Discrete Scale Invariance and the "Second Black Monday"

Evidence is offered for log-periodic (in time) fluctuations in the S&P 500 stock index during the three years prior to the October 27, 1997 "correction". These fluctuations were expected on the basis of a discretely scale invariant rupture phenomenology of stock market crashes proposed earlier.Comment: LaTeX file, 4 pages, 2 figure

Gravitational Analogues of Non-linear Born Electrodynamics

Gravitational analogues of the nonlinear electrodynamics of Born and of Born and Infeld are introduced and applied to the black hole problem. This work is mainly devoted to the 2-dimensional case in which the relevant lagrangians are nonpolynomial in the scalar curvature.Comment: 20 pages, 2 figures, included a detailed discussion of "non-trace" field equation

Autonomy and Singularity in Dynamic Fracture

The recently developed weakly nonlinear theory of dynamic fracture predicts $1/r$ corrections to the standard asymptotic linear elastic $1/\sqrt{r}$ displacement-gradients, where $r$ is measured from the tip of a tensile crack. We show that the $1/r$ singularity does not automatically conform with the notion of autonomy (autonomy means that any crack tip nonlinear solution is uniquely determined by the surrounding linear elastic $1/\sqrt{r}$ fields) and that it does not automatically satisfy the resultant Newton's equation in the crack parallel direction. We show that these two properties are interrelated and that by requiring that the resultant Newton's equation is satisfied, autonomy of the $1/r$ singular solution is retained. We further show that the resultant linear momentum carried by the $1/r$ singular fields vanishes identically. Our results, which reveal the physical and mathematical nature of the new solution, are in favorable agreement with recent near tip measurements.Comment: 4 pages, 2 figures, related papers: arXiv:0902.2121 and arXiv:0807.486

Phase locking below rate threshold in noisy model neurons

The property of a neuron to phase-lock to an oscillatory stimulus before adapting its spike rate to the stimulus frequency plays an important role for the auditory system. We investigate under which conditions neurons exhibit this phase locking below rate threshold. To this end, we simulate neurons employing the widely used leaky integrate-and-fire (LIF) model. Tuning parameters, we can arrange either an irregular spontaneous or a tonic spiking mode. When the neuron is stimulated in both modes, a significant rise of vector strength prior to a noticeable change of the spike rate can be observed. Combining analytic reasoning with numerical simulations, we trace this observation back to a modulation of interspike intervals, which itself requires spikes to be only loosely coupled. We test the limits of this conception by simulating an LIF model with threshold fatigue, which generates pronounced anticorrelations between subsequent interspike intervals. In addition we evaluate the LIF response for harmonic stimuli of various frequencies and discuss the extension to more complex stimuli. It seems that phase locking below rate threshold occurs generically for all zero mean stimuli. Finally, we discuss our findings in the context of stimulus detection

Finite-distance singularities in the tearing of thin sheets

We investigate the interaction between two cracks propagating in a thin sheet. Two different experimental geometries allow us to tear sheets by imposing an out-of-plane shear loading. We find that two tears converge along self-similar paths and annihilate each other. These finite-distance singularities display geometry-dependent similarity exponents, which we retrieve using scaling arguments based on a balance between the stretching and the bending of the sheet close to the tips of the cracks.Comment: 4 pages, 4 figure

Computing with cells: membrane systems - some complexity issues.

Membrane computing is a branch of natural computing which abstracts computing models from the structure and the functioning of the living cell. The main ingredients of membrane systems, called P systems, are (i) the membrane structure, which consists of a hierarchical arrangements of membranes which delimit compartments where (ii) multisets of symbols, called objects, evolve according to (iii) sets of rules which are localised and associated with compartments. By using the rules in a nondeterministic/deterministic maximally parallel manner, transitions between the system configurations can be obtained. A sequence of transitions is a computation of how the system is evolving. Various ways of controlling the transfer of objects from one membrane to another and applying the rules, as well as possibilities to dissolve, divide or create membranes have been studied. Membrane systems have a great potential for implementing massively concurrent systems in an efficient way that would allow us to solve currently intractable problems once future biotechnology gives way to a practical bio-realization. In this paper we survey some interesting and fundamental complexity issues such as universality vs. nonuniversality, determinism vs. nondeterminism, membrane and alphabet size hierarchies, characterizations of context-sensitive languages and other language classes and various notions of parallelism

A next-to-leading order analysis of deeply virtual Compton scattering

We present a complete, next-to-leading-order (NLO), leading-twist QCD analysis of deeply virtual Compton scattering (DVCS) observables, in the ${\bar {MS}}$ scheme, and in the kinematic ranges of the H1, ZEUS and HERMES experiments. We use a modified form of Radyushkin's ansatz for the input model for the generalized parton distributions. We present results for leading order (LO) and NLO for representative observables and find that they compare favourably to the available data.Comment: 5 pages, 2 figures, revtex, published version, we modify Radyushkin's ansatz for the GPDs to correct for finite hadronic mass effects, and, using the latest MRST PDFs, now agree with the H1 data (modified figs). Typo in Eq.(3) correcte

From Crystalline to Amorphous Germania Bilayer Films at the Atomic Scale: Preparation and Characterization

A new two-dimensional (2D) germanium dioxide film has been prepared. The film consists of interconnected germania tetrahedral units forming a bilayer structure, weakly coupled to the supporting Pt(111) metal-substrate. Density functional theory calculations predict a stable structure of 558-membered rings for germania films, while for silica films 6-membered rings are preferred. By varying the preparation conditions the degree of order in the germania films is tuned. Crystalline, intermediate ordered and purely amorphous film structures are resolved by analysing scanning tunnelling microscopy images

From Crystalline to Amorphous Germania Bilayer Films at the Atomic Scale: Preparation and Characterization

A new two-dimensional (2D) germanium dioxide film has been prepared. The film consists of interconnected germania tetrahedral units forming a bilayer structure, weakly coupled to the supporting Pt(111) metal-substrate. Density functional theory calculations predict a stable structure of 558-membered rings for germania films, while for silica films 6-membered rings are preferred. By varying the preparation conditions the degree of order in the germania films is tuned. Crystalline, intermediate ordered and purely amorphous film structures are resolved by analysing scanning tunnelling microscopy images

Measurement in Quantum Physics

The conceptual problems in quantum mechanics -- related to the collapse of the wave function, the particle-wave duality, the meaning of measurement -- arise from the need to ascribe particle character to the wave function. As will be shown, all these problems dissolve when working instead with quantum fields, which have both wave and particle character. Otherwise the predictions of quantum physics, including Bell's inequalities, coincide with those of the standard treatments. The transfer of the results of the quantum measurement to the classical realm is also discussed.Comment: 34 pages, in Latex, revised and expanded version with an extra appendix on decoherenc