Cooperativity and Stability in a Langevin Model of Protein Folding

We present two simplified models of protein dynamics based on Langevin's equation of motion in a viscous medium. We explore the effect of the potential energy function's symmetry on the kinetics and thermodynamics of simulated folding. We find that an isotropic potential energy function produces, at best, a modest degree of cooperativity. In contrast, a suitable anisotropic potential energy function delivers strong cooperativity.Comment: 45 pages, 16 figures, 2 tables. LaTeX. Submitted to the Journal of Chemical Physic

Rigidity theory in presence of noise for localization and control of multiagent systems

This thesis work aims at analyzing the formation, structure and response to noise the so-called bearing rigidity matrix, a mathematical tool applied in the fields of distributed control and estimation of multi-agent systems (e.g. UAV swarms or UGV fleets). At first, a basic theoretical background is established in order to better contextualize the experiments. Secondly, the aforementioned matrix is built using a soft-coded algorithmic approach and numerically simulated. Configuration-agnostic performance indices and descriptors are then established from an algebraic point of view in order to characterize the validity of the theoretical assumptions and the effect of the noise on the measurements. Such measurements are simulated in a sequence of diverse fleet scenarios. The actual application of the bearing rigidity matrix in non-static scenarios concerning the efforts of control and estimation escapes the scope of this research and therefore will not be discussed in the following.Questo lavoro di tesi ha come obbiettivo quello di analizzare la costruzione, struttura e risposta al rumore della cosiddetta matrice di rigidità di bearing, uno strumento mate- matico utilizzato nei campi del controllo e della stima distribuiti di sistemi multi agenti (consistenti ad esempio in flotte di quadri rotori o robot terrestri a controllo remoto). Per prima cosa verrà stabilita una base teorica per meglio contestualizzare gli esperimenti ese- guiti. Secondariamente la matrice di cui sopra verrà costruita in maniera programmatica secondo un approccio algoritmico soft-code e simulata numericamente. Una volta stabi- liti indici di performance di carattere algebrico agnostici alla configurazione considerata, questi verranno utilizzati per stabilire la validità dei fondamenti teorici e valutare l’effetto del rumore nelle misurazioni. Tali misurazioni verranno simulate in una vasta sequenza di configurazioni di flotta. L’applicazione della matrice di rigidità di bearing in contesti dinamici riguardanti il controllo e la stima non rientra negli obbiettivi di questo testo e non verranno pertanto considerati in quanto segue

Coplanar k-unduloids are nondegenerate

We prove each embedded, constant mean curvature (CMC) surface in Euclidean space with genus zero and finitely many coplanar ends is nondegenerate: there is no nontrivial square-integrable solution to the Jacobi equation, the linearization of the CMC condition. This implies that the moduli space of such coplanar surfaces is a real-analytic manifold and that a neighborhood of these in the full CMC moduli space is itself a manifold. Nondegeneracy further implies (infinitesimal and local) rigidity in the sense that the asymptotes map is an analytic immersion on these spaces, and also that the coplanar classifying map is an analytic diffeomorphism.Comment: 19 pages, no figures; improvements to expositio

Optical Flow in Mostly Rigid Scenes

The optical flow of natural scenes is a combination of the motion of the observer and the independent motion of objects. Existing algorithms typically focus on either recovering motion and structure under the assumption of a purely static world or optical flow for general unconstrained scenes. We combine these approaches in an optical flow algorithm that estimates an explicit segmentation of moving objects from appearance and physical constraints. In static regions we take advantage of strong constraints to jointly estimate the camera motion and the 3D structure of the scene over multiple frames. This allows us to also regularize the structure instead of the motion. Our formulation uses a Plane+Parallax framework, which works even under small baselines, and reduces the motion estimation to a one-dimensional search problem, resulting in more accurate estimation. In moving regions the flow is treated as unconstrained, and computed with an existing optical flow method. The resulting Mostly-Rigid Flow (MR-Flow) method achieves state-of-the-art results on both the MPI-Sintel and KITTI-2015 benchmarks.Comment: 15 pages, 10 figures; accepted for publication at CVPR 201

Rigid formation control of double-integrator systems

In this paper, we study rigid formation control systems modelled by double integrators. Two kinds of double-integrator formation systems are considered, namely formation stabilisation systems and flocking control systems. Novel observations on the measurement requirement, the null space and eigenvalues of the system Jacobian matrix will be provided, which reveal important properties of system dynamics and the associated convergence results.We also establish some new links between single-integrator formation systems and double-integrator formation systems via a parameterised Hamiltonian system, which, in addition, provide novel stability criteria for different equilibria in double-integrator formation systems by using available results in single-integrator formation systems.This work is supported by NICTA, which is funded by the Australian Government as represented by the Department of Broadband, Communications and the Digital Economy and the Australian Research Council through the ICT Centre of Excellence program. It is also partially supported by National Natural Science Foundation of China [grant number 61501282]. B. D. O. Anderson was supported by the ARC [grant number DP130103610]. H.-S. Ahn is supported by the National Research Foundation of Korea [grant number NRF- 2013R1A2A2A01067449]. Z. Sun is supported by the Prime Minister’s Australia Asia Incoming Endeavour Postgraduate Award from Australian Government

Lunar simulation model and optical studies for Lunar Orbiter system support

Lunar model which simulates topographic and photometric characteristics of lunar surfac