Hypoxia-inducible factor (HIF) network:insights from mathematical models

Oxygen is a crucial molecule for cellular function. When oxygen demand exceeds supply, the oxygen sensing pathway centred on the hypoxia inducible factor (HIF) is switched on and promotes adaptation to hypoxia by up-regulating genes involved in angiogenesis, erythropoiesis and glycolysis. The regulation of HIF is tightly modulated through intricate regulatory mechanisms. Notably, its protein stability is controlled by the oxygen sensing prolyl hydroxylase domain (PHD) enzymes and its transcriptional activity is controlled by the asparaginyl hydroxylase FIH (factor inhibiting HIF-1).To probe the complexity of hypoxia-induced HIF signalling, efforts in mathematical modelling of the pathway have been underway for around a decade. In this paper, we review the existing mathematical models developed to describe and explain specific behaviours of the HIF pathway and how they have contributed new insights into our understanding of the network. Topics for modelling included the switch-like response to decreased oxygen gradient, the role of micro environmental factors, the regulation by FIH and the temporal dynamics of the HIF response. We will also discuss the technical aspects, extent and limitations of these models. Recently, HIF pathway has been implicated in other disease contexts such as hypoxic inflammation and cancer through crosstalking with pathways like NF?B and mTOR. We will examine how future mathematical modelling and simulation of interlinked networks can aid in understanding HIF behaviour in complex pathophysiological situations. Ultimately this would allow the identification of new pharmacological targets in different disease settings.

Form follows function:model-driven engineering for clinical trials

We argue that, for certain constrained domains, elaborate model transformation technologies-implemented from scratch in general-purpose programming languages-are unnecessary for model-driven engineering; instead, lightweight configuration of commercial off-the-shelf productivity tools suffices. In particular, in the CancerGrid project, we have been developing model-driven techniques for the generation of software tools to support clinical trials. A domain metamodel captures the community's best practice in trial design. A scientist authors a trial protocol, modelling their trial by instantiating the metamodel; customized software artifacts to support trial execution are generated automatically from the scientist's model. The metamodel is expressed as an XML Schema, in such a way that it can be instantiated by completing a form to generate a conformant XML document. The same process works at a second level for trial execution: among the artifacts generated from the protocol are models of the data to be collected, and the clinician conducting the trial instantiates such models in reporting observations-again by completing a form to create a conformant XML document, representing the data gathered during that observation. Simple standard form management tools are all that is needed. Our approach is applicable to a wide variety of information-modelling domains: not just clinical trials, but also electronic public sector computing, customer relationship management, document workflow, and so on. © 2012 Springer-Verlag.

Breaks in the UK household sector money demand function

We use non-parametric procedures to identify breaks in the underlying series of UK household sector money demand functions. Money demand functions are estimated using cointegration techniques and by employing both the Simple Sum and Divisia measures of money. P-star models are also estimated for out-of-sample inflation forecasting. Our findings suggest that the presence of breaks affects both the estimation of cointegrated money demand functions and the inflation forecasts. P-star forecast models based on Divisia measures appear more accurate at longer horizons and the majority of models with fundamentals perform better than a random walk model.

Bridging large and small scales of water models using hybrid Molecular Dynamics/Fluctuating Hydrodynamics framework

This thesis presents a two-dimensional water model investigation and development of a multiscale method for the modelling of large systems, such as virus in water or peptide immersed in the solvent. We have implemented a two-dimensional ‘Mercedes Benz’ (MB) or BN2D water model using Molecular Dynamics. We have studied its dynamical and structural properties dependence on the model’s parameters. For the first time we derived formulas to calculate thermodynamic properties of the MB model in the microcanonical (NVE) ensemble. We also derived equations of motion in the isothermal–isobaric (NPT) ensemble. We have analysed the rotational degree of freedom of the model in both ensembles. We have developed and implemented a self-consistent multiscale method, which is able to communicate micro- and macro- scales. This multiscale method assumes, that matter consists of the two phases. One phase is related to micro- and the other to macroscale. We simulate the macro scale using Landau Lifshitz-Fluctuating Hydrodynamics, while we describe the microscale using Molecular Dynamics. We have demonstrated that the communication between the disparate scales is possible without introduction of fictitious interface or approximations which reduce the accuracy of the information exchange between the scales. We have investigated control parameters, which were introduced to control the contribution of each phases to the matter behaviour. We have shown, that microscales inherit dynamical properties of the macroscales and vice versa, depending on the concentration of each phase. We have shown, that Radial Distribution Function is not altered and velocity autocorrelation functions are gradually transformed, from Molecular Dynamics to Fluctuating Hydrodynamics description, when phase balance is changed. In this work we test our multiscale method for the liquid argon, BN2D and SPC/E water models. For the SPC/E water model we investigate microscale fluctuations which are computed using advanced mapping technique of the small scales to the large scales, which was developed by Voulgarakisand et. al.

The Localization Procedures of the Vector of Weighting Coefficients for Fuzzy Models of Choice

The author analyzes the localization procedures of the vector of weighting coefficients which are based on presenting the function of value by additive reduction adapted to fuzzy models of choice.

Reliability for Beta Models

In the area of stress-strength models there has been a large amount of work as regards estimation of the reliability R = Pr(X2 < X1 ) when X1 and X2 are independent random variables belonging to the same univariate family of distributions. The algebraic form for R = Pr(X2 < X1 ) has been worked out for the majority of the well-known distributions including Normal, uniform, exponential, gamma, weibull and pareto. However, there are still many other distributions for which the form of R is not known. We have identified at least some 30 distributions with no known form for R. In this paper we consider some of these distributions and derive the corresponding forms for the reliability R. The calculations involve the use of various special functions.

Structuring of Ranked Models

Prognostic procedures can be based on ranked linear models. Ranked regression type models are designed on the basis of feature vectors combined with set of relations defined on selected pairs of these vectors. Feature vectors are composed of numerical results of measurements on particular objects or events. Ranked relations defined on selected pairs of feature vectors represent additional knowledge and can reflect experts' opinion about considered objects. Ranked models have the form of linear transformations of feature vectors on a line which preserve a given set of relations in the best manner possible. Ranked models can be designed through the minimization of a special type of convex and piecewise linear (CPL) criterion functions. Some sets of ranked relations cannot be well represented by one ranked model. Decomposition of global model into a family of local ranked models could improve representation. A procedures of ranked models decomposition is described in this paper.

Comparative Analysis of Viscoelastic Models Involving Fractional Derivatives of Different Orders

Mathematics Subject Classification: 74D05, 26A33

Triangular Models and Asymptotics of Continuous Curves with Bounded and Unbounded Semigroup Generators

2000 Mathematics Subject Classification: Primary 47A48, Secondary 60G12.

Verification of Procedural Programs via Building their Generalized Nets Models

Магдалина Василева Тодорова - В статията е описан подход за верификация на процедурни програми чрез изграждане на техни модели, дефинирани чрез обобщени мрежи. Подходът интегрира концепцията “design by contract” с подходи за верификация от тип доказателство на теореми и проверка на съгласуваност на модели. За целта разделно се верифицират функциите, които изграждат програмата относно спецификации според предназначението им. Изгражда се обобщен мрежов модел, специфициащ връзките между функциите във вид на коректни редици от извиквания. За главната функция на програмата се построява обобщен мрежов модел и се проверява дали той съответства на мрежовия модел на връзките между функциите на програмата. Всяка от функциите на програмата, която използва други функции се верифицира и относно спецификацията, зададена чрез мрежовия модел на връзките между функциите на програмата.

Maximization of a Linear Utility Function over the Set of the Housing Market Short-Term Equilibria

AMS subject classification: 90C05, 90A14.

Parameterized Link Functions in Generalized Linear Random Effect Models: a Case Study on Breast Cancer Treatment

In non-linear random effects some attention has been very recently devoted to the analysis ofsuitable transformation of the response variables separately (Taylor 1996) or not (Oberg and Davidian 2000) from the transformations of the covariates and, as far as we know, no investigation has been carried out on the choice of link function in such models. In our study we consider the use of a random effect model when a parameterized family of links (Aranda-Ordaz 1981, Prentice 1996, Pregibon 1980, Stukel 1988 and Czado 1997) is introduced. We point out the advantages and the drawbacks associated with the choice of this data-driven kind of modeling. Difficulties in the interpretation of regression parameters, and therefore in understanding the influence of covariates, as well as problems related to loss of efficiency of estimates and overfitting, are discussed. A case study on radiotherapy usage in breast cancer treatment is discussed.

Multiple Dipole Source Models for Scalp-Recorded Event-Related Potentials: Example from Complex Visual Processing in the Human Brain

2000 Mathematics Subject Classification: 62P10, 92C20

A cell-permeable tool for analysing APP intracellular domain function and manipulation of PIKfyve activity

The mechanisms for regulating PIKfyve complex activity are currently emerging. The PIKfyve complex, consisting of the phosphoinositide kinase PIKfyve (also known as FAB1), VAC14 and FIG4, is required for the production of phosphatidylinositol-3,5-bisphosphate (PI(3,5)P2). PIKfyve function is required for homeostasis of the endo/lysosomal system and is crucially implicated in neuronal function and integrity, as loss of function mutations in the PIKfyve complex lead to neurodegeneration in mouse models and human patients. Our recent work has shown that the intracellular domain of the Amyloid Precursor Protein (APP), a molecule central to the aetiology of Alzheimer's disease binds to VAC14 and enhances PIKfyve function. Here we utilise this recent advance to create an easy-to-use tool for increasing PIKfyve activity in cells. We fused APP's intracellular domain (AICD) to the HIV TAT domain, a cell permeable peptide allowing proteins to penetrate cells. The resultant TAT-AICD fusion protein is cell permeable and triggers an increase of PI(3,5)P2. Using the PI(3,5)P2 specific GFP-ML1Nx2 probe we show that cell-permeable AICD alters PI(3,5)P2 dynamics. TAT-AICD also provides partial protection from pharmacological inhibition of PIKfyve. All three lines of evidence show that the APP intracellular domain activates the PIKfyve complex in cells, a finding that is important for our understanding of the mechanism of neurodegeneration in Alzheimer's disease.

Analysis of purchasing activity with discounted cash flow inventory models = Beszerzési tevékenység elemzése diszkontált pénzáramlású készletmodellel

A klasszikus tételnagyság probléma két fontosabb készletezési költséget ragad meg: rendelési és készlettartási költségek. Ebben a dolgozatban a vállalatok készpénz áramlásának a beszerzési tevékenységre gyakorolt hatását vizsgáljuk. Ebben az elemzésben a készpénzáramlási egyenlőséget használjuk, amely nagyban emlékeztet a készletegyenletekre. Eljárásunkban a beszerzési és rendelési folyamatot diszkontálva vizsgáljuk. A költségfüggvény lineáris készpénztartási, a pénzkiadás haszonlehetőség és lineáris kamatköltségből áll. Bemutatjuk a vizsgált modell optimális megoldását. Az optimális megoldást egy számpéldával illusztráljuk. = The classical economic order quantity model has two types of costs: ordering and inventory holding costs. In this paper we try to investigate the effect of purchasing activity on cash flow of a firm. In the examinations we use a cash flow identity similar to that of in inventory modeling. In our approach we analyze the purchasing and ordering process with discounted costs. The cost function of the model consists of linear cash holding, linear opportunity cost of spending cash, and linear interest costs. We show the optimal solution of the proposed model. The optimal solutions will be presented by numerical examples.