Fundamental conical defects: The d-cone, its e-cone, and its p-cone.

We consider well-known surface disclinations by cutting, joining, and folding pieces of paper card. The resulting shapes have a discrete, folded vertex whose geometry is described easily by Gauss's mapping, in particular, we can relate the degree of angular excess, or deficit, to the size of fold line rotations by the area enclosed by the vector diagram of these rotations. This is well known for the case of a so-called "d-cone" of zero angular deficit, and we formulate the same for a general disclination. This method allows us to observe kinematic properties in a meaningful way without needing to consider equilibrium. Importantly, the simple vector nature of our analysis shows that some disclinations are primitive; and that other types, such as d-cones, are amalgamations of them

Constrained Estimation: Consistency and Asymptotics

We review some of the recent results obtained for constrained estimation, involving possibly nondifferentiable criterion functions. New tools are required to push consistency and asymptotic results beyond those that can be reached by classical means

Super-Linear Convergence of Dual Augmented-Lagrangian Algorithm for Sparsity Regularized Estimation

We analyze the convergence behaviour of a recently proposed algorithm for regularized estimation called Dual Augmented Lagrangian (DAL). Our analysis is based on a new interpretation of DAL as a proximal minimization algorithm. We theoretically show under some conditions that DAL converges super-linearly in a non-asymptotic and global sense. Due to a special modelling of sparse estimation problems in the context of machine learning, the assumptions we make are milder and more natural than those made in conventional analysis of augmented Lagrangian algorithms. In addition, the new interpretation enables us to generalize DAL to wide varieties of sparse estimation problems. We experimentally confirm our analysis in a large scale $\ell_1$-regularized logistic regression problem and extensively compare the efficiency of DAL algorithm to previously proposed algorithms on both synthetic and benchmark datasets.Comment: 51 pages, 9 figure

Rigidity and flexibility of biological networks

The network approach became a widely used tool to understand the behaviour of complex systems in the last decade. We start from a short description of structural rigidity theory. A detailed account on the combinatorial rigidity analysis of protein structures, as well as local flexibility measures of proteins and their applications in explaining allostery and thermostability is given. We also briefly discuss the network aspects of cytoskeletal tensegrity. Finally, we show the importance of the balance between functional flexibility and rigidity in protein-protein interaction, metabolic, gene regulatory and neuronal networks. Our summary raises the possibility that the concepts of flexibility and rigidity can be generalized to all networks.Comment: 21 pages, 4 figures, 1 tabl

The position of graptolites within Lower Palaeozoic planktic ecosystems.

An integrated approach has been used to assess the palaeoecology of graptolites both as a discrete group and also as a part of the biota present within Ordovician and Silurian planktic realms. Study of the functional morphology of graptolites and comparisons with recent ecological analogues demonstrates that graptolites most probably filled a variety of niches as primary consumers, with modes of life related to the colony morphotype. Graptolite coloniality was extremely ordered, lacking any close morphological analogues in Recent faunas. To obtain maximum functional efficiency, graptolites would have needed varying degrees of coordinated automobility. A change in lifestyle related to ontogenetic changes was prevalent within many graptolite groups. Differing lifestyle was reflected by differing reproductive strategies, with synrhabdosomes most likely being a method for rapid asexual reproduction. Direct evidence in the form of graptolithophage 'coprolitic' bodies, as well as indirect evidence in the form of probable defensive adaptations, indicate that graptolites comprised a food item for a variety of predators. Graptolites were also hosts to a variety of parasitic organisms and provided an important nutrient source for scavenging organisms

Metallic tube type energy absorbers: a synopsis

This paper presents an overview of energy absorbers in the form of tubes in which the material used is predominantly mild steel and/or aluminium. A brief summary is also made of frusta type energy absorbers. The common modes of deformation such as lateral and axial compression, indentation and inversion are reviewed. Theoretical, numerical and experimental methods which help to understand the behaviour of such devices under various loading conditions are outlined. Although other forms of energy absorbing materials and structures exist such as composites and honeycombs, this is deemed outside the scope of this review. However, a brief description will be given on these materials. It is hoped that this work will provide a useful platform for researchers and design engineers to gain a useful insight into the progress made over the last few decades in the field of tube type energy absorbers

The critical merger distance between two co-rotating quasi-geostrophic vortices

This paper examines the critical merger or strong interaction distance between two equal-potential-vorticity quasi-geostrophic vortices. The interaction between the two vortices depends on five parameters: their volume ratio, their height-to-width aspect ratios and their vertical and horizontal offsets. Due to the size of the parameter space, a direct investigation solving the full quasi-geostrophic equations is impossible. We instead determine the critical merger distance approximately using an asymptotic approach. We associate the merger distance with the margin of stability for a family of equilibrium states having prescribed aspect and volume ratios, and vertical offset. The equilibrium states are obtained using an asymptotic solution method which models vortices by ellipsoids. The margin itself is determined by a linear stability analysis. We focus on the interaction between oblate to moderately prolate vortices, the shapes most commonly found in turbulence. Here, a new unexpected instability is found and discussed for prolate vortices which is manifested by the tilting of vortices toward each other. It implies than tall vortices may merge starting from greater separation distances than previously thought.Publisher PDFPeer reviewe

Variational integrator for the rotating shallow-water equations on the sphere

We develop a variational integrator for the shallow‐water equations on a rotating sphere. The variational integrator is built around a discretization of the continuous Euler–Poincaré reduction framework for Eulerian hydrodynamics. We describe the discretization of the continuous Euler–Poincaré equations on arbitrary simplicial meshes. Standard numerical tests are carried out to verify the accuracy and excellent conservational properties of the discrete variational integrator

Vibrissa-based design of tapered tactile sensors for object sensing

Numerous mammals possess whiskers (tactile hairs, also known as vibrissae) to explore their environment. These complex mechano-sensitive vibrissae are located, e.g. in the snout region (mystacial vibrissae). Because of the deformation of the vibrissa by contact with objects and obstacles, the animal gets additional information about the environment. Despite different morphology of animal vibrissae (e.g., cylindrically or conically shaped, precurved, multi-layer structure), these biological tactile hairs are modeled in a mechanical way to develop and analyze models concerning their bending behavior with a glance to get hints for a technical implementation as a technical sensor. At first, we investigate the bending behavior of cylindrically shaped and tapered rods which are one-sided clamped and are under the load of an external force, using the Euler-Bernoulli non-linear bending theory. Then, a quasi-static sweep of these rods along various obstacle profiles is used for an obstacle profile reconstruction procedure. While scanning the object, the clamping reactions are determined, which are the only observables an animal relies on in biology. In plotting these observables and using them in a reconstruction algorithm to determine the scanned contour, we try to identify special features in dependence on the different geometries of the rods. The clamping reactions tremendously depend on the form and position of the profile which is shown in several numerical simulations