Channel model and lower capacity bound for the transmission based on nonlinear Fourier transform

The integrability of the nonlinear Schräodinger equation (NLSE) by the inverse scattering transform shown in a seminal work [1] gave an interesting opportunity to treat the corresponding nonlinear channel similar to a linear one by using the nonlinear Fourier transform. Integrability of the NLSE is in the background of the old idea of eigenvalue communications [2] that was resurrected in recent works [3{7]. In [6, 7] the new method for the coherent optical transmission employing the continuous nonlinear spectral data | nonlinear inverse synthesis was introduced. It assumes the modulation and detection of data using directly the continuous part of nonlinear spectrum associated with an integrable transmission channel (the NLSE in the case considered). Although such a transmission method is inherently free from nonlinear impairments, the noisy signal corruptions, arising due to the ampli¯er spontaneous emission, inevitably degrade the optical system performance. We study properties of the noise-corrupted channel model in the nonlinear spectral domain attributed to NLSE. We derive the general stochastic equations governing the signal evolution inside the nonlinear spectral domain and elucidate the properties of the emerging nonlinear spectral noise using well-established methods of perturbation theory based on inverse scattering transform [8]. It is shown that in the presence of small noise the communication channel in the nonlinear domain is the additive Gaussian channel with memory and signal-dependent correlation matrix. We demonstrate that the effective spectral noise acquires colouring", its autocorrelation function becomes slow decaying and non-diagonal as a function of \frequencies", and the noise loses its circular symmetry, becoming elliptically polarized. Then we derive a low bound for the spectral effiency for such a channel. Our main result is that by using the nonlinear spectral techniques one can significantly increase the achievable spectral effiency compared to the currently available methods [9]. REFERENCES 1. Zakharov, V. E. and A. B. Shabat, Sov. Phys. JETP, Vol. 34, 62{69, 1972. 2. Hasegawa, A. and T. Nyu, J. Lightwave Technol., Vol. 11, 395{399, 1993. 3. Yousefi, M. I. and F. R. Kschischang, IEEE Trans. Inf. Theory, Vol. 60, 4312{4328, 2014. 4. Yousefi, M. I. and F. R. Kschischang, IEEE Trans. Inf. Theory, Vol. 60, 4329{4345 2014. 5. Yousefi, M. I. and F. R. Kschischang, IEEE Trans. Inf. Theory, Vol. 60, 4346{4369, 2014. 6. Prilepsky, J. E., S. A. Derevyanko, K. J. Blow, I. Gabitov, and S. K. Turitsyn, Phys. Rev. Lett., Vol. 113, 013901, 2014. 7. Le, S. T., J. E. Prilepsky, and S. K. Turitsyn, Opt. Express, Vol. 22, 26720{26741, 2014. 8. Kaup, D. J. and A. C. Newell, Proc. R. Soc. Lond. A, Vol. 361, 413{446, 1978. 9. Essiambre, R.-J., G. Kramer, P. J. Winzer, G. J. Foschini, and B. Goebel, J. Lightwave Technol., Vol. 28, 662{701, 2010.

Marking high-technology market evolution through the foci of market stories:the case of local area networks

Previous research suggests that changing consumer and producer knowledge structures play a role in market evolution and that the sociocognitive processes of product markets are revealed in the sensemaking stories of market actors that are rebroadcasted in commercial publications. In this article, the authors lend further support to the story-based nature of market sensemaking and the use of the sociocognitive approach in explaining the evolution of high-technology markets. They examine the content (i.e., subject matter or topic) and volume (i.e., the number) of market stories and the extent to which content and volume of market stories evolve as a technology emerges. Data were obtained from a content analysis of 10,412 article abstracts, published in key trade journals, pertaining to Local Area Network (LAN) technologies and spanning the period 1981 to 2000. Hypotheses concerning the evolving nature (content and volume) of market stories in technology evolution are tested. The analysis identified four categories of market stories - technical, product availability, product adoption, and product discontinuation. The findings show that the emerging technology passes initially through a 'technical-intensive' phase whereby technology related stories dominate, through a 'supply-push' phase, in which stories presenting products embracing the technology tend to exceed technical stories while there is a rise in the number of product adoption reference stories, to a 'product-focus' phase, with stories predominantly focusing on product availability. Overall story volume declines when a technology matures as the need for sensemaking reduces. When stories about product discontinuation surface, these signal the decline of current technology. New technologies that fail to maintain the 'product-focus' stage also reflect limited market acceptance. The article also discusses the theoretical and managerial implications of the study's findings. © 2002 Elsevier Science Inc. All rights reserved.

Cognitive neuroscience: the evolution of a discipline

Preface. The evolution of cognitive neuroscience has been spurred by the development of increasingly sophisticated investigative techniques to study human cognition. In Methods in Mind, experts examine the wide variety of tools available to cognitive neuroscientists, paying particular attention to the ways in which different methods can be integrated to strengthen empirical findings and how innovative uses for established techniques can be developed. The book will be a uniquely valuable resource for the researcher seeking to expand his or her repertoire of investigative techniques. Each chapter explores a different approach. These include transcranial magnetic stimulation, cognitive neuropsychiatry, lesion studies in nonhuman primates, computational modeling, psychophysiology, single neurons and primate behavior, grid computing, eye movements, fMRI, electroencephalography, imaging genetics, magnetoencephalography, neuropharmacology, and neuroendocrinology. As mandated, authors focus on convergence and innovation in their fields; chapters highlight such cross-method innovations as the use of the fMRI signal to constrain magnetoencephalography, the use of electroencephalography (EEG) to guide rapid transcranial magnetic stimulation at a specific frequency, and the successful integration of neuroimaging and genetic analysis. Computational approaches depend on increased computing power, and one chapter describes the use of distributed or grid computing to analyze massive datasets in cyberspace. Each chapter author is a leading authority in the technique discussed.

The evolution of learning systems:to Bayes or not to be

Bayesian algorithms pose a limit to the performance learning algorithms can achieve. Natural selection should guide the evolution of information processing systems towards those limits. What can we learn from this evolution and what properties do the intermediate stages have? While this question is too general to permit any answer, progress can be made by restricting the class of information processing systems under study. We present analytical and numerical results for the evolution of on-line algorithms for learning from examples for neural network classifiers, which might include or not a hidden layer. The analytical results are obtained by solving a variational problem to determine the learning algorithm that leads to maximum generalization ability. Simulations using evolutionary programming, for programs that implement learning algorithms, confirm and expand the results. The principal result is not just that the evolution is towards a Bayesian limit. Indeed it is essentially reached. In addition we find that evolution is driven by the discovery of useful structures or combinations of variables and operators. In different runs the temporal order of the discovery of such combinations is unique. The main result is that combinations that signal the surprise brought by an example arise always before combinations that serve to gauge the performance of the learning algorithm. This latter structures can be used to implement annealing schedules. The temporal ordering can be understood analytically as well by doing the functional optimization in restricted functional spaces. We also show that there is data suggesting that the appearance of these traits also follows the same temporal ordering in biological systems. © 2006 American Institute of Physics.