Bias Analysis in Entropy Estimation

We consider the problem of finite sample corrections for entropy estimation. New estimates of the Shannon entropy are proposed and their systematic error (the bias) is computed analytically. We find that our results cover correction formulas of current entropy estimates recently discussed in literature. The trade-off between bias reduction and the increase of the corresponding statistical error is analyzed.Comment: 5 pages, 3 figure

Reachability-based Identification, Analysis, and Control Synthesis of Robot Systems

We introduce reachability analysis for the formal examination of robots. We propose a novel identification method, which preserves reachset conformance of linear systems. We additionally propose a simultaneous identification and control synthesis scheme to obtain optimal controllers with formal guarantees. In a case study, we examine the effectiveness of using reachability analysis to synthesize a state-feedback controller, a velocity observer, and an output feedback controller.Comment: This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessibl

Template-based searches for gravitational waves: efficient lattice covering of flat parameter spaces

The construction of optimal template banks for matched-filtering searches is an example of the sphere covering problem. For parameter spaces with constant-coefficient metrics a (near-) optimal template bank is achieved by the A_n* lattice, which is the best lattice-covering in dimensions n <= 5, and is close to the best covering known for dimensions n <= 16. Generally this provides a substantially more efficient covering than the simpler hyper-cubic lattice. We present an algorithm for generating lattice template banks for constant-coefficient metrics and we illustrate its implementation by generating A_n* template banks in n=2,3,4 dimensions.Comment: 10 pages, submitted to CQG for proceedings of GWDAW1

Grothendieck groups and a categorification of additive invariants

A topologically-invariant and additive homology class is mostly not a natural transformation as it is. In this paper we discuss turning such a homology class into a natural transformation; i.e., a "categorification" of it. In a general categorical set-up we introduce a generalized relative Grothendieck group from a cospan of functors of categories and also consider a categorification of additive invariants on objects. As an example, we obtain a general theory of characteristic homology classes of singular varieties.Comment: 27 pages, to appear in International J. Mathematic

Composition and structure of magnetic high-temperature-phase, stable Fe-Au core-shell nanoparticles with zero-valent bcc Fe core

Advanced quantitative TEM/EDXS methods were used to characterize different ultrastructures of magnetic Fe–Au core–shell nanoparticles formed by laser ablation in liquids. The findings demonstrate the presence of Au-rich alloy shells with varying composition in all structures and elemental bcc Fe cores. The identified structures are metastable phases interpreted by analogy to the bulk phase diagram. Based on this, we propose a formation mechanism of these complex ultrastructures. To show the magnetic response of these magnetic core nanoparticles protected by a noble metal shell, we demonstrate the formation of nanostrands in the presence of an external magnetic field. We find that it is possible to control the lengths of these strands by the iron content within the alloy nanoparticles