Exact solution to the mean exit time problem for free inertial processes driven by Gaussian white noise

We obtain the exact analytical expression, up to a quadrature, for the mean exit time, T(x,v), of a free inertial process driven by Gaussian white noise from a region (0,L) in space. We obtain a completely explicit expression for T(x,0) and discuss the dependence of T(x,v) as a function of the size L of the region. We develop a new method that may be used to solve other exit time problems.

Exact solution to the exit-time problem for an undamped free particle driven by Gaussian white noise

In a recent paper [Phys. Rev. Lett. 75, 189 (1995)] we have presented the exact analytical expression for the mean exit time, T(x,v), of a free inertial process driven by Gaussian white noise out of a region (0,L) in space. In this paper we give a detailed account of the method employed and present results on asymptotic properties and averages of T(x,v).

Approximation and support theorem for a wave equation in two space dimensions

We prove a characterization of the support of the law of the solution for a stochastic wave equation with two-dimensional space variable, driven by a noise white in time and correlated in space. The result is a consequence of an approximation theorem, in the convergence of probability, for equations obtained by smoothing the random noise. For some particular classes of coefficients, approximation in the Lp-norm for p¿1 is also proved.

An embedded real-time red peach detection system based on an OV7670 camera, ARM Cortex-M4 processor and 3D Look-Up Tables

This work proposes the development of an embedded real-time fruit detection system for future automatic fruit harvesting. The proposed embedded system is based on an ARM Cortex-M4 (STM32F407VGT6) processor and an Omnivision OV7670 color camera. The future goal of this embedded vision system will be to control a robotized arm to automatically select and pick some fruit directly from the tree. The complete embedded system has been designed to be placed directly in the gripper tool of the future robotized harvesting arm. The embedded system will be able to perform real-time fruit detection and tracking by using a three-dimensional look-up-table (LUT) defined in the RGB color space and optimized for fruit picking. Additionally, two different methodologies for creating optimized 3D LUTs based on existing linear color models and fruit histograms were implemented in this work and compared for the case of red peaches. The resulting system is able to acquire general and zoomed orchard images and to update the relative tracking information of a red peach in the tree ten times per second.

The Role of the Delay Time in the Modeling of Biological Range Expansions

The time interval between successive migrations of biological species causes a delay time in the reaction-diffusion equations describing their space-time dynamics. This lowers the predicted speed of the waves of advance, as compared to classical models. It has been shown that this delay-time effect improves the modeling of human range expansions. Here, we demonstrate that it can also be important for other species. We present two new examples where the predictions of the time-delayed and the classical (Fisher) approaches are compared to experimental data. No free or adjustable parameters are used. We show that the importance of the delay effect depends on the dimensionless product of the initial growth rate and the delay time. We argue that the delay effect should be taken into account in the modeling of range expansions for biological species