Identifying Roadkill Hotspots Using a Running Average

The identification of roadkill hotspots is necessary prior to the consideration of wildlife road mortality mitigation measures. In a previous study, 178 roadkill specimens were tallied via a driving survey along 21.4 km (13.3 mi) on three connected roadways in Baldwin County, Georgia. Roadkill locations were recorded to the nearest 0.16 km (0.1 mi) using the vehicle odometer. In the current study, location data were used to generate three graphical displays of roadkill distribution: 1) a linear graph of roadkills per 0.16 km (0.1 mi) bin; 2) a linear graph of roadkills per 0.8 km (0.5 mi) bin; and 3) a linear graph with a continuous running average incorporating 0.48 km (0.3 mi). The number and position of the peaks on each graph were compared in relation to roadway features that may influence animal movement and mortality such as vegetative boundaries, stream crossings, hills, and curves. The running average plot provided the best visual illustration of roadkill hotspot locations in relation to roadside features. The running average is a good technique to quickly and accurately identify hotspot locations and could help resource managers plan mitigation strategies to decrease wildlife road mortality

Do quasi-regular structures really exist in the solar photosphere? I. Observational evidence

Two series of solar-granulation images -- the La Palma series of 5 June 1993 and the SOHO MDI series of 17--18 January 1997 -- are analysed both qualitatively and quantitatively. New evidence is presented for the existence of long-lived, quasi-regular structures (first reported by Getling and Brandt (2002)), which no longer appear unusual in images averaged over 1--2-h time intervals. Such structures appear as families of light and dark concentric rings or families of light and dark parallel strips (``ridges'' and ``trenches'' in the brightness distributions). In some cases, rings are combined with radial ``spokes'' and can thus form ``web'' patterns. The characteristic width of a ridge or trench is somewhat larger than the typical size of granules. Running-average movies constructed from the series of images are used to seek such structures. An algorithm is developed to obtain, for automatically selected centres, the radial distributions of the azimuthally averaged intensity, which highlight the concentric-ring patterns. We also present a time-averaged granulation image processed with a software package intended for the detection of geological structures in aerospace images. A technique of running-average-based correlations between the brightness variations at various points of the granular field is developed and indications are found for a dynamical link between the emergence and sinking of hot and cool parcels of the solar plasma. In particular, such a correlation analysis confirms our suggestion that granules -- overheated blobs -- may repeatedly emerge on the solar surface. Based on our study, the critical remarks by Rast (2002) on the original paper by Getling and Brandt (2002) can be dismissed.Comment: 21 page, 8 figures; accepted by "Solar Physics

Skellam Type Processes of Order K and Beyond

In this article, we introduce Skellam process of order k and its running average. We also discuss the time-changed Skellam process of order k. In particular we discuss space-fractional Skellam process and tempered space-fractional Skellam process via time changes in Poisson process by independent stable subordinator and tempered stable subordinator, respectively. We derive the marginal probabilities, Levy measures, governing difference-differential equations of the introduced processes. Our results generalize Skellam process and running average of Poisson process in several directions.Comment: 22 pages, 1 figur

A Fast And Accurate Scoreboard Algorithm For estimating Stationary Backgrounds In An Image Sequence

This paper presents a stationary background estimation algorithm for color image sequence. The algorithm employs the running mode and running average algorithms, which are two commonly used algorithms, as the estimation core. A scoreboard is used to kept the pixel variations in the image sequence and is used to select between the running mode or the running average algorithm in each estimation. Our evaluation results show that by selecting, intelligently, the estimation core between the two algorithms according to the scoreboard values, the proposed background estimation algorithm has excellent performance in terms of estimation accuracy and speed.published_or_final_versio

Mimicking an It\^{o} process by a solution of a stochastic differential equation

Given a multi-dimensional It\^{o} process whose drift and diffusion terms are adapted processes, we construct a weak solution to a stochastic differential equation that matches the distribution of the It\^{o} process at each fixed time. Moreover, we show how to match the distributions at each fixed time of functionals of the It\^{o} process, including the running maximum and running average of one of the components of the process. A consequence of this result is that a wide variety of exotic derivative securities have the same prices when the underlying asset price is modeled by the original It\^{o} process or the mimicking process that solves the stochastic differential equation.Comment: Published in at http://dx.doi.org/10.1214/12-AAP881 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

DoWG Unleashed: An Efficient Universal Parameter-Free Gradient Descent Method

This paper proposes a new easy-to-implement parameter-free gradient-based optimizer: DoWG (Distance over Weighted Gradients). We prove that DoWG is efficient -- matching the convergence rate of optimally tuned gradient descent in convex optimization up to a logarithmic factor without tuning any parameters, and universal -- automatically adapting to both smooth and nonsmooth problems. While popular algorithms following the AdaGrad framework compute a running average of the squared gradients to use for normalization, DoWG maintains a new distance-based weighted version of the running average, which is crucial to achieve the desired properties. To complement our theory, we also show empirically that DoWG trains at the edge of stability, and validate its effectiveness on practical machine learning tasks.Comment: 22 pages, 1 table, 4 figure