Topological Complexity of Smooth Random Functions

This book provides an overview of multiple aspects of spatial language understanding and explores recent trends of modeling based on very large foundational models and their applications. The authors address the following five main themes: spatial semantic representations in both symbolic and sub-symbolic spaces; spatial information extraction computational models; reasoning over spatial language; commonsense spatial understanding; and multiple modern and state-of-the-art downstream applications of spatial language understanding including dialogue systems, narrative discourse, and grounding language in the physical world with the multi-modal problem settings. One of the essential functions of natural language is to express spatial relationships between objects. Linguistic constructs can encode highly complex structures of objects, spatial relations between them, and patterns of motion through space relative to a reference point. The complexity of spatial language understanding and its

If you knew your future, would you try to fight fate?Aside from a delay, there will be no problems. The flight will be smooth, it will land safely. Everyone who gets on the plane will get off. But almost all of them will be forever changed.Because on this ordinary, short, domestic flight, something extraordinary happens. People learn how and when they are going to die. For some, their death is far in the future—age 103!—and they laugh. But for six passengers, their predicted deaths are not far away at all.How do they know this? There were ostensibly more interesting people on the flight (the bride and groom, the jittery, possibly famous woman, the giant Hemsworth-esque guy who looks like an off-duty superhero, the frazzled, gorgeous flight attendant) but none would become as famous as “The Death Lady.”Not a single passenger or crew member will later recall noticing her board the plane. She wasn’t exceptionally old or young, rude or polite. She wasn’t drunk or nervous or pregnant. Her a

Rediscover the Puffin Classics collection and bring the best-loved classics to a new generation - including this bold edition of The Adventures of Huckleberry Finn.Huckleberry Finn's childhood wasn't exactly smooth sailing but everything changed when he met Tom Sawyer. Bound by an oath to make trouble, the Gang embark on a daring adventure down the Mississippi river, every turn . . .until they meet Jim.Will the Gang work together to help him?

Embrace your dark side with this officially licensed Nightshade Society notebook featuring humorous, macabre quotes from the hit series Wednesday."I don't do social media. I find it to be a soul-sucking void of meaningless affirmation."--Wednesday AddamsJoin the most gothic Addams family member and the Nightshade Society at Nevermore Academy with this notebook that's perfectly suited for school, work, or home. With smooth writing paper, lined pages, and dark humor from the show, this blank journal will hold your notes, thoughts, sketches, secrets, and more.WEDNESDAY © 2022-2024 MGM.WEDNESDAY is a trademark of Tee & Charles Addams Foundation. © 2024 MGM. ARR. Based on the Characters Created by Charles Addams.

This textbook introduces readers to the fundamental notions of modern probability theory. The only prerequisite is a working knowledge in real analysis. Highlighting the connections between martingales and Markov chains on one hand, and Brownian motion and harmonic functions on the other, this book provides an introduction to the rich interplay between probability and other areas of analysis.Arranged into three parts, the book begins with a rigorous treatment of measure theory, with applications to probability in mind. The second part of the book focuses on the basic concepts of probability theory such as random variables, independence, conditional expectation, and the different types of convergence of random variables. In the third part, in which all chapters can be read independently, the reader will encounter three important classes of stochastic processes: discrete-time martingales, countable state-space Markov chains, and Brownian motion. Each chapter ends with a selection of illu

A young Indian woman finds the false rumors that she killed her husband surprisingly useful―until other women in the village start asking for her help getting rid of their own husbands―in this razor-sharp debut.“Shroff captures the complexity of female friendship with acuity, wit, and a certain kind of magic irreverence…The Bandit Queens is tender, unpredictable, and brimming with laugh-out-loud moments.” –Téa Obreht, New York Times bestselling author of The Tiger’s WifeGeeta’s no-good husband disappeared five years ago. She didn’t kill him, but everyone thinks she did―no matter how much she protests. But she soon discovers that being known as a “self-made” widow has some surprising perks. No one messes with her, no one threatens her, and no one tries to control (ahem, marry) her. It’s even been good for her business; no one wants to risk getting on her bad side by not buying her jewelry. Freedom must look good on Geeta, because other women in the village have started asking for her he

This book provides a series of gesture and behavior recognition methods based on multimodal datarepresentation. The data modalities include image data and skeleton data, and the modeling methods includetraditional codebook, topological graph, and LSTM architectures. The tasks include single gesture recognitionclassification, single action recognition classification, continuous gesture classification, complex behaviorclassification of human interaction and other tasks of different complexity. This book focuses on the dataprocessing methods of each modality, and the modeling methods for different tasks. We hope the reader canlearn basic gesture and action recognition methods from this book, and develop a model system that suits theirneeds on this basis. This book can be used as a textbook for graduate, postgraduate and PhD students majoring in computerscience, automation, etc. It can also be used as a reference for the reader who is interested in gesturerecognition, human action inter

Chunyan Li is a course instructor with many years of experience in teaching about time series analysis. His book is essential for students and researchers in oceanography and other subjects in the Earth sciences, looking for a complete coverage of the theory and practice of time series data analysis using MATLAB. This textbook covers the topic's core theory in depth, and provides numerous instructional examples, many drawn directly from the author's own teaching experience, using data files, examples, and exercises. The book explores many concepts, including time; distance on Earth; wind, current, and wave data formats; finding a subset of ship-based data along planned or random transects; error propagation; Taylor series expansion for error estimates; the least squares method; base functions and linear independence of base functions; tidal harmonic analysis; Fourier series and the generalized Fourier transform; filtering techniques: sampling theorems: finite sampling effects; wavelet

An epic sci-fi graphic novel romance between two non-binary characters as they find one another through time, distance, and war. An amazing story that explores the complexity of human nature and what brings us together. When they were kids, Fassen's fighter spaceship crash-landed on a planet that Lu's survey force was exploring. It was a forbidden meeting between a kid from a war-focused resistance movement and a kid whose community and planet are dedicated to peace and secrecy.Lu and Fassen are from different worlds and separate solar systems. But their friendship keeps them in each other's orbit as they grow up. They stay in contact in secret as their communities are increasingly threatened by the omnipresent, ever-expanding empire.As the empire begins a new attack against Fassen's people--and discovers Lu's in the process--the two of them have the chance to reunite at last. They finally are able to be together...but at what cost? This beautifully illustrated graphic novel is an epic

A multitude of processes in hydrology and environmental engineering are either random or entail random components which are characterized by random variables. These variables are described by frequency distributions. This book provides an overview of different systems of frequency distributions, their properties, and applications to the fields of water resources and environmental engineering. A variety of systems are covered, including the Pearson system, Burr system, and systems commonly applied in economics, such as the D'Addario, Dagum, Stoppa, and Esteban systems. The latter chapters focus on the Singh system and the frequency distributions deduced from Bessel functions, maximum entropy theory, and the transformations of random variables. The final chapter introduces the genetic theory of frequency distributions. Using real-world data, this book provides a valuable reference for researchers, graduate students, and professionals interested in frequency analysis.

Optimization techniques are at the core of data science, including data analysis and machine learning. An understanding of basic optimization techniques and their fundamental properties provides important grounding for students, researchers, and practitioners in these areas. This text covers the fundamentals of optimization algorithms in a compact, self-contained way, focusing on the techniques most relevant to data science. An introductory chapter demonstrates that many standard problems in data science can be formulated as optimization problems. Next, many fundamental methods in optimization are described and analyzed, including: gradient and accelerated gradient methods for unconstrained optimization of smooth (especially convex) functions; the stochastic gradient method, a workhorse algorithm in machine learning; the coordinate descent approach; several key algorithms for constrained optimization problems; algorithms for minimizing nonsmooth functions arising in data science; found

Starting middle school is hard enough when you don’t know anyone; it’s even harder when you’re shy. A contemporary middle-grade graphic novel for fans of Guts and Real Friends about how dealing with anxiety and OCD can affect everyday life.As long as Maggie rolls the right number, nothing can go wrong…right?Maggie just wants to get through her first year of middle school. But between finding the best after-school clubs, trying to make friends, and avoiding the rumored monster on school grounds, she’s having a tough time…so she might need a little help from her twenty-sided dice. But what happens if Maggie rolls the wrong number?A touching middle-grade graphic novel that explores the complexity of anxiety, OCD, and learning to trust yourself and the world around you.“A charming, compassionate story that’s sure to resonate with anyone who’s ever stayed up worrying.” ―Gale Galligan, adaptor and illustrator of the Baby-Sitters Club graphic novel series

Starting middle school is hard enough when you don’t know anyone; it’s even harder when you’re shy. A contemporary middle-grade graphic novel for fans of Guts and Real Friends about how dealing with anxiety and OCD can affect everyday life.As long as Maggie rolls the right number, nothing can go wrong…right? Maggie just wants to get through her first year of middle school. But between finding the best after-school clubs, trying to make friends, and avoiding the rumored monster on school grounds, she’s having a tough time…so she might need a little help from her twenty-sided dice. But what happens if Maggie rolls the wrong number? A touching middle-grade graphic novel that explores the complexity of anxiety, OCD, and learning to trust yourself and the world around you. “A charming, compassionate story that’s sure to resonate with anyone who’s ever stayed up worrying.” —Gale Galligan, adaptor and illustrator of the Baby-Sitters Club graphic novel series

In this gorgeous graphic novel that Entertainment Weekly called "one of the most astounding . . . of the year," fairy tales are the only way one teen boy can express himself to his parents, who are Vietnamese immigrants. But how will he find the words to tell them that he's gay?Tiến and his mother come from different cultures--she's an immigrant from Vietnam still struggling to learn English; he's been raised in America--but through the fairy tales he checks out from the local library, those differences are erased. But though Tiến's mother's understanding of the language of her adopted homeland continues to improve as they read her tales of love, loss, and travel across distant shores together, there's one conversation that still eludes Tiến--how to come out to her and his father. Is there even a way to explain what he's going through in Vietnamese? And without one, how will his parents ever accept him? This beautifully illustrated graphic novel speaks to the complexity of family, and

A multitude of processes in hydrology and environmental engineering are either random or entail random components which are characterized by random variables. These variables are described by frequency distributions. This book provides an overview of different systems of frequency distributions, their properties, and applications to the fields of water resources and environmental engineering. A variety of systems are covered, including the Pearson system, Burr system, and systems commonly applied in economics, such as the D'Addario, Dagum, Stoppa, and Esteban systems. The latter chapters focus on the Singh system and the frequency distributions deduced from Bessel functions, maximum entropy theory, and the transformations of random variables. The final chapter introduces the genetic theory of frequency distributions. Using real-world data, this book provides a valuable reference for researchers, graduate students, and professionals interested in frequency analysis.

The Mahler measure is a fascinating notion and an exciting topic in contemporary mathematics, interconnecting with subjects as diverse as number theory, analysis, arithmetic geometry, special functions and random walks. This friendly and concise introduction to the Mahler measure is a valuable resource for both graduate courses and self-study. It provides the reader with the necessary background material, before presenting the recent achievements and the remaining challenges in the field. The first part introduces the univariate Mahler measure and addresses Lehmer's question, and then discusses techniques of reducing multivariate measures to hypergeometric functions. The second part touches on the novelties of the subject, especially the relation with elliptic curves, modular forms and special values of L-functions. Finally, the Appendix presents the modern definition of motivic cohomology and regulator maps, as well as Deligne–Beilinson cohomology. The text includes many exercises to

This book provides an introduction to the mathematical and algorithmic foundations of data science, including machine learning, high-dimensional geometry, and analysis of large networks. Topics include the counterintuitive nature of data in high dimensions, important linear algebraic techniques such as singular value decomposition, the theory of random walks and Markov chains, the fundamentals of and important algorithms for machine learning, algorithms and analysis for clustering, probabilistic models for large networks, representation learning including topic modelling and non-negative matrix factorization, wavelets and compressed sensing. Important probabilistic techniques are developed including the law of large numbers, tail inequalities, analysis of random projections, generalization guarantees in machine learning, and moment methods for analysis of phase transitions in large random graphs. Additionally, important structural and complexity measures are discussed such as matrix no

Exploring the origins and evolution of magnetic fields in planets, stars and galaxies, this book gives a basic introduction to magnetohydrodynamics and surveys the observational data, with particular focus on geomagnetism and solar magnetism. Pioneering laboratory experiments that seek to replicate particular aspects of fluid dynamo action are also described. The authors provide a complete treatment of laminar dynamo theory, and of the mean-field electrodynamics that incorporates the effects of random waves and turbulence. Both dynamo theory and its counterpart, the theory of magnetic relaxation, are covered. Topological constraints associated with conservation of magnetic helicity are thoroughly explored and major challenges are addressed in areas such as fast-dynamo theory, accretion-disc dynamo theory and the theory of magnetostrophic turbulence. The book is aimed at graduate-level students in mathematics, physics, Earth sciences and astrophysics, and will be a valuable resource for

Exploring the origins and evolution of magnetic fields in planets, stars and galaxies, this book gives a basic introduction to magnetohydrodynamics and surveys the observational data, with particular focus on geomagnetism and solar magnetism. Pioneering laboratory experiments that seek to replicate particular aspects of fluid dynamo action are also described. The authors provide a complete treatment of laminar dynamo theory, and of the mean-field electrodynamics that incorporates the effects of random waves and turbulence. Both dynamo theory and its counterpart, the theory of magnetic relaxation, are covered. Topological constraints associated with conservation of magnetic helicity are thoroughly explored and major challenges are addressed in areas such as fast-dynamo theory, accretion-disc dynamo theory and the theory of magnetostrophic turbulence. The book is aimed at graduate-level students in mathematics, physics, Earth sciences and astrophysics, and will be a valuable resource for

Abstract Algebra with Applications provides a friendly and concise introduction to algebra, with an emphasis on its uses in the modern world. The first part of this book covers groups, after some preliminaries on sets, functions, relations, and induction, and features applications such as public-key cryptography, Sudoku, the finite Fourier transform, and symmetry in chemistry and physics. The second part of this book covers rings and fields, and features applications such as random number generators, error correcting codes, the Google page rank algorithm, communication networks, and elliptic curve cryptography. The book's masterful use of colorful figures and images helps illustrate the applications and concepts in the text. Real-world examples and exercises will help students contextualize the information. Intended for a year-long undergraduate course in algebra for mathematics, engineering, and computer science majors, the only prerequisites are calculus and a bit of courage when ask

Language is a sophisticated tool which we use to communicate in a multitude of ways. Updated and expanded in its second edition, this book introduces language and linguistics - presenting language in all its amazing complexity while systematically guiding you through the basics. The reader will emerge with an appreciation of the diversity of the world's languages, as well as a deeper understanding of the structure of human language, the ways it is used, and its broader social and cultural context. Part I is devoted to the nuts and bolts of language study - speech sounds, sound patterns, sentence structure, and meaning - and includes chapters dedicated to the functional aspects of language: discourse, prosody, pragmatics, and language contact. The fourteen language profiles included in Part II reveal the world's linguistic variety while expanding on the similarities and differences between languages. Using knowledge gained from Part I, the reader can explore how language functions when

Analytical mechanics is the foundation of many areas of theoretical physics including quantum theory and statistical mechanics, and has wide-ranging applications in engineering and celestial mechanics. This introduction to the basic principles and methods of analytical mechanics covers Lagrangian and Hamiltonian dynamics, rigid bodies, small oscillations, canonical transformations and Hamilton–Jacobi theory. This fully up-to-date textbook includes detailed mathematical appendices and addresses a number of advanced topics, some of them of a geometric or topological character. These include Bertrand's theorem, proof that action is least, spontaneous symmetry breakdown, constrained Hamiltonian systems, non-integrability criteria, KAM theory, classical field theory, Lyapunov functions, geometric phases and Poisson manifolds. Providing worked examples, end-of-chapter problems, and discussion of ongoing research in the field, it is suitable for advanced undergraduate students and graduate st

Language is a sophisticated tool which we use to communicate in a multitude of ways. Updated and expanded in its second edition, this book introduces language and linguistics - presenting language in all its amazing complexity while systematically guiding you through the basics. The reader will emerge with an appreciation of the diversity of the world's languages, as well as a deeper understanding of the structure of human language, the ways it is used, and its broader social and cultural context. Part I is devoted to the nuts and bolts of language study - speech sounds, sound patterns, sentence structure, and meaning - and includes chapters dedicated to the functional aspects of language: discourse, prosody, pragmatics, and language contact. The fourteen language profiles included in Part II reveal the world's linguistic variety while expanding on the similarities and differences between languages. Using knowledge gained from Part I, the reader can explore how language functions when

Bird song is one of the most remarkable and impressive sounds in the natural world, and has inspired not only students of natural history, but also great writers, poets and composers. Extensively updated from the first edition, the main thrust of this book is to suggest that the two main functions of song are attracting a mate and defending territory. It shows how this evolutionary pressure has led to the amazing variety and complexity we see in the songs of different species throughout the world. Writing primarily for students and researchers in animal behavior, the authors review over 1000 scientific papers and reveal how scientists are beginning to unravel and understand how and why birds communicate with the elaborate vocalizations we call song. Highly illustrated throughout and written in straightforward language, Bird Song also holds appeal for amateur ornithologists with some knowledge of biology.

Using a mix of ethnographic, survey, and comparative historical methodologies, this book offers an unprecedented insight into the corruption economies of Ukrainian and Belarusian universities, hospitals, and secondary schools. Its detailed analysis suggests that political turnover in hybrid political regimes has a strong impact on petty economic crime in service-provision bureaucracies. Theoretically, the book rejects the dominant paradigm that attributes corruption to the allegedly ongoing political transition. Instead, it develops a more nuanced approach that appreciates the complexity of corruption economies in non-Western societies, embraces the local meanings and functions of corruption, and recognizes the stability of new post-transitional regimes in Eastern Europe and beyond. This book offers a critical look at the social costs of transparency, develops a blueprint for a 'sociology of corruption', and offers concrete and feasible policy recommendations. It will appeal to scholar

The purpose of this book is to provide a comprehensive discussion of the available results for discrete time branching processes with random control functions. The independence of individuals’ reprodu

Halsey L. Royden's Real Analysis has contributed to educating generations of mathematical analysis students. The 5th Edition of this classic text presents some important updates while presenting the measure theory, integration theory and elements of metric, topological, Hilbert and Banach spaces that a modern analyst should know. Part I continues to consider Lebesgue measure and integration for functions of a real variable. In this revision, the treatment of general measure and integration is moved to Part II rather than Part III; material formerly in Part II is placed in Part III and a brief Part IV. This brings measure and integration on Euclidean space closer to their origin, the case of real variables; it also presents the opportunity to foreshadow more strongly, in the context of general measure and integration, concepts which later appear in general spaces. The text assumes an undergraduate course on the fundamental concepts of analysis.

This textbook integrates traditional statistical data analysis with new computational experimentation capabilities and concepts of algorithmic complexity and chaotic behavior in nonlinear dynamic syst

Using a mix of ethnographic, survey, and comparative historical methodologies, this book offers an unprecedented insight into the corruption economies of Ukrainian and Belarusian universities, hospitals, and secondary schools. Its detailed analysis suggests that political turnover in hybrid political regimes has a strong impact on petty economic crime in service-provision bureaucracies. Theoretically, the book rejects the dominant paradigm that attributes corruption to the allegedly ongoing political transition. Instead, it develops a more nuanced approach that appreciates the complexity of corruption economies in non-Western societies, embraces the local meanings and functions of corruption, and recognizes the stability of new post-transitional regimes in Eastern Europe and beyond. This book offers a critical look at the social costs of transparency, develops a blueprint for a 'sociology of corruption', and offers concrete and feasible policy recommendations. It will appeal to scholar

The workings of the brain have long held a fascination for scientists. Yet, faced as they have been with the obvious anatomical and biochemical complexity of the brain, understanding its functions--mo

The workings of the brain have long held a fascination for scientists. Yet, faced as they have been with the obvious anatomical and biochemical complexity of the brain, understanding its functions--mo

From the backyards of suburban Florida to the parched desert of New Mexico, Because of the Sun explores the complexity of family, the saving grace of friendship, and the healing that can begin when th

This book provides an introduction to the topological classification of smooth structurally stable diffeomorphisms on closed orientable 2- and 3-manifolds.The topological classification is one of the

Exploring the full scope of differential topology, this comprehensive account of geometric techniques for studying the topology of smooth manifolds offers a wide perspective on the field. Building up from first principles, concepts of manifolds are introduced, supplemented by thorough appendices giving background on topology and homotopy theory. Deep results are then developed from these foundations through in-depth treatments of the notions of general position and transversality, proper actions of Lie groups, handles (up to the h-cobordism theorem), immersions and embeddings, concluding with the surgery procedure and cobordism theory. Fully illustrated and rigorous in its approach, little prior knowledge is assumed, and yet growing complexity is instilled throughout. This structure gives advanced students and researchers an accessible route into the wide-ranging field of differential topology.

Concentration inequalities for functions of independent random variables is an area of probability theory that has witnessed a great revolution in the last few decades, and has applications in a wide

Beyond Grief explores high-style funerary sculptures and their functions during the turn of the twentieth century. Many scholars have overlooked these monuments, viewing them as mere oddities, a part

With an Introduction by Max Allan CollinsThe author of Get Carter returns to his greatest invention, a smooth-operating hardcase named Jack Carter, who is about to burn a city down in order to silence

This book examines the use of algorithmic techniques to compress random and non-random sequential strings found in chains of polymers. The book is an introduction to algorithmic complexity. Examples t

Beyond Grief explores high-style funerary sculptures and their functions during the turn of the twentieth century. Many scholars have overlooked these monuments, viewing them as mere oddities, a part

Chow introduces partial differential equations of evolutional type with coefficients that are random functions of space and time. Such random functions or random fields may be generalized random field