51 research outputs found
Ergodicity, Decisions, and Partial Information
In the simplest sequential decision problem for an ergodic stochastic process
X, at each time n a decision u_n is made as a function of past observations
X_0,...,X_{n-1}, and a loss l(u_n,X_n) is incurred. In this setting, it is
known that one may choose (under a mild integrability assumption) a decision
strategy whose pathwise time-average loss is asymptotically smaller than that
of any other strategy. The corresponding problem in the case of partial
information proves to be much more delicate, however: if the process X is not
observable, but decisions must be based on the observation of a different
process Y, the existence of pathwise optimal strategies is not guaranteed.
The aim of this paper is to exhibit connections between pathwise optimal
strategies and notions from ergodic theory. The sequential decision problem is
developed in the general setting of an ergodic dynamical system (\Omega,B,P,T)
with partial information Y\subseteq B. The existence of pathwise optimal
strategies grounded in two basic properties: the conditional ergodic theory of
the dynamical system, and the complexity of the loss function. When the loss
function is not too complex, a general sufficient condition for the existence
of pathwise optimal strategies is that the dynamical system is a conditional
K-automorphism relative to the past observations \bigvee_n T^n Y. If the
conditional ergodicity assumption is strengthened, the complexity assumption
can be weakened. Several examples demonstrate the interplay between complexity
and ergodicity, which does not arise in the case of full information. Our
results also yield a decision-theoretic characterization of weak mixing in
ergodic theory, and establish pathwise optimality of ergodic nonlinear filters.Comment: 45 page
Genome-wide association and Mendelian randomisation analysis provide insights into the pathogenesis of heart failure
Heart failure (HF) is a leading cause of morbidity and mortality worldwide. A small proportion of HF cases are attributable to monogenic cardiomyopathies and existing genome-wide association studies (GWAS) have yielded only limited insights, leaving the observed heritability of HF largely unexplained. We report results from a GWAS meta-analysis of HF comprising 47,309 cases and 930,014 controls. Twelve independent variants at 11 genomic loci are associated with HF, all of which demonstrate one or more associations with coronary artery disease (CAD), atrial fibrillation, or reduced left ventricular function, suggesting shared genetic aetiology. Functional analysis of non-CAD-associated loci implicate genes involved in cardiac development (MYOZ1, SYNPO2L), protein homoeostasis (BAG3), and cellular senescence (CDKN1A). Mendelian randomisation analysis supports causal roles for several HF risk factors, and demonstrates CAD-independent effects for atrial fibrillation, body mass index, and hypertension. These findings extend our knowledge of the pathways underlying HF and may inform new therapeutic strategies
ARDD 2020: from aging mechanisms to interventions
Aging is emerging as a druggable target with growing interest from academia, industry and investors. New technologies such as artificial intelligence and advanced screening techniques, as well as a strong influence from the industry sector may lead to novel discoveries to treat age-related diseases. The present review summarizes presentations from the 7th Annual Aging Research and Drug Discovery (ARDD) meeting, held online on the 1st to 4th of September 2020. The meeting covered topics related to new methodologies to study aging, knowledge about basic mechanisms of longevity, latest interventional strategies to target the aging process as well as discussions about the impact of aging research on society and economy. More than 2000 participants and 65 speakers joined the meeting and we already look forward to an even larger meeting next year. Please mark your calendars for the 8th ARDD meeting that is scheduled for the 31st of August to 3rd of September, 2021, at Columbia University, USA
Rogue waves and solitons on a cnoidal background
Solutions of the nonlinear Schr¨odinger equation, appearing
as rogue waves on a spatially-periodic background envelope, are obtained
using the Darboux transformation scheme. Several particular
examples are illustrated numerically. These include soliton and breather
solutions on a periodic background as well as higher-order structures.
The results enrich our knowledge of possible analytic solutions that
describe the appearance of rogue waves in a variety of situations.The authors acknowledge the support of the Australian Research Council (Discovery Project
number DP110102068). N.A. and A.A. acknowledge support from the Volkswagen Stiftung
Feto-placental Adaptations to Maternal Obesity in the Baboon
Photograph of a scene with 89er reenactors at Fort Reno
- …