The aim of the book is to give an accessible introduction of mathematical models and signal processing methods in speech and hearing sciences for senior undergraduate and beginning graduate students with basic knowledge of linear algebra, differential equations, numerical analysis, and probability. Speech and hearing sciences are fundamental to numerous technological advances of the digital world in the past decade, from music compression in MP3 to digital hearing aids, from network based voice enabled services to speech interaction with mobile phones. Mathematics and computation are intimately related to these leaps and bounds. On the other hand, speech and hearing are strongly interdisciplinary areas where dissimilar scientific and engineering publications and approaches often coexist and make it difficult for newcomers to enter.

This book presents mathematical models and numerical simulations of crowd dynamics. The core topic is the development of a new multiscale paradigm, which bridges the microscopic and macroscopic scales taking the most from each of them for capturing the relevant clues of complexity of crowds. The background idea is indeed that most of the complex trends exhibited by crowds are due to an intrinsic interplay between individual and collective behaviors. The modeling approach promoted in this book pursues actively this intuition and profits from it for designing general mathematical structures susceptible of application also in fields different from the inspiring original one. The book considers also the two most traditional points of view: the microscopic one, in which pedestrians are tracked individually and the macroscopic one, in which pedestrians are assimilated to a continuum. Selected existing models are critically analyzed. The work is addressed to researchers and graduate students.

Speech dynamics refer to the temporal characteristics in all stages of the human speech communication process. This speech “chain” starts with the formation of a linguistic message in a speaker's brain and ends with the arrival of the message in a listener's brain. Given the intricacy of the dynamic speech process and its fundamental importance in human communication, this monograph is intended to provide a comprehensive material on mathematical models of speech dynamics and to address the following issues: How do we make sense of the complex speech process in terms of its functional role of speech communication? How do we quantify the special role of speech timing? How do the dynamics relate to the variability of speech that has often been said to seriously hamper automatic speech recognition? How do we put the dynamic process of speech into a quantitative form to enable detailed analyses? And finally, how can we incorporate the knowledge of speech dynamics into computerized speech analysis and recognition algorithms? The answers to all these questions require building and applying computational models for the dynamic speech process. What are the compelling reasons for carrying out dynamic speech modeling? We provide the answer in two related aspects. First, scientific inquiry into the human speech code has been relentlessly pursued for several decades. As an essential carrier of human intelligence and knowledge, speech is the most natural form of human communication. Embedded in the speech code are linguistic (as well as para-linguistic) messages, which are conveyed through four levels of the speech chain. Underlying the robust encoding and transmission of the linguistic messages are the speech dynamics at all the four levels. Mathematical modeling of speech dynamics provides an effective tool in the scientific methods of studying the speech chain. Such scientific studies help understand why humans speak as they do and how humans exploit redundancy and variability by way of multitiered dynamic processes to enhance the efficiency and effectiveness of human speech communication. Second, advancement of human language technology, especially that in automatic recognition of natural-style human speech is also expected to benefit from comprehensive computational modeling of speech dynamics. The limitations of current speech recognition technology are serious and are well known. A commonly acknowledged and frequently discussed weakness of the statistical model underlying current speech recognition technology is the lack of adequate dynamic modeling schemes to provide correlation structure across the temporal speech observation sequence. Unfortunately, due to a variety of reasons, the majority of current research activities in this area favor only incremental modifications and improvements to the existing HMM-based state-of-the-art. For example, while the dynamic and correlation modeling is known to be an important topic, most of the systems nevertheless employ only an ultra-weak form of speech dynamics; e.g., differential or delta parameters. Strong-form dynamic speech modeling, which is the focus of this monograph, may serve as an ultimate solution to this problem. After the introduction chapter, the main body of this monograph consists of four chapters. They cover various aspects of theory, algorithms, and applications of dynamic speech models, and provide a comprehensive survey of the research work in this area spanning over past 20~years. This monograph is intended as advanced materials of speech and signal processing for graudate-level teaching, for professionals and engineering practioners, as well as for seasoned researchers and engineers specialized in speech processing

This book describes the theoretical and computational aspects of the mimetic finite difference method for a wide class of multidimensional elliptic problems, which includes diffusion, advection-diffusion, Stokes, elasticity, magnetostatics and plate bending problems. The modern mimetic discretization technology developed in part by the Authors allows one to solve these equations on unstructured polygonal, polyhedral and generalized polyhedral meshes. The book provides a practical guide for those scientists and engineers that are interested in the computational properties of the mimetic finite difference method such as the accuracy, stability, robustness, and efficiency. Many examples are provided to help the reader to understand and implement this method. This monograph also provides the essential background material and describes basic mathematical tools required to develop further the mimetic discretization technology and to extend it to various applications.

This book introduces speech and hearing sciences students to the principles of "signal" and "system" analysis. Beginning with an examination of what signals and systems are, the book develops a thorough background from which many of the most important issues in speech and hearing can be tackled. Numerous illustrations.

A recent study indicates that 20 million people in the United States have significant sensorineural hearing loss. Approximately 95% of those people have partial losses, with varying degrees of residual hearing. These percentages are similar in other developed countries. What changes in the function of the cochlea or inner ear cause such losses? What does the world sound like to the 19 million people with residual hearing? How should we transform sounds to correct for the hearing loss and maximize restoration of normal hearing? Answers to such questions require detailed models of the way that sounds are processed by the nervous system, both for listeners with normal hearing and for those with sensorineural hearing loss. This book contains chapters describing the work of 25 different research groups. A great deal of research in recent years has been aimed at obtaining a better physiological description of the altered processes that cause sensorineural hearing loss and a better understanding of transformations that occur in the perception of those sounds that are sufficiently intense that they can still be heard. Efforts to understand these changes in function have lead to a better understanding of normal function as well. This research has been based on rigorous mathematical models, computer simulations of mechanical and physiological processes, and signal processing simulations of the altered perceptual experience of listeners with sensorineural hearing loss. This book provides examples of all these approaches to modeling sensorineural hearing loss and a summary of the latest research in the field.

Signal and Acoustic Modeling for Speech and Communication Disorders demonstrates how speech signal processing and acoustic modeling can be instrumental in early detection and successful intervention with speech deficits resulting from Parkinson’s disease, Autism Spectrum disorder, cleft palate, intellectual disabilities, and neuro-motor impairments. Utilizing some of the most advanced methods in signal and acoustic modeling, this eminent group of contributors show how such technologies can inure to the benefit of healthcare and to society writ large. Paradoxically, what most of us take for granted still remains a Sisyphean battle for those with speech and language disorders, who struggle every day to make themselves heard and understood. The purpose of this book is to stimulate a vibrant discussion among speech scientists, system designers, and practitioners on how to best marshal the latest advances in signal and acoustic modeling to address some of the most challenging speech and communication disorders affecting a wide variety of patient populations across the world.