scholarly journals Renewal theory provides a universal quantitative framework to characterise the continuous regeneration of rotational events in cardiac fibrillation

2019 ◽  
Author(s):  
Dhani Dharmaprani ◽  
Madeline Schopp ◽  
Pawel Kuklik ◽  
Darius Chapman ◽  
Anandaroop Lahiri ◽  
...  
Keyword(s):  
Systematic Review ◽  
Renewal Theory ◽  
Distribution Functions ◽  
Exponential Distributions ◽  
Continuous Formation ◽  
Cardiac Fibrillation ◽  
Constant Rate ◽  
Source Data ◽  
Phase Singularities ◽  
Event Times

ABSTRACTBackgroundCardiac fibrillation is thought to be maintained by rotational activity, with pivoting regions called phase singularities (PSs). Despite a century of research, no clear quantitative framework exists to model the fundamental processes responsible for the continuous formation and destruction of rotors in fibrillation.ObjectiveWe conducted a multi-modality, multi-species study of AF/VF under the hypothesis that PS formation/destruction in fibrillation can be modelled as self-regenerating renewal processes, producing exponential distributions of inter-event times governed by constant rate-parameters defined by the prevailing properties of the system.MethodsPS formation/destruction was studied and cross-validated in 5 models, using basket recordings and optical mapping from: i) human persistent AF (n = 20), ii) tachypaced sheep AF (n = 5), iii) rat AF (n = 4), iv) rat VF (n = 11) and v) computer simulated AF (SIM). Hilbert phase maps were constructed. PS lifetime data were fitted by exponential probability distribution functions (PDFs) computed using maximum entropy theory, and the rate parameter (λ) determined. A systematic review was conducted to cross-validate with source data from literature.ResultsPS destruction/formation distributions showed good fits to an exponential in all systems (R2≥ 0.90). In humans,λ= 4.6%/ms (95%CI,4.3,4.9)), sheep 4.4%/ms (95%CI,4.1,4.7)), rat AF 38%/ms (95%CI,22,55), rat VF 46%/ms (95%CI,31.2,60.2) and SIM 5.4%/ms (95%CI,4.1,6.7). All PS distributions identified through systematic review were exponential with λ comparable to experimental data.ConclusionThese results provide a universal quantitative framework to explain rotor formation and destruction in AF/VF, and a platform for therapeutic advances in cardiac fibrillation.

scholarly journals Relationship between Age and Value of Information for a Noisy Ornstein–Uhlenbeck Process

Entropy ◽  
2021 ◽  
Vol 23 (8) ◽  
pp. 940
Author(s):  
Zijing Wang ◽  
Mihai-Alin Badiu ◽  
Justin P. Coon
Keyword(s):  
Value Of Information ◽  
Markov Models ◽  
Upper Bounds ◽  
Distribution Functions ◽  
Lower And Upper Bounds ◽  
Uhlenbeck Process ◽  
Source Data ◽  
Non Linear ◽  
Queue Model ◽  
Selection Of

The age of information (AoI) has been widely used to quantify the information freshness in real-time status update systems. As the AoI is independent of the inherent property of the source data and the context, we introduce a mutual information-based value of information (VoI) framework for hidden Markov models. In this paper, we investigate the VoI and its relationship to the AoI for a noisy Ornstein–Uhlenbeck (OU) process. We explore the effects of correlation and noise on their relationship, and find logarithmic, exponential and linear dependencies between the two in three different regimes. This gives the formal justification for the selection of non-linear AoI functions previously reported in other works. Moreover, we study the statistical properties of the VoI in the example of a queue model, deriving its distribution functions and moments. The lower and upper bounds of the average VoI are also analysed, which can be used for the design and optimisation of freshness-aware networks. Numerical results are presented and further show that, compared with the traditional linear age and some basic non-linear age functions, the proposed VoI framework is more general and suitable for various contexts.

Cluster headache: review of current understandings

2012 ◽  
pp. 5-12
Author(s):  
Reinaldo Teixeira Ribeiro ◽  
André Leite Gonçalves ◽  
Maria Eduarda Nobre ◽  
Deusvenir de Souza Carvalho ◽  
Mario Fernando Prieto Peres
Keyword(s):  
Systematic Review ◽  
Cluster Headache ◽  
The United States ◽  
Search Term ◽  
National Library ◽  
Trigeminal Autonomic Cephalalgia ◽  
Treatment Approaches ◽  
Source Data ◽  
Subsequent Reference ◽  
Tension Type Headaches

Cluster headache (CH) is the trigeminal autonomic cephalalgia whose pain is considered to be one of the most severe known to man. Although diagnosed less frequently than migraine and tension-type headaches, CH is nonetheless an important clinical entity, particularly given our evolving understanding of its actual epidemiology, pathophysiology, current diagnostic criteria and treatment approaches. We carried out a systematic review through the United States National Library of Medicine (PUBMED) by using the search term "cluster headache" and the results were narrowed to manuscripts published in the last ten years with subsequent reference searches and verification of source data. This article presents a review of the current understanding of the most important aspects of CH, with emphasis on mechanisms and treatment approaches.

A geometric interpretation of the relations between the exponential and generalized Erlang distributions

1982 ◽  
Vol 14 (04) ◽  
pp. 885-897 ◽  
Author(s):  
Michel Dehon ◽  
Guy Latouche
Keyword(s):  
Vector Space ◽  
Convex Subset ◽  
Geometric Interpretation ◽  
Distribution Functions ◽  
Real Vector ◽  
Exponential Distributions ◽  
Geometric Aspect ◽  
Linear Combinations ◽  
Exponential Random Variables ◽  
Erlang Distributions

Linear combinations of exponential distribution functions are considered, and the class of distribution functions so obtainable is investigated. Convex combinations correspond to hyperexponential distributions, while non-convex combinations yield, among other, generalized Erlang distributions obtainable as sums of independent exponential random variables with different parameters. For a given number n of different exponential distributions, the class investigated is an (n – 1)-dimensional convex subset of the n-dimensional real vector space generated by the n distribution functions. The geometric aspect of this subset is revealed, together with the location of hyperexponential and generalized Erlang distributions.

scholarly journals Renewal Theory as a Universal Quantitative Framework to Characterize Phase Singularity Regeneration in Mammalian Cardiac Fibrillation

2019 ◽  
Vol 12 (12) ◽  
Author(s):  
Dhani Dharmaprani ◽  
Madeline Schopp ◽  
Pawel Kuklik ◽  
Darius Chapman ◽  
Anandaroop Lahiri ◽  
...  
Keyword(s):  
Renewal Theory ◽  
Phase Singularity ◽  
Cardiac Fibrillation

Stochastic models as functionals: some remarks on the renewal case

1989 ◽  
Vol 26 (02) ◽  
pp. 296-303 ◽  
Author(s):  
Rudolf Grübel
Keyword(s):  
Stochastic Model ◽  
Asymptotic Behaviour ◽  
Stochastic Models ◽  
Renewal Theory ◽  
Lifetime Distribution ◽  
Exponential Distributions ◽  
New Approach ◽  
Renewal Measure

We regard the standard stochastic model of renewal theory as a functional which associates with a lifetime distribution μ the corresponding renewal measure v = Σ0 ∞ μ ∗ n . The behaviour of this functional near exponential distributions is investigated. The literature mainly deals with the asymptotic behaviour of v([0, t]) and v[t, t + 1]) as t → ∞— this new approach leads to expansions which are valid uniformly in t ∈ R.

ON THE DOUBLING DISTRIBUTIONS OF DAY 7-MEGAKARYOCYTE (MKC) PROGENITORS

1987 ◽  
Author(s):  
J M Paulus ◽  
R Fernandez-Delgado ◽  
J C Grosdent ◽  
J Lecocq ◽  
M Prenant
Keyword(s):  
Bone Marrow ◽  
Conditioned Medium ◽  
Renewal Process ◽  
Coefficient Of Variation ◽  
Phase 1 ◽  
Renewal Theory ◽  
Fixed Time ◽  
Mouse Bone Marrow ◽  
Exponential Distributions ◽  
Significant Variability

It has often been assumed that hemopoietic progenitors undergo a rather uniform, deterministic number of proliferative cycles before they generate the elements which are recognizable by pano-ptiG and cytochemical methods. We now confirm and extend previous data on the distribution of the number of doublings undergone before polyploi'dization by day 7-MKC progenitors. Cultures of mouse bone marrow were stimulated by erythropoietin, WEHI conditioned medium (CM) and/or pokeweed CM. In all cases, cumulative doubling distributions of pure MKC colonies could be precisely fitted by exponential lines, whose slope and length depended on the stimulus or combination of stimuli used. The frequency of single MKC could be fitted by the same line as that plotting the number of doublings in MKC colonies, suggesting that single MKC and MKC colonies can be generated by the same class of progenitors. Exponential shape implies that the coefficient of variation (SD/mean) of doubling numbers is one, indicating significant variability in proliferative behavior among day 7-MKC progenitors. Such exponential distributions are best explained in the framework of Renewal Theory (Cox, Methuen, 1962). Whatever the distribution of the number of progenitor renewals in fixed time, the distribution of renewals will be geometric (i.e discontinuous exponential) if the total time spent by individual colonies in the proliferation phase (1) is distributed exponentially, and (2) is independent from the renewal process itself. These results suggest that the wave of MKC progenitor mitoses is randomly arrested by a differentia-tive event which strikes progenitor clones independently from their proliferative past.

scholarly journals PackIO and EphysViewer: software tools for acquisition and analysis of neuroscience data

2016 ◽  
Author(s):  
Brendon O. Watson ◽  
Rafael Yuste ◽  
Adam M. Packer
Keyword(s):  
Open Source ◽  
General Purpose ◽  
Analysis Tool ◽  
Temporal Precision ◽  
Open Source Data ◽  
Source Data ◽  
Timing Data ◽  
Multiple Devices ◽  
Event Times ◽  
Set Up

AbstractWe present an open-source synchronization software package, PackIO, that can record and generate voltage signals to enable complex experimental paradigms across multiple devices. This general purpose package is built on National Instruments data acquisition and generation hardware and has temporal precision up to the limit of the hardware. PackIO acts as a flexibly programmable master clock that can record experimental data (e.g. voltage traces), timing data (e.g. event times such as imaging frame times) while generating stimuli (e.g. voltage waveforms, voltage triggers to drive other devices, etc.). PackIO is particularly useful to record from and synchronize multiple devices, for example when simultaneously acquiring electrophysiology while generating and recording imaging timing data. Experimental control is easily enabled by an intuitive graphical user interface. We also release an open-source data visualisation and analysis tool, EphysViewer, written in MATLAB, as well as a module to import data into Python. These flexible and programmable tools allow experimenters to configure and set up customised input and output protocols in a synchronized fashion for controlling, recording, and analysing experiments.

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