Deformed Ginibre ensembles and integrable systems

We consider three Ginibre ensembles (real, complex and quaternion-real) with deformed measures and relate them to known integrable systems by presenting partition functions of these ensembles in form of fermionic expectation values. We also introduce double deformed Dyson–Wigner ensembles and compare their fermionic representations with those of Ginibre ensembles.     

Quantum Information as a General Paradigm

Quantum–mechanical systems may be understood in terms of information. When they interact, they modify the information they carry or represent in two, and only two, ways: by selecting a part of the initial amount of (potential) information and by sharing information with other systems. As a consequence, quantum systems are informationally shielded. These features are shown to be general features of nature. In particular, it is shown that matter arises from quantum–mechanical processes through the constitution of larger ensembles that share some information while living organisms make use of a special form of information selection.     

Stimulus-induced response patterns of medium-embedded neurons

Neuronal ensembles in living organisms are often embedded in a media that provides additional interaction pathways and autoregulation. The underlying mechanisms include but are not limited to modulatory activity of some distantly propagated neuromediators like serotonin, variation of extracellular potassium concentration in brain tissue, and calcium waves propagation in networks of astrocytes. Interaction of these diverse processes can lead to formation of complex spatiotemporal patterns, both self-sustained or triggered by external signal. Besides network effects, many dynamical features of such systems originate from reciprocal interaction between single neuron and surrounding medium. In the present paper we study the response of such systems to the application of a single stimulus pulse. We use a minimal mathematical model representing a forced excitable unit that is embedded in a diffusive or (spatially inhomogeneous) excitable medium. We illustrate three different mechanisms for the formation of response patterns: (i) self-sustained depolarization, (ii) propagation of depolarization due to “nearest-neighbor” networks, and (iii) re-entrant waves.     

The influence of interparticle interaction on magnetization curves of nano-and microcrystal ensembles

Reconstruction of magnetization curves for real close-packed systems of highly anisotropic ferrimagnetic BaFe₁₂O₁₉ single-domain nano-and microcrystals is carried out on the basis of the results of a study of interparticle magnetic interaction. These curves allowed us to distinguish general laws of magnetization of ensembles of randomly oriented single-domain particles predicted by the Stoner-Wohlfarth theory and to discuss special features found for microcrystals.     

Entropy and the Shannon-McMillan-Breiman Theorem for Beta Random Matrix Ensembles

We show that beta ensembles in Random Matrix Theory with generic real analytic potential have the asymptotic equipartition property. In addition, we prove a Central Limit Theorem for the density of the eigenvalues of these ensembles.     

Transitive ensembles of random matrices related to orthogonal polynomials

Transitive correlations of eigenvalues for random matrix ensembles intermediate between real symmetric and hermitian, self-dual quaternion and hermitian, and antisymmetric and hermitian are studied. Expressions for exact n-point correlation functions are obtained for random matrix ensembles related to general orthogonal polynomials. The asymptotic formulas in the limit of large matrix dimension are evaluated at the spectrum edges for the ensembles related to the Legendre polynomials. The results interpolate known asymptotic formulas for random matrix eigenvalues.     

Pattern formation and encoding rhythms analysis on a spiking/bursting neuronal network

In this work we study the formation of patterns of neuronal activity when some input are presented to the network. For this task a recently developed model of neuron is utilized. This model requires a very low computational effort but presents many characteristics of more complex models such as, spiking, bursting and sub-threshold oscillations, and therefore the realistic study of the behavior of big ensembles of neurons can be aborded, even under real time conditions. New results of the application of the wavelet transform technique to the analysis of pattern formation and the possible encoding of rhythms are presented; they show that this simple, low-computational, neuron model behaves much like more complex ones.     

Instability-driven SiGe island growth

Three-dimensional islanding is generally assumed to proceed through nucleation and growth. Here we present studies showing the growth of Si1-xGex islands (0.2相似文献   

Synchronizability of network ensembles with prescribed statistical properties

It has been shown that synchronizability of a network is determined by the local structure rather than the global properties. With the same global properties, networks may have very different synchronizability. In this paper, we numerically studied, through the spectral properties, the synchronizability of ensembles of networks with prescribed statistical properties. Given a degree sequence, it is found that the eigenvalues and eigenratios characterizing network synchronizability have well-defined distributions, and statistically, the networks with extremely poor synchronizability are rare. Moreover, we compared the synchronizability of three network ensembles that have the same nodes and average degree. Our work reveals that the synchronizability of a network can be significantly affected by the local pattern of connections, and the homogeneity of degree can greatly enhance network synchronizability for networks of a random nature.     

Synchronizability of stochastic network ensembles in a model of interacting dynamical units

Synchronization is an important phenomenon which occurs in the dynamics of complex systems. Synchronized states emerge both from an adjustment of the system parameters and from an application of a proper external stimulus. In the present paper we study synchronized activity in a neural network model whose dynamics is driven by an external activation. In this context we are interested in its synchronizability, i.e. the existence of inputs causing the model system to synchronize. Furthermore, we investigate global synchronizability properties of stochastic network structure ensembles (instead of single realizations of a network architecture). We study the small world network, a model of preferential linking structure, and the classical Erd?s-Renyi random graph as particular examples of network topologies. Their synchronizability properties are investigated by analytical arguments and numerical simulations. Our analysis shows the emergence of synchronizable states of network ensembles for a wide range of the parameter values. In addition we observe and study the transition behaviour from synchronizability to nonsynchronizability.     

Scheme for the preparation of macroscopicW-type state of atomic ensembles in cavity QED coulped with optical fibers

We propose a potentially practical scheme to generate macroscopic W-type state of N atomic ensembles in cavity QED system consisting of N atomic ensembles trapped in N single-mode cavities connected by(N 1)optical fibers.We show that the N-qubit W-type state of atomic ensembles can be realized with high success probabilities if the coulping strength of the cavity-fiber is much stronger than that of cavity-atom.We also show that both the growth of atomic number in each ensemble and the increase of the number of atomic ensembles can diminish the detrimental influence from dissipative processes.This idea provides a scalable way to an atomic-ensemble-based quantum network,which is plausible with current available technology.     

Grand Canonical Ensembles of Sparse Networks and Bayesian Inference

Maximum entropy network ensembles have been very successful in modelling sparse network topologies and in solving challenging inference problems. However the sparse maximum entropy network models proposed so far have fixed number of nodes and are typically not exchangeable. Here we consider hierarchical models for exchangeable networks in the sparse limit, i.e., with the total number of links scaling linearly with the total number of nodes. The approach is grand canonical, i.e., the number of nodes of the network is not fixed a priori: it is finite but can be arbitrarily large. In this way the grand canonical network ensembles circumvent the difficulties in treating infinite sparse exchangeable networks which according to the Aldous-Hoover theorem must vanish. The approach can treat networks with given degree distribution or networks with given distribution of latent variables. When only a subgraph induced by a subset of nodes is known, this model allows a Bayesian estimation of the network size and the degree sequence (or the sequence of latent variables) of the entire network which can be used for network reconstruction.     

Koopman analysis of nonlinear systems with a neural network representation

The observation and study of nonlinear dynamical systems has been gaining popularity over years in different fields. The intrinsic complexity of their dynamics defies many existing tools based on individual orbits, while the Koopman operator governs evolution of functions defined in phase space and is thus focused on ensembles of orbits, which provides an alternative approach to investigate global features of system dynamics prescribed by spectral properties of the operator. However, it is difficult to identify and represent the most relevant eigenfunctions in practice. Here, combined with the Koopman analysis, a neural network is designed to achieve the reconstruction and evolution of complex dynamical systems. By invoking the error minimization, a fundamental set of Koopman eigenfunctions are derived, which may reproduce the input dynamics through a nonlinear transformation provided by the neural network. The corresponding eigenvalues are also directly extracted by the specific evolutionary structure built in.     

The Ginibre Ensemble of Real Random Matrices and its Scaling Limits

We give a closed form for the correlation functions of ensembles of a class of asymmetric real matrices in terms of the Pfaffian of an antisymmetric matrix formed from a 2 × 2 matrix kernel associated to the ensemble. We apply this result to the real Ginibre ensemble and compute the bulk and edge scaling limits of its correlation functions as the size of the matrices becomes large.     

Effects of spin interactions in disordered electronic systems: Loop expansions and exact relations among local gauge invariant models

Spindependent ensembles for disordered electronic systems are examined in the region of extended states. We derive relations between spindependent and previously studied spinless ensembles. We prove that these relations are valid in all orders of a graph theory, on the basis of which we propose them to be exact. These exact relations and supplementary two loop order calculations in 2+ dimensions are used to reveal the existence of universality classes for the critical behaviour at the mobility edges. The mobility edge behaviour of a spindependent ensemble with real (random) hopping agrees with that of the spinless phase invariant ensemble except for a crossover to the real matrix ensemble in the limit of vanishing spinflip amplitudes. Anomalous properties in the band center are also discussed. We derive a transformation which maps arbitrary correlation functions of a complex spindependent ensemble into those of the real matrix ensemble. This relation implies the absence of a mobility edge for the complex spindependent ensemble within the validity region of the theory.     

Disentangling the Information in Species Interaction Networks

Shannon’s entropy measure is a popular means for quantifying ecological diversity. We explore how one can use information-theoretic measures (that are often called indices in ecology) on joint ensembles to study the diversity of species interaction networks. We leverage the little-known balance equation to decompose the network information into three components describing the species abundance, specificity, and redundancy. This balance reveals that there exists a fundamental trade-off between these components. The decomposition can be straightforwardly extended to analyse networks through time as well as space, leading to the corresponding notions for alpha, beta, and gamma diversity. Our work aims to provide an accessible introduction for ecologists. To this end, we illustrate the interpretation of the components on numerous real networks. The corresponding code is made available to the community in the specialised Julia package EcologicalNetworks.jl.     

Parametric Representation of 3D Grain Ensembles in Polycrystalline Microstructures

As a straightforward generalization of the well-known Voronoi construction, Laguerre tessellations have long found application in the modelling, analysis and simulation of polycrystalline microstructures. The application of Laguerre tessellations to real (as opposed to computed) microstructures—such as those obtained by modern 3D characterization techniques like X-ray microtomography or focused-ion-beam serial sectioning—is hindered by the mathematical difficulty of determining the correct seed location and weighting factor for each of the grains in the measured volume. In this paper, we propose an alternative to the Laguerre approach, representing grain ensembles with convex cells parametrized by orthogonal regression with respect to 3D image data. Applying our algorithm to artificial microstructures and to microtomographic data sets of an Al-5 wt% Cu alloy, we demonstrate that the new approach represents statistical features of the underlying data—like distributions of grain sizes and coordination numbers—as well as or better than a recently introduced approximation method based on the Laguerre tessellation; furthermore, our method reproduces the local arrangement of grains (i.e., grain shapes and connectivities) much more accurately. The additional computational cost associated with orthogonal regression is marginal.     

Poisson Statistics for Beta Ensembles on the Real Line at High Temperature

Journal of Statistical Physics - This paper studies beta ensembles on the real line in a high temperature regime, that is, the regime where $$\beta N \rightarrow const \in (0, \infty )$$, with N...     

The Interpolating Airy Kernels for the \beta =1 and \beta =4 Elliptic Ginibre Ensembles

We consider two families of non-Hermitian Gaussian random matrices, namely the elliptic Ginibre ensembles of asymmetric $N$ -by- $N$ matrices with Dyson index $\beta =1$ (real elements) and with $\beta =4$ (quaternion-real elements). Both ensembles have already been solved for finite $N$ using the method of skew-orthogonal polynomials, given for these particular ensembles in terms of Hermite polynomials in the complex plane. In this paper we investigate the microscopic weakly non-Hermitian large- $N$ limit of each ensemble in the vicinity of the largest or smallest real eigenvalue. Specifically, we derive the limiting matrix-kernels for each case, from which all the eigenvalue correlation functions can be determined. We call these new kernels the “interpolating” Airy kernels, since we can recover—as opposing limiting cases—not only the well-known Airy kernels for the Hermitian ensembles, but also the complementary error function and Poisson kernels for the maximally non-Hermitian ensembles at the edge of the spectrum. Together with the known interpolating Airy kernel for $\beta =2$ , which we rederive here as well, this completes the analysis of all three elliptic Ginibre ensembles in the microscopic scaling limit at the spectral edge.