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Stochastic Integration for Levy Processes with Values in Banach Spaces
Get PDFA stochastic integral of Banach space valued deterministic functions with respect to Banach space valued
Levy processes is defined. There are no conditions on the Banach spaces nor on the Levy processes. The
integral is defined analogously to the Pettis integral. The integrability of a function is characterized by
means of a radonifying property of an integral operator associated to the integrand. The integral is used to
prove a Levy-Ito decomposition for Banach space valued Levy processes and to study existence and
uniqueness of solutions of stochastic Cauchy problems driven by Levy processes
Nonparametric Regression of Covariance Structures in Longitudinal Studies
Get PDFIn this paper we propose a nonparametric data-driven approach to model
covariance structures for longitudinal data. Based on a modi¯ed Cholesky decomposition,
the within-subject covariance matrix is decomposed into a unit lower triangular matrix in-
volving generalized autoregressive coe±cients and a diagonal matrix involving innovation
variances. Local polynomial smoothing estimation is proposed to model the nonpara-
metric smoothing functions of the mean, generalized autoregressive coe±cients and (log)
innovation variances, simultaneously. We provide theoretical justi¯cation of consistency of
the ¯tted smoothing curves in the mean, generalized autoregressive parameters and (log)
innovation variances. Two real data sets are analyzed for illustration. Simulation studies
are made to evaluate the e±cacy of the proposed method
Semiparametric Mean-Covariance Regression Analysis for Longitudinal Data
Get PDFE±cient estimation of the regression coe±cients in longitudinal data anal-
ysis requires a correct speci¯cation of the covariance structure. Existing ap-
proaches usually focus on modeling the mean with speci¯cation of certain co-
variance structures, which may lead to ine±cient or biased estimators of pa-
rameters in the mean if misspeci¯cation occurs. In this paper, we propose a
data-driven approach based on semiparametric regression models for the mean
and the covariance simultaneously, motivated by the modi¯ed Cholesky de-
composition. A regression spline based approach using generalized estimating equations is developed to estimate the parameters in the mean and the covari-
ance. The resulting estimators for the regression coe±cients in both the mean
and the covariance are shown to be consistent and asymptotically normally dis-
tributed. In addition, the nonparametric functions in these two structures are
estimated at their optimal rate of convergence. Simulation studies and a real
data analysis show that the proposed approach yields highly e±cient estimators
for the parameters in the mean, and provides parsimonious estimation for the
covariance structure
Capturing the essence of a metabolic network: A flux balance analysis approach
Get PDFAs genome-scale metabolic reconstructions emerge, tools to manage their size and complexity will be increasingly important. Flux Balance Analysis (FBA) is a constraint-based approach widely used to study the metabolic capabilities of cellular or subcellular systems. FBA problems are highly underdetermined and many different phenotypes can satisfy any set of constraints through which the metabolic system is represented.
Two of the main concerns in FBA are exploring the space of solutions for a given metabolic network and finding a specific phenotype which is representative for a given task such as maximal growth rate. Here we introduce a recursive algorithm suitable for overcoming both of these concerns. The method proposed is able to find the alternate optimal patterns of active reactions of a FBA problem and identify the minimal subnetwork able to perform a specific task as optimally as the whole.
Our method represents an alternative to and an extension of other approaches conceived for exploring the space of solutions of an FBA problem. It may also be particularly helpful in defining a scaffold of reactions upon which to build up a dynamic model, when the important pathways of the system have not yet been well-defined
R-groups and geometric structure in the representation theory of SL(N)
Get PDFLet be a nonarchimedean local field of characteristic zero and let . This article is devoted to studying the influence of the elliptic representations of on the -theory. We provide full arithmetic details. This study reveals an intricate geometric structure. One point of interest is that the -group is realized as an isotropy group. Our results illustrate, in a special case, part (3) of the recent conjecture in \cite{ABP}
The structure of blocks with a Klein four defect group
Get PDFWe prove Erdmann's conjecture stating that every block with a Klein four defect group has a simple module with trivial source, and deduce from this that Puig's finiteness conjecture holds for source algebras of blocks with a Klein four defect group. The proof uses the classification of finite simple groups
Developing a High-Performance Computing/Numerical Analysis Roadmap
No full textA roadmap activity in the UK has leveraged US and European
efforts for identifying the challenges and barriers in
the development of high-performance computing (HPC)
algorithms and software. The activity has identified the
Grand Challenge to provide:
1. Algorithms and software that application developers
can reuse in the form of high-quality, high performance,
sustained software components, libraries
and modules
2. A community environment that allows the sharing of
software, communication of interdisciplinary knowledge
and the development of appropriate skills.
Through a series of workshops and discussions with UK
HPC application groups and numerical analysts, five areas
of challenge have emerged
Towards a genome-scale kinetic model of cellular metabolism
No full textBackground:
Advances in bioinformatic techniques and analyses have led to the availability of genome-scale metabolic reconstructions. The size and complexity of such networks often means that their potential behaviour can only be analysed with constraint-based methods. Whilst requiring minimal experimental data, such methods are unable to give insight into cellular substrate concentrations. Instead, the long-term goal of systems biology is to use kinetic modelling to characterize fully the mechanics of each enzymatic reaction, and to combine such knowledge to predict system behaviour.
Results:
We describe a method for building a parameterized genome-scale kinetic model of a metabolic network. Simplified linlog kinetics are used and the parameters are extracted from a kinetic model repository. We demonstrate our methodology by applying it to yeast metabolism. The resultant model has 956 metabolic reactions involving 820 metabolites, and, whilst approximative, has considerably broader remit than any existing models of its type. Control analysis is used to identify key steps within the system.
Conclusions:
Our modelling framework may be considered a stepping-stone toward the long-term goal of a fully-parameterized model of yeast metabolism. The model is available in SBML format from the BioModels database and at http://www.mcisb.org/resources/genomescale/
A new bound for the smallest x with \pi(x) > \li(x)
Get PDFWe reduce the leading term in Lehman's theorem. This improved estimate allows us to refine the main theorem of Bays & Hudson[2]. Entering 2,000,000 zeta zeros, we prove that there exists x in the interval [exp(727.951858), exp(727.952178)] for which \pi(x) - li(x) > 3.2 \times 10^151. There are at least 10^154 successive integers x in this interval for which \pi(x) > li(x). This interval is strictly a sub-interval of the interval in Bays & Hudson, and is narrower by a factor of about 12
State constrained reachability for stochastic hybrid systems
Get PDFThe stochastic hybrid systems constitute well established classes of realistic models of hybrid discrete/continuous dynamics subject to random perturbations, autonomous uncontrollable transitions, nondeterminism or uncertainty. Stochastic reachability analysis is a key factor in the verification and deployment of stochastic hybrid systems. The encouraging recent progress prompts us to rene the problem to cover more realistic situations. We extend the so called constrained reachability problem from the probabilistic discrete case to stochastic hybrid systems. Then we dene mathematically this problem, and we obtain the reach probabilities as solutions of a boundary value problem. The last problem is well studied and numerical, even symbolic solutions exist. This characterization is useful in stochastic control, in probabilistic path planning and for nano-systems