Non-Hermitian Localization in Biological Networks

We explore the spectra and localization properties of the N-site banded one-dimensional non-Hermitian random matrices that arise naturally in sparse neural networks. Approximately equal numbers of random excitatory and inhibitory connections lead to spatially localized eigenfunctions, and an intricate eigenvalue spectrum in the complex plane that controls the spontaneous activity and induced response. A finite fraction of the eigenvalues condense onto the real or imaginary axes. For large N, the spectrum has remarkable symmetries not only with respect to reflections across the real and imaginary axes, but also with respect to 90 degree rotations, with an unusual anisotropic divergence in the localization length near the origin. When chains with periodic boundary conditions become directed, with a systematic directional bias superimposed on the randomness, a hole centered on the origin opens up in the density-of-states in the complex plane. All states are extended on the rim of this hole, while the localized eigenvalues outside the hole are unchanged. The bias dependent shape of this hole tracks the bias independent contours of constant localization length. We treat the large-N limit by a combination of direct numerical diagonalization and using transfer matrices, an approach that allows us to exploit an electrostatic analogy connecting the "charges" embodied in the eigenvalue distribution with the contours of constant localization length. We show that similar results are obtained for more realistic neural networks that obey "Dale's Law" (each site is purely excitatory or inhibitory), and conclude with perturbation theory results that describe the limit of large bias g, when all states are extended. Related problems arise in random ecological networks and in chains of artificial cells with randomly coupled gene expression patterns

Mitigation of impact of nitrogen cycling associated with agriculture and food consumption on regional environments

Session 2: Nitrogen, Green House Gasses and Agricultur

Maximization of thermal entanglement of arbitrarily interacting two qubits

We investigate the thermal entanglement of interacting two qubits. We maximize it by tuning a local Hamiltonian under a given interaction Hamiltonian. We prove that the optimizing local Hamiltonian takes a simple form which dose not depend on the temperature and that the corresponding optimized thermal entanglement decays as $1/(T log T)$ at high temperatures. We also find that at low temperatures the thermal entanglement is maximum without any local Hamiltonians and that the second derivative of the maximized thermal entanglement changes discontinuously at the boundary between the high- and low-temperature phases.Comment: 23 pages, 4 figure

Spatiotemporal Behavior of Void Collapse in Shocked Solids

Molecular dynamics simulations on a three dimensional defective Lennard-Jones solid containing a void are performed in order to investigate detailed properties of hot spot generation. In addition to the temperature, I monitor the number of energetically colliding particles per unit volume which characterizes the intensity of shock-enhanced chemistry. The quantity is found to saturate for nanoscale voids and to be maximized after voids have completely collapsed. It makes an apparent comparison to the temperature which requires much larger void for the enhancement and becomes maximum during the early stage of the collapse. It is also found that the average velocity and the temperature of ejected molecules inside a cubic void are enhanced during the collapse because of the focusing of momentum and energy towards the center line of a void.Comment: 4 pages, 5 figures. A new figure and some references are adde

A variational approach to Ising spin glasses in finite dimensions

We introduce a hierarchical class of approximations of the random Ising spin glass in $d$ dimensions. The attention is focused on finite clusters of spins where the action of the rest of the system is properly taken into account. At the lower level (cluster of a single spin) our approximation coincides with the SK model while at the highest level it coincides with the true $d$-dimensional system. The method is variational and it uses the replica approach to spin glasses and the Parisi ansatz for the order parameter. As a result we have rigorous bounds for the quenched free energy which become more and more precise when larger and larger clusters are considered.Comment: 16 pages, Plain TeX, uses Harvmac.tex, 4 ps figures, submitted to J. Phys. A: Math. Ge

Impurity effects in few-electron quantum dots: Incipient Wigner molecule regime

Numerically exact path-integral Monte Carlo data are presented for $N\leq 10$ strongly interacting electrons confined in a 2D parabolic quantum dot, including a defect to break rotational symmetry. Low densities are studied, where an incipient Wigner molecule forms. A single impurity is found to cause drastic effects: (1) The standard shell-filling sequence with magic numbers $N=4,6,9$, corresponding to peaks in the addition energy $\Delta(N)$, is destroyed, with a new peak at N=8, (2) spin gaps decrease, (3) for N=8, sub-Hund's rule spin S=0 is induced, and (4) spatial ordering of the electrons becomes rather sensitive to spin. We also comment on the recently observed bunching phenomenon.Comment: 7 pages, 1 table, 4 figures, accepted for publication in Europhysics Letter

Non-Hermitian Delocalization and Eigenfunctions

Recent literature on delocalization in non-Hermitian systems has stressed criteria based on sensitivity of eigenvalues to boundary conditions and the existence of a non-zero current. We emphasize here that delocalization also shows up clearly in eigenfunctions, provided one studies the product of left- and right-eigenfunctions, as required on physical grounds, and not simply the squared modulii of the eigenfunctions themselves. We also discuss the right- and left-eigenfunctions of the ground state in the delocalized regime and suggest that the behavior of these functions, when considered separately, may be viewed as ``intermediate'' between localized and delocalized.Comment: 8 pages, 11 figures include

Dislocation nucleation in shocked fcc solids: effects of temperature and preexisting voids

Quantitative behaviors of shock-induced dislocation nucleation are investigated by means of molecular dynamics simulations on fcc Lennard-Jones solids: a model Argon. In perfect crystals, it is found that Hugoniot elastic limit (HEL) is a linearly decreasing function of temperature: from near-zero to melting temperatures. In a defective crystal with a void, dislocations are found to nucleate on the void surface. Also HEL drastically decreases to 15 percent of the perfect crystal when a void radius is 3.4 nanometer. The decrease of HEL becomes larger as the void radius increases, but HEL becomes insensitive to temperature.Comment: 4 pages. (ver.2) All figures have been revised. Two citations are newly added. Numerical unit is unified in the context of solid argon. (ver. 3) A minor revision including new reference

Effects of kinked linear defects on planar flux line arrays

In the hard core limit, interacting vortices in planar type II superconductors can be modeled as non-interacting one dimensional fermions propagating in imaginary time. We use this analogy to derive analytical expressions for the probability density and imaginary current of vortex lines interacting with an isolated bent line defect and to understand the pinning properties of such systems. When there is an abrupt change of the direction of the pinning defect, we find a sinusoidal modulation of the vortex density in directions both parallel and perpendicular to the defect.Comment: 13 figure

Efficacy of combined peroxisome proliferator-activated receptor-α ligand and glucocorticoid therapy in a murine model of atopic dermatitis.

Although topical glucocorticoids (GCs) show potent anti-inflammatory activity in inflamed skin, they can also exert numerous harmful effects on epidermal structure and function. In contrast, topical applications of ligands of peroxisome proliferator-activated receptor-α (PPARα) not only reduce inflammation but also improve cutaneous barrier homeostasis. Therefore, we examined whether sequential topical GCs followed by topical Wy14643 (a ligand of PPARα) might be more effective than either alone for atopic dermatitis (AD) in a hapten (oxazolone (Ox))-induced murine model with multiple features of AD (Ox-AD). Despite expected anti-inflammatory benefits, topical GC alone induced (i) epidermal thinning; (ii) reduced expression of involucrin, loricrin, and filaggrin; and (iii) allowed outside-to-inside penetration of an epicutaneous tracer. Although Wy14643 alone yielded significant therapeutic benefits in mice with mild or moderate Ox-AD, it was less effective in severe Ox-AD. Yet, topical application of Wy14643 after GC was not only significantly effective comparable with GC alone, but it also prevented GC-induced structural and functional abnormalities in permeability barrier homeostasis. Moreover, rebound flares were largely absent after sequential treatment with GC and Wy14643. Together, these results show that GC and PPARα ligand therapy together is not only effective but also prevents development of GC-induced side effects, including rebound flares, in murine AD