scholarly journals Damped White Noise Diffusion with Memory for Diffusing Microprobes in Ageing Fibrin Gels

2019 ◽  
Author(s):  
R.R.L. Aure ◽  
C.C. Bernido ◽  
M.V. Carpio-Bernido ◽  
R.G. Bacabac
Keyword(s):  
White Noise ◽  
Stochastic Approach ◽  
Analytical Framework ◽  
White Noise Process ◽  
Fibrin Gels ◽  
Tracer Particles ◽  
With Memory ◽  
White Noise Functional ◽  
Probability Density Function Pdf

ABSTRACTFrom observations of colloidal tracer particles in fibrin undergoing gelation, we introduce an analytical framework that allows determination of the probability density function (PDF) for a stochastic process beyond fractional Brownian motion. Using passive microrheology via videomicroscopy, mean square displacements (MSD) of tracer particles suspended in fibrin at different ageing times are obtained. The anomalous diffusion is then described by a damped white noise process with memory, with analytical results closely matching experimental plots of MSD and PDF. We further show that the white noise functional stochastic approach applied to passive microrheology reveals the existence of a gelation parameterμwhich elucidates the dynamics of constrained tracer particles embedded in a time dependent soft material. This study offers experimental insights on the ageing of fibrin gels while presenting a white noise functional stochastic approach that could be applied to other systems exhibiting non-Markovian diffusive behavior.

scholarly journals Damped White Noise Diffusion with Memory for Diffusing Microprobes in Ageing Fibrin Gels

2019 ◽  
Vol 117 (6) ◽  
pp. 1029-1036 ◽  
Author(s):  
Rev R.L. Aure ◽  
Christopher C. Bernido ◽  
M. Victoria Carpio-Bernido ◽  
Rommel G. Bacabac
Keyword(s):  
White Noise ◽  
Fibrin Gels ◽  
With Memory

Memory Laws as a Misuse of Legislation

2021 ◽  
pp. 1-16
Author(s):  
Eran Fish
Keyword(s):  
Free Speech ◽  
Fundamental Rights ◽  
Social Cooperation ◽  
Coordination Problem ◽  
Legal Coercion ◽  
The Right ◽  
With Memory

Memory laws are often accused of enforcing an inaccurate, manipulative or populist view of history. Some are also said to violate fundamental rights, in particular the right to free speech. These accusations are not entirely unjustified. Yet, a discussion of memory legislation that concentrates on these faults might be missing its mark. The main problem with memory legislation is not necessarily with the merits of any particular law. Rather, the determination of historical facts is not the kind of matter that should be entrusted to the legislator in the first place. The role of legislation is to make social cooperation possible despite substantial disagreement, but only when such social cooperation is indeed required. Disputes about historical facts, I argue, are not a coordination problem that requires a legislative solution. Still less can they justify legal coercion.

WHITE NOISE ANALYSIS: SOME APPLICATIONS IN COMPLEX SYSTEMS, BIOPHYSICS AND QUANTUM MECHANICS

2012 ◽  
Vol 26 (29) ◽  
pp. 1230014 ◽  
Author(s):  
CHRISTOPHER C. BERNIDO ◽  
M. VICTORIA CARPIO-BERNIDO
Keyword(s):  
Quantum Mechanics ◽  
Probability Density Function ◽  
Complex Systems ◽  
White Noise ◽  
Noise Analysis ◽  
Social Systems ◽  
White Noise Analysis ◽  
The Past ◽  
White Noise Calculus ◽  
With Memory

The white noise calculus originated by T. Hida is presented as a powerful tool in investigating physical and social systems. Combined with Feynman's sum-over-all histories approach, we parameterize paths with memory of the past, and evaluate the corresponding probability density function. We discuss applications of this approach to problems in complex systems and biophysics. Examples in quantum mechanics with boundaries are also given where Markovian paths are considered.

scholarly journals Stochastic boundary value problems: a white noise functional approach

1993 ◽  
Vol 95 (3) ◽  
pp. 391-419 ◽  
Author(s):  
Helge Holden ◽  
Tom Lindstr�m ◽  
Bernt �ksendal ◽  
Jan Ub�e ◽  
Tu-Sheng Zhang
Keyword(s):  
White Noise ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Functional Approach ◽  
White Noise Functional ◽  
Stochastic Boundary

scholarly journals Empirical White Noise Processes and the Subjective Probabilistic Approaches

2019 ◽  
Vol 48 (1) ◽  
pp. 19-30
Author(s):  
András Rövid ◽  
László Palkovics ◽  
Péter Várlaki
Keyword(s):  
White Noise ◽  
Random Number ◽  
White Noise Process ◽  
Random Number Generators ◽  
Noise Process ◽  
Complementary Approach ◽  
Fuzzy Random

The paper discusses the identification of the empirical white noise processes generated by deterministic numerical algorithms.The introduced fuzzy-random complementary approach can identify the inner hidden correlational patterns of the empirical white noise process if the process has a real hidden structure of this kind. We have shown how the characteristics of auto-correlated white noise processes change as the order of autocorrelation increases. Although in this paper we rely on random number generators to get approximate white noise processes, in our upcoming research we are planning to turn the focus on physical white noise processes in order to validate our hypothesis.

A metamodel for stormwater detention basins design

2007 ◽  
Vol 56 (12) ◽  
pp. 37-44 ◽  
Author(s):  
T. Leviandier ◽  
S. Payraudeau
Keyword(s):  
Urban Areas ◽  
Hydraulic Properties ◽  
Deterministic System ◽  
End User ◽  
Acceptable Risk ◽  
Rainfall Model ◽  
Rainfall Statistics ◽  
Probability Density Function Pdf ◽  
Optimisation Procedure

The aim of storm basins is to protect urban areas against some predefined risk of exceeding a given value of downstream runoff, or a risk of overflow for a bounded storage capacity. This risk results from the combination of a natural hazard and hydraulic properties. The correct way to address this issue is to use a stochastic rainfall model, but it may require unavailable data and be cumbersome to use in the framework of an optimisation procedure. We give the end user a way to by-pass this step, by means of a metamodel. The problem is to calculate the parameters of the probability density function (pdf) of outputs as a function of the pdf of inputs and of the parameters of the dynamic deterministic system between inputs and outputs. We propose to apply a metamodel, which is a new way of designing approximate but generic derived distribution, based on conditional probabilities. For application to dimensioning of basins, the determination of the parameter(s) corresponding to an acceptable risk simply consists of solving an algebraic equation representing the metamodel. The methodology needs usual rainfall statistics and a specific parameter inferred from analysis of storms, or supposed to have a regional value.

Tensor Bogolyubov representations of the renormalized square of white noise (RSWN) algebra

2019 ◽  
Vol 22 (04) ◽  
pp. 1950025
Author(s):  
Habib Rebei ◽  
Luigi Accardi ◽  
Hajer Taouil
Keyword(s):  
White Noise ◽  
Lebesgue Measure ◽  
Absolutely Continuous ◽  
First Order ◽  
Commutation Relations ◽  
Hyperbolic Sine ◽  
Arbitrary Complex ◽  
Borel Functions ◽  
Complex Valued

We introduce the quadratic analog of the tensor Bogolyubov representation of the CCR. Our main result is the determination of the structure of these maps: each of them is uniquely determined by two arbitrary complex-valued Borel functions of modulus [Formula: see text] and two maps of [Formula: see text] into itself whose inverses induce transformations that map the Lebesgue measure [Formula: see text] into measures [Formula: see text] absolutely continuous with respect to it. Furthermore, the Radon–Nikodyn derivatives [Formula: see text], of these measures with respect to [Formula: see text], must satisfy the relation [Formula: see text] for [Formula: see text]-almost every [Formula: see text]. This makes a surprising bridge with the hyperbolic sine and cosine defining the structure of usual (i.e. first-order) Bogolyubov transformations. The reason of the surprise is that the linear and quadratic commutation relations are completely different.

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