The algorithmic beauty of plant roots – an L-System model for dynamic root growth simulation

Understanding the impact of root architecture on plant resource efficiency is important, in particular, in the light of upcoming shortages of mineral fertilizers and changed environmental conditions. In the 1950s, a great number of root systems of European cultivated plants were excavated and studied by L. Kutschera (1960). Her work gave enormous insight into the variety of root system architectures and helped to realize the importance of belowground processes to plant productivity. We analysed the resulting hand drawings by using mathematical modelling and found root system parameters for a newly developed parametric L-System model. In this way we were able to first reproduce the illustrations, second computationally analyse root system traits and finally access the dynamic root architecture development.     

Localization from Incomplete Noisy Distance Measurements

We consider the problem of positioning a cloud of points in the Euclidean space ? ^d , using noisy measurements of a subset of pairwise distances. This task has applications in various areas, such as sensor network localization and reconstruction of protein conformations from NMR measurements. It is also closely related to dimensionality reduction problems and manifold learning, where the goal is to learn the underlying global geometry of a data set using local (or partial) metric information. Here we propose a reconstruction algorithm based on semidefinite programming. For a random geometric graph model and uniformly bounded noise, we provide a precise characterization of the algorithm’s performance: in the noiseless case, we find a radius r ₀ beyond which the algorithm reconstructs the exact positions (up to rigid transformations). In the presence of noise, we obtain upper and lower bounds on the reconstruction error that match up to a factor that depends only on the dimension d, and the average degree of the nodes in the graph.     

A dual algorithm for the minimum covering weighted ball problem in {\mathbb{R}^n}

The nonlinear convex programming problem of finding the minimum covering weighted ball of a given finite set of points in ${\mathbb{R}^n}$ is solved by generating a finite sequence of subsets of the points and by finding the minimum covering weighted ball of each subset in the sequence until all points are covered. Each subset has at most n + 1 points and is affinely independent. The radii of the covering weighted balls are strictly increasing. The minimum covering weighted ball of each subset is found by using a directional search along either a ray or a circular arc, starting at the solution to the previous subset. The step size is computed explicitly at each iteration.     

Homogenization of spatially dispersive metamaterial arrays in terms of generalized electric and magnetic polarizations

An anisotropic homogenization theory for spatially dispersive periodic arrays is developed, based on the microscopic Maxwell equations, that yields causal, macroscopic permittivities, and inverse permeabilities for the fundamental Floquet modes of the arrays. (Macroscopic magnetoelectric coefficients are not required.) Reality conditions, reciprocity relations, passivity conditions, and causality relations are derived for these spatially dispersive macroscopic constitutive parameters. A significant feature of the formulation is that the macroscopic permittivities and permeabilities reduce to their anisotropic-continuum definitions in terms of ordinary macroscopic averages at the low spatial and temporal frequencies. In addition, diamagnetic metamaterial arrays require no special considerations or modifications to accommodate their unusual characteristics. A numerical example of a 2D array comprised of circular–cylinder inclusions is given that confirms the theoretical results for the computed electric and magnetic or diamagnetic macroscopic polarizations.     

The Beneficial Role of Random Strategies in Social and Financial Systems

In this paper we focus on the beneficial role of random strategies in social sciences by means of simple mathematical and computational models. We briefly review recent results obtained by two of us in previous contributions for the case of the Peter principle and the efficiency of a Parliament. Then, we develop a new application of random strategies to the case of financial trading and discuss in detail our findings about forecasts of markets dynamics.     

Study of Dependence for Some Stochastic Processes

Abstract

This article is concerned with studying the following problem: Consider a multivariate stochastic process whose law is characterized in terms of some infinitesimal characteristics, such as the infinitesimal generator in case of finite Markov chains. Under what conditions imposed on these infinitesimal characteristics of this multivariate process, the univariate components of the process agree in law with given univariate stochastic processes. Thus, in a sense, we study a stochastic processe' counterpart of the stochastic dependence problem, which in case of real valued random variables is solved in terms of Sklar's theorem.     

Exact and heuristic approaches for the index tracking problem with UCITS constraints

Index tracking aims at determining an optimal portfolio that replicates the performance of an index or benchmark by investing in a smaller number of constituents or assets. The tracking portfolio should be cheap to maintain and update, i.e., invest in a smaller number of constituents than the index, have low turnover and low transaction costs, and should avoid large positions in few assets, as required by the European Union Directive UCITS (Undertaking for Collective Investments in Transferable Securities) rules. The UCITS rules make the problem hard to be satisfactorily modeled and solved to optimality: no exact methods but only heuristics have been proposed so far. The aim of this paper is twofold. First, we present the first Mixed Integer Quadratic Programming (MIQP) formulation for the constrained index tracking problem with the UCITS rules compliance. This allows us to obtain exact solutions for small- and medium-size problems based on real-world datasets. Second, we compare these solutions with the ones provided by the state-of-art heuristic Differential Evolution and Combinatorial Search for Index Tracking (DECS-IT), obtaining information about the heuristic performance and its reliability for the solution of large-size problems that cannot be solved with the exact approach. Empirical results show that DECS-IT is indeed appropriate to tackle the index tracking problem in such cases. Furthermore, we propose a method that combines the good characteristics of the exact and of the heuristic approaches.     

Divalent Sialylated Precision Glycooligomers Binding to Polyomaviruses and the Effect of Different Linkers

Divalent precision glycooligomers terminating in N‐acetylneuraminic acid (Neu5Ac) or 3′‐sialyllactose (3′‐SL) with varying linkers between scaffold and the glycan portions are synthesized via solid phase synthesis for co‐crystallization studies with the sialic acid‐binding major capsid protein VP1 of human Trichodysplasia spinulosa‐associated Polyomavirus. High‐resolution crystal structures of complexes demonstrate that the compounds bind to VP1 depending on the favorable combination of carbohydrate ligand and linker. It is found that artificial linkers can replace portions of natural carbohydrate linkers as long as they meet certain requirements such as size or flexibility to optimize contact area between ligand and receptor binding sites. The obtained results will influence the design of future high affinity ligands based on the structures presented here, and they can serve as a blueprint to develop multivalent glycooligomers as inhibitors of viral adhesion.     

Fabrication of micro-patterned substrates for plasmonic sensing by piezo-dispensing of colloidal nanoparticles

Analytical and Bioanalytical Chemistry - In this work we describe a very fast and flexible method for fabrication of plasmon-supporting substrates with micro-patterning capability, which is...