We generalize the Ihara-Selberg zeta function to hypergraphs in a natural way. Hashimoto’s factorization results for biregular bipartite graphs apply, leading to exact factorizations. For (d, r)-regular hypergraphs, we show that a modified Riemann hypothesis is true if and only if the hypergraph is Ramanujan in the sense of Winnie Li and Patrick Solé. Finally, we give an example to show how the...

Holomorphic maps between complex manifolds have many properties which distinguish them among general smooth maps. Consider, for example, the case of a map between Riemann surfaces. A holomorphic map is represented locally, in suitable co-ordinates, by one of the models z 7→ z for k ≥ 0. These models are very different from the models of generic smooth maps between surfaces, which are, in additi...

In this paper, we consider the asymptotic form of the generalization error for the restricted Boltzmann machine in Bayesian estimation. It has been shown that obtaining the maximum pole of zeta functions is related to the asymptotic form of the generalization error for hierarchical learning models (Watanabe, 2001a,b). The zeta function is defined by using a Kullback function. We use two methods...

We give a new and bijective proof for the formula of the growth function of the positive braid monoid with respect to Artin generators.

Let f = (f1, . . . , fl) : U → Kl, with K = R or C, be a K-analytic mapping defined on an open set U ⊆ Kn, and let Φ be a smooth function on U with compact support. In this paper, we give a description of the possible poles of the local zeta function attached to (f , Φ) in terms of a log-principalization of the ideal If = (f1, . . . , fl). When f is a non-degenerate mapping, we give an explicit...

It is the purpose of this work to pursue a novel physical interpretation of the nontrivial Riemann zeta zeros and prove why the location of these zeros zn = 1/2 + iλn corresponds physically to tachyonic-resonances/tachyonic-condensates, originating from the scattering of two on-shell tachyons in bosonic string theory. Namely, we prove that if there were nontrivial zeta zeros (violating the Riem...

Purpose: To optimize the preparation of insulin-chitosan nanoparticles (ICNS) using response surface methodology (RSM). Methods: ICNS were formulated through ionic cross linking method. The effects of the ratio between insulin and chitosan, pH of the medium and rotation speed on insulin encapsulation efficiency (EE) were investigated. Box-Behnken experimental design coupled with response surfac...

The zeta potential of the protein corona around carboxyl particles has been measured using tunable resistive pulse sensing (TRPS). A simple and rapid assay for characterising zeta potentials within buffer, serum and plasma is presented monitoring the change, magnitude and distribution of proteins on the particle surface. First, we measure the change in zeta potential of carboxyl-functionalised ...

Abstract. Dynamical zeta functions provide a powerful method to analyze low dimensional dynamical systems when the underlying symbolic dynamics is under control. On the other hand even simple one dimensional maps can show an intricate structure of the grammar rules that may lead to a non smooth dependence of global observable on parameters changes. A paradigmatic example is the fractal diffusio...