Innate immune signaling pathways initiate host defenses against viral pathogens. Receptors specific for viral nucleic acids activate these pathways culminating in cell-to-cell communication and/or cell death. In mammals, this cell- to-cell communication is achieved through the production of interferons and pro- inflammatory cytokines, which activate antiviral defenses in uninfected neighboring cells and instruct adaptive immune responses. The production of these signaling molecules is essential for the defense against viral infection, but must also be tightly regulated to prevent unnecessary inflammation. As an antiviral defense, cell death is also an effective mechanism to limit viral replication and spread but comes with the cost of tissue damage and inflammation. Therefore, regulating these antiviral responses is critical for controlling the spread of infection as well as preventing unnecessary pathologies related to excessive signaling. Hundreds of genes are involved in controlling these immune responses and a wide variety of mechanisms are utilized to regulate them. One mechanism to regulate gene function is the generation of protein variants through alternative translation. While polycistronic transcripts are a common feature of bacterial and viral gene expression, the process of alternative translation as a means to regulate gene function is not a feature generally attributed to mammalian mRNA. This dissertation describes a novel regulator of antiviral signaling that is generated through alternative translation. Expression of the transcript encoding the antiviral adaptor protein, MAVS, results in the production of two proteins: the full-length MAVS adaptor and a truncated variant, miniMAVS. Production of these proteins is in part regulated by cis-acting elements that control translation initiation. Production of miniMAVS regulates antiviral signaling by limiting interferon production induced by full-length MAVS, whereas both MAVS variants positively regulate cell death. To identify other examples of alternative translation in mammalian cells a genome-wide ribosomal profiling technique was used to generate a candidate list of antiviral truncation variants. This dissertation therefore demonstrates that protein variants generated through alternative translation of polycistronic mRNAs can be an effective mechanism for immune regulation and may be more common than previously understood.

Model reduction is a common theme within the simulation, control and optimization of complex dynamical systems. For instance, in control problems for partial differential equations, the associated large-scale systems have to be solved very often. To attack these problems in reasonable time it is absolutely necessary to reduce the dimension of the underlying system. We focus on model reduction by balanced truncation where a system theoretical background provides some desirable properties of the reduced-order system. The major computational task in balanced truncation is the solution of large-scale Lyapunov equations, thus the method is of limited use for really large-scale applications. We develop an effective implementation of balancing-related model reduction methods in exploiting the structure of the underlying problem. This is done by a data-sparse approximation of the large-scale state matrix A using the hierarchical matrix format. Furthermore, we integrate the corresponding formatted arithmetic in the sign function method for computing approximate solution factors of the Lyapunov equations. This approach is well-suited for a class of practical relevant problems and allows the application of balanced truncation and related methods to systems coming from 2D and 3D FEM and BEM discretizations.

In this thesis, a novel approach is presented for blade loss simulation of an aircraft gas turbine rotor mounted on rolling element bearings with squeeze film dampers, seal rub and enclosed in a flexible housing. The modal truncation augmentation (MTA) method provides an efficient tool for modeling this large order system with localized nonlinearities in the ball bearings. The gas turbine engine, which is composed of the power turbine and gas generator rotors, is modeled with 38 lumped masses. A nonlinear angular contact bearing model is employed, which has ball and race degrees of freedom and uses a modified Hertzian contact force between the races and balls and for the seal rub. This combines a dry contact force and viscous damping force. A flexible housing with seal rub is also included whose modal description is imported from ANSYS. Prediction of the maximum contact load and the corresponding stress on an elliptical contact area between the races and balls is made during the blade loss simulations. A finite-element based squeeze film damper (SFD), which determines the pressure profile of the oil film and calculates damper forces for any type of whirl orbit is utilized in the simulation. The new approach is shown to provide efficient and accurate predictions of whirl amplitudes, maximum contact load and stress in the bearings, transmissibility, thermal growths, maximum and minimum damper pressures and the amount of unbalanced force for incipient oil film cavitation. It requires about 4 times less computational time than the traditional approaches and has an error of less than 5 %.

A truncated sample consists of realizations of a pair of random variables (L, T) subject to the constraint that L ≤T. The major study interest with a truncated sample is to find the marginal distributions of L and T. Many studies have been done with the assumption that L and T are independent. We introduce a new way to specify a Cox model for a truncated sample, assuming that the truncation time is a predictor of T, and this causes the dependence between L and T. We develop an algorithm to obtain the adjusted risk sets and use the Kaplan-Meier estimator to estimate the Marginal distribution of L. We further extend our method to more practical situation, in which the Cox model includes other covariates associated with T. Simulation studies have been conducted to investigate the performances of the Cox model and the new estimators.

This thesis centers on nonparametric inferences of the cumulative hazard function of a right truncated variable. We present three variance estimators for the Nelson-Aalen estimator of the cumulative hazard function and conduct a simulation study to investigate their performances. A close match between the sampling standard deviation and the estimated standard error is observed when an estimated survival probability is not close to 1. However, the problem of poor tail performance exists due to the limitation of the proposed variance estimators. We further analyze an AIDS blood transfusion sample for which the disease latent time is right truncated. We compute three variance estimators, yielding three sets of confidence intervals. This work provides insights of two-sample tests for right truncated data in the future research.

Many statistical methods for truncated data rely on the assumption that the failure and truncation time are independent, which can be unrealistic in applications. The study cohorts obtained from bone marrow transplant (BMT) registry data are commonly recognized as truncated samples, the time-to-failure is truncated by the transplant time. There are clinical evidences that a longer transplant waiting time is a worse prognosis of survivorship. Therefore, it is reasonable to assume the dependence between transplant and failure time. To better analyze BMT registry data, we utilize a Cox analysis in which the transplant time is both a truncation variable and a predictor of the time-to-failure. An inverse-probability-weighted (IPW) estimator is proposed to estimate the distribution of transplant time. Usefulness of the IPW approach is demonstrated through a simulation study and a real application.

Cross-sectional surveys are often used in epidemiological studies to identify subjects with a disease. When estimating the survival function from onset of disease, this sampling mechanism introduces bias, which must be accounted for. If the onset times of the disease are assumed to be coming from a stationary Poisson process, this bias, which is caused by the sampling of prevalent rather than incident cases, is termed length-bias. A one-sample Kolomogorov-Smirnov type of goodness-of-fit test for right-censored length-biased data is proposed and investigated with Weibull, log-normal and log-logistic models. Algorithms detailing how to efficiently generate right-censored length-biased survival data of these parametric forms are given. Simulation is employed to assess the effects of sample size and censoring on the power of the test. Finally, the test is used to evaluate the goodness-of-fit using length-biased survival data of patients with dementia from the Canadian Study of Health and Aging.

Dans cette thèse, nous présentons des avancements récents en Théorie des Champs Doubles (TCD) et Théories des Champs Exceptionnels (TCE). Ces théories ont la particularité d’être des reformulations de supergravité dans lesquelles les symétries de dualité sont explicites avant toute réduction dimensionnelle. Ces reformulations se basent sur la définition d’un espace-temps étendu qui géométrise le groupe de T-dualité en TCD et les groupes exceptionnels de U-dualité en TCE. Tous les champs de cet espace sont soumis à une contrainte de section qui restreint leur dépendance en coordonnées. Il existe plusieurs solutions à la contrainte de section, qui correspondent donc à des théories différentes. Dans ce sens, le formalisme des théories des champs étendues amène à une unification de ces théories. De plus, grâce à un outil spécifique aux théories des champs étendues, l’ansatz de Scherk-Schwarz généralisé, il est possible de réécrire les ansatz compliqué de type Kaluza-Klein en supergravité sous une forme élégante et compacte: un produit matriciel en dimensions supérieures. Ici, nous présentons plusieurs exemples de l’efficacité de l’ansatz de Scherk-Schwarz généralisé. En particulier, nous prouvons deux conjectures concernant les troncations cohérentes: la réduction dite “de Pauli” de la corde bosonique ainsi que la supergravité de type IIB sur AdS5 x S5. La dernière application de cet ansatz concerne la théorie de type IIB généralisée, apparue récemment dans l’étude des système intégrables, et son plongement dans la TCE E6(6). Enfin, nous présentons la complétion supersymétrique de la TCE E8(8) bosonique. / In this thesis, recent developments in Double Field Theory (DFT) and Exceptional Field Theory (EFT) are presented. They are reformulation of supergravity in which duality symmetries are made manifest before dimensional reduction. This is achieved through the definition of an extended spacetime that “geometrises” the T-duality group O(d,d) in DFT and exceptional U-duality groups in EFT. All functions on this extended space are subject to a covariant `section constraint', whose solutions then restrict the coordinates dependency of the fields. There exist different solutions to the section constraint that correspond to different theories. In this sense, different theories are unified within the formalism of extended field theories. Moreover, extended field theories possess a powerful tool to study compactifications: the generalised Scherk-Schwarz ansatz.Here, we present several examples of the effectiveness of the generalised Scherk-Schwarz ansatz. In particular, we proved two conjectures regarding consistent truncations: the so-called Pauli reduction of the bosonic string on group manifolds and type IIB supergravity on AdS5 x S5. Another application is presented on the embedding of generalised type IIB within the E6(6) EFT, which recently appeared in the study of integrable systems.Finally, we present the supersymmetric completion of the bosonic E8(8) EFT.

Cross-sectional surveys are often used in epidemiological studies to identify subjects with a disease. When estimating the survival function from onset of disease, this sampling mechanism introduces bias, which must be accounted for. If the onset times of the disease are assumed to be coming from a stationary Poisson process, this bias, which is caused by the sampling of prevalent rather than incident cases, is termed length-bias. A one-sample Kolomogorov-Smirnov type of goodness-of-fit test for right-censored length-biased data is proposed and investigated with Weibull, log-normal and log-logistic models. Algorithms detailing how to efficiently generate right-censored length-biased survival data of these parametric forms are given. Simulation is employed to assess the effects of sample size and censoring on the power of the test. Finally, the test is used to evaluate the goodness-of-fit using length-biased survival data of patients with dementia from the Canadian Study of Health and Aging.

In recent years, advances in computer technology combined with new ab initio computational methods have allowed for dramatic improvement in the prediction of energetic properties. Unfortunately, even with these advances, the extensive computational cost, in terms of computer time, memory, and disk space of the sophisticated methods required to achieve chemical accuracy - defined as 1 kcal/mol from reliable experimental data effectively - limits the size of molecules [i.e. less than 10-15 non-hydrogen atoms] that can be studied. Several schemes were explored to help reduce the computational cost while still maintaining chemical accuracy. Specifically, a study was performed to assess the accuracy of ccCA to compute atomization energies, ionization potentials, electron affinities, proton affinities, and enthalpies of formation for third-row (Ga-Kr) containing molecules. Next, truncation of the correlation consistent basis sets for the hydrogen atom was examined as a possible means to reduce the computational cost of ab initio methods. It was determined that energetic properties could be extrapolated to the complete basis set (CBS) limit utilizing a series of truncated hydrogen basis sets that was within 1 kcal/mol of the extrapolation of the full correlation consistent basis sets. Basis set truncation for the hydrogen atom was then applied to ccCA in the development of two reduced basis set composite methods, ccCA(aug) and ccCA(TB). The effects that the ccCA(aug) and ccCA(TB) methods had upon enthalpies of formation and the overall percent disk space saved as compared to ccCA was examined for the hydrogen containing molecules of the G2/97 test suite. Additionally, the Weizmann-n (Wn) methods were utilized to compute the several properties for the alkali metal hydroxides as well as the ground and excited states of the alkali monoxides anion and radicals. Finally, a multi-reference variation to the correlation consistent Composite Approach [MR-ccCA] was presented and utilized in the computation of the potential energy surfaces for the N2 and C2 molecules.