Dynamic Critical Behavior of a Swendsen-Wang-Type Algorithm for the Ashkin-Teller Model

We study the dynamic critical behavior of a Swendsen-Wang-type algorithm for the Ashkin--Teller model. We find that the Li--Sokal bound on the autocorrelation time ($\tau_{{\rm int},{\cal E}} \ge {\rm const} \times C_H$) holds along the self-dual curve of the symmetric Ashkin--Teller model, and is almost but not quite sharp. The ratio $\tau_{{\rm int},{\cal E}} / C_H$ appears to tend to infinity either as a logarithm or as a small power ($0.05 \leq p \leq 0.12$). In an appendix we discuss the problem of extracting estimates of the exponential autocorrelation time.Comment: 59 pages including 3 figures, uuencoded g-compressed ps file. Postscript size = 799740 byte

Critical Exponents, Hyperscaling and Universal Amplitude Ratios for Two- and Three-Dimensional Self-Avoiding Walks

We make a high-precision Monte Carlo study of two- and three-dimensional self-avoiding walks (SAWs) of length up to 80000 steps, using the pivot algorithm and the Karp-Luby algorithm. We study the critical exponents $\nu$ and $2\Delta_4 -\gamma$ as well as several universal amplitude ratios; in particular, we make an extremely sensitive test of the hyperscaling relation $d\nu = 2\Delta_4 -\gamma$. In two dimensions, we confirm the predicted exponent $\nu = 3/4$ and the hyperscaling relation; we estimate the universal ratios $\ / \ = 0.14026 \pm 0.00007$, $\ / \ = 0.43961 \pm 0.00034$ and $\Psi^* = 0.66296 \pm 0.00043$ (68\% confidence limits). In three dimensions, we estimate $\nu = 0.5877 \pm 0.0006$ with a correction-to-scaling exponent $\Delta_1 = 0.56 \pm 0.03$ (subjective 68\% confidence limits). This value for $\nu$ agrees excellently with the field-theoretic renormalization-group prediction, but there is some discrepancy for $\Delta_1$. Earlier Monte Carlo estimates of $\nu$, which were $\approx\! 0.592$, are now seen to be biased by corrections to scaling. We estimate the universal ratios $\ / \ = 0.1599 \pm 0.0002$ and $\Psi^* = 0.2471 \pm 0.0003$; since $\Psi^* > 0$, hyperscaling holds. The approach to $\Psi^*$ is from above, contrary to the prediction of the two-parameter renormalization-group theory. We critically reexamine this theory, and explain where the error lies.Comment: 87 pages including 12 figures, 1029558 bytes Postscript (NYU-TH-94/09/01

Regularity Properties and Pathologies of Position-Space Renormalization-Group Transformations

We reconsider the conceptual foundations of the renormalization-group (RG) formalism, and prove some rigorous theorems on the regularity properties and possible pathologies of the RG map. Regarding regularity, we show that the RG map, defined on a suitable space of interactions (= formal Hamiltonians), is always single-valued and Lipschitz continuous on its domain of definition. This rules out a recently proposed scenario for the RG description of first-order phase transitions. On the pathological side, we make rigorous some arguments of Griffiths, Pearce and Israel, and prove in several cases that the renormalized measure is not a Gibbs measure for any reasonable interaction. This means that the RG map is ill-defined, and that the conventional RG description of first-order phase transitions is not universally valid. For decimation or Kadanoff transformations applied to the Ising model in dimension $d \ge 3$, these pathologies occur in a full neighborhood $\{ \beta > \beta_0 ,\, |h| < \epsilon(\beta) \}$ of the low-temperature part of the first-order phase-transition surface. For block-averaging transformations applied to the Ising model in dimension $d \ge 2$, the pathologies occur at low temperatures for arbitrary magnetic-field strength. Pathologies may also occur in the critical region for Ising models in dimension $d \ge 4$. We discuss in detail the distinction between Gibbsian and non-Gibbsian measures, and give a rather complete catalogue of the known examples. Finally, we discuss the heuristic and numerical evidence on RG pathologies in the light of our rigorous theorems.Comment: 273 pages including 14 figures, Postscript, See also ftp.scri.fsu.edu:hep-lat/papers/9210/9210032.ps.

Musical evolution in the lab exhibits rhythmic universals

Music exhibits some cross-cultural similarities, despite its variety across the world. Evidence from a broad range of human cultures suggests the existence of musical universals1, here defined as strong regularities emerging across cultures above chance. In particular, humans demonstrate a general proclivity for rhythm2, although little is known about why music is particularly rhythmic and why the same structural regularities are present in rhythms around the world. We empirically investigate the mechanisms underlying musical universals for rhythm, showing how music can evolve culturally from randomness. Human participants were asked to imitate sets of randomly generated drumming sequences and their imitation attempts became the training set for the next participants in independent transmission chains. By perceiving and imitating drumming sequences from each other, participants turned initially random sequences into rhythmically structured patterns. Drumming patterns developed into rhythms that are more structured, easier to learn, distinctive for each experimental cultural tradition and characterized by all six statistical universals found among world music1; the patterns appear to be adapted to human learning, memory and cognition. We conclude that musical rhythm partially arises from the influence of human cognitive and biological biases on the process of cultural evolution

Inflammatory biomarkers in Alzheimer's disease plasma

Introduction:Plasma biomarkers for Alzheimer’s disease (AD) diagnosis/stratification are a“Holy Grail” of AD research and intensively sought; however, there are no well-established plasmamarkers.Methods:A hypothesis-led plasma biomarker search was conducted in the context of internationalmulticenter studies. The discovery phase measured 53 inflammatory proteins in elderly control (CTL;259), mild cognitive impairment (MCI; 199), and AD (262) subjects from AddNeuroMed.Results:Ten analytes showed significant intergroup differences. Logistic regression identified five(FB, FH, sCR1, MCP-1, eotaxin-1) that, age/APOε4 adjusted, optimally differentiated AD andCTL (AUC: 0.79), and three (sCR1, MCP-1, eotaxin-1) that optimally differentiated AD and MCI(AUC: 0.74). These models replicated in an independent cohort (EMIF; AUC 0.81 and 0.67). Twoanalytes (FB, FH) plus age predicted MCI progression to AD (AUC: 0.71).Discussion:Plasma markers of inflammation and complement dysregulation support diagnosis andoutcome prediction in AD and MCI. Further replication is needed before clinical translatio