The goal of Optimal Transport (OT) is to define geometric tools that are useful to compare probability distributions. Their use dates back to 1781. Recent years have witnessed a new revolution in the spread of OT, thanks to the emergence of approximate solvers that can scale to sizes and dimensions that are relevant to data sciences. Thanks to this newfound scalability, OT is being increasingly used to unlock various problems in imaging sciences (such as color or texture processing), computer vision and graphics (for shape manipulation) or machine learning (for regression, classification and density fitting). This monograph reviews OT with a bias toward numerical methods and their applications in data sciences, and sheds lights on the theoretical properties of OT that make it particularly useful for some of these applications. Computational Optimal Transport presents an overview of the main theoretical insights that support the practical effectiveness of OT before explaining how to turn these insights into fast computational schemes. Written for readers at all levels, the authors provide descriptions of foundational theory at two-levels. Generally accessible to all readers, more advanced readers can read the specially identified more general mathematical expositions of optimal transport tailored for discrete measures. Furthermore, several chapters deal with the interplay between continuous and discrete measures, and are thus targeting a more mathematically-inclined audience. This monograph will be a valuable reference for researchers and students wishing to get a thorough understanding of Computational Optimal Transport, a mathematical gem at the interface of probability, analysis and optimization.

Sequential decision problems arise in virtually every human process. They span finance, energy, transportation, health, e-commerce, and supply chains and include pure learning problems that arise in laboratory or field experiments. They even cover search algorithms to maximize uncertain functions. An important dimension of every problem setting is the need to make decisions in the presence of different forms of uncertainty and evolving information processes.

Warren B. Powell's work in sequential decision problems started in the 1980s and spanned rail, energy, health, finance, e-commerce, supply chain management, and even learning for materials science. His work on a wide range of problems highlighted the importance of using a variety of methods. In the process, he came to realize that any sequential decision problem can be modeled using a single universal framework that involves searching over methods for making decisions.

The goal of this book is to enable readers to understand how to approach, model and solve a sequential decision problem. To that end, it uses a teach-by-example style to illustrate a modeling framework that can represent any sequential decision problem. It tackles the challenge of designing methods, called policies, for making decisions and describes four classes of policies that are universal in that they span any method that might be used; whether from the academic literature or heuristics used in practice. While this does not mean that every problem can be solved immediately, the framework helps avoid the tendency in the academic literature of focusing on narrow classes of methods.

This monograph is about verifiable computing (VC). VC refers to cryptographic protocols called interactive proofs (IPs) and arguments that enable a prover to provide a guarantee to a verifier that the prover performed a requested computation correctly. This monograph covers different notions of mathematical proofs and their applications in computer science and cryptography. Informally, what we mean by a proof is anything that convinces someone that a statement is true, and a proof system is any procedure that decides what is and is not a convincing proof. Introduced in the 1980s, IPs and arguments represented a major conceptual expansion of what constitutes a proof that a statement is true. Traditionally, a proof is a static object that can be easily checked step-by-step for correctness. In contrast, IPs allow for interaction between prover and verifier, as well as a tiny but nonzero probability that an invalid proof passes verification. Arguments (but not IPs) even permit there to be proofs of false statements, so long as those proofs require exorbitant computational power to find. To an extent, these notions mimic in-person interactions that mathematicians use to convince each other that a claim is true, without going through the painstaking process of writing out and checking a traditional static proof. Celebrated theoretical results from the 1980s and 1990s, such as IP = PSPACE and MIP = NEXP showed that, in principle, surprisingly complicated statements can be verified efficiently. What is more, any argument can in principle be transformed into one that is zero-knowledge, which means that proofs reveal no information other than their own validity. Zero-knowledge arguments have a myriad of applications in cryptography. Within the last decade, general-purpose zero-knowledge arguments have made the jump from theory to practice. This has opened new doors in the design of cryptographic systems, and generated additional insights into the power of IPs and arguments (zero-knowledge or otherwise). There are now no fewer than five promising approaches to designing efficient, general-purpose zero-knowledge arguments. This monograph covers these approaches in a unified manner, emphasizing commonalities between them.

B-tree indexes have been ubiquitous in databases for decades. Their contribution to efficient database query processing can hardly be overstated. B-tree indexes have been used in a wide variety of computing systems from handheld devices to mainframes and server farms. Over the years, many techniques have been added to the basic design in order to improve efficiency or to add functionality. Examples include separation of updates to structure or contents, utility operations such as non-logged yet transactional index creation, and robust query processing such as graceful degradation during index-to-index navigation. An earlier survey of modern b-tree techniques, published in 2011, has been widely used for education and reference. Unfortunately, it omits some of the techniques known then and of course those invented since. This monograph is intended to complement the earlier survey and to bring the combined contents more up-to-date. This monograph adds new techniques for tree structures and a few new techniques in query processing, and log-structured merge-forests and stepped-merge forests are now covered. Lastly, concurrency control and in-memory b-trees, from thread-private via shared-but-transient to persistent are also dealt with in this updated work.

In today's fast-paced retail world, consumers face an overwhelming array of product choices, and retailers are constantly seeking new ways to steer their purchasing decisions. Behavioral Retail Operations: Tactics to Win Customers delves into the intricate relationship between consumer psychology and strategic retail tactics. Drawing on decades of research, the authors explore how factors such as pricing, promotions, and store layout influence shopper behavior in both physical and online settings. From understanding the subtle psychological effects of price framing to uncovering how sensory elements like music and color shape the shopping experience, this monograph provides a comprehensive look at the tools retailers use to maximize profitability. Offering a deep dive into the art of influencing consumer behavior, this monograph is essential for both researchers and practitioners aiming to bridge the gap between theory and real-world retail strategy.

The best way to learn math is by problem solving, but the challenge is that most elementary students don't know how to start thinking about a math problem that they haven't seen before. This book is especially designed to overcome this challenge by teaching seven basic problem solving strategies. The book contains more than 100 challenging problems that are suitable for elementary-school students, along with their step-by-step solution to help the reader master these strategies.

This book will help you:
- Learn seven useful problem solving strategies that can be used in many challenging math problems.
- Ace your math tests in school, even the challenge problems that your teacher gives
- Get prepared for various math contests and education programs for gifted students, such as the GATE and Math Kangaroo.
- Become an independent learner via the step-by-step instructions of this book.
- Stay ahead of the curriculum when transitioning into higher grades and the middle school.
- Become a creative thinker who can succeed in STEM fields.
- Turn into a life-long math enthusiast who enjoys thinking and problem solving.

This monograph presents the main complexity theorems in convex optimization and their corresponding algorithms. It begins with the fundamental theory of black-box optimization and proceeds to guide the reader through recent advances in structural optimization and stochastic optimization. The presentation of black-box optimization, strongly influenced by the seminal book by Nesterov, includes the analysis of cutting plane methods, as well as (accelerated) gradient descent schemes. Special attention is also given to non-Euclidean settings (relevant algorithms include Frank-Wolfe, mirror descent, and dual averaging), and discussing their relevance in machine learning. The text provides a gentle introduction to structural optimization with FISTA (to optimize a sum of a smooth and a simple non-smooth term), saddle-point mirror prox (Nemirovski's alternative to Nesterov's smoothing), and a concise description of interior point methods. In stochastic optimization it discusses stochastic gradient descent, mini-batches, random coordinate descent, and sublinear algorithms. It also briefly touches upon convex relaxation of combinatorial problems and the use of randomness to round solutions, as well as random walks based methods.

The performance of a query crucially depends on the ability of the query optimizer to choose a good execution plan from a large space of alternatives. With the discovery of algebraic transformation rules and the emergence of new application-specific contexts, extensibility has become a key requirement for query optimizers. This monograph describes extensible query optimizers in detail, focusing on the Volcano/Cascades framework used by several database systems including Microsoft SQL Server.

The authors explain the need for extensible query optimizer architectures and how the optimizer navigates the search space efficiently. Several important transformations that are commonly used in practice are then discussed. The cost estimation is described as an essential component that the optimizer relies upon to quantitatively compare alternative plans in the search space. The authors also discuss how database systems manage plans over their lifetime as data and workloads change. The monograph concludes with a few open challenges.

Financial Machine Learning surveys the nascent literature on machine learning in the study of financial markets. The authors highlight the best examples of what this line of research has to offer and recommend promising directions for future research. This survey is designed for both financial economists interested in grasping machine learning tools, as well as for statisticians and machine learners seeking interesting financial contexts where advanced methods may be deployed. This survey is organized as follows. Section 2 analyzes the theoretical benefits of highly parameterized machine learning models in financial economics. Section 3 surveys the variety of machine learning methods employed in the empirical analysis of asset return predictability. Section 4 focuses on machine learning analyses of factor pricing models and the resulting empirical conclusions for risk-return tradeoffs. Section 5 presents the role of machine learning in identifying optimal portfolios and stochastic discount factors. Section 6 offers brief conclusions and directions for future work.

Causality has the potential to truly transform the way we solve a large number of real-world problems. Yet, so far, its potential largely remains to be unlocked as causality often requires crucial assumptions which cannot be tested in practice. This monograph, entitled Causal Deep Learning (CDL), presents a new way of looking at causality. The causal deep learning framework in this monograph spans three dimensions: (1) a structural dimension, which incorporates partial yet testable causal knowledge rather than assuming either complete or no causal knowledge among the variables of interest; (2) a parametric dimension, which encompasses parametric forms that capture the type of relationships among the variables of interest; and (3) a temporal dimension, which captures exposure times or how the variables of interest interact (possibly causally) over time. The CDL framework used enables precise categorisation and comparison of causal statistical learning methods. This categorisation is used to provide a comprehensive review of the CDL field. More importantly, CDL enables progress on a variety of real-world problems by aiding partial causal knowledge (including independencies among variables) and quantitatively characterising causal relationships among variables of interest (possibly over time). The framework used clearly identifies which assumptions are testable and which are not, so the resulting solutions can be judiciously adopted in practice. This formulation helps to combine or chain causal representations to solve specific problems without losing track of which assumptions are required to build these solutions, pushing real-world impact in healthcare, economics and business, environmental sciences and education, through causal deep learning.

Factor Graphs for Robot Perception reviews the use of factor graphs for the modeling and solving of large-scale inference problems in robotics. Factor graphs are a family of probabilistic graphical models, other examples of which are Bayesian networks and Markov random fields, well known from the statistical modeling and machine learning literature. They provide a powerful abstraction that gives insight into particular inference problems, making it easier to think about and design solutions, and write modular software to perform the actual inference. This book illustrates their use in the simultaneous localization and mapping problem and other important problems associated with deploying robots in the real world. Factor graphs are introduced as an economical representation within which to formulate the different inference problems, setting the stage for the subsequent sections on practical methods to solve them. The book explains the nonlinear optimization techniques for solving arbitrary nonlinear factor graphs, which requires repeatedly solving large sparse linear systems. Factor Graphs for Robot Perception will be of interest to students, researchers and practicing roboticists with an interest in the broad impact factor graphs have had, and continue to have, in robot perception.

Since its introduction by Andrew Yao in the 1980s, multi-party computation has developed from a theoretical curiosity to an important tool for building large-scale privacy-preserving applications. Secure multi-party computation (MPC) enables a group to jointly perform a computation without disclosing any participant's private inputs. The participants agree on a function to compute, and then can use an MPC protocol to jointly compute the output of that function on their secret inputs without revealing them. This monograph provides an introduction to multi-party computation for practitioners interested in building privacy-preserving applications and researchers who want to work in the area. The authors introduce the foundations of MPC and describe the current state of the art. The goal is to enable readers to understand what is possible today, and what may be possible in the future. It provides a starting point for building applications using MPC and for developing MPC protocols, implementations, tools, and applications. Those seeking a concise, accessible introduction to the topic which quickly enables them to build practical systems or conduct further research will find this essential reading.

Alphanomics: The Informational Underpinnings of Market Efficiency is intended to be a compact introduction to academic research on market efficiency, behavioral finance, and fundamental analysis and is dedicated to the kind of decision-driven and prospectively-focused research that is much needed in a market constantly seeking to become more efficient. The authors refer to this type of research as Alphanomics, the informational economics behind market efficiency. Alpha refers to the abnormal returns, which provide the incentive for some subpopulation of investors to engage in information acquisition and costly arbitrage activities. Nomics refers to the economics of alpha extraction, which encompasses the costs and incentives of informational arbitrage as a sustainable business proposition. Some of the questions that are addressed include: why do we believe markets are efficient?; what problems have this belief engendered?; what factors can impede and/or facilitate market efficiency?; what roles do investor sentiment and costly arbitrage play in determining an equilibrium level of informational efficiency?; what is the essence of value investing?; how is it related to fundamental analysis (the study of historical financial data)?; and how might we distinguish between risk and mispricing based explanations for predictability patterns in returns? The first two sections review the evolution of academic thinking on market efficiency and introduce the noise trader model as a rational alternative. Section 3 surveys the literature on investor sentiment and its role as a source of both risks and returns. Section 4 discusses the role of fundamental analysis in value investing. Section 5 reviews the literature on limits to arbitrage, and section 6 discusses research methodology issues associated with the need to distinguish mispricing from risk.

Spin glass models were introduced by physicists in the 1970s to model the statistical properties of certain magnetic materials. Over the last half century, these models have motivated a blossoming line of mathematical work with applications to multiple fields, at first sight distant from physics. This tutorial is deliberately written in a somewhat non-standard style, from several viewpoints. Rather than developing the theory in the most general setting, the authors focus on two concrete problems that are motivated by questions in statistical estimation. Their treatment is far from exhaustive, but they do not hesitate to pursue detours that are interesting, but indirectly related to the original questions posed by the examples. The authors also present a mixture of non-rigorous and rigorous techniques. The authors clearly indicate when something is proven and explain non-rigorous techniques on examples for which rigorous alternatives are available. Written by two recognized experts and based on a course given at Stanford University, this tutorial is a unique introduction to a topic that has many avenues for furthering research in statistics, mathematics, and computer science. It provides an accessible tutorial to understand and use the theories being deployed in physics for over 50 years.

Austrian Economics and Entrepreneurship surveys the rich history of entrepreneurship research within and inspired by the Austrian school of economics. Unlike most schools of the past 150 years or so, the Austrian tradition places entrepreneurship at the heart of economic theory and practice. Understanding the entrepreneurial function in society is vital for explaining the real-world market process, but also for a proper understanding of the fundamental concepts and theories of economics. These include action, choice, exchange, prices, supply and demand, money, capital, competition, economic development, and business cycles, to name only a few. This monograph surveys the development of Austrian theories of entrepreneurship, examining the contributions of leading members of the tradition in addition to those of some lesser-known writers and scholars. The authors explore some ways in which Austrian work contributes to modern entrepreneurship research, especially through the Judgment-Based Approach. The monograph concludes with a discussion of the professional roles now played by Austrians in the contemporary entrepreneurship discipline.

In this comprehensive survey of unconditional pseudorandom generators (PRGs), the authors present the reader with an intuitive introduction to some of the most important frameworks and techniques for constructing unconditional PRGs for restricted models of computation. The authors discuss four major paradigms for designing PRGs: several PRGs based on k-wise uniform generators, small-bias generators, and simple combinations thereof, several PRGs based on recycling random bits to take advantage of communication Bottlenecks, connections between PRGs and computational hardness, and PRG frameworks based on random restrictions. The authors explain how to use these paradigms to construct PRGs that work unconditionally, with no unproven mathematical assumptions. The PRG constructions use ingredients such as finite field arithmetic, expander graphs, and randomness extractors. The analyses use techniques such as Fourier analysis, sandwiching approximators, and simplification-under-restrictions lemmas. Paradigms for Unconditional Pseudorandom Generators offers the reader a grounding in an important topic widely used in theoretical computer science and cryptography.

Visualization recommendation systems help data analysts navigate large, complex datasets by generating visualizations of meaningful patterns, outliers, and insights that could influence downstream decision-making. However, recommendations can easily mislead or confuse analysts when they are not developed with care. This monograph reviews how visualization recommendation systems have been designed over the last 25 years, and classifies them by their underlying recommendation goals and high-level implementation strategies, including the user interfaces provided for navigating and interpreting the recommended visualizations. To understand their efficacy, this work also reviews how visualization recommendation systems are evaluated in the literature. Given these observations, several open challenges and promising directions for future work in designing effective visualization recommendation systems are presented.

The astonishing growth of generative tools in recent years has empowered many exciting applications in text-to-image generation and text-to-video generation. The underlying principle behind these generative tools is the concept of diffusion, a particular sampling mechanism that has overcome some shortcomings that were deemed difficult in the previous approaches. The goal of this monograph is to discuss the essential ideas underlying the diffusion models. The target audience includes undergraduate and graduate students who are interested in doing research on diffusion models or applying these models to solve other problems.

Accounting for Risk is about using accounting information to assess risk and the required return for bearing that risk. The focus is on investing in firms and the equity claims on firms: How much should an investor discount the price of a share in a firm for risk, and how can accounting information help to answer that question? That discount is variously called the required return, the expected return, or the cost of capital.

The monograph links two strands of research - the first is accounting-based valuation research where value is assessed from expected cash flows, earnings, or residual earnings. The focus has been on forecasting those payoffs however forecasting payoffs is only one part of valuation. The other issue is how those expected payoffs should be discounted for risk. This monograph engages the question whether accounting information aid in the determination of risk and the discount rate? The second strand of research is asset pricing. While asset pricing might suggest this research is involved in determining prices, it is actually in pursuit of the required return to investing - the risk discount to price. Can accounting information about risk and return be utilized in building operational pricing models?

Accounting for Risk also enhances financial statement analysis. While traditional financial statement analysis-ratio analysis-was conducted without much reference to finance theory, modern financial statement analysis derives from accounting-based valuation models that are based on the no-arbitrage theory on the pricing of expected dividends. That brings accounting and finance closer together. The key is an understanding of the accounting principles underlying the recognition and measurement in the financial statements. This requires an appreciation of how accounting handles risk, thereby generating accounting numbers that convey information about risk and expected return.

Lattice-based cryptography is the use of conjectured hard problems on point lattices in Rn as the foundation for secure cryptographic systems. Attractive features of lattice cryptography include apparent resistance to quantum attacks (in contrast with most number-theoretic cryptography), high asymptotic efficiency and parallelism, security under worst-case intractability assumptions, and solutions to long-standing open problems in cryptography. This monograph surveys most of the major developments in lattice cryptography over the past ten years. The main focus is on the foundational short integer solution (SIS) and learning with errors (LWE) problems (and their more efficient ring-based variants), their provable hardness assuming the worst-case intractability of standard lattice problems, and their many cryptographic applications.