Stochastic Processes In Project Management

Performance of planned activities not always leads to the achievement of planned results in innovation projects with a high degree of uncertainty. Management of such specific projects requires the usage of specific methods and processes. It is necessary to develop own stochastic process methods rather than use classical methods of deterministic management. The main peculiarity of stochastic processes of projects consists in the inability to carry out more than one experiment. Implementation of a project is a stochastic process, which is carried out only once. For the purposes of the research, stochastic project management is the process of organisation, planning and control over projects, in which the decisions and actions of managers are described by stochastic functions. If the project realisation is described by stochastic processes, the project management process is indeed described by stochastic processes. This research suggests a project management approach based on the focus on the project product and project management as stochastic processes based on stochastic functions. It is demonstrated that stochastic function values, which underlie the stochastic processes, are formed by the intellectual instruments of those involved in the project and are developed on the basis of their knowledge and skills. The latter, in turn, are the result of studying and practical work on the project. Therefore, it is difficult to predict decisions and actions of managers and contractors, even if internal and external influences on them are specified. Then, any decisions or actions of such persons with regard to the external observer are described by stochastic functions. The purpose of this study is to describe the processes of stochastic project management. The purpose of the study is the project management process. The subject of research is the methods of stochastic project management. Within the framework of the study, all groups of processes of stochastic control will be mathematically described and the conditions of their impact determined. The processes of stochastic project management are outlined and formally presented. These are the processes of project management organisation, the processes of project management support, processes of project content definition, processes of defining the resources, required for the project works, processes of project planning, processes of influence on contractors of actions (works)

Scattering from an external field in quantum chromodynamics at high energies: from foundations to interdisciplinary connections

We review the factorization of the $S$-matrix elements in the context of particle scattering off an external field, which can serve as a model for the field of a large nucleus. The factorization takes the form of a convolution of light cone wave functions describing the physical incoming and outgoing states in terms of bare partons, and products of Wilson lines. The latter represent the interaction between the bare partons and the external field. Specializing to elastic scattering amplitudes of onia at very high energies, we introduce the color dipole model, which formulates the calculation of the modulus-squared of the wave functions in quantum chromodynamics with the help of a branching random walk, and the scattering amplitudes as observables on this classical stochastic process. Methods developed for general branching processes produce analytical formulas for the asymptotics of such observables, and thus enable one to derive exact large-rapidity expressions for onium-nucleus cross sections, from which electron-nucleus cross sections may be inferred.Comment: 97 pages, 24 figures. Lecture notes of the QCD Master Class, Saint-Jacut-de-la-Mer, September 202

Exploratory movement analysis and report building with R package stmove

Abstract Background As GPS tags and data loggers have become lighter, cheaper, and longer-lasting, there has been a growing influx of data on animal movement. Simultaneously, methods of analyses and software to apply such methods to movement data have expanded dramatically. Even so, for many interdisciplinary researchers and managers without familiarity with the field of movement ecology and the open-source tools that have been developed, the analysis of movement data has remained an overwhelming challenge. Description Here we present stmove , an R package designed to take individual relocation data and generate a visually rich report containing a set of preliminary results that ecologists and managers can use to guide further exploration of their data. Not only does this package make report building and exploratory data analysis (EDA) simple for users who may not be familiar with the extent of available analytical tools, but it sets forth a framework of best practice analyses, which offers a common starting point for the interpretation of terrestrial movement data. Results Using data from African elephants ( Loxodonta africana ) collected in southern Africa, we demonstrate stmove ’s report building function through the main analyses included: path visualization, primary statistic calculation, summary in space and time, and space-use construction. Conclusions The stmove package provides consistency and increased accessibility to managers and researchers who are interested in movement analysis but who may be unfamiliar with the full scope of movement packages and analytical tools. If widely adopted, the package will promote comparability of results across movement ecology studies

Simulation and Analysis of Animal Movement Paths using Numerus Model Builder

ABSTRACT Animal movement paths are represented by point-location time series called relocation data. How well such paths can be simulated, when the rules governing movement depend on the internal state of individuals and environmental factors (both local and, when memory is involved, global) remains an open question. To answer this, we formulate and test models able to capture the essential statistics of multiphase versions of such paths (viz., movement-phase-specific step-length and turning-angle means, variances, auto-correlation, and cross correlation values), as well as broad scale movement patterns. The latter may include patchy coverage of the landscape, as well as the existence of home-range boundaries and gravitational centers-of-movement (e.g., centered around nests). Here we present a Numerus Model Builder implementation of two kinds of models: a high-frequency, multi-mode, biased, correlated random walk designed to simulate real movement data at a scale that permits simulation and identification of path segments that range from minutes to days; and a model that uses statistics extracted from relocation data—either empirical or simulated—to construct movement modes and phases at subhourly to daily scales. We evaluate how well our derived statistical movement model captures patterns produced by our more detailed simulation model as a way to evaluate how well derived statistical movement models may capture patterns occurring in empirical data

Field testing a novel high residence positioning system for monitoring the fine‐scale movements of aquatic organisms

1. Acoustic telemetry is an important tool for studying the behaviour of aquatic organisms in the wild. 2. VEMCO high residence (HR) tags and receivers are a recent introduction in the field of acoustic telemetry and can be paired with existing algorithms (e.g. VEMCO positioning system [VPS]) to obtain high‐resolution two‐dimensional positioning data. 3. Here, we present results of the first documented field test of a VPS composed of HR receivers (hereafter, HR‐VPS). We performed a series of stationary and moving trials with HR tags (mean HR transmission period = 1.5 s) to evaluate the precision, accuracy and temporal capabilities of this positioning technology. In addition, we present a sample of data obtained for five European perch Perca fluviatilis implanted with HR tags (mean HR transmission period = 4 s) to illustrate how this technology can estimate the fine‐scale behaviour of aquatic animals. 4. Accuracy and precision estimates (median [5th–95th percentile]) of HR‐VPS positions for all stationary trials were 5.6 m (4.2–10.8 m) and 0.1 m (0.02–0.07 m), respectively, and depended on the location of tags within the receiver array. In moving tests, tracks generated by HR‐VPS closely mimicked those produced by a handheld GPS held over the tag, but these differed in location by an average of ≈9 m. 5. We found that estimates of animal speed and distance travelled for perch declined when positional data for acoustically tagged perch were thinned to mimic longer transmission periods. These data also revealed a trade‐off between capturing real nonlinear animal movements and the inclusion of positioning error. 6. Our results suggested that HR‐VPS can provide more representative estimates of movement metrics and offer an advancement for studying fine‐scale movements of aquatic organisms, but high‐precision survey techniques may be needed to test these systems

Cosmic Ray Propagation through the Magnetic Fields of the Galaxy with Extended Halo

In this project we perform theoretical studies of 3-dimensional cosmic ray propagation in magnetic field configurations of the Galaxy with an extended halo. We employ our newly developed Markov stochastic process methods to solve the diffusive cosmic ray transport equation. We seek to understand observations of cosmic ray spectra, composition under the constraints of the observations of diffuse gamma ray and radio emission from the Galaxy. The model parameters are directly are related to properties of our Galaxy, such as the size of the Galactic halo, particle transport in Galactic magnetic fields, distribution of interstellar gas, primary cosmic ray source distribution and their confinement in the Galaxy. The core of this investigation is the development of software for cosmic ray propagation models with the Markov stochastic process approach. Values of important model parameters for the halo diffusion model are examined in comparison with observations of cosmic ray spectra, composition and the diffuse gamma-ray background. This report summarizes our achievement in the grant period at the Florida Institute of Technology. Work at the co-investigator's institution, the University of New Hampshire, under a companion grant, will be covered in detail by a separate report

Critical random hypergraphs: The emergence of a giant set of identifiable vertices

We consider a model for random hypergraphs with identifiability, an analogue of connectedness. This model has a phase transition in the proportion of identifiable vertices when the underlying random graph becomes critical. The phase transition takes various forms, depending on the values of the parameters controlling the different types of hyperedges. It may be continuous as in a random graph. (In fact, when there are no higher-order edges, it is exactly the emergence of the giant component.) In this case, there is a sequence of possible sizes of ``components'' (including but not restricted to N^{2/3}). Alternatively, the phase transition may be discontinuous. We are particularly interested in the nature of the discontinuous phase transition and are able to exhibit precise asymptotics. Our method extends a result of Aldous [Ann. Probab. 25 (1997) 812-854] on component sizes in a random graph.Comment: Published at http://dx.doi.org/10.1214/009117904000000847 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

A quantitative mirror on the Euribor market using implied probability density functions

This paper presents a set of probability density functions for Euribor outturns in three months’ time, estimated from the prices of options on Euribor futures. It is the first official and freely available dataset to span the complete history of Euribor futures options, thus comprising over ten years of daily data, from 13 January 1999 onwards. Time series of the statistical moments of these option-implied probability density functions are documented until April 2010. Particular attention is given to how these probability density functions, and their associated summary statistics, reacted to the unfolding financial crisis between 2007 and 2009. In doing so, it shows how option-implied probability density functions could be used to contribute to monetary policy and financial stability analysis. JEL Classification: C13, C14, G12, G13financial, financial market, options, probability density functions