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The Relevance of the Time Domain to Neural Network Models
A significant amount of effort in neural modeling is directed towards understanding the representation of information in various parts of the brain, such as cortical maps [6], and the paths along which sensory information is processed. Though the time domain is integral an integral aspect of the functioning of biological systems, it has proven very challenging to incorporate the time domain effectively in neural network models. A promising path that is being explored is to study the importance of synchronization in biological systems. Synchronization plays a critical role in the interactions between neurons in the brain, giving rise to perceptual phenomena, and explaining multiple effects su...
Hybrid Systems: Computation and Control
This volume contains the proceedings of the Fourth Workshop on Hybrid - stems: Computation and Control (HSCC 2001) held in Rome, Italy on March 28-30, 2001. The Workshop on Hybrid Systems attracts researchers from in- stry and academia interested in modeling, analysis, synthesis, and implemen- tion of dynamic and reactive systems involving both discrete (integer, logical, symbolic) and continuous behaviors. It is a forum for the discussion of the - test developments in all aspects of hybrid systems, including formal models and computational representations, algorithms and heuristics, computational tools, and new challenging applications. The Fourth HSCC International Workshop continues the s...
Modelling, Estimation and Control of Networked Complex Systems
The paradigm of complexity is pervading both science and engineering, le- ing to the emergence of novel approaches oriented at the development of a systemic view of the phenomena under study; the de?nition of powerful tools for modelling, estimation, and control; and the cross-fertilization of di?erent disciplines and approaches. One of the most promising paradigms to cope with complexity is that of networked systems. Complex, dynamical networks are powerful tools to model, estimate, and control many interesting phenomena, like agent coordination, synch- nization, social and economics events, networks of critical infrastructures, resourcesallocation,informationprocessing,controlovercommunica...
Design and Analysis of Biomolecular Circuits
The book deals with engineering aspects of the two emerging and intertwined fields of synthetic and systems biology. Both fields hold promise to revolutionize the way molecular biology research is done, the way today’s drug discovery works and the way bio-engineering is done. Both fields stress the importance of building and characterizing small bio-molecular networks in order to synthesize incrementally and understand large complex networks inside living cells. Reminiscent of computer-aided design (CAD) of electronic circuits, abstraction is believed to be the key concept to achieve this goal. It allows hiding the overwhelming complexity of cellular processes by encapsulating network parts into abstract modules. This book provides a unique perspective on how concepts and methods from CAD of electronic circuits can be leveraged to overcome complexity barrier perceived in synthetic and systems biology.
Mathematical and Statistical Methods for Multistatic Imaging
This book covers recent mathematical, numerical, and statistical approaches for multistatic imaging of targets with waves at single or multiple frequencies. The waves can be acoustic, elastic or electromagnetic. They are generated by point sources on a transmitter array and measured on a receiver array. An important problem in multistatic imaging is to quantify and understand the trade-offs between data size, computational complexity, signal-to-noise ratio, and resolution. Another fundamental problem is to have a shape representation well suited to solving target imaging problems from multistatic data. In this book the trade-off between resolution and stability when the data are noisy is add...
Geometric Aspects of Functional Analysis
As in the previous Seminar Notes, the current volume reflects general trends in the study of Geometric Aspects of Functional Analysis, understood in a broad sense. A classical theme in the Local Theory of Banach Spaces which is well represented in this volume is the identification of lower-dimensional structures in high-dimensional objects. More recent applications of high-dimensionality are manifested by contributions in Random Matrix Theory, Concentration of Measure and Empirical Processes. Naturally, the Gaussian measure plays a central role in many of these topics, and is also studied in this volume; in particular, the recent breakthrough proof of the Gaussian Correlation Conjecture is revisited. The interplay of the theory with Harmonic and Spectral Analysis is also well apparent in several contributions. The classical relation to both the primal and dual Brunn-Minkowski theories is also well represented, and related algebraic structures pertaining to valuations and valent functions are discussed. All contributions are original research papers and were subject to the usual refereeing standards.
Introduction to Sofic and Hyperlinear Groups and Connes' Embedding Conjecture
This monograph presents some cornerstone results in the study of sofic and hyperlinear groups and the closely related Connes' embedding conjecture. These notions, as well as the proofs of many results, are presented in the framework of model theory for metric structures. This point of view, rarely explicitly adopted in the literature, clarifies the ideas therein, and provides additional tools to attack open problems. Sofic and hyperlinear groups are countable discrete groups that can be suitably approximated by finite symmetric groups and groups of unitary matrices. These deep and fruitful notions, introduced by Gromov and Radulescu, respectively, in the late 1990s, stimulated an impressive ...
Pseudodifferential Equations Over Non-Archimedean Spaces
Focusing on p-adic and adelic analogues of pseudodifferential equations, this monograph presents a very general theory of parabolic-type equations and their Markov processes motivated by their connection with models of complex hierarchic systems. The Gelfand-Shilov method for constructing fundamental solutions using local zeta functions is developed in a p-adic setting and several particular equations are studied, such as the p-adic analogues of the Klein-Gordon equation. Pseudodifferential equations for complex-valued functions on non-Archimedean local fields are central to contemporary harmonic analysis and mathematical physics and their theory reveals a deep connection with probability and number theory. The results of this book extend and complement the material presented by Vladimirov, Volovich and Zelenov (1994) and Kochubei (2001), which emphasize spectral theory and evolution equations in a single variable, and Albeverio, Khrennikov and Shelkovich (2010), which deals mainly with the theory and applications of p-adic wavelets.
Vector-Valued Partial Differential Equations and Applications
Collating different aspects of Vector-valued Partial Differential Equations and Applications, this volume is based on the 2013 CIME Course with the same name which took place at Cetraro, Italy, under the scientific direction of John Ball and Paolo Marcellini. It contains the following contributions: The pullback equation (Bernard Dacorogna), The stability of the isoperimetric inequality (Nicola Fusco), Mathematical problems in thin elastic sheets: scaling limits, packing, crumpling and singularities (Stefan Müller), and Aspects of PDEs related to fluid flows (Vladimir Sverák). These lectures are addressed to graduate students and researchers in the field.
