show that the generalization analysis of the kernel learning algorithms reduces to investigation of the suprema of the Rademacher chaos process of order two over candidate kernels, which we refer to as Rademacher chaos complexity. Next, we show how to estimate the empirical Rademacher ...

Our work presents a new approach to developing, analyzing, and proving correctness of programs intended for execution on a quantum computer. We provide tools to write quantum as well as classical specifications, develop quantum and classical solutions for them, and analyses various properties of quantum specifications and quantum programs, such as implementability, time and space complexity, an...

conclusions the use of tdf in patients with hbeag-negative chb seemed to be a highly cost-effective strategy. compared with the other available medication options, tdf was the most cost-saving strategy. thus, tdf may be the best option as a first-line medication. patients can also be switched from other medications to tdf. results the results revealed that the tdf treatment strategy was more ef...