Almost all palindromes are composite

We study the distribution of palindromic numbers (with respect to a fixed base $g\ge 2$) over certain congruence classes, and we derive a nontrivial upper bound for the number of prime palindromes $n\le x$ as $x\to\infty$. Our results show that almost all palindromes in a given base are composite.Comment: 19 page

Applicability of self-consistent mean-field theory

Within the constrained Hartree-Fock (CHF) theory, an analytic condition is derived to estimate whether a concept of the self-consistent mean field is realized or not in level repulsive region. The derived condition states that an iterative calculation of CHF equation does not converge when the quantum fluctuations coming from two-body residual interaction and quadrupole deformation become larger than a single-particle energy difference between two avoided crossing orbits. By means of the numerical calculation, it is shown that the analytic condition works well for a realistic case.Comment: 11 pages, 8 figure

Replica symmetry breaking in an adiabatic spin-glass model of adaptive evolution

We study evolutionary canalization using a spin-glass model with replica theory, where spins and their interactions are dynamic variables whose configurations correspond to phenotypes and genotypes, respectively. The spins are updated under temperature T_S, and the genotypes evolve under temperature T_J, according to the evolutionary fitness. It is found that adaptation occurs at T_S < T_S^{RS}, and a replica symmetric phase emerges at T_S^{RSB} < T_S < T_S^{RS}. The replica symmetric phase implies canalization, and replica symmetry breaking at lower temperatures indicates loss of robustness.Comment: 5pages, 2 figure

Laminar-dependent effects of cortical state on auditory cortical spontaneous activity

Cortical circuits spontaneously generate coordinated activity even in the absence of external inputs. The character of this activity depends on cortical state. We investigated how state affects the organization of spontaneous activity across layers of rat auditory cortex in vivo, using juxtacellular recording of morphologically identified neurons and large-scale electrophysiological recordings. Superficial pyramidal cells (PCs) and putative fast-spiking interneurons (FSs) were consistently suppressed during cortical desynchronization. PCs in deep layers showed heterogeneous responses to desynchronization, with some cells showing increased rates, typically large tufted PCs of high baseline firing rate, but not FSs. Consistent results were found between desynchronization occurring spontaneously in unanesthetized animals, and desynchronization evoked by electrical stimulation of the pedunculopontine tegmental (PPT) nucleus under urethane anesthesia. We hypothesize that reduction in superficial layer firing may enhance the brain's extraction of behaviorally relevant signals from noisy brain activity

Statistical Mechanics of Dictionary Learning

Finding a basis matrix (dictionary) by which objective signals are represented sparsely is of major relevance in various scientific and technological fields. We consider a problem to learn a dictionary from a set of training signals. We employ techniques of statistical mechanics of disordered systems to evaluate the size of the training set necessary to typically succeed in the dictionary learning. The results indicate that the necessary size is much smaller than previously estimated, which theoretically supports and/or encourages the use of dictionary learning in practical situations.Comment: 6 pages, 4 figure

Artificial Protein Hydrogel Materials

Recombinant DNA methods were used to create a new class of artificial proteins that undergo reversible gelation in response to changes in pH or temperature. These proteins consist of terminal a-helical "leucine zipper" domains flanking a central, water-soluble polyelectrolyte segment. The formation of coiled-coil aggregates of the terminal domains in near-neutral pH solution triggers formation of a polymer hydrogel, with the central polyelectrolyte segment retaining solvent and preventing precipitation of the chains. Dissociation of the coiled-coil aggregates through elevation of pH or temperature causes dissolution of the gel and a return to the viscous behavior characteristic of a polymer solution. The pH and temperature range of the hydrogel state and its viscoelastic properties may be systematically varied through precise changes of the length, composition and charge density of the terminal and central blocks. Such control is of value in designing hydrogels with predetermined physical properties and makes these biosynthetic triblock copolymer systems attractive candidates for use in molecular and cellular encapsulation and in controlled reagent delivery

Comment on ``the Klein-Gordon Oscillator''

The different ways of description of the $S=0$ particle with oscillator-like interaction are considered. The results are in conformity with the previous paper of S. Bruce and P. Minning.Comment: LaTeX file, 5p

Zitterbewegung of Klein-Gordon particles and its simulation by classical systems

The Klein-Gordon equation is used to calculate the Zitterbewegung (ZB, trembling motion) of spin-zero particles in absence of fields and in the presence of an external magnetic field. Both Hamiltonian and wave formalisms are employed to describe ZB and their results are compared. It is demonstrated that, if one uses wave packets to represent particles, the ZB motion has a decaying behavior. It is also shown that the trembling motion is caused by an interference of two sub-packets composed of positive and negative energy states which propagate with different velocities. In the presence of a magnetic field the quantization of energy spectrum results in many interband frequencies contributing to ZB oscillations and the motion follows a collapse-revival pattern. In the limit of non-relativistic velocities the interband ZB components vanish and the motion is reduced to cyclotron oscillations. The exact dynamics of a charged Klein-Gordon particle in the presence of a magnetic field is described on an operator level. The trembling motion of a KG particle in absence of fields is simulated using a classical model proposed by Morse and Feshbach -- it is shown that a variance of a Gaussian wave packet exhibits ZB oscillations.Comment: 16 pages and 7 figure

Quantum Interference of Impurity Bound States in Bi2_{2}Sr2_{2}Ca(Cu1−x_{1-x}Znx_{x})2_{2}O8+δ_{8+\delta} Probed by Scanning Tunneling Spectroscopy

In conventional superconductors, magnetic impurities form an impurity band due to quantum interference of the impurity bound states, leading to suppression of the superconducting transition temperature. Such quantum interference effects can also be expected in d-wave superconductors. Here, we use scanning tunneling microscopy to investigate the effect of multiple non-magnetic impurities on the local electronic structure of the high-temperature superconductor Bi$_{2}$Sr$_{2}$Ca(Cu$_{1-x}$Zn$_{x}$)$_{2}$O$_{8+\delta}$. We find several fingerprints of quantum interference of the impurity bound states including: (i) a two-dimensional modulation of local density-of-states with a period of approximately 5.4 \AA\ along the $a$- and $b$-axes, which is indicative of the d-wave superconducting nature of the cuprates; (ii) abrupt spatial variations of the impurity bound state energy; (iii)an appearance of positive energy states; (iv) a split of the impurity bound state. All of these findings provide important insight into how the impurity band in d-wave superconductors is formed.Comment: 5 pages, 3 figures, to be published in PR