Dilation Theory: A Guided Tour

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.

C*-Envelope and Dilation Theory of Semigroup Dynamical Systems

Integral Equations and Operator Theory ◽

10.1007/s00020-021-02636-6 ◽

2021 ◽

Vol 93 (3) ◽

Author(s):

Boyu Li

Keyword(s):

Dynamical Systems ◽

Dilation Theory

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.

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

Factorization of an adjontable Markov operator

Infinite Dimensional Analysis Quantum Probability and Related Topics ◽

10.1142/s0219025719500139 ◽

2019 ◽

Vol 22 (02) ◽

pp. 1950013

Author(s):

Carlo Pandiscia

Keyword(s):

Hilbert Space ◽

Matrix Algebra ◽

Unitary Operator ◽

Markov Operator ◽

Factorization Property ◽

Markov Operators ◽

Dilation Theory ◽

Probability Spaces

In this work, we propose a method to investigate the factorization property of a adjontable Markov operator between two algebraic probability spaces without using the dilation theory. Assuming the existence of an anti-unitary operator on Hilbert space related to Stinespring representations of our Markov operator, which satisfy some particular modular relations, we prove that it admits a factorization. The method is tested on the two typologies of maps which we know admits a factorization, the Markov operators between commutative probability spaces and adjontable homomorphism. Subsequently, we apply these methods to particular adjontable Markov operator between matrix algebra which fixes the diagonal.

A guided tour through oriented matroid axioms

Acta Mathematicae Applicatae Sinica English Series ◽

10.1007/bf02007436 ◽

1993 ◽

Vol 9 (2) ◽

pp. 125-134

Author(s):

Achim Bachem ◽

Walter Kern

Keyword(s):

Oriented Matroid ◽

Guided Tour

A guided tour: small RNA function in Archaea

Molecular Microbiology ◽

10.1046/j.1365-2958.2001.02381.x ◽

2001 ◽

Vol 40 (3) ◽

pp. 509-519 ◽

Cited By ~ 82

Author(s):

Patrick P. Dennis ◽

Arina Omer ◽

Todd Lowe

Keyword(s):

Small Rna ◽

Guided Tour