Temporal Factors in Pattern Vision

1965 ◽  
Vol 17 (4) ◽  
pp. 282-291 ◽  
Author(s):  
Adriana Fiorentini ◽  
D. M. Mackay
Keyword(s):  
Brownian Motion ◽  
Visual Field ◽  
Duty Cycle ◽  
Retinal Image ◽  
Exposure Duration ◽  
Time Interval ◽  
Critical Interval ◽  
Noise Field ◽  
Temporal Factors ◽  
Similar Dependence

A sequence of uncorrelated randomly patterned visual stimuli (“visual noise”) is normally seen as a field of particles in “Brownian motion.” When each frame of the sequence is followed by a blank flash superimposed on the same region of the visual field, the apparent structure of the noise field is strikingly altered, its form varying with the time interval between frame and flash. At a critical interval, many dots seem to cohere, to form maggot-like objects. Some of the factors determining this critical interval have been studied. They include the brightness, repetition frequency and exposure duration of the noise field, and the distance of its retinal image from the fovea. The critical interval for “perceptual blanking” is quite different from that for the “maggot effect,” but the two show a suggestively similar dependence upon the duty cycle of the noise display. It is of some neurological interest that the phenomenon is not appreciably visible with dichoptic mixing of noise and blank stimuli.

SMOLYANOV–WEIZSÄCKER SURFACE MEASURES GENERATED BY DIFFUSIONS ON THE SET OF TRAJECTORIES IN RIEMANNIAN MANIFOLDS

2008 ◽  
Vol 11 (01) ◽  
pp. 21-31 ◽  
Author(s):  
ILYA V. TELYATNIKOV
Keyword(s):  
Brownian Motion ◽  
Euclidean Space ◽  
Diffusion Process ◽  
Riemannian Manifolds ◽  
Marginal Distribution ◽  
Diffusion Processes ◽  
Ambient Space ◽  
Time Interval ◽  
Standard Brownian Motion ◽  
Limit Surface

We consider surface measures on the set of trajectories in a smooth compact Riemannian submanifold of Euclidean space generated by diffusion processes in the ambient space. A construction of surface measures on the path space of a smooth compact Riemannian submanifold of Euclidean space was introduced by Smolyanov and Weizsäcker for the case of the standard Brownian motion. The result presented in this paper extends the result of Smolyanov and Weizsäcker to the case when we consider measures generated by diffusion processes in the ambient space with nonidentical correlation operators. For every partition of the time interval, we consider the marginal distribution of the diffusion process in the ambient space under the condition that it visits the manifold at all times of the partition, when the mesh of the partition tends to zero. We prove the existence of some limit surface measures and the equivalence of the above measures to the distribution of some diffusion process on the manifold.

scholarly journals Two-dimensional stochastic modeling for predicting bankruptcy for manufacturing companies

2021 ◽  
Vol 54 (2) ◽  
pp. 123-129
Author(s):  
James C. Fu ◽  
Winnie H. W. Fu
Keyword(s):  
Brownian Motion ◽  
Real Data ◽  
Bankruptcy Prediction ◽  
Boundary Crossing ◽  
Time Interval ◽  
Two Dimensional ◽  
Manufacturing Companies ◽  
Boundary Crossing Probability ◽  
Data Set ◽  
Crossing Probability

Increasing accuracy of the model prediction on business bankruptcy helps reduce substantial losses for owners, creditors, investors and workers, and, further, minimize an economic and social problem frequently. In this study, we propose a stochastic model of financial working capital and cashflow as a two-dimensional Brownian motion X(t) = (X1(t),X2(t)) on the business bankruptcy prediction. The probability of bankruptcy occurring in a time interval [0,T] is defined by the boundary crossing probability of the two-dimensional Brownian motion entering a predetermined threshold domain. Mathematically, we extend the result in Fu and Wu (2016) on the boundary crossing probability of a high dimensional Brownian motion to an unbounded convex hull. The proposed model is applied to a real data set of companies in US and the numerical results show the proposed method performs well.

Brief cytochalasin-induced disruption of microfilaments during a critical interval in 1-cell C. elegans embryos alters the partitioning of developmental instructions to the 2-cell embryo

Development ◽  
1990 ◽  
Vol 108 (1) ◽  
pp. 159-172 ◽  
Author(s):  
D.P. Hill ◽  
S. Strome
Keyword(s):  
Cell Cycle ◽  
Asymmetric Cell Division ◽  
Critical Time ◽  
Time Interval ◽  
Critical Interval ◽  
Cell Stage ◽  
C Elegans ◽  
Daughter Cells ◽  
Correct Pattern ◽  
Cell Embryo

We are investigating the involvement of the microfilament cytoskeleton in the development of early Caenorhabditis elegans embryos. We previously reported that several cytoplasmic movements in the zygote require that the microfilament cytoskeleton remain intact during a narrow time interval approximately three-quarters of the way through the first cell cycle. In this study, we analyze the developmental consequences of brief, cytochalasin D-induced microfilament disruption during the 1-cell stage. Our results indicate that during the first cell cycle microfilaments are important only during the critical time interval for the 2-cell embryo to undergo the correct pattern of subsequent divisions and to initiate the differentiation of at least 4 tissue types. Disruption of microfilaments during the critical interval results in aberrant division and P-granule segregation patterns, generating some embryos that we classify as ‘reverse polarity’, ‘anterior duplication’, and ‘posterior duplication’ embryos. These altered patterns suggest that microfilament disruption during the critical interval leads to the incorrect distribution of developmental instructions responsible for early pattern formation. The strict correlation between unequal division, unequal germ-granule partitioning, and the generation of daughter cells with different cell cycle periods observed in these embryos suggests that the three processes are coupled. We hypothesize that (1) an ‘asymmetry determinant’, normally located at the posterior end of the zygote, governs asymmetric cell division, germ-granule segregation, and the segregation of cell cycle timing elements during the first cell cycle, and (2) the integrity or placement of this asymmetry determinant is sensitive to microfilament disruption during the critical time interval.

The first-passage density of the Brownian motion process to a curved boundary

1992 ◽  
Vol 29 (02) ◽  
pp. 291-304 ◽  
Author(s):  
J. Durbin ◽  
D. Williams
Keyword(s):  
Brownian Motion ◽  
Brownian Bridge ◽  
Sample Path ◽  
Practical Method ◽  
Time Interval ◽  
Brownian Motion Process ◽  
First Passage ◽  
Curved Boundary ◽  
Multiple Integrals ◽  
High Degree

An expression for the first-passage density of Brownian motion to a curved boundary is expanded as a series of multiple integrals. Bounds are given for the error due to truncation of the series when the boundary is wholly concave or wholly convex. Extensions to the Brownian bridge and to continuous Gauss–Markov processes are given. The series provides a practical method for calculating the probability that a sample path crosses the boundary in a specified time-interval to a high degree of accuracy. A numerical example is given.

The integral of geometric Brownian motion

2001 ◽  
Vol 33 (1) ◽  
pp. 223-241 ◽  
Author(s):  
Daniel Dufresne
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Brownian Motion ◽  
Laplace Transform ◽  
Finite Time ◽  
Geometric Brownian Motion ◽  
Time Interval ◽  
Finite Time Interval ◽  
Special Cases ◽  
The Laplace Transform

This paper is about the probability law of the integral of geometric Brownian motion over a finite time interval. A partial differential equation is derived for the Laplace transform of the law of the reciprocal integral, and is shown to yield an expression for the density of the distribution. This expression has some advantages over the ones obtained previously, at least when the normalized drift of the Brownian motion is a non-negative integer. Bougerol's identity and a relationship between Brownian motions with opposite drifts may also be seen to be special cases of these results.

scholarly journals The Integral of the Supremum Process of Brownian Motion

2009 ◽  
Vol 46 (2) ◽  
pp. 593-600 ◽  
Author(s):  
Svante Janson ◽  
Niclas Petersson
Keyword(s):  
Brownian Motion ◽  
Laplace Transform ◽  
Explicit Formula ◽  
Local Time ◽  
Time Interval ◽  
Standard Brownian Motion ◽  
Excursion Theory ◽  
Double Laplace Transform ◽  
The Laplace Transform ◽  
Supremum Process

In this paper we study the integral of the supremum process of standard Brownian motion. We present an explicit formula for the moments of the integral (or area)(T) covered by the process in the time interval [0,T]. The Laplace transform of(T) follows as a consequence. The main proof involves a double Laplace transform of(T) and is based on excursion theory and local time for Brownian motion.

scholarly journals X-raying winds in distant quasars: The first high-redshift wind duty cycle

2020 ◽  
Vol 638 ◽  
pp. A136
Author(s):  
E. Bertola ◽  
M. Dadina ◽  
M. Cappi ◽  
C. Vignali ◽  
G. Chartas ◽  
...  
Keyword(s):  
Duty Cycle ◽  
High Redshift ◽  
Cosmic Time ◽  
Theoretical Models ◽  
Host Galaxy ◽  
Time Interval ◽  
Absorption Column ◽  
X Ray ◽  
Spatially Resolved ◽  
First Time

Aims. Theoretical models of wind-driven feedback from active galactic nuclei (AGN) often identify ultra-fast outflows as being the main agent in the generation of galaxy-sized outflows, which are possibly the main actors in establishing so-called AGN-galaxy co-evolution. Ultra-fast outflows are well characterized in local AGN but much less is known in quasars at the cosmic time when star formation and AGN activity peaked (z ≃ 1–3). It is therefore necessary to search for evidence of ultra-fast outflows in high-z sources to test wind-driven AGN feedback models. Methods. Here we present a study of Q2237+030, the Einstein Cross, a quadruply-imaged radio-quiet lensed quasar located at z = 1.695. We performed a systematic and comprehensive temporally and spatially resolved X-ray spectral analysis of all the available Chandra and XMM-Newton data (as of September 2019). Results. We find clear evidence for spectral variability, possibly due to absorption column density (or covering fraction) variability intrinsic to the source. For the first time in this quasar, we detect a fast X-ray wind outflowing at vout ≃ 0.1c that would be powerful enough (Ėkin ≃ 0.1 Lbol) to significantly affect the evolution of the host galaxy. We report also on the possible presence of an even faster component of the wind (vout ∼ 0.5c). For the first time in a high-z quasar, given the large sample and long time interval spanned by the analyzed X-ray data, we are able to roughly estimate the wind duty cycle as ≃0.46 (0.31) at 90% (95%) confidence level. Finally, we also confirm the presence of a Fe Kα emission line with variable energy, which we discuss in the light of microlensing effects as well as considering our findings on the source.

scholarly journals Square of Brownian motion

1975 ◽  
Vol 59 ◽  
pp. 1-8
Author(s):  
Hisao Nomoto
Keyword(s):  
Stochastic Process ◽  
Brownian Motion ◽  
Correlation Function ◽  
Finite Time ◽  
Present Note ◽  
Point Of View ◽  
Time Interval ◽  
Sample Function ◽  
Finite Time Interval ◽  
Zero Crossings

Let Xt be a stochastic process and Yt be its square process. The present note is concerned with the solution of the equation assuming Yt is given. In [4], F. A. Grünbaum proved that certain statistics of Yt are enough to determine those of Xt when it is a centered, nonvanishing, Gaussian process with continuous correlation function. In connection with this result, we are interested in sample function-wise inference, though it is far from generalities. A glance of the equation shows that the difficulty is related how to pick up a sign of . Thus if we know that Xt has nice sample process such as the zero crossings are finite, no tangencies, in any finite time interval, then observations of these statistics will make it sure to find out sample functions of Xt from those of Yt (see [2]). The purpose of this note is to consider the above problem from this point of view.

Boundary crossing probability for Brownian motion and general boundaries

1997 ◽  
Vol 34 (1) ◽  
pp. 54-65 ◽  
Author(s):  
Liqun Wang ◽  
Klaus Pötzelberger
Keyword(s):  
Brownian Motion ◽  
Piecewise Linear ◽  
Linear Functions ◽  
Boundary Crossing ◽  
Time Interval ◽  
Linear Boundary ◽  
Piecewise Linear Functions ◽  
Boundary Crossing Probability ◽  
Crossing Probability ◽  
Crossing Probabilities

An explicit formula for the probability that a Brownian motion crosses a piecewise linear boundary in a finite time interval is derived. This formula is used to obtain approximations to the crossing probabilities for general boundaries which are the uniform limits of piecewise linear functions. The rules for assessing the accuracies of the approximations are given. The calculations of the crossing probabilities are easily carried out through Monte Carlo methods. Some numerical examples are provided.

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