Zipf’s laws of meaning in Catalan

In his pioneering research, G. K. Zipf formulated a couple of statistical laws on the relationship between the frequency of a word with its number of meanings: the law of meaning distribution, relating the frequency of a word and its frequency rank, and the meaning-frequency law, relating the frequency of a word with its number of meanings. Although these laws were formulated more than half a century ago, they have been only investigated in a few languages. Here we present the first study of these laws in Catalan. We verify these laws in Catalan via the relationship among their exponents and that of the rank-frequency law. We present a new protocol for the analysis of these Zipfian laws that can be extended to other languages. We report the first evidence of two marked regimes for these laws in written language and speech, paralleling the two regimes in Zipf’s rank-frequency law in large multi-author corpora discovered in early 2000s. Finally, the implications of these two regimes will be discussed.

E. Schrödinger’s 1931 paper “On the Reversal of the Laws of Nature” [“Über die Umkehrung der Naturgesetze”, Sitzungsberichte der preussischen Akademie der Wissenschaften, physikalisch-mathematische Klasse, 8 N9 144–153]

We present an English translation of Erwin Schrödinger’s paper on “On the Reversal of the Laws of Nature‘’. In this paper, Schrödinger analyses the idea of time reversal of a diffusion process. Schrödinger’s paper acted as a prominent source of inspiration for the works of Bernstein on reciprocal processes and of Kolmogorov on time reversal properties of Markov processes and detailed balance. The ideas outlined by Schrödinger also inspired the development of probabilistic interpretations of quantum mechanics by Fényes, Nelson and others as well as the notion of “Euclidean Quantum Mechanics” as probabilistic analogue of quantization. In the second part of the paper, Schrödinger discusses the relation between time reversal and statistical laws of physics. We emphasize in our commentary the relevance of Schrödinger’s intuitions for contemporary developments in statistical nano-physics.

Physics of evolution and unity of physics

The article considers the question of the possibility of constructing classical mechanics and empirical branches of physics, such as thermodynamics, statistical physics and kinetics on a general theoretical basis. The principles of constructing mechanics, thermodynamics, statistical physics, and kinetics are briefly given. It is shown how the construction of the above sections of physics on a unified basis became possible, relying on the mechanics of a structured body. The essence of this mechanics is that, unlike Newton’s mechanics, built for a body model in the form of a material point, this mechanics is built based on a body model in the form of a structured body. Moreover, the structured body is specified in the form of an equilibrium system of potentially interacting material points. It is shown how the equation of motion of a structured body is derived. The peculiarity of this equation is that it takes into account the transformation of the energy of motion of a structured body into internal energy when it moves in an inhomogeneous field of forces. This makes it possible to describe dissipative processes within the framework of the mechanics of a structured body without invoking statistical laws. Examples are given of how the empirical principles of the phenomenological branches of physics directly follow from the fundamental laws of physics.

Emergent Statistical Laws in Single-Cell Transcriptomic Data

Large scale data on single-cell gene expression have the potential to unravel the specific transcriptional programs of different cell types. The structure of these expression datasets suggests a similarity with several other complex systems that can be analogously described through the statistics of their basic building blocks. Transcriptomes of single cells are collections of messenger RNA abundances transcribed from a common set of genes just as books are different collections of words from a shared vocabulary, genomes of different species are specific compositions of genes belonging to evolutionary families, and ecological niches can be described by their species abundances. Following this analogy, we identify several emergent statistical laws in single-cell transcriptomic data closely similar to regularities found in linguistics, ecology or genomics. A simple mathematical framework can be used to analyze the relations between different laws and the possible mechanisms behind their ubiquity. Importantly, treatable statistical models can be useful tools in transcriptomics to disentangle the actual biological variability from general statistical effects present in most component systems and from the consequences of the sampling process inherent to the experimental technique.

TRAFFIC VOLUMES TEST OF AIRPORT RUNWAY

Currently, airport pavement design only considers the different horizontal standard deviation at the end and the middle of the runway, which had ignored the longitudinal distribution of airport runway traffic volume (ARTV). Especially for short take-off and landing aircraft, the take-off and landing distribution are not full of the whole runway. In allusion to the characteristics of ARTV, this paper developed a test system for the wheel track distribution and conducted a test of a short take-off and landing aircraft. Based on the statistics and analysis of test results, the horizontal and longitudinal distribution statistical laws of ARTV were obtained. At last, the longitudinal passage factor was proposed, and the planar distribution model was established to evaluate the ARTV at each point of the runway. By comparison with current design specifications, it is indicated that the pavement thickness will be designed more conservative without considering the planar distribution of traffic volumes.

Earthquake clusters expected from bare statistics: How bursts and swarms emerge from exogenous and epidemic aftershock processes.

<p>Earthquake catalogs exhibit strong spatio-temporal correlations. As such, earthquakes are often classified into clusters of correlated activity. Clusters themselves are traditionally classified in two different kinds: (i) bursts, with a clear hierarchical structure between a single strong mainshock, preceded by a few foreshocks and followed by a power-law decaying aftershock sequence, and (ii) swarms, exhibiting a non-trivial activity rate that cannot be reduced to such a simple hierarchy between events. </p><p>The Epidemic Aftershock Sequence (ETAS) model is a linear Hawkes point process able to reproduce earthquake clusters from empirical statistical laws [Ogata, 1998]. Although not always explicit, the ETAS model is often interpreted as the outcome of a background activity driven by external forces and a Galton-Watson branching process with one-to-one causal links between events [Saichev et al., 2005]. Declustering techniques based on field observations [Baiesi & Paczuski, 2004] can be used to infer the most likely causal links between events in a cluster. Following this method, Zaliapin and Ben‐Zion (2013) determined the statistical properties of earthquake clusters characterizing bursts and swarms, finding a relationship between the predominant cluster-class and the heat flow in seismic regions.</p><p>Here, I show how the statistical properties of clusters are related to the fundamental statistics of the underlying seismogenic process, modeled in two point-process paradigms [Baró, 2020].</p><p>The classification of clusters into bursts and swarms appears naturally in the standard ETAS model with homogeneous rates and are determined by the average branching ratio (nb) and the ratio between exponents α and b characterizing the production of aftershocks and the distribution of magnitudes, respectively. The scale-free ETAS model, equivalent to the BASS model [Turcotte, et al., 2007], and usual in cold active tectonic regions, is imposed by α=b and reproduces bursts. In contrast, by imposing α<0.5b, we recover the properties of swarms, characteristic of regions with high heat flow. </p><p>Alternatively, the same declustering methodology applied to a non-homogeneous Poisson process with a non-factorizable intensity, i.e. in absence of causal links, recovers swarms with α=0, i.e. a Poisson Galton-Watson process, with similar statistical properties to the ETAS model in the regime α<0.5b.</p><p>Therefore, while bursts are likely to represent actual causal links between events, swarms can either denote causal links with low α/b ratio or variations of the background rate caused by exogenous processes introducing local and transient stress changes. Furthermore, the redundancy in the statistical laws can be used to test the hypotheses posed by the ETAS model as a memory‐less branching process. </p><p>References:</p><ul><li> <p>Baiesi, M., & Paczuski, M. (2004). <em>Physical Review E</em>, 69, 66,106. doi:10.1103/PhysRevE.69.066106.</p> </li> <li> <p>Baró, J. (2020).  <em>Journal of Geophysical Research: Solid Earth,</em> 125, e2019JB018530. doi:10.1029/2019JB018530.</p> </li> <li> <p>Ogata, Y. (1998) <em>Annals of the Institute of Statistical Mathematics,</em> 50(2), 379–402. doi:10.1023/A:1003403601725.</p> </li> <li> <p>Saichev, A., Helmstetter, A. & Sornette, D. (2005) <em>Pure appl. geophys.</em> 162, 1113–1134. doi:10.1007/s00024-004-2663-6.</p> </li> <li> <p>Turcotte, D. L., Holliday, J. R., and Rundle, J. B. (2007), <em>Geophys. Res. Lett.</em>, 34, L12303, doi:10.1029/2007GL029696.</p> </li> <li> <p>Zaliapin, I., and Ben‐Zion, Y. (2013), <em>J. Geophys. Res. Solid Earth</em>, 118, 2865– 2877, doi:10.1002/jgrb.50178.</p> </li> </ul>

Slab Avalanche Release: Data and Field Experiments

Starting zone sizes are shown to obey statistical laws, named “power laws”, stating that the recurrence time of an event of a given size increases in a precise proportion with its size. Extrapolation of such laws fitted on small-sized events allows a determination of recurrence times for big and uncommon events. The key role of the weak layer (WL) failure is illustrated by “Propagation Saw Tests” (PST), showing that the collapse of a WL zone of a few decimeters may act as a switch, triggering a very large scale spontaneous WL failure. However, the consequences of such a collapse may be damped down by sintering of broken WL grains. We analyze bridging indexes, often used to estimate WL resistance to collapse under loading. We define a new bridging index, extending the usual one to the case of elastic bending, and we discuss the validity domains of both of them.

This sweet word “freedom” (On the formulation of the problem of freedom in the Italian political thought of the twentieth century)

People from century to century tried to determine the degree of its independence from external circumstances. And every time he found himself in front of a fact that changed the world raises the question of freedom in new ways. All the historically important battles of the twentieth century can be reduced to a confrontation over what it means to be free. The rationalistic understanding of human life that prevailed in the previous few centuries gave rise to the illusion that the world can be well organized if its structure is properly explained. Practice has shown that not everything is so simple and a rationalistic approach that suggests considering freedom as a known necessity does not allow us to liberate and make humanity happy. The statistical laws prevailing in society give rise to so many manifestations of necessity that it sometimes occurs to us that there is nothing in social life but chance. The collapse of the Soviet Union, and the usual gap relationships and the imbalance of social and political forces have forced the Europeans to search for ways to preserve their own cultural identity. Violation of ideological balance as a result of the falling interest of people towards communism creates a situation in which only the religious consciousness can become a pillar of modern embarrassed man. However, in this circumstance, there is another side: the flight into the illusory world of thoughts, in the area of supposed freedom. Today in the beginning of the third Millennium, we have to admit that so far from the final solution to the problem of freedom as thinkers of the past centuries.