On Weighted Multivariate Sign Functions

Multivariate sign functions are often used for robust estimation and inference. We propose using data dependent weights in association with such functions. The proposed weighted sign functions retain desirable robustness properties, while significantly improving efficiency in estimation and inference compared to unweighted multivariate sign-based methods. Using weighted signs, we demonstrate methods of robust location estimation and robust principal component analysis. We extend the scope of using robust multivariate methods to include robust sufficient dimension reduction and functional outlier detection. Several numerical studies and real data applications demonstrate the efficacy of the proposed methodology.Comment: Keywords: Multivariate sign, Principal component analysis, Data depth, Sufficient dimension reductio

Dimension reduction for functionals on solenoidal vector fields

We study integral functionals constrained to divergence-free vector fields in $L^p$ on a thin domain, under standard $p$-growth and coercivity assumptions, $1<p<\infty$. We prove that as the thickness of the domain goes to zero, the Gamma-limit with respect to weak convergence in $L^p$ is always given by the associated functional with convexified energy density wherever it is finite. Remarkably, this happens despite the fact that relaxation of nonconvex functionals subject to the limiting constraint can give rise to a nonlocal functional as illustrated in an example.Comment: 25 page

Characterisation of components and mechanisms involved in redox-regulation of protein import into chloroplasts

The vast majority of chloroplast proteins is encoded in the nucleus and thus has to be posttranslationally imported into the organelle, a process that is facilitated by two multimeric protein machineries, the Toc and Tic complexes (translocon at the outer/inner envelope of chloroplasts). Regulation of protein import, e.g. by redox signals, is a crucial step to adapt the protein content to the biochemical requirements of the organelle. In particular, one subunit of the Tic complex, Tic62, has been proposed as a redox sensor, whose possible function is to regulate protein import by sensing and reacting to the redox state of the organelle. To elucidate a potential redox regulation of protein import, structural features, redox-dependent properties and the evolutional origin of Tic62 were investigated. The results show that Tic62 consists of two very different modules: the N-terminal part was found to be mainly -helical and possesses dehydrogenase activity in vitro. It is furthermore an evolutionary ancient domain, as it is highly conserved in all photosynthetic organisms from flowering plants to cyanobacteria and even green sulfur bacteria. In contrast to this, the C-terminus is largely disordered and interacts specifically with ferredoxin-NADP+ oxidoreductase (FNR), a key enzyme in photosynthetic electron transfer reactions. Moreover, this domain was found to exist only in flowering plants, and thus the full-length Tic62 protein seems to be one of the evolutionary youngest Tic components. The results of this study make also clear that Tic62 is a target of redox regulation itself, as its localization and interaction properties depend on the metabolic redox state: oxidized conditions lead to fast membrane binding and interaction with the Tic complex, whereas reduced conditions cause solubilization of Tic62 into the stroma and increased interaction with FNR. This novel shuttling behaviour indicates a dynamic composition of the Tic complex. The NADP+/NADPH ratio was furthermore found to be able to influence the import efficiency of many precursor proteins. Interestingly, the import of not all preproteins depends on the stromal redox state. Hence it was proposed that not a single stable Tic translocon exists, but several Tic subcomplexes with different subunit compositions, which might mediate the import of different precursor groups in a redox-dependent or -independent fashion. Another redox signal that was analyzed in regard to an impact on protein import is the reversible reduction of disulfide bridges, which was found to affect the channel and receptor proteins of the Toc complex. The import of all proteins that use the Toc translocon for entering the chloroplast was shown to be influenced by disulfide bridge formation. Thus it can be concluded that a variety of redox signals, acting both on the Toc and Tic complexes, are able to influence chloroplast protein import

WavePacket: A Matlab package for numerical quantum dynamics. II: Open quantum systems, optimal control, and model reduction

WavePacket is an open-source program package for numeric simulations in quantum dynamics. It can solve time-independent or time-dependent linear Schr\"odinger and Liouville-von Neumann-equations in one or more dimensions. Also coupled equations can be treated, which allows, e.g., to simulate molecular quantum dynamics beyond the Born-Oppenheimer approximation. Optionally accounting for the interaction with external electric fields within the semi-classical dipole approximation, WavePacket can be used to simulate experiments involving tailored light pulses in photo-induced physics or chemistry. Being highly versatile and offering visualization of quantum dynamics 'on the fly', WavePacket is well suited for teaching or research projects in atomic, molecular and optical physics as well as in physical or theoretical chemistry. Building on the previous Part I which dealt with closed quantum systems and discrete variable representations, the present Part II focuses on the dynamics of open quantum systems, with Lindblad operators modeling dissipation and dephasing. This part also describes the WavePacket function for optimal control of quantum dynamics, building on rapid monotonically convergent iteration methods. Furthermore, two different approaches to dimension reduction implemented in WavePacket are documented here. In the first one, a balancing transformation based on the concepts of controllability and observability Gramians is used to identify states that are neither well controllable nor well observable. Those states are either truncated or averaged out. In the other approach, the H2-error for a given reduced dimensionality is minimized by H2 optimal model reduction techniques, utilizing a bilinear iterative rational Krylov algorithm

Thermodynamics of the Massive Gross-Neveu Model

We study the thermodynamics of massive Gross-Neveu models with explicitly broken discrete or continuous chiral symmetries for finite temperature and fermion densities. The large $N$ limit is discussed bearing attention to the no-go theorems for symmetry breaking in two dimensions which apply to the massless cases. The main purpose of the study is to serve as analytical orientation for the more complex problem of chiral transition in $4-$dimensional QCD with quarks. For any non-vanishing fermion mass we find, at finite densities, lines of first order phase transitions. For small mass values traces of would-be second order transitions and a tricritical point are recognizable. We study the thermodynamics of these models, and in the model with broken continuous chiral symmetry we examine the properties of the pion like state.Comment: 34 pages (+18 figures, available upon request to [email protected]), LATEX file, uses art12a.sty, macro included, UGVA-DPT 1994/06-85

Sequential Design for Optimal Stopping Problems

We propose a new approach to solve optimal stopping problems via simulation. Working within the backward dynamic programming/Snell envelope framework, we augment the methodology of Longstaff-Schwartz that focuses on approximating the stopping strategy. Namely, we introduce adaptive generation of the stochastic grids anchoring the simulated sample paths of the underlying state process. This allows for active learning of the classifiers partitioning the state space into the continuation and stopping regions. To this end, we examine sequential design schemes that adaptively place new design points close to the stopping boundaries. We then discuss dynamic regression algorithms that can implement such recursive estimation and local refinement of the classifiers. The new algorithm is illustrated with a variety of numerical experiments, showing that an order of magnitude savings in terms of design size can be achieved. We also compare with existing benchmarks in the context of pricing multi-dimensional Bermudan options.Comment: 24 page

Isospin-dependent clusterization of Neutron-Star Matter

Because of the presence of a liquid-gas phase transition in nuclear matter, compact-star matter can present a region of instability against the formation of clusters. We investigate this phase separation in a matter composed of neutrons, protons and electrons, within a Skyrme-Lyon mean-field approach. Matter instability and phase properties are characterized through the study of the free-energy curvature. The effect of beta-equilibrium is also analyzed in detail, and we show that the opacity to neutrinos has an influence on the presence of clusterized matter in finite-temperature proto-neutron stars.Comment: To appear in Nuclear Physics

Design methodology for a school prototype: Jean Prouvé’s Jules Ferry School Group in Dieulouard, France, 1952–1953

The catastrophic destruction of buildings in France during World War II demanded that reconstruction become one of the primary objectives in the immediate post-war period. This favoured a culture of experimentation, and created a context for Jean Prouvé to develop designs for school buildings. He developed these designs with a research-based process focusing on technical solutions and their prototypes, and with models whose fundamental premises were rapid and easy assembly-disassembly, lightness and economy. The constant correlation between the projected object and the object created in the workshop shaped the basis for the precision of his designs. This article analyses the methodology followed by Prouvé in the Jules Ferry School Group in Dieulouard, France (1952–1953), in the singular context of the post-war period, illustrating the route followed in developing the model rather than the aesthetics of the building. The prototype used in his schools, and the models generated from this system, demonstrate his architectural methods