An Underlying Theory for Gravity

A new direction to understand gravity has recently been explored by considering classical gravity to be a derived interaction from an underlying theory. This underlying theory would involve new degrees of freedom at a deeper level and it would be structurally different from classical gravitation. It may conceivably be a quantum theory or a non-quantum theory. The relation between this underlying theory and Einstein's gravity is similar to the connection between statistical mechanics and thermodynamics. We discuss the apparent lack of evidence of any quantum nature of gravity in this context.Comment: Contributed paper to VIIth International Conference on Gravitation and Cosmology, 14 - 19 December, 2011 GOA, INDIA. 4 page

Two-sided estimates for order statistics of log-concave random vectors

We establish two-sided bounds for expectations of order statistics ($k$-th maxima) of moduli of coordinates of centered log-concave random vectors with uncorrelated coordinates. Our bounds are exact up to multiplicative universal constants in the unconditional case for all $k$ and in the isotropic case for $k \leq n-cn^{5/6}$. We also derive two-sided estimates for expectations of sums of $k$ largest moduli of coordinates for some classes of random vectors.Comment: 25 page

Peculiar liquid-feeding and pathogen transmission behavior of Aedes togoi and comparison with Anopheles sinensis

Female mosquitoes transmit various diseases as vectors during liquid-feeding. Identifying the determinants of vector efficiency is a major scientific challenge in establishing strategies against these diseases. Infection rate and transmission efficiency are interconnected with the mosquito-induced liquid-feeding flow as main indexes of vector efficiency. However, the relationship between liquid-feeding characteristics and pathogen remains poorly understood. The liquid-feeding behavior of Aedes togoi and Anopheles sinensis was comparatively investigated in conjunction with vector efficiency via micro-particle image velocimetry. The flow rates and ratio of the ejection volume of Aedes togoi were markedly higher than those of Anophels sinensis. These differences would influence pathogen re-ingestion. Wall shear stresses of these mosquito species were also clearly discriminatory affecting the infective rates of vector-borne diseases. The variations in volume of two pump chambers and diameter of proboscis of these mosquito species were compared to determine the differences in the liquid-feeding process. Liquid-feeding characteristics influence vector efficiency; hence, this study can elucidate the vector efficiency of mosquitoes and the vector-pathogen interactions and contribute to the development of strategies against vector-borne diseases.112Ysciescopu

Distributional and classical solutions to the Cauchy Boltzmann problem for soft potentials with integrable angular cross section

This paper focuses on the study of existence and uniqueness of distributional and classical solutions to the Cauchy Boltzmann problem for the soft potential case assuming $S^{n-1}$ integrability of the angular part of the collision kernel (Grad cut-off assumption). For this purpose we revisit the Kaniel--Shinbrot iteration technique to present an elementary proof of existence and uniqueness results that includes large data near a local Maxwellian regime with possibly infinite initial mass. We study the propagation of regularity using a recent estimate for the positive collision operator given in [3], by E. Carneiro and the authors, that permits to study such propagation without additional conditions on the collision kernel. Finally, an $L^{p}$-stability result (with $1\leq p\leq\infty$) is presented assuming the aforementioned condition.Comment: 19 page

A Homological Approach to Belief Propagation and Bethe Approximations

We introduce a differential complex of local observables given a decomposition of a global set of random variables into subsets. Its boundary operator allows us to define a transport equation equivalent to Belief Propagation. This definition reveals a set of conserved quantities under Belief Propagation and gives new insight on the relationship of its equilibria with the critical points of Bethe free energy.Comment: 14 pages, submitted for the 2019 Geometric Science of Information colloquiu

Three-dimensional structures of the tracheal systems of Anopheles sinensis and Aedes togoi pupae

Mosquitoes act as a vector for the transmission of disease. The World Health Organization has recommended strict control of mosquito larvae because of their few, fixed, and findable features. The respiratory system of mosquito larvae and pupae in the water has a weak point. As aquatic organisms, mosquito larvae and pupae inhale atmosphere oxygen. However, the mosquito pupae have a non-feeding stage, unlike the larvae. Therefore, detailed study on the tracheal system of mosquito pupae is helpful for understanding their survival strategy. In this study, the three-dimensional (3D) structures of the tracheal systems of Anopheles sinensis and Aedes togoi pupae were comparatively investigated using synchrotron X-ray microscopic computed tomography. The respiratory frequencies of the dorsal trunks were also investigated. Interestingly, the pupae of the two mosquito species possess special tracheal systems of which the morphological and functional features are distinctively different. The respiratory frequency of Ae. togoi is higher than that of An. sinensis. These differences in the breathing phenomena and 3D structures of the respiratory systems of these two mosquito species provide an insight into the tracheal systems of mosquito pupae. ? 2017 The Author(s).111Ysciescopu

Local majority dynamics on preferential attachment graphs

Suppose in a graph $G$ vertices can be either red or blue. Let $k$ be odd. At each time step, each vertex $v$ in $G$ polls $k$ random neighbours and takes the majority colour. If it doesn't have $k$ neighbours, it simply polls all of them, or all less one if the degree of $v$ is even. We study this protocol on the preferential attachment model of Albert and Barab\'asi, which gives rise to a degree distribution that has roughly power-law $P(x) \sim \frac{1}{x^{3}}$, as well as generalisations which give exponents larger than $3$. The setting is as follows: Initially each vertex of $G$ is red independently with probability $\alpha < \frac{1}{2}$, and is otherwise blue. We show that if $\alpha$ is sufficiently biased away from $\frac{1}{2}$, then with high probability, consensus is reached on the initial global majority within $O(\log_d \log_d t)$ steps. Here $t$ is the number of vertices and $d \geq 5$ is the minimum of $k$ and $m$ (or $m-1$ if $m$ is even), $m$ being the number of edges each new vertex adds in the preferential attachment generative process. Additionally, our analysis reduces the required bias of $\alpha$ for graphs of a given degree sequence studied by the first author (which includes, e.g., random regular graphs)

Persistence length of a polyelectrolyte in salty water: a Monte-Carlo study

We address the long standing problem of the dependence of the electrostatic persistence length $l_e$ of a flexible polyelectrolyte (PE) on the screening length $r_s$ of the solution within the linear Debye-Huckel theory. The standard Odijk, Skolnick and Fixman (OSF) theory suggests $l_e \propto r_s^2$, while some variational theories and computer simulations suggest $l_e \propto r_s$. In this paper, we use Monte-Carlo simulations to study the conformation of a simple polyelectrolyte. Using four times longer PEs than in previous simulations and refined methods for the treatment of the simulation data, we show that the results are consistent with the OSF dependence $l_e \propto r_s^2$. The linear charge density of the PE which enters in the coefficient of this dependence is properly renormalized to take into account local fluctuations.Comment: 7 pages, 6 figures. Various corrections in text and reference

Attractive Interactions Between Rod-like Polyelectrolytes: Polarization, Crystallization, and Packing

We study the attractive interactions between rod-like charged polymers in solution that appear in the presence of multi-valence counterions. The counterions condensed to the rods exhibit both a strong transversal polarization and a longitudinal crystalline arrangement. At short distances between the rods, the fraction of condensed counterions increases, and the majority of these occupy the region between the rods, where they minimize their repulsive interactions by arranging themselves into packing structures. The attractive interaction is strongest for multivalent counterions. Our model takes into account the hard-core volume of the condensed counterions and their angular distribution around the rods. The hard core constraint strongly suppresses longitudinal charge fluctuations.Comment: 4 figures, uses revtex, psfig and epsf. The new version contains a different introduction, and the bibliography has been expande

Exactly Solvable Pairing Model Using an Extension of Richardson-Gaudin Approach

We introduce a new class of exactly solvable boson pairing models using the technique of Richardson and Gaudin. Analytical expressions for all energy eigenvalues and first few energy eigenstates are given. In addition, another solution to Gaudin's equation is also mentioned. A relation with the Calogero-Sutherland model is suggested.Comment: 9 pages of Latex. In the proceedings of Blueprints for the Nucleus: From First Principles to Collective Motion: A Festschrift in Honor of Professor Bruce Barrett, Istanbul, Turkey, 17-23 May 200