scholarly journals A Model for the Frequency Distribution of Multi-Scale Phenomena

Information ◽  
2020 ◽  
Vol 11 (12) ◽  
pp. 580
Author(s):  
Paola Favati ◽  
Grazia Lotti ◽  
Ornella Menchi ◽  
Francesco Romani
Keyword(s):  
Mixed Model ◽  
Temporal Evolution ◽  
Steady State Solution ◽  
Abstract Model ◽  
Multi Scale ◽  
Functional Relationships ◽  
Log Normal ◽  
Frequency Behavior ◽  
General Abstract ◽  
Difficult Cases

Frequency analysis is often used to investigate the structure of systems representing multi-scale real-world phenomena. In many different environments, functional relationships characterized by a power law have been recognized, but, in many cases this simple model has turned out to be absolutely inadequate and other models have been proposed. In this paper, we propose a general abstract model which constitutes a unifying framework, including many models found in literature, like the mixed model, the exponential cut-off and the log-normal. It is based on a discrete-time stochastic process, which leads to a recurrence relation describing the temporal evolution of the system. The steady state solution of the system highlights the probability distribution, which underlies the frequency behavior. A particular instance of the general model, called cubic-cut-off, was analyzed and tested in a number of experiments, producing good answers in difficult cases, even in the presence of peculiar behaviors.

scholarly journals Dynamical model for social distancing in the U.S. during the COVID-19 epidemic

2020 ◽  
Vol 8 (1) ◽  
pp. 141-149
Author(s):  
Shirish M. Chitanvis
Keyword(s):  
New York ◽  
Monte Carlo ◽  
Temporal Evolution ◽  
Social Experiment ◽  
Social Distancing ◽  
Back Testing ◽  
Moderate Growth ◽  
Log Normal ◽  
Very High ◽  
The U.S

AbstractBackground Social distancing has led to a “flattening of the curve” in many states across the U.S. This is part of a novel, massive, global social experiment which has served to mitigate the COVID-19 pandemic in the absence of a vaccine or effective anti-viral drugs. Hence it is important to be able to forecast hospitalizations reasonably accurately.Methods We propose on phenomenological grounds a random walk/generalized diffusion equation which incorporates the effect of social distancing to describe the temporal evolution of the probability of having a given number of hospitalizations. The probability density function is log-normal in the number of hospitalizations, which is useful in describing pandemics where the number of hospitalizations is very high.Findings We used this insight and data to make forecasts for states using Monte Carlo methods. Back testing validates our approach, which yields good results about a week into the future. States are beginning to reopen at the time of submission of this paper and our forecasts indicate possible precursors of increased hospitalizations. However, the trends we forecast for hospitalizations as well as infections thus far show moderate growth.Additionally we studied the reproducibility Ro in New York (Italian strain) and California (Wuhan strain). We find that even if there is a difference in the transmission of the two strains, social distancing has been able to control the progression of COVID 19.

scholarly journals Bayesian CMB foreground separation with a correlated log-normal model

2014 ◽  
Vol 10 (S306) ◽  
pp. 16-18
Author(s):  
Niels Oppermann ◽  
Torsten A. Enßlin
Keyword(s):  
Power Spectrum ◽  
Bayesian Methods ◽  
Natural Extension ◽  
Superior Performance ◽  
Normal Model ◽  
Spatial Correlations ◽  
Angular Power Spectrum ◽  
Cross Correlations ◽  
Log Normal ◽  
Frequency Behavior

AbstractThe extraction of foreground and CMB maps from multi-frequency observations relies mostly on the different frequency behavior of the different components. Existing Bayesian methods additionally make use of a Gaussian prior for the CMB whose correlation structure is described by an unknown angular power spectrum. We argue for the natural extension of this by using non-trivial priors also for the foreground components. Focusing on diffuse Galactic foregrounds, we propose a log-normal model including unknown spatial correlations within each component and cross-correlations between the different foreground components. We present case studies at low resolution that demonstrate the superior performance of this model when compared to an analysis with flat priors for all components.

scholarly journals Modeling the electrical energy discharged by lightning flashes using capacitors for application with lightning datasets

2021 ◽  
Author(s):  
Vicente Salinas ◽  
Eric C. Bruning ◽  
Edward R. Mansell ◽  
Matthew Brothers
Keyword(s):  
Electric Fields ◽  
Temporal Evolution ◽  
Electrical Energy ◽  
Electrostatic Energy ◽  
Energy Estimates ◽  
Discharge Energy ◽  
Parallel Plate Capacitor ◽  
Individual Values ◽  
Multi Scale ◽  
Local Charge

AbstractThis study employed a parallel plate capacitor model by which the electrostatic energy of lightning flashes could be estimated by considering only their physical dimensions and breakdown electric fields in two simulated storms. The capacitor model has previously been used to approximate total stormelectrostatic energy but is modified here to use the geometry of individual lightning flashes to mimic the local charge configuration where flashes were initiated. The energy discharged may then be diagnosed without context of a storm’s entire charge structure. The capacitor model was evaluated using simulated flashes from two storms modeled by the National Severe Storms Laboratory’s Collaborative Model for Multi-scale Atmospheric Simulation (COMMAS). Initial capacitor model estimates followed the temporal evolution of the flash discharge energy of COMMAS for each storm but demonstrated the need to account for an adjustment factor to represent the fraction of energy a flash dissipates, as this model assumes the entire pre-flash energy is discharged by a flash. Individual values of were obtained simply by using the ratio of the COMMAS flash to capacitor energy. Median values were selected to represent the flash populations for each storm, and were in range of = 0.019−0.021. Application of aligned the magnitudes of the capacitor model discharge energy estimates to those of COMMAS and to those estimated in previous studies. Therefore, by considering a within range of , application of the capacitor model for observed lightning datasets is suggested.

scholarly journals Dynamical model for social distancing in the U.S. during the COVID-19 epidemic

2020 ◽  
Author(s):  
Shirish M Chitanvis
Keyword(s):  
New York ◽  
Monte Carlo ◽  
Probability Density Function ◽  
Temporal Evolution ◽  
Social Experiment ◽  
Social Distancing ◽  
Back Testing ◽  
Log Normal ◽  
Very High ◽  
The U.S

Background Social distancing has led to a flattening of the curve in many states across the U.S. This is part of a novel, massive, global social experiment which has served to mitigate the pandemic in the absence of a vaccine or effective anti-viral drugs. Hence it is important to be able to forecast hospitalizations reasonably accurately. Methods We propose on phenomenological grounds a generalized diffusion equation which in- corporates the effect of social distancing to forecast the temporal evolution of the probability of having a given number of hospitalizations. The probability density function is log-normal in the number of hospitalizations, which is useful in describing pandemics where the number of hospital- izations is very high. Findings We used this insight and data to make forecasts for states using Monte Carlo methods. Back testing validates our approach, which yields good results about a week into the future. States are beginning to reopen at the time of publication and our forecasts indicate possible precursors of increased hospitalizations. Additionally we studied the reproducibility Ro in New York (Italian strain) and California (Wuhan strain). We find that even if there is a difference in the transmission of the two strains, social distancing has been able to control the progression of COVID 19. Funding None.

Multi-Scale Modeling and Oxygen Impact on Tumor Temporal Evolution: Application on Rectal Cancer During Radiotherapy

2018 ◽  
Vol 37 (4) ◽  
pp. 871-880
Author(s):  
Sena Apeke ◽  
Laurent Gaubert ◽  
Nicolas Boussion ◽  
Philippe Lambin ◽  
Dimitris Visvikis ◽  
...  
Keyword(s):  
Rectal Cancer ◽  
Temporal Evolution ◽  
Multi Scale ◽  
Scale Modeling ◽  
Multi Scale Modeling

scholarly journals SZNAJD SOCIOPHYSICS MODEL ON A TRIANGULAR LATTICE: FERRO AND ANTIFERROMAGNETIC OPINIONS

2001 ◽  
Vol 12 (10) ◽  
pp. 1509-1512 ◽  
Author(s):  
IKSOO CHANG
Keyword(s):  
Phase Transition ◽  
Relaxation Time ◽  
Trade Union ◽  
Triangular Lattice ◽  
Master Curve ◽  
Mixed Model ◽  
Initial Concentration ◽  
The Third ◽  
The Family ◽  
Log Normal

The Sznajd sociophysics model is generalized on the triangular lattice with pure antiferromagnetic opinion and also with both ferromagnetic and antiferromagnetic opinions. The slogan of the trade union "united we stand, divided we fall" can be realized via the propagation of ferromagnetic opinion of adjacent people in the union, but the propagation of antiferromagnetic opinion can be observed among the third countries between two big super powers or among the family members of conflicting parents. Fixed points are found in both models. The distributions of relaxation time of the mixed model are dispersed and become closer to log–normal as the initial concentration of down spins approaches 0.5, whereas for pure antiferromagnetic spins, they are collapsed into one master curve, which is roughly log–normal. We do not see the phase transition in the model.

scholarly journals Perils and pitfalls of mixed-effects regression models in biology

PeerJ ◽  
2020 ◽  
Vol 8 ◽  
pp. e9522 ◽  
Author(s):  
Matthew J. Silk ◽  
Xavier A. Harrison ◽  
David J. Hodgson
Keyword(s):  
Biological Sciences ◽  
Regression Models ◽  
Mixed Model ◽  
Mixed Effects ◽  
Biological Research ◽  
Functional Relationships ◽  
Fixed And Random Effects ◽  
Statistical Relationships ◽  
Biological Literature ◽  
Selection Of

Biological systems, at all scales of organisation from nucleic acids to ecosystems, are inherently complex and variable. Biologists therefore use statistical analyses to detect signal among this systemic noise. Statistical models infer trends, find functional relationships and detect differences that exist among groups or are caused by experimental manipulations. They also use statistical relationships to help predict uncertain futures. All branches of the biological sciences now embrace the possibilities of mixed-effects modelling and its flexible toolkit for partitioning noise and signal. The mixed-effects model is not, however, a panacea for poor experimental design, and should be used with caution when inferring or deducing the importance of both fixed and random effects. Here we describe a selection of the perils and pitfalls that are widespread in the biological literature, but can be avoided by careful reflection, modelling and model-checking. We focus on situations where incautious modelling risks exposure to these pitfalls and the drawing of incorrect conclusions. Our stance is that statements of significance, information content or credibility all have their place in biological research, as long as these statements are cautious and well-informed by checks on the validity of assumptions. Our intention is to reveal potential perils and pitfalls in mixed model estimation so that researchers can use these powerful approaches with greater awareness and confidence. Our examples are ecological, but translate easily to all branches of biology.

scholarly journals Reconstruction of networks with direct and indirect genetic effects

2019 ◽  
Author(s):  
Willem Kruijer ◽  
Pariya Behrouzi ◽  
Daniela Bustos-Korts ◽  
María Xosé Rodríguez-Álvarez ◽  
Seyed Mahdi Mahmoudi ◽  
...  
Keyword(s):  
Causal Inference ◽  
Indirect Effects ◽  
Fixed Effects ◽  
Genetic Variance ◽  
Mixed Model ◽  
R Package ◽  
Genetic Effects ◽  
Phenotypic Trait ◽  
Individual Plant ◽  
Functional Relationships

ABSTRACTGenetic variance of a phenotypic trait can originate from direct genetic effects, or from indirect effects, i.e., through genetic effects on other traits, affecting the trait of interest. This distinction is often of great importance, for example when trying to improve crop yield and simultaneously controlling plant height. As suggested by Sewall Wright, assessing contributions of direct and indirect effects requires knowledge of (1) the presence or absence of direct genetic effects on each trait, and (2) the functional relationships between the traits. Because experimental validation of such relationships is often unfeasible, it is increasingly common to reconstruct them using causal inference methods. However, most of the current methods require all genetic variance to be explained by a small number of QTLs with fixed effects. Only few authors considered the ‘missing heritability’ case, where contributions of many undetectable QTLs are modelled with random effects. Usually, these are treated as nuisance terms, that need to be eliminated by taking residuals from a multi-trait mixed model (MTM). But fitting such MTM is challenging, and it is impossible to infer the presence of direct genetic effects. Here we propose an alternative strategy, where genetic effects are formally included in the graph. This has important advantages: (1) genetic effects can be directly incorporated in causal inference, implemented via our PCgen algorithm, which can analyze many more traits and (2) we can test the existence of direct genetic effects and improve the orientation of edges between traits. Finally, we show that reconstruction is much more accurate if individual plant or plot data are used, instead of genotypic means. We have implemented the PCgen-algorithm in the R-package pcgen.

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