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Poisson Line Cox Process

Author : Harpreet S. Dhillon,Vishnu Vardhan Chetlur
Publisher : Morgan & Claypool Publishers
Release : 2020-06-24
Category : Computers
ISBN : 9781681738437

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Book Poisson Line Cox Process Description/Summary:

This book provides a comprehensive treatment of the Poisson line Cox process (PLCP) and its applications to vehicular networks. The PLCP is constructed by placing points on each line of a Poisson line process (PLP) as per an independent Poisson point process (PPP). For vehicular applications, one can imagine the layout of the road network as a PLP and the vehicles on the roads as the points of the PLCP. First, a brief historical account of the evolution of the theory of PLP is provided to familiarize readers with the seminal contributions in this area. In order to provide a self-contained treatment of this topic, the construction and key fundamental properties of both PLP and PLCP are discussed in detail. The rest of the book is devoted to the applications of these models to a variety of wireless networks, including vehicular communication networks and localization networks. Specifically, modeling the locations of vehicular nodes and roadside units (RSUs) using PLCP, the signal-to-interference-plus-noise ratio (SINR)-based coverage analysis is presented for both ad hoc and cellular network models. For a similar setting, the load on the cellular macro base stations (MBSs) and RSUs in a vehicular network is also characterized analytically. For the localization networks, PLP is used to model blockages, which is shown to facilitate the characterization of asymptotic blind spot probability in a localization application. Finally, the path distance characteristics for a special case of PLCP are analyzed, which can be leveraged to answer critical questions in the areas of transportation networks and urban planning. The book is concluded with concrete suggestions on future directions of research. Based largely on the original research of the authors, this is the first book that specifically focuses on the self-contained mathematical treatment of the PLCP. The ideal audience of this book is graduate students as well as researchers in academia and industry who are familiar with probability theory, have some exposure to point processes, and are interested in the field of stochastic geometry and vehicular networks. Given the diverse backgrounds of the potential readers, the focus has been on providing an accessible and pedagogical treatment of this topic by consciously avoiding the measure theoretic details without compromising mathematical rigor.

Poisson Line Cox Process

Author : Harpreet S. Dhillon,Vishnu Vardhan Chetlur
Publisher : Springer Nature
Release : 2022-06-01
Category : Computers
ISBN : 9783031023798

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Book Poisson Line Cox Process Description/Summary:

This book provides a comprehensive treatment of the Poisson line Cox process (PLCP) and its applications to vehicular networks. The PLCP is constructed by placing points on each line of a Poisson line process (PLP) as per an independent Poisson point process (PPP). For vehicular applications, one can imagine the layout of the road network as a PLP and the vehicles on the roads as the points of the PLCP. First, a brief historical account of the evolution of the theory of PLP is provided to familiarize readers with the seminal contributions in this area. In order to provide a self-contained treatment of this topic, the construction and key fundamental properties of both PLP and PLCP are discussed in detail. The rest of the book is devoted to the applications of these models to a variety of wireless networks, including vehicular communication networks and localization networks. Specifically, modeling the locations of vehicular nodes and roadside units (RSUs) using PLCP, the signal-to-interference-plus-noise ratio (SINR)-based coverage analysis is presented for both ad hoc and cellular network models. For a similar setting, the load on the cellular macro base stations (MBSs) and RSUs in a vehicular network is also characterized analytically. For the localization networks, PLP is used to model blockages, which is shown to facilitate the characterization of asymptotic blind spot probability in a localization application. Finally, the path distance characteristics for a special case of PLCP are analyzed, which can be leveraged to answer critical questions in the areas of transportation networks and urban planning. The book is concluded with concrete suggestions on future directions of research. Based largely on the original research of the authors, this is the first book that specifically focuses on the self-contained mathematical treatment of the PLCP. The ideal audience of this book is graduate students as well as researchers in academia and industry who are familiar with probability theory, have some exposure to point processes, and are interested in the field of stochastic geometry and vehicular networks. Given the diverse backgrounds of the potential readers, the focus has been on providing an accessible and pedagogical treatment of this topic by consciously avoiding the measure theoretic details without compromising mathematical rigor.

Lectures on the Poisson Process

Author : Günter Last,Mathew Penrose
Publisher : Cambridge University Press
Release : 2017-10-26
Category : Mathematics
ISBN : 9781107088016

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Book Lectures on the Poisson Process Description/Summary:

A modern introduction to the Poisson process, with general point processes and random measures, and applications to stochastic geometry.

Poisson Line Cox Process

Author : Harpreet S Dhillon,Vishnu Vardhan Chetlur
Publisher : Unknown
Release : 2020-06-24
Category : Uncategorized
ISBN : 1681738449

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Book Poisson Line Cox Process Description/Summary:

This book provides a comprehensive treatment of the Poisson line Cox process (PLCP) and its applications to vehicular networks. The PLCP is constructed by placing points on each line of a Poisson line process (PLP) as per an independent Poisson point process (PPP). For vehicular applications, one can imagine the layout of the road network as a PLP and the vehicles on the roads as the points of the PLCP. First, a brief historical account of the evolution of the theory of PLP is provided to familiarize readers with the seminal contributions in this area. In order to provide a self-contained treatment of this topic, the construction and key fundamental properties of both PLP and PLCP are discussed in detail. The rest of the book is devoted to the applications of these models to a variety of wireless networks, including vehicular communication networks and localization networks. Specifically, modeling the locations of vehicular nodes and roadside units (RSUs) using PLCP, the signal-to-interference-plus-noise ratio (SINR)-based coverage analysis is presented for both ad hoc and cellular network models. For a similar setting, the load on the cellular macro base stations (MBSs) and RSUs in a vehicular network is also characterized analytically. For the localization networks, PLP is used to model blockages, which is shown to facilitate the characterization of asymptotic blind spot probability in a localization application. Finally, the path distance characteristics for a special case of PLCP are analyzed, which can be leveraged to answer critical questions in the areas of transportation networks and urban planning. The book is concluded with concrete suggestions on future directions of research. Based largely on the original research of the authors, this is the first book that specifically focuses on the self-contained mathematical treatment of the PLCP. The ideal audience of this book is graduate students as well as researchers in academia and industry who are familiar with probability theory, have some exposure to point processes, and are interested in the field of stochastic geometry and vehicular networks. Given the diverse backgrounds of the potential readers, the focus has been on providing an accessible and pedagogical treatment of this topic by consciously avoiding the measure theoretic details without compromising mathematical rigor.

Stochastic Geometry and Its Applications

Author : Sung Nok Chiu,Dietrich Stoyan,Wilfrid S. Kendall,Joseph Mecke
Publisher : John Wiley & Sons
Release : 2013-06-27
Category : Mathematics
ISBN : 9781118658253

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Book Stochastic Geometry and Its Applications Description/Summary:

An extensive update to a classic text Stochastic geometry and spatial statistics play a fundamental role in many modern branches of physics, materials sciences, engineering, biology and environmental sciences. They offer successful models for the description of random two- and three-dimensional micro and macro structures and statistical methods for their analysis. The previous edition of this book has served as the key reference in its field for over 18 years and is regarded as the best treatment of the subject of stochastic geometry, both as a subject with vital applications to spatial statistics and as a very interesting field of mathematics in its own right. This edition: Presents a wealth of models for spatial patterns and related statistical methods. Provides a great survey of the modern theory of random tessellations, including many new models that became tractable only in the last few years. Includes new sections on random networks and random graphs to review the recent ever growing interest in these areas. Provides an excellent introduction to theory and modelling of point processes, which covers some very latest developments. Illustrate the forefront theory of random sets, with many applications. Adds new results to the discussion of fibre and surface processes. Offers an updated collection of useful stereological methods. Includes 700 new references. Is written in an accessible style enabling non-mathematicians to benefit from this book. Provides a companion website hosting information on recent developments in the field www.wiley.com/go/cskm Stochastic Geometry and its Applications is ideally suited for researchers in physics, materials science, biology and ecological sciences as well as mathematicians and statisticians. It should also serve as a valuable introduction to the subject for students of mathematics and statistics.

Poisson Processes

Author : J. F. C. Kingman
Publisher : Clarendon Press
Release : 1992-12-17
Category : Mathematics
ISBN : 9780191591242

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Book Poisson Processes Description/Summary:

In the theory of random processes there are two that are fundamental, and occur over and over again, often in surprising ways. There is a real sense in which the deepest results are concerned with their interplay. One, the Bachelier Wiener model of Brownian motion, has been the subject of many books. The other, the Poisson process, seems at first sight humbler and less worthy of study in its own right. Nearly every book mentions it, but most hurry past to more general point processes or Markov chains. This comparative neglect is ill judged, and stems from a lack of perception of the real importance of the Poisson process. This distortion partly comes about from a restriction to one dimension, while the theory becomes more natural in more general context. This book attempts to redress the balance. It records Kingman's fascination with the beauty and wide applicability of Poisson processes in one or more dimensions. The mathematical theory is powerful, and a few key results often produce surprising consequences.

Spatial Point Patterns

Author : Adrian Baddeley,Ege Rubak,Rolf Turner
Publisher : CRC Press
Release : 2015-11-11
Category : Mathematics
ISBN : 9781482210217

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Book Spatial Point Patterns Description/Summary:

Modern Statistical Methodology and Software for Analyzing Spatial Point PatternsSpatial Point Patterns: Methodology and Applications with R shows scientific researchers and applied statisticians from a wide range of fields how to analyze their spatial point pattern data. Making the techniques accessible to non-mathematicians, the authors draw on th

Point Processes

Author : D.R. Cox,Valerie Isham
Publisher : Routledge
Release : 2018-12-19
Category : Mathematics
ISBN : 9781351423861

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Book Point Processes Description/Summary:

There has been much recent research on the theory of point processes, i.e., on random systems consisting of point events occurring in space or time. Applications range from emissions from a radioactive source, occurrences of accidents or machine breakdowns, or of electrical impluses along nerve fibres, to repetitive point events in an individual's medical or social history. Sometimes the point events occur in space rather than time and the application here raneg from statistical physics to geography. The object of this book is to develop the applied mathemathics of point processes at a level which will make the ideas accessible both to the research worker and the postgraduate student in probability and statistics and also to the mathemathically inclined individual in another field interested in using ideas and results. A thorough knowledge of the key notions of elementary probability theory is required to understand the book, but specialised "pure mathematical" coniderations have been avoided.

Stochastic Geometry

Author : David Coupier
Publisher : Springer
Release : 2019-04-09
Category : Mathematics
ISBN : 9783030135478

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Book Stochastic Geometry Description/Summary:

This volume offers a unique and accessible overview of the most active fields in Stochastic Geometry, up to the frontiers of recent research. Since 2014, the yearly meeting of the French research structure GDR GeoSto has been preceded by two introductory courses. This book contains five of these introductory lectures. The first chapter is a historically motivated introduction to Stochastic Geometry which relates four classical problems (the Buffon needle problem, the Bertrand paradox, the Sylvester four-point problem and the bicycle wheel problem) to current topics. The remaining chapters give an application motivated introduction to contemporary Stochastic Geometry, each one devoted to a particular branch of the subject: understanding spatial point patterns through intensity and conditional intensities; stochastic methods for image analysis; random fields and scale invariance; and the theory of Gibbs point processes. Exposing readers to a rich theory, this book will encourage further exploration of the subject and its wide applications.

An Introduction to the Theory of Point Processes

Author : D.J. Daley,David Vere-Jones
Publisher : Springer Science & Business Media
Release : 2007-11-12
Category : Mathematics
ISBN : 9780387213378

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Book An Introduction to the Theory of Point Processes Description/Summary:

This is the second volume of the reworked second edition of a key work on Point Process Theory. Fully revised and updated by the authors who have reworked their 1988 first edition, it brings together the basic theory of random measures and point processes in a unified setting and continues with the more theoretical topics of the first edition: limit theorems, ergodic theory, Palm theory, and evolutionary behaviour via martingales and conditional intensity. The very substantial new material in this second volume includes expanded discussions of marked point processes, convergence to equilibrium, and the structure of spatial point processes.

Stochastic Geometry, Spatial Statistics and Random Fields

Author : Evgeny Spodarev
Publisher : Springer
Release : 2013-02-11
Category : Mathematics
ISBN : 9783642333057

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Book Stochastic Geometry, Spatial Statistics and Random Fields Description/Summary:

This volume provides a modern introduction to stochastic geometry, random fields and spatial statistics at a (post)graduate level. It is focused on asymptotic methods in geometric probability including weak and strong limit theorems for random spatial structures (point processes, sets, graphs, fields) with applications to statistics. Written as a contributed volume of lecture notes, it will be useful not only for students but also for lecturers and researchers interested in geometric probability and related subjects.

Point Process Calculus in Time and Space

Author : Pierre Brémaud
Publisher : Springer
Release : 2020-12-06
Category : Mathematics
ISBN : 3030627527

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Book Point Process Calculus in Time and Space Description/Summary:

This book provides an introduction to the theory and applications of point processes, both in time and in space. Presenting the two components of point process calculus, the martingale calculus and the Palm calculus, it aims to develop the computational skills needed for the study of stochastic models involving point processes, providing enough of the general theory for the reader to reach a technical level sufficient for most applications. Classical and not-so-classical models are examined in detail, including Poisson–Cox, renewal, cluster and branching (Kerstan–Hawkes) point processes.The applications covered in this text (queueing, information theory, stochastic geometry and signal analysis) have been chosen not only for their intrinsic interest but also because they illustrate the theory. Written in a rigorous but not overly abstract style, the book will be accessible to earnest beginners with a basic training in probability but will also interest upper graduate students and experienced researchers.

Advanced Spatial Modeling with Stochastic Partial Differential Equations Using R and INLA

Author : Elias T. Krainski,Virgilio Gómez-Rubio,Haakon Bakka,Amanda Lenzi,Daniela Castro-Camilo,Daniel Simpson,Finn Lindgren,Håvard Rue
Publisher : CRC Press
Release : 2018-12-07
Category : Mathematics
ISBN : 9780429629853

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Book Advanced Spatial Modeling with Stochastic Partial Differential Equations Using R and INLA Description/Summary:

Modeling spatial and spatio-temporal continuous processes is an important and challenging problem in spatial statistics. Advanced Spatial Modeling with Stochastic Partial Differential Equations Using R and INLA describes in detail the stochastic partial differential equations (SPDE) approach for modeling continuous spatial processes with a Matérn covariance, which has been implemented using the integrated nested Laplace approximation (INLA) in the R-INLA package. Key concepts about modeling spatial processes and the SPDE approach are explained with examples using simulated data and real applications. This book has been authored by leading experts in spatial statistics, including the main developers of the INLA and SPDE methodologies and the R-INLA package. It also includes a wide range of applications: * Spatial and spatio-temporal models for continuous outcomes * Analysis of spatial and spatio-temporal point patterns * Coregionalization spatial and spatio-temporal models * Measurement error spatial models * Modeling preferential sampling * Spatial and spatio-temporal models with physical barriers * Survival analysis with spatial effects * Dynamic space-time regression * Spatial and spatio-temporal models for extremes * Hurdle models with spatial effects * Penalized Complexity priors for spatial models All the examples in the book are fully reproducible. Further information about this book, as well as the R code and datasets used, is available from the book website at http://www.r-inla.org/spde-book. The tools described in this book will be useful to researchers in many fields such as biostatistics, spatial statistics, environmental sciences, epidemiology, ecology and others. Graduate and Ph.D. students will also find this book and associated files a valuable resource to learn INLA and the SPDE approach for spatial modeling.

Discrete Stochastic Processes

Author : Robert G. Gallager
Publisher : Springer Science & Business Media
Release : 2012-12-06
Category : Technology & Engineering
ISBN : 9781461523291

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Book Discrete Stochastic Processes Description/Summary:

Stochastic processes are found in probabilistic systems that evolve with time. Discrete stochastic processes change by only integer time steps (for some time scale), or are characterized by discrete occurrences at arbitrary times. Discrete Stochastic Processes helps the reader develop the understanding and intuition necessary to apply stochastic process theory in engineering, science and operations research. The book approaches the subject via many simple examples which build insight into the structure of stochastic processes and the general effect of these phenomena in real systems. The book presents mathematical ideas without recourse to measure theory, using only minimal mathematical analysis. In the proofs and explanations, clarity is favored over formal rigor, and simplicity over generality. Numerous examples are given to show how results fail to hold when all the conditions are not satisfied. Audience: An excellent textbook for a graduate level course in engineering and operations research. Also an invaluable reference for all those requiring a deeper understanding of the subject.

Mathematical Constants II

Author : Steven R. Finch
Publisher : Cambridge University Press
Release : 2018-12-31
Category : Mathematics
ISBN : 9781108470599

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Book Mathematical Constants II Description/Summary:

Famous mathematical constants include the ratio of circular circumference to diameter, π = 3.14 ..., and the natural logarithm base, e = 2.178 .... Students and professionals can often name a few others, but there are many more buried in the literature and awaiting discovery. How do such constants arise, and why are they important? Here the author renews the search he began in his book Mathematical Constants, adding another 133 essays that broaden the landscape. Topics include the minimality of soap film surfaces, prime numbers, elliptic curves and modular forms, Poisson-Voronoi tessellations, random triangles, Brownian motion, uncertainty inequalities, Prandtl-Blasius flow (from fluid dynamics), Lyapunov exponents, knots and tangles, continued fractions, Galton-Watson trees, electrical capacitance (from potential theory), Zermelo's navigation problem, and the optimal control of a pendulum. Unsolved problems appear virtually everywhere as well. This volume continues an outstanding scholarly attempt to bring together all significant mathematical constants in one place.

Stochastic Geometry Analysis of Multi-Antenna Wireless Networks

Author : Xianghao Yu,Chang Li,Jun Zhang,Khaled B. Letaief
Publisher : Springer
Release : 2019-03-27
Category : Computers
ISBN : 9789811358807

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Book Stochastic Geometry Analysis of Multi-Antenna Wireless Networks Description/Summary:

This book presents a unified framework for the tractable analysis of large-scale, multi-antenna wireless networks using stochastic geometry. This mathematical analysis is essential for assessing and understanding the performance of complicated multi-antenna networks, which are one of the foundations of 5G and beyond networks to meet the ever-increasing demands for network capacity. Describing the salient properties of the framework, which makes the analysis of multi-antenna networks comparable to that of their single-antenna counterparts, the book discusses effective design approaches that do not require complex system-level simulations. It also includes various application examples with different multi-antenna network models to illustrate the framework’s effectiveness.

Network Connectivity

Author : Chen Chen,Hanghang Tong
Publisher : Morgan & Claypool Publishers
Release : 2022-01-26
Category : Computers
ISBN : 9781636392967

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Book Network Connectivity Description/Summary:

Networks naturally appear in many high-impact domains, ranging from social network analysis to disease dissemination studies to infrastructure system design. Within network studies, network connectivity plays an important role in a myriad of applications. The diversity of application areas has spurred numerous connectivity measures, each designed for some specific tasks. Depending on the complexity of connectivity measures, the computational cost of calculating the connectivity score can vary significantly. Moreover, the complexity of the connectivity would predominantly affect the hardness of connectivity optimization, which is a fundamental problem for network connectivity studies. This book presents a thorough study in network connectivity, including its concepts, computation, and optimization. Specifically, a unified connectivity measure model will be introduced to unveil the commonality among existing connectivity measures. For the connectivity computation aspect, the authors introduce the connectivity tracking problems and present several effective connectivity inference frameworks under different network settings. Taking the connectivity optimization perspective, the book analyzes the problem theoretically and introduces an approximation framework to effectively optimize the network connectivity.Lastly, the book discusses the new research frontiers and directions to explore for network connectivity studies. This book is an accessible introduction to the study of connectivity in complex networks. It is essential reading for advanced undergraduates, Ph.D. students, as well as researchers and practitioners who are interested in graph mining, data mining, and machine learning.

6G Mobile Wireless Networks

Author : Yulei Wu,Sukhdeep Singh,Tarik Taleb,Abhishek Roy,Harpreet S. Dhillon,Madhan Raj Kanagarathinam,Aloknath De
Publisher : Springer Nature
Release : 2021-08-24
Category : Computers
ISBN : 9783030727772

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Book 6G Mobile Wireless Networks Description/Summary:

This book is the world’s first book on 6G Mobile Wireless Networks that aims to provide a comprehensive understanding of key drivers, use cases, research requirements, challenges and open issues that are expected to drive 6G research. In this book, we have invited world-renowned experts from industry and academia to share their thoughts on different aspects of 6G research. Specifically, this book covers the following topics: 6G Use Cases, Requirements, Metrics and Enabling Technologies, PHY Technologies for 6G Wireless, Reconfigurable Intelligent Surface for 6G Wireless Networks, Millimeter-wave and Terahertz Spectrum for 6G Wireless, Challenges in Transport Layer for Tbit/s Communications, High-capacity Backhaul Connectivity for 6G Wireless, Cloud Native Approach for 6G Wireless Networks, Machine Type Communications in 6G, Edge Intelligence and Pervasive AI in 6G, Blockchain: Foundations and Role in 6G, Role of Open-source Platforms in 6G, and Quantum Computing and 6G Wireless. The overarching aim of this book is to explore the evolution from current 5G networks towards the future 6G networks from a service, air interface and network perspective, thereby laying out a vision for 6G networks. This book not only discusses the potential 6G use cases, requirements, metrics and enabling technologies, but also discusses the emerging technologies and topics such as 6G PHY technologies, reconfigurable intelligent surface, millimeter-wave and THz communications, visible light communications, transport layer for Tbit/s communications, high-capacity backhaul connectivity, cloud native approach, machine-type communications, edge intelligence and pervasive AI, network security and blockchain, and the role of open-source platform in 6G. This book provides a systematic treatment of the state-of-the-art in these emerging topics and their role in supporting a wide variety of verticals in the future. As such, it provides a comprehensive overview of the expected applications of 6G with a detailed discussion of their requirements and possible enabling technologies. This book also outlines the possible challenges and research directions to facilitate the future research and development of 6G mobile wireless networks.

Edge Intelligence in the Making

Author : Sen Lin,Zhi Zhou,Zhaofeng Zhang,Xu Chen,Junshan Zhang
Publisher : Springer Nature
Release : 2022-06-01
Category : Computers
ISBN : 9783031023804

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Book Edge Intelligence in the Making Description/Summary:

With the explosive growth of mobile computing and Internet of Things (IoT) applications, as exemplified by AR/VR, smart city, and video/audio surveillance, billions of mobile and IoT devices are being connected to the Internet, generating zillions of bytes of data at the network edge. Driven by this trend, there is an urgent need to push the frontiers of artificial intelligence (AI) to the network edge to fully unleash the potential of IoT big data. Indeed, the marriage of edge computing and AI has resulted in innovative solutions, namely edge intelligence or edge AI. Nevertheless, research and practice on this emerging inter-disciplinary field is still in its infancy stage. To facilitate the dissemination of the recent advances in edge intelligence in both academia and industry, this book conducts a comprehensive and detailed survey of the recent research efforts and also showcases the authors' own research progress on edge intelligence. Specifically, the book first reviews the background and present motivation for AI running at the network edge. Next, it provides an overview of the overarching architectures, frameworks, and emerging key technologies for deep learning models toward training/inference at the network edge. To illustrate the research problems for edge intelligence, the book also showcases four of the authors' own research projects on edge intelligence, ranging from rigorous theoretical analysis to studies based on realistic implementation. Finally, it discusses the applications, marketplace, and future research opportunities of edge intelligence. This emerging interdisciplinary field offers many open problems and yet also tremendous opportunities, and this book only touches the tip of iceberg. Hopefully, this book will elicit escalating attention, stimulate fruitful discussions, and open new directions on edge intelligence.

Modeling and Optimization in Software-Defined Networks

Author : Konstantinos Poularakis,Leandros Tassiulas,T.V. Lakshman
Publisher : Springer Nature
Release : 2022-06-01
Category : Computers
ISBN : 9783031023828

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Book Modeling and Optimization in Software-Defined Networks Description/Summary:

This book provides a quick reference and insights into modeling and optimization of software-defined networks (SDNs). It covers various algorithms and approaches that have been developed for optimizations related to the control plane, the considerable research related to data plane optimization, and topics that have significant potential for research and advances to the state-of-the-art in SDN. Over the past ten years, network programmability has transitioned from research concepts to more mainstream technology through the advent of technologies amenable to programmability such as service chaining, virtual network functions, and programmability of the data plane. However, the rapid development in SDN technologies has been the key driver behind its evolution. The logically centralized abstraction of network states enabled by SDN facilitates programmability and use of sophisticated optimization and control algorithms for enhancing network performance, policy management, and security.Furthermore, the centralized aggregation of network telemetry facilitates use of data-driven machine learning-based methods. To fully unleash the power of this new SDN paradigm, though, various architectural design, deployment, and operations questions need to be addressed. Associated with these are various modeling, resource allocation, and optimization opportunities.The book covers these opportunities and associated challenges, which represent a ``call to arms'' for the SDN community to develop new modeling and optimization methods that will complement or improve on the current norms.