scholarly journals Reconstructing the Intrinsic Statistical Properties of Intermittent Locomotion Through Corrections for Boundary Effects

2021 ◽  
Vol 83 (4) ◽  
Author(s):  
Luca Cocconi ◽  
Alexander Kuhn-Régnier ◽  
Malte Neuss ◽  
Ana B. Sendova-Franks ◽  
Kim Christensen
Keyword(s):  
Random Walk ◽  
Probability Density ◽  
Null Model ◽  
Statistical Properties ◽  
Boundary Effects ◽  
One Dimension ◽  
Arbitrary Convex ◽  
Bounded Space ◽  
Convex Geometries ◽  
The One

AbstractLocomotion characteristics are often recorded within bounded spaces, a constraint which introduces geometry-specific biases and potentially complicates the inference of behavioural features from empirical observations. We describe how statistical properties of an uncorrelated random walk, namely the steady-state stopping location probability density and the empirical step probability density, are affected by enclosure in a bounded space. The random walk here is considered as a null model for an organism moving intermittently in such a space, that is, the points represent stopping locations and the step is the displacement between them. Closed-form expressions are derived for motion in one dimension and simple two-dimensional geometries, in addition to an implicit expression for arbitrary (convex) geometries. For the particular choice of no-go boundary conditions, we demonstrate that the empirical step distribution is related to the intrinsic step distribution, i.e. the one we would observe in unbounded space, via a multiplicative transformation dependent solely on the boundary geometry. This conclusion allows in practice for the compensation of boundary effects and the reconstruction of the intrinsic step distribution from empirical observations.

A Validated 2D-LC-UV Method for Simultaneous Determination of Imatinib and N-demethylimatinib in Plasma and Its Clinical Application for Therapeutic Drug Monitoring with GIST Patients

2020 ◽  
Vol 17 ◽  
Author(s):  
Houli Li ◽  
Di Zhang ◽  
Xiaoliang Cheng ◽  
Qiaowei Zheng ◽  
Kai Cheng ◽  
...  
Keyword(s):  
Therapeutic Drug Monitoring ◽  
One Dimension ◽  
Therapeutic Drug ◽  
Plasma Samples ◽  
Column Temperature ◽  
Injection Volume ◽  
Target Analytes ◽  
The One ◽  
Middle Column

Background: The trough concentration (Cmin) of Imatinib (IM) is closely related to the treatment outcomes and adverse reactions of patients with gastrointestinal stromal tumors (GIST). However, the drug plasma level has great interand intra-individual variability, and therapeutic drug monitoring (TDM) is highly recommended. Objective: To develop a novel, simple, and economical two-dimensional liquid chromatography method with ultraviolet detector (2D-LC-UV) for simultaneous determination of IM and its major active metabolite, N-demethyl imatinib (NDIM) in human plasma, and then apply the method for TDM of the drug. Method: Sample was processed by simple protein precipitation. Two target analytes were separated on the one-dimension column, captured on the middle column, and then transferred to the two-dimension column for further analysis. The detection was performed at 264 nm. The column temperature was maintained at 40˚C and the injection volume was 500 μL. Totally 32 plasma samples were obtained from patients with GIST who were receiving IM. Method: Sample was processed by simple protein precipitation. Two target analytes were separated on the one-dimension column, captured on the middle column, and then transferred to the two-dimension column for further analysis. The detection was performed at 264 nm. The column temperature was maintained at 40˚C and the injection volume was 500 μL. Totally 32 plasma samples were obtained from patients with GIST who were receiving IM. Conclusion: The novel 2D-LC-UV method is simple, stable, highly automated and independent of specialized technicians, which greatly increases the real-time capability of routine TDM for IM in hospital.

scholarly journals A fractional generalization of the dirichlet distribution and related distributions

2021 ◽  
Vol 24 (1) ◽  
pp. 112-136
Author(s):  
Elvira Di Nardo ◽  
Federico Polito ◽  
Enrico Scalas
Keyword(s):  
Monte Carlo ◽  
Probability Density Function ◽  
Monte Carlo Simulations ◽  
Probability Density ◽  
Dirichlet Distribution ◽  
One Dimensional ◽  
Reasonable Approximation ◽  
Generalized Dirichlet Distribution ◽  
The One ◽  
Generalized Dirichlet

Abstract This paper is devoted to a fractional generalization of the Dirichlet distribution. The form of the multivariate distribution is derived assuming that the n partitions of the interval [0, Wn ] are independent and identically distributed random variables following the generalized Mittag-Leffler distribution. The expected value and variance of the one-dimensional marginal are derived as well as the form of its probability density function. A related generalized Dirichlet distribution is studied that provides a reasonable approximation for some values of the parameters. The relation between this distribution and other generalizations of the Dirichlet distribution is discussed. Monte Carlo simulations of the one-dimensional marginals for both distributions are presented.

scholarly journals Assessing a Linear Nanosystem's Limiting Reliability from its Components

2008 ◽  
Vol 45 (03) ◽  
pp. 879-887 ◽  
Author(s):  
Nader Ebrahimi
Keyword(s):  
Present State ◽  
Size Range ◽  
Two Dimensions ◽  
The Other ◽  
One Dimension ◽  
Present Moment ◽  
One Dimensional ◽  
The One ◽  
Fixed Moment ◽  
Nanosized Systems

Nanosystems are devices that are in the size range of a billionth of a meter (1 x 10-9) and therefore are built necessarily from individual atoms. The one-dimensional nanosystems or linear nanosystems cover all the nanosized systems which possess one dimension that exceeds the other two dimensions, i.e. extension over one dimension is predominant over the other two dimensions. Here only two of the dimensions have to be on the nanoscale (less than 100 nanometers). In this paper we consider the structural relationship between a linear nanosystem and its atoms acting as components of the nanosystem. Using such information, we then assess the nanosystem's limiting reliability which is, of course, probabilistic in nature. We consider the linear nanosystem at a fixed moment of time, say the present moment, and we assume that the present state of the linear nanosystem depends only on the present states of its atoms.

A stochastic process whose successive intervals between events form a first order Markov chain — I

1968 ◽  
Vol 5 (03) ◽  
pp. 648-668
Author(s):  
D. G. Lampard
Keyword(s):  
Markov Chain ◽  
Point Processes ◽  
Electronic Device ◽  
Statistical Properties ◽  
Time Intervals ◽  
First Order ◽  
Stochastic Point Process ◽  
Order Markov Chain ◽  
The One ◽  
Stochastic Point Processes

In this paper we discuss a counter system whose output is a stochastic point process such that the time intervals between pairs of successive events form a first order Markov chain. Such processes may be regarded as next, in order of complexity, in a hierarchy of stochastic point processes, to “renewal” processes, which latter have been studied extensively. The main virtue of the particular system which is studied here is that virtually all its important statistical properties can be obtained in closed form and that it is physically realizable as an electronic device. As such it forms the basis for a laboratory generator whose output may be used for experimental work involving processes of this kind. Such statistical properties as the one and two-dimensional probability densities for the time intervals are considered in both the stationary and nonstationary state and also discussed are corresponding properties of the successive numbers arising in the stores of the counter system. In particular it is shown that the degree of coupling between successive time intervals may be adjusted in practice without altering the one dimensional probability density for the interval lengths. It is pointed out that operation of the counter system may also be regarded as a problem in queueing theory involving one server alternately serving two queues. A generalization of the counter system, whose inputs are normally a pair of statistically independent Poisson processes, to the case where one of the inputs is a renewal process is considered and leads to some interesting functional equations.

scholarly journals Data assimilation in Agent-based models using creation and annihilation operators

2019 ◽  
Author(s):  
Daniel Tang
Keyword(s):  
Real World ◽  
Null Model ◽  
The State ◽  
Actual State ◽  
Agent Based Models ◽  
Agent Based ◽  
Predator Prey ◽  
Predator Prey Model ◽  
The One ◽  
The Relationship

Agent-based models are a powerful tool for studying the behaviour of complex systems that can be described in terms of multiple, interacting ``agents''. However, because of their inherently discrete and often highly non-linear nature, it is very difficult to reason about the relationship between the state of the model, on the one hand, and our observations of the real world on the other. In this paper we consider agents that have a discrete set of states that, at any instant, act with a probability that may depend on the environment or the state of other agents. Given this, we show how the mathematical apparatus of quantum field theory can be used to reason probabilistically about the state and dynamics the model, and describe an algorithm to update our belief in the state of the model in the light of new, real-world observations. Using a simple predator-prey model on a 2-dimensional spatial grid as an example, we demonstrate the assimilation of incomplete, noisy observations and show that this leads to an increase in the mutual information between the actual state of the observed system and the posterior distribution given the observations, when compared to a null model.

Digital Fractional Order Savitzky-Golay Differentiator and Its Application

2011 ◽  
Author(s):  
Dali Chen ◽  
Dingyu Xue ◽  
YangQuan Chen
Keyword(s):  
Fractional Order ◽  
Least Square ◽  
One Dimension ◽  
Order Derivative ◽  
Noisy Signal ◽  
Fractional Order Derivative ◽  
Least Square Fitting ◽  
Image Enhancing ◽  
The One ◽  
Derivatives Of

Firstly the one-dimension digital fractional order Savitzky-Golay differentiator (1-D DFOSGD), which generalizes the Savitzky-Golay filter from the integer order to the fractional order, is proposed to estimate the fractional order derivative of the noisy signal. The polynomial least square fitting technology and the Riemann-Liouville fractional order derivative definition are used to ensure robust and accuracy. Experiments demonstrate that 1-D DFOSGD can estimate the fractional order derivatives of both ideal signal and noisy signal accurately. Secondly, the two-dimension DFOSGD is obtained from 1-D DFOSGD by defining a group of direction operators, and a new image enhancing method based on 2-D DFOSGD is presented. Experiments demonstrate that 2-D DFOSGD has very good performance on image enhancement.

Limit theorems and absorption problems for quantum radom walks in one dimension

2002 ◽  
Vol 2 (Special) ◽  
pp. 578-595
Author(s):  
N. Konno
Keyword(s):  
Random Walks ◽  
Limit Theorems ◽  
The Other ◽  
One Dimension ◽  
Unitary Matrices ◽  
Quantum Random Walks ◽  
One Dimensional ◽  
The Difference ◽  
The One

In this paper we consider limit theorems, symmetry of distribution, and absorption problems for two types of one-dimensional quantum random walks determined by $2 \times 2$ unitary matrices using our PQRS method. The one type was introduced by Gudder in 1988, and the other type was studied intensively by Ambainis et al. in 2001. The difference between both types of quantum random walks is also clarified.

The One-Center δ’-Interaction in One Dimension

1988 ◽  
pp. 91-96
Author(s):  
Sergio Albeverio ◽  
Friedrich Gesztesy ◽  
Raphael Høegh-Krohn ◽  
Helge Holden
Keyword(s):  
One Dimension ◽  
The One

scholarly journals A Continuous-Time Random Walk Extension of the Gillis Model

Entropy ◽  
2020 ◽  
Vol 22 (12) ◽  
pp. 1431
Author(s):  
Gaia Pozzoli ◽  
Mattia Radice ◽  
Manuele Onofri ◽  
Roberto Artuso
Keyword(s):  
Random Walk ◽  
Continuous Time ◽  
Continuous Time Random Walk ◽  
Hitting Times ◽  
Occupation Times ◽  
Theoretical Predictions ◽  
Normal Diffusion ◽  
Heavy Tailed ◽  
The One ◽  
Waiting Periods

We consider a continuous-time random walk which is the generalization, by means of the introduction of waiting periods on sites, of the one-dimensional non-homogeneous random walk with a position-dependent drift known in the mathematical literature as Gillis random walk. This modified stochastic process allows to significantly change local, non-local and transport properties in the presence of heavy-tailed waiting-time distributions lacking the first moment: we provide here exact results concerning hitting times, first-time events, survival probabilities, occupation times, the moments spectrum and the statistics of records. Specifically, normal diffusion gives way to subdiffusion and we are witnessing the breaking of ergodicity. Furthermore we also test our theoretical predictions with numerical simulations.

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