275 research outputs found
Cutoff for the Ising model on the lattice
Introduced in 1963, Glauber dynamics is one of the most practiced and
extensively studied methods for sampling the Ising model on lattices. It is
well known that at high temperatures, the time it takes this chain to mix in
on a system of size is . Whether in this regime there is
cutoff, i.e. a sharp transition in the -convergence to equilibrium, is a
fundamental open problem: If so, as conjectured by Peres, it would imply that
mixing occurs abruptly at for some fixed , thus providing
a rigorous stopping rule for this MCMC sampler. However, obtaining the precise
asymptotics of the mixing and proving cutoff can be extremely challenging even
for fairly simple Markov chains. Already for the one-dimensional Ising model,
showing cutoff is a longstanding open problem.
We settle the above by establishing cutoff and its location at the high
temperature regime of the Ising model on the lattice with periodic boundary
conditions. Our results hold for any dimension and at any temperature where
there is strong spatial mixing: For this carries all the way to the
critical temperature. Specifically, for fixed , the continuous-time
Glauber dynamics for the Ising model on with periodic boundary
conditions has cutoff at , where is
the spectral gap of the dynamics on the infinite-volume lattice. To our
knowledge, this is the first time where cutoff is shown for a Markov chain
where even understanding its stationary distribution is limited.
The proof hinges on a new technique for translating to mixing
which enables the application of log-Sobolev inequalities. The technique is
general and carries to other monotone and anti-monotone spin-systems.Comment: 34 pages, 3 figure
Conformal proper times according to the Woodhouse causal axiomatics of relativistic spacetimes
On the basis of the Woodhouse causal axiomatics, we show that conformal
proper times and an extra variable in addition to those of space and time,
precisely and physically identified from experimental examples, together give a
physical justification for the `chronometric hypothesis' of general relativity.
Indeed, we show that, with a lack of these latter two ingredients, no clock
paradox solution exists in which the clock and message functions are solely at
the origin of the asymmetry. These proper times originate from a given
conformal structure of the spacetime when ascribing different compatible
projective structures to each Woodhouse particle, and then, each defines a
specific Weylian sheaf structure. In addition, the proper time
parameterizations, as two point functions, cannot be defined irrespective of
the processes in the relative changes of physical characteristics. These
processes are included via path-dependent conformal scale factors, which act
like sockets for any kind of physical interaction and also represent the values
of the variable associated with the extra dimension. As such, the differential
aging differs far beyond the first and second clock effects in Weyl geometries,
with the latter finally appearing to not be suitable.Comment: 25 pages, 2 figure
Theology, News and Notes - Vol. 23, No. 04
Theology News & Notes was a theological journal published by Fuller Theological Seminary from 1954 through 2014.https://digitalcommons.fuller.edu/tnn/1060/thumbnail.jp
Performance and Simulation of the RICE detector
The RICE experiment (Radio Ice Cherenkov Experiment) at the South Pole,
co-deployed with the AMANDA experiment, seeks to detect ultra-high energy (UHE)
electron neutrinos interacting in cold polar ice. Such interactions produce
electromagnetic showers, which emit radio-frequency Cherenkov radiation. We
describe the experimental apparatus and the procedures used to measure the
neutrino flux.Comment: preprint, to be submitted to Astropart. Phy
Functional mechanisms underlying pleiotropic risk alleles at the 19p13.1 breast-ovarian cancer susceptibility locus
A locus at 19p13 is associated with breast cancer (BC) and ovarian cancer (OC) risk. Here we analyse 438 SNPs in this region in 46,451 BC and 15,438 OC cases, 15,252 BRCA1 mutation carriers and 73,444 controls and identify 13 candidate causal SNPs associated with serous OC (P=9.2 × 10-20), ER-negative BC (P=1.1 × 10-13), BRCA1-associated BC (P=7.7 × 10-16) and triple negative BC (P-diff=2 × 10-5). Genotype-gene expression associations are identified for candidate target genes ANKLE1 (P=2 × 10-3) and ABHD8 (P<2 × 10-3). Chromosome conformation capture identifies interactions between four candidate SNPs and ABHD8, and luciferase assays indicate six risk alleles increased transactivation of the ADHD8 promoter. Targeted deletion of a region containing risk SNP rs56069439 in a putative enhancer induces ANKLE1 downregulation; and mRNA stability assays indicate functional effects for an ANKLE1 3′-UTR SNP. Altogether, these data suggest that multiple SNPs at 19p13 regulate ABHD8 and perhaps ANKLE1 expression, and indicate common mechanisms underlying breast and ovarian cancer risk
On the mechanisms governing gas penetration into a tokamak plasma during a massive gas injection
A new 1D radial fluid code, IMAGINE, is used to simulate the penetration of gas into a tokamak plasma during a massive gas injection (MGI). The main result is that the gas is in general strongly braked as it reaches the plasma, due to mechanisms related to charge exchange and (to a smaller extent) recombination. As a result, only a fraction of the gas penetrates into the plasma. Also, a shock wave is created in the gas which propagates away from the plasma, braking and compressing the incoming gas. Simulation results are quantitatively consistent, at least in terms of orders of magnitude, with experimental data for a D 2 MGI into a JET Ohmic plasma. Simulations of MGI into the background plasma surrounding a runaway electron beam show that if the background electron density is too high, the gas may not penetrate, suggesting a possible explanation for the recent results of Reux et al in JET (2015 Nucl. Fusion 55 093013)
Velocity-space sensitivity of the time-of-flight neutron spectrometer at JET
The velocity-space sensitivities of fast-ion diagnostics are often described by so-called weight functions. Recently, we formulated weight functions showing the velocity-space sensitivity of the often dominant beam-target part of neutron energy spectra. These weight functions for neutron emission spectrometry (NES) are independent of the particular NES diagnostic. Here we apply these NES weight functions to the time-of-flight spectrometer TOFOR at JET. By taking the instrumental response function of TOFOR into account, we calculate time-of-flight NES weight functions that enable us to directly determine the velocity-space sensitivity of a given part of a measured time-of-flight spectrum from TOFOR
Relationship of edge localized mode burst times with divertor flux loop signal phase in JET
A phase relationship is identified between sequential edge localized modes (ELMs) occurrence times in a set of H-mode tokamak plasmas to the voltage measured in full flux azimuthal loops in the divertor region. We focus on plasmas in the Joint European Torus where a steady H-mode is sustained over several seconds, during which ELMs are observed in the Be II emission at the divertor. The ELMs analysed arise from intrinsic ELMing, in that there is no deliberate intent to control the ELMing process by external means. We use ELM timings derived from the Be II signal to perform direct time domain analysis of the full flux loop VLD2 and VLD3 signals, which provide a high cadence global measurement proportional to the voltage induced by changes in poloidal magnetic flux. Specifically, we examine how the time interval between pairs of successive ELMs is linked to the time-evolving phase of the full flux loop signals. Each ELM produces a clear early pulse in the full flux loop signals, whose peak time is used to condition our analysis. The arrival time of the following ELM, relative to this pulse, is found to fall into one of two categories: (i) prompt ELMs, which are directly paced by the initial response seen in the flux loop signals; and (ii) all other ELMs, which occur after the initial response of the full flux loop signals has decayed in amplitude. The times at which ELMs in category (ii) occur, relative to the first ELM of the pair, are clustered at times when the instantaneous phase of the full flux loop signal is close to its value at the time of the first ELM
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