Inference of Kinetic Ising Model on Sparse Graphs

Based on dynamical cavity method, we propose an approach to the inference of kinetic Ising model, which asks to reconstruct couplings and external fields from given time-dependent output of original system. Our approach gives an exact result on tree graphs and a good approximation on sparse graphs, it can be seen as an extension of Belief Propagation inference of static Ising model to kinetic Ising model. While existing mean field methods to the kinetic Ising inference e.g., naïve mean-field, TAP equation and simply mean-field, use approximations which calculate magnetizations and correlations at time t from statistics of data at time t?1, dynamical cavity method can use statistics of data at times earlier than t?1 to capture more correlations at different time steps. Extensive numerical experiments show that our inference method is superior to existing mean-field approaches on diluted networks.     

Thouless-anderson-palmer equations for neural networks

Previous derivation of the Thouless-Anderson-Palmer (TAP) equations for the Hopfield model by the cavity method yielded results that were inconsistent with those of the perturbation theory as well as the results derived by the replica theory of the model. Here we present a derivation of the TAP equation for the Hopfield model by the cavity method and show that it agrees with the form derived by perturbation theory. We also use the cavity method to derive TAP equations for the pseudoinverse neural network model. These equations are consistent with the results of the replica theory of these models.     

Theory of an induced-moment spin glass

We review the derivation of generalised TAP equations for general quantum spin systems and apply the theory to a simple induced-moment spin glass model. We consider two-level systems with a singlet ground state and a triplet excited state, which interact via long range random exchange couplings. For not too large energy splitting the spin glass state can be stabilised.     

Universal scaling of wave propagation failure in arrays of coupled nonlinear cells

We study the onset of the propagation failure of wave fronts in systems of coupled cells. We introduce a new method to analyze the scaling of the critical external field at which fronts cease to propagate, as a function of intercellular coupling. We find the universal scaling of the field throughout the range of couplings and show that the field becomes exponentially small for large couplings. Our method is generic and applicable to a wide class of cellular dynamics in chemical, biological, and engineering systems. We confirm our results by direct numerical simulations.     

Data reduction by applying an image-based modeling and rendering technique to CG models

We applied an image-based modeling and rendering technique to reduce the data size of a CG model to be obtained as a visualization result. To date, this technique has been applied to the reconstruction of 3D graphical models from real objects; the size of the models can be reduced effectively because both color information and geometric information can be reduced. We applied a silhouette-and-voxel method that does not require design data for geometric simplification. Using our system, we simplified two models, one of which, involving medical data, was reduced by about 85% in file size. An accompanying subjective quality test showed that our approach maintains approximately the same visual quality as the geometric simplification method traditionally used.     

Critical phenomena with convergent series expansions in a finite volume

Linked cluster expansions are generalized from an infinite to a finite volume. They are performed to 20th order in the expansion parameter to approach the critical region from the symmetric phase. A new criterion is proposed to distinguish first- from second-order transitions within a finite-size scaling analysis. The criterion applies also to other methods for investigating the phase structure, such as Monte Carlo simulations. Our computational tools are illustrated with the example of scalar (O(N) models with four- and six-point couplings forN=1 andN=4 in three dimensions. It is shown how to localize the tricritical line in these models. We indicate some further applications of our methods to the electroweak transition as well as to models for superconductivity.     

Mirror symmetry,mirror map and applications to complete intersection Calabi-Yau spaces

We extend the discussion of mirror symmetry, Picard-Fuchs equations, instanton corrected Yukawa couplings and the topological one-loop partition function to the case of complete intersections with higher dimensional moduli spaces. We will develop a new method of obtaining the instanton corrected Yukawa couplings through a study of the solutions of the Picard-Fuchs equations. This leads to closed formulas for the prepotential for the Kähler moduli fields induced from the ambient space for all complete intersections in nonsingular weighted projective spaces. As examples we treat part of the moduli space of the phenomenologically interesting three-generation models which are found in this class. We also apply our method to solve the simplest model in which a topology change was observed and discuss examples of complete intersections in singular ambient spaces.     

Granger causality and the inverse Ising problem

The inference of the couplings of an Ising model with given means and correlations is called the inverse Ising problem. This approach has received a lot of attention as a tool to analyze neural data. We show that autoregressive methods may be used to learn the couplings of an Ising model, also in the case of asymmetric connections and for multispin interactions. We find that, for each link, the linear Granger causality is two times the corresponding transfer entropy (i.e., the information flow on that link) in the weak coupling limit. For sparse connections and a low number of samples, the ?₁ regularized least squares method is used to detect the interacting pairs of spins. Nonlinear Granger causality is related to multispin interactions.     

Disentangling the spin-parity of a resonance via the gold-plated decay mode

Searching for new resonances and finding out their properties is an essential part of any existing or future particle physics experiment. The nature of a new resonance is characterized by its spin, charge conjugation,parity, and its couplings with the existing particles of the Standard Model. If a new resonance is found in the four lepton final state produced via two intermediate Z bosons, the resonance could be a new heavy scalar or a Z boson or even a higher spin particle. In such cases a step by step methodology as enunciated in this paper can be followed to determine the spin, parity and the coupling to two Z bosons of the parent particles, in a fully model-independent way. In our approach we show how three uni-angular distributions and a few experimentally measurable observables can conclusively tell us about the spin, parity as well as the couplings of the new resonance to two Z bosons. We have performed a numerical analysis to validate our approach and showed how the uni-angular observables can be used to disentangle the spin parity as well as the coupling of the resonance.     

The Renormalization Group and Its Finite Lattice Approximations

We investigate finite lattice approximations to the Wilson renormalization group in models of unconstrained spins. We discuss first the properties of the renormalization group transformation (RGT) that control the accuracy of this type of approximation and explain different methods and techniques to practically identify them. We also discuss how to determine the anomalous dimension of the field. We apply our considerations to a linear sigma model in two dimensions in the domain of attraction of the Ising fixed point using a Bell–Wilson RGT. We are able to identify optimal RGTs which allow accurate computations of quantities such as critical exponents, fixed-point couplings and eigenvectors with modest statistics. We finally discuss the advantages and limitations of this type of approach.     

Signal-to-noise analysis of Hopfield neural networks with a formulation of the dynamics in terms of transition probabilities

We study Hopfield neural networks with infinite connectivity using signal-to-noise analysis with a formulation of the dynamics in terms of transition probabilities. We focus our study on models where the strongest effects of the feedback correlations appear. We introduce an analysis of the path probability of one neuron in order to obtain the contribution of all feedback correlations to the dynamics of this neuron. In this way, we obtain a complete theory for dynamics with order parameter equations identical to those obtained with general functional analysis for finite temperature. In the first part of this work, we present our method in the fully connected Little-Hopfield neural network. We obtain, in a simple and direct way, the order parameter equations found by general functional analysis. In the second part, the exposed method is applied to the fully connected Ashkin-Teller neural network. It is shown that the retrieval quality is improved by introducing four-spin couplings. Simulation results support our theoretical predictions.     

Bulk-boundary correlators in the hermitian matrix model and minimal Liouville gravity

We construct the one matrix model (MM) correlators corresponding to the general bulk-boundary correlation numbers of the minimal Liouville gravity (LG) on the disc. To find agreement between both discrete and continuous approach, we investigate the resonance transformation mixing boundary and bulk couplings. It leads to consider two sectors, depending on whether the matter part of the LG correlator is vanishing due to the fusion rules. In the vanishing case, we determine the explicit transformation of the boundary couplings at the first order in bulk couplings. In the non-vanishing case, no bulk-boundary resonance is involved and only the first order of pure boundary resonances have to be considered. Those are encoded in the matrix polynomials determined in our previous paper. We checked the agreement for the bulk-boundary correlators of MM and LG in several non-trivial cases. In this process, we developed an alternative method to derive the boundary resonance encoding polynomials.     

Hamiltonian Tri-Integrable Couplings of the AKNS Hierarchy

We propose a systematic approach for generating Hamiltonian tri-integrable couplings of soliton hierarchies. The resulting approach is based on semi-direct sums of matrix Lie algebras consisting of 4 × 4 block matrix Lie algebras. We apply the approach to the AKNS soliton hierarchy, and Hamiltonian structures of the obtained tri-integrable couplings are constructed by the variational identity.     

Spectral and transport properties of the PT-symmetric dimer model

We study the scattering properties of the PT-symmetric tight-binding model with balanced gain and loss parameters. Our main interest is to establish the link between the spectral properties of scattering states and transport characteristics for the case of non-equal couplings between gain/loss sites. The analytical approach we have used allows one to reveal a quite unexpected role of this set-up in comparison with that of equal couplings. In particular, we demonstrate that for the exceptional points characterized by equal eigenvalues of the transfer matrix, the transmission coefficient can be different from one in contrast with the model with equal couplings. The analytical results are complemented by the numerical data.     

Valence bond calculations of vicinal proton coupling constants in cyclopropane

Vicinal proton couplings in cyclopropane have been calculated using Dirac-Van Vleck and variational methods in valence bond formalism. The couplings may be considered as taking place along a path comprising either three or four intervening bonds. Inclusion of all exchange integrals in the appropriate fragment models leads to a satisfactory ratio of J_cis/J_trans . In this respect valence bond results appear to be superior to those obtained using a molecular orbital approach. The present valence bond results on couplings in cyclopropane are not affected by the choice of models for bonding in cyclopropane, namely the Coulson-Moffitt model or the Walsh model.     

Asymptotic behaviour and reduction of couplings for models including nonrenormalizable interactions

We study equivalence relations among parametrizations of models including nonrenormalizable polynomial interactions. The method of reduction of couplings allows for a classification of the parameter associated to the nonrenormalizable perturbations and stability considerations. The relation to effective models is briefly discussed.     

Light propagation and oscillations in two-dimensional graded square photonic lattices

We have studied the optical oscillations and transitions in two-dimensional graded square photonic lattices (GSPL) formed by evanescently coupled optical waveguide arrays with parabolic confinements in all transverse directions. When we retain only the orthogonal couplings, decoupled one-dimensional models can be used to obtain the various normal modes, which correspond to a variety of optical oscillations. Six different combinations of Bloch oscillation (BO), dipole oscillation (DO), and reflections from the boundaries of finite lattice are classified on the phase diagram. If we include the diagonal couplings, transitions among various oscillations are obtained with the Hamiltonian optics approach and confirmed by the field-evolution analysis. We studied in detail a typical example in which a switching occurs from the constituent BO and DO to both DOs in the two orthogonal directions. The method to analyze the complex field evolution in GSPL can be extended to similar systems with different types of lattices and/or confinements.     

Dynamics and performance of susceptibility propagation on synthetic data

We study the performance and convergence properties of the susceptibility propagation (SusP) algorithm for solving the Inverse Ising problem. We first study how the temperature parameter (T) in a Sherrington-Kirkpatrick model generating the data influences the performance and convergence of the algorithm. We find that at the high temperature regime (T > 4), the algorithm performs well and its quality is only limited by the quality of the supplied data. In the low temperature regime (T < 4), we find that the algorithm typically does not converge, yielding diverging values for the couplings. However, we show that by stopping the algorithm at the right time before divergence becomes serious, good reconstruction can be achieved down to T ≈ 2. We then show that dense connectivity, loopiness of the connectivity, and high absolute magnetization all have deteriorating effects on the performance of the algorithm. When absolute magnetization is high, we show that other methods can be work better than SusP. Finally, we show that for neural data with high absolute magnetization, SusP performs less well than TAP inversion.     

视场外激光干扰图像对目标获取性能的影响分析

以现有的目标获取性能模型NVLESD(Night Vision and Electronic Sensors Directorate)为基础,分析杂波对于"人在回路"目标获取性能的影响。针对视场外激光干扰图像的特点,运用图像边缘概率尺度修正后的目标获取性能模型对激光干扰图像进行分析。对CCD探测器的视场外干扰实验结果表明,该方法能够较好地反映激光干扰图像对于搜索探测概率的影响,从而验证了方法的有效性。