Novel non-equilibrium critical behavior in unidirectionally coupled stochastic processes

Phase transitions from an active into an absorbing, inactive state are generically described by the critical exponents of directed percolation (DP), with upper critical dimension d_c = 4. In the framework of single-species reaction-diffusion systems, this universality class is realized by the combined processes A -> A + A, A + A -> A, and A -> \emptyset. We study a hierarchy of such DP processes for particle species A, B,..., unidirectionally coupled via the reactions A -> B, ... (with rates \mu_{AB}, ...). When the DP critical points at all levels coincide, multicritical behavior emerges, with density exponents \beta_i which are markedly reduced at each hierarchy level i >= 2. This scenario can be understood on the basis of the mean-field rate equations, which yield \beta_i = 1/2^{i-1} at the multicritical point. We then include fluctuations by using field-theoretic renormalization group techniques in d = 4-\epsilon dimensions. In the active phase, we calculate the fluctuation correction to the density exponent for the second hierarchy level, \beta_2 = 1/2 - \epsilon/8 + O(\epsilon^2). Monte Carlo simulations are then employed to determine the values for the new scaling exponents in dimensions d<= 3, including the critical initial slip exponent. Our theory is connected to certain classes of growth processes and to certain cellular automata, as well as to unidirectionally coupled pair annihilation processes. We also discuss some technical and conceptual problems of the loop expansion and their possible interpretation.Comment: 29 pages, 19 figures, revtex, 2 columns, revised Jan 1995: minor changes and additions; accepted for publication in Phys. Rev.

Magnetic phases and reorientation transitions in antiferromagnetically coupled multilayers

In antiferromagnetically coupled superlattices grown on (001) faces of cubic substrates, e.g. based on materials combinations as Co/Cu, Fe/Si, Co/Cr, or Fe/Cr, the magnetic states evolve under competing influence of bilinear and biquadratic exchange interactions, surface-enhanced four-fold in-plane anisotropy, and specific finite-size effects. Using phenomenological (micromagnetic) theory, a comprehensive survey of the magnetic states and reorientation transitions has been carried out for multilayer systems with even number of ferromagnetic sub-layers and magnetizations in the plane. In two-layer systems (N=2) the phase diagrams in dependence on components of the applied field in the plane include ``swallow-tail'' type regions of (metastable) multistate co-existence and a number of continuous and discontinuous reorientation transitions induced by radial and transversal components of the applied field. In multilayers (N \ge 4) noncollinear states are spatially inhomogeneous with magnetization varying across the multilayer stack. For weak four-fold anisotropy the magnetic states under influence of an applied field evolve by a complex continuous reorientation into the saturated state. At higher anisotropy they transform into various inhomogeneous and asymmetric structures. The discontinuous transitions between the magnetic states in these two-layers and multilayers are characterized by broad ranges of multi-phase coexistence of the (metastable) states and give rise to specific transitional domain structures.Comment: Manuscript 34 pages, 14 figures; submitted for publicatio

Noise-induced behaviors in neural mean field dynamics

The collective behavior of cortical neurons is strongly affected by the presence of noise at the level of individual cells. In order to study these phenomena in large-scale assemblies of neurons, we consider networks of firing-rate neurons with linear intrinsic dynamics and nonlinear coupling, belonging to a few types of cell populations and receiving noisy currents. Asymptotic equations as the number of neurons tends to infinity (mean field equations) are rigorously derived based on a probabilistic approach. These equations are implicit on the probability distribution of the solutions which generally makes their direct analysis difficult. However, in our case, the solutions are Gaussian, and their moments satisfy a closed system of nonlinear ordinary differential equations (ODEs), which are much easier to study than the original stochastic network equations, and the statistics of the empirical process uniformly converge towards the solutions of these ODEs. Based on this description, we analytically and numerically study the influence of noise on the collective behaviors, and compare these asymptotic regimes to simulations of the network. We observe that the mean field equations provide an accurate description of the solutions of the network equations for network sizes as small as a few hundreds of neurons. In particular, we observe that the level of noise in the system qualitatively modifies its collective behavior, producing for instance synchronized oscillations of the whole network, desynchronization of oscillating regimes, and stabilization or destabilization of stationary solutions. These results shed a new light on the role of noise in shaping collective dynamics of neurons, and gives us clues for understanding similar phenomena observed in biological networks

Dominant next-to-leading order QCD corrections to Higgs plus three jet production in vector-boson fusion

We present the calculation of the dominant next to leading order QCD corrections to Higgs boson production in association with three jets via vector boson fusion in the form of a NLO parton-level Monte Carlo program. QCD corrections to integrated cross sections are modest, while the shapes of some kinematical distributions change appreciably at NLO. Scale uncertainties are shown to be reduced at NLO for the total cross section and for distributions. We consider a central jet veto at the LHC and analyze the veto probability for typical vector boson fusion cuts. Scale uncertainties of the veto probability are sufficiently small at NLO for precise Higgs coupling measurements at the LHC.Comment: 40 pages, 17 figures, 2 tables, published versio

More is different: 50 years of nuclear BCS

Many of the concepts which are at the basis of the development associated with a quantitative treatment of the variety of phenomena associated with the spontaneous breaking of gauge symmetry in nuclei have been instrumental in connection with novel studies of soft matter, namely of protein evolution and protein folding. Although the route to these subjects and associated development does not necessarily imply the nuclear physics connection, such a connection has proven qualitatively and quantitatively inspiring. In particular to model protein evolution in terms of the alignment of quasispins displaying twenty different projections, one for each of the twenty amino acids occurring in nature, and the associated symmetry breaking in information (sequence) space. Emergent properties of the corresponding phase transition are domain walls which stabilize local elementary structures (LES), few groups of 10-20 aminoacids which become structured already in the denatured state provide the molecular recognition directing protein folding. In fact, their docking is closely related to the transition state of the process. While the two-step, yes or no, folding process, does not provide direct information concerning LES, one can force LES from virtual to become real, observable final state entities. Getting again inspiration from the nuclear case (virtual processes contributing to pair correlations can be forced to become real with the help of a probe which itself changes particle number by two), one would expect that to make real virtual LES, that is segments of the protein which already at an early stage of the folding process flicker in and out of their native conformation, one needs a probe which itself displays a similar behaviour. Peptides displaying a sequence identical to LES are such probes.Comment: Contribution to the Volume 50 years of Nuclear BCS edited by World Scientifi

Transformation of UML Behavioral Diagrams to Support Software Model Checking

Unified Modeling Language (UML) is currently accepted as the standard for modeling (object-oriented) software, and its use is increasing in the aerospace industry. Verification and Validation of complex software developed according to UML is not trivial due to complexity of the software itself, and the several different UML models/diagrams that can be used to model behavior and structure of the software. This paper presents an approach to transform up to three different UML behavioral diagrams (sequence, behavioral state machines, and activity) into a single Transition System to support Model Checking of software developed in accordance with UML. In our approach, properties are formalized based on use case descriptions. The transformation is done for the NuSMV model checker, but we see the possibility in using other model checkers, such as SPIN. The main contribution of our work is the transformation of a non-formal language (UML) to a formal language (language of the NuSMV model checker) towards a greater adoption in practice of formal methods in software development.Comment: In Proceedings FESCA 2014, arXiv:1404.043

Fold-Hopf Bursting in a Model for Calcium Signal Transduction

We study a recent model for calcium signal transduction. This model displays spiking, bursting and chaotic oscillations in accordance with experimental results. We calculate bifurcation diagrams and study the bursting behaviour in detail. This behaviour is classified according to the dynamics of separated slow and fast subsystems. It is shown to be of the Fold-Hopf type, a type which was previously only described in the context of neuronal systems, but not in the context of signal transduction in the cell.Comment: 13 pages, 5 figure