Finding a Spherically Symmetric Cosmology from Observations in Observational Coordinates -- Advantages and Challenges

One of the continuing challenges in cosmology has been to determine the large-scale space-time metric from observations with a minimum of assumptions -- without, for instance, assuming that the universe is almost Friedmann-Lema\^{i}tre-Robertson-Walker (FLRW). If we are lucky enough this would be a way of demonstrating that our universe is FLRW, instead of presupposing it or simply showing that the observations are consistent with FLRW. Showing how to do this within the more general spherically symmetric, inhomogeneous space-time framework takes us a long way towards fulfilling this goal. In recent work researchers have shown how this can be done both in the traditional Lema\^{i}tre-Tolman-Bondi (LTB) 3 + 1 coordinate framework, and in the observational coordinate (OC) framework. In this paper we investigate the stability of solutions, and the use of data in the OC field equations including their time evolution and compare both approaches with respect to the singularity problem at the maximum of the angular-diameter distance, the stability of solutions, and the use of data in the field equations. This allows a more detailed account and assessment of the OC integration procedure, and enables a comparison of the relative advantages of the two equivalent solution frameworks. Both formulations and integration procedures should, in principle, lead to the same results. However, as we show in this paper, the OC procedure manifests certain advantages, particularly in the avoidance of coordinate singularities at the maximum of the angular-diameter distance, and in the stability of the solutions obtained. This particular feature is what allows us to do the best fitting of the data to smooth data functions and the possibility of constructing analytic solutions to the field equations.Comment: 31 page

Two-dimensional SIR epidemics with long range infection

We extend a recent study of susceptible-infected-removed epidemic processes with long range infection (referred to as I in the following) from 1-dimensional lattices to lattices in two dimensions. As in I we use hashing to simulate very large lattices for which finite size effects can be neglected, in spite of the assumed power law $p({\bf x})\sim |{\bf x}|^{-\sigma-2}$ for the probability that a site can infect another site a distance vector ${\bf x}$ apart. As in I we present detailed results for the critical case, for the supercritical case with $\sigma = 2$, and for the supercritical case with $0< \sigma < 2$. For the latter we verify the stretched exponential growth of the infected cluster with time predicted by M. Biskup. For $\sigma=2$ we find generic power laws with $\sigma-$dependent exponents in the supercritical phase, but no Kosterlitz-Thouless (KT) like critical point as in 1-d. Instead of diverging exponentially with the distance from the critical point, the correlation length increases with an inverse power, as in an ordinary critical point. Finally we study the dependence of the critical exponents on $\sigma$ in the regime $0<\sigma <2$, and compare with field theoretic predictions. In particular we discuss in detail whether the critical behavior for $\sigma$ slightly less than 2 is in the short range universality class, as conjectured recently by F. Linder {\it et al.}. As in I we also consider a modified version of the model where only some of the contacts are long range, the others being between nearest neighbors. If the number of the latter reaches the percolation threshold, the critical behavior is changed but the supercritical behavior stays qualitatively the same.Comment: 14 pages, including 29 figure

Large-scale production of cellulose-binding domains : adsorption studies using CBD-FITC conjugates

A method for the gram-scale production of cellulose-binding domains (CBD) through the proteolytic digestion of a commercial nzymatic preparation (Celluclast) was developed. The CBD obtained, isolated from Trichoderma reesei cellobiohydrolase I, is highly pure and heavily glycosylated. The purified peptide has a molecular weight of 8.43 kDa, comprising the binding module, a part of the linker, and about 30% glycosidic moiety. Its properties may thus be different from recombinant ones expressed in bacteria. CBDfluorescein isothiocyanate conjugates were used to study the CBD-cellulose interaction. The presence of fluorescent peptides adsorbed on crystalline and amorphous cellulose fibers suggests that amorphous regions have a higher concentration of binding sites. The adsorption is reversible, but desorption is a very slow process.Fundação para a Ciência e a Tecnologia (FCT

A new proposal for Galactic dark matter: Effect of f(T) gravity

It is still a challenging problem to the theoretical physicists to know the exact nature of the galactic dark matter which causes the galactic rotational velocity to be more or less a constant. We have proposed that the dark matter as an effect of f(T) gravity. Assuming the flat rotation curves as input we have shown that f(T) gravity can explain galactic dynamics. Here, we don' have to introduce dark matter. Spacetime metric inspired by f(T) gravity describes the region up to which the tangential velocity of the test particle is constant. This inherent property appears to be enough to produce stable circular orbits as well as attractive gravity.Comment: 7 pages and 1 figure. Minor corrections are made. Accepted for publication in Int.J.Theor.Phy

The Business Model: Recent Developments and Future Research

This article provides a broad and multifaceted review of the received literature on business models in which the authors examine the business model concept through multiple subject-matter lenses. The review reveals that scholars do not agree on what a business model is and that the literature is developing largely in silos, according to the phenomena of interest of the respective researchers. However, the authors also found emerging common themes among scholars of business models. Specifically, (1) the business model is emerging as a new unit of analysis; (2) business models emphasize a system-level, holistic approach to explaining how firms “do business”; (3) firm activities play an important role in the various conceptualizations of business models that have been proposed; and (4) business models seek to explain how value is created, not just how it is captured. These emerging themes could serve as catalysts for a more unified study of business models