791 research outputs found
Morita equivalence of dual operator algebras
We consider a variant of the notion of Morita equivalence appropriate to
weak* closed algebras of Hilbert space operators, which we call {\em weak
Morita equivalence}. We obtain new variants, appropriate to the dual algebra
setting, of the basic theory of strong Morita equivalence, and new
nonselfadjoint variants of aspects of Rieffel's -algebraic Morita
equivalence.Comment: 19 pages. Revised to include a more general framework yet, to which
all of the results in the first version and most of the proofs, extend
immediatel
Costly defense traits in structured populations
We propose a model for the dynamics of frequencies of a costly defense trait.
More precisely, we consider Lotka-Volterra-type models involving a prey (or
host) population consisting of two types and a predator (or parasite)
population, where one type of prey individuals - modeling carriers of a defense
trait - is more effective in defending against the predators but has a weak
reproductive disadvantage. Under certain assumptions we prove that the relative
frequency of these defenders in the total prey population converges to
spatially structured Wright-Fisher diffusions with frequency-dependent
migration rates. For the many-demes limit (mean-field approximation) hereof, we
show that the defense trait goes to fixation/extinction if and only if the
selective disadvantage is smaller/larger than an explicit function of the
ecological model parameters.Comment: 48 page
Fuzzy Sets, Fuzzy Logic and Their Applications
The present book contains 20 articles collected from amongst the 53 total submitted manuscripts for the Special Issue âFuzzy Sets, Fuzzy Loigic and Their Applicationsâ of the MDPI journal Mathematics. The articles, which appear in the book in the series in which they were accepted, published in Volumes 7 (2019) and 8 (2020) of the journal, cover a wide range of topics connected to the theory and applications of fuzzy systems and their extensions and generalizations. This range includes, among others, management of the uncertainty in a fuzzy environment; fuzzy assessment methods of human-machine performance; fuzzy graphs; fuzzy topological and convergence spaces; bipolar fuzzy relations; type-2 fuzzy; and intuitionistic, interval-valued, complex, picture, and Pythagorean fuzzy sets, soft sets and algebras, etc. The applications presented are oriented to finance, fuzzy analytic hierarchy, green supply chain industries, smart health practice, and hotel selection. This wide range of topics makes the book interesting for all those working in the wider area of Fuzzy sets and systems and of fuzzy logic and for those who have the proper mathematical background who wish to become familiar with recent advances in fuzzy mathematics, which has entered to almost all sectors of human life and activity
Compositional Falsification of Cyber-Physical Systems with Machine Learning Components
Cyber-physical systems (CPS), such as automotive systems, are starting to
include sophisticated machine learning (ML) components. Their correctness,
therefore, depends on properties of the inner ML modules. While learning
algorithms aim to generalize from examples, they are only as good as the
examples provided, and recent efforts have shown that they can produce
inconsistent output under small adversarial perturbations. This raises the
question: can the output from learning components can lead to a failure of the
entire CPS? In this work, we address this question by formulating it as a
problem of falsifying signal temporal logic (STL) specifications for CPS with
ML components. We propose a compositional falsification framework where a
temporal logic falsifier and a machine learning analyzer cooperate with the aim
of finding falsifying executions of the considered model. The efficacy of the
proposed technique is shown on an automatic emergency braking system model with
a perception component based on deep neural networks
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