Cell reorientation under cyclic stretching

Mechanical cues from the extracellular microenvironment play a central role in regulating the structure, function and fate of living cells. Nevertheless, the precise nature of the mechanisms and processes underlying this crucial cellular mechanosensitivity remains a fundamental open problem. Here we provide a novel framework for addressing cellular sensitivity and response to external forces by experimentally and theoretically studying one of its most striking manifestations -- cell reorientation to a uniform angle in response to cyclic stretching of the underlying substrate. We first show that existing approaches are incompatible with our extensive measurements of cell reorientation. We then propose a fundamentally new theory that shows that dissipative relaxation of the cell's passively-stored, two-dimensional, elastic energy to its minimum actively drives the reorientation process. Our theory is in excellent quantitative agreement with the complete temporal reorientation dynamics of individual cells, measured over a wide range of experimental conditions, thus elucidating a basic aspect of mechanosensitivity.Comment: For supplementary materials, see http://www.nature.com/ncomms/2014/140530/ncomms4938/extref/ncomms4938-s1.pd

The Ring Theory and the Representation Theory of Quantum Schubert Cells

In recent years the quantum Schubert cell algebras, introduced by Lusztig and De Concini--Kac, and Procesi, have garnered much interest as this versatile class of objects are furtive testing grounds for noncommutative algebraic geometry. We unify the two main approaches to analyzing the structure of the torus-invariant prime spectra of quantum Schubert cell algebras, a ring theoretic one via Cauchon\u27s deleting derivations and a representation theoretic characterization of Yakimov via Demazure modules. As a result one can combine the strengths of the two approaches. In unifying the theories, we resolve two questions of Cauchon and Mériaux, one of which involves the Cauchon diagram containment problem. Moreover, we discover explicit quantum-minor formulas for the final generators arising from iterating the deleting derivation method on any quantum Schubert cell algebras. These formulas will play a large role in subsequent research. Lastly, we provide an independent and elegant proof of the Cauchon--Mériaux classification. The main results in this thesis appear in arXiv:1203.3780 and are joint with Milen Yakimov

Semiklassische Betrachtung von zwei Bosonen auf einer Linie mit Kontaktwechselwirkung

In dieser Arbeit wird das quantenmechanische Problem zweier Bosonen mit Kontaktwechselwirkung in einem eindimensionalen Kastenpotential behandelt. Dabei ist liegt der Fokus auf der genäherten Beschreibung der (globalen) Zustansdichte mit Hilfe der semiklassischen Kurzzeitnäherung und führt zu einer zwei-Teilchen-Version der Weyl-Formel für den glatten Anteil der Zustandsdichte. Die Ergebnisse werden dann auf die lokale Zustandsdichte verallgemeinert und die auftretenden Friedel-Oszillationen analytisch beschrieben

From few to many particles: Semiclassical approaches to interacting quantum systems

While modern computational methods provide a powerful approach to predict the behavior of physical systems, gaining intuition of emergent phenomena requires almost invariably the use of approximation methods. The ideas and methods of semiclassical physics presented in this thesis provide a systematic road to address non-perturbative regimes, where classical information find its way into the description of quantum properties of systems of few to many interacting particles. The first part of the thesis provides a semiclassical description of few-particle systems using cluster expansions and novel analytic results for short-range interacting bosons in one and three dimensions are derived. In the second part, complementary approaches for many-particle systems are used to study the non-equilibrium scrambling dynamics in quantum-critical bosonic systems with large particle numbers, revealing an unscrambling mechanism due to criticality that is verified in extensive numerical simulations

Finding symmetry breaking order parameters with Euclidean neural networks

Curie's principle states that “when effects show certain asymmetry, this asymmetry must be found in the causes that gave rise to them.” We demonstrate that symmetry equivariant neural networks uphold Curie's principle and can be used to articulate many symmetry-relevant scientific questions as simple optimization problems. We prove these properties mathematically and demonstrate them numerically by training a Euclidean symmetry equivariant neural network to learn symmetry breaking input to deform a square into a rectangle and to generate octahedra tilting patterns in perovskites

Classical and Quantum Signatures of Quantum Phase Transitions in a (Pseudo) Relativistic Many-Body System

We identify a (pseudo) relativistic spin-dependent analogue of the celebrated quantum phase transition driven by the formation of a bright soliton in attractive one-dimensional bosonic gases. In this new scenario, due to the simultaneous existence of the linear dispersion and the bosonic nature of the system, special care must be taken with the choice of energy region where the transition takes place. Still, due to a crucial adiabatic separation of scales, and identified through extensive numerical diagonalization, a suitable effective model describing the transition is found. The corresponding mean-field analysis based on this effective model provides accurate predictions for the location of the quantum phase transition when compared against extensive numerical simulations. Furthermore, we numerically investigate the dynamical exponents characterizing the approach from its finite-size precursors to the sharp quantum phase transition in the thermodynamic limit

Estimation of Combustion Parameters from Engine Vibrations Based on Discrete Wavelet Transform and Gradient Boosting

An optimal control of the combustion process of an engine ensures lower emissions and fuel consumption plus high efficiencies. Combustion parameters such as the peak firing pressure (PFP) and the crank angle (CA) corresponding to 50% of mass fraction burned (MFB50) are essential for a closed-loop control strategy. These parameters are based on the measured in-cylinder pressure that is typically gained by intrusive pressure sensors (PSs). These are costly and their durability is uncertain. To overcome these issues, the potential of using a virtual sensor based on the vibration signals acquired by a knock sensor (KS) for control of the combustion process is investigated. The present work introduces a data-driven approach where a signal-processing technique, designated as discrete wavelet transform (DWT), will be used as the preprocessing step for extracting informative features to perform regression tasks of the selected combustion parameters with extreme gradient boosting (XGBoost) regression models. The presented methodology will be applied to data from two different spark-ignited, single cylinder gas engines. Finally, an analysis is obtained where the important features based on the model’s decisions are identified