Dynamics of lattice spins as a model of arrhythmia

We consider evolution of initial disturbances in spatially extended systems with autonomous rhythmic activity, such as the heart. We consider the case when the activity is stable with respect to very smooth (changing little across the medium) disturbances and construct lattice models for description of not-so-smooth disturbances, in particular, topological defects; these models are modifications of the diffusive XY model. We find that when the activity on each lattice site is very rigid in maintaining its form, the topological defects - vortices or spirals - nucleate a transition to a disordered, turbulent state.Comment: 17 pages, revtex, 3 figure

Magnetic Field-Induced Condensation of Triplons in Han Purple Pigment BaCuSi2_2O6_6

Besides being an ancient pigment, BaCuSi$_2$O$_6$ is a quasi-2D magnetic insulator with a gapped spin dimer ground state. The application of strong magnetic fields closes this gap creating a gas of bosonic spin triplet excitations called triplons. The topology of the spin lattice makes BaCuSi$_2$O$_6$ an ideal candidate for studying the Bose-Einstein condensation of triplons as a function of the external magnetic field, which acts as a chemical potential. In agreement with quantum Monte Carlo numerical simulations, we observe a distinct lambda-anomaly in the specific heat together with a maximum in the magnetic susceptibility upon cooling down to liquid Helium temperatures.Comment: published on August 20, 200

The Shapes of Flux Domains in the Intermediate State of Type-I Superconductors

In the intermediate state of a thin type-I superconductor magnetic flux penetrates in a disordered set of highly branched and fingered macroscopic domains. To understand these shapes, we study in detail a recently proposed "current-loop" (CL) model that models the intermediate state as a collection of tense current ribbons flowing along the superconducting-normal interfaces and subject to the constraint of global flux conservation. The validity of this model is tested through a detailed reanalysis of Landau's original conformal mapping treatment of the laminar state, in which the superconductor-normal interfaces are flared within the slab, and of a closely-related straight-lamina model. A simplified dynamical model is described that elucidates the nature of possible shape instabilities of flux stripes and stripe arrays, and numerical studies of the highly nonlinear regime of those instabilities demonstrate patterns like those seen experimentally. Of particular interest is the buckling instability commonly seen in the intermediate state. The free-boundary approach further allows for a calculation of the elastic properties of the laminar state, which closely resembles that of smectic liquid crystals. We suggest several new experiments to explore of flux domain shape instabilities, including an Eckhaus instability induced by changing the out-of-plane magnetic field, and an analog of the Helfrich-Hurault instability of smectics induced by an in-plane field.Comment: 23 pages, 22 bitmapped postscript figures, RevTex 3.0, submitted to Phys. Rev. B. Higher resolution figures may be obtained by contacting the author

The fourteenth-century poll tax returns and the study of English surname distribution

The modern-day distributions of English surnames have been considered in genealogical, historical, and philological research as possible indicators of their origins. However, many centuries have passed since hereditary surnames were first used, and so their distribution today does not necessarily reflect their original spread, misrepresenting their origins. Previously, medieval data with national coverage have not been available for a study of surname distribution, but with the recent publication of the fourteenth-century poll tax returns, this has changed. By presenting discrepancies in medieval and nineteenth-century distributions, it is shown that more recent surname data may not be a suitable guide to surname origins and can be usefully supplemented by medieval data in order to arrive at more accurate conclusions

General theory of instabilities for patterns with sharp interfaces in reaction-diffusion systems

An asymptotic method for finding instabilities of arbitrary $d$-dimensional large-amplitude patterns in a wide class of reaction-diffusion systems is presented. The complete stability analysis of 2- and 3-dimensional localized patterns is carried out. It is shown that in the considered class of systems the criteria for different types of instabilities are universal. The specific nonlinearities enter the criteria only via three numerical constants of order one. The performed analysis explains the self-organization scenarios observed in the recent experiments and numerical simulations of some concrete reaction-diffusion systems.Comment: 21 pages (RevTeX), 8 figures (Postscript). To appear in Phys. Rev. E (April 1st, 1996

Associative memory storing an extensive number of patterns based on a network of oscillators with distributed natural frequencies in the presence of external white noise

We study associative memory based on temporal coding in which successful retrieval is realized as an entrainment in a network of simple phase oscillators with distributed natural frequencies under the influence of white noise. The memory patterns are assumed to be given by uniformly distributed random numbers on $[0,2\pi)$ so that the patterns encode the phase differences of the oscillators. To derive the macroscopic order parameter equations for the network with an extensive number of stored patterns, we introduce the effective transfer function by assuming the fixed-point equation of the form of the TAP equation, which describes the time-averaged output as a function of the effective time-averaged local field. Properties of the networks associated with synchronization phenomena for a discrete symmetric natural frequency distribution with three frequency components are studied based on the order parameter equations, and are shown to be in good agreement with the results of numerical simulations. Two types of retrieval states are found to occur with respect to the degree of synchronization, when the size of the width of the natural frequency distribution is changed.Comment: published in Phys. Rev.

The spike-timing-dependent learning rule to encode spatiotemporal patterns in a network of spiking neurons

We study associative memory neural networks based on the Hodgkin-Huxley type of spiking neurons. We introduce the spike-timing-dependent learning rule, in which the time window with the negative part as well as the positive part is used to describe the biologically plausible synaptic plasticity. The learning rule is applied to encode a number of periodical spatiotemporal patterns, which are successfully reproduced in the periodical firing pattern of spiking neurons in the process of memory retrieval. The global inhibition is incorporated into the model so as to induce the gamma oscillation. The occurrence of gamma oscillation turns out to give appropriate spike timings for memory retrieval of discrete type of spatiotemporal pattern. The theoretical analysis to elucidate the stationary properties of perfect retrieval state is conducted in the limit of an infinite number of neurons and shows the good agreement with the result of numerical simulations. The result of this analysis indicates that the presence of the negative and positive parts in the form of the time window contributes to reduce the size of crosstalk term, implying that the time window with the negative and positive parts is suitable to encode a number of spatiotemporal patterns. We draw some phase diagrams, in which we find various types of phase transitions with change of the intensity of global inhibition.Comment: Accepted for publication in Physical Review

Initial sequencing and analysis of the human genome

The human genome holds an extraordinary trove of information about human development, physiology, medicine and evolution. Here we report the results of an international collaboration to produce and make freely available a draft sequence of the human genome. We also present an initial analysis of the data, describing some of the insights that can be gleaned from the sequence.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/62798/1/409860a0.pd

Spiral-Wave Turbulence and Its Control in the Presence of Inhomogeneities in Four Mathematical Models of Cardiac Tissue

Regular electrical activation waves in cardiac tissue lead to the rhythmic contraction and expansion of the heart that ensures blood supply to the whole body. Irregularities in the propagation of these activation waves can result in cardiac arrhythmias, like ventricular tachycardia (VT) and ventricular fibrillation (VF), which are major causes of death in the industrialised world. Indeed there is growing consensus that spiral or scroll waves of electrical activation in cardiac tissue are associated with VT, whereas, when these waves break to yield spiral- or scroll-wave turbulence, VT develops into life-threatening VF: in the absence of medical intervention, this makes the heart incapable of pumping blood and a patient dies in roughly two-and-a-half minutes after the initiation of VF. Thus studies of spiral- and scroll-wave dynamics in cardiac tissue pose important challenges for in vivo and in vitro experimental studies and for in silico numerical studies of mathematical models for cardiac tissue. A major goal here is to develop low-amplitude defibrillation schemes for the elimination of VT and VF, especially in the presence of inhomogeneities that occur commonly in cardiac tissue. We present a detailed and systematic study of spiral- and scroll-wave turbulence and spatiotemporal chaos in four mathematical models for cardiac tissue, namely, the Panfilov, Luo-Rudy phase 1 (LRI), reduced Priebe-Beuckelmann (RPB) models, and the model of ten Tusscher, Noble, Noble, and Panfilov (TNNP). In particular, we use extensive numerical simulations to elucidate the interaction of spiral and scroll waves in these models with conduction and ionic inhomogeneities; we also examine the suppression of spiral- and scroll-wave turbulence by low-amplitude control pulses. Our central qualitative result is that, in all these models, the dynamics of such spiral waves depends very sensitively on such inhomogeneities. We also study two types of control schemes that have been suggested for the control of spiral turbulence, via low amplitude current pulses, in such mathematical models for cardiac tissue; our investigations here are designed to examine the efficacy of such control schemes in the presence of inhomogeneities. We find that a local pulsing scheme does not suppress spiral turbulence in the presence of inhomogeneities; but a scheme that uses control pulses on a spatially extended mesh is more successful in the elimination of spiral turbulence. We discuss the theoretical and experimental implications of our study that have a direct bearing on defibrillation, the control of life-threatening cardiac arrhythmias such as ventricular fibrillation

Measurement of the H → γ γ and H → ZZ∗ → 4 cross-sections in pp collisions at √s = 13.6 TeV with the ATLAS detector

The inclusive Higgs boson production cross section is measured in the di-photon and the Z Z∗ → 4 decay channels using 31.4 and 29.0 fb−1 of pp collision data respectively, collected with the ATLAS detector at a centre of-mass energy of √s = 13.6 TeV. To reduce the model dependence, the measurement in each channel is restricted to a particle-level phase space that closely matches the chan nel’s detector-level kinematic selection, and it is corrected for detector effects. These measured fiducial cross-sections are σfid,γ γ = 76+14 −13 fb, and σfid,4 = 2.80 ± 0.74 fb, in agreement with the corresponding Standard Model predic tions of 67.6±3.7 fb and 3.67±0.19 fb. Assuming Standard Model acceptances and branching fractions for the two chan nels, the fiducial measurements are extrapolated to the full phase space yielding total cross-sections of σ (pp → H) = 67+12 −11 pb and 46±12 pb at 13.6 TeV from the di-photon and Z Z∗ → 4 measurements respectively. The two measure ments are combined into a total cross-section measurement of σ (pp → H) = 58.2±8.7 pb, to be compared with the Stan dard Model prediction of σ (pp → H)SM = 59.9 ± 2.6 p