Exponents appearing in heterogeneous reaction-diffusion models in one dimension

We study the following 1D two-species reaction diffusion model : there is a small concentration of B-particles with diffusion constant $D_B$ in an homogenous background of W-particles with diffusion constant $D_W$; two W-particles of the majority species either coagulate ($W+W \longrightarrow W$) or annihilate ($W+W \longrightarrow \emptyset$) with the respective probabilities $p_c=(q-2)/(q-1)$ and $p_a=1/(q-1)$; a B-particle and a W-particle annihilate ($W+B \longrightarrow \emptyset$) with probability 1. The exponent $\theta(q,\lambda=D_B/D_W)$ describing the asymptotic time decay of the minority B-species concentration can be viewed as a generalization of the exponent of persistent spins in the zero-temperature Glauber dynamics of the 1D $q$-state Potts model starting from a random initial condition : the W-particles represent domain walls, and the exponent $\theta(q,\lambda)$ characterizes the time decay of the probability that a diffusive "spectator" does not meet a domain wall up to time $t$. We extend the methods introduced by Derrida, Hakim and Pasquier ({\em Phys. Rev. Lett.} {\bf 75} 751 (1995); Saclay preprint T96/013, to appear in {\em J. Stat. Phys.} (1996)) for the problem of persistent spins, to compute the exponent $\theta(q,\lambda)$ in perturbation at first order in $(q-1)$ for arbitrary $\lambda$ and at first order in $\lambda$ for arbitrary $q$.Comment: 29 pages. The three figures are not included, but are available upon reques

Geometrical aspects of isoscaling

The property of isoscaling in nuclear fragmentation is studied using a simple bond percolation model with ``isospin'' added as an extra degree of freedom. It is shown analytically, first, that isoscaling is expected to exist in such a simple model with the only assumption of fair sampling with homogeneous probabilities. Second, numerical percolations of hundreds of thousands of grids of different sizes and with different $N$ to $Z$ ratios confirm this prediction with remarkable agreement. It is thus concluded that isoscaling emerges from the simple assumption of fair sampling with homogeneous probabilities, a requirement which, if put in the nomenclature of the minimum information theory, translates simply into the existence of equiprobable configurations in maximum entropy states

The Thermodynamics of Quarks and Gluons

This is an introduction to the study of strongly interacting matter. We survey its different possible states and discuss the transition from hadronic matter to a plasma of deconfined quarks and gluons. Following this, we summarize the results provided by lattice QCD finite temperature and density, and then investigate the nature of the deconfinement transition. Finally we give a schematic overview of possible ways to study the properties of the quark-gluon plasma.Comment: 19 pages, 21 figures; lecture given at the QGP Winter School, Jaipur/India, Feb.1-3, 2008; to appear in Springer Lecture Notes in Physic

Accretion, Outflows, and Winds of Magnetized Stars

Many types of stars have strong magnetic fields that can dynamically influence the flow of circumstellar matter. In stars with accretion disks, the stellar magnetic field can truncate the inner disk and determine the paths that matter can take to flow onto the star. These paths are different in stars with different magnetospheres and periods of rotation. External field lines of the magnetosphere may inflate and produce favorable conditions for outflows from the disk-magnetosphere boundary. Outflows can be particularly strong in the propeller regime, wherein a star rotates more rapidly than the inner disk. Outflows may also form at the disk-magnetosphere boundary of slowly rotating stars, if the magnetosphere is compressed by the accreting matter. In isolated, strongly magnetized stars, the magnetic field can influence formation and/or propagation of stellar wind outflows. Winds from low-mass, solar-type stars may be either thermally or magnetically driven, while winds from massive, luminous O and B type stars are radiatively driven. In all of these cases, the magnetic field influences matter flow from the stars and determines many observational properties. In this chapter we review recent studies of accretion, outflows, and winds of magnetized stars with a focus on three main topics: (1) accretion onto magnetized stars; (2) outflows from the disk-magnetosphere boundary; and (3) winds from isolated massive magnetized stars. We show results obtained from global magnetohydrodynamic simulations and, in a number of cases compare global simulations with observations.Comment: 60 pages, 44 figure

An Opinion Dynamics Model for the Diffusion of Innovations

We study the dynamics of the adoption of new products by agents with continuous opinions and discrete actions (CODA). The model is such that the refusal in adopting a new idea or product is increasingly weighted by neighbor agents as evidence against the product. Under these rules, we study the distribution of adoption times and the final proportion of adopters in the population. We compare the cases where initial adopters are clustered to the case where they are randomly scattered around the social network and investigate small world effects on the final proportion of adopters. The model predicts a fat tailed distribution for late adopters which is verified by empirical data.Comment: 14 pages, 8 figures, revised text, a new section with empirical evidence has been adde

Advancing biological understanding and therapeutics discovery with small-molecule probes

Small-molecule probes can illuminate biological processes and aid in the assessment of emerging therapeutic targets by perturbing biological systems in a manner distinct from other experimental approaches. Despite the tremendous promise of chemical tools for investigating biology and disease, small-molecule probes were unavailable for most targets and pathways as recently as a decade ago. In 2005, the NIH launched the decade-long Molecular Libraries Program with the intent of innovating in and broadening access to small-molecule science. This Perspective describes how novel small-molecule probes identified through the program are enabling the exploration of biological pathways and therapeutic hypotheses not otherwise testable. These experiences illustrate how small-molecule probes can help bridge the chasm between biological research and the development of medicines but also highlight the need to innovate the science of therapeutic discovery

Robust analysis of silhouettes by morphological size distributions

peer reviewedWe address the topic of real-time analysis and recognition of silhouettes. The method that we propose first produces object features obtained by a new type of morphological operators, which can be seen as an extension of existing granulometric filters, and then insert them into a tailored classification scheme. Intuitively, given a binary segmented image, our operator produces the set of all the largest rectangles that can be wedged inside any connected component of the image. The latter are obtained by a standard background subtraction technique and morphological filtering. To classify connected components into one of the known object categories, the rectangles of a connected component are submitted to a machine learning algorithm called EXtremely RAndomized trees (Extra-trees). The machine learning algorithm is fed with a static database of silhouettes that contains both positive and negative instances. The whole process, including image processing and rectangle classification, is carried out in real-time. Finally we evaluate our approach on one of today's hot topics: the detection of human silhouettes. We discuss experimental results and show that our method is stable and computationally effective. Therefore, we assess that algorithms like ours introduce new ways for the detection of humans in video sequences