Network growth model with intrinsic vertex fitness

© 2013 American Physical SocietyWe study a class of network growth models with attachment rules governed by intrinsic node fitness. Both the individual node degree distribution and the degree correlation properties of the network are obtained as functions of the network growth rules. We also find analytical solutions to the inverse, design, problems of matching the growth rules to the required (e.g., power-law) node degree distribution and more generally to the required degree correlation function. We find that the design problems do not always have solutions. Among the specific conditions on the existence of solutions to the design problems is the requirement that the node degree distribution has to be broader than a certain threshold and the fact that factorizability of the correlation functions requires singular distributions of the node fitnesses. More generally, the restrictions on the input distributions and correlations that ensure solvability of the design problems are expressed in terms of the analytical properties of their generating functions

The resistance of randomly grown trees

Copyright @ 2011 IOP Publishing Ltd. This is a preprint version of the published article which can be accessed from the link below.An electrical network with the structure of a random tree is considered: starting from a root vertex, in one iteration each leaf (a vertex with zero or one adjacent edges) of the tree is extended by either a single edge with probability p or two edges with probability 1 − p. With each edge having a resistance equal to 1 omega, the total resistance Rn between the root vertex and a busbar connecting all the vertices at the nth level is considered. A dynamical system is presented which approximates Rn, it is shown that the mean value (Rn) for this system approaches (1 + p)/(1 − p) as n → ∞, the distribution of Rn at large n is also examined. Additionally, a random sequence construction akin to a random Fibonacci sequence is used to approximate Rn; this sequence is shown to be related to the Legendre polynomials and its mean is shown to converge with |(Rn) − (1 + p)/(1 − p)| ∼ n−1/2.Engineering and Physical Sciences Research Council (EPSRC

Why does the Engel method work? Food demand, economies of size and household survey methods

Estimates of household size economies are needed for the analysis of poverty and inequality. This paper shows that Engel estimates of size economies are large when household expenditures are obtained by respondent recall but small when expenditures are obtained by daily recording in diaries. Expenditure estimates from recall surveys appear to have measurement errors correlated with household size. As well as demonstrating the fragility of Engel estimates of size economies, these results help resolve a puzzle raised by Deaton and Paxson (1998) about differences between rich and poor countries in the effect of household size on food demand

Norm-dependent Random Matrix Ensembles in External Field and Supersymmetry

The class of norm-dependent Random Matrix Ensembles is studied in the presence of an external field. The probability density in those ensembles depends on the trace of the squared random matrices, but is otherwise arbitrary. An exact mapping to superspace is performed. A transformation formula is derived which gives the probability density in superspace as a single integral over the probability density in ordinary space. This is done for orthogonal, unitary and symplectic symmetry. In the case of unitary symmetry, some explicit results for the correlation functions are derived.Comment: 19 page

Exact Solution of a Drop-push Model for Percolation

Motivated by a computer science algorithm known as `linear probing with hashing' we study a new type of percolation model whose basic features include a sequential `dropping' of particles on a substrate followed by their transport via a `pushing' mechanism. Our exact solution in one dimension shows that, unlike the ordinary random percolation model, the drop-push model has nontrivial spatial correlations generated by the dynamics itself. The critical exponents in the drop-push model are also different from that of the ordinary percolation. The relevance of our results to computer science is pointed out.Comment: 4 pages revtex, 2 eps figure

Growing random sequences

We consider the random sequence x[n] = x[n-1] + yxq, with y > 0, where q = 0, 1,..., n - 1 is chosen randomly from a probability distribution P[n] (q). When all q are chosen with equal probability, i.e. P[n](q) = 1/n, we obtain an exact solution for the mean and the divergence of the second moment as functions of n and y. For y = 1 we examine the divergence of the mean value of x[n], as a function of n, for the random sequences generated by power law and exponential P[n](q) and for the non-random sequence P[n](q) = δ[q,β(n-1)]

Particle detection experiment for Applications Technology Satellite 1 /ATS-1/ Final report

Applications technology satellite particle detection experiment for measuring energy spectra of earth magnetic fiel

First detection of triply-deuterated methanol

We report the first detection of triply-deuterated methanol, with 12 observed transitions, towards the low-mass protostar IRAS 16293-2422, as well as multifrequency observations of 13CH3OH, used to derive the column density of the main isotopomer CH3OH. The derived fractionation ratio [CD3OH]/[CH3OH] averaged on a 10'' beam is 1.4%. Together with previous CH2DOH and CHD2OH observations, the present CD3OH observations are consistent with a formation of methanol on grain surfaces, if the atomic D/H ratio is 0.1 to 0.3 in the accreting gas. Such a high atomic ratio can be reached in the frame of gas-phase chemical models including all deuterated isotopomers of H3+.Comment: Accepted by A&

Bosonic Description of Spinning Strings in 2+12+1 Dimensions

We write down a general action principle for spinning strings in 2+1 dimensional space-time without introducing Grassmann variables. The action is written solely in terms of coordinates taking values in the 2+1 Poincare group, and it has the usual string symmetries, i.e. it is invariant under a) diffeomorphisms of the world sheet and b) Poincare transformations. The system can be generalized to an arbitrary number of space-time dimensions, and also to spinning membranes and p-branes.Comment: Latex, 12 page