New Constructions of Zero-Correlation Zone Sequences

In this paper, we propose three classes of systematic approaches for constructing zero correlation zone (ZCZ) sequence families. In most cases, these approaches are capable of generating sequence families that achieve the upper bounds on the family size ($K$) and the ZCZ width ($T$) for a given sequence period ($N$). Our approaches can produce various binary and polyphase ZCZ families with desired parameters $(N,K,T)$ and alphabet size. They also provide additional tradeoffs amongst the above four system parameters and are less constrained by the alphabet size. Furthermore, the constructed families have nested-like property that can be either decomposed or combined to constitute smaller or larger ZCZ sequence sets. We make detailed comparisons with related works and present some extended properties. For each approach, we provide examples to numerically illustrate the proposed construction procedure.Comment: 37 pages, submitted to IEEE Transactions on Information Theor

Design of sequences with good correlation properties

This thesis is dedicated to exploring sequences with good correlation properties. Periodic sequences with desirable correlation properties have numerous applications in communications. Ideally, one would like to have a set of sequences whose out-of-phase auto-correlation magnitudes and cross-correlation magnitudes are very small, preferably zero. However, theoretical bounds show that the maximum magnitudes of auto-correlation and cross-correlation of a sequence set are mutually constrained, i.e., if a set of sequences possesses good auto-correlation properties, then the cross-correlation properties are not good and vice versa. The design of sequence sets that achieve those theoretical bounds is therefore of great interest. In addition, instead of pursuing the least possible correlation values within an entire period, it is also interesting to investigate families of sequences with ideal correlation in a smaller zone around the origin. Such sequences are referred to as sequences with zero correlation zone or ZCZ sequences, which have been extensively studied due to their applications in 4G LTE and 5G NR systems, as well as quasi-synchronous code-division multiple-access communication systems. Paper I and a part of Paper II aim to construct sequence sets with low correlation within a whole period. Paper I presents a construction of sequence sets that meets the Sarwate bound. The construction builds a connection between generalised Frank sequences and combinatorial objects, circular Florentine arrays. The size of the sequence sets is determined by the existence of circular Florentine arrays of some order. Paper II further connects circular Florentine arrays to a unified construction of perfect polyphase sequences, which include generalised Frank sequences as a special case. The size of a sequence set that meets the Sarwate bound, depends on a divisor of the period of the employed sequences, as well as the existence of circular Florentine arrays. Paper III-VI and a part of Paper II are devoted to ZCZ sequences. Papers II and III propose infinite families of optimal ZCZ sequence sets with respect to some bound, which are used to eliminate interference within a single cell in a cellular network. Papers V, VI and a part of Paper II focus on constructions of multiple optimal ZCZ sequence sets with favorable inter-set cross-correlation, which can be used in multi-user communication environments to minimize inter-cell interference. In particular, Paper~II employs circular Florentine arrays and improves the number of the optimal ZCZ sequence sets with optimal inter-set cross-correlation property in some cases.Doktorgradsavhandlin

A Direct Construction of Prime-Power-Length Zero-Correlation Zone Sequences for QS-CDMA System

In recent years, zero-correlation zone (ZCZ) sequences are being studied due to their significant applications in quasi-synchronous code division multiple access (QS-CDMA) systems and other wireless communication domains. However, the lengths of most existing ZCZ sequences are limited, and their parameters are not flexible, which are leading to practical limitations in their use in QS-CDMA and other communication systems. The current study proposes a direct construction of ZCZ sequences of prime-power length with flexible parameters by using multivariable functions. In the proposed construction, we first present a multivariable function to generate a vector with specific properties; this is further used to generate another class of multivariable functions to generate the desired $(p^t,(p-1)p^n,p^{n+t+1})$-ZCZ sequence set, where $p$ is a prime number, $t,n$ are positive integers, and $t\leq n$. The constructed ZCZ sequence set is optimal for the binary case and asymptotically optimal for the non-binary case by the \emph{Tang-Fan-Matsufuji} bound. Moreover, a relation between the second-order cosets of first-order generalized Reed-Muller code and the proposed ZCZ sequences is also established. The proposed construction of ZCZ sequences is compared with existing constructions, and it is observed that the parameters of this ZCZ sequence set are a generalization of that of in some existing works. Finally, the performance of the proposed ZCZ-based QS-CDMA system is compared with the Walsh-Hadamard and Gold code-based QS-CDMA system

Chip and Signature Interleaving in DS CDMA Systems

Siirretty Doriast

Irreversibility Measures in a Quantum Setting

A satisfactory understanding of macroscopic irreversibility has remained elusive since the advent of thermodynamics. Progress has nevertheless been made in understanding irreversibility measures classically; this work explores irreversibility in a quantum setting. Entropy production quantifies the irreversibility associated with open stochastic dynamical systems, and our main aim has been to extend this concept. Understanding the thermodynamics of open quantum systems better will eventually improve the efficiency of increasingly feasible nanoscale operations. An exact method to model the thermodynamic properties of open quantum systems is the stochastic Liouville-von Neumann (SLN) equation, based on unravelling Feynman-Vernon influence functionals. We extend its use from the one heat bath case to a system in a non-equilibrium stationary state due to coupling to more than one heat bath. An asymmetry in the probabilistic specification of a closed deterministic system can lead to a disparity between the likelihoods of a particular forward and corresponding backward behaviour starting from a specified time. Such a comparison is a test of a property denoted obversibility, quantified in terms of dissipation production – rather than entropy production – as a measure of irreversibility. We evaluate dissipation production in a deterministic two-level quantum system described by a statistical ensemble of state vectors. We identify the conditions under which the dissipation production fulfills an Evans-Searles Fluctuation Theorem and for which the system will display time-asymmetric average behaviour as it evolves. Finally, we use a Kraus operator formalism to present a minimal model for the random evolution in the Bloch sphere of individual trajectory realisations of the coherence vector of a qubit and use it to evaluate the entropy production associated with weak quantum measurement, with both one and two measurement operators, before speculating on the consequences of our results to our understanding of quantum measurement and the associated indeterminism

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

Scalable approximate inference methods for Bayesian deep learning

This thesis proposes multiple methods for approximate inference in deep Bayesian neural networks split across three parts. The first part develops a scalable Laplace approximation based on a block- diagonal Kronecker factored approximation of the Hessian. This approximation accounts for parameter correlations – overcoming the overly restrictive independence assumption of diagonal methods – while avoiding the quadratic scaling in the num- ber of parameters of the full Laplace approximation. The chapter further extends the method to online learning where datasets are observed one at a time. As the experiments demonstrate, modelling correlations between the parameters leads to improved performance over the diagonal approximation in uncertainty estimation and continual learning, in particular in the latter setting the improvements can be substantial. The second part explores two parameter-efficient approaches for variational inference in neural networks, one based on factorised binary distributions over the weights, one extending ideas from sparse Gaussian processes to neural network weight matrices. The former encounters similar underfitting issues as mean-field Gaussian approaches, which can be alleviated by a MAP-style method in a hierarchi- cal model. The latter, based on an extension of Matheron’s rule to matrix normal distributions, achieves comparable uncertainty estimation performance to ensembles with the accuracy of a deterministic network while using only 25% of the number of parameters of a single ResNet-50. The third part introduces TyXe, a probabilistic programming library built on top of Pyro to facilitate turning PyTorch neural networks into Bayesian ones. In contrast to existing frameworks, TyXe avoids introducing a layer abstraction, allowing it to support arbitrary architectures. This is demonstrated in a range of applications, from image classification with torchvision ResNets over node labelling with DGL graph neural networks to incorporating uncertainty into neural radiance fields with PyTorch3d

Explicit Multistage Schemes for the Solution of the Three-Dimensional Compressible Euler/Navier-Stokes Equations

The objective of this study was to develop a high-resolution-explicit-multi-block numerical algorithm, suitable for efficient computation of the three-dimensional, time-dependent Euler and Navier-Stokes equations. The resulting algorithm has employed a finite volume approach, using MUSCL-type differencing to obtain state variables at cell interface. Variable interpolations were written in the $\kappa$-scheme formulation. Inviscid fluxes were calculated via Roe\u27s flux-difference splitting, and van Leer\u27s flux-vector splitting techniques, which are considered state of the art. The viscous terms were discretized using a second-order, central-difference operator. Two classes of explicit time integration has been investigated for solving the compressible inviscid/viscous flow problems--two-stage predictor-corrector schemes, and multistage time-stepping schemes. The coefficients of the multistage time-stepping schemes have been modified successfully to achieve better performance with upwind differencing. A technique was developed to optimize the coefficients for good high-frequency damping at relatively high CFL numbers. Local time-stepping, implicit residual smoothing, and multigrid procedure were added to the explicit time stepping scheme to accelerate convergence to steady-state. The developed algorithm was implemented successfully in a multi-block code, which provides complete topological and geometric flexibility. The only requirement is C° continuity of the grid across the block interface. The algorithm has been validated on a diverse set of three-dimensional test cases of increasing complexity. The cases studied were: (1) supersonic corner flow; (2) supersonic plume flow; (3) laminar and turbulent flow over a flat plate; (4) transonic flow over an ONERA M6 wing, and (5) unsteady flow of a compressible jet impinging on a ground plane (with and without cross flow). The emphasis of the test cases was validation of code, and assessment of performance, as well as demonstration of flexibility

Communications Biophysics

Contains research objectives, summary of research and reports on two research project.National Institutes of Health (Grant 5 PO1 GM14940-03)National Institutes of Health (Grant 5 TO1 GM01555-03)National Aeronautics and Space Administration (Grant NGL 22-009-304