Combining domain knowledge and statistical models in time series analysis

This paper describes a new approach to time series modeling that combines subject-matter knowledge of the system dynamics with statistical techniques in time series analysis and regression. Applications to American option pricing and the Canadian lynx data are given to illustrate this approach.Comment: Published at http://dx.doi.org/10.1214/074921706000001049 in the IMS Lecture Notes Monograph Series (http://www.imstat.org/publications/lecnotes.htm) by the Institute of Mathematical Statistics (http://www.imstat.org

Lotka-Volterra predator-prey model with periodically varying carrying capacity

We study the stochastic spatial Lotka-Volterra (LV) model for predator-prey interaction subject to a periodically varying carrying capacity. The LV model with on-site lattice occupation restrictions that represent finite food resources for the prey exhibits a continuous active-to-absorbing phase transition. The active phase is sustained by spatio-temporal patterns in the form of pursuit and evasion waves. Monte Carlo simulations on a two-dimensional lattice are utilized to investigate the effect of seasonal variations of the environment on species coexistence. The results of our simulations are also compared to a mean-field analysis. We find that the parameter region of predator and prey coexistence is enlarged relative to the stationary situation when the carrying capacity varies periodically. The stationary regime of our periodically varying LV system shows qualitative agreement between the stochastic model and the mean-field approximation. However, under periodic carrying capacity switching environments, the mean-field rate equations predict period-doubling scenarios that are washed out by internal reaction noise in the stochastic lattice model. Utilizing visual representations of the lattice simulations and dynamical correlation functions, we study how the pursuit and evasion waves are affected by ensuing resonance effects. Correlation function measurements indicate a time delay in the response of the system to sudden changes in the environment. Resonance features are observed in our simulations that cause prolonged persistent spatial correlations. Different effective static environments are explored in the extreme limits of fast- and slow periodic switching. The analysis of the mean-field equations in the fast-switching regime enables a semi-quantitative description of the stationary state.Comment: 17 pages, 20 figure

Selfish Herd Optimisation based fractional order cascaded controllers for AGC study

In a modern, and complex power system (PS), robust controller is obligatory to regulate the frequency under uncertain load/parameter change of the system. In addition to this, presence of nonlinearities, load frequency control (LFC) of a Power System becomes more challenging which necessitates a suitable, and robust controller. Single stage controller does not perform immensely against aforesaid changed conditions. So, a novel non-integer/fractional order (FO) based two-stage controller incorporated with 2-degrees of freedom (2-DOF), derivative filter (N), named as 2-DOF-FOPIDN-FOPDN controller, is adopted to improve the dynamic performance of a 3-area power system. Each area of the power system consists of both non-renewable and renewable generating units. Again, to support the superior performance of 2-DOF-FOPIDN-FOPDN controller, it is compared with the result produced by PID, FOPID, and 2-DOF-PIDN-PDN controllers. The optimal design of these controllers is done by applying Selfish Herd Optimisation (SHO) technique. Further, the robustness of the 2-DOF-FOPIDN-FOPDN controller is authenticated by evaluating the system performance under parameter variation. The work is further extended to prove the supremacy of SHO algorithm over a recently published article based on pathfinder algorithm (PFA)

Mathematical Modeling of Biological Systems

Mathematical modeling is a powerful approach supporting the investigation of open problems in natural sciences, in particular physics, biology and medicine. Applied mathematics allows to translate the available information about real-world phenomena into mathematical objects and concepts. Mathematical models are useful descriptive tools that allow to gather the salient aspects of complex biological systems along with their fundamental governing laws, by elucidating the system behavior in time and space, also evidencing symmetry, or symmetry breaking, in geometry and morphology. Additionally, mathematical models are useful predictive tools able to reliably forecast the future system evolution or its response to specific inputs. More importantly, concerning biomedical systems, such models can even become prescriptive tools, allowing effective, sometimes optimal, intervention strategies for the treatment and control of pathological states to be planned. The application of mathematical physics, nonlinear analysis, systems and control theory to the study of biological and medical systems results in the formulation of new challenging problems for the scientific community. This Special Issue includes innovative contributions of experienced researchers in the field of mathematical modelling applied to biology and medicine

The paradox of enrichment in predator-prey systems

>Magister Scientiae - MScIn principle, an enrichment of resources in predator-prey systems show prompts destabilisation of a framework, accordingly, falling trophic communication, a phenomenon known to as the \Paradox of Enrichment" [54]. After it was rst genius postured by Rosenzweig [48], various resulting examines, including recently those of Mougi-Nishimura [43] as well as that of Bohannan-Lenski [8], were completed on this problem over numerous decades. Nonetheless, there has been a universal none acceptance of the \paradox" word within an ecological eld due to diverse interpretations [51]. In this dissertation, some theoretical exploratory works are being surveyed in line with giving a concise outline proposed responses to the paradox. Consequently, a quantity of di usion-driven models in mathematical ecology are evaluated and analysed. Accordingly, piloting the way for the spatial structured pattern (we denote it by SSP) formation in nonlinear systems of partial di erential equations [36, 40]. The central point of attention is on enrichment consequences which results toward a paradoxical state. For this purpose, evaluating a number of compartmental models in ecology similar to those of [48] will be of great assistance. Such displays have greater in uence in pattern formations due to diversity in meta-population. Studying the outcomes of initiating an enrichment into [9] of Braverman's model, with a nutrient density (denoted by n) and bacteria compactness (denoted by b) respectively, suits the purpose. The main objective behind being able to transform [9]'s system (2.16) into a new model as a result of enrichment. Accordingly, n has a logistic- type growth with linear di usion, while b poses a Holling Type II and nonlinear di usion r2 nb2 [9, 40]. Five fundamental questions are imposed in order to address and guide the study in accordance with the following sequence: (a) What will be the outcomes of introducing enrichment into [9]'s model? (b) How will such a process in (i) be done in order to change the system (2.16)'s stability state [50]? (c) Whether the paradox does exist in a particular situation or not [51]? Lastly, (d) If an absurdity in (d) does exist, is it reversible [8, 16, 54]? Based on the problem statement above, the investigation will include various matlab simulations. Therefore, being able to give analysis on a local asymptotic stability state when a small perturbation has been introduced [40]. It is for this reason that a bifurcation relevance comes into e ect [58]. There are principal de nitions that are undertaken as the research evolves around them. A study of quantitative response is presented in predator-prey systems in order to establish its stability properties. Due to tradeo s, there is a great likelihood that the growth rate, attack abilities and defense capacities of species have to be examined in line with reviewing parameters which favor stability conditions. Accordingly, an investigation must also re ect chances that leads to extinction or coexistence [7]. Nature is much more complex than scienti c models and laboratories [39]. Therefore, di erent mechanisms have to be integrated in order to establish stability even when a system has been under enrichment [51]. As a result, SSP system is modeled by way of reaction-di usion di erential equations simulated both spatially and temporally. The outcomes of such a system will be best suitable for real-world life situations which control similar behaviors in the future. Comparable models are used in the main compilation phase of dissertation and truly re ected in the literature. The SSP model can be regarded as between (2018-2011), with a stability control study which is of an original

A METHODOLOGY FOR TECHNOLOGY-TUNED DECISION BEHAVIOR ALGORITHMS FOR TACTICS EXPLORATION

In 2016, the USAF found that current development and acquisition methods may be inadequate to achieve air superiority in 2030. The airspace is expected to be highly contested by 2030 due to the Anti-Access/Area Denial strategies being employed by adversaries. Capability gaps must be addressed in order to maintain air superiority. The USAF identified new development and acquisition paradigms as the number one non-material capability development area. The idea of a new development and acquisition paradigm is not new. Such a paradigm shift occurred during the transition from threat-based acquisition during the cold war to capability-based acquisition during the war on terror. Investigation into current US development and acquisition methods found several notional methodologies. Effectiveness-Based Design and Technology Identification, Evaluation, and Selection for Systems-of-Systems have been proposed as notional solutions. Both methodologies seek to evaluate the means – the technologies used to perform a mission – and the ways – the tactics used to complete a mission – of the technology design space. Proper evaluation of the ways would provide critical information to the decision-maker during technology selection. These findings suggest that a new paradigm focused on effectiveness-based acquisition is needed to improve current development and acquisition methods. To evaluate the ways design space, current methods must move away from a fixed or constrained mission model to one that is minimally defined and capable of exploring tactics for each unique technology. The proposed Technology-tuned Decision Behavior Algorithms for Tactics Exploration (Tech-DEBATE) methodology enables the exploration of the ways, or more formally, the mission action design space. The methodology enables further exploration of the technology design space by improving the quantification of mission effectiveness through deep reinforcement learning in a minimally defined mission environment. The data's foundation is based on traceable tactical alternatives that increase the confidence in the measures of effectiveness for each technology-tactic alternative. The methodology enables more informed decisions for technology investment, thereby reducing risks in the development and acquisition of new technologies. The reduction in risk inherently reduces the costs and development time associated with investment in new technologies. The Tech-DEBATE methodology provides a new methodology for technology evaluation through its emphasis on quantifying mission effectiveness in a minimally defined mission to inform technology investment decisions.Ph.D

Sequential decision making in artificial musical intelligence

Over the past 60 years, artificial intelligence has grown from a largely academic field of research to a ubiquitous array of tools and approaches used in everyday technology. Despite its many recent successes and growing prevalence, certain meaningful facets of computational intelligence have not been as thoroughly explored. Such additional facets cover a wide array of complex mental tasks which humans carry out easily, yet are difficult for computers to mimic. A prime example of a domain in which human intelligence thrives, but machine understanding is still fairly limited, is music. Over the last decade, many researchers have applied computational tools to carry out tasks such as genre identification, music summarization, music database querying, and melodic segmentation. While these are all useful algorithmic solutions, we are still a long way from constructing complete music agents, able to mimic (at least partially) the complexity with which humans approach music. One key aspect which hasn't been sufficiently studied is that of sequential decision making in musical intelligence. This thesis strives to answer the following question: Can a sequential decision making perspective guide us in the creation of better music agents, and social agents in general? And if so, how? More specifically, this thesis focuses on two aspects of musical intelligence: music recommendation and human-agent (and more generally agent-agent) interaction in the context of music. The key contributions of this thesis are the design of better music playlist recommendation algorithms; the design of algorithms for tracking user preferences over time; new approaches for modeling people's behavior in situations that involve music; and the design of agents capable of meaningful interaction with humans and other agents in a setting where music plays a roll (either directly or indirectly). Though motivated primarily by music-related tasks, and focusing largely on people's musical preferences, this thesis also establishes that insights from music-specific case studies can also be applicable in other concrete social domains, such as different types of content recommendation. Showing the generality of insights from musical data in other contexts serves as evidence for the utility of music domains as testbeds for the development of general artificial intelligence techniques. Ultimately, this thesis demonstrates the overall usefulness of taking a sequential decision making approach in settings previously unexplored from this perspectiveComputer Science

A Methodological Framework for Parametric Combat Analysis

This work presents a taxonomic structure for understanding the tension between certain factors of stability for game-theoretic outcomes such as Nash optimality, Pareto optimality, and balance optimality and then applies such game-theoretic concepts to the advancement of strategic thought on spacepower. This work successfully adapts and applies combat modeling theory to the evaluation of cislunar space conflict. This work provides evidence that the reliability characteristics of small spacecraft share similarities to the reliability characteristics of large spacecraft. Using these novel foundational concepts, this dissertation develops and presents a parametric methodological framework capable of analyzing the efficacy of heterogeneous force compositions in the context of space warfare. This framework is shown to be capable of predicting a stochastic distribution of numerical outcomes associated with various modes of conflict and parameter values. Furthermore, this work demonstrates a general alignment in results between the game-theoretic concepts of the framework and Media Interaction Warfare Theory in terms of evaluating force efficacy, providing strong evidence for the validity of the methodological framework presented in this dissertation