342,620 research outputs found

    Symmetry in Applied Mathematics

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    Applied mathematics and symmetry work together as a powerful tool for problem reduction and solving. We are communicating applications in probability theory and statistics (A Test Detecting the Outliers for Continuous Distributions Based on the Cumulative Distribution Function of the Data Being Tested, The Asymmetric Alpha-Power Skew-t Distribution), fractals - geometry and alike (Khovanov Homology of Three-Strand Braid Links, Volume Preserving Maps Between p-Balls, Generation of Julia and Mandelbrot Sets via Fixed Points), supersymmetry - physics, nanostructures -chemistry, taxonomy - biology and alike (A Continuous Coordinate System for the Plane by Triangular Symmetry, One-Dimensional Optimal System for 2D Rotating Ideal Gas, Minimal Energy Configurations of Finite Molecular Arrays, Noether-Like Operators and First Integrals for Generalized Systems of Lane-Emden Equations), algorithms, programs and software analysis (Algorithm for Neutrosophic Soft Sets in Stochastic Multi-Criteria Group Decision Making Based on Prospect Theory, On a Reduced Cost Higher Order Traub-Steffensen-Like Method for Nonlinear Systems, On a Class of Optimal Fourth Order Multiple Root Solvers without Using Derivatives) to specific subjects (Facility Location Problem Approach for Distributed Drones, Parametric Jensen-Shannon Statistical Complexity and Its Applications on Full-Scale Compartment Fire Data). Diverse topics are thus combined to map out the mathematical core of practical problems

    Theory and applications of quantum process calculus

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    Formal methods is an area in theoretical computer science that provides the theories and tools for describing and verifying the correctness of computing systems. Usually, such systems comprise of concurrent and communicating components. The success of this field led to the development of quantum formal methods by transferring the ideas of formal methods to quantum systems. In particular, formal methods provides a systematic methodology for verification of systems. Quantum process calculus is a specialised field in quantum formal methods that helps to describe and analyse the behaviour of systems that combine quantum and classical elements. We focus on the theory and applications of quantum process calculus in particular to use Communicating Quantum Processes (CQP), a quantum process calculus, to model and analyse quantum information processing (QIP) systems. Previous work on CQP defined labelled transition relations for CQP in order to describe external interactions and also established the theory of behavioural equivalence in CQP based on probabilistic branching bisimilarity. This theory formalizes the idea of observational indistinguishability in order to prove or verify the correctness of a system, and an important property of the equivalence is the congruence property. We use the theory to analyse two versions of a quantum error correcting code system. We use the equational theory of CQP from the previous work and define an additional three new axioms in order to analyse quantum protocols comprising quantum secret-sharing, quantum error correction, remote-CNOT and superdense coding. We have expanded the framework of modelling in CQP from providing an abstract view of the quantum system to describe a realistic QIP system such as linear optical quantum computing (LOQC) and its associated experimental processes. By extending the theory of behavioural equivalence of CQP, we have formally verified two models of an LOQC CNOT gate using CQP. The two models use different measurement semantics in order to work at different levels of abstraction. This flexibility of the process calculus approach allows descriptions from detailed hardware implementations up to more abstract specifications. The orbital angular momentum (OAM) property of light allows us to perform experiments in studying higher dimensional quantum systems and their applications to quantum technologies. In relation to this work, we have extended CQP to model higher dimensional quantum protocols

    Bisimulation for higher-order process calculi

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    A higher-order process calculus is a calculus for communicating systems which contains higher-order constructs like communication of terms. We analyse the notion of bisimulation in these calculi. We argue that %, if static binding is assumed, both the standard definition of bisimulation (i.e., the one for CCS and related calculi), as well as higher-order bisimulation \cite{AsGi88,Bou89,Tho90} are in general unsatisfactory, because over-discriminating. We propose and study a new form of bisimulation for such calculi, called context bisimulation, which yields a more satisfactory discriminanting power. A drawback of context bisimulation is the heavy use of universal quantification in its definition. A major goal of the paper is to find characterisations which make bisimilarities easier to verify. An important role in our theory is played by the factorisation theorem: When comparing the behaviour of two processes, it allows us to «isolate» subcomponents which might cause differences, so that the analysis can be concentrated on them

    A distributed Real-Time Java system based on CSP

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    CSP is a fundamental concept for developing software for distributed real time systems. The CSP paradigm constitutes a natural addition to object orientation and offers higher order multithreading constructs. The CSP channel concept that has been implemented in Java deals with single- and multi-processor environments and also takes care of the real time priority scheduling requirements. For this, the notion of priority and scheduling has been carefully examined and as a result it was reasoned that priority scheduling should be attached to the communicating channels rather than to the processes. In association with channels, a priority based parallel construct is developed for composing processes: hiding threads and priority indexing from the user. This approach simplifies the use of priorities for the object oriented paradigm. Moreover, in the proposed system, the notion of scheduling is no longer connected to the operating system but has become part of the application instead

    Coded Modulation Assisted Radial Basis Function Aided Turbo Equalisation for Dispersive Rayleigh Fading Channels

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    In this contribution a range of Coded Modulation (CM) assisted Radial Basis Function (RBF) based Turbo Equalisation (TEQ) schemes are investigated when communicating over dispersive Rayleigh fading channels. Specifically, 16QAM based Trellis Coded Modulation (TCM), Turbo TCM (TTCM), Bit-Interleaved Coded Modulation (BICM) and iteratively decoded BICM (BICM-ID) are evaluated in the context of an RBF based TEQ scheme and a reduced-complexity RBF based In-phase/Quadrature-phase (I/Q) TEQ scheme. The Least Mean Square (LMS) algorithm was employed for channel estimation, where the initial estimation step-size used was 0.05, which was reduced to 0.01 for the second and the subsequent TEQ iterations. The achievable coding gain of the various CM schemes was significantly increased, when employing the proposed RBF-TEQ or RBF-I/Q-TEQ rather than the conventional non-iterative Decision Feedback Equaliser - (DFE). Explicitly, the reduced-complexity RBF-I/Q-TEQ-CM achieved a similar performance to the full-complexity RBF-TEQ-CM, while attaining a significant complexity reduction. The best overall performer was the RBF-I/Q-TEQ-TTCM scheme, requiring only 1.88~dB higher SNR at BER=10-5, than the identical throughput 3~BPS uncoded 8PSK scheme communicating over an AWGN channel. The coding gain of the scheme was 16.78-dB

    Burst-by-Burst Adaptive Decision Feedback Equalised TCM, TTCM and BICM for H.263-Assisted Wireless Video Telephony

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    Decision Feedback Equaliser (DFE) aided wideband Burst-by-Burst (BbB) Adaptive Trellis Coded Modulation (TCM), Turbo Trellis Coded Modulation (TTCM) and Bit-Interleaved Coded Modulation (BICM) assisted H.263-based video transceivers are proposed and characterised in performance terms when communicating over the COST 207 Typical Urban wideband fading channel. Specifically, four different modulation modes, namely 4QAM, 8PSK, 16QAM and 64QAM are invoked and protected by the above-mentioned coded modulation schemes. The TTCM assisted scheme was found to provide the best video performance, although at the cost of the highest complexity. A range of lower-complexity arrangements will also be characterised. Finally, in order to confirm these findings in an important practical environment, we have also investigated the adaptive TTCM scheme in the CDMA-based Universal Mobile Telecommunications System's (UMTS) Terrestrial Radio Access (UTRA) scenario and the good performance of adaptive TTCM scheme recorded when communicating over the COST 207 channels was retained in the UTRA environment
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