Storage Capacity of Two-dimensional Neural Networks

We investigate the maximum number of embedded patterns in the two-dimensional Hopfield model. The grand state energies of two specific network states, namely, the energies of the pure-ferromagnetic state and the state of specific one stored pattern are calculated exactly in terms of the correlation function of the ferromagnetic Ising model. We also investigate the energy landscape around them by computer simulations. Taking into account the qualitative features of the phase diagrams obtained by Nishimori, Whyte and Sherrington [Phys. Rev. E {\bf 51}, 3628 (1995)], we conclude that the network cannot retrieve more than three patterns.Comment: 13pages, 7figures, revtex

On a new definition of quantum entropy

It is proved here that, as a consequence of the unitary quantum evolution, the expectation value of a properly defined quantum entropy operator (as opposed to the non-evolving von Neumann entropy) can only increase during non adiabatic transformations and remains constant during adiabatic ones. Thus Clausius formulation of the second law is established as a theorem in quantum mechanics, in a way that is equivalent to the previously established formulation in terms of minimal work principle [A. E. Allahverdyan and T. M. Nieuwenhuizen, Phys. Rev. E 71, 046107 (2005)]. The corresponding Quantum Mechanical Principle of Entropy Increase is then illustrated with an exactly solvable example, namely the driven harmonic oscillator. Attention is paid to both microcanonical and canonical initial condition. The results are compared to their classical counterparts.Comment: 4 pages, 3 figure

Derivation of Boltzmann Principle

We present a derivation of Boltzmann principle $S_{B}=k_{B}\ln \mathcal{W}$ based on classical mechanical models of thermodynamics. The argument is based on the heat theorem and can be traced back to the second half of the nineteenth century with the works of Helmholtz and Boltzmann. Despite its simplicity, this argument has remained almost unknown. We present it in a modern, self-contained and accessible form. The approach constitutes an important link between classical mechanics and statistical mechanics

Detection of Bordetella trematum in a diabetic patient with a skin and soft tissue infection

A 38-year-old obese male with spastic diplegia and diabetes was hospitalized due to progressive ulcers of both lower extremities (Figure 1A). Computed tomography showed subcutaneous inflammation with suspected fascial involvement. The patient underwent surgical debridement, after which clindamycin was started empirically. Cultures from tissue samples grew gram-negative rods, identified by matrix-assisted laser desorption/ionization time-of-flight mass spectrometry (MALDI-TOF MS) as Bordetella trematum (Figure 1B) and, in minor quantity, Myroides odoratimimus. Antimicrobial susceptibility testing of B. trematum was performed to obtain minimal inhibitory concentrations (in μg/mL; ampicillin ≤2; piperacillin ≤4; cefuroxime ≥64; ceftazidime 4; meropenem ≤0.25; moxifloxacin 2). Following the debridement, the patient’s condition improved substantially (Figure 1C), and he was discharged soon thereafter

Angular Correlations in Internal Pair Conversion of Aligned Heavy Nuclei

We calculate the spatial correlation of electrons and positrons emitted by internal pair conversion of Coulomb excited nuclei in heavy ion collisions. The alignment or polarization of the nucleus results in an anisotropic emission of the electron-positron pairs which is closely related to the anisotropic emission of $\gamma$-rays. However, the angular correlation in the case of internal pair conversion exhibits diverse patterns. This might be relevant when investigating atomic processes in heavy-ion collisions performed at the Coulomb barrier.Comment: 27 pages + 6 eps figures, uses revtex.sty and epsf.sty, tar-compressed and uuencoded with uufile

On the Geometry of Supersymmetric Quantum Mechanical Systems

We consider some simple examples of supersymmetric quantum mechanical systems and explore their possible geometric interpretation with the help of geometric aspects of real Clifford algebras. This leads to natural extensions of the considered systems to higher dimensions and more complicated potentials.Comment: 18 page

Analysis of the Accuracy of Prediction of the Celestial Pole Motion

VLBI observations carried out by global networks provide the most accurate values of the precession-nutation angles determining the position of the celestial pole; as a rule, these results become available two to four weeks after the observations. Therefore, numerous applications, such as satellite navigation systems, operational determination of Universal Time, and space navigation, use predictions of the coordinates of the celestial pole. In connection with this, the accuracy of predictions of the precession- nutation angles based on observational data obtained over the last three years is analyzed for the first time, using three empiric nutation models---namely, those developed at the US Naval Observatory, the Paris Observatory, and the Pulkovo Observatory. This analysis shows that the last model has the best of accuracy in predicting the coordinates of the celestial pole. The rms error for a one-month prediction proposed by this model is below 100 microarcsecond.Comment: 13 p

Measurement of the 187Re({\alpha},n)190Ir reaction cross section at sub-Coulomb energies using the Cologne Clover Counting Setup

Uncertainties in adopted models of particle+nucleus optical-model potentials directly influence the accuracy in the theoretical predictions of reaction rates as they are needed for reaction-network calculations in, for instance, {\gamma}-process nucleosynthesis. The improvement of the {\alpha}+nucleus optical-model potential is hampered by the lack of experimental data at astrophysically relevant energies especially for heavier nuclei. Measuring the Re187({\alpha},n)Ir190 reaction cross section at sub-Coulomb energies extends the scarce experimental data available in this mass region and helps understanding the energy dependence of the imaginary part of the {\alpha}+nucleus optical-model potential at low energies. Applying the activation method, after the irradiation of natural rhenium targets with {\alpha}-particle energies of 12.4 to 14.1 MeV, the reaction yield and thus the reaction cross section were determined via {\gamma}-ray spectroscopy by using the Cologne Clover Counting Setup and the method of {\gamma}{\gamma} coincidences. Cross-section values at five energies close to the astrophysically relevant energy region were measured. Statistical model calculations revealed discrepancies between the experimental values and predictions based on widely used {\alpha}+nucleus optical-model potentials. However, an excellent reproduction of the measured cross-section values could be achieved from calculations based on the so-called Sauerwein-Rauscher {\alpha}+nucleus optical-model potential. The results obtained indicate that the energy dependence of the imaginary part of the {\alpha}+nucleus optical-model potential can be described by an exponential decrease. Successful reproductions of measured cross sections at low energies for {\alpha}-induced reactions in the mass range 141{\leq}A{\leq}187 confirm the global character of the Sauerwein-Rauscher potential

Equivalent forms of Dirac equations in curved spacetimes and generalized de Broglie relations

One may ask whether the relations between energy and frequency and between momentum and wave vector, introduced for matter waves by de Broglie, are rigorously valid in the presence of gravity. In this paper, we show this to be true for Dirac equations in a background of gravitational and electromagnetic fields. We first transform any Dirac equation into an equivalent canonical form, sometimes used in particular cases to solve Dirac equations in a curved spacetime. This canonical form is needed to apply the Whitham Lagrangian method. The latter method, unlike the WKB method, places no restriction on the magnitude of Planck's constant to obtain wave packets, and furthermore preserves the symmetries of the Dirac Lagrangian. We show using canonical Dirac fields in a curved spacetime, that the probability current has a Gordon decomposition into a convection current and a spin current, and that the spin current vanishes in the Whitham approximation, which explains the negligible effect of spin on wave packet solutions, independent of the size of Planck's constant. We further discuss the classical-quantum correspondence in a curved spacetime based on both Lagrangian and Hamiltonian formulations of the Whitham equations. We show that the generalized de Broglie relations in a curved spacetime are a direct consequence of Whitham's Lagrangian method, and not just a physical hypothesis as introduced by Einstein and de Broglie, and by many quantum mechanics textbooks.Comment: PDF, 32 pages in referee format. Added significant material on canonical forms of Dirac equations. Simplified Theorem 1 for normal Dirac equations. Added section on Gordon decomposition of the probability current. Encapsulated main results in the statement of Theorem