Multistability of delayed complex-valued recurrent neural networks with discontinuous real-imaginarytype activation functions

In this paper, the multistability issue is discussed for delayed complex-valued recurrent neural networks with discontinuous real-imaginary-type activation functions. Based on a fixed theorem and stability definition, sufficient criteria are established for the existence and stability of multiple equilibria of complex-valued recurrent neural networks. The number of stable equilibria is larger than that of real-valued recurrent neural networks, which can be used to achieve high-capacity associative memories. One numerical example is provided to show the effectiveness and superiority of the presented results.     

Multistability in bidirectional associative memory neural networks

In this Letter, the multistability issue is studied for Bidirectional Associative Memory (BAM) neural networks. Based on the existence and stability analysis of the neural networks with or without delay, it is found that the 2n-dimensional networks can have n³ equilibria and n² equilibria of them are locally exponentially stable, where each layer of the BAM network has n neurons. Furthermore, the results has been extended to (n+m)-dimensional BAM neural networks, where there are n and m neurons on the two layers respectively. Finally, two numerical examples are presented to illustrate the validity of our results.     

Multistability and multiperiodicity of delayed Cohen-Grossberg neural networks with a general class of activation functions

In this paper, by using analysis approach and decomposition of state space, the multistability and multiperiodicity issues are discussed for Cohen-Grossberg neural networks (CGNNs) with time-varying delays and a general class of activation functions, where the general class of activation functions consist of nondecreasing functions with saturation’s including piecewise linear functions with two corner points and standard activation functions as its special case. Based on the Cauchy convergence principle, some sufficient conditions are obtained for checking the existence and uniqueness of equilibrium points of the n-neuron CGNNs. It is shown that the n-neuron CGNNs can have 2ⁿ locally exponentially stable equilibrium points located in saturation regions. Also, some conditions are derived for ascertaining equilibrium points to be locally exponentially stable or globally exponentially attractive and to be located in any designated region. As an extension of multistability, some similar results are presented for ascertaining multiple periodic orbits when external inputs of the n-neuron CGNNs are periodic. Finally, three examples are given to illustrate the effectiveness of the obtained results.     

A theoretical prediction on the ground‐state complexes bound by metal ions to thymine base isomers

Stability orderings of 150 stable complexes formed by metal ions (Na⁺, K⁺, Ca²⁺, Mg²⁺, and Zn²⁺) and 13 stable thymine tautomers in both solvent and gas phases are obtained, and the optimal binding site for a metal ion in a specific thymine tautomer is identified. Results indicate that the complex with the canonical thymine tautomer (T1) is more stable than those with the rare ones, and the monodentate complex M–T1o4(o2) are their ground‐state form in the solvent phase. The ground‐state thymine complexes bound by Ca²⁺, Mg²⁺, or Zn²⁺ become bidentate M–T3o4lo2,n3, which is derived from a rare thymine tautomer T3o4l, whereas those bound by Na⁺ and K⁺ are still monodentate complexes M–T1o4(o2), however, in the gas phase. The differences in stability are discussed in detail from the binding strength of metal ions, relative energy of the corresponding thymine tautomers, and solution effect. Copyright © 2011 John Wiley & Sons, Ltd.     

非定域位势e-μr/r·e-μr′/r′·e-αR/R及e-μr/r·e-μr′/r′·e(-(β(r+r′))1/2·R))/R的Regge渐近行为

本文证明了两个物理上有兴趣的非定域位势e^-μr/r·e^-μr′/r′·e^-αR/R及e^-μr/r·e^-μr′/r′·e^{(-(β(r+r′))1/2·R)})/R的分波S矩阵元对动量变数k在除沿虚轴的割线(-∞i,0),(μi,∞i)的全平面,对角动量变数λ在右半平面Reλ>-1/2的半纯性和当k,λ分别趋于无穷大时的渐近性质。最后得到了Regge渐近行为。     

Influence of the rhenium carrier in eluate of Re-188 on its binding with potassium-sodium salt of hydroxyethylidene biphosphonic acid

The results of investigation of the regularity of ¹⁸⁸Re binding with KNaHEDP and hydrolysis of the complex compound (¹⁸⁸Re-KNaHEDP) have shown that its quality depends to a considerable extent on the reaction conditions. Concentrations of a reducing agent (Sn²⁺) and stable rhenium in the ¹⁸⁸Re eluate, as the carrier, influence essentially the rate of formation and stability of ¹⁸⁸Re complex with KNaHEDP. The results of the kinetic investigations of the ¹⁸⁸Re-KNaHEDP complex formation prove that the reaction character bears a direct relationship to the concentrations of the complexing agent (Re) and the reducer (Sn²⁺). The higher ratio of Re⁷⁺: Sn²⁺ concentrations, the more effectively ¹⁸⁸Re binds with KNaHEDP. The obtained results prove that for ¹⁸⁸Re binding with KNaHEDP with the efficiency not less than 95% the optimum concentration of stable rhenium in the reaction mixture is 0.54×10⁻⁶ mol·ml⁻¹ (0.1 mgMml⁻¹) and the ratio of Re⁷⁺: Sn²⁺ concentrations should not be lower than 10: 1.     

Relative equilibria of D2H + and H2D+

Relative equilibria of molecules are classical trajectories corresponding to steady rotations about stationary axes during which the shape of the molecule does not change. They can be used to explain and predict features of quantum spectra at high values of the total angular momentum J in much the same way that absolute equilibria are used at low J. This paper gives a classification of the symmetry types of relative equilibria of AB₂ molecules and computes the relative equilibria bifurcation diagrams and normal mode frequencies for D₂H⁺ and H₂D⁺. These are then fed into a harmonic quantization procedure to produce a number of predictions concerning the structures of energy level clusters and their rearrangements as J increases. In particular the formation of doublet pairs is predicted for H₂D⁺ from J ≈ 26.     

Symmetry dependence of rms Charge Radii

The nucleon number dependence of rms charge radii is often approximated by some simple formula containing the mass number only, R(A)=r(A)A^1/3, where r(A) is a slowly varying function of A. However, for nuclei off the stability line, the mass number A=N + Z is not enough to characterise the dependence of the R(Z, N) radius surface on the nucleon numbers Z and N. In the present work, an additional term has been included, depending on the symmetry parameter I=(N ? Z)/A. Several parametrisations were tried, using weighted least-squares procedures for the fit to a present-day data base. The best fit (with χ²/ń=17) was found for R(A, I)=r(A)A^1/3 + b_I/(I ? I_stab), where I_stab=(N_stab ? Z_stab)/A is the value of the symmetry parameter of the stable isobar with mass number A, and b_I=?0.83 fm. The formula R(A, I)=[r(A) + a_I(I ? I_stab)]A^1/3 is only slightly inferior to the previous one, moreover, it is supported by simple model calculations; here a_I=?0.20 fm (χ²/ń=20). The difficulty in determining the right parametrisation is caused by the fact that the surface R_exp(A, I) is not smooth: there are strong shell and deformation effects. To avoid the distorting effect of these deviations on the parameter values, more than half of the original data had to be omitted.     

Stability analysis of a class of generalized neural networks with delays

In this Letter, we discuss the global asymptotic stability and exponential stability of the equilibrium point of a class of generalized neural networks with delays. By introducing a new type of Lyapunov functionals and making use of matrix inequality technique, some sufficient conditions for existence and uniqueness of equilibrium and global exponential stability of the delayed Cohen–Grossberg neural networks are obtained. The conditions of the presented results are less restrictive than those of the earlier literature.     

Fast convergence of spike sequences to periodic patterns in recurrent networks

The dynamical attractors are thought to underlie many biological functions of recurrent neural networks. Here we show that stable periodic spike sequences with precise timings are the attractors of the spiking dynamics of recurrent neural networks with global inhibition. Almost all spike sequences converge within a finite number of transient spikes to these attractors. The convergence is fast, especially when the global inhibition is strong. These results support the possibility that precise spatiotemporal sequences of spikes are useful for information encoding and processing in biological neural networks.     

Clustering in neural networks with heterogeneous and asymmetrical coupling strengths

The existence and stability of phase-clustered states have been studied previously in networks of weakly coupled oscillators with uniform coupling strengths [Physica D 63 (1993) 424]. However, several studies have shown that if the coupling is uniform and repulsive, it is hard to obtain stable phase-clustered states in networks of realistic neural oscillators when noise is present [Neural Comput. 7 (1995) 307; Phys. Rev. E 57 (1998) 2150]. This problem was avoided by introducing heterogeneity in the distribution of coupling strengths [J. Phys. Soc. Jpn. 72 (2003) 443]. It has been shown that heterogeneous coupling strengths make the occurrence of stable clustered states possible in small networks of repulsively coupled neural oscillators of all kinds [J. Comput. Neurosci. 14 (2003) 139; SIAM J. Appl. Math., submitted for publication]. The present work extends these results to large networks of N identical neurons that are globally coupled with heterogeneous and asymmetrical coupling strengths. Conditions for the existence and stability of a state of n synchronized clusters at evenly distributed phases, called the state of n splay-phase clusters, are derived. Clusters of different sizes, i.e. containing different numbers of neurons, are studied. The existence of such a state is guaranteed if the strength of the coupling originating from one neuron to other neurons is inversely proportional to the size of the cluster to which it belongs. This condition is called the rule of inverse cluster-size. At the state of n splay-phase clusters, the N-neuron network behaves like a network of n “big neurons”. Stability of this state is determined by n eigenvalues of which only one determines the stability of intra-cluster phase differences. The remaining n−1 conditions determine the stability of inter-cluster phase differences, but only n_h=(n− mod (n,2))/2 of them have distinct real parts due to symmetry. Heterogeneous coupling makes the stability conditions depend on coupling strengths. This analysis not only reveals how clustered states occur in more general kinds of networks, but also illustrates how the stability of clustered states can be achieved in networks of repulsively coupled neural oscillators. Results on clustered states with phases that are not evenly distributed in the phase space are also presented. Potential applications of these results are discussed.     

Synthesization of high-capacity auto-associative memories using complex-valued neural networks

In this paper, a novel design procedure is proposed for synthesizing high-capacity auto-associative memories based on complex-valued neural networks with real-imaginary-type activation functions and constant delays. Stability criteria dependent on external inputs of neural networks are derived. The designed networks can retrieve the stored patterns by external inputs rather than initial conditions. The derivation can memorize the desired patterns with lower-dimensional neural networks than real-valued neural networks, and eliminate spurious equilibria of complex-valued neural networks.One numerical example is provided to show the effectiveness and superiority of the presented results.     

Multiplicity of metastable retrieval phases in networks of multistate neurons

It is demonstrated that networks of multistate neurons storing an ensemble of multistate patterns exhibit a multiplicity of metastable retrieval phases. These phases are described by solutions of fixed-point equations with characteristic retrieval errors. They emerge if the gain of the neural input-output relation is varied. The number of these phases increases asQ ² with the numberQ of gray levels available to each neuron. Implications for the optimal gain function and basins of attraction are briefly discussed. Again, networks endowed with pseudoinverse couplings are found to perform better than networks with Hebbian couplings: at moderate loading levels phases with retrieval errors are destabilized, whereas the error-free phase remains stable up to the theoretically possible maximum, if the gain parameter is properly chosen.     

混沌神经网络的延时反馈控制研究

针对混沌神经网络，提出了一种改进的延时反馈控制方法. 利用该方法，当延时参数τ为奇数时，被控神经网络收敛于记忆模式以及它的反相模式的2周期上. 若选取不同的延时参数，被控网络则收敛于不同的周期态上. 关键词： 控制混沌 延时反馈控制 混沌神经网络     

Long-lived diatomic dications: potential curves and radiative lifetimes for CaBr2+ and CaI2+ including relativistic effects

Relativistic effective core potential calculations have been employed in the framework of a spin–orbit configuration interaction to compute the lowest-lying electronic states of the CaBr²⁺ and CaI²⁺ dications, and the results are compared with the data for the isovalent CaCl²⁺ system studied earlier. The ground X²Π state in all three dications arises from a strong polarization of X(²P°)(X= Cl, Br or I) by the Ca²⁺(¹S) ion and is bound by 0·96–1·55eV with respect to the corresponding diabatic dissociation limits. It is split by the spinorbit interaction into the X₁ ²Π_3/2 and X₂ ²Π_1/2 components, with the energy splittings calculated to be 647 cm^-1(CaCl²⁺), 2115 cm^-1(CaBr²⁺) and 3544 cm^-1(CaI²⁺). The X₁ and X₂ states are found to be thermodynamically stable in CaCl²⁺ and CaBr²⁺, while in CaI²⁺ the lowest dissociation limit, Ca⁺+(²S)+ I^{+ 3}P₂), lies 1700 and 5200 cm^-1 lower than the X₁ and X₂ minima respectively. The X₁ and X₂ states in CaI²⁺ are extremely long-lived, however, owing to the high and very broad potential barriers to dissociation. The first electronic excited state, A²σ⁺, is also bound in all the above systems, although it is pre-dissociated in CaBr²⁺and CaI²⁺ at large internuclear distances. All other low-lying electronic states of CaX²⁺ are repulsive. Electric-dipole moments are calculated for the A→ X₁, X₂ transitions. The corresponding radiative lifetimes are found to be very long in CaCl²⁺ : τ(A→X₁) = 19·3 ms and τ(A→X₂) = 9·9 ms (the values are given for ν' = 0), and become very significantly shorter for CaBr²⁺ and CaI²⁺ because of the stronger spin-orbit interaction in the heavier systems. This effect is especially noticeable for the A →X₂ transitions, for which the values are computed to be 364 μs in CaBr²⁺ and 50·3 μs in CaI²⁺. The theoretical data obtained should aid in the future spectroscopic detection of these species. To data no experiment of this type has been successfully carried out for any of the thermodynamically stable diatomic dications.     

Neutron scattering from equilibrium-swollen networks

Small-angle neutron scattering measurements were performed on end-linked poly (dimethylsiloxane) (PDMS) networks swollen to equilibrium with d-benzene. Comparison was made with equivalent concentration PDMS solutions. Equilibrium-swollen networks consistently displayed a linear scattering regime at low q followed by a good-solvent-like scaling regime at high q in agreement with the predictions of the Gel Tensile Blob (GTB) model. Data are fit using the unified function modified for the GTB model (3-parameter fit). Equilibrium-swollen networks display a base structural size, the gel tensile-blob size, ξ, that was found to be independent of the molecular weight between crosslinks for the series of molecular weights studied, consistent with the predictions of the model. The length of the extended tensile structure, L, can be larger than the length of the fully extended network strand. The predicted scaling relationship for L, L ∼ Q^1/2N_avg, where N_avg = (1/fN_c²+1/4N_e² , Q is the equilibrium swelling ratio, N_c is the molecular weight between crosslinks, N_e is the entanglement molecular weight and f is the crosslink functionality is in agreement with experimental results for the networks studied.     

Stochastic exponential stability of the delayed reaction-diffusion recurrent neural networks with Markovian jumping parameters

Some criteria for the global stochastic exponential stability of the delayed reaction-diffusion recurrent neural networks with Markovian jumping parameters are presented. The jumping parameters considered here are generated from a continuous-time discrete-state homogeneous Markov process, which are governed by a Markov process with discrete and finite state space. By employing a new Lyapunov-Krasovskii functional, a linear matrix inequality (LMI) approach is developed to establish some easy-to-test criteria of global exponential stability in the mean square for the stochastic neural networks. The criteria are computationally efficient, since they are in the forms of some linear matrix inequalities.     

Radial sternheimer shielding-antishielding for He,Ne, and Ar isoelectronic series

Sternheimer quadrupole shielding-antishielding factors γ(r) are reported for the positive ions of B³⁺, Al³⁺, Ca²⁺ and Sc³⁺ for the first time. The trends in γ(r) within the isoelectronic series corresponding to He, Ne and Ar atoms, respectively, are discussed by combining the present results with those reported earlier.     

Luminescence of Ca(NbO3)2:Pr3+: Pr3+ and self-trapped exciton emission

Photoluminescence and time resolved photoluminescence spectra of Ca(NbO₃)₂ doped with Pr³⁺, excited under 37,000 cm^?1 (270 nm), obtained at high hydrostatic pressure up to 20 kbar applied in a sapphire anvil cells, are presented. At ambient conditions, the emission spectrum obtained in the time interval 0–1 μs is dominated by spin allowed transitions from the ³P₀ state. The luminescence related to transitions from ¹D₂, characterized by a decay time equal to 33 μs, is observed when one excites directly the Pr³⁺ ion with 30,770 cm^?1 (325 nm) wavelength. The introduction of Pr³⁺ impurities in Ca(NbO₃)₂ does not quench the self-trapped exciton (STE) luminescence. This luminescence, peaking at 20,000 cm^?1 (500 nm), having a decay time of 61 ± 1 μs, still occurs when the crystal is excited with a wavelength of 37,000 cm^?1 (270 nm) or shorter. Under such excitation a fraction of the STE luminescence is reabsorbed by Pr³⁺ ions; in this case the emission lifetime of the ¹D₂ → ³H₄ transition of Pr³⁺ is 64 ± 3 μs. This effect is stable also at high pressure.     

Theoretical study of the CH3 + NS and related reactions: mechanism of HCN formation

More than thirty equilibrium and transition structures on the [CH₃NS] potential energy surface have been located using the B3LYP/6-311 + + G(d,p) method. Thioformaldoxime (3) turns out to be the most stable isomer followed by thionitrone (2), a three-membered ring, thionitrosyl methane (1) and thiazyl methane. These isomers are connected to each other by 1,2H and 1,3H shifts and ring—chain rearrangement, but the associated energy barriers are rather high, making most of them stable with respect to unimolecular transformations. Starting from CH₃ + NS, a possible initial atmospheric reaction, HCN formation appears to be the most favoured process through a cascade involvement of 1, 2 and 3. The standard heats of formation, ΔH ⁰ _f,298 are calculated to be: 3, 149kJmol^?1; and 1, 218kJmol^?1; using the CCSD(T)/6-311+ +G(3df,2p) method, with an error of ±10kJ mol^?1.