A multi-cluster,n-particle generalization of the three-particle faddeev wavefunction equations

Recent work applying certain forms of many-body scattering theory to problems such as molecular potential energy surfaces and equations for nonequilibrium statistical mechanics indicates that a formulation of the theory based directly on multi-cluster, n-particle, wave function components could be of some utility. Such a formulation is derived in this paper using techniques from the Baer-Kouri-Levin-Tobocman and Bencze-Redish-Sloan-Polyzou theories of multi-particle scattering. It is based on components corresponding to the various multi-cluster partitions of an n-particle scattering system and is a generalization of the three-body Faddeev wave function formalism, to which it reduces when n = 3. Except for the full breakup partition, which does not enter the equations, the new components are defined for all possible m-cluster partitions of the n-particles, 2 ≤ m ≤ n ? 1. The sum of all the components yields the solution to the Schrödinger equation for scattering and either the Schrödinger equation solution or an easily identified spurious solution in the case of bound states. Both the two-cluster components and two-cluster transition operators are shown to be solutions of equations involving quantities carrying only two-cluster partition labels. Discussions of the Born term and a multiple scattering representation for the non-rearrangement transition operator and the inclusion of distortion operators in the formalism are also included.     

Phase locking in networks of synaptically coupled McKean relaxation oscillators

We use geometric dynamical systems methods to derive phase equations for networks of weakly connected McKean relaxation oscillators. We derive an explicit formula for the connection function when the oscillators are coupled with chemical synapses modeled as the convolution of some input spike train with an appropriate synaptic kernel. The theory allows the systematic investigation of the way in which a slow recovery variable can interact with synaptic time scales to produce phase-locked solutions in networks of pulse coupled neural relaxation oscillators. The theory is exact in the singular limit that the fast and slow time scales of the neural oscillator become effectively independent. By focusing on a pair of mutually coupled McKean oscillators with alpha function synaptic kernels, we clarify the role that fast and slow synapses of excitatory and inhibitory type can play in producing stable phase-locked rhythms. In particular we show that for fast excitatory synapses there is coexistence of a stable synchronous, a stable anti-synchronous, and one stable asynchronous solution. For slower synapses the anti-synchronous solution can lose stability, whilst for even slower synapses it can regain stability. The case of inhibitory synapses is similar up to a reversal of the stability of solution branches. Using a return-map analysis the case of strong pulsatile coupling is also considered. In this case it is shown that the synchronous solution can co-exist with a continuum of asynchronous states.     

Epidemic outbreaks in growing scale-free networks with local structure

The class of generative models has already attracted considerable interest from researchers in recent years and much expanded the original ideas described in BA model. Most of these models assume that only one node per time step joins the network. In this paper, we grow the network by adding n interconnected nodes as a local structure into the network at each time step with each new node emanating m new edges linking the node to the preexisting network by preferential attachment. This successfully generates key features observed in social networks. These include power-law degree distribution p_k∼k^−(3+μ), where μ=(n−1)/m is a tuning parameter defined as the modularity strength of the network, nontrivial clustering, assortative mixing, and modular structure. Moreover, all these features are dependent in a similar way on the parameter μ. We then study the susceptible-infected epidemics on this network with identical infectivity, and find that the initial epidemic behavior is governed by both of the infection scheme and the network structure, especially the modularity strength. The modularity of the network makes the spreading velocity much lower than that of the BA model. On the other hand, increasing the modularity strength will accelerate the propagation velocity.     

The exterior gravitational field of a charged spinning source in the poincaré gauge theory: A Kerr-newman metric with dynamic torsion

We present a new exact solution of the Poincaré gauge theory, namely a charged Kerr-NUT metric with an effective cosmological constant which is consistently coupled to a dynamic torsion field. The solution is given in terms of an orthonormal basis in Boyer-Lindquist coordinates and depends on the constants m₀ (mass), j₀ (angular momentum), q₀ (electric charge), and n₀ (NUT parameter). Whereas m₀,j₀, and q₀ can be specified arbitrarily, the NUT parameter and the effective cosmological constant are determined by the coupling constants of our model. The torsion of the solution is centered around the coordinate origin and vanishes asymptotically for large radial distance. For n₀=0, we find the exterior gravitational field of a charged spinning source.     

Fuzzy analysis of community detection in complex networks

A snowball algorithm is proposed to find community structures in complex networks by introducing the definition of community core and some quantitative conditions. A community core is first constructed, and then its neighbors, satisfying the quantitative conditions, will be tied to this core until no node can be added. Subsequently, one by one, all communities in the network are obtained by repeating this process. The use of the local information in the proposed algorithm directly leads to the reduction of complexity. The algorithm runs in O(n+m) time for a general network and O(n) for a sparse network, where n is the number of vertices and m is the number of edges in a network. The algorithm fast produces the desired results when applied to search for communities in a benchmark and five classical real-world networks, which are widely used to test algorithms of community detection in the complex network. Furthermore, unlike existing methods, neither global modularity nor local modularity is utilized in the proposal. By converting the considered problem into a graph, the proposed algorithm can also be applied to solve other cluster problems in data mining.     

A Cube Dismantling Problem Related to Bootstrap Percolation

An n×n×?×n hypercube is made from n ^d unit hypercubes. Two unit hypercubes are neighbours if they share a (d?1)-dimensional face. In each step of a dismantling process, we remove a unit hypercube that has precisely d neighbours. A move is balanced if the neighbours are in d orthogonal directions. In the extremal case, there are n ^d?1 independent unit hypercubes left at the end of the dismantling. We call this set of hypercubes a solution. If a solution is projected in d orthogonal directions and we get the entire [n] ^d?1 hypercube in each direction, then the solution is perfect. We show that it is possible to use a greedy algorithm to test whether a set of hypercubes forms a solution. Perfect solutions turn out to be precisely those which can be reached using only balanced moves. Every perfect solution corresponds naturally to a Latin hypercube. However, we show that almost all Latin hypercubes do not correspond to solutions. In three dimensions, we find at least n perfect solutions for every n, and we use our greedy algorithm to count the perfect solutions for n??6. We also construct an infinite family of imperfect solutions and show that the total size of its three orthogonal projections is asymptotic to the minimum possible value. Our results solve several conjectures posed in a proceedings paper by Barát, Korondi and Varga. If our dismantling process is reversed we get a build-up process very closely related to well-studied models of bootstrap percolation. We show that in an important special case our build-up reaches the same maximal position as bootstrap percolation.     

Effects of synaptic depression and adaptation on spatiotemporal dynamics of an excitatory neuronal network

We analyze the spatiotemporal dynamics of a system of integro-differential equations that describes a one-dimensional excitatory neuronal network with synaptic depression and spike frequency adaptation. Physiologically suggestive forms are used for both types of negative feedback. We also consider the effects of employing two different types of firing rate function, a Heaviside step function and a piecewise linear function. We first derive conditions for the existence of traveling fronts and pulses in the case of a Heaviside step firing rate, and show that adaptation plays a relatively minor role in determining the characteristics of traveling waves. We then derive conditions for the existence and stability of stationary pulses or bumps, and show that a purely excitatory network with synaptic depression cannot support stable bumps. However, bumps do not exist in the presence of adaptation. Finally, in the case of a piecewise linear firing rate function, we show numerically that the network also supports self-sustained oscillations between an Up state and a Down state, in which a spatially localized oscillating core periodically emits pulses at each cycle.     

Hydrogen induced change of the atomic magnetic moments in Fe/V-superlattices

We have studied the change of the magnetic saturation of (Fe_n/V_m)₃₀ superlattices (30 periods with n monolayers of Fe and m monolayers of V) upon loading with hydrogen using a highly sensitive Faraday balance and in situ loading with hydrogen. We find that the measured magnetic saturation moment for all samples increases with the hydrogen. The measured magnetic saturation moment for all samples increases with the hydrogen concentration. For the superlattice (Fe₃/V₁₁)₃₀ we find the maximum increase, corresponding to a change of the atomic magnetic moments of +0.35 μ_B/Fe atom. We attribute this remarkable effect to a change of the Fe and V magnetic moments at the interfaces caused by the charge transfer from the hydrogen atoms to the vanadium d bands.     

Improved fictitious charge method for calculations of electric potential and field generated by point-to-plane electrodes

In the framework of standard tip-to-plane electrode geometry favorable to corona streamer discharge development at atmospheric pressure, this work is devoted to the improvement of fictitious charge method for calculations of electric potential and field repartition when the tip is powered by a DC voltage. It is in fact dedicated to implement the image charge method (generally used in plane-to-plane electrodes) in the case of a point-to-plane geometry. The numerical method is based on the solution an open system of n equations with m unknowns (n >> m) where m is the number of fictitious charges and n the number of contours at the surface of the tip electrode defining the boundary conditions. This numerical technique can accurately interpolate the shape of the electrode tip whatever its geometry and hence allows us to accurately calculate the electric potential and field even at a position very close to the electrode. It is noteworthy that the solution of such open system of equations cannot be obtained from conventional techniques (Cramer, Gauss, matrix inversion, etc.). We used the method of least squares which enables us to close the equation systems and to find the optimal solution fulfilling all the required boundary conditions. The present method is therefore based on the coupling between the conventional method of fictitious charges using image charge method and the optimization by the Least Squares Method. The results of simulation show that the punctual fictitious charges have given the most accurate results when the electrode has symmetry of revolution like the present geometry of a pen shape anode cylinder ended by a sharp tip set in front of cathode plane.     

Ab initio study of formation, migration and binding properties of helium-vacancy clusters in aluminum

Ab initio calculations based on density functional theory have been performed to study the dissolution and migration of helium, and the stability of small helium-vacancy clusters He_nV_m (n, m=0-4) in aluminum. The results indicate that the octahedral configuration is more stable than the tetrahedral. Interstitial helium atoms are predicted to have attractive interactions and jump between two octahedral sites via an intermediate tetrahedral site with low migration energy. The binding energies of an interstitial He atom and an isolated vacancy to a He_nV_m cluster are also obtained from the calculated formation energies of the clusters. We find that the di- and tri-vacancy clusters are not stable, but He atoms can increase the stability of vacancy clusters.     

On the dynamical structure of the Dicke maser model

For suitable states of the Dicke maser model we study the time evolution of the mean photon number n(t) in the limit N → ∞. Here N is the number of maser active atoms. Our starting point is a well-tuned cavity with only one mode of the radiation field excited. Introducing new dynamical variables we are able to exploit fully the conservation laws so as to get a simple but completely rigorous solution. We find that n(t) is periodic, and given by a Weierstrassian elliptic function, provided a net polarization is present in the cavity. No approximation is involved.     

Exact solution of the O(n) model on a random lattice

We present an exact solution of the O(n) model on a random lattice. The coupling constant space of our model is parametrized in terms of a set of moment variables and the same type of universality with respect to the potential as observed for the one-matrix model is found. In addition we find a large degree of universality with respect to n; namely for n gE ] − 2,2[ the solution can be presented in a form which is valid not only for any potential, but also for any n (not necessarily rational). The cases n = ±2 are treated separately. We give explicit expressions for the genus-zero contribution to the one- and two-loop correlators as well as for the genus-one contribution to the one-loop correlator and the free energy. It is shown how one can obtain from these results any multi-loop correlator and the free energy to any genus and the structure of the higher-genera contributions is described. Furthermore we describe how the calculation of the higher-genera contributions can be pursued in the scaling limit.     

The Jacobi map

This paper defines nth order Jacobi fields to be solutions to a second-order nonlinear differential equation defined by the Jacobi map. nth order Jacobi fields arise naturally as acceleration vector fields of geodesic variations. As a main theorem we prove necessity and sufficiency conditions for an nth order Jacobi field to be the acceleration vector field of a variation of geodesics normal to a submanifold. An m geodesic, m ≥ 2, is a smooth curve whose mth covariant derivative vanishes. We prove an index theorem giving bounds for the total m focal multiplicity along an m geodesic m normal to a submanifold in a flat manifold.     

A glycine receptor is involved in the organization of swimming movements in an invertebrate chordate

Background  

Rhythmic motor patterns for locomotion in vertebrates are generated in spinal cord neural networks known as spinal Central Pattern Generators (CPGs). A key element in pattern generation is the role of glycinergic synaptic transmission by interneurons that cross the cord midline and inhibit contralaterally-located excitatory neurons. The glycinergic inhibitory drive permits alternating and precisely timed motor output during locomotion such as walking or swimming. To understand better the evolution of this system we examined the physiology of the neural network controlling swimming in an invertebrate chordate relative of vertebrates, the ascidian larva Ciona intestinalis.     

Diffusive capture processes for information search

We show how effectively the diffusive capture processes (DCP) on complex networks can be applied to information search in the networks. Numerical simulations show that our method generates only 2% of traffic compared with the most popular flooding-based query-packet-forwarding (FB) algorithm. We find that the average searching time, 〈T〉, of the our model is more scalable than another well known n-random walker model and comparable to the FB algorithm both on real Gnutella network and scale-free networks with γ=2.4. We also discuss the possible relationship between 〈T〉 and 〈k²〉, the second moment of the degree distribution of the networks.     

The instanton vacuum of generalized CP models

It has recently been pointed out that the existence of massless chiral edge excitations has important strong coupling consequences for the topological concept of an instanton vacuum. In the first part of this paper we elaborate on the effective action for “edge excitations” in the Grassmannian U (m + n)/U (m) × U (n) non-linear sigma model in the presence of the θ term. This effective action contains complete information on the low energy dynamics of the system and defines the renormalization of the theory in an unambiguous manner. In the second part of this paper we revisit the instanton methodology and embark on the non-perturbative aspects of the renormalization group including the anomalous dimension of mass terms. The non-perturbative corrections to both the β and γ functions are obtained while avoiding the technical difficulties associated with the idea of constrained instantons. In the final part of this paper we present the detailed consequences of our computations for the quantum critical behavior at θ = π. In the range 0 ? m, n ? 1 we find quantum critical behavior with exponents that vary continuously with varying values of m and n. Our results display a smooth interpolation between the physically very different theories with m = n = 0 (disordered electron gas, quantum Hall effect) and m = n = 1 (O (3) non-linear sigma model, quantum spin chains) respectively, in which cases the critical indices are known from other sources. We conclude that instantons provide not only a qualitative assessment of the singularity structure of the theory as a whole, but also remarkably accurate numerical estimates of the quantum critical details (critical indices) at θ = π for varying values of m and n.     

Stability of bumps in piecewise smooth neural fields with nonlinear adaptation

We study the linear stability of stationary bumps in piecewise smooth neural fields with local negative feedback in the form of synaptic depression or spike frequency adaptation. The continuum dynamics is described in terms of a nonlocal integrodifferential equation, in which the integral kernel represents the spatial distribution of synaptic weights between populations of neurons whose mean firing rate is taken to be a Heaviside function of local activity. Discontinuities in the adaptation variable associated with a bump solution means that bump stability cannot be analyzed by constructing the Evans function for a network with a sigmoidal gain function and then taking the high-gain limit. In the case of synaptic depression, we show that linear stability can be formulated in terms of solutions to a system of pseudo-linear equations. We thus establish that sufficiently strong synaptic depression can destabilize a bump that is stable in the absence of depression. These instabilities are dominated by shift perturbations that evolve into traveling pulses. In the case of spike frequency adaptation, we show that for a wide class of perturbations the activity and adaptation variables decouple in the linear regime, thus allowing us to explicitly determine stability in terms of the spectrum of a smooth linear operator. We find that bumps are always unstable with respect to this class of perturbations, and destabilization of a bump can result in either a traveling pulse or a spatially localized breather.     

On the periodic orbits of a strongly chaotic system

A point particle sliding freely on a two-dimensional surface of constant negative curvature (Hadamard-Gutzwiller model) exemplifies the simplest chaotic Hamiltonian system. Exploiting the close connection between hyperbolic geometry and the group SU(1,1)/⦅±1⦆, we construct an algorithm (symboliv dynamics), which generates the periodic orbits of the system. For the simplest compact Riemann surface having as its fundamental group the “octagon group”, we present an enumeration of more than 206 million periodic orbits. For the length of the nth primitive periodic orbit we find a simple expression in terms of algebraic numbers of the form m + √2n (m, nϵN are governed by a particular Beatty sequence), which reveals a strange arithmetical structure of chaos. Knowledge of the length spectrum is crucial for quantization via the Selberg trace formula (periodic orbit theory), which in turn is expected to unravel the mystery of quantum chaos.