We are interested in modeling the Darwinian evolution of a population described by two levels of biological parameters: individuals characterized by an heritable phenotypic trait submitted to mutation and natural selection and cells in these individuals influencing their ability to consume resources and to reproduce. Our models are rooted in the microscopic description of a random (discrete) population of individuals characterized by one or several adaptive traits and cells characterized by their type. The population is modeled as a stochastic point process whose generator captures the probabilistic dynamics over continuous time of birth, mutation and death for individuals and birth and death for cells. The interaction between individuals (resp. between cells) is described by a competition between individual traits (resp. between cell types). We are looking for tractable large population approximations. By combining various scalings on population size, birth and death rates and mutation step, the single microscopic model is shown to lead to contrasting nonlinear macroscopic limits of different nature: deterministic approximations, in the form of ordinary, integro- or partial differential equations, or probabilistic ones, like stochastic partial differential equations or superprocesses.

Kinesin-1 transports various cargos along the axon, while the light chain subunits play a role in selecting the types of cargos to transport. However, the mechanisms of cargo recognition and interaction have yet to be characterized. Both c-Jun kinase-interacting protein-1 (JIP1) and alcadein-1 (ALC1) are kinesin-1 cargos and compete with each other for the axonal transport machinery. I identified two polar patches of KLC1 that play a role in the interactions with JIP1 and ALC1, respectively. The main components of these two polar patches are asparagine “clamps” surrounded by positively charged lysines. Consistent with this finding, negatively charged residues of JIP1 and ALC1 are required to interact with KLC1. By structural modeling, I narrowed down the possible key residues of KLC1 that are required for interaction with c-Jun kinase interacting protein-3 (JIP3). Together, these findings reveal the versatility of KLC in the mode of interaction with many different cargos.

Kinesin-1 transports various cargos along the axon, while the light chain subunits play a role in selecting the types of cargos to transport. However, the mechanisms of cargo recognition and interaction have yet to be characterized. Both c-Jun kinase-interacting protein-1 (JIP1) and alcadein-1 (ALC1) are kinesin-1 cargos and compete with each other for the axonal transport machinery. I identified two polar patches of KLC1 that play a role in the interactions with JIP1 and ALC1, respectively. The main components of these two polar patches are asparagine “clamps” surrounded by positively charged lysines. Consistent with this finding, negatively charged residues of JIP1 and ALC1 are required to interact with KLC1. By structural modeling, I narrowed down the possible key residues of KLC1 that are required for interaction with c-Jun kinase interacting protein-3 (JIP3). Together, these findings reveal the versatility of KLC in the mode of interaction with many different cargos.

The thesis considers the Ginzburg-Landau process on the lattice $\Z^d$ whose potential is a bounded perturbation of the Gaussian potential. For such processes the thesis establishes the decay rate to equilibrium in the variance sense is $C_g t^{-d/2} + o\left(t^{-d/2}\right)$, for any local function $g$ that is bounded, mean zero, and having finite triple norm; $\triplenorm{g}=\sum_{x \in \Z^d} \norm{\partial_{\eta(x)}g}_\infty.$ The constant $C_g$ is computed explicitly. This extends the decay to equilibrium result of Janvresse, Landim, Quastel, and Yau [JLQY99] for zero-range process, and the related result of Landim and Yau [LY03] for Ginzburg-Landau processes. The thesis also considers additive functionals $\int_{0}^{t} g(\eta_s) ds$ of Ginzburg-Landau processes, where $g$ is a bounded, mean zero, local function having finite triple norm. A central limit is proven for $a^{-1}(t)\int_{0}^{t} g(\eta_s) ds$ with $a(t)= \sqrt{t}$ in $d \ge 3$, $a(t)=\sqrt{t \log{t}}$ in $d=2$, and $a(t)= t^{3/4}$ in $d=1$ and an explicit form of the asymptotic variance in each case. Corresponding invariance principles are also obtained. Standard arguments of Kipnis and Varadhan [KV86] are employed in the case $d \ge 3$. Martingale methods together with $L^2$ decay estimates for the semigroup associated with the process are employed to establish the result in the cases $d=1$ and $d=2$. This extends similar results for noninteracting random walks (see[CG84]), the symmetric simple exclusion processes (see [Kip87]), and the zero-range process (see [QJS02]).

The thesis considers the Ginzburg-Landau process on the lattice $\Z^d$ whose potential is a bounded perturbation of the Gaussian potential. For such processes the thesis establishes the decay rate to equilibrium in the variance sense is $C_g t^{-d/2} + o\left(t^{-d/2}\right)$, for any local function $g$ that is bounded, mean zero, and having finite triple norm; $\triplenorm{g}=\sum_{x \in \Z^d} \norm{\partial_{\eta(x)}g}_\infty.$ The constant $C_g$ is computed explicitly. This extends the decay to equilibrium result of Janvresse, Landim, Quastel, and Yau [JLQY99] for zero-range process, and the related result of Landim and Yau [LY03] for Ginzburg-Landau processes. The thesis also considers additive functionals $\int_{0}^{t} g(\eta_s) ds$ of Ginzburg-Landau processes, where $g$ is a bounded, mean zero, local function having finite triple norm. A central limit is proven for $a^{-1}(t)\int_{0}^{t} g(\eta_s) ds$ with $a(t)= \sqrt{t}$ in $d \ge 3$, $a(t)=\sqrt{t \log{t}}$ in $d=2$, and $a(t)= t^{3/4}$ in $d=1$ and an explicit form of the asymptotic variance in each case. Corresponding invariance principles are also obtained. Standard arguments of Kipnis and Varadhan [KV86] are employed in the case $d \ge 3$. Martingale methods together with $L^2$ decay estimates for the semigroup associated with the process are employed to establish the result in the cases $d=1$ and $d=2$. This extends similar results for noninteracting random walks (see[CG84]), the symmetric simple exclusion processes (see [Kip87]), and the zero-range process (see [QJS02]).

We present a dynamic asset pricing model based on a heterogenous class of traders. These traders are homogenous in the sense that they are fundamentalists who base their investment decisions on an exogenoulsy given fundamental value. They are heterogenous in the sense that each trader is working with a different frequency of the underlying price data. As a result we have a system of interacting investors who together influence the market price. We derive a system that characterizes out-of-equilibrium dynamics of prices in this market which is structurally equivalent to the Nosé-Hoover thermostat equation in non-equilibrium thermodynamics. We explore the time series properties of these prices and find that they exhibit fat tails of returns distributions, volatility clustering and power laws. (author's abstract) / Series: Working Papers SFB "Adaptive Information Systems and Modelling in Economics and Management Science"

<p>The 1D Wigner crystal is a long sought after strongly correlated quantum state. Here we present electronic transport data of asymmetric quantum point contacts (QPC) tuned to the spin-incoherent regime, which provides evidence for achieving the 1D Wigner state. Our result can be distinguished in several particularly noticeable ways. First, we utilize an asymmetric point contact geometry that is simple to fabricate and has not been studied previously. We are able to tune to the conductance anomalies simply by asymmetrically applying voltages to the gates. Second, we observe clear suppression of the first plateau and direct jumps to the second in these asymmetric QPCs at liquid helium temperatures (4.2 K). Such conductance behavior is indicative of Wigner crystal row formation.</p> <p>This thesis suggests that the novel geometry and gating scheme allows for a novel way to search for strongly correlated electronic behavior in quasi-1D quantum wires. A key finding is the importance of asymmetric QPCs for observation of anomalous transport characteristics. We have observed a strongly developed e<super>2</super>/h feature under asymmetric voltage gating and zero applied magnetic field. Such a feature is attributed to enhanced spin energies in the system. We believe the asymmetric design allows for a relaxing of the 1D confinement so that a quasi-1D electron conformation develops, which in turn allows for various possible magnetic states. In addition, by optimally tuning the confinement potential, we observe an unexpected suppression of the 2e<super>2</super>/h plateau. This provides further evidence for unusual electron arrangements in the asymmetric quantum point contact.</p> <p>I also discuss transport studies on the new FeSe superconductor. Our collaboration discovered the superconducting &beta;-FeSe compound with a Tc approximately 8 K. The crystal lattice structure of &beta;-FeSe is by far the simplest of the Fe superconductors. One of the most interesting observations regarding FeSe is that the crystal structure undergoes a structural transition at approximately 105 K from tetragonal to orthorhombic (or triclinic) symmetry. We believe this structural transition to be closely related to the origin of superconductivity in this class of materials.</p> <p>Transport studies also seem to support this claim. From Hall effect measurements of bulk FeSe, we find that FeSe is likely a two band (electron and hole) superconductor, which suggests it is quite different from the cuprates, and that very unconventional superconducting mechanisms are at play. The temperature dependence of the Hall coefficient is measured, and found to rapidly increase below 105 K. This suggests the scattering time related to hole bands dominate the transport at low temperature. As there is no magnetic ordering observed at low temperature, we do not expect the scattering from random Fe magnetic impurities to play a significant role in the enhanced hole scattering times. Thus, we speculate that this change is related to the structural transition observed.</p> / Dissertation

A new approach to the process of Directed Evolution is proposed, which utilizes different machine learning algorithms. Directed Evolution is a process of improving a protein for catalytic purposes by introducing random mutations in its sequence to create variants. Through these mutations, Directed Evolution explores the sequence space, which is defined as all the possible sequences for a given number of amino acids. Each variant sequence is divided into one of two classes, positive or negative, according to their activity or stability. By employing machine learning algorithms for feature selection on the sequence of these variants of the protein, attributes or amino acids in its sequence important for the classification into positive or negative, can be identified. Support Vector Machines (SVMs) were utilized to identify the important individual amino acids for any protein, which have to be preserved to maintain its activity. The results for the case of beta-lactamase show that such residues can be identified with high accuracy while using a small number of variant sequences. Another class of machine learning problems, Boolean Learning, was used to extend this approach to identifying interactions between the different amino acids in a proteins sequence using the variant sequences. It was shown through simulations that such interactions can be identified for any protein with a reasonable number of variant sequences. For experimental verification of this approach, two fluorescent proteins, mRFP and DsRed, were used to generate variants, which were screened for fluorescence. Using Boolean Learning, an interacting pair was identified, which was shown to be important for the fluorescence. It was also shown through experiments and simulations that knowing such pairs can increase the fraction active variants in the library. A Boolean Learning algorithm was also developed for this application, which can learn Boolean functions from data in the presence of classification noise.

In solving target tracking problems, the Kalman filter (KF) is a systematic estimation algorithm. Whether the state of a moving target adapts to the changes in the observations depends on the model assumptions. The interacting multiple model (IMM) algorithm uses interaction of a bank of parallel KFs by updating associated model probabilities. Every parallel KF has its model probability adjusted by the dynamic system. For moving targets of different dynamic linear models, an IMM with two KFs generally performs well. In this thesis, in order to improve the performance of target tracking and state estimation, multi-sensor data fusion technique will be used. Same types of IMMs can be incorporated in the cooperative IMM-based algorithm. The IMM-based estimators exchange with each other the estimates, model robabilities and model transition probabilities. A distributed algorithm for multi-sensor tracking usually needs a fusion center that integrates decisions or estimates, but the proposed cooperative IMM-based algorithm does not use the architecture. Cooperative IMM estimator structures exchange weights and estimates on the platforms to avoid accumulation of errors. Performance of data fusion may degrade due to different kinds of undesirable environmental effects. The simulations show that an IMM estimator with smaller measurement noise level can be used to compensate the other IMM, which is affected by larger measurement noise. In addition, failure of a sensor will cause the problem that model probabilities can not be updated in the corresponding estimator. Kalman filters will not be able to perform state correction for the moving target. To tackle the problem, we can use the estimates from other IMM estimators by adjusting the corresponding weights and model probabilities. The simulations show that the proposed cooperative IMM structure effectively improve the tracking performance.

Professional workers are the core value contributors to an enterprise in today¡¦s highly competitive environment of knowledge economy. Under the pressure of global competition, employment flexibility is an unavoidable trend. Contract workers with professional background have been growing rapidly in recent years, and it has been regarded as a competitive strategy to integrate corporate resources to enhance business performance. While more and more enterprises are adopting flexibility strategies as well as utilizing different types of contingent employment to replace traditional long-term employment, the other existing employees not only have to face the changes of employment relationships, but also have to get used to cope with lots of contract-based professionals working in the organization. The purpose of this research is to understand different cognition, attitude and behaviors from the professionals under different employment relationships, as well as the way they interact, while the organization is adopting the human resource strategy of numerical flexibility. The information was collected and analyzed based on qualitative research method and used the professional workers as sampling, including one regular employee and one contractor for every comparative pair. There are total twenty-four professionals from four leading global high-tech companies were interviewed. The result shows that both the regular and contract-based professionals recognized the employment flexibility strategy negatively, and believed that it¡¦s mainly for reducing employment cost only, which might reflected the short-term benefit, but would cause the negative impact on the organization¡¦s performance in the long run. The implementations of differentiated treatments to different employment models caused disagreement from the workers who had expected their employers to provide a fair working environment, sufficient human capital investment and stable career development in the organization. The findings are, a respecting and open-minded organizational culture, a fair workplace, proper contingent employment proportion, and supportive management are the key factors to facilitate the positive interaction among professionals under different employment relationships. Moreover, professional workers have higher motivation and take into account the importance of personal performance, therefore, regular employee will invest personal resources to solve problems from interacting with contract professionals in order to achieve tasks. Meanwhile, the contract professionals are affected by occupational commitment as well as their intention to extend employment contract in the future. Employment status does not influence their performance, however, reduction of unfair treatments regarding human resource practices will motivate their willingness on organizational citizenship behavior and performance improvement.