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.     

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.     

重频Yb:YAG片状激光器电光调$lt;i$gt;Q$lt;/i$gt;时空演化模拟计算和实验研究

基于Yb³⁺抽运动力学,结合光线追迹的方法,建立了抽运过程中的放大自发辐射模型,得到激光介质中三维含时储能分布.将速率方程理论和角谱传播理论结合,对谐振腔内调Q脉冲的形成、传播过程进行建模计算,得到激光脉冲的时间-空间分布和光束质量因子变化规律.同时进行了激光二极管抽运重频Yb：YAG片状激光器电光调Q实验,并与模拟计算的结果进行了对比校核,印证了计算模型的正确性.这为主动调Q固体激光器的设计提供了参考. 关键词： Yb：YAG激光器 Q')" href="#">调Q 时空演化     

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.     

Solution of approximate gluon evolution equation for small-x at fixed ‘ρ’

A simple method has been applied to solve the approximate gluon evolution equation for small-x at fixedρ(≡√ln(x ₀/x)/ln[ln(Q ²/Λ²)/ln(Q ₀ ² /Λ²)]. Numerical comparison is made with the predictions from ‘double asymptotic scaling’ and fit. Better agreement is found between our solution and fit nearρ=1. The solution gives approximate double scaling in this region having ‘hard’ pomeron with small contamination.     

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.     

Homology of Fortuin–Kasteleyn Clusters of Potts Models on the Torus

Topological properties of Fortuin–Kasteleyn clusters are studied on the torus. Namely, the probability that their topology yields a given subgroup of the first homology group of the torus is computed for Q=1, 2, 3 and 4. The expressions generalize those obtained by Pinson for percolation (Q=1). Numerical results are also presented for three tori of different moduli. They agree with the theoretical predictions for Q=1, 2 and 3. For Q=4 agreement is not ruled out but logarithmic corrections are probably present and they make it harder to decide.     

Gluon distributions in real and virtual photon and the photon structure function

Gluon distributions in real and virtual photons are calculated using evolution equations in the NLO approximation. The quark distributions in the photon determined on the basis of the QCD sum rule approach in [1] are taken as an input. It is shown that gluon distribution in the photon can be reliably determined up tox=0.03÷0.05, much lower than the corresponding values in the case of quark distributions. Two variants of the calculations are considered: (1) it is assumed that there are no intrinsic gluons in the photon at some low normalization pointQ ²=Q ₀ ² ∼1GeV²; (2) it is assumed that gluonic content of the photon at lowQ ₀ ² is described by gluonic content of vector mesonsρ, ω, ϕ. The gluon distributions in these two variants appear to be different. This fact permits one to clarify the origin of nonperturbative gluonic content of the photon by comparing the results with experiment. Structure functionsF ₂(x) for real and virtual photon are calculated and it is shown that in the regionx≥0.2 where QCD approach is valid, there is a good agreement with experiment.     

Perturbative and non-perturbative evolutions of structure functions at low-x

Approximate solutions of Altarelli-Parisi equations are obtained in low-x limit and have tested them in EMC low-x and low-Q ² data. The results are compared with the phenomenological non-perturbative evolutions. Data conform to perturbative as well as non-perturbative evolutions but do not conform to the predictions of non-linear evolution.     

TDPAC characterization of tin oxides using181Ta

In connection with a general study of the evolution of tin-oxygen thin films, we report here on the hyperfine interactions of¹⁸¹Ta substitutionally replacting tin in the isolated phases SnO and SnO₂. For this purpose, pure SnO pressed powder and a thin SnO₂ film were implanted with¹⁸¹Hf. In both cases, unique quadrupole frequencies were found after thermal annealing treatments. The results indicate that the following hyperfine parameters: υ _Q = 740.6(2.1) MHz, η=0.07(2) and υ _Q = 971.5(1.9) MHz, η=0.72(1) characterize¹⁸¹Ta in SnO and SnO₂, respectively.     

Effects of L-spin longitudinal quadrupolar relaxation in heteronuclear recoupling and S-spin magic-angle spinning NMR

In experiments on S–L heteronuclear spin systems with evolution of the S-spin magnetization under the influence of a quadrupolar nucleus (L-spin), effects of longitudinal quadrupolar (T_1Q) relaxation of the L-spin coherence on the sub-millisecond time scale have been documented and explored, and methods for minimizing their effect have been demonstrated. The longitudinal relaxation results in heteronuclear dephasing even in the reference signal S₀ of S{L} REDOR, REAPDOR, RIDER, or SPIDER experiments, due to T_1Q-relaxation of the transiently generated S_yL_z coherence, reducing or even eliminating the observable dephasing ΔS. Pulse sequences for measuring an improved reference signal S₀₀ with minimal heteronuclear recoupling but the same number of pulses as for S₀ and S have been demonstrated. From the observed intensity ΔS₀ = S₀₀ − S₀ and the SPIDER signal ΔS/S₀, T_1Q can be estimated. Accelerated decays analogous to the dipolar S₀ curves will occur in T₂ measurements for J-coupled S–L spin pairs. Even in the absence of recoupling pulses, fast T_1Q relaxation of the unobserved nucleus shortens the transverse relaxation time T_2S,MAS of the observed nucleus, in particular at low spinning frequencies, due to unavoidable heteronuclear dipolar evolution during a rotation period. The observed spinning-frequency dependence of T_2S,MAS matches the theoretical prediction and may be used to estimate T_1Q. The effects are demonstrated on several ¹³C{¹⁴N} spin systems, including an arginine derivative, the natural N-acetylated polysaccharide chitin, and a model peptide, (POG)₁₀.     

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.

     

Application of molecular topology to the prediction of mosquito repellents of a group of terpenoid compounds

A topological-mathematical model based on multilinear regression analysis has been built to search new terpenoid actives as mosquito repellents. The structural depiction was performed using topological indices, and a four-variable model for the prediction of corrected repellent ratio (r ² = 0.9672, Q ² = 0.9435) was selected. The model was checked by cross-validation, internal validation, and randomization test. The results confirm its capability to predict the property analyzed. After carrying out a virtual screening upon such a model, new structures with potential repellent activity against mosquitoes are proposed.     

Development of a Resonator with Automatic Tuning and Coupling Capability to Minimize Sample Motion Noise for in Vivo EPR Spectroscopy

EPR spectroscopy has been applied to measure free radicals in vivo; however, respiratory, cardiac, and other movements of living animals are a major source of noise and spectral distortion. Sample motions result in changes in resonator frequency, Q, and coupling. These instabilities limit the applications that can be performed and the quality of data that can be obtained. Therefore, it is of great importance to develop resonators with automatic tuning and automatic coupling capability. We report the development of automatic tuning and automatic coupling provisions for a 750-MHz transversely oriented electric field reentrant resonator using two electronically tunable high Q hyperabrupt varactor diodes and feedback loops. In both moving phantoms and living mice, these automatic coupling control and automatic tuning control provisions resulted in an 8- to 10-fold increase in signal-to-noise ratio.     

Evolution of 2+ γ wave functions and gamma-stiffness in well-deformed rare-earth nuclei

The evolution of the structure of the gamma-vibrational band head 2⁺ _γ in well-deformed rare-earth nuclei is studied within the framework of RPA calculations using a quasiboson approximation based on the Nilsson model. The obtained evolution of the quasiparticle structure of the gamma-vibrational band head is shown to correlate well with the evolution of the same nuclei within the IBA symmetry triangle when described in the extended consistent-Q formalism. An empirical relation is presented that links the IBA parameter χ with the quasiparticle structure of the gamma-vibrational band head.     

Vertex form factors of the rho-meson nucleon interaction at low momentum transfer

We calculated the one pion loop contributions to the form factors of the rho-nucleon interaction within a field theoretical model using effective Lagrangians. The results show that the tensor interaction is likely to be described well within such an approach. We obtain a magnetic coupling in the range of 3.5–7.1 atQ ²=0, depending on the choice of pion-nucleon form factor and a dipole form for theQ ² dependence tensor form factor with a scale of roughly 900 MeV for space-like momentum transfer. The results agree with the findings of the recent analysis of thep-N interaction and support a small scale parameter (0.5 GeV) for the pion-nucleon form factor.This work is supported by BMFT (06BO7027) and COSY-KFA Jülich (41140512)     

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.     

Some consequences of neutral current systematics

Two kinds of general consequences of the ΔS=0 weak hadron neutral current independent of a gauge model are presented. Firstly are results which depend on the quark parton model. These involve bounds among neutrino inclusive cross-section and a bound onQ(Z, N) in terms of these inclusive cross-sections. Secondly are results which are independent of the quark-parton model and depend only on the SU(3) structure of the most general ΔS=0 neutral current. These tests of isopin and speciallyU-spin properties of the current are given forv+N→v+hadron+anything,v+N→v+baryon+meson ande ⁺ e ⁻→baryon+anti-baryon. In addition some conjectures are made with regard to the semi-inclusive neutrino-reactions using the quark parton model.     

Model for nucleon valence structure functions at allx,allp ⊥ and allQ 2 from the correspondence between QCD and DTU

We propose a simple parametrization of the nucleon valence structure functions at allx, allp _⊥ and allQ ². We use the DTU parton model to fix the parametrization at a reference point (Q ₀ ² =3 GeV²) and we mimic the QCD evolution by replacing the dimensioned parameters of the DTU parton model by functions depending onQ ². Excellent agreement is obtained with existing data.     

Measurement of the proton structure function F 2 at low x and low Q 2 at HERA

We report on a measurement of the proton structure functionF ₂ in the range 3.5×10⁻⁵≤x≤4×10⁻³ and 1.5 GeV²≤Q ²≤15GeV² at theep collider HERA operating at a centre-of-mass energy of √s=300GeV. The rise ofF ₂ with decreasingx observed in the previous HERA measurements persists in this lowerx andQ ² range. TheQ ² evolution ofF ₂, even at the lowestQ ² andx measured, is consistent with perturbative QCD. supported by EU HCM contract ERB-CHRX-CT93-0376