Mathematical modeling and evolution of signal transduction pathways and networks

Magdeburg, Univ., Fak. für Naturwiss., Diss., 2013

Mathematical models of influenza A virus infection : from intracellular replication to virus growth in cell populations

Magdeburg, Univ., Fak. für Verfahrens- und Systemtechnik, Diss., 2015

Optimal designs for the prediction in hierarchical random coefficient regression models

Magdeburg, Univ., Fak. für Mathematik, Diss., 2015

In search of mathematical primitives for deriving universal projective hash families

We provide some guidelines for deriving new projective hash families of cryptographic interest. Our main building blocks are so called group action systems; we explore what properties of this mathematical primitives may lead to the construction of cryptographically useful projective hash families. We point out different directions towards new constructions, deviating from known proposals arising from Cramer and Shoup's seminal work.

A mathematical model to describe fat oxidation kinetics during graded exercise.

PURPOSE: The purpose of this study was to develop a mathematical model (sine model, SIN) to describe fat oxidation kinetics as a function of the relative exercise intensity [% of maximal oxygen uptake (%VO2max)] during graded exercise and to determine the exercise intensity (Fatmax) that elicits maximal fat oxidation (MFO) and the intensity at which the fat oxidation becomes negligible (Fatmin). This model included three independent variables (dilatation, symmetry, and translation) that incorporated primary expected modulations of the curve because of training level or body composition. METHODS: Thirty-two healthy volunteers (17 women and 15 men) performed a graded exercise test on a cycle ergometer, with 3-min stages and 20-W increments. Substrate oxidation rates were determined using indirect calorimetry. SIN was compared with measured values (MV) and with other methods currently used [i.e., the RER method (MRER) and third polynomial curves (P3)]. RESULTS: There was no significant difference in the fitting accuracy between SIN and P3 (P = 0.157), whereas MRER was less precise than SIN (P < 0.001). Fatmax (44 +/- 10% VO2max) and MFO (0.37 +/- 0.16 g x min(-1)) determined using SIN were significantly correlated with MV, P3, and MRER (P < 0.001). The variable of dilatation was correlated with Fatmax, Fatmin, and MFO (r = 0.79, r = 0.67, and r = 0.60, respectively, P < 0.001). CONCLUSIONS: The SIN model presents the same precision as other methods currently used in the determination of Fatmax and MFO but in addition allows calculation of Fatmin. Moreover, the three independent variables are directly related to the main expected modulations of the fat oxidation curve. SIN, therefore, seems to be an appropriate tool in analyzing fat oxidation kinetics obtained during graded exercise.

Risk prediction of prevalent diabetes in a Swiss population using a weighted genetic score--the CoLaus Study.

AIMS/HYPOTHESIS: Several susceptibility genes for type 2 diabetes have been discovered recently. Individually, these genes increase the disease risk only minimally. The goals of the present study were to determine, at the population level, the risk of diabetes in individuals who carry risk alleles within several susceptibility genes for the disease and the added value of this genetic information over the clinical predictors. METHODS: We constructed an additive genetic score using the most replicated single-nucleotide polymorphisms (SNPs) within 15 type 2 diabetes-susceptibility genes, weighting each SNP with its reported effect. We tested this score in the extensively phenotyped population-based cross-sectional CoLaus Study in Lausanne, Switzerland (n = 5,360), involving 356 diabetic individuals. RESULTS: The clinical predictors of prevalent diabetes were age, BMI, family history of diabetes, WHR, and triacylglycerol/HDL-cholesterol ratio. After adjustment for these variables, the risk of diabetes was 2.7 (95% CI 1.8-4.0, p = 0.000006) for individuals with a genetic score within the top quintile, compared with the bottom quintile. Adding the genetic score to the clinical covariates improved the area under the receiver operating characteristic curve slightly (from 0.86 to 0.87), yet significantly (p = 0.002). BMI was similar in these two extreme quintiles. CONCLUSIONS/INTERPRETATION: In this population, a simple weighted 15 SNP-based genetic score provides additional information over clinical predictors of prevalent diabetes. At this stage, however, the clinical benefit of this genetic information is limited.

Efficient knowledge retrieval to calibrate input variables in forest fire prediction

Forest fires are a serious threat to humans and nature from an ecological, social and economic point of view. Predicting their behaviour by simulation still delivers unreliable results and remains a challenging task. Latest approaches try to calibrate input variables, often tainted with imprecision, using optimisation techniques like Genetic Algorithms. To converge faster towards fitter solutions, the GA is guided with knowledge obtained from historical or synthetical fires. We developed a robust and efficient knowledge storage and retrieval method. Nearest neighbour search is applied to find the fire configuration from knowledge base most similar to the current configuration. Therefore, a distance measure was elaborated and implemented in several ways. Experiments show the performance of the different implementations regarding occupied storage and retrieval time with overly satisfactory results.

A musculoskeletal shoulder model based on pseudo-inverse and null-space optimization.

The goal of the present work was assess the feasibility of using a pseudo-inverse and null-space optimization approach in the modeling of the shoulder biomechanics. The method was applied to a simplified musculoskeletal shoulder model. The mechanical system consisted in the arm, and the external forces were the arm weight, 6 scapulo-humeral muscles and the reaction at the glenohumeral joint, which was considered as a spherical joint. The muscle wrapping was considered around the humeral head assumed spherical. The dynamical equations were solved in a Lagrangian approach. The mathematical redundancy of the mechanical system was solved in two steps: a pseudo-inverse optimization to minimize the square of the muscle stress and a null-space optimization to restrict the muscle force to physiological limits. Several movements were simulated. The mathematical and numerical aspects of the constrained redundancy problem were efficiently solved by the proposed method. The prediction of muscle moment arms was consistent with cadaveric measurements and the joint reaction force was consistent with in vivo measurements. This preliminary work demonstrated that the developed algorithm has a great potential for more complex musculoskeletal modeling of the shoulder joint. In particular it could be further applied to a non-spherical joint model, allowing for the natural translation of the humeral head in the glenoid fossa.

Validity of impedance-based equations for the prediction of total body water as measured by deuterium dilution in African women.

BACKGROUND: Little information is available on the validity of simple and indirect body-composition methods in non-Western populations. Equations for predicting body composition are population-specific, and body composition differs between blacks and whites. OBJECTIVE: We tested the hypothesis that the validity of equations for predicting total body water (TBW) from bioelectrical impedance analysis measurements is likely to depend on the racial background of the group from which the equations were derived. DESIGN: The hypothesis was tested by comparing, in 36 African women, TBW values measured by deuterium dilution with those predicted by 23 equations developed in white, African American, or African subjects. These cross-validations in our African sample were also compared, whenever possible, with results from other studies in black subjects. RESULTS: Errors in predicting TBW showed acceptable values (1.3-1.9 kg) in all cases, whereas a large range of bias (0.2-6.1 kg) was observed independently of the ethnic origin of the sample from which the equations were derived. Three equations (2 from whites and 1 from blacks) showed nonsignificant bias and could be used in Africans. In all other cases, we observed either an overestimation or underestimation of TBW with variable bias values, regardless of racial background, yielding no clear trend for validity as a function of ethnic origin. CONCLUSIONS: The findings of this cross-validation study emphasize the need for further fundamental research to explore the causes of the poor validity of TBW prediction equations across populations rather than the need to develop new prediction equations for use in Africa.

Semigroup analysis of structured populations with distributed states-at-birth arising in mathematical aquaculture

Motivated by the modelling of structured parasite populations in aquaculture we consider a class of physiologically structured population models, where individuals may be recruited into the population at different sizes in general. That is, we consider a size-structured population model with distributed states-at-birth. The mathematical model which describes the evolution of such a population is a first order nonlinear partial integro-differential equation of hyperbolic type. First, we use positive perturbation arguments and utilise results from the spectral theory of semigroups to establish conditions for the existence of a positive equilibrium solution of our model. Then we formulate conditions that guarantee that the linearised system is governed by a positive quasicontraction semigroup on the biologically relevant state space. We also show that the governing linear semigroup is eventually compact, hence growth properties of the semigroup are determined by the spectrum of its generator. In case of a separable fertility function we deduce a characteristic equation and investigate the stability of equilibrium solutions in the general case using positive perturbation arguments.

Patients' prediction of extubation success.

The spontaneous breathing trial (SBT)-relying on objective criteria assessed by the clinician-is the major diagnostic tool to determine if patients can be successfully extubated. However, little is known regarding the patient's subjective perception of autonomous breathing. We performed a prospective observational study in 211 mechanically ventilated adult patients successfully completing a SBT. Patients were randomly assigned to be interviewed during this trial regarding their prediction of extubation success. We compared post-extubation outcomes in three patient groups: patients confident (confidents; n = 115) or not (non-confidents; n = 38) of their extubation success and patients not subjected to interview (control group; n = 58). Extubation success was more frequent in confidents than in non-confidents (90 vs. 45%; p < 0.001/positive likelihood ratio = 2.00) or in the control group (90 vs. 78%; p = 0.04). On the contrary, extubation failure was more common in non-confidents than in confidents (55 vs. 10%; p < 0.001/negative likelihood ratio = 0.19). Logistic regression analysis showed that extubation success was associated with patient's prediction [OR (95% CI): 9.2 (3.74-22.42) for confidents vs.non-confidents] as well as to age [0.72 (0.66-0.78) for age 75 vs. 65 and 1.31 (1.28-1.51) for age 55 vs. 65]. Our data suggest that at the end of a sustained SBT, extubation success might be correlated to the patients' subjective perception of autonomous breathing. The results of this study should be confirmed by a large multicenter trial.

The feasibility of forecasting influenza epidemics in Cuba

A large influenza epidemic took place in Havana during the winter of 1988. The epidemiologic surveillance unit of the Pedro Kouri Institute of Tropical Medicine detected the begining of the epidemic wave. The Rvachev-Baroyan mathematical model of the geographic spread of an epidemic was used to forecast this epidemic under routine conditions of the public health system. The expected number of individuals who would attend outpatient services, because of influenza-like illness, was calculated and communicated to the health authorities within enough time to permit the introduction of available control measures. The approximate date of the epidemic peak, the daily expected number of individuals attending medical services, and the approximate time of the end of the epidemic wave were estimated. The prediction error was 12%. The model was sufficienty accurate to warrant its use as a pratical forecasting tool in the Cuban public health system.

Psychoses a l'adolescence, les neurosciences ameliorent-elles la prediction? [Adolescent psychosis, can neuroscience improve prediction?]

Developments in the field of neuroscience have created a high level of interest in the subject of adolescent psychosis, particularly in relation to prediction and prevention. As the medical practice of adolescent psychosis and its treatment is characterised by a heterogeneity which is both symptomatic and evolutive, the somewhat poor prognosis of chronic development justifies the research performed: apparent indicators of schizophrenic disorders on the one hand and specific endophenotypes on the other are becoming increasingly important. The significant progresses made on the human genome show that the genetic predetermination in current psychiatric pathologies is complex and subject to moderating effects and there is therefore significant potential for nature-nurture interactions (between the environment and the genes). The road to be followed in researching the phenotypic expression of a psychosis gene is long and winding and is susceptible to many external influences at various levels with different effects. Neurobiological, neurophysiological, neuropsychological and neuroanatomical studies help to identify endophenotypes, which allow researchers to create identifying "markers" along this winding road. The endophenotypes could make it possible to redefine the nosological categories and enhance understanding of the physiopathology of schizophrenia. In a predictive approach, large-scale retrospective and prospective studies make it possible to identify risk factors, which are compatible with the neurodevelopmental hypothesis of schizophrenia. However, the predictive value of such markers or risk indicators is not yet sufficiently developed to offer a reliable early-detection method or possible schizophrenia prevention measures. Nonetheless, new developments show promise against the background of a possible future nosographic revolution, based on a paradigm shift. It is perhaps on the basis of homogeneous endophenotypes in particular that we will be able to understand what protects against, or indeed can trigger, psychosis irrespective of the clinical expression or attempts to isolate the common genetic and biological bases according to homogeneous clinical characteristics, which have to date, proved unsuccessful