Ergodic Theory and Encoding of Individual Sequences

Author(s):  
Rudolf Ahlswede
Author(s):  
Karl E. Petersen
Keyword(s):  

Author(s):  
Raffaella Carbone ◽  
Federico Girotti

AbstractWe introduce a notion of absorption operators in the context of quantum Markov processes. The absorption problem in invariant domains (enclosures) is treated for a quantum Markov evolution on a separable Hilbert space, both in discrete and continuous times: We define a well-behaving set of positive operators which can correspond to classical absorption probabilities, and we study their basic properties, in general, and with respect to accessibility structure of channels, transience and recurrence. In particular, we can prove that no accessibility is allowed between the null and positive recurrent subspaces. In the case, when the positive recurrent subspace is attractive, ergodic theory will allow us to get additional results, in particular about the description of fixed points.


2021 ◽  
Vol 423 ◽  
pp. 132914
Author(s):  
Francesco Fanelli ◽  
Eduard Feireisl ◽  
Martina Hofmanová

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Suman Pokhrel ◽  
Benjamin R. Kraemer ◽  
Scott Burkholz ◽  
Daria Mochly-Rosen

AbstractIn December 2019, a novel coronavirus, termed severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), was identified as the cause of pneumonia with severe respiratory distress and outbreaks in Wuhan, China. The rapid and global spread of SARS-CoV-2 resulted in the coronavirus 2019 (COVID-19) pandemic. Earlier during the pandemic, there were limited genetic viral variations. As millions of people became infected, multiple single amino acid substitutions emerged. Many of these substitutions have no consequences. However, some of the new variants show a greater infection rate, more severe disease, and reduced sensitivity to current prophylaxes and treatments. Of particular importance in SARS-CoV-2 transmission are mutations that occur in the Spike (S) protein, the protein on the viral outer envelope that binds to the human angiotensin-converting enzyme receptor (hACE2). Here, we conducted a comprehensive analysis of 441,168 individual virus sequences isolated from humans throughout the world. From the individual sequences, we identified 3540 unique amino acid substitutions in the S protein. Analysis of these different variants in the S protein pinpointed important functional and structural sites in the protein. This information may guide the development of effective vaccines and therapeutics to help arrest the spread of the COVID-19 pandemic.


Entropy ◽  
2019 ◽  
Vol 21 (3) ◽  
pp. 302 ◽  
Author(s):  
Jean-Charles Delvenne

In this discussion paper we argue that category theory may play a useful role in formulating, and perhaps proving, results in ergodic theory, topogical dynamics and open systems theory (control theory). As examples, we show how to characterize Kolmogorov–Sinai, Shannon entropy and topological entropy as the unique functors to the nonnegative reals satisfying some natural conditions. We also provide a purely categorical proof of the existence of the maximal equicontinuous factor in topological dynamics. We then show how to define open systems (that can interact with their environment), interconnect them, and define control problems for them in a unified way.


1989 ◽  
Vol 9 (4) ◽  
pp. 609-618
Author(s):  
Sergey Yuzvinsky

Ergodic theory is one of several fields of mathematics where the name Vladimir Abramovich Rokhlin (spelled also ‘Rochlin’ and ‘Rohlin’) is well known to the specialists. That name is attached to some very often used theorems, but the goal of this paper is not just to remind the reader of these theorems. I put them in the context of the general development of ergodic theory during the thirty years 1940–70. Most of all, I want to emphasize that Rokhlin was not only a researcher producing powerful results but also a founder of schools at the two best Universities in the USSR. For at least 10 years (1958–68) these schools dominated ergodic theory. This paper is not biographical. Rokhlin's life certainly deserves a better biographer. However, I mention certain circumstances of a non-mathematical nature where it seems to be appropriate.


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