Nonlinear neural networks. II. Information processing

Information processing in nonlinear neural networks with a finite numberq of stored patterns is studied. Each network is characterized completely by its synaptic kernelQ. At low temperatures, the nonlinearity typically results in 2^q–2–q metastable, pure states in addition to theq retrieval states that are associated with theq stored patterns. These spurious states start appearing at a temperature , which depends onq. We give sufficient conditions to guarantee that the retrieval states bifurcate first at a critical temperatureT _c and that /T _c 0 asq. Hence, there is a large temperature range whereonly the retrieval states and certain symmetric mixtures thereof exist. The latter are unstable, as they appear atT _c . For clipped synapses, the bifurcation and stability structure is analyzed in detail and shown to approach that of the (linear) Hopfield model asq. We also investigate memories that forget and indicate how forgetfulness can be explained in terms of the eigenvalue spectrum of the synaptic kernelQ.     

Learning withQ-state clock neurons

We study the optimal learning capacity for neural networks withQ-state clock neurons, i.e. the states arecomplex numbers with magnitude 1 and azimuthal anglesn·2/Q, withn=0, 1, ...,Q–1. Performing a phase space analysis, the learning capacity _c for given stability can be expressed by means of a double-integral with a simple geometrical interpretation, which for vanishing reduces to _c (Q) = 4Q/(3Q–4), forQ3. Then we define a training algorithm, which generalizes the well-known AdaTron algorithm fromQ=2 toQ3 and converges very fast to the network with optimal stability, if the numberp of random patterns to be learned is smaller than _c (Q). Finally, in the conclusions, we also give hints on applications for image recognition and in a note added in proof we generalize some results to Potts model networks.     

TDPAC measurement of quadrupole interaction at111Cd in the nearly heavy fermion system USn2.9

Quadrupole interaction at¹¹¹Cd probe has been studied in the nearly heavy fermion system USn_3– using the TDPAC method. We observe a large quadrupole interaction frequency withv _Q =89.9(10) MHz at 300 K which is much higher than the earlier reported result. The observed frequency shows a linear temperature dependence in the range 25–300 K.     

On stationary topological solitons in a two-dimensional anisotropic Heisenberg model

We study stationary two-dimensional solitons in an easy-axis Heisenberg magnet with the Hamiltonian density wherei=1, 2,a=1, 2, 3, and (x _i ) is the angle between unit vector s(x _i ) and the easy axis, 0<p<. Stable solitons with a topological chargeQ=1 and localized distributionss ^a (x _i ) withQ=2 are found. The existence of the bound states of two solitons withQ=1 is shown numerically for 0<p<.     

Intrinsic point defects in niobium: Trapping at100Pd and111In impurities observed by PAC

Radiation-induced lattice defects in high-purity niobium have been investigated in the temperature range of 30K to 540 K by means of - perturbed angular correlation (PAC) measurements using the radioactive probes¹⁰⁰Pd/¹⁰⁰Rh and¹¹¹In/¹¹¹Cd. Both probes were produced within the niobium samples by means of heavy-ion nuclear reactions. At the Pd impurities trapping of defects occurred during heavy-ion irradiation at about 30 K in two defined configurations: defect 1(Pd) withv _Q1=e ² qQ/h=42(±2) MHz, ₁=0 and defect 2 (Pd) withv _Q2=(±2) MHz, ₂=1. Two defects were observed at the In impurities in annealing stage III (around 250 K) after heavy-ion as well as electron irradiations: defect 1(In) withv _Q1=87(±1) MHz, ₁=0 and defect 2(In) withv _Q2=105(±2) MHz, ₂=0.65(±0.02). A third defect (defect 3(In):v _Q3=177(±2) MHz, ₃0.2) appeared above 260 K after heavy-ion irradiation only. The data are interpreted in terms of interstitial trapping at the Pd impurities and vacancy trapping at the In impurities. Information on the microscopic structure of defect 1(In) and 2(In) is obtained from a PAC-single-crystal experiment. For defect 1(In) axial 111-symmetry is found, which leads us to identify this defect with a monovacancy as nearest neighbor with respect to the In probe. Defect 2(In) is the trapped divacancy for which an orientation is found that is consistent with both vacancies being nearest neighbor to the probe but second nearest neighbors to each other.     

Magnetic monopole interactions: Shell structure of meson and baryon states

It is suggested that a low-mass magnetic monopole of Dirac chargeg=(137/2)e may be interacting with ac-quark's magnetic dipole moment to produce Zeeman splitting of meson states. The massM ₀=2397 MeV of the monopole is in contrast to the 10¹⁶-GeV monopoles of grand unification theories (GUT). It is shown that shell structure of energyE _n =M ₀+1/4nM ₀+ exists for meson states. The presence of symmetric meson states leads to the identification of the shell structure. The possible existence of the 2397-MeV magnetic monopole is shown to quantize quark masses in agreement with calculations of quantum chromodynamics (QCD). From the shell structure of meson states, the existence of two new mesons is predicted:(1814±50 MeV) withI ^G(J ^PC =0⁺(0^–+) and _c (3907±100 MeV) withJ ^PC =0^–+. The presence of shell structure for baryon states is shown.     

Electrical properties and defect model of tin-doped indium oxide layers

Tin-doped In₂O₃ layers were prepared by the spray technique with doping concentrationsc _Sn between 1 and 20 at. % and annealed at 500 °C in gas atmospheres of varying oxygen partial pressures. The room-temperature electrical properties were measured. Maximum carrier concentrationsN=1.5×10²¹cm^–3 and minimum resistivities =1.3×10^–4 cm are obtained if the layers are doped withc _Sn9 at. % and annealed in an atmosphere of oxygen partial pressurep _O2 10^–20 bar. At fixed doping concentration, the carrier mobility increases with decreasing oxygen pressure. The maximum obtainable mobility can be described in terms of electron scattering by ionized impurities. From an analysis of the carrier concentration and additional precision measurements of the lattice constants and film thicknesses, a defect model for In₂O₃:Sn is developed. This comprises two kinds of interstitial oxygen, one of which is loosely bound to tin, the other forming a strongly bound Sn₂O₄ complex. At low doping concentrationc _Sn4 at. % the carrier concentration is governed by the loosely bound tin-oxygen defects which decompose if the oxygen partial pressure is low. The carrier concentration follows from a relationN=K ₁ ·p _O2 ^–1/8 ·(3 ×10¹⁰ × c_Sn –N)^1/4 with an equilibrium constantK ₁=1.4×10¹⁵ cm^–9/4bar^1/8, determined from our measurements.     

Magnetic and electric hyperfine interactions in the system EuSm

Magnetic and electric hyperfine interactions in the system EuSm were investigated with the isomeric 11/2^– state in¹⁴⁵Eu by applying the time-differential perturbed angular distribution (TDPAD) method. The temperature dependence of paramagnetism was studied between 90 K and 1000 K by measuring the magnetic hyperfine interaction frequency _L=g_NN¹ (T)B_ext. The paramagnetic correction factor strictly follows the Curie-Weiss relation =1+C/(T-), withC=–50(2) K and =–29(5) K. This is compatible with a hyperfine field ofB _int(0)=–25(1) T, a valence of two for Eu in Sm, and antiferromagnetic order at low temperatures.The temperature dependence of the electric quandrupole coupling constant v_Q, investigated between 100 K and 400 K, can be reproduced by a linear temperature variation v_Q(T)=v_Q(0) (1-AT), with v_Q(0)=16.2(4) MHz andA=7.2(8)·10^–4 K^–1.The paramagnetic relaxation time _rel of the nuclear alignment is proportional to the temperature of the sample, with _rel T^–1=3.7(2) ·10^–9s K^–1.This leads to the Korringa relation _J T=const=5.1(5)·10^–11s K for the relaxation time of the 4f electronic spinJ. Assuming that the relaxation ofJ is mainly caused by exchange interaction between conduction electrons and localized 4f electrons at the Eu site, an exchange integral of |J _eff|=0.10(2) eV can be deduced.     

Excitation of the 7s2P1/2, 3/2 levels of Xe+ due to charge exchange in the negative glow of a glow discharge in a neon-xenon mixture

It is shown that in the negative glow of a glow discharge in mixtures of neon with xenon (xenon contents of 5.5·10^–3 to 2% of the total pressure P of the mixture) with P=15 torr and discharge currents i=40 mA (cathode diameter 30 mm), the 7s²P_{1/2, 3/2} levels of the Xe⁺ ion are excited by the charge exchange reaction Xe ^m + Ne⁺ Xe^+* + Ne.The effective cross section Q_3/2 for excitation of the 7s²P_3/2 level is estimated to lie between 10^–14 and 10^–15 cm² and Q_3/26.5 × Q_1/2, where Q_1/2 is the effective cross section for excitation of the 7s²P_1/2 level.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii Fizika, No. 3, pp. 96–99, March, 1979.     

Measurement of the diffractive structure function in deep inelastic scattering at HERA

This paper presents an analysis of the inclusive properties of diffractive deep inelastic scattering events produced inep interactions at HERA. The events are characterised by a rapidity gap between the outgoing proton system and the remaining hadronic system. Inclusive distributions are presented and compared with Monte Carlo models for diffractive processes. The data are consistent with models where the pomeron structure function has a hard and a soft contribution. The diffractive structure function is measured as a function ofx , the momentum fraction lost by the proton, of , the momentum fraction of the struck quark with respect tox , and ofQ ² in the range 6.3·10^–4x <>^–2, 0.1<0.8 and=">Q ²<100>². The dependence is consistent with the formx wherea=1.30±0.08(stat) _–0.14 ^+0.08 (sys) in all bins of andQ ². In the measuredQ ² range, the diffractive structure function approximately scales withQ ² at fixed . In an Ingelman-Schlein type model, where commonly used pomeron flux factor normalisations are assumed, it is found that the quarks within the pomeron do not saturate the momentum sum rule.supported by Worldlab, Lausanne, Switzerland     

Geometry of KDV (2): Three examples

LetQ be a 1-dimensional Schrödinger operator with spectrum bounded from –. Byaddition I mean a map of the formQQ=Q–2D ² lge withQe=e, to the left of specQ, and either _– ⁰ e ² or ₀ e² finite. Theadditive class ofQ is obtained by composite addition and a subsequent closure; it is a substitute for the KDV invariant manifold even if the individual KDV flows have no existence. KDV(1) = McKean [1987] suggested that the additive class ofQ is the same as itsunimodular spectral class defined in terms of the 2×2 spectral weightdF by fixing (a) the measure class ofdF, and (b) the value of detdF. The present paper verifies this for (1) the scattering case, (2) Hill's case, and (3) when the additive class is finite-dimensional (Neumann case).This paper is dedicated to the memory of Mark Kac by a grateful student. Courant Institute of Mathematical Sciences, New York, New York.     

Deep bandtail states picosecond intensity-dependent carrier dynamics of GaN epilayer under high excitation

Picosecond carrier dynamics of deep bandtail states (3.1 eV) in an unintentionally n-doped GaN epilayer at room temperature under high excitation densities (i.e., N ₀ = 1.0× 10¹⁹– 1.1× 10²⁰ cm^–3) have been investigated with nondegenerate femtosecond pump–probe (267/400 nm) reflectance ( R/R ₀). All R/R ₀ traces possess a 2 ps buildup time that represents an overall time for the initial non-thermal carrier population to relax towards the continuum extremes and then into the probed tail states. We observe a saturation of R/R ₀ initial (first 10 ps) recovery rate _i at a density of 5– 6×10¹⁹ cm^–3 close to the Mott transition threshold obtained from time-integrated PL measurements. Such a saturation phenomenon has been identified as the trap-bottleneck due to the bandtail states and deep traps. As N ₀ is further increased, _i accelerates due to the onset of Auger recombination as the trap-bottleneck becomes effective. The best fit by the Auger model for N ₀ in the range of the mid-10¹⁹–10²⁰ cm^–3 yields an Auger coefficient of C _a 5.0× 10^–30 cm⁶ s^–1.     

Narrow-band extreme-ultraviolet laser radiation tunable in the range 90.5–95 nm

Tunable, narrowband extreme ultraviolet radiation in the range 90.5–95 nm with only limited intensity variations is produced by frequency-tripling ultraviolet light from a frequency-doubled dye laser in a gas-jet of xenon. Acetylene gas is found to be an efficient medium for third-harmonic generation in this wavelength range as well. The extreme-ultraviolet radiation is applied in a spectroscopic study of the b ¹ II _u , v=6–8 and v=10–12, o ¹ II _u , v=0 and b¹ _u ⁺ , v=9 states of molecular nitrogen. From linewidth measurements a value k _p=6×10¹⁰ s^–1 for the predissociation rate of the b ¹ II _u , v=11 state is deduced.     

Exact ground states of two-dimensional ±J Ising spin glasses

In this paper we study the problem of finding an exact ground state of a two-dimensional ±J Ising spin glass on a square lattice with nearest neighbor interactions and periodic boundary conditions when there is a concentrationp of negative bonds, withp ranging between 0.1 and 0.9. With our exact algorithm we can determine ground states of grids of sizes up to 50×50 in a moderate amount of computation time (up to 1 hr each) for several values ofp. For the ground-state energy of an infinite spin-glass system withp=0.5 we estimateE _0.5 =–1.4015±0.0008. We report on extensive computational tests based on more than 22,000 experiments.     

Time-energy uncertainty and relativistic canonical commutation relations in quantum spacetime

It is shown that the time operatorQ ⁰ appearing in the realization of the RCCR's [Q,P^v]=–jhg^v, on Minkowski quantum spacetime is a self adjoint operator on Hilbert space of square integrable functions over _m =×v _m , where is a timelike hyperplane. This result leads to time-energy uncertainty relations that match their space-momentum counterparts. The operators Q appearing in Born's metric operator in quantum spacetime emerge as internal spacetime operators for exciton states, and the condition that the metric operator should possess a ground exciton state assumes the significance of achieving minimal spacetime4-momentum uncertainty in fundamental standards for spacetime measurements.Supported in part by NSERC research grant No. A5206.     

Dynamic restoration of 24% chromium ferritic steels

Kinetics of ferrite dynamic recrystallization with 24% chromium steels was studied by means of laboratory tests. Recrystallization was studied in a temperature range of 1173 to 1573 K at deformation rates to 5×10¹ s^–1. The kinetics of ferrite dynamic recrystallization was evaluated by means of a parametric equation dependent on the Zener-Hollomon parameter. The results proved that in using the recrystallization activation energyQ _RD= = 273·9 k J mol^–1 the constants of the parametric equation, determined earlier for austenite, are valid for ferrite as well. In addition, the dependence of the grarn size on deformation stress and on carbonitride stabilization was assessed.     

The electric field gradient at iodine impurities in zinc and cadmium

The electric quadrupole interaction at iodine implanted in zinc and cadmium single crystals is investigated, using the - perturbed angular correlation technique. The results show that the implanted¹²⁹Te and¹³²Te isotopes occupy two well-defined sites, identified by the electric field gradient parameters. One fraction of the impurities is substitutionally implanted, witheq _zz=–1.49(9)10¹⁸ and –1.58(15)10¹⁸V/cm², in Zn and Cd respectively. The other fraction is identified as an impurity-divacancy configuration with |eq _zz |=3.81(8)10¹⁸V/cm²; =0.72(4) for Zn and |eq _zz |=3.55(11)10¹⁸V/cm²; =0.53(13) for Cd. The electronic enhancement in the electric fieldgradient at the substitutional site equalsK=–0.66 and –0.56 respectively and follows the empirical trend ofK versus the impurity valence for the s-p elements in Zinc.     

RF properties of superconducting vanadium

Q values of a superconducting vanadium cavity in theT E ₀₁₁ mode at 9.6 GHz were measured to determine the residual surface resistanceR ₀ and the reduced energy gap 2(0)/kT _c with respect to different surface treatments such as electropolishing, oxipolishing and anodizing. The residual surface resistance was found to be lowest for the oxipolished cavity, corresponding to a residualQ of 2×10⁸ at 1.2 K. Independent of the surface treatment the reduced energy-gap value amounted to 3.52±0.1. The influence of different vanadium oxides on the rf properties of superconducting vanadium was investigated.     

Gamow-Teller beta decay of the very neutron-deficientN=50 nuclide98Cd

For the first time, detailed decay-spectroscopic investigations were performed for the very neutron-deficientN=50 nuclide⁹⁸Cd. The⁹⁸Cd activity was produced in spallation reactions between 600 MeV protons and a natural tin target, yielding a⁹⁸Cd beam intensity of 10 to 60 atoms/s at the collector of the ISOLDE massseparator. By means of-ray and conversion-electron spectroscopy, 19 transitions were found to follow the ⁺/EC decay⁹⁸Cd⁹⁸Ag. The transitions at 61 and 107 keV were shown to beM1(+E2) andE2, respectively, and the⁹⁸Cd half-life was measured as 9.2±0.3 s. TheQ _EC value of⁹⁸Cd is determined semiempirically and is compared to model predictions together with the measuredQ _EC values of the neighbouring cadmium isotopes^100,102Cd and theN=50 isotones⁹²Mo,⁹⁴Ru, and⁹⁶Pd, taken from the literature. The newly established decay scheme of⁹⁸Cd includes 9 excited states of⁹⁸Ag. Four states at 1691, 1861, 2164, and 2544 keV are directly fed by 0⁺ 1⁺ Gamow-Teller beta transitions with a summed strength of 3.5 _–0.7 ^+0.8 . This value corresponds to 25±5% of the strength predicted for the GT transformation of a g_9/2 proton (in⁹⁸Cd) into a g_7/2 neutron (in⁹⁸Ag) by the extreme single-particle shell model. The GT-strength splitting and quenching, observed for⁹⁸Cd, are compared with the corresponding data for lighter even-even N=50 isotones, and are discussed with reference to the predictions of more sophisticated nuclear models. We find that only in some cases it is possible to explain qualitatively the observed GT strength distribution and its total magnitude without renormalizing the free-neutron value of the axial-vector coupling constant.Dedicated to Prof. P. Armbruster on the occasion of his 60th birthday     

The computer as a physical system: A microscopic quantum mechanical Hamiltonian model of computers as represented by Turing machines

In this paper a microscopic quantum mechanical model of computers as represented by Turing machines is constructed. It is shown that for each numberN and Turing machineQ there exists a HamiltonianH _N ^Q and a class of appropriate initial states such that if c is such an initial state, then _Q ^N (t)=exp(–1H _N ^Q t) _Q ^N (0) correctly describes at timest ₃,t ₆,,t _3N model states that correspond to the completion of the first, second, , Nth computation step ofQ. The model parameters can be adjusted so that for an arbitrary time interval aroundt ₃,t ₆,,t _3N, the machine part of _Q ^N (t) is stationary.