Statistics on Graphs, Exponential Formula and Combinatorial Physics

The concern of this paper is a famous combinatorial formula known under the name "exponential formula". It occurs quite naturally in many contexts (physics, mathematics, computer science). Roughly speaking, it expresses that the exponential generating function of a whole structure is equal to the exponential of those of connected substructures. Keeping this descriptive statement as a guideline, we develop a general framework to handle many different situations in which the exponential formula can be applied

A/r/cography: art, research and communication

This article aims at establishing the foundations for a/r/cography as an “art and communication”-based research methodology, inspired by a/r/tography yet more encompassing, and particularly suitable for the digital art world. As part of the larger family of practice-based research methodologies, a/r/tography presents various ways through which it can be explored, but since it is aimed at the arts and education, its scope is forcibly hampered by the fact that not all researchers and art practitioners are necessarily teachers. However, since most of its underlying principles can be extended for non-teachers, thus arose the idea to propose a methodology that would retain ontological, epistemological and methodological assumptions, but would expand beyond the limitations imposed by the role of the teacher. This extension is called a/r/cography and is structured upon the interchangeable roles of artist, researcher and communicator, as being intrinsic to the underlying living inquiry processes. Furthermore, this proposal is supported by the author’s own experience from a/r/cographic processes in the creation, exhibition and communication of digital artworks.info:eu-repo/semantics/publishedVersio

Approximate substitutions and the normal ordering problem

In this paper, we show that the infinite generalised Stirling matrices associated with boson strings with one annihilation operator are projective limits of approximate substitutions, the latter being characterised by a finite set of algebraic equations

An individual-based model to explore the impacts of lesser-known social dynamics on wolf populations

The occurrence of wolf populations in human-dominated landscapes is challenging worldwide because of conflicts with human activities. Modeling is an important tool to project wolf dynamics and expansion, and help in decision making concerning management and conservation. However, some individual behaviors and pack dynamics of the wolf life cycle are still unclear to ecologists. Here we present an individual-based model (IBM) to project wolf populations while exploring the lesser-known processes of the wolf life cycle. IBMs are bottom-up models that simulate the fate of individuals interacting with each other, with population-level properties emerging from the individual-level simulations. IBMs are particularly adapted to represent social species such as the wolf that exhibits complex individual interactions. Our IBM projects wolf demography including fine-scale individual behavior and pack dynamics based on up-to-date scientific literature. We explore four processes of the wolf life cycle whose consequences on population dynamics are still poorly understood: the pack dissolution following the loss of a breeder, the adoption of young dispersers by packs, the establishment of new packs through budding, and the different breeder replacement strategies. While running different versions of the IBM to explore these processes, we also illustrate the modularity and flexibility of our model, an asset to model wolf populations experiencing different ecological and demographic conditions. The different parameterization of pack dissolution, territory establishment by budding, and breeder replacement processes influence the projections of wolf populations. As such, these processes require further field investigation to be better understood. The adoption process has a lesser impact on model projections. Being coded in R to facilitate its understanding, we expect that our model will be used and further adapted by ecologists for their own specific applications

Mitochondrial genome of an Allegheny Woodrat (\u3ci\u3eNeotoma magister\u3c/i\u3e)

The Allegheny woodrat (Neotoma magister) is endemic to the eastern United States. Population numbers have decreased rapidly over the last four decades due to habitat fragmentation, disease-related mortality, genetic isolation and inbreeding depression; however, effective management is hampered by limited genetic resources. To begin addressing this need, we sequenced and assembled the entire Allegheny woodrat mitochondrial genome. The genome assembly is 16,310 base pairs in length, with an overall base composition of 34% adenine, 27% thymine, 26% cytosine and 13% guanine. This resource will facilitate our understanding of woodrat population genetics and behavioral ecology

Heisenberg-Weyl algebra revisited: Combinatorics of words and paths

The Heisenberg-Weyl algebra, which underlies virtually all physical representations of Quantum Theory, is considered from the combinatorial point of view. We provide a concrete model of the algebra in terms of paths on a lattice with some decomposition rules. We also discuss the rook problem on the associated Ferrers board; this is related to the calculus in the normally ordered basis. From this starting point we explore a combinatorial underpinning of the Heisenberg-Weyl algebra, which offers novel perspectives, methods and applications.Comment: 5 pages, 3 figure

Dobinski-type relations: Some properties and physical applications

We introduce a generalization of the Dobinski relation through which we define a family of Bell-type numbers and polynomials. For all these sequences we find the weight function of the moment problem and give their generating functions. We provide a physical motivation of this extension in the context of the boson normal ordering problem and its relation to an extension of the Kerr Hamiltonian.Comment: 7 pages, 1 figur

Degrees of entanglement for multipartite systems

We propose a unified mathematical scheme, based on a classical tensor isomorphism, for characterizing entanglement that works for pure states of multipartite systems of any number of particles. The degree of entanglement is indicated by a set of absolute values of the determinants for each subspace of the multipartite systems. Unlike other schemes, our scheme provides indication of the degrees of entanglement when the qubits are measured or lost successively, and leads naturally to the necessary and sufficient conditions for multipartite pure states to be separable. For systems with a large number of particles, a rougher indication of the degree of entanglement is provided by the set of mean values of the determinantal values for each subspace of the multipartite systems.Comment: 12 pages, no figure

Monomiality principle, Sheffer-type polynomials and the normal ordering problem

We solve the boson normal ordering problem for $(q(a^\dag)a+v(a^\dag))^n$ with arbitrary functions $q(x)$ and $v(x)$ and integer $n$, where $a$ and $a^\dag$ are boson annihilation and creation operators, satisfying $[a,a^\dag]=1$. This consequently provides the solution for the exponential $e^{\lambda(q(a^\dag)a+v(a^\dag))}$ generalizing the shift operator. In the course of these considerations we define and explore the monomiality principle and find its representations. We exploit the properties of Sheffer-type polynomials which constitute the inherent structure of this problem. In the end we give some examples illustrating the utility of the method and point out the relation to combinatorial structures.Comment: Presented at the 8'th International School of Theoretical Physics "Symmetry and Structural Properties of Condensed Matter " (SSPCM 2005), Myczkowce, Poland. 13 pages, 31 reference