A Guided Tour through the Land of Operator Semigroups

What do pure mathematicians do, and why do they do it? Looking beyond the conventional answers, this book offers an eclectic panorama of the lives and values and hopes and fears of mathematicians in the twenty-first century, assembling material from a startlingly diverse assortment of scholarly, journalistic, and pop culture sources. Drawing on the author's personal experiences as well as the thoughts and opinions of mathematicians from Archimedes and Omar Khayyám to such contemporary giants as Alexander Grothendieck and Robert Langlands, the book reveals the charisma and romance of mathematics as well as its darker side. In this portrait of mathematics as a community united around a set of common intellectual, ethical, and existential challenges, the book touches on a wide variety of questions, such as: Are mathematicians to blame for the 2008 financial crisis? How can we talk about the ideas we were born too soon to understand? And how should you react if you are asked to explain number theory at a dinner party? The book takes readers on an unapologetic guided tour of the mathematical life, from the philosophy and sociology of mathematics to its reflections in film and popular music, with detours through the mathematical and mystical traditions of Russia, India, medieval Islam, the Bronx, and beyond.

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Performance vs. hardware requirements in state-of-the-art automatic speech recognition

EURASIP Journal on Audio Speech and Music Processing ◽

10.1186/s13636-021-00217-4 ◽

2021 ◽

Vol 2021 (1) ◽

Author(s):

Alexandru-Lucian Georgescu ◽

Alessandro Pappalardo ◽

Horia Cucu ◽

Michaela Blott

Keyword(s):

Speech Recognition ◽

Automatic Speech Recognition ◽

State Of The Art ◽

Decision Makers ◽

Computing Power ◽

Trade Off ◽

Speech Features ◽

Commercial Applications ◽

Guided Tour ◽

Embedded Applications

AbstractThe last decade brought significant advances in automatic speech recognition (ASR) thanks to the evolution of deep learning methods. ASR systems evolved from pipeline-based systems, that modeled hand-crafted speech features with probabilistic frameworks and generated phone posteriors, to end-to-end (E2E) systems, that translate the raw waveform directly into words using one deep neural network (DNN). The transcription accuracy greatly increased, leading to ASR technology being integrated into many commercial applications. However, few of the existing ASR technologies are suitable for integration in embedded applications, due to their hard constrains related to computing power and memory usage. This overview paper serves as a guided tour through the recent literature on speech recognition and compares the most popular ASR implementations. The comparison emphasizes the trade-off between ASR performance and hardware requirements, to further serve decision makers in choosing the system which fits best their embedded application. To the best of our knowledge, this is the first study to provide this kind of trade-off analysis for state-of-the-art ASR systems.

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A guided tour of the Common Lisp interface manager

ACM SIGPLAN Lisp Pointers ◽

10.1145/121994.121996 ◽

1990 ◽

Vol IV (1) ◽

pp. 17-37 ◽

Cited By ~ 4

Author(s):

Ramana Rao ◽

William M. York ◽

Dennis Doughty

Keyword(s):

Common Lisp ◽

The Common ◽

Guided Tour

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On improvements of the order of approximation in the Poisson limit theorem

Journal of Applied Probability ◽

10.1017/s0021900200103808 ◽

1996 ◽

Vol 33 (01) ◽

pp. 146-155 ◽

Cited By ~ 1

Author(s):

K. Borovkov ◽

D. Pfeifer

Keyword(s):

Limit Theorem ◽

Random Variables ◽

Poisson Approximation ◽

Order Of Approximation ◽

Operator Semigroups ◽

Bernoulli Random Variables ◽

Usual Rate ◽

Poisson Limit ◽

Poisson Measures ◽

Special Case

In this paper we consider improvements in the rate of approximation for the distribution of sums of independent Bernoulli random variables via convolutions of Poisson measures with signed measures of specific type. As a special case, the distribution of the number of records in an i.i.d. sequence of length n is investigated. For this particular example, it is shown that the usual rate of Poisson approximation of O(1/log n) can be lowered to O(1/n 2). The general case is discussed in terms of operator semigroups.

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