The kernel is in the least core for permutation games

Permutation games are totally balanced transferable utility cooperative games arising from certain sequencing and re-assignment optimization problems. It is known that for permutation games the bargaining set and the core coincide, consequently, the kernel is a subset of the core. We prove that for permutation games the kernel is contained in the least core, even if the latter is a lower dimensional subset of the core. By means of a 5-player permutation game we demonstrate that, in sense of the lexicographic center procedure leading to the nucleolus, this inclusion result can not be strengthened. Our 5-player permutation game is also an example (of minimum size) for a game with a non-convex kernel.

A Kullback-Leibler relatív entrópia függvény alkalmazása páros összehasonlítás mátrix egy prioritásvektora meghatározására (Applying the Kullback-Leibler relative entropy function for determining priorities for the pairwise comparison matrix)

A dolgozatban a döntéselméletben fontos szerepet játszó páros összehasonlítás mátrix prioritásvektorának meghatározására új megközelítést alkalmazunk. Az A páros összehasonlítás mátrix és a prioritásvektor által definiált B konzisztens mátrix közötti eltérést a Kullback-Leibler relatív entrópia-függvény segítségével mérjük. Ezen eltérés minimalizálása teljesen kitöltött mátrix esetében konvex programozási feladathoz vezet, nem teljesen kitöltött mátrix esetében pedig egy fixpont problémához. Az eltérésfüggvényt minimalizáló prioritásvektor egyben azzal a tulajdonsággal is rendelkezik, hogy az A mátrix elemeinek összege és a B mátrix elemeinek összege közötti különbség éppen az eltérésfüggvény minimumának az n-szerese, ahol n a feladat mérete. Így az eltérésfüggvény minimumának értéke két szempontból is lehet alkalmas az A mátrix inkonzisztenciájának a mérésére. _____ In this paper we apply a new approach for determining a priority vector for the pairwise comparison matrix which plays an important role in Decision Theory. The divergence between the pairwise comparison matrix A and the consistent matrix B defined by the priority vector is measured with the help of the Kullback-Leibler relative entropy function. The minimization of this divergence leads to a convex program in case of a complete matrix, leads to a fixed-point problem in case of an incomplete matrix. The priority vector minimizing the divergence also has the property that the difference of the sums of elements of the matrix A and the matrix B is n times the minimum of the divergence function where n is the dimension of the problem. Thus we developed two reasons for considering the value of the minimum of the divergence as a measure of inconsistency of the matrix A.

Improved stochastic optimization of railway timetables

We present a general model to find the best allocation of a limited amount of supplements (extra minutes added to a timetable in order to reduce delays) on a set of interfering railway lines. By the best allocation, we mean the solution under which the weighted sum of expected delays is minimal. Our aim is to finely adjust an already existing and well-functioning timetable. We model this inherently stochastic optimization problem by using two-stage recourse models from stochastic programming, building upon earlier research from the literature. We present an improved formulation, allowing for an efficient solution using a standard algorithm for recourse models. We show that our model may be solved using any of the following theoretical frameworks: linear programming, stochastic programming and convex non-linear programming, and present a comparison of these approaches based on a real-life case study. Finally, we introduce stochastic dependency into the model, and present a statistical technique to estimate the model parameters from empirical data.

(Tables 4-5, page 160) REE contents in ferromanganese concretions from the Gulf of Bothnia and the Barents Sea

Ferromanganese concretions from the Svalbard shelf in the Barents Sea show slightly convex shale-normalized REE patterns with no Eu anomalies. Concretions from the Gulf of Bothnia, northern part of the Baltic Sea, exhibit an enrichment of light REE and negative Eu anomalies. This difference is interpreted as a consequence of different conveyor mechanisms of the REE to the sediment. It is suggested that dissolving biogenic debris contributes to the convex pattern obtained in the Barents Sea, whereas an inorganic suspended fraction with scavenged REE is the main carrier in the Gulf of Bothnia. During oxic diagenesis in the sediment, the scavenged REE are set free into the porewater and contribute to the distribution pattern in concretions found in the Gulf of Bothnia. Small Mn-rich spheroidal concretions are enriched two to five times in REE compared to average shale, whereas Mn-poor flat concretions are low in REE. Specific surface area of the concretion and the depth of burial in the oxidized surface sediment are two factors that strongly affect the enrichment of the REE. Weak Ce anomalies are present in the analysed concretions and a redox level dependence is seen.

Estudo do balanço de umidade por meio de modelos regionais para o clima do passado e do futuro sobre a América do Sul

In the context of climate change over South America (SA) has been observed that the combination of high temperatures and rain more temperatures less rainfall, cause different impacts such as extreme precipitation events, favorable conditions for fires and droughts. As a result, these regions face growing threat of water shortage, local or generalized. Thus, the water availability in Brazil depends largely on the weather and its variations in different time scales. In this sense, the main objective of this research is to study the moisture budget through regional climate models (RCM) from Project Regional Climate Change Assessments for La Plata Basin (CLARIS-LPB) and combine these RCM through two statistical techniques in an attempt to improve prediction on three areas of AS: Amazon (AMZ), Northeast Brazil (NEB) and the Plata Basin (LPB) in past climates (1961-1990) and future (2071-2100). The moisture transport on AS was investigated through the moisture fluxes vertically integrated. The main results showed that the average fluxes of water vapor in the tropics (AMZ and NEB) are higher across the eastern and northern edges, thus indicating that the contributions of the trade winds of the North Atlantic and South are equally important for the entry moisture during the months of JJA and DJF. This configuration was observed in all the models and climates. In comparison climates, it was found that the convergence of the flow of moisture in the past weather was smaller in the future in various regions and seasons. Similarly, the majority of the SPC simulates the future climate, reduced precipitation in tropical regions (AMZ and NEB), and an increase in the LPB region. The second phase of this research was to carry out combination of RCM in more accurately predict precipitation, through the multiple regression techniques for components Main (C.RPC) and convex combination (C.EQM), and then analyze and compare combinations of RCM (ensemble). The results indicated that the combination was better in RPC represent precipitation observed in both climates. Since, in addition to showing values be close to those observed, the technique obtained coefficient of correlation of moderate to strong magnitude in almost every month in different climates and regions, also lower dispersion of data (RMSE). A significant advantage of the combination of methods was the ability to capture extreme events (outliers) for the study regions. In general, it was observed that the wet C.EQM captures more extreme, while C.RPC can capture more extreme dry climates and in the three regions studied.

Preferência e competição alimentar em um grupo de Sapajus flavius em fragmento de Mata Atlântica em Caaporã – Paraíba – Brasil

Feeding is the primary selective pressure in all forms of animals. Nutritional ecological models predict consequences of preferred and non-preferred food consumption on behavioural, physiological and morphological adaptations. At same time, socioecological models infer socio-organizarion patterns based on feeding competition faced by animals. A list of preferred foods, and inferences regarding the intensity of feeding competition and its behavioural consequences are information of much importance for management of populations in fragments. In this work we observed the feeding behavior and spatial positioning of a group of more than 100 blond capuchin monkeys (Sapajus flavius) that inhabit a fragment of Atlantic forest, surrounded by sugarcane plantation. We compared the consumption of different food items with their monthly availability in the area to define the preferred and fallback food items. We recorded the vocalizations of aggression and the inter-individual distance (area of Minimum Convex Polygon/n individuals) to infer the type of food competition experienced by animals. In the year studied the fruit feeding time correlated with top consumed fruit productivity, indicating preference for fruits. Our data indicate that the species Elaeis sp., Cecropia palmata, Inga spp. and Simarouba amara are the preferred food items in the diet. Available all year round and uniformly distributed, sugarcane was a regular item in the diet and its was characterized as a staple fallback food for this group. Although fruits are preferential food items, direct competition rate did not correlate to fruit productivity in the area, maintaining the high rates throughout the year (2.45 events/ hour). The inter-individual distance index positively correlated with rain fall indicating scramble food competition. The number of neighbours of females carrying infants was smaller when fruit productivity is low, indicating that females carrying infants are suffering increased indirect competition. Our data indicates that blond capuchins in this fragment make use of sugar cane as a staple fallback food, which evidence the importance of sugar cane landscape for the survival of this critically endangered capuchin species in fragmented habitats in Northeast Brazil. A preliminary list of preferred and important foods is offered, and can assist in the choice of trees for reforestation, better fragments to be preserved and areas of release and translocation of animals. We did not observe an increase of contest competition while using preferred foods, but when using staple FBF. This may be due the altered environment, which results in high competition food throughout the year. Both the food preference as the social and behavioral consequences of high food competition experienced by animals in this fragment must be accompanied over the years to ensure the survival of this population.

Preferência e competição alimentar em um grupo de Sapajus flavius em fragmento de Mata Atlântica em Caaporã – Paraíba – Brasil

Feeding is the primary selective pressure in all forms of animals. Nutritional ecological models predict consequences of preferred and non-preferred food consumption on behavioural, physiological and morphological adaptations. At same time, socioecological models infer socio-organizarion patterns based on feeding competition faced by animals. A list of preferred foods, and inferences regarding the intensity of feeding competition and its behavioural consequences are information of much importance for management of populations in fragments. In this work we observed the feeding behavior and spatial positioning of a group of more than 100 blond capuchin monkeys (Sapajus flavius) that inhabit a fragment of Atlantic forest, surrounded by sugarcane plantation. We compared the consumption of different food items with their monthly availability in the area to define the preferred and fallback food items. We recorded the vocalizations of aggression and the inter-individual distance (area of Minimum Convex Polygon/n individuals) to infer the type of food competition experienced by animals. In the year studied the fruit feeding time correlated with top consumed fruit productivity, indicating preference for fruits. Our data indicate that the species Elaeis sp., Cecropia palmata, Inga spp. and Simarouba amara are the preferred food items in the diet. Available all year round and uniformly distributed, sugarcane was a regular item in the diet and its was characterized as a staple fallback food for this group. Although fruits are preferential food items, direct competition rate did not correlate to fruit productivity in the area, maintaining the high rates throughout the year (2.45 events/ hour). The inter-individual distance index positively correlated with rain fall indicating scramble food competition. The number of neighbours of females carrying infants was smaller when fruit productivity is low, indicating that females carrying infants are suffering increased indirect competition. Our data indicates that blond capuchins in this fragment make use of sugar cane as a staple fallback food, which evidence the importance of sugar cane landscape for the survival of this critically endangered capuchin species in fragmented habitats in Northeast Brazil. A preliminary list of preferred and important foods is offered, and can assist in the choice of trees for reforestation, better fragments to be preserved and areas of release and translocation of animals. We did not observe an increase of contest competition while using preferred foods, but when using staple FBF. This may be due the altered environment, which results in high competition food throughout the year. Both the food preference as the social and behavioral consequences of high food competition experienced by animals in this fragment must be accompanied over the years to ensure the survival of this population.

Uma interface para o controle de robôs móveis por intermédio de gestos

The main objective of this work was to enable the recognition of human gestures through the development of a computer program. The program created captures the gestures executed by the user through a camera attached to the computer and sends it to the robot command referring to the gesture. They were interpreted in total ve gestures made by human hand. The software (developed in C ++) widely used the computer vision concepts and open source library OpenCV that directly impact the overall e ciency of the control of mobile robots. The computer vision concepts take into account the use of lters to smooth/blur the image noise reduction, color space to better suit the developer's desktop as well as useful information for manipulating digital images. The OpenCV library was essential in creating the project because it was possible to use various functions/procedures for complete control lters, image borders, image area, the geometric center of borders, exchange of color spaces, convex hull and convexity defect, plus all the necessary means for the characterization of imaged features. During the development of the software was the appearance of several problems, as false positives (noise), underperforming the insertion of various lters with sizes oversized masks, as well as problems arising from the choice of color space for processing human skin tones. However, after the development of seven versions of the control software, it was possible to minimize the occurrence of false positives due to a better use of lters combined with a well-dimensioned mask size (tested at run time) all associated with a programming logic that has been perfected over the construction of the seven versions. After all the development is managed software that met the established requirements. After the completion of the control software, it was observed that the overall e ectiveness of the various programs, highlighting in particular the V programs: 84.75 %, with VI: 93.00 % and VII with: 94.67 % showed that the nal program performed well in interpreting gestures, proving that it was possible the mobile robot control through human gestures without the need for external accessories to give it a better mobility and cost savings for maintain such a system. The great merit of the program was to assist capacity in demystifying the man set/machine therefore uses an easy and intuitive interface for control of mobile robots. Another important feature observed is that to control the mobile robot is not necessary to be close to the same, as to control the equipment is necessary to receive only the address that the Robotino passes to the program via network or Wi-Fi.

An evaluation of home range models for marine fish tracking and fine scale habitat use and movement patterns of age 1 Greenland cod (Gadus macrocephalus ogac)

My thesis examines fine-scale habitat use and movement patterns of age 1 Greenland cod (Gadus macrocephalus ogac) tracked using acoustic telemetry. Recent advances in tracking technologies such as GPS and acoustic telemetry have led to increasingly large and detailed datasets that present new opportunities for researchers to address fine-scale ecological questions regarding animal movement and spatial distribution. There is a growing demand for home range models that will not only work with massive quantities of autocorrelated data, but that can also exploit the added detail inherent in these high-resolution datasets. Most published home range studies use radio-telemetry or satellite data from terrestrial mammals or avian species, and most studies that evaluate the relative performance of home range models use simulated data. In Chapter 2, I used actual field-collected data from age-1 Greenland cod tracked with acoustic telemetry to evaluate the accuracy and precision of six home range models: minimum convex polygons, kernel densities with plug-in bandwidth selection and the reference bandwidth, adaptive local convex hulls, Brownian bridges, and dynamic Brownian bridges. I then applied the most appropriate model to two years (2010-2012) of tracking data collected from 82 tagged Greenland cod tracked in Newman Sound, Newfoundland, Canada, to determine diel and seasonal differences in habitat use and movement patterns (Chapter 3). Little is known of juvenile cod ecology, so resolving these relationships will provide valuable insight into activity patterns, habitat use, and predator-prey dynamics, while filling a knowledge gap regarding the use of space by age 1 Greenland cod in a coastal nursery habitat. By doing so, my thesis demonstrates an appropriate technique for modelling the spatial use of fish from acoustic telemetry data that can be applied to high-resolution, high-frequency tracking datasets collected from mobile organisms in any environment.

On Provable Algorithms for Determination of Continuous Protein Interdomain Motions from Residual Dipolar Couplings

Dynamics of biomolecules over various spatial and time scales are essential for biological functions such as molecular recognition, catalysis and signaling. However, reconstruction of biomolecular dynamics from experimental observables requires the determination of a conformational probability distribution. Unfortunately, these distributions cannot be fully constrained by the limited information from experiments, making the problem an ill-posed one in the terminology of Hadamard. The ill-posed nature of the problem comes from the fact that it has no unique solution. Multiple or even an infinite number of solutions may exist. To avoid the ill-posed nature, the problem needs to be regularized by making assumptions, which inevitably introduce biases into the result.

Here, I present two continuous probability density function approaches to solve an important inverse problem called the RDC trigonometric moment problem. By focusing on interdomain orientations we reduced the problem to determination of a distribution on the 3D rotational space from residual dipolar couplings (RDCs). We derived an analytical equation that relates alignment tensors of adjacent domains, which serves as the foundation of the two methods. In the first approach, the ill-posed nature of the problem was avoided by introducing a continuous distribution model, which enjoys a smoothness assumption. To find the optimal solution for the distribution, we also designed an efficient branch-and-bound algorithm that exploits the mathematical structure of the analytical solutions. The algorithm is guaranteed to find the distribution that best satisfies the analytical relationship. We observed good performance of the method when tested under various levels of experimental noise and when applied to two protein systems. The second approach avoids the use of any model by employing maximum entropy principles. This 'model-free' approach delivers the least biased result which presents our state of knowledge. In this approach, the solution is an exponential function of Lagrange multipliers. To determine the multipliers, a convex objective function is constructed. Consequently, the maximum entropy solution can be found easily by gradient descent methods. Both algorithms can be applied to biomolecular RDC data in general, including data from RNA and DNA molecules.

Advanced Applications of 3D Dosimetry and 3D Printing in Radiation Therapy

As complex radiotherapy techniques become more readily-practiced, comprehensive 3D dosimetry is a growing necessity for advanced quality assurance. However, clinical implementation has been impeded by a wide variety of factors, including the expense of dedicated optical dosimeter readout tools, high operational costs, and the overall difficulty of use. To address these issues, a novel dry-tank optical CT scanner was designed for PRESAGE 3D dosimeter readout, relying on 3D printed components and omitting costly parts from preceding optical scanners. This work details the design, prototyping, and basic commissioning of the Duke Integrated-lens Optical Scanner (DIOS).

The convex scanning geometry was designed in ScanSim, an in-house Monte Carlo optical ray-tracing simulation. ScanSim parameters were used to build a 3D rendering of a convex ‘solid tank’ for optical-CT, which is capable of collimating a point light source into telecentric geometry without significant quantities of refractive-index matched fluid. The model was 3D printed, processed, and converted into a negative mold via rubber casting to produce a transparent polyurethane scanning tank. The DIOS was assembled with the solid tank, a 3W red LED light source, a computer-controlled rotation stage, and a 12-bit CCD camera. Initial optical phantom studies show negligible spatial inaccuracies in 2D projection images and 3D tomographic reconstructions. A PRESAGE 3D dose measurement for a 4-field box treatment plan from Eclipse shows 95% of voxels passing gamma analysis at 3%/3mm criteria. Gamma analysis between tomographic images of the same dosimeter in the DIOS and DLOS systems show 93.1% agreement at 5%/1mm criteria. From this initial study, the DIOS has demonstrated promise as an economically-viable optical-CT scanner. However, further improvements will be necessary to fully develop this system into an accurate and reliable tool for advanced QA.

Pre-clinical animal studies are used as a conventional means of translational research, as a midpoint between in-vitro cell studies and clinical implementation. However, modern small animal radiotherapy platforms are primitive in comparison with conventional linear accelerators. This work also investigates a series of 3D printed tools to expand the treatment capabilities of the X-RAD 225Cx orthovoltage irradiator, and applies them to a feasibility study of hippocampal avoidance in rodent whole-brain radiotherapy.

As an alternative material to lead, a novel 3D-printable tungsten-composite ABS plastic, GMASS, was tested to create precisely-shaped blocks. Film studies show virtually all primary radiation at 225 kVp can be attenuated by GMASS blocks of 0.5cm thickness. A state-of-the-art software, BlockGen, was used to create custom hippocampus-shaped blocks from medical image data, for any possible axial treatment field arrangement. A custom 3D printed bite block was developed to immobilize and position a supine rat for optimal hippocampal conformity. An immobilized rat CT with digitally-inserted blocks was imported into the SmART-Plan Monte-Carlo simulation software to determine the optimal beam arrangement. Protocols with 4 and 7 equally-spaced fields were considered as viable treatment options, featuring improved hippocampal conformity and whole-brain coverage when compared to prior lateral-opposed protocols. Custom rodent-morphic PRESAGE dosimeters were developed to accurately reflect these treatment scenarios, and a 3D dosimetry study was performed to confirm the SmART-Plan simulations. Measured doses indicate significant hippocampal sparing and moderate whole-brain coverage.

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.

Some examples of special Lagrangian tori

A short paper giving some examples of smooth hypersurfaces M of degree n+1 in complex projective n-space that are defined by real polynomial equations and whose real slice contains a component diffeomorphic to an n-1 torus, which is then special Lagrangian with respect to the Calabi-Yau metric on M.

Optimal Capital Requirements in Financial Networks with Fire Sales

I explore and analyze a problem of finding the socially optimal capital requirements for financial institutions considering two distinct channels of contagion: direct exposures among the institutions, as represented by a network and fire sales externalities, which reflect the negative price impact of massive liquidation of assets.These two channels amplify shocks from individual financial institutions to the financial system as a whole and thus increase the risk of joint defaults amongst the interconnected financial institutions; this is often referred to as systemic risk. In the model, there is a trade-off between reducing systemic risk and raising the capital requirements of the financial institutions. The policymaker considers this trade-off and determines the optimal capital requirements for individual financial institutions. I provide a method for finding and analyzing the optimal capital requirements that can be applied to arbitrary network structures and arbitrary distributions of investment returns.

In particular, I first consider a network model consisting only of direct exposures and show that the optimal capital requirements can be found by solving a stochastic linear programming problem. I then extend the analysis to financial networks with default costs and show the optimal capital requirements can be found by solving a stochastic mixed integer programming problem. The computational complexity of this problem poses a challenge, and I develop an iterative algorithm that can be efficiently executed. I show that the iterative algorithm leads to solutions that are nearly optimal by comparing it with lower bounds based on a dual approach. I also show that the iterative algorithm converges to the optimal solution.

Finally, I incorporate fire sales externalities into the model. In particular, I am able to extend the analysis of systemic risk and the optimal capital requirements with a single illiquid asset to a model with multiple illiquid assets. The model with multiple illiquid assets incorporates liquidation rules used by the banks. I provide an optimization formulation whose solution provides the equilibrium payments for a given liquidation rule.

I further show that the socially optimal capital problem using the ``socially optimal liquidation" and prioritized liquidation rules can be formulated as a convex and convex mixed integer problem, respectively. Finally, I illustrate the results of the methodology on numerical examples and

discuss some implications for capital regulation policy and stress testing.

Description of manganese deposits from the Papago mine, Saipan, Mariana Islands

Saipan, situated about 15° N. and 146° E., is one of the larger and more southerly of the Mariana Islands. The 15 small islands of this chain are strung along an eastwardly convex ridge for more than 400 miles north to south, midway between Honshu and New Guinea and about 1,200 miles east of the Philippines. Paralleling this ridge 60 to 100 miles further east is a deep submarine trench, beyond which lies the Pacific Basin proper. To the west is the Philippine Sea, generally deeper than 2,000 fathoms. The trench coincides with a zone of negative gravity anomalies, earthquake foci occur at increasing depths westward from it, and silica- and alumina-rich volcanic rocks characterize the emergent island chain itself. The contrast between these features and those of the Pacific Basin proper to the east is held to favor the conclusion that the Mariana island arc and trench define the structural and petrographic front of Asia.