Related papers: Moment sequences, transformations, and Spidernet g…
We introduce a class of partial differential equations on metric graphs associated with mixed evolution: on some edges we consider diffusion processes, on other ones transport phenomena. This yields a system of equations with possibly…
Conventional studies of network growth models mainly look at the steady state degree distribution of the graph. Often long time behavior is considered, hence the initial condition is ignored. In this contribution, the time evolution of the…
Graph-based methods pervade the inference toolkits of numerous disciplines including sociology, biology, neuroscience, physics, chemistry, and engineering. A challenging problem encountered in this context pertains to determining the…
We consider quantum graphs with transparent branching points. To design such networks, the concept of transparent boundary conditions is applied to the derivation of the vertex boundary conditions for the linear Schrodinger equation on…
Discrete analogs of the index transforms with squares of Bessel functions of the first and second kind $J_\nu(z),\ Y_\nu(z)$ are introduced and investigated. The corresponding inversion theorems for suitable classes of functions and…
We enumerate the independent sets of several classes of regular and almost regular graphs and compute the corresponding generating functions. We also note the relations between these graphs and other combinatorial objects and, in some…
We study the behavior of the random walk in a continuum independent long-range percolation model, in which two given vertices $x$ and $y$ are connected with probability that asymptotically behaves like $|x-y|^{-\alpha}$ with $\alpha>d$,…
After a brief review of the key theorems concerning recurrent sequences, we give an explicit computation of the inverse of the Vandermonde matrix. This will then be used to derive sub-exponential decay error terms in the ergodic theorem of…
Graphs are used in many disciplines to model the relationships that exist between objects in a complex discrete system. Researchers may wish to compare a network of interest to a "typical" graph from a family (or ensemble) of graphs which…
We construct models for first- and second-order Fermi acceleration of particles, incorporating generic frame transformations, dispersion relations, and conservation laws. Within this framework, we study deformations of Lorentz symmetry via…
Fractional moments have been investigated by many authors to represent the density of univariate and bivariate random variables in different contexts. Fractional moments are indeed important when the density of the random variable has…
The problem of what moments can exist for the coding radius of a finitary map between two i.i.d. processes, has been extensively studied in the case of $\mathbb{Z}$-processes. Here we treat this problem for factor maps between…
Assuming a $q$-variant of the prime $k$-tuple conjecture uniformly, we compute mixed moments of the number of primes in disjoint short intervals and progressions, respectively. This involves estimating the mean of singular series along…
We use a version of the Trotter-Kato approximation theorem for strongly continuous semigroups in order to study flows on growing networks. For that reason we use the abstract notion of direct limits in the sense of category theory.
We develop a structural approach to simultaneous embeddability in temporal sequences of graphs, inspired by graph minor theory. Our main result is a classification theorem for 2-connected temporal sequences: we identify five obstruction…
In this paper a connection between Hamburger moment sequences and their moment subsequences is given and the determinacy of these problems are related.
We consider series of the form $$ \frac{p}{q} +\sum_{j=2}^\infty \frac{1}{x_j}, $$ where $x_1=q$ and the integer sequence $(x_n)$ satisfies a certain non-autonomous recurrence of second order, which entails that $x_n|x_{n+1}$ for $n\geq 1$.…
The invariant is one of central topics in science, technology and engineering. The differential invariant is essential in understanding or describing some important phenomena or procedures in mathematics, physics, chemistry, biology or…
Graph transformation is concerned with the manipulation of graphs by means of rules. Graph grammars have been traditionally studied using techniques from category theory. In previous works, we introduced Matrix Graph Grammars (MGGs) as a…
We present an analytic method for computing the moments of a sum of independent and identically distributed random variables. The limiting behavior of these sums is very important to statistical theory, and the moment expressions that we…