Min-Max Theorems for Packing and Covering Odd (u,v)(u,v)-trails

We investigate the problem of packing and covering odd $(u,v)$-trails in a graph. A $(u,v)$-trail is a $(u,v)$-walk that is allowed to have repeated vertices but no repeated edges. We call a trail odd if the number of edges in the trail is odd. Let $\nu(u,v)$ denote the maximum number of edge-disjoint odd $(u,v)$-trails, and $\tau(u,v)$ denote the minimum size of an edge-set that intersects every odd $(u,v)$-trail. We prove that $\tau(u,v)\leq 2\nu(u,v)+1$. Our result is tight---there are examples showing that $\tau(u,v)=2\nu(u,v)+1$---and substantially improves upon the bound of $8$ obtained in [Churchley et al 2016] for $\tau(u,v)/\nu(u,v)$. Our proof also yields a polynomial-time algorithm for finding a cover and a collection of trails satisfying the above bounds. Our proof is simple and has two main ingredients. We show that (loosely speaking) the problem can be reduced to the problem of packing and covering odd $(uv,uv)$-trails losing a factor of 2 (either in the number of trails found, or the size of the cover). Complementing this, we show that the odd-$(uv,uv)$-trail packing and covering problems can be tackled by exploiting a powerful min-max result of [Chudnovsky et al 2006] for packing vertex-disjoint nonzero $A$-paths in group-labeled graphs

Discrete space-time geometry and skeleton conception of particle dynamics

It is shown that properties of a discrete space-time geometry distinguish from properties of the Riemannian space-time geometry. The discrete geometry is a physical geometry, which is described completely by the world function. The discrete geometry is nonaxiomatizable and multivariant. The equivalence relation is intransitive in the discrete geometry. The particles are described by world chains (broken lines with finite length of links), because in the discrete space-time geometry there are no infinitesimal lengths. Motion of particles is stochastic, and statistical description of them leads to the Schr\"{o}dinger equation, if the elementary length of the discrete geometry depends on the quantum constant in a proper way.Comment: 22 pages, 0 figure

Physics of Fashion Fluctuations

We consider a market where many agents trade many different types of products with each other. We model development of collective modes in this market, and quantify these by fluctuations that scale with time with a Hurst exponent of about 0.7. We demonstrate that individual products in the model occationally become globally accepted means of exchange, and simultaneously become very actively traded. Thus collective features similar to money spontaneously emerge, without any a priori reason.Comment: 9 pages RevTeX, 5 Postscript figure

Strong Field Control of the Interatomic Coulombic Decay Process in Quantum Dots

In recent years the laser induced interatomic Coulombic decay ICD process in paired quantum dots has been predicted [J. Chem. Phys. 138 2013 214104]. In this work we target the enhancement of ICD by scanning over a range of strong field laser intensities. The GaAs quantum dots are modeled by a one dimensional double well potential in which simulations are done with the space resolved multi configuration time dependent Hartree method including antisymmetrization to account for the fermions. As a novelty a complementary state resolved ansatz is developed to consolidate the interpretation of transient state populations, widths obtained for the ICD and the competing direct ionization channel, and Fano peak profiles in the photoelectron spectra. The major results are that multi photon processes are unimportant even for the strongest fields. Further, below pi to pi pulses display the highest ICD efficiency while the direct ionization becomes less dominan

Speaking up for the lost voices: representation and inclusion of people with communication impairment in brain tumour research

Brain tumours and their associated treatments can lead to progressive impairments of communication, adversely affecting quality-of-life. This commentary explores our concerns that people with speech, language, and communication needs face barriers to representation and inclusion in brain tumour research; we then offer possible solutions to support their participation. Our main concerns are that there is currently poor recognition of the nature of communication difficulties following brain tumours, limited focus on the psychosocial impact, and lack of transparency on why people with speech, language, and communication needs were excluded from research or how they were supported to take part. We propose solutions focusing on working towards more accurate reporting of symptoms and the impact of impairment, using innovative qualitative methods to collect data on the lived experiences of speech, language, and communication needs, and empowering speech and language therapists to become part of research teams as experts and advocates for this population. These solutions would support the accurate representation and inclusion of people with communication needs after brain tumour in research, allowing healthcare professionals to learn more about their priorities and needs

Analysis of weighted networks

The connections in many networks are not merely binary entities, either present or not, but have associated weights that record their strengths relative to one another. Recent studies of networks have, by and large, steered clear of such weighted networks, which are often perceived as being harder to analyze than their unweighted counterparts. Here we point out that weighted networks can in many cases be analyzed using a simple mapping from a weighted network to an unweighted multigraph, allowing us to apply standard techniques for unweighted graphs to weighted ones as well. We give a number of examples of the method, including an algorithm for detecting community structure in weighted networks and a new and simple proof of the max-flow/min-cut theorem.Comment: 9 pages, 3 figure

Sabitov polynomials for volumes of polyhedra in four dimensions

In 1996 I.Kh. Sabitov proved that the volume of a simplicial polyhedron in a 3-dimensional Euclidean space is a root of certain polynomial with coefficients depending on the combinatorial type and on edge lengths of the polyhedron only. Moreover, the coefficients of this polynomial are polynomials in edge lengths of the polyhedron. This result implies that the volume of a simplicial polyhedron with fixed combinatorial type and edge lengths can take only finitely many values. In particular, this yields that the volume of a flexible polyhedron in a 3-dimensional Euclidean space is constant. Until now it has been unknown whether these results can be obtained in dimensions greater than 3. In this paper we prove that all these results hold for polyhedra in a 4-dimensional Euclidean space.Comment: 23 pages; misprints corrected, Lemma 6.1 slightly rewritten, title change

Deciphering the Chemical Basis of Fluorescence of a Selenium-Labeled Uracil Probe when Bound at the Bacterial Ribosomal A-Site

We unveil in this work the main factors that govern the turn-on/off fluorescence of a Se-modified uracil probe at the ribosomal RNA A-site. Whereas the constraint into an “in-plane” conformation of the two rings of the fluorophore is the main driver for the observed turn-on fluorescence emission in the presence of the antibiotic paromomycin, the electrostatics of the environment plays a minor role during the emission process. Our computational strategy clearly indicates that, in the absence of paromomycin, the probe prefers conformations that show a dark S1 electronic state with participation of nπ* electronic transition contributions between the selenium atom and the π-system of the uracil moiety

Realizability of the Lorentzian (n,1)-Simplex

In a previous article [JHEP 1111 (2011) 072; arXiv:1108.4965] we have developed a Lorentzian version of the Quantum Regge Calculus in which the significant differences between simplices in Lorentzian signature and Euclidean signature are crucial. In this article we extend a central result used in the previous article, regarding the realizability of Lorentzian triangles, to arbitrary dimension. This technical step will be crucial for developing the Lorentzian model in the case of most physical interest: 3+1 dimensions. We first state (and derive in an appendix) the realizability conditions on the edge-lengths of a Lorentzian n-simplex in total dimension n=d+1, where d is the number of space-like dimensions. We then show that in any dimension there is a certain type of simplex which has all of its time-like edge lengths completely unconstrained by any sort of triangle inequality. This result is the d+1 dimensional analogue of the 1+1 dimensional case of the Lorentzian triangle.Comment: V1: 15 pages, 2 figures. V2: Minor clarifications added to Introduction and Discussion sections. 1 reference updated. This version accepted for publication in JHEP. V3: minor updates and clarifications, this version closely corresponds to the version published in JHE