Chip and Signature Interleaving in DS CDMA Systems

Siirretty Doriast

2012 program of study : coherent structures

The 2012 GFD Program theme was Coherent structures with Professors Jeffrey Weiss of the University of Colorado at Boulder and Edgar Knobloch of the University of California at Berkeley serving as principal lecturers. Together they introduced the audience in the cottage and on the porch to a fascinating mixture of models, mathematics and applications. Deep insights snaked through the whole summer, as the principal lecturers stayed on to participate in the traditional debates and contributed stoutly to the supervision of the fellows. The first ten chapters of this volume document these lectures, each prepared by pairs of the summer's GFD fellows. Following the principal lecture notes are the written reports of the fellows' own research projects. In 2012, the Sears Public Lecture was delivered by Professor Howard Bluestein, of the University of Oklahoma on the topic of "Probing tornadoes with mobile doppler radars". The topic was particularly suitable for the summer's theme: a tornado is a special examples of a vortex, perhaps the mother of all coherent structures in fluid dynamics. Howie "Cb" showed how modern and innovative measurement techniques can yield valuable information about the formation and evolution of tornadoes, as well as truly amazing images.Funding was provided by the Office of Naval Research under Grant No. N00014-09-10844 and the National Science Foundation under Contract No. OCE-0824636

Sample Path Analysis of Integrate-and-Fire Neurons

Computational neuroscience is concerned with answering two intertwined questions that are based on the assumption that spatio-temporal patterns of spikes form the universal language of the nervous system. First, what function does a specific neural circuitry perform in the elaboration of a behavior? Second, how do neural circuits process behaviorally-relevant information? Non-linear system analysis has proven instrumental in understanding the coding strategies of early neural processing in various sensory modalities. Yet, at higher levels of integration, it fails to help in deciphering the response of assemblies of neurons to complex naturalistic stimuli. If neural activity can be assumed to be primarily driven by the stimulus at early stages of processing, the intrinsic activity of neural circuits interacts with their high-dimensional input to transform it in a stochastic non-linear fashion at the cortical level. As a consequence, any attempt to fully understand the brain through a system analysis approach becomes illusory. However, it is increasingly advocated that neural noise plays a constructive role in neural processing, facilitating information transmission. This prompts to gain insight into the neural code by studying the stochasticity of neuronal activity, which is viewed as biologically relevant. Such an endeavor requires the design of guiding theoretical principles to assess the potential benefits of neural noise. In this context, meeting the requirements of biological relevance and computational tractability, while providing a stochastic description of neural activity, prescribes the adoption of the integrate-and-fire model. In this thesis, founding ourselves on the path-wise description of neuronal activity, we propose to further the stochastic analysis of the integrate-and fire model through a combination of numerical and theoretical techniques. To begin, we expand upon the path-wise construction of linear diffusions, which offers a natural setting to describe leaky integrate-and-fire neurons, as inhomogeneous Markov chains. Based on the theoretical analysis of the first-passage problem, we then explore the interplay between the internal neuronal noise and the statistics of injected perturbations at the single unit level, and examine its implications on the neural coding. At the population level, we also develop an exact event-driven implementation of a Markov network of perfect integrate-and-fire neurons with both time delayed instantaneous interactions and arbitrary topology. We hope our approach will provide new paradigms to understand how sensory inputs perturb neural intrinsic activity and accomplish the goal of developing a new technique for identifying relevant patterns of population activity. From a perturbative perspective, our study shows how injecting frozen noise in different flavors can help characterize internal neuronal noise, which is presumably functionally relevant to information processing. From a simulation perspective, our event-driven framework is amenable to scrutinize the stochastic behavior of simple recurrent motifs as well as temporal dynamics of large scale networks under spike-timing-dependent plasticity

Development and application of high-resolution solid-state NMR methods for probing polymorphism of active pharmaceutical ingredients

The objective of the work presented in this thesis is to apply advanced high-resolution solid-state NMR methods for the structural characterisation of organic crystalline systems, specifically active pharmaceutical ingredients (APIs). The determination of the crystal packing is an important stage in the development of new APIs, and solid-state magic angle spinning (MAS) NMR is well suited to complement existing techniques. Improvements in spectral resolution in recent years have led to the development of homonuclear correlation experiments capable of identifying intermolecular proximities between 1H nuclei. These experiments provide a powerful probe of the local environment of each 1H nucleus in the three-dimensional structure, and the majority of the research presented in this thesis is focussed on the development of detailed analysis methods that may be used to extract more detailed structural information from 2D solid-state NMR correlation spectra. Throughout this thesis, experimental solid-state NMR results are analysed alongside computational data, including density matrix simulations of experiments and first principles calculations of shielding tensors. The results of simulations of a 1H DQ (double-quantum) correlation experiment are compared to experiment, in order to investigate the dependence of the DQ build-up (change in peak intensity as a function of the recoupling pulse duration) on the precise nature of the dipolar coupled proton network. It is found (for a simple dipeptide) that quantitative information on the relative H{H distance may be obtained by comparison of the maximum intensity reached in the corresponding 1H DQ build-up curves. This method is then applied to pharmaceutically relevant systems. It is shown that differences between two polymorphs of an API may be identified in the 1H DQ build-up of particular peaks, and, following the analysis for the dipeptide, this difference may be ascribed to differences in specific intermolecular distances. In the study of a second API, -indomethacin, it is shown that the standard 1H DQ experiment provides insufficient resolution to identify specific DQ peaks. A recently developed 1H(DQ){13C correlation experiment is used to exploit the higher resolution in the 13C dimension, hence allowing the extraction of DQ build-up curves which may be used, in conjunction with simulations, to obtain structural data. Finally, a recently discovered polymorph of the API ibuprofen is studied using 13C CPMAS (cross polarisation) solid-state NMR. Through the use of first-principles calculations, the 13C spectra of both the well known and new polymorphs are assigned, and the conversion of an amorphous solid to the new polymorph is monitored through the use of temperature-controlled solid-state NMR experiments

Dynamical Systems

Complex systems are pervasive in many areas of science integrated in our daily lives. Examples include financial markets, highway transportation networks, telecommunication networks, world and country economies, social networks, immunological systems, living organisms, computational systems and electrical and mechanical structures. Complex systems are often composed of a large number of interconnected and interacting entities, exhibiting much richer global scale dynamics than the properties and behavior of individual entities. Complex systems are studied in many areas of natural sciences, social sciences, engineering and mathematical sciences. This special issue therefore intends to contribute towards the dissemination of the multifaceted concepts in accepted use by the scientific community. We hope readers enjoy this pertinent selection of papers which represents relevant examples of the state of the art in present day research. [...

Analysis of spatial point patterns on surfaces

With the advent of improved data acquisition technologies more complex spatial datasets can be collected at scale meaning theoretical and methodological developments in spatial statistics are imperative in order to analyse and generate meaningful conclusions. Spatial statistics has seen a plethora of applications in life sciences with particular emphasis on ecology, epidemiology and cell microscopy. Applications of these techniques provides researchers with insight on how the locations of objects of interest can be influenced by their neighbours and the environment. Examples include understanding the spatial distribution of trees observed within some window, and understanding how neighbouring trees and potentially soil contents can influence this. Whilst the literature for spatial statistics is rich the common assumption is that point processes are usually restricted to some d-dimensional Euclidean space, for example cell locations in a rectangular window of 2-dimensional Euclidean space. As such current theory is not capable of handling patterns which lie on more complex spaces, for example cubes and ellipsoids. Recent efforts have successfully extended methodology from Euclidean space to spheres by using the chordal distance (the shortest distance between any two points on a sphere) in place of the Euclidean distance. In this thesis we build on this work by considering point processes lying on more complex surfaces. Our first significant contribution discusses the construction of functional summary statistics for Poisson processes which lie on compact subsets of Rd which are off lower dimension. We map the process from its original space to the sphere where it is possible to take advantage of rotational symmetries which allow for well-defined summary statistics. These in turn can be used to determine whether an observed point patterns exhibits clustered or regular behaviour. Partnering this work we also provide a hypothesis testing procedure based on these functional summary statistics to determine whether an observed point pattern is complete spatially random. Two test statistics are proposed, one based on the commonly used L-function for planar processes and the other a standardisation of the K-function. These test statistics are compared in an extensive simulation study across ellipsoids of varying dimensions and processes which display differing levels of aggregation or regularity. Estimates of first order properties of a point process are extremely important. They can provide a graphical illustration of inhomogeneity and are useful in second order analysis. We demonstrate how kernel estimation can be extended from a Euclidean space to a Riemannian manifold where the Euclidean metric is now substituted for a Riemannian one. Many of the desirable properties for Euclidean kernel estimates carry over to the Riemannian setting. The issue of edge correction is also discussed and two criteria for bandwidth selection are proposed. These two selection criteria are explored through a simulation study. Finally, an important area of research in spatial statistics is exploring the interaction between different processes, for example how different species of plant spatially interact within some window. Under the framework of marked point processes we show that functional summary statistics for multivariate point patterns can be constructed on the sphere. This is extended to more general convex shapes through an appropriate mapping from the original shape to the sphere. A number of examples highlight that these summary statistics can capture independence, aggregation and repulsion between components of a multivariate process on both the sphere and more general surfaces.Open Acces

Modified Gravity and Cosmology

In this review we present a thoroughly comprehensive survey of recent work on modified theories of gravity and their cosmological consequences. Amongst other things, we cover General Relativity, Scalar-Tensor, Einstein-Aether, and Bimetric theories, as well as TeVeS, f(R), general higher-order theories, Horava-Lifschitz gravity, Galileons, Ghost Condensates, and models of extra dimensions including Kaluza-Klein, Randall-Sundrum, DGP, and higher co-dimension braneworlds. We also review attempts to construct a Parameterised Post-Friedmannian formalism, that can be used to constrain deviations from General Relativity in cosmology, and that is suitable for comparison with data on the largest scales. These subjects have been intensively studied over the past decade, largely motivated by rapid progress in the field of observational cosmology that now allows, for the first time, precision tests of fundamental physics on the scale of the observable Universe. The purpose of this review is to provide a reference tool for researchers and students in cosmology and gravitational physics, as well as a self-contained, comprehensive and up-to-date introduction to the subject as a whole.Comment: 312 pages, 15 figure