We classify infinite networks, by introducing the new problem of percolation on the average. This classification plays a fundamental role for understanding the thermodynamic properties of statistical mechanics spin models with discrete symmetry. Indeed, in the main theorem of the paper, we prove that the qstates Potts model presents spontaneous magnetization at finite temperature if it is defin...

Gases reach equilibrium when left to themselves. Why do they behave in this way? The canonical answer to this question, originally proffered by Boltzmann, is that the systems have to be ergodic. This answer has been criticised on different grounds and is now widely regarded as flawed. In this paper we argue that some of the main arguments against Boltzmann’s answer, in particular, arguments bas...

How to quickly and efficiently get real-time emergency data from a massive network is becoming a major problem in monitoring internet public opinion. In this paper, we propose a clustering algorithm based on simplified cluster hypothesis to improve system efficiency. Meanwhile, by analysis of the emergency’s characteristics under the dynamic web environment, we propose a multi-strategy quantita...

Many have documented the difficulty of using the current paradigm of Randomized Controlled Trials (RCTs) to test and validate the effectiveness of alternative medical systems such as Ayurveda. This paper critiques the applicability of RCTs for all clinical knowledge-seeking endeavors, of which Ayurveda research is a part. This is done by examining statistical hypothesis testing, the underlying ...

Jacob Cohen (1994) raised a number of questions about the logic and information value of the null hypothesis statistical test (NHST). Specifically, he suggested that: (a) The NHST does not tell us what we want to know; (b) the null hypothesis is always false; and (c) the NHST lacks logical integrity. It is the author's view that although there may be good reasons to give up the NHST, these part...

The Riemann hypothesis is, and will hopefully remain for a long time, a great motivation to uncover and explore new parts of the mathematical world. After reviewing its impact on the development of algebraic geometry we discuss three strategies, working concretely at the level of the explicit formulas. The first strategy is “analytic” and is based on Riemannian spaces and Selberg’s work on the ...

We describe a method for planning to achieve goals under uncertainty that makes use of decision-theoretic methods to guide search. Given a probabilistic model of the world and a utility measure on world states, we wish to nd plans (sequences of actions) with high expected utility. Finding a plan maximizing the expected utility is combinatorial in nature. In previous research, we coped with the ...

We describe a method for planning to achieve goals under uncertainty that makes use of decision-theoretic methods to guide search. Given a probabilistic model of the world and a utility measure on world states, we wish to nd plans (sequences of actions) with high expected utility. Finding a plan maximizing the expected utility is combinatorial in nature. In previous research, we coped with the ...