scholarly journals Intermittent quasistatic dynamical systems: weak convergence of fluctuations

2018 ◽  
Vol 5 (1) ◽  
pp. 8-34 ◽  
Author(s):  
Juho Leppänen
Keyword(s):  
Dynamical Systems ◽  
Weak Convergence ◽  
Time Evolution ◽  
Martingale Problem ◽  
Statistical Properties ◽  
Time Dependent ◽  
Stochastic Diffusion ◽  
Interval Maps ◽  
Well Posed ◽  
Over Time

Abstract This paper is about statistical properties of quasistatic dynamical systems. These are a class of non-stationary systems that model situations where the dynamics change very slowly over time due to external influences. We focus on the case where the time-evolution is described by intermittent interval maps (Pomeau-Manneville maps) with time-dependent parameters. In a suitable range of parameters, we obtain a description of the statistical properties as a stochastic diffusion, by solving a well-posed martingale problem. The results extend those of a related recent study due to Dobbs and Stenlund, which concerned the case of quasistatic (uniformly) expanding systems.

scholarly journals Quasistatic dynamical systems

2016 ◽  
Vol 37 (8) ◽  
pp. 2556-2596 ◽  
Author(s):  
NEIL DOBBS ◽  
MIKKO STENLUND
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Time Evolution ◽  
Chaotic Maps ◽  
Martingale Problem ◽  
Initial Distribution ◽  
Initial State ◽  
Statistical Behavior ◽  
Long Time ◽  
Well Posed

We introduce the notion of a quasistatic dynamical system, which generalizes that of an ordinary dynamical system. Quasistatic dynamical systems are inspired by the namesake processes in thermodynamics, which are idealized processes where the observed system transforms (infinitesimally) slowly due to external influence, tracing out a continuous path of thermodynamic equilibria over an (infinitely) long time span. Time evolution of states under a quasistatic dynamical system is entirely deterministic, but choosing the initial state randomly renders the process a stochastic one. In the prototypical setting where the time evolution is specified by strongly chaotic maps on the circle, we obtain a description of the statistical behavior as a stochastic diffusion process, under surprisingly mild conditions on the initial distribution, by solving a well-posed martingale problem. We also consider various admissible ways of centering the process, with the curious conclusion that the ‘obvious’ centering suggested by the initial distribution sometimes fails to yield the expected diffusion.

scholarly journals Co-clustering of Time-Dependent Data via the Shape Invariant Model

2021 ◽  
Author(s):  
Alessandro Casa ◽  
Charles Bouveyron ◽  
Elena Erosheva ◽  
Giovanna Menardi
Keyword(s):  
Time Evolution ◽  
Time Dependent ◽  
Dependent Data ◽  
Multiple Features ◽  
Invariant Model ◽  
Curve Registration ◽  
Shape Invariant ◽  
Low Dimensional ◽  
Suitable Modification ◽  
Over Time

AbstractMultivariate time-dependent data, where multiple features are observed over time for a set of individuals, are increasingly widespread in many application domains. To model these data, we need to account for relations among both time instants and variables and, at the same time, for subject heterogeneity. We propose a new co-clustering methodology for grouping individuals and variables simultaneously, designed to handle both functional and longitudinal data. Our approach borrows some concepts from the curve registration framework by embedding the shape invariant model in the latent block model, estimated via a suitable modification of the SEM-Gibbs algorithm. The resulting procedure allows for several user-defined specifications of the notion of cluster that can be chosen on substantive grounds and provides parsimonious summaries of complex time-dependent data by partitioning data matrices into homogeneous blocks. Along with the explicit modelling of time evolution, these aspects allow for an easy interpretation of the clusters, from which also low-dimensional settings may benefit.

scholarly journals Detection of Acetaminophen and Its Glucuronide in Fingerprint by SALDI Mass Spectrometry Using Zeolite and Study of Time-Dependent Changes in Detected Ion Amount

Analytica ◽  
2021 ◽  
Vol 2 (3) ◽  
pp. 66-75
Author(s):  
Toshiki Horikoshi ◽  
Chihiro Kitaoka ◽  
Yosuke Fujii ◽  
Takashi Asano ◽  
Jiawei Xu ◽  
...  
Keyword(s):  
Mass Spectrometry ◽  
Glucuronic Acid ◽  
Laser Desorption ◽  
The Body ◽  
Time Dependent ◽  
Laser Desorption Ionization ◽  
Fingerprint Analysis ◽  
Desorption Ionization ◽  
Acid Conjugate ◽  
Over Time

The ingredients of an antipyretic (acetaminophen, AAP) and their metabolites excreted into fingerprint were detected by surface-assisted laser desorption ionization (SALDI) mass spectrometry using zeolite. In the fingerprint taken 4 h after AAP ingestion, not only AAP but also the glucuronic acid conjugate of AAP (GAAP), caffeine (Caf), ethenzamide (Eth), salicylamide (Sala; a metabolite of Eth), and urea were detected. Fingerprints were collected over time to determine how the amounts of AAP and its metabolite changed with time, and the time dependence of the peak intensities of protonated AAP and GAAP was measured. It was found that the increase of [GAAP+H]+ peak started later than that of [AAP+H]+ peak, reflecting the metabolism of AAP. Both AAP and GAAP reached maximum concentrations approximately 3 h after ingestion, and were excreted from the body with a half-life of approximately 3.3 h. In addition, fingerprint preservation was confirmed by optical microscopy, and fingerprint shape was retained even after laser irradiation of the fingerprint. Our method may be used in fingerprint analysis.

scholarly journals The time-dependent angular analysis of Bd → KSℓℓ, a new benchmark for new physics

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Sébastien Descotes-Genon ◽  
Martín Novoa-Brunet ◽  
K. Keri Vos
Keyword(s):  
Time Evolution ◽  
Form Factors ◽  
New Physics ◽  
Time Dependent ◽  
Angular Analysis ◽  
Time Dependent Analysis ◽  
Tensor Operators

Abstract We consider the time-dependent analysis of Bd→ KSℓℓ taking into account the time-evolution of the Bd meson and its mixing into $$ {\overline{B}}_d $$ B ¯ d . We discuss the angular conventions required to define the angular observables in a transparent way with respect to CP conjugation. The inclusion of time evolution allows us to identify six new observables, out of which three could be accessed from a time-dependent tagged analysis. We also show that these observables could be obtained by time-integrated measurements in a hadronic environment if flavour tagging is available. We provide simple and precise predictions for these observables in the SM and in NP models with real contributions to SM and chirally flipped operators, which are independent of form factors and charm-loop contributions. As such, these observables provide robust and powerful cross-checks of the New Physics scenarios currently favoured by global fits to b → sℓℓ data. In addition, we discuss the sensitivity of these observables with respect to NP scenarios involving scalar and tensor operators, or CP-violating phases. We illustrate how these new observables can provide a benchmark to discriminate among the various NP scenarios in b → sμμ. We discuss the extension of these results for Bs decays into f0, η or η′.

scholarly journals Coagulation Processes with Gibbsian Time Evolution

2012 ◽  
Vol 49 (03) ◽  
pp. 612-626
Author(s):  
Boris L. Granovsky ◽  
Alexander V. Kryvoshaev
Keyword(s):  
Stochastic Process ◽  
Recurrence Relation ◽  
Time Evolution ◽  
Nonnegative Function ◽  
Gibbs Distribution ◽  
Time Dependent ◽  
Explicit Solutions ◽  
Gibbs Distributions ◽  
Giant Cluster ◽  
Positive Integers

We prove that a stochastic process of pure coagulation has at any timet≥ 0 a time-dependent Gibbs distribution if and only if the rates ψ(i,j) of single coagulations are of the form ψ(i;j) =if(j) +jf(i), wherefis an arbitrary nonnegative function on the set of positive integers. We also obtain a recurrence relation for weights of these Gibbs distributions that allow us to derive the general form of the solution and the explicit solutions in three particular cases of the functionf. For the three corresponding models, we study the probability of coagulation into one giant cluster by timet> 0.

scholarly journals Risk Factors for Prostate Cancer Detection After a Negative Biopsy: A Novel Multivariable Longitudinal Approach

2010 ◽  
Vol 28 (10) ◽  
pp. 1714-1720 ◽  
Author(s):  
Peter H. Gann ◽  
Angela Fought ◽  
Ryan Deaton ◽  
William J. Catalona ◽  
Edward Vonesh
Keyword(s):  
Prostate Cancer ◽  
Risk Factors ◽  
Specific Antigen ◽  
Time Dependent ◽  
Negative Biopsy ◽  
Gland Volume ◽  
Piecewise Exponential ◽  
Over Time ◽  
Negative Biopsies

Purpose To introduce a novel approach for the time-dependent quantification of risk factors for prostate cancer (PCa) detection after an initial negative biopsy. Patients and Methods Data for 1,871 men with initial negative biopsies and at least one follow-up biopsy were available. Piecewise exponential regression models were developed to quantify hazard ratios (HRs) and define cumulative incidence curves for PCa detection for subgroups with specific patterns of risk factors over time. Factors evaluated included age, race, serum prostate-specific antigen (PSA) concentration, PSA slope, digital rectal examination, dysplastic glands or prostatitis on biopsy, ultrasound gland volume, urinary symptoms, and number of negative biopsies. Results Four hundred sixty-five men had PCa detected, after a mean follow-up time of 2.8 years. All of the factors were independent predictors of PCa detection except for PSA slope, as a result of its correlation with time-dependent PSA level, and race. PSA (HR = 3.90 for > 10 v 2.5 to 3.9 ng/mL), high-grade prostatic intraepithelial neoplasia/atypical glands (HR = 2.97), gland volume (HR = 0.39 for > 50 v < 25 mL), and number of repeat biopsies (HR = 0.36 for two v zero repeat biopsies) were the strongest predictors. Men with high-risk versus low-risk event histories had a 20-fold difference in PCa detection over 5 years. Conclusion Piecewise exponential models provide an approach to longitudinal analysis of PCa risk that allows clinicians to see the interplay of risk factors as they unfold over time for individual patients. With these models, it is possible to identify distinct subpopulations with dramatically different needs for monitoring and repeat biopsy.

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