Bernstein-Markov: a survey

We give a survey of recent results, due mainly to the authors, concerning Bernstein-Markov type inequalities and connections with potential theory.Comment: This will appear soon in a special issue of Dolomites Research Notes on Approximation (DRNA): "Ten years of Padua Points

Fast three dimensional r-adaptive mesh redistribution

This paper describes a fast and reliable method for redistributing a computational mesh in three dimensions which can generate a complex three dimensional mesh without any problems due to mesh tangling. The method relies on a three dimensional implementation of the parabolic Monge–Ampère (PMA) technique, for finding an optimally transported mesh. The method for implementing PMA is described in detail and applied to both static and dynamic mesh redistribution problems, studying both the convergence and the computational cost of the algorithm. The algorithm is applied to a series of problems of increasing complexity. In particular very regular meshes are generated to resolve real meteorological features (derived from a weather forecasting model covering the UK area) in grids with over 2×107 degrees of freedom. The PMA method computes these grids in times commensurate with those required for operational weather forecasting

Analyzing Social Policy from a Network Perspective

Governance models influence the approach that public service organizations take when implementing programs, policies, and practices. The networked model of governance supports the involvement of multiple actors who span organizational boundaries and roles to implement solutions to address complex social problems. This paper presents the utility of network analysis for the study of policy implementation from a network perspective. The paper describes networks within the context of social work policy implementation, basic network components, common structural variables, and sources of data for the study of policy implementation. A study of a statewide policy implementation is partially presented as an illustration of the use of network analysis in social policy research. The illustration uses primary and secondary data with network analysis techniques to identify and describe the patterns of interactions that comprise the structure of the implementation network. The illustration will present examples of the study findings to demonstrate the utility of network analysis in identifying central network actors and describing the density of the network according to different network variables. The paper concludes with a summary of the utility of network analysis in the study of policy implementation with recommendations for future research

The Earth Mover\u27s Distance Through the Lens of Algebraic Combinatorics

The earth mover\u27s distance (EMD) is a metric for comparing two histograms, with burgeoning applications in image retrieval, computer vision, optimal transport, physics, cosmology, political science, epidemiology, and many other fields. In this thesis, however, we approach the EMD from three distinct viewpoints in algebraic combinatorics. First, by regarding the EMD as the symmetric difference of two Young diagrams, we use combinatorial arguments to answer statistical questions about histogram pairs. Second, we adopt as a natural model for the EMD a certain infinite-dimensional module, known as the first Wallach representation of the Lie algebra su(p,q), which arises in the Howe duality setting in Type A; in this setting, we show how the second fundamental theorem of invariant theory generalizes the northwest corner rule\u27\u27 from optimal transport theory, yielding a simple interpretation of the partial matching\u27\u27 case of the EMD via separation into invariants and harmonics. Third, we reapproach partial matching in the context of crystal bases of Types A, B, and C, which leads us to introduce a variation of the EMD in terms of distance on a crystal graph. Having exploited these three approaches, we generalize all of our EMD results to an arbitrary number of histograms rather than only two at a time. In the final chapter, we observe a combinatorial connection between generalized BGG resolutions arising in Type-A Howe duality and certain non-holomorphic discrete series representations of the group SU(p,q)

Rational Design of Pore Size and Functionality in a Series of Isoreticular Zwitterionic Metal-Organic Frameworks

The isoreticular expansion and functionalization of charged-polarized porosity has been systematically explored by the rational design of 11 isostructural zwitterionic metal-organic frameworks (ZW-MOFs). This extended series of general structural composition {[M3F(L1)3(L2)1.5]·guests}n was prepared by employing the solvothermal reaction of Co and Ni tetrafluoroborates with a binary ligand system composed of zwitterionic pyridinium derivatives and traditional functionalized ditopic carboxylate auxiliary ligands (HL1·Cl = 1-(4-carboxyphenyl)-4,4′-bipyridinium chloride, Hcpb·Cl; or 1-(4-carboxyphenyl-3-hydroxyphenyl)-4,4′-bipyridinium chloride, Hchpb·Cl; and H2L2 = benzene-1,4-dicarboxylic acid, H2bdc; 2-aminobenzene-1,4-dicarboxylic acid, H2abdc; 2,5-dihydroxy-1,4-benzenedicarboxylic acid, H2dhbdc; biphenyl-4,4′-dicarboxylic acid, H2bpdc; or stilbene-4,4′-dicarboxylic acid, H2sdc). Single-crystal structure analyses revealed cubic crystal symmetry (I-43m, a = 31-36 Å) with a 3D pore system of significant void space (73-81%). The pore system features three types of pores being systematically tunable in size ranging from 17.4 to 18.8 Å (pore I), 8.2 to 12.8 Å (pore II), and 4.8 to 10.4 Å (pore III) by the choice of auxiliary ligands. All members of this series have noninterpenetrating structures and exhibit robust architectures, as evidenced by their permanent porosity and high thermal stability (up to 300 °C). The structural integrity and specific surface areas could be systematically optimized using supercritical CO2 exchange methods for framework activation resulting in BET surface areas ranging from 1250 to 2250 m2/g. Most interestingly, as a structural landmark, we found the pore surfaces lined with charge gradients employed by the pyridinium ligands. This key feature results in significant adsorption of carbon dioxide and methane which is attributed to polarization effects. With this contribution we pioneer the reticulation of pyridinium building blocks into extended zwitterionic networks in which specific properties can be targeted

Design of Surface Modifications for Nanoscale Sensor Applications

Nanoscale biosensors provide the possibility to miniaturize optic, acoustic and electric sensors to the dimensions of biomolecules. This enables approaching single-molecule detection and new sensing modalities that probe molecular conformation. Nanoscale sensors are predominantly surface-based and label-free to exploit inherent advantages of physical phenomena allowing high sensitivity without distortive labeling. There are three main criteria to be optimized in the design of surface-based and label-free biosensors: (i) the biomolecules of interest must bind with high affinity and selectively to the sensitive area; (ii) the biomolecules must be efficiently transported from the bulk solution to the sensor; and (iii) the transducer concept must be sufficiently sensitive to detect low coverage of captured biomolecules within reasonable time scales. The majority of literature on nanoscale biosensors deals with the third criterion while implicitly assuming that solutions developed for macroscale biosensors to the first two, equally important, criteria are applicable also to nanoscale sensors. We focus on providing an introduction to and perspectives on the advanced concepts for surface functionalization of biosensors with nanosized sensor elements that have been developed over the past decades (criterion (iii)). We review in detail how patterning of molecular films designed to control interactions of biomolecules with nanoscale biosensor surfaces creates new possibilities as well as new challenges