Look-up table and Gaussian filter-based inverse halftoning method excellent in gray-scale reproducibility of details and flat regions

Halftoning is a technique in which gray-scale images are converted into binary ones, and has been used widely in many practical image processing applications. On the other hand, inverse halftoning is a technique of reproducing a grayscale image from a binary one. One of the sophisticated inverse halftoning methods which can yield a high quality grayscale image is that based on a look-up table (LUT). In this paper, a new inverse halftoning method based on a combination of this LUT method and a Gaussian filter is discussed. Here, the output gray-scale image is reproduced by blending the output of the LUT-based inverse halftoning and that of the Gaussian filtering appropriately in accordance with local statistics of the image. The effectiveness and the validity of the described method are verified through experiments.     

Physical consideration of an image in image restoration using Bayes’ formula

We consider image restoration by Bayes’ formula and investigate the relationship between an image and a prior probability from the following two viewpoints: hyperparameter estimation and the accuracy of a restored image. The Q-Ising model is adopted as a prior probability in Bayes’ formula. Not the Q-Ising energy, but the Potts energy plays an important role in the hyperparameter estimation. From the viewpoint of the hyperparameter estimation, the relationship between a natural image and a prior probability is characterized through the Potts energy and magnetization of an image. The Potts energy and magnetization of an image are defined by a set of pixels’ state of an image. The closer to the average Potts energy and magnetization over a prior probability the Potts energy and magnetization of a natural image is, the closer to the true value of a hyperparameter the estimated value of a hyperparameter from a degraded image is. For the accuracy of a restored image, the image which has a smaller Q-Ising energy is better restored by Bayes’ formula composed of the Q-Ising prior. The consideration for the relationship between an image and a prior probability is expected to be valid for a more complicated prior probability.     

Two-cycles in spin-systems: sequential versus synchronous updating in multi-state Ising-type ferromagnets

Hamiltonians for general multi-state spin-glass systems with Ising symmetry are derived for both sequential and synchronous updating of the spins. The possibly different behaviour caused by the way of updating is studied in detail for the (anti)-ferromagnetic version of the models, which can be solved analytically without any approximation, both thermodynamically via a free-energy calculation and dynamically using the generating functional approach. Phase diagrams are discussed and the appearance of two-cycles in the case of synchronous updating is examined. A comparative study is made for the Q-Ising and the Blume-Emery-Griffiths ferromagnets and some interesting physical differences are found. Numerical simulations confirm the results obtained.Received: 9 August 2004, PACS: 05.70.Fh Phase transitions: general studies - 64.60.Cn Order-disorder transformations; statistical mechanics of model systems - 75.10.Hk Classical spin models     

Parallel Dynamics of Extremely Diluted Symmetric Q-Ising Neural Networks

The parallel dynamics of extremely diluted symmetric Q-Ising neural networks is studied for arbitrary Q using a probabilistic approach. In spite of the extremely diluted architecture the feedback correlations arising from the symmetry prevent a closed-form solution in contrast with the extremely diluted asymmetric model. A recursive scheme is found determining the complete time evolution of the order parameters taking into account all feedback. It is based upon the evolution of the distribution of the local field, as in the fully connected model. As an illustrative example an explicit analysis is carried out for the Q=2 and Q=3 model. These results agree with and extend the partial results existing for Q=2. For Q>2 the analysis is entirely new. Finally, equilibrium fixed-point equations are derived and a capacity-gain function diagram is obtained.     

Karhunen-Loeve及多尺度金字塔联合变换的彩色逆半调算法

红绿蓝(RGB)颜色空间中的各颜色分量具有高度相关性,直接分通道实施的彩色逆半调方法会残留大量人眼敏感的半调纹理,且逆半调图像色偏较大。从分析矢量误差分散半调系统模型入手,推导其加噪特性,针对性地提出了一种Karhunen-Loeve(K-L)及多尺度金字塔联合变换的彩色逆半调算法。算法以K-L变换减弱彩色分量相关性,再利用多尺度中值金字塔算子以及维纳(Wiener)滤波分离并抑制高频细节子图中的半调噪声,最后进行中值金字塔、K-L逆变换重构结果图像。实验表明,该算法能有效去除半调噪声、减小重建图像的颜色偏差,与直接分通道逆半调算法相比峰值信噪比值提高约2~3 dB,且重建图像视觉效果良好。     

Parallel Dynamics of Fully Connected Q-Ising Neural Networks

Using a probabilistic approach, the parallel dynamics of fully connected Q-Ising neural networks is studied for arbitrary Q. A novel recursive scheme is set up to determine the time evolution of the order parameters through the evolution of the distribution of the local field, taking into account all feedback correlations. In contrast to extremely diluted and layered network architectures, the local field is no longer normally distributed but contains a discrete part. As an illustrative example, an explicit analysis is carried out for the first four time steps. For the case of the Q = 2 and Q = 3 model the results are compared with extensive numerical simulations and excellent agreement is found. Finally, equilibrium fixed-point equations are derived and compared with the thermodynamic approach based upon the replica-symmetric mean-field approximation.     

Large Deviation Techniques Applied to Systems with Long-Range Interactions

We discuss a method to solve models with long-range interactions in the microcanonical and canonical ensemble. The method closely follows the one introduced by R.S. Ellis, Physica D 133:106 (1999), which uses large deviation techniques. We show how it can be adapted to obtain the solution of a large class of simple models, which can show ensemble inequivalence. The model Hamiltonian can have both discrete (Ising, Potts) and continuous (HMF, Free Electron Laser) state variables. This latter extension gives access to the comparison with dynamics and to the study of non-equilibrium effects. We treat both infinite range and slowly decreasing interactions and, in particular, we present the solution of the α-Ising model in one-dimension with 0 ⩽ α < 1.     

Algebraic Geometry in Discrete Quantum Integrable Model and Baxter's T–Q Relation

We study the diagonalization problem of certain discrete quantum integrable models by the method of Baxter's T–Q relation from the algebraic geometry aspect. Among those the Hofstadter type model (with the rational magnetic flux), discrete quantum pendulum and discrete sine-Gordon model are our main concern in this report. By the quantum inverse scattering method, the Baxter's T–Q relation is formulated on the associated spectral curve, a high genus Riemann surface in general, arisen from the study of spectrum problem of the system. In the case of degenerated spectral curve where the spectral variables lie on rational curves, we obtain the complete and explicit solution of the T–Q polynomial equation associated to the model, and the intimate relation between the Baxter's T–Q relation and algebraic Bethe Ansatz is clearly revealed. The algebraic geometry of a general spectral curve attached to the model and certain qualitative properties of solutions of the Baxter's T–Q relation are discussed incorporating the physical consideration.     

Retrieval and chaos in layeredQ-Ising neural networks

Using a probabilistic approach, we study the parallel dynamics of theQ-Ising layered networks for arbitraryQ. By introducing auxiliary thermal fields, we express the stochastic dynamics within the gain function formulation of the deterministic dynamics. Evolution equations are derived for arbitraryQ at both zero and finite temperatures. An explicit analysis of the fixed-point equations is carried out for bothQ=3 andQ. The retrieval properties are discussed in terms of the gain parameter, the storage capacity, and the temperature. Using the time evolution of the distance between two network configurations, we investigate the possibility of microscopic chaos. Chaotic behavior is always present for arbitrary finiteQ. However, in the limitQ the existence of chaos depends on the parameters of the system.     

基于马尔科夫链的射频识别防碰撞测试

分析了自适应Q值算法的防碰撞原理以及射频识别(RFID)通信的时序,定义防碰撞过程的识别效率、识别速度和标签数目及Q值的数据状态(Q,n).在此基础上讨论并建立了多标签的状态转移过程的马尔科夫链模型.通过蒙特卡罗统计方法,对马尔科夫链模型求解,得出识别效率和识别速度.用软件无线电测试方案实现防碰撞测试,有效地实现了RFID防碰撞过程的识别效率和识别速度的量化分析.模型仿真结果和测试数据的一致证明了测试模型的有效性和测试方法的正确性. 关键词： 射频识别 防碰撞测试 马尔科夫链 时隙计数器     

Electrostatic induction in Einstein-Maxwell theory

We investigate the physics of an exact static solution representing a mass Q and a charged mass P. We find that the electric field has a neutral point, and we ascribe this to the effect of a pseudocharge induced on Q. The induced field is local in that it does not have inverse square strength at infinity.     

On the parallel dynamics of theQ-state Potts andQ-Ising neural networks

Using a probabilistic approach, the parallel dynamics of theQ-state Potts andQ-Ising neural networks are studied at zero and at nonzero temperatures. Evolution equations are derived for the first time step and arbitraryQ. These formulas constitute recursion relations for the exact parallel dynamics of the extremely diluted asymmetric versions of these networks. An explicit analysis, including dynamical capacity-temperature diagrams and the temperature dependence of the overlap, is carried out forQ=3. Both types of models are compared.On leave of absence from the Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna 141980, Russia.     

The glassy phase of Gallager codes

Gallager codes are the best error-correcting codes to date. In this paper we study them by using the tools of statistical mechanics. The corresponding statistical mechanics model is a spin model on a sparse random graph. The model can be solved by elementary methods (i.e. without replicas) in a large connectivity limit. For low enough temperatures it presents a completely frozen glassy phase (q _EA = 1). The same scenario is shown to hold for finite connectivities. In this case we adopt the replica approach and exhibit a one-step replica symmetry breaking order parameter. We argue that our ansatz yields the exact solution of the model. This allows us to determine the whole phase diagram and to understand the performances of Gallager codes. Received 9 April 2001     

The Canonical Solutions of the Q-Systems¶ and the Kirillov–Reshetikhin Conjecture

We study a class of systems of functional equations closely related to various kinds of integrable statistical and quantum mechanical models. We call them the finite and infinite $Q$-systems according to the number of functions and equations. The finite Q-systems appear as the thermal equilibrium conditions (the Sutherland–Wu equation) for certain statistical mechanical systems. Some infinite Q-systems appear as the relations of the normalized characters of the KR modules of the Yangians and the quantum affine algebras. We give two types of power series formulae for the unique solution (resp. the unique canonical solution) for a finite (resp. infinite) Q-system. As an application, we reformulate the Kirillov–Reshetikhin conjecture on the multiplicities formula of the KR modules in terms of the canonical solutions of Q-systems. Received: 2 August 2001 / Accepted: 27 December 2001     

Peierls Instability for the Holstein Model with Rational Density

We consider the static Holstein model, describing a chain of fermions interacting with a classical phonon field, when the interaction is weak and the density is a rational number p = P/Q, with P, Q relative prime integers. We show that the energy of the system, as a function of the phonon field, has one (if Q is even) or two (if Q is odd) stationary points, defined up to a lattice translation, which are local minima in the space of fields periodic with period equal to the inverse of the density.     

Retrieval and chaos in extremely dilutedQ-Ising neural networks

Using a probabilistic approach, the deterministic and the stochastic parallel dynamics of aQ-Ising neural network are studied at finiteQ and in the limitQ. Exact evolution equations are presented for the first time-step. These formulas constitute recursion relations for the parallel dynamics of the extremely diluted asymmetric versions of these networks. An explicit analysis of the retrieval properties is carried out in terms of the gain parameter, the loading capacity, and the temperature. The results for theQ network are compared with those for theQ=3 andQ=4 models. Possible chaotic microscopic behavior is studied using the time evolution of the distance between two network configurations. For arbitrary finiteQ the retrieval regime is always chaotic. In the limitQ the network exhibits a dynamical transition toward chaos.     

Nonlinear neural networks. I. General theory

A neural network is called nonlinear if the introduction of new data into the synaptic efficacies has to be performed through anonlinear operation. The original Hopfield model is linear, whereas, for instance, clipped synapses constitute a nonlinear model. Here a general theory is presented to obtain the statistical mechanics of a neural network with finitely many patterns and arbitrary (symmetric) nonlinearity. The problem is reduced to minimizing a free energy functional over all solutions of a fixed-point equation with synaptic kernelQ. The case of clipped synapses with bimodal and Gaussian probability distribution is analyzed in detail. To this end, a simple theory is developed that gives the spectrum ofQ and thereby all the solutions that bifurcate from the high-temperature phase.     

Non-Equilibrium Steady States of Finite¶Quantum Systems Coupled to Thermal Reservoirs

We study the non-equilibrium statistical mechanics of a 2-level quantum system, ?, coupled to two independent free Fermi reservoirs ?₁, ?₂, which are in thermal equilibrium at inverse temperatures β₁≠β₂. We prove that, at small coupling, the combined quantum system ?+?₁+?₂ has a unique non-equilibrium steady state (NESS) and that the approach to this NESS is exponentially fast. We show that the entropy production of the coupled system is strictly positive and relate this entropy production to the heat fluxes through the system. A part of our argument is general and deals with spectral theory of NESS. In the abstract setting of algebraic quantum statistical mechanics we introduce the new concept of the C-Liouvillean, L, and relate the NESS to zero resonance eigenfunctions of L ^*. In the specific model ?+?₁+?₂ we study the resonances of L ^* using the complex deformation technique developed previously by the authors in [JP1]. Dedicated to Jean Michel Combes on the occasion of his sixtieth birthday Received: 12 July 2001 / Accepted: 11 October 2001     

Quenching Evolution in a Quantum-Classical Hybrid System

The adiabatic theorem, an important theory in quantum mechanics, tells that a quantum system subjected to gradually changing external conditions remains to the same instantaneous eigenstate of its Hamiltonian as it initially in. In this paper, we study the quench evolution that is another extreme circumstance where the external conditions vary rapidly such that the quantum system can not follow the change and remains in its initial state (or wavefunction). We examine the matter-wave pressure and derive the requirement for such an evolution. The study is conducted by considering a quantum particle in an infinitely deep potential, the potential width Q is assumed to be change rapidly. We show that the total energy of the quantum subsystem decreases as Q increases, and this rapidly change exerts a force on the wall which plays the role of boundary of the potential. For Q < Q₀ (Q₀ is the initial width of the potential), the force is repulsive, and for Q > Q₀, the force is positive. The condition for the quenching evolution evolution is given via a spin-\( \frac{1}{2} \) in a rotating magnetic field.

     

A Discussion on Finite Quasi-cardinals in Quasi-set Theory

Quasi-set theory Q is an alternative set-theory designed to deal mathematically with collections of indistinguishable objects. The intended interpretation for those objects is the indistinguishable particles of non-relativistic quantum mechanics, under one specific interpretation of that theory. The notion of cardinal of a collection in Q is treated by the concept of quasi-cardinal, which in the usual formulations of the theory is introduced as a primitive symbol, since the usual means of cardinal definition fail for collections of indistinguishable objects. In a recent work, Domenech and Holik have proposed a definition of quasi-cardinality in Q. They claimed their definition of quasi-cardinal not only avoids the introduction of that notion as a primitive one, but also that it may be seen as a first step in the search for a version of Q that allows for a greater representative power. According to them, some physical systems can not be represented in the usual formulations of the theory, when the quasi-cardinal is considered as primitive. In this paper, we discuss their proposal and aims, and also, it is presented a modification from their definition we believe is simpler and more general.