2,789 research outputs found
Invariant Measures for Dissipative Dynamical Systems: Abstract Results and Applications
In this work we study certain invariant measures that can be associated to
the time averaged observation of a broad class of dissipative semigroups via
the notion of a generalized Banach limit. Consider an arbitrary complete
separable metric space which is acted on by any continuous semigroup
. Suppose that possesses a global
attractor . We show that, for any generalized Banach limit
and any distribution of initial
conditions , that there exists an invariant probability measure
, whose support is contained in , such that for all
observables living in a suitable function space of continuous mappings
on .
This work is based on a functional analytic framework simplifying and
generalizing previous works in this direction. In particular our results rely
on the novel use of a general but elementary topological observation, valid in
any metric space, which concerns the growth of continuous functions in the
neighborhood of compact sets. In the case when does not
possess a compact absorbing set, this lemma allows us to sidestep the use of
weak compactness arguments which require the imposition of cumbersome weak
continuity conditions and limits the phase space to the case of a reflexive
Banach space. Two examples of concrete dynamical systems where the semigroup is
known to be non-compact are examined in detail.Comment: To appear in Communications in Mathematical Physic
Asymptotics of the Coleman-Gurtin model
This paper is concerned with the integrodifferential equation \partial_t
u-\Delta u -\int_0^\infty \kappa(s)\Delta u(t-s)\,\d s + \varphi(u)=f arising
in the Coleman-Gurtin's theory of heat conduction with hereditary memory, in
presence of a nonlinearity of critical growth. Rephrasing the
equation within the history space framework, we prove the existence of global
and exponential attractors of optimal regularity and finite fractal dimension
for the related solution semigroup, acting both on the basic weak-energy space
and on a more regular phase space.Comment: Accepted in Discrete and Continuous Dynamical Systems, Serie
Copyright Tensions in a Digital Age
The rapid and exponential expansion of our ability to duplicate and disseminate information by digital means has rejuvenated inherent tensions in the law pertaining to copyright and has created some new ones. Not since the advent of radio in the early 1900s have such tensions come so squarely into focus. Even though courts are rarely, if ever, called upon to address certain of these tensions since the passage of the Copyright Act of 1976, they are being called upon to do so no
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Frio pilot in CO2 sequestration in brine-bearing sandstones: The University of Texas at Austin, Bureau of Economic Geology, report to the Texas Commission on Environmental Quality to accompany a class V application for an experimental technology pilot injection well.
GEOSEQ project (LBNL, LLNL, ORNL), NETL, Schlumberger–Doll Research Center, Transpetco, Sandia TechnologiesJackson School of Geoscience
When Do People Trust Their Social Groups?
Trust facilitates cooperation and supports positive outcomes in social
groups, including member satisfaction, information sharing, and task
performance. Extensive prior research has examined individuals' general
propensity to trust, as well as the factors that contribute to their trust in
specific groups. Here, we build on past work to present a comprehensive
framework for predicting trust in groups. By surveying 6,383 Facebook Groups
users about their trust attitudes and examining aggregated behavioral and
demographic data for these individuals, we show that (1) an individual's
propensity to trust is associated with how they trust their groups, (2)
smaller, closed, older, more exclusive, or more homogeneous groups are trusted
more, and (3) a group's overall friendship-network structure and an
individual's position within that structure can also predict trust. Last, we
demonstrate how group trust predicts outcomes at both individual and group
level such as the formation of new friendship ties.Comment: CHI 201
Experimental evidence for the influence of structure and meaning on linear order in the noun phrase
Recent work has used artificial language experiments to argue that hierarchical representations drive learners’ expectations about word order in complex noun phrases like these two green cars (Culbertson & Adger 2014; Martin, Ratitamkul, et al. 2019). When trained on a novel language in which individual modifiers come after the Noun, English speakers overwhelmingly assume that multiple nominal modifiers should be ordered such that Adjectives come closest to the Noun, then Numerals, then Demonstratives (i.e., N-Adj-Num-Dem or some subset thereof). This order transparently reflects a constituent structure in which Adjectives combine with Nouns to the exclusion of Numerals and Demonstratives, and Numerals combine with Noun+Adjective units to the exclusion of Demonstratives. This structure has also been claimed to derive frequency asymmetries in complex noun phrase order across languages (e.g., Cinque 2005). However, we show that features of the methodology used in these experiments potentially encourage participants to use a particular metalinguistic strategy that could yield this outcome without implicating constituency structure. Here, we use a more naturalistic artificial language learning task to investigate whether the preference for hierarchy-respecting orders is still found when participants do not use this strategy. We find that the preference still holds, and, moreover, as Culbertson & Adger (2014) speculate, that its strength reflects structural distance between modifiers. It is strongest when ordering Adjectives relative to Demonstratives, and weaker when ordering Numerals relative to Adjectives or Demonstratives relative to Numerals. Our results provide the strongest evidence yet for the psychological influence of hierarchical structure on word order preferences during learning
The short memory limit for long time statistics in a stochastic Coleman-Gurtin model of heat conduction
We study a class of semi-linear differential Volterra equations with
polynomial-type potentials that incorporates the effects of memory while being
subjected to random perturbations via an additive Gaussian noise. We show that
for a broad class of non-linear potentials and sufficiently regular noise the
system always admits invariant probability measures, defined on the extended
phase space, that possess higher regularity properties dictated by the
structure of the nonlinearities in the equation. Furthermore, we investigate
the singular limit as the memory kernel collapses to a Dirac function.
Specifically, provided sufficiently many directions in the phase space are
stochastically forced, we show that there is a unique stationary measure to
which the system converges, in a suitable Wasserstein distance, at exponential
rates independent of the decay of the memory kernel. We then prove the
convergence of the statistically steady states to the unique invariant
probability of the classical stochastic reaction-diffusion equation in the
desired singular limit. As a consequence, we establish the validity of the
small memory approximation for solutions on the infinite time horizon
Identification of a novel picornavirus related to cosaviruses in a child with acute diarrhea
Diarrhea, the third leading infectious cause of death worldwide, causes approximately 2 million deaths a year. Approximately 40% of these cases are of unknown etiology. We previously developed a metagenomic strategy for identification of novel viruses from diarrhea samples. By applying mass sequencing to a stool sample collected in Melbourne, Australia from a child with acute diarrhea, one 395 bp sequence read was identified that possessed only limited identity to known picornaviruses. This initial fragment shared only 55% amino acid identity to its top BLAST hit, the VP3 protein of Theiler's-like virus, suggesting that a novel picornavirus might be present in this sample. By using a combination of mass sequencing, RT-PCR, 5' RACE and 3' RACE, 6562 bp of the viral genome was sequenced, which includes the entire putative polyprotein. The overall genomic organization of this virus was similar to known picornaviruses. Phylogenetic analysis of the polyprotein demonstrated that the virus was divergent from previously described picornaviruses and appears to belong to the newly proposed picornavirus genus, Cosavirus. Based on the analysis discussed here, we propose that this virus represents a new species in the Cosavirus genus, and it has tentatively been named Human Cosavirus E1 (HCoSV-E1)
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