The computability-theoretic and reverse mathematical aspects of various combinatorial principles, such as König’s Lemma and Ramsey’s Theorem, have received a great deal of attention and are active areas of research. We carry on this study of effective combinatorics by analyzing various partition theorems (such as Ramsey’s Theorem) with the aim of understanding the complexity of solutions to com...

We study the Roberge-Weiss phase transition numerically. The is associated with discontinuities in quark-number density at specific values of imaginary quark chemical potential. parameterize number $\rho_q$ by polynomial fit function to compute canonical partition functions. demonstrate that this approach provides a good framework for analyzing lattice QCD data finite and high temperature. show...

In this paper, we present a recurrent canonical piecewise linear (RCPL) network based on canonical piecewise-linear (CPL) function and autoregressive moving average model, and apply it to adaptive channel equalization. It, is shown that a recurrent neural network with piecewise linear activation function realizes an RCPL network. RCPL network has several advantages: First, i t can make use of s...

We study the problem of modulation and coding for doubly dispersive, i.e., time and frequency selective fading channels. Using the recent result that under-spread linear systems are approximately diagonalized by biorthogonal Weyl-Heisenberg bases, we arrive at a canonical formulation of modulation and code design. For coherent reception with maximum likelihood decoding, we derive the code desig...