Finite-state neural networks. A step toward the simulation of very large systems

Neural networks composed of neurons withQ _N states and synapses withQ states are studied analytically and numerically. Analytically it is shown that these finite-state networks are much more efficient at information storage than networks with continuous synapses. In order to take the utmost advantage of networks with finite-state elements, a multineuron and multisynapse coding scheme is introduced which allows the simulation of networks having 1.0×10⁹ couplings at a speed of 7.1×10⁹ coupling evaluations per second on asingle processor of the Cray-YMP. A local learning algorithm is also introduced which allows for the efficient training of large networks with finite-state elements.     

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.     

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.     

Influencing the satellite transitions of half-integer quadrupolar nuclei for the enhancement of magic angle spinning spectra

Double frequency sweeps can induce spin transitions in a set of satellites of a half-integer quadrupolar nucleus by simultaneously passing through resonance for a satellite pair. It is shown that by transferring population from the outer spin levels to the inner |1/2 and |−1/2 levels an increased intensity for central transition spectra is obtained. Although Magic Angle Spinning in principle interferes with this process, and the adiabaticity of the passages is different for every crystallite in a powder, enhanced spectra with undistorted line shapes are obtained for I=3/2 (²³Na) and 5/2 (²⁷Al) spins experiencing quadrupolar interactions with ω_Q in the range 0.1–3 MHz. Even at spinning speeds up to 30 kHz significant enhancements are obtained. An analysis of the combined effects of double frequency sweeps (DFS) and MAS indeed shows strongly different effects for different crystallites in powder ranging from no gain at all to the theoretical maximum gain of 2I. As the effects are randomly distributed over all orientations on a sphere this is averaged over the whole line shape. Therefore, undistorted powder patterns are obtained enhanced by the average gain over the individual crystallites. Saturation of the satellite transitions, which can only be achieved if spin–spin relaxation is sufficiently strong, leads to identical results. Optimization of the sweeps should be toward an optimal effect on the population transfer to the central levels and chosen short with respect to spin–lattice relaxation times.     

基于电子倍增电荷耦合器件的哈特曼-夏克波前传感器质心探测误差分析

哈特曼-夏克(Hartmann-Shack,H-S)波前传感器的探测误差是自适应光学系统中的一个主要误差源.本文分析了电子倍增电荷耦合器件(electron multiplying charge-coupled devices,EMCCD)的各种噪声源对H-S波前传感器质心探测误差的影响,推导了基于EMCCD的H-S波前传感器的质心探测误差的数学表达式,并进行了数值仿真和实验研究.结果表明,基于EMCCD的H-S波前传感器的质心探测误差与增益直接相关,在增益小于P_max/(Q·N_mean)时质心探测误差随着增益的增大而减小,在增益大于P_max/(Q·N_mean)时质心探测误差随着增益的增大而增大,其中P_max是EMCCD的峰值电荷,Q是量子效率,N_mean是平均入射光强. 关键词： 自适应光学 电子倍增电荷耦合器件 波前传感器 质心探测误差     

Q value related mass determinations using a Penning trap

We report here about measurements of reaction and decay Q values by precise determination of pairs of atomic masses. These were performed with the Penning trap mass spectrometer SMILETRAP. Measurements with Penning traps give reliable and accurate masses, in particular Q values, due to the fact that certain systematic errors to a great deal cancel in the mass difference between the two atoms defining the Q value. Some Q values that are of fundamental interest will be discussed here, for example, a new Q value for the ⁶Li (n,γ) ⁷Li reaction, for the β-decay of tritium, related to properties of the electron neutrino mass, and for the neutrino-less double β-decay of ⁷⁶Ge, related to the question of whether the neutrino is a Majorana particle or not. In case of the latter two we report the most accurate Q values, namely 18,589.8(12) eV for the tritium decay and 2,038.997(46) keV for the neutrino-less double β-decay of ⁷⁶Ge.     

用时域ABCD矩阵对调Q锁模激光器的研究

用时域ABCD矩阵讨论了调Q锁模脉冲激光器输出脉冲的宽度和啁啾特性,主要给出了调Q元件作为幅度调制元件时的时域ABCD矩阵,并将光脉冲在激光腔中往返一周的ABCD矩阵写出,用此矩阵讨论了它对锁模脉冲的影响.给出了Nd:YAG激光器中用Cr⁴⁺:YAG作调Q元件时的调Q锁模脉冲激光器特性,并讨论了腔内色散、饱和吸收强度、增益带宽对输出脉冲特性的影响.用时域ABCD矩阵大大简化了计算过程.     

Measurement ofJand Dipolar Couplings from Simplified Two-Dimensional NMR Spectra

Simple procedures are described for recording complementary in-phase and antiphaseJ-coupled NMR spectra. The sum and difference of these spectra contain only the upfield and the downfield components of a doublet, making it possible to measure theJsplitting directly from these combinations without an increase in resonance overlap relative to the decoupled spectrum. The approach is demonstrated for measurement of¹J_NHsplittings and²J_HNC′splittings in oriented and isotropic ubiquitin. Dipolar couplings obtained from differences in the splittings measured in the oriented and isotropic phases are in excellent agreement with dipolar couplings obtained from direct measurement of the splitting or from a conventional E.COSY-type measurement.     

A Model of spin catalysis in bacterial photosynthetic reaction centres

A model of influence of non-heme Fe²⁺ ion on kinetics of electron transfer between quinone anion-radicals Q_A⁻ and Q_B⁻ in bacterial reaction centres is proposed and investigated. Physical mechanism of the influence is associated with singlet-triplet transitions in Q_A⁻Q_B⁻ Pair caused by interactions with paramagnetic Fe²⁺. The model incorporates exchange couplings between the particles and zero-field splittings in high-spin Fe²⁺. These interactions are shown to catalyze electron transfer in triplet pairs and alter the reaction yield significantly.     

Z′ search in e+e− annihilation

Expectations for constraints on extra Z bosons are derived for LEP2 and future linear e⁺e^? colliders. For typical GUTs, a Z′ with M_Z′ ≤ 3 to $6sqrt {s}$ may cause observable effects. The Z′ discovery limits are dominated by statistical errors. However, if a Z′ signal is observed, the discrimination between different models becomes much worse if systematic errors are taken into account. Discrimination between models is possible for $M_{Z^{?ime}} < 3sqrt {s}$. A determination of Z′ff couplings independently of models becomes attractive with future colliders. Anticipated bounds are determined.     

Two new integrable couplings of the soliton hierarchies with self-consistent sources

A kind of integrable coupling of soliton equations hierarchy with self-consistent sources associated with sl(4) has been presented (Yu F J and Li L 2009 Appl. Math. Comput. 207 171; Yu F J 2008 Phys. Lett. A 372 6613). Based on this method, we construct two integrable couplings of the soliton hierarchy with self-consistent sources by using the loop algebra sl(4). In this paper, we also point out that there are some errors in these references and we have corrected these errors and set up new formula. The method can be generalized to other soliton hierarchy with self-consistent sources.     

Electromagnetic form factor via Bethe-Salpeter amplitude in Minkowski space

For a relativistic system of two scalar particles, we find the Bethe-Salpeter amplitude in Minkowski space and use it to compute the electromagnetic form factor. The comparison with Euclidean space calculation shows that the Wick rotation in the form factor integral induces errors which increase with the momentum transfer Q². At JLab domain (Q ² = 10 GeV^2/c²), they are about 30%. Static approximation results in an additional and more significant error. On the contrary, the form factor calculated in light-front dynamics is almost indistinguishable from the Minkowski space one.     

Electroweak form factors of non-strange baryons

We compute electroweak form factors of the nucleon and photon transition form factors of non-strange baryon resonances up to the third resonance region in a model with instanton-induced interaction. The calculation is based on the Bethe-Salpeter equation for three light constituent quarks and is fully relativistic (U. L?ring et al., Eur. Phys. J. A 10, 309 (2001)). Static nucleon properties and photon resonance couplings are in good agreement with experiment and the Q² behaviour of the experimentally known form factors up to large momentum transfer is accounted for. Received: 4 April 2002 / Accepted: 2 May 2002     

All Stable Characteristic Classes of Homological Vector Fields

An odd vector field Q on a supermanifold M is called homological, if Q ² = 0. The operator of Lie derivative L _Q makes the algebra of smooth tensor fields on M into a differential tensor algebra. In this paper, we give a complete classification of certain invariants of homological vector fields called characteristic classes. These take values in the cohomology of the operator L _Q and are represented by Q-invariant tensors made up of the homological vector field and a symmetric connection on M by means of the algebraic tensor operations and covariant differentiation.     

Measurement of charged current triple gauge boson couplings using W pairs at LEP

Triple gauge boson couplings are measured from W-pair events recorded by the OPAL detector at LEP at centre-of-mass energies of 183 - 209 GeV with a total integrated luminosity of 680 pb^-1. Only CP-conserving couplings are considered and SU(2) x U(1) relations are used, resulting in four independent couplings, and g^z₅. Determining each coupling in a separate fit, assuming the other couplings to take their Standard Model values, we obtain , g^z₁ = 0.987 ^{+ 0.034}_-0.033, and g^z₅ = -0.04 ^{+ 0.13}_-0.12, where the errors include both statistical and systematic uncertainties. Fits are also performed allowing some of the couplings to vary simultaneously. All results are consistent with the Standard Model predictions.Received: 14 July 2003, Published online: 9 March 2004     

Effect of laser dye deterioration on performance

Loss of gain in a dye medium as a result of decomposition by pump photons is considered in terms of disappearance of dye molecules and the appearance of a new, single chemical product having absorption in the fluorescence band. The cases of small signal gain and saturated gain are applied to a single pass through a transversely excited amplifier. Loss of output, defined as “quantum yield of laser deterioration”,Q _L , is related to the true quantum yield of molecular destruction of the dye,Q _M , and other known parameters. For the experimentally common, saturated gain condition, the smallestQ _L can be isQ _M , which requires a photochemically bleachable dye with high gain, preferably at high concentration, in a long cavity, operating at high injection and pumping fluxes. Reversing these conditions, the highest valueQ _L can be, compared withQ _M , is unrestricted. This work was performed under the auspices of the U.S. Energy Research and Development Administration. Contract No. W 7405 Eng 48.     

A Two-Dimensional One Component Plasma and a Test Charge: Polarization Effects and Effective Potential

We study the effective interactions between a test charge Q and a one-component plasma, i.e. a complex made up of mobile point particles with charge q, and a uniform oppositely charged background. The background has the form of a flat disk, in which the mobile charges can move. The test particle is approached perpendicularly to the disk, along its axis of symmetry. All particles interact by a logarithmic potential. The long and short distance features of the effective potential—the free energy of the system for a given distance between Q and the disk—are worked out analytically in detail. They crucially depend on the sign of Q/q, and on the global charge borne by the discotic complex, that can vanish. While most results are obtained at the intermediate coupling Γ≡βq ²=2 (β being the inverse temperature), we have also investigated situations with stronger couplings: Γ=4 and 6. We have found that at large distances, the sign of the effective force reflects subtle details of the charge distribution on the disk, whereas at short distances, polarization effects invariably lead to effective attractions.     

Measurement of Small One-Bond Proton–Carbon Residual Dipolar Coupling Constants in Partially Oriented C Natural Abundance Oligosaccharide Samples: Analysis of Heteronuclear JCH-Modulated Spectra with the BIRD Inversion Pulse

Two 2D J-modulated HSQC-based experiments were designed for precise determination of small residual dipolar one-bond carbon–proton coupling constants in ¹³C natural abundance carbohydrates. Crucial to the precision of a few hundredths of Hz achieved by these methods was the use of long modulation intervals and BIRD pulses, which acted as semiselective inversion pulses. The BIRD pulses eliminated effective evolution of all but ¹J_CH couplings, resulting in signal modulation that can be described by simple modulation functions. A thorough analysis of such modulation functions for a typical four-spin carbohydrate spin system was performed for both experiments. The results showed that the evolution of the ¹H–¹H and long-range ¹H–¹³C couplings during the BIRD pulses did not necessitate the introduction of more complicated modulation functions. The effects of pulse imperfections were also inspected. While weakly coupled spin systems can be analyzed by simple fitting of cross peak intensities, in strongly coupled spin systems the evolution of the density matrix needs to be considered in order to analyse data accurately. However, if strong coupling effects are modest the errors in coupling constants determined by the “weak coupling” analysis are of similar magnitudes in oriented and isotropic samples and are partially cancelled during dipolar coupling calculation. Simple criteria have been established as to when the strong coupling treatment needs to be invoked.     

Efficient Hopfield pattern recognition on a scale-free neural network

Neural networks are supposed to recognise blurred images (or patterns) of N pixels (bits) each. Application of the network to an initial blurred version of one of P pre-assigned patterns should converge to the correct pattern. In the “standard" Hopfield model, the N “neurons” are connected to each other via N² bonds which contain the information on the stored patterns. Thus computer time and memory in general grow with N². The Hebb rule assigns synaptic coupling strengths proportional to the overlap of the stored patterns at the two coupled neurons. Here we simulate the Hopfield model on the Barabási-Albert scale-free network, in which each newly added neuron is connected to only m other neurons, and at the end the number of neurons with q neighbours decays as 1/q ³. Although the quality of retrieval decreases for small m, we find good associative memory for 1 ≪ m ≪ N. Hence, these networks gain a factor N/m ≫ 1 in the computer memory and time. Received 12 January 2003 Published online 11 April 2003 RID="a" ID="a"e-mail: stauffer@thp.uni-koeln.de