400 research outputs found
The poisson process in quantum stochastic calculus
Given a compensated Poisson process based on , the Wiener-Poisson isomorphism is constructed. We restrict the isomorphism to and prove some novel properties of the Poisson exponentials . A new proof of the result is also given. The analogous results for are briefly mentioned.
The concept of a compensated Poisson process over is generalised to any measure space as an isometry satisfying certain properties. For such a generalised Poisson process we recall the construction of the generalised Wiener-Poisson isomorphism, , using Charlier polynomials. Two alternative constructions of are also provided, the first using exponential vectors and then deducing the connection with Charlier polynomials, and the second using the theory of reproducing kernel Hilbert spaces.
Given any measure space , we construct a canonical generalised Poisson process , where is the maximal ideal space, with the completion of its Borel -field with respect to , of a -algebra . The Gelfand transform is unitarily implemented by the Wiener-Poisson isomorphism . This construction only uses operator algebra theory and makes no a priori use of Poisson measures.
A new Fock space proof of the quantum Ito formula for is given. If is a real, bounded, predictable process with respect to a compensated Poisson process , we show that if , then on , and that is an essentially self-adjoint quantum semimartingale. We prove, using the classical Ito formula, that if is a regular self-adjoint quantum semimartingale, then is an essentially self-adjoint quantum semimartingale satisfying the quantum Duhamel formula, and hence the quantum Ito formula. The equivalent result for the sum of a Brownian and Poisson martingale, provided that the sum is essentially self-adjoint with core , is also proved
Cardiac Electromechanics: The effect of contraction model on the mathematical problem and accuracy of the numerical scheme
Models of cardiac electromechanics usually contain a contraction model determining the active tension induced at the cellular level, and the equations of nonlinear elasticity to determine tissue deformation in response to this active tension. All contraction models are dependent on cardiac electro-physiology, but can also be dependent on\ud
the stretch and stretch-rate in the fibre direction. This fundamentally affects the mathematical problem being solved, through classification of the governing PDEs, which affects numerical schemes that can be used to solve the governing equations. We categorise contraction models into three types, and for each consider questions such as classification and the most appropriate choice from two numerical methods (the explicit and implicit schemes). In terms of mathematical classification, we consider the question of strong ellipticity of the total strain energy (important for precluding ‘unnatural’ material behaviour) for stretch-rate-independent contraction models; whereas for stretch-rate-dependent contraction models we introduce a corresponding third-order problem and explain how certain choices of boundary condition could lead to constraints on allowable initial condition. In terms of suitable numerical methods, we show that an explicit approach (where the contraction model is integrated in the timestep prior to the bulk deformation being computed) is: (i) appropriate for stretch-independent contraction models; (ii) only conditionally-stable, with the stability criterion independent of timestep, for contractions models which just depend on stretch (but not stretch-rate), and (iii) inappropriate for stretch-rate-dependent models
A Decentralized Communication Policy for Multi Agent Multi Armed Bandit Problems
This paper proposes a novel policy for a group of agents to, individually as
well as collectively, solve a multi armed bandit (MAB) problem. The policy
relies solely on the information that an agent has obtained through sampling of
the options on its own and through communication with neighbors. The option
selection policy is based on an Upper Confidence Based (UCB) strategy while the
communication strategy that is proposed forces agents to communicate with other
agents who they believe are most likely to be exploring than exploiting. The
overall strategy is shown to significantly outperform an independent
Erd\H{o}s-R\'{e}nyi (ER) graph based random communication policy. The policy is
shown to be cost effective in terms of communication and thus to be easily
scalable to a large network of agents.Comment: This is the full version of a preprint that will appear in the
proceedings of the 2020 European Control Conference (ECC
On estimation of autoregressive conditional duration (ACD) models based on different error distributions
Autoregressive Conditional Duration (ACD) models playa central role in modelling high frequency financial data. The Maximum Likelihood (ML) and Quasi Maximum Likelihood (QML) methods are widely used in parameter estimation. This paper
considers a semi parametric approach based on the theory of Estimating Function (EF) in estimation of A CD models. We use a number of popular distributions with positive supports for errors and estimate the parameter(s) using the both EF and . ML approaches. A simulation study is conducted to compare the performance of the EF and the corresponding ML estimates for ACD(1.1), ACD(l,2) and ACD(2,l) models. It is shown that the EF approach provides comparable estimates with the ML estimates using a shorter computation time. Finally, both methods are applied to model a real financial data set and provide empirical evidence to support the use EF approach in practice
Alveolar rhabdomyosarcoma of the neck in a two-months-old baby: diagnostic challenges
Rhabdomyosarcoma (RMS) is the most common soft tissue malignancy in children and adolescents. The rarity of its occurrence in infant poses a great difficulty in terms of diagnosis and management. Here, we report an aggressive case of alveolar rhabdomyosarcoma in an infant who presented with neck swelling and neurological complications. The Magnetic Resonance Imaging (MRI) revealed a soft tissue swelling of the neck with intraspinal extension and spinal cord compression, raising the possibility of a neurogenic or malignant nerve sheath tumour. Histopathological examination revealed a primitive, small round cell tumour with no rhabdoid differentiation. The clinical presentation, neurological symptoms, tumor location and the histopathologic features were highly suggestive of neuroblastoma. However, the tumour cells were positive for desmin with focal and weak nuclear positivity for myogenin and MyoD1; immunoexpressions which were in favour of rhabdomyosarcoma. Fluorescent in situ hybridization (FISH) confirmed the presence of a translocation t(2;13)(q35;q14), supporting the diagnosis of alveolar rhabdomyosarcoma. Despite chemotherapy, patient succumbed to death after two months due to septic shock. Rhabdomyosarcoma is highly aggressive mesenchymal neoplasm which may present with diagnostic difficulty. This case highlights the importance of molecular studies in making an accurate diagnosis so that appropriate chemotherapy may be instituted
An integrative computational model for intestinal tissue renewal
Objectives\ud
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The luminal surface of the gut is lined with a monolayer of epithelial cells that acts as a nutrient absorptive engine and protective barrier. To maintain its integrity and functionality, the epithelium is renewed every few days. Theoretical models are powerful tools that can be used to test hypotheses concerning the regulation of this renewal process, to investigate how its dysfunction can lead to loss of homeostasis and neoplasia, and to identify potential therapeutic interventions. Here we propose a new multiscale model for crypt dynamics that links phenomena occurring at the subcellular, cellular and tissue levels of organisation.\ud
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Methods\ud
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At the subcellular level, deterministic models characterise molecular networks, such as cell-cycle control and Wnt signalling. The output of these models determines the behaviour of each epithelial cell in response to intra-, inter- and extracellular cues. The modular nature of the model enables us to easily modify individual assumptions and analyse their effects on the system as a whole.\ud
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Results\ud
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We perform virtual microdissection and labelling-index experiments, evaluate the impact of various model extensions, obtain new insight into clonal expansion in the crypt, and compare our predictions with recent mitochondrial DNA mutation data. \ud
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Conclusions\ud
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We demonstrate that relaxing the assumption that stem-cell positions are fixed enables clonal expansion and niche succession to occur. We also predict that the presence of extracellular factors near the base of the crypt alone suffices to explain the observed spatial variation in nuclear beta-catenin levels along the crypt axis
Recursos fitogenéticos: bases para un futuro resiliente al clima y libre de hambre en el Caribe
En toda la región Caribe, el cambio climático no solamente planteará desafíos sino también una amplia gama
de oportunidades, que ofrecen mayor importancia a la riqueza de recursos fitogenéticos de la región.
Materializar el potencial de estos recursos para contribuir a garantizar la seguridad alimentaria y crear sistemas
agrícolas más resilientes frente al cambio climático requerirá de una mayor cooperación regional. Los objetivos
centrales de esta cooperación deberán ser: desarrollar intervenciones oportunas en las fronteras nacionales que
mejoren la colecta, conservación y el intercambio de los recursos fitogenéticos
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