Algebraic duality theorems for infinite LP problems

In this paper we consider a primal-dual infinite linear programming problem-pair, i.e. LPs on infinite dimensional spaces with infinitely many constraints. We present two duality theorems for the problem-pair: a weak and a strong duality theorem. We do not assume any topology on the vector spaces, therefore our results are algebraic duality theorems. As an application, we consider transferable utility cooperative games with arbitrarily many players.

Algebraic theory of minimal nondeterministic finite automata with applications

Since the 1950s, the theory of deterministic and nondeterministic finite automata (DFAs and NFAs, respectively) has been a cornerstone of theoretical computer science. In this dissertation, our main object of study is minimal NFAs. In contrast with minimal DFAs, minimal NFAs are computationally challenging: first, there can be more than one minimal NFA recognizing a given language; second, the problem of converting an NFA to a minimal equivalent NFA is NP-hard, even for NFAs over a unary alphabet. Our study is based on the development of two main theories, inductive bases and partials, which in combination form the foundation for an incremental algorithm, ibas, to find minimal NFAs. An inductive basis is a collection of languages with the property that it can generate (through union) each of the left quotients of its elements. We prove a fundamental characterization theorem which says that a language can be recognized by an n-state NFA if and only if it can be generated by an n-element inductive basis. A partial is an incompletely-specified language. We say that an NFA recognizes a partial if its language extends the partial, meaning that the NFA’s behavior is unconstrained on unspecified strings; it follows that a minimal NFA for a partial is also minimal for its language. We therefore direct our attention to minimal NFAs recognizing a given partial. Combining inductive bases and partials, we generalize our characterization theorem, showing that a partial can be recognized by an n-state NFA if and only if it can be generated by an n-element partial inductive basis. We apply our theory to develop and implement ibas, an incremental algorithm that finds minimal partial inductive bases generating a given partial. In the case of unary languages, ibas can often find minimal NFAs of up to 10 states in about an hour of computing time; with brute-force search this would require many trillions of years.

Geophysical Analysis of a Central Florida Karst Terrain using Light Detection and Ranging (LIDAR) and Ground Penetrating Radar (GPR) Derived Surfaces

Airborne LIDAR (Light Detecting and Ranging) is a relatively new technique that rapidly and accurately measures micro-topographic features. This study compares topography derived from LIDAR with subsurface karst structures mapped in 3-dimensions with ground penetrating radar (GPR). Over 500 km of LIDAR data were collected in 1995 by the NASA ATM instrument. The LIDAR data was processed and analyzed to identify closed depressions. A GPR survey was then conducted at a 200 by 600 m site to determine if the target features are associated with buried karst structures. The GPR survey resolved two major depressions in the top of a clay rich layer at ~10m depth. These features are interpreted as buried dolines and are associated spatially with subtle (< 1m) trough-like depressions in the topography resolved from the LIDAR data. This suggests that airborne LIDAR may be a useful tool for indirectly detecting subsurface features associated with sinkhole hazard.

Algebraic Theory of Minimal Nondeterministic Finite Automata with Applications

Since the 1950s, the theory of deterministic and nondeterministic finite automata (DFAs and NFAs, respectively) has been a cornerstone of theoretical computer science. In this dissertation, our main object of study is minimal NFAs. In contrast with minimal DFAs, minimal NFAs are computationally challenging: first, there can be more than one minimal NFA recognizing a given language; second, the problem of converting an NFA to a minimal equivalent NFA is NP-hard, even for NFAs over a unary alphabet. Our study is based on the development of two main theories, inductive bases and partials, which in combination form the foundation for an incremental algorithm, ibas, to find minimal NFAs. An inductive basis is a collection of languages with the property that it can generate (through union) each of the left quotients of its elements. We prove a fundamental characterization theorem which says that a language can be recognized by an n-state NFA if and only if it can be generated by an n-element inductive basis. A partial is an incompletely-specified language. We say that an NFA recognizes a partial if its language extends the partial, meaning that the NFA's behavior is unconstrained on unspecified strings; it follows that a minimal NFA for a partial is also minimal for its language. We therefore direct our attention to minimal NFAs recognizing a given partial. Combining inductive bases and partials, we generalize our characterization theorem, showing that a partial can be recognized by an n-state NFA if and only if it can be generated by an n-element partial inductive basis. We apply our theory to develop and implement ibas, an incremental algorithm that finds minimal partial inductive bases generating a given partial. In the case of unary languages, ibas can often find minimal NFAs of up to 10 states in about an hour of computing time; with brute-force search this would require many trillions of years.

Método híbrido para projeto de superfícies seletivas em frequência

This thesis presents a hybrid technique of frequency selective surfaces project (FSS) on a isotropic dielectric layer, considering various geometries for the elements of the unit cell. Specifically, the hybrid technique uses the equivalent circuit method in conjunction with genetic algorithm, aiming at the synthesis of structures with response single-band and dual-band. The equivalent circuit method allows you to model the structure by using an equivalent circuit and also obtaining circuits for different geometries. From the obtaining of the parameters of these circuits, you can get the transmission and reflection characteristics of patterned structures. For the optimization of patterned structures, according to the desired frequency response, Matlab™ optimization tool named optimtool proved to be easy to use, allowing you to explore important results on the optimization analysis. In this thesis, numeric and experimental results are presented for the different characteristics of the analyzed geometries. For this, it was determined a technique to obtain the parameter N, which is based on genetic algorithms and differential geometry, to obtain the algebraic rational models that determine values of N more accurate, facilitating new projects of FSS with these geometries. The optimal results of N are grouped according to the occupancy factor of the cell and the thickness of the dielectric, for modeling of the structures by means of rational algebraic equations. Furthermore, for the proposed hybrid model was developed a fitness function for the purpose of calculating the error occurred in the definitions of FSS bandwidths with transmission features single band and dual band. This thesis deals with the construction of prototypes of FSS with frequency settings and band widths obtained with the use of this function. The FSS were initially reviewed through simulations performed with the commercial software Ansoft Designer ™, followed by simulation with the equivalent circuit method for obtaining a value of N in order to converge the resonance frequency and the bandwidth of the FSS analyzed, then the results obtained were compared. The methodology applied is validated with the construction and measurement of prototypes with different geometries of the cells of the arrays of FSS.

Método híbrido para projeto de superfícies seletivas em frequência

This thesis presents a hybrid technique of frequency selective surfaces project (FSS) on a isotropic dielectric layer, considering various geometries for the elements of the unit cell. Specifically, the hybrid technique uses the equivalent circuit method in conjunction with genetic algorithm, aiming at the synthesis of structures with response single-band and dual-band. The equivalent circuit method allows you to model the structure by using an equivalent circuit and also obtaining circuits for different geometries. From the obtaining of the parameters of these circuits, you can get the transmission and reflection characteristics of patterned structures. For the optimization of patterned structures, according to the desired frequency response, Matlab™ optimization tool named optimtool proved to be easy to use, allowing you to explore important results on the optimization analysis. In this thesis, numeric and experimental results are presented for the different characteristics of the analyzed geometries. For this, it was determined a technique to obtain the parameter N, which is based on genetic algorithms and differential geometry, to obtain the algebraic rational models that determine values of N more accurate, facilitating new projects of FSS with these geometries. The optimal results of N are grouped according to the occupancy factor of the cell and the thickness of the dielectric, for modeling of the structures by means of rational algebraic equations. Furthermore, for the proposed hybrid model was developed a fitness function for the purpose of calculating the error occurred in the definitions of FSS bandwidths with transmission features single band and dual band. This thesis deals with the construction of prototypes of FSS with frequency settings and band widths obtained with the use of this function. The FSS were initially reviewed through simulations performed with the commercial software Ansoft Designer ™, followed by simulation with the equivalent circuit method for obtaining a value of N in order to converge the resonance frequency and the bandwidth of the FSS analyzed, then the results obtained were compared. The methodology applied is validated with the construction and measurement of prototypes with different geometries of the cells of the arrays of FSS.

Locally recurrent functions, density topologies and algebraic genericity

We study the algebraic and topological genericity of certain subsets of locally recurrent functions, obtaining (among other results) algebrability and spaceability within these classes.

Fibrillar Elastomeric Micropatterns Create Tunable Adhesion Even to Rough Surfaces

Acknowledgements V.B., N.K.G., and E.A. contributed with conception and experimental design. V.B. performed the experiments. V.B., R.H., A.G., and R.M.M. carried out analysis and interpretation of data. V.B., R.H., A.G., and E.A. wrote the manuscript. V.B. and R.H. contributed equally to this work. V.B. acknowledges funding by SPP 1420 of the German Science Foundation DFG. E.A., N.K.G., and R.H. acknowledge funding from the European Research Council under the European Union/ERC Advanced Grant “Switch2Stick,” Agreement No. 340929.

Locally recurrent functions, density topologies and algebraic genericity

We study the algebraic and topological genericity of certain subsets of locally recurrent functions, obtaining (among other results) algebrability and spaceability within these classes.

The optical response of nanostructured surfaces and the composite diffracted evanescent wave model

Investigations of the optical response of subwavelength-structure arrays milled into thin metal films have revealed surprising phenomena, including reports of unexpectedly high transmission of light. Many studies have interpreted the optical coupling to the surface in terms of the resonant excitation of surface plasmon polaritons (SPPs), but other approaches involving composite diffraction of surface evanescent waves (CDEW) have also been proposed. Here we present a series of measurements on very simple one-dimensional subwavelength structures to test the key properties of the surface waves, and compare them to the CDEW and SPP models. We find that the optical response of the silver metal surface proceeds in two steps: a diffractive perturbation in the immediate vicinity (2–3 mu m) of the structure, followed by excitation of a persistent surface wave that propagates over tens of micrometres. The measured wavelength and phase of this persistent wave are significantly shifted from those expected for resonance excitation of a conventional SPP on a pure silver surface.

On surfaces with prescribed shape operator

The problem of immersing a simply connected surface with a prescribed shape operator is discussed. I show that, aside from some special degenerate cases, such as when the shape operator can be realized by a surface with one family of principal curves being geodesic, the space of such realizations is a convex set in an affine space of dimension at most 3. The cases where this maximum dimension of realizability is achieved are analyzed and it is found that there are two such families of shape operators, one depending essentially on three arbitrary functions of one variable and another depending essentially on two arbitrary functions of one variable. The space of realizations is discussed in each case, along with some of their remarkable geometric properties. Several explicit examples are constructed.

Introducing molaR: a New R Package for Quantitative Topographic Analysis of Teeth (and Other Topographic Surfaces)

© 2016 Springer Science+Business Media New YorkResearchers studying mammalian dentitions from functional and adaptive perspectives increasingly have moved towards using dental topography measures that can be estimated from 3D surface scans, which do not require identification of specific homologous landmarks. Here we present molaR, a new R package designed to assist researchers in calculating four commonly used topographic measures: Dirichlet Normal Energy (DNE), Relief Index (RFI), Orientation Patch Count (OPC), and Orientation Patch Count Rotated (OPCR) from surface scans of teeth, enabling a unified application of these informative new metrics. In addition to providing topographic measuring tools, molaR has complimentary plotting functions enabling highly customizable visualization of results. This article gives a detailed description of the DNE measure, walks researchers through installing, operating, and troubleshooting molaR and its functions, and gives an example of a simple comparison that measured teeth of the primates Alouatta and Pithecia in molaR and other available software packages. molaR is a free and open source software extension, which can be found at the doi:10.13140/RG.2.1.3563.4961(molaR v. 2.0) as well as on the Internet repository CRAN, which stores R packages.

Organic functionalisation, doping and characterisation of semiconductor surfaces for future CMOS device applications

Organic Functionalisation, Doping and Characterisation of Semiconductor Surfaces for Future CMOS Device Applications Semiconductor materials have long been the driving force for the advancement of technology since their inception in the mid-20th century. Traditionally, micro-electronic devices based upon these materials have scaled down in size and doubled in transistor density in accordance with the well-known Moore’s law, enabling consumer products with outstanding computational power at lower costs and with smaller footprints. According to the International Technology Roadmap for Semiconductors (ITRS), the scaling of metal-oxide-semiconductor field-effect transistors (MOSFETs) is proceeding at a rapid pace and will reach sub-10 nm dimensions in the coming years. This scaling presents many challenges, not only in terms of metrology but also in terms of the material preparation especially with respect to doping, leading to the moniker “More-than-Moore”. Current transistor technologies are based on the use of semiconductor junctions formed by the introduction of dopant atoms into the material using various methodologies and at device sizes below 10 nm, high concentration gradients become a necessity. Doping, the controlled and purposeful addition of impurities to a semiconductor, is one of the most important steps in the material preparation with uniform and confined doping to form ultra-shallow junctions at source and drain extension regions being one of the key enablers for the continued scaling of devices. Monolayer doping has shown promise to satisfy the need to conformally dope at such small feature sizes. Monolayer doping (MLD) has been shown to satisfy the requirements for extended defect-free, conformal and controllable doping on many materials ranging from the traditional silicon and germanium devices to emerging replacement materials such as III-V compounds This thesis aims to investigate the potential of monolayer doping to complement or replace conventional doping technologies currently in use in CMOS fabrication facilities across the world.

Permanent open water surfaces in central Siberia from ENVISAT ASAR wide swath data 2003/2004, link to shapefile

Permanent water bodies not only store dissolved CO2 but are essential for the maintenance of wetlands in their proximity. From the viewpoint of greenhouse gas (GHG) accounting wetland functions comprise sequestration of carbon under anaerobic conditions and methane release. The investigated area in central Siberia covers boreal and sub-arctic environments. Small inundated basins are abundant on the sub-arctic Taymir lowlands but also in parts of severe boreal climate where permafrost ice content is high and feature important freshwater ecosystems. Satellite radar imagery (ENVISAT ScanSAR), acquired in summer 2003 and 2004, has been used to derive open water surfaces with 150 m resolution, covering an area of approximately 3 Mkm**2. The open water surface maps were derived using a simple threshold-based classification method. The results were assessed with Russian forest inventory data, which includes detailed information about water bodies. The resulting classification has been further used to estimate the extent of tundra wetlands and to determine their importance for methane emissions. Tundra wetlands cover 7% (400,000 km**2) of the study region and methane emissions from hydromorphic soils are estimated to be 45,000 t/d for the Taymir peninsula.

A monoidal algebraic model for rational SO(2)-spectra

The category of rational SO(2)--equivariant spectra admits an algebraic model. That is, there is an abelian category A(SO(2)) whose derived category is equivalent to the homotopy category of rational$SO(2)--equivariant spectra. An important question is: does this algebraic model capture the smash product of spectra? The category A(SO(2)) is known as Greenlees' standard model, it is an abelian category that has no projective objects and is constructed from modules over a non--Noetherian ring. As a consequence, the standard techniques for constructing a monoidal model structure cannot be applied. In this paper a monoidal model structure on A(SO(2)) is constructed and the derived tensor product on the homotopy category is shown to be compatible with the smash product of spectra. The method used is related to techniques developed by the author in earlier joint work with Roitzheim. That work constructed a monoidal model structure on Franke's exotic model for the K_(p)--local stable homotopy category. A monoidal Quillen equivalence to a simpler monoidal model category that has explicit generating sets is also given. Having monoidal model structures on the two categories removes a serious obstruction to constructing a series of monoidal Quillen equivalences between the algebraic model and rational SO(2)--equivariant spectra.