Related papers: $p$-adic fractal strings of arbitrary rational dim…

The purpose of this paper is to study the fractal phenomena in large data sets and the associated questions of dimension reduction. We examine situations where the classical Principal Component Analysis is not effective in identifying the…

Fractals are self-repeating patterns which have dimensions given by fractions rather than integers. While the dimension of a system unambiguously defines its properties, a fractional dimensional system can exhibit interesting properties.…

In this paper we study some problems related with the theory of multidimensional $p$-adic wavelets in connection with the theory of multidimensional $p$-adic pseudo-differential operators (in the $p$-adic Lizorkin space). We introduce a new…

In this article we discuss the limit $p$ approaches to one of tree-level $p$-adic open string amplitudes and its connections with the topological zeta functions. There is empirical evidence that $p$-adic strings are related to the ordinary…

For an algebraically closed non-archimedean extension $C/\mathbb{Q}_p$, we define a Tannakian category of $p$-adic Hodge structures over $C$ that is a local, $p$-adic analog of the global, archimedean category of $\mathbb{Q}$-Hodge…

Investigating a model of scale-invariant random spatial network suggested by Aldous, Kendall constructed a random metric $T$ on $\mathbb{R}^d$, for which the distance between points is given by the optimal connection time, when travelling…

We present a string theory that reproduces the large-$N$ expansion of two dimensional Yang-Mills gauge theory on arbitrary surfaces. First, a new class of topological sigma models is introduced, with path integrals localized to the moduli…

We discuss classical composite p-brane solutions and their quantization using the conjecture that their fluctuations may be described via degrees of freedom of Dirichlet strings ended on these p-branes. We work with Dirichlet (super)strings…

To any spectral triple (A,D,H) a dimension d is associated, in analogy with the Hausdorff dimension for metric spaces. Indeed d is the unique number, if any, such that |D|^-d has non trivial logarithmic Dixmier trace. Moreover, when d is…

Topological defects in the framework of effective quantum gravity model are investigated, based on the hypothesis of an effective fractal dimension of the universe. This is done by using Caputo fractional derivatives to determine the…

We extend Feynman's analysis of the infinite ladder AC circuit to fractal AC circuits. We show that the characteristic impedances can have positive real part even though all the individual impedances inside the circuit are purely imaginary.…

This article, based on the Klein lecture, contains some new results and new speculations on various topics. They include discussion of open strings in the AdS space, unusual features of D-branes, conformal gauge theories in higher…

The partition function of two dimensional QCD on a Riemann surface of area $A$ is expanded as a power series in $1/N$ and $A$. It is shown that the coefficients of this expansion are precisely determined by a sum over maps from a two…

The gravitational field of both local and global non static cosmic strings in the context of Lyra geometry are investigated. Local strings are characterized by having an energy momentum tensor whose only non null components are $T_{tt} =…

We study in a rigorous mathematical way p-adic quantum field theories whose N-point amplitudes are the expectation of products of vertex operators. We show that this type of amplitudes admit a series expansion where each term is an Igusa's…

In the first section we review recent results on the harmonic analysis of fractals generated by iterated function systems with emphasis on spectral duality. Classical harmonic analysis is typically based on groups whereas the fractals are…

If the QCD axion solves the strong CP problem then light axion-like-particles (ALPs) are expected to be ubiquitous in string theory - the string axiverse. Such ALPs can be the QCD axion and constitute dark matter (DM) or radiation,…

It is shown that the topological invariants associated with the two-dimensional world-surface in string theory have nontrivial fluctuations around their nonexistent classical dynamics. Additionally it is proved that the underlying…

Properties of the set $T_s$ of "particularly non-normal numbers" of the unit interval are studied in details ($T_s$ consists of real numbers $x$, some of whose s-adic digits have the asymptotic frequencies in the nonterminating $s-$ adic…

We examine the effects of gravitational fields produced by topological defects on a Dirac field and a Dirac oscillator in a spinning cosmic string spacetime. We obtain the eigenfunctions and the energy levels of the relativistic field in…