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The cones of nonnegative polynomials and sums of squares arise as central objects in convex algebraic geometry and have their origin in the seminal work of Hilbert ([Hil88]). Depending on the number of variables n and the degree d of the polynomials, Hilbert famously characterizes all cases of equality between the cone of nonnegative polynomials and the cone of sums of squares. This equality precisely holds for bivariate forms, quadratic forms and ternary quartics ([Hil88]). Since then, a lot of work has been done in understanding the difference between these two cones, which has major consequences for many practical applications such as for polynomial optimization problems. Roughly speaking, minimizing polynomial functions (constrained as well as unconstrained) can be done efficiently whenever certain nonnegative polynomials can be written as sums of squares (see Section 2.3 for the precise relationship). The underlying reason is the fundamental difference that checking nonnegativity of polynomials is an NP-hard problem whenever the degree is greater or equal than four ([BCSS98]), whereas checking whether a polynomial can be written as a sum of squares is a semidefinite feasibility problem (see Section 2.2). Although the complexity status of the semidefinite feasibility problem is still an open problem, it is polynomial for fixed number of variables. Hence, understanding the difference between nonnegative polynomials and sums of squares is highly desirable both from a theoretical and a practical viewpoint.
HIV vaccine preclinical testing is difficult because HIV’s only relevant hosts are humans and no correlates of protection are known. To this end, we are working on the humanization of different mouse strains with human peripheral blood mononuclear cells (PBMCs) as well as human hematopoietic stem cells (HSC) to generate a useful small animal model.
We generated immune deficient mice (NOD Scid IL2gc -/- /NOD Rag1-/- IL2gc -/-) expressing human MHC class II (HLA-DQ8) on a mouse class II deficient background (Ab-/-). Here, the human HLA-DQ8 should interact with the matching T cell receptors of transferred matching human PBMCs and therefore could support the functionality of the transferred human CD4+ cells in the mice.
Mice that were adoptively transferred with human HLA-DQ8 PBMCs only showed engraftment of CD3+ T cells. Surprisingly, the presence of HLA class II did not significantly change the repopulation rates in the mice. Also, the presence of HLA class II did not advance B cell engraftment, such that humoral immune responses were undetectable. However, the overall survival of DQ8-expressing mice was significantly prolonged, compared to mice expressing mouse MHC class II molecules, and correlated with an increased time span until onset of GvHD.
To avoid GVHD and to increase and maintain the level of human cell reconstitution over a long period of time, the same mouse strains were reconstituted with human HSC. Compared to PBMC-repopulated mice, HSC-reconstituted mice develop almost all subpopulations of the human immune system detectable at week 12 after HSC transfer. These mice developed adaptive immune responses after Tetanus Toxoide (TT) immunizations. In addition, we are testing the susceptibility of these humanized mice to different HIV strains with a detailed look at immune responses.
Tuning and optimization of the field distribution for 4-rod radio frequency quadrupole linacs
(2014)
In this thesis, the tuning process of the 4-rod Radio Frequency Quadrupole has been analyzed and a theory for the prediction of the tuning plate's influence on the longitudinal voltage distribution was developed together with RF design options for the optimization of the fringe fields.
The basic principles of the RFQ's particle dynamics and resonant behavior are introduced in the theory part of this thesis. All studies that are presented are based on the work on four RFQs of recent linac projects. These RFQs are described in one chapter. Here, the projects are introduced together with details about the RFQ parameters and performance. In the meantime two of these RFQs are in full operation at NSCL at MSU and FNAL. One is operating in the test phase of the MedAustron Cancer Therapy Center and the fourth one for LANL is about to be built. The longitudinal voltage distribution has been studied in detail with a focus on the influence of the RF design with tuning elements and parameters like the electrodes overlap or the distance between stems. The theory for simulation methods for the field flatness that were developed as part of this thesis, as well as its simulation with CST MWS have been analyzed and compared to measurements. The lumped circuit model has proven to predict results with an accuracy that can be used in the tuning process of 4-rod RFQs. Together with results from the tuning studies, the studies on the fringe fields of the 4-rod structure lead to a proposal for a 4-rod RFQ model with an improved field distribution in the transverse and longitudinal electric field.
Fast nuclei are ionizing radiation which can cause deleterious effects to irradiated cells. The modelling of the interactions of such ions with matter and the related effects are very important to physics, radiobiology, medicine and space science and technology. A powerful method to study the interactions of ionizing radiation with biological systems was developed in the field of microdosimetry. Microdosimetry spectra characterize the energy deposition to objects of cellular size, i.e., a few micrometers.
In the present thesis the interaction of ions with tissue-like media was investigated using the Monte Carlo model for Heavy-Ion Therapy (MCHIT) developed at the Frankfurt Institute for Advanced Studies. MCHIT is a Geant4-based application intended to benchmark the physical models of Geant4 and investigate the physical properties of therapeutic ion beams. We have implemented new features in MCHIT in order to calculate microdosimetric quantities characterizing the radiation fields of accelerated nucleons and nuclei. The results of our Monte Carlo simulations were compared with recent experimental microdosimetry data.
In addition to microdosimetry calculations with MCHIT, we also investigated the biological properties of ion beams, e.g. their relative biological effectiveness (RBE), by means of the modified Microdosimetric-Kinetic model (MKM). The MKM uses microdosimetry spectra in describing cell response to radiation. MCHIT+MKM allowed us to study the physical and biological properties of ion beams. The main results of the thesis are as follows:
MCHIT is able to describe the spatial distribution of the physical dose in tissue-like media and microdosimetry spectra for ions with energies relevant to space research and ion-beam cancer therapy; MCHIT+MKM predicts a reduction of the biological effectiveness of ions propagating in extended medium due to nuclear fragmentation reactions; We predicted favourable biological dose-depth profiles for monoenergetic helium and lithium beams similar to the one for carbon beam. Well-adjusted biological dose distributions for H-1, He-4, C-12 and O-16 with a very flat spread-out Bragg peak (SOBP) plateau were calculated with MCHIT+MKM; MCHIT+MKM predicts less damage to healthy tissues in the entrance channel for SOBP He-4 and C-12 beams compared to H-1 and O-16 ones. No definitive advantages for oxygen ions with respect to carbon were found.
Bei ca. 95% der chronisch myeloischen Leukämie (CML) und 20-30% der akuten lymphatischen Leukämie (ALL) des Erwachsenen liegt eine reziproke Chromosomentranslokation t(9;22)(q34;q11) vor, in deren Rahmen das BCR (Breakpoint Cluster Region) Gen auf Chromosom 22 mit dem ABL (Abelson-Leukämie-Virus) Gen auf Chromosom 9 fusioniert. Auf Chromosom 22 gibt es zwei verschiedene Bruchpunkte, die somit zur Bildung von unterschiedlichen Fusionsgenen führen. Bei der CML findet man den sogenannten „großen“ Bruchpunkt (M-bcr), während bei der Ph+ ALL der sogenannte „kleine“ Bruchpunkt (m-bcr) vorkommt. Das hybride Fusionsgen auf Chromosom 22q+ (Philadelphia-Chromosom) kodiert für das jeweilige BCR/ABL Protein, während das Fusionsgen auf Chromosom 9q+ für das reziproke ABL/BCR Protein kodiert. Das ABL-Protein ist eine Nicht-Rezeptor Tyrosinkinase, die eine wichtige Rolle in der Signaltransduktion und der Regulation des Zellwachstums spielt. Im BCR/ABL Fusionsprotein wird die Kinase-Aktivität von ABL, die im Normalfall streng reguliert ist, durch die Fusion mit BCR konstitutiv aktiv. Dadurch kommt es zur Deregulierung intrazellulärer Signalwege, welche die maligne Transformation hämatopoetischer Zellen verursacht. Eine zielgerichtete Inhibierung von BCR/ABL mittels ABL-Kinase-Inhibitoren induziert Apoptose in BCR/ABL transformierten Zellen, was eine komplette Remission im größten Teil Ph+ Leukämie Patienten zur Folge hat.
Mathematical modeling of Arabidopsis thaliana with focus on network decomposition and reduction
(2014)
Systems biology has become an important research field during the last decade. It focusses on the understanding of the systems which emit the measured data. An important part of this research field is the network analysis, investigating biological networks. An essential point of the inspection of these network models is their validation, i.e., the successful comparison of predicted properties to measured data. Here especially Petri nets have shown their usefulness as modeling technique, coming with sound analysis methods and an intuitive representation of biological network data.
A very important tool for network validation is the analysis of the Transition-invariants (TI), which represent possible steady-state pathways, and the investigation of the liveness property. The computational complexity of the determination of both, TI and liveness property, often hamper their investigation.
To investigate this issue, a metabolic network model is created. It describes the core metabolism of Arabidopsis thaliana, and it is solely based on data from the literature. The model is too complex to determine the TI and the liveness property.
Several strategies are followed to enable an analysis and validation of the network. A network decomposition is utilized in two different ways: manually, motivated by idea to preserve the integrity of biological pathways, and automatically, motivated by the idea to minimize the number of crossing edges. As a decomposition may not be preserving important properties like the coveredness, a network reduction approach is suggested, which is mathematically proven to conserve these important properties. To deal with the large amount of data coming from the TI analysis, new organizational structures are proposed. The liveness property is investigated by reducing the complexity of the calculation method and adapting it to biological networks.
The results obtained by these approaches suggest a valid network model. In conclusion, the proposed approaches and strategies can be used in combination to allow the validation and analysis of highly complex biological networks.
Cancer is a disease characterized by uncontrolled cell growth and the capacity to disseminate to distant organs. The properties of cancers are caused by genetic and epigenetic alterations when compared to their normal counterparts. Genetic mutations occur in oncogenes and tumor suppressor genes and are the initial drivers of cellular transformation (Lengauer et al., 1998; Vogelstein and Kinzler, 2004). In addition, epigenetic alterations, which influence the expression of oncogenes and tumor suppressor genes independently from sequence alterations, are also involved in the transformation process (Esteller and Herman, 2001; Sharma et al., 2010). Genetic alterations and epigenetic regulatory signals cooperate in tumor etiology. Glioblastoma multiforme (GBM) is a frequent and aggressive malignant brain tumor in humans. The median survival of GBM patients is about 15 months after diagnosis. Like in other cancers, genetic and epigenetic alterations can be detected in GBM. Genetic alterations in GBM affect cell growth, apoptosis, angiogenesis, and invasion; however, epigenetic alterations in GBM also affect the expression of oncogenes or tumor suppresser genes that increase tumor malignancy (Nagarajan and Costello, 2009).
Reprogramming is a cellular process in which somatic cells can be induced to assume the properties of less differentiated stem cells. This process can be mediated through epigenetic modifications of the genome of somatic cells by the action of four defined transcription factors (Oct4, Sox2, Klf4 and Myc) or by the action of the miR 302/367 cluster (Anokye-Danso et al., 2011; Takahashi and Yamanaka, 2006; Takahashi et al., 2007) and result in the generation of induced pluripotent stem cells (iPS cells). Reprogramming of somatic cells by the miR 302/367 cluster can generate nontumorigenic iPS cells through the inhibition of the epithelial to mesenchymal transition (EMT), cell cycle regulatory genes and epigenetic modifiers (Lin and Ying, 2013).
We consider a class of nonautonomous nonlinear competitive parabolic systems on bounded radial domains under Neumann or Dirichlet boundary conditions. We show that, if the initial profiles satisfy a reflection inequality with respect to a hyperplane, then bounded positive solutions are asymptotically (in time) foliated Schwarz symmetric with respect to antipodal points. Additionally, a related result for (positive and sign changing solutions) of scalar equations with Neumann or Dirichlet boundary conditions is given. The asymptotic shape of solutions to cooperative systems is also discussed.
A multiple filter test for the detection of rate changes in renewal processes with varying variance
(2014)
The thesis provides novel procedures in the statistical field of change point detection in time series.
Motivated by a variety of neuronal spike train patterns, a broad stochastic point process model is introduced. This model features points in time (change points), where the associated event rate changes. For purposes of change point detection, filtered derivative processes (MOSUM) are studied. Functional limit theorems for the filtered derivative processes are derived. These results are used to support novel procedures for change point detection; in particular, multiple filters (bandwidths) are applied simultaneously in oder to detect change points in different time scales.
The human endothelin receptors, ETA and ETB, are two members of the G-protein coupled receptors family (GPCRs) and they are key players in cardiovascular regulation. The characterization of their functionality in vitro has been limited by the possibility to obtain high quality samples using conventional expression systems. The Cell-Free expression system is an alternative technique for the production of membrane protein as well as GPCRs and can overcome some of the limitations that are commonly encountered using an in vivo approach. Cell-Free expression protocols for the two receptors ETA and ETB have been optimized by implementing post- and co-translational association to lipid bilayers. The efficiency of the reconstitution or association to liposomes and nanodiscs has systematically been studied and the ligand binding properties of the two receptors have been analyzed using a set of different complementary techniques. In several different conditions a high affinity binding of the peptide ligand ET-1 to both endothelin receptors could be obtained and the highest activity values were detected in sample prepared using a co-translational approach in presence of nanodiscs. Furthermore, the characteristic differential binding pattern of selected agonists and antagonists to the two receptors was confirmed. In samples obtained from several Cell-Free expression conditions, two intrinsic properties of the functionally folded ETB receptor, such as the proteolytic processing based on conformational recognition as well as the formation of SDS-resistant complexes with the peptide ligand ET-1, were detected. ETA and ETB are able to induce in vivo the activation of hetrotrimeric G proteins upon stimulation with an agonist, leading to the dissociation of the heterotrimeric complex and the exchange of GDP to GTP in the Galpha subunit. The Cell-Free expression system was chosen for the production of two G alpha subunit, Galpha s and Galpha q. Soluble expression of the two proteins was achieved and the production of active Galpha s was confirmed using fluorescent as well as radioactive assays. In conclusion, the obtained results document a new process for the production of ligand binding competent endothelin receptors, as well as Galpha proteins, using a Cell-Free expression system. The combination of this expression system and the nanodiscs technology appears to be a promising tool for the further characterization of membrane proteins as well as GPCRs.