arXiv · cond-mat/0109003
This is a Comment on "Universal Fluctuations in Correlated Systems".
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B. Zheng, S. Trimper. 2001-09-01. Comment on "Universal Fluctuations in Correlated Systems". https://doi.org/10.1103/physrevlett.87.188901
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Scale-free temporal organization, in which fluctuations show similar statistical structures across timescales, is a feature of many complex systems considered to support optimal functioning. Alterations of such scaling have been reported in several pathologies, but whether comparable alterations characterize the temporal organization of language remains largely unexplored. We address this question in the domain of psychosis, where language anomalies are pervasively documented. Specifically, we apply detrended fluctuation analysis (DFA) to quantify temporal scaling in Qwen3-derived continuous cosine similarity time series, capturing trajectories through semantic space computed from transcripts of picture descriptions across three independent datasets. DFA scaling exponents α were extracted to characterize the strength of long-range temporal correlations. Across all datasets, patients exhibited significantly elevated α relative to controls, indicating increased temporal persistence in semantic fluctuations. This analysis opens a window into the multi-timescale organization of meaning as it unfolds in discourse and reveals a signature of altered temporal scaling. This alteration parallels known departures from critical scaling in brain dynamics in psychosis, suggesting the exploration of possible links between these two.
The Brownian Castle is a new interface growth model that is a variation on the well-known ballistic deposition model that results in an entirely new universality class. We present numerical verification that the interface width for BC interfaces displays modified Family-Vicsek scaling properties up to finite size corrections. Specifically, we find a growth exponent of $β=0.470 \pm 0.012$ and a roughness exponent of $α=1.01 \pm 0.018$. The scaling is modified at short times with a size scaling exponent that described the early time dependence of interface width on length. The probability distribution of heights for the BC interface shows significant deviations from simple Gaussian behavior and the probability distribution of height changes shows a Cauchy-Lorentz form consistent with expectations for a process involving relatively large jumps.
Heat flow sustained by a temperature difference generates a gradient of matter as observed, for example, in atomistic simulations of hard-core gases. We use path-ensemble theory to represent the coupled thermal and diffusive transport by dynamics on a graph. Calibrated from a single equilibrium simulation, this model accurately predicts nonequilibrium mass distribution in a hard-core gas across a wide range of applied temperature gradients. It also enables estimation of transport properties, such as the Soret coefficient, using analytical expressions.