Abstract In recent years there has been a growing interest in studying bilinear time series models. However, there are difficult problems related to the order identification of these models. In this paper, we consider the bilinear time series models, Xt = BXt-k et-1 + et , k>i, k=i and k<i, and propose some methods of order identification based on the structure of autocovarance of {X2t} and the third-order-automoment of {xt}. Decision rules as well as simulated bilinear time series are compared. An advantage of our methods is its simple of implementation.

In this paper we continue the considerations of [5] (CSC/09-05). A numerical study for the parameter identification problem with linear elastic material and large deformations is presented. We discuss the numerical implementation in MATLAB and illustrate some results for a 2D test problem.

Age, period, and cohort are three temporal dimensions that can make unique contributions to social and epidemiological changes that occur in populations over time. However, while the theoretical underpinnings for each temporal dimension are well established, the statistical techniques to assess the distinctive contributions of age, period and cohort are controversial. Unless questionable assumptions are imposed on the data, traditional linear regression models are incapable of estimating the independent contribution of each temporal dimension due to the linear dependence between age, period and cohort (A=P-C). Two recently developed methods, Hierarchical Age-PeriodCohort (HAPC) and Intrinsic Estimator (IE) models, enable researchers to estimate how all three temporal dimensions contribute to an outcome of interest without resorting to such assumptions. However, some simulation studies suggest that these new methods provide biased estimates of each temporal dimension. In this dissertation, I investigated whether practitioners can avoid biased results by first understanding the structure of the data. In Chapters 2 and 3, I examined whether visual plots of descriptive statistics and model selection statistics could identify various types of data structures through a series of simulation analyses. The results showed that preliminary data analysis is useful for identifying data structures that are compatible with the assumptions of HAPC and IE models. Moreover, when the data satisfied assumptions such as three-dimensionality and slight deviations from perfect functional forms, both HAPC and IE models tended to provide unbiased estimates of age, period and cohort effects. In Chapter 4, I provided a step-by-step demonstration for applying HAPC models by investigating the unique contributions of age, period and cohort to educational inequalities in the health of a large sample of U.S. adults. This study found that age and cohort effects contribute most to variability in health, and also that cross-validation is a useful way to incorporate HAPC models when preliminary analyses do not definitively show that the data structure is three dimensional.

For channel estimation without data-induced interference in data-dependent superimposed training (DDST) scheme, the data sequence is shifted by subtracting a data-dependent sequence before added to training sequence at transmitter. The distorted term causes the data identification problem (DIP) at the receiver. In this thesis, we propose two precoding schemes based on previous work. To maintain low peak-to-average power ratio (PAPR), the precoding matrix is restricted to a diagonal matrix. The first scheme is proposed to enlarge the minimum distance between the closest codewords, termed as efficient diagonal scheme. Conditions to make sure the precoding matrix is efficient for M-ary phase shift keying (MPSK) and M-ary quadrature amplitude modulation (MQAM) modulation are listed in this paper. The second scheme pursues a lowest complexity at receiver which means the amount of searching set is reduced. It is a trade-off between the better bit error rate (BER) performance and a lower complexity at receiver. The simulation results show that PAPR have been improved and the DIP is solved in both schemes.

In this paper we discuss the identification of parameter functions in material models for elastic large deformations. A model of the the forward problem is given, where the displacement of a deformed material is found as the solution of a n onlinear PDE. Here, the crucial point is the definition of the 2nd Piola-Kirchhoff stress tensor by using several material laws including a number of material parameters. In the main part of the paper we consider the identification of such parameters from measured displacements, where the inverse problem is given as an optimal control problem. We introduce a solution of the identification problem with Lagrange and SQP methods. The presented algorithm is applied to linear elastic material with large deformations.

In this study, transmissivity and storage coefficient of a semi-infinite, confined, homogeneous and isotropic aquifer, where the flow is one-dimensional and linear, are determined using Marquardt algorithm, considering two independent cases: constant drawdown in the adjacent stream / or constant discharge from the aquifer due to pumping at a constant rate. In the first case piezometric head and discharge measurements are utilized. Hydraulic diffusivity, which is the ratio of transmissivity to storage coefficient, is determined from piezometric head measurements / whereas their product is determined from discharge measurements. Then, the two parameters are calculated easily. In the second case piezometric head observations are utilized only and transmissivity and storage coefficient are determined simultaneously. Convergence to true values is very fast for both cases even for poor initial estimates. Three examples, two using synthetic data for both cases and one using actual field data for the second case, are presented. Conventional type-curve matching method is used for comparison of the results. It is observed that the results of Marquardt algorithm are in a reasonable agreement with those of type-curve matching method.

In this paper we continue the considerations of [5] (CSC/09-05). A numerical study for the parameter identification problem with linear elastic material and large deformations is presented. We discuss the numerical implementation in MATLAB and illustrate some results for a 2D test problem.

Les lymphocytes T sont une composante essentielle du système immunitaire de l'organisme. Ils peuvent reconnaître et répondre à un antigène étranger en vertu de leur récepteur d'antigène. En effet, les cellules T qui n'ont pas encore rencontrées des antigènes, sont appelées "naïves". Lors d'un premier contact antigénique, l'expansion clonale des lymphocytes T spécifiques a un antigène augmente fortement leur fréquence, et déséquilibre transitoirement de façon plus ou moins intense le compartiment lymphocytaire T périphérique. Cet équilibre doit être rétabli pour ne pas menacer à terme le bon fonctionnement du système immunitaire. Outre le risque de réponse explosive lors d'une réexposition à l'antigène, l'accumulation de clones T de taille disproportionnée gênerait considérablement le recrutement de lymphocytes T spécifiques de nouveaux antigènes. Ainsi, après élimination de l'antigène ou son confinement dans l'organisme, différents mécanismes interviennent. Il faut en effet d'une part assurer le maintien d'un compartiment de cellules T naïves de taille suffisante pour faire face à de nouvelles stimulations antigéniques. D'autre part, la constitution d'un panel de cellules T mémoires est nécessaire pour permettre une réponse immunitaire plus rapide et plus efficace lors de réexpositions antigéniques. Donc les mécanismes d'homéostasie des cellules T sont essentielles pour maintenir le nombre de cellules T à un niveau à peu près constant en contrôlant la division cellulaire et la mortalité des cellules. [...] / T lymphocytes are a fundamental component of the immune system that can recognise and respond to foreign antigens by virtue of their clonally expressed T cell antigen receptor (TCR). T cells that have yet to encounter the antigen they recognise are termed 'naive' as they have not been activated to respond. Homeostatic mechanisms maintain the number of T cells at an approximately constant level by controling cell division and death. In normal replete hosts, cell turnover within the naive compartment is very low and naive cells are maintained in a resting state.However, disruption of the homeostatic balance can arise from a wide variety of causes (viral infection (e.g. HIV), or drugs used in peritransplant induction therapy or cancer chemotherapy) and can result in T cell deciency or T lymphopenia. Under conditions of T lymphopenia, naive T cells undergo cell division with a subtle change in the cell surface phenotype (CD44 expression), termed homeostatic proliferation or lymphopenia induced proliferation (LIP). In this thesis, our purpose is to understand the process of T cell homeostatic through mathematical approach. At first, we build a new model that describes the proliferation of T cells in vitro under lymphopenic conditions. Our nonlinear model is composed of ordinary differential equations and partial differential equations structured by age (maturity of cell) and CD44 expression. To better understand the homeostasis of T cells, we identify the parameters that define T cell division by using experimental data. Next, we consider an age-structured model system describing the T cell homeostatic in vivo, and we investigate its asymptotic behaviour. Finally, an optimal strategy is applied in the in vivo model to rebuild immunity under conditions of T lympopenia.

The numerical algorithms for non-stationary mathematical models in non-standard domains are investigated in the dissertation. The problem definition domain is represented by branching structures with conjugation equations considered at the branching points. The numerical analysis of the conjugation equations and non-classical boundary conditions distinguish considered problems among the classical problems of mathematical physics presented in the literature. The scope of the dissertation covers the investigation of stability and convergence of the numerical algorithms on branching structures with different conjugation equations, the construction and implementation of parallel algorithms, the investigation of the numerical schemes for the problems with nonlocal integral conditions. The modeling of the excitation of neuron and photoexcited carrier decay in a semiconductor, also the problem of the identification of nonlinear model are considered in the dissertation. / Disertacijoje nagrinėjami nestacionarių matematinių modelių nestandartinėse srityse skaitiniai sprendimo algoritmai. Uždavinio formulavimo sritis yra šakotosios strukturos (ang. branching structures), kurių išsišakojimo taškuose apibrežiami tvermės dėsniai. Tvermės dėsnių skaitinė analizė ir nestandartinių kraštinių sąlygų analizė skiria nagrinėjamus uždavinius nuo klasikinių aprašytų literatūroje matematinės fizikos uždaviniu. Disertacijoje suformuluoti uždaviniai apima skaitinių algoritmų šakotose struktūrose su skirtingais srautų tvermės dėsniais stabilumo ir konvergavimo tyrimą, lygiagrečiųjų algoritmų sudarymą ir taikymą, skaitinių schemų uždaviniams su nelokaliomis integralinėmis sąlygomis tyrimą. Disertacijoje sprendžiami taikomieji neurono sužadinimo ir impulso relaksacijos lazerio apšviestame puslaidininkyje uždaviniai, netiesinio modelio identifikavimo uždavinys.

In this paper we discuss the identification of parameter functions in material models for elastic large deformations. A model of the the forward problem is given, where the displacement of a deformed material is found as the solution of a n onlinear PDE. Here, the crucial point is the definition of the 2nd Piola-Kirchhoff stress tensor by using several material laws including a number of material parameters. In the main part of the paper we consider the identification of such parameters from measured displacements, where the inverse problem is given as an optimal control problem. We introduce a solution of the identification problem with Lagrange and SQP methods. The presented algorithm is applied to linear elastic material with large deformations.