On the Algebraic Properties of Convex Bodies

AMS subject classification: 52A01, 13C99.

Piecewise Convex Curves and their Integral Representation

2000 Mathematics Subject Classification: 52A10.

Efficiency improvement of non-uniformly-aged PV arrays

The utilization of solar energy by photovoltaic (PV) systems have received much research and development (R&D) attention across the globe. In the past decades, a large number of PV array have been installed. Since the installed PV arrays often operate in harsh environments, non-uniform aging can occur and impact adversely on the performance of PV systems, especially in the middle and late periods of their service life. Due to the high cost of replacing aged PV modules by new modules, it is appealing to improve energy efficiency of aged PV systems. For this purpose, this paper presents a PV module reconfiguration strategy to achieve the maximum power generation from non-uniformly aged PV arrays without significant investment. The proposed reconfiguration strategy is based on the cell-unit structure of PV modules, the operating voltage limit of gird-connected converter, and the resulted bucket-effect of the maximum short circuit current. The objectives are to analyze all the potential reorganization options of the PV modules, find the maximum power point and express it in a proposition. This proposition is further developed into a novel implementable algorithm to calculate the maximum power generation and the corresponding reconfiguration of the PV modules. The immediate benefits from this reconfiguration are the increased total power output and maximum power point voltage information for global maximum power point tracking (MPPT). A PV array simulation model is used to illustrate the proposed method under three different cases. Furthermore, an experimental rig is built to verify the effectiveness of the proposed method. The proposed method will open an effective approach for condition-based maintenance of emerging aging PV arrays.

Why (and When) are Preferences Convex? Threshold Effects and Uncertain Quality

It is often assumed (for analytical convenience, but also in accordance with common intuition) that consumer preferences are convex. In this paper, we consider circumstances under which such preferences are (or are not) optimal. In particular, we investigate a setting in which goods possess some hidden quality with known distribution, and the consumer chooses a bundle of goods that maximizes the probability that he receives some threshold level of this quality. We show that if the threshold is small relative to consumption levels, preferences will tend to be convex; whereas the opposite holds if the threshold is large. Our theory helps explain a broad spectrum of economic behavior (including, in particular, certain common commercial advertising strategies), suggesting that sensitivity to information about thresholds is deeply rooted in human psychology.

Convex and exact games with non-transferable utility

We generalize exactness to games with non-transferable utility (NTU). A game is exact if for each coalition there is a core allocation on the boundary of its payoff set. Convex games with transferable utility are well-known to be exact. We consider ve generalizations of convexity in the NTU setting. We show that each of ordinal, coalition merge, individual merge and marginal convexity can be uni¯ed under NTU exactness. We provide an example of a cardinally convex game which is not NTU exact. Finally, we relate the classes of Π-balanced, totally Π-balanced, NTU exact, totally NTU exact, ordinally convex, cardinally convex, coalition merge convex, individual merge convex and marginal convex games to one another.

A cardinally convex game with empty core

In this note we present a cardinally convex game (Sharkey, 1981) with empty core. Sharkey assumes that V (N) is convex, we do not do so, hence we do not contradict Sharkey's result.

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.

An Empirical Evaluation of Preconditioning Data for Accelerating Convex Hull Computations

The convex hull describes the extent or shape of a set of data and is used ubiquitously in computational geometry. Common algorithms to construct the convex hull on a finite set of n points (x,y) range from O(nlogn) time to O(n) time. However, it is often the case that a heuristic procedure is applied to reduce the original set of n points to a set of s < n points which contains the hull and so accelerates the final hull finding procedure. We present an algorithm to precondition data before building a 2D convex hull with integer coordinates, with three distinct advantages. First, for all practical purposes, it is linear; second, no explicit sorting of data is required and third, the reduced set of s points is constructed such that it forms an ordered set that can be directly pipelined into an O(n) time convex hull algorithm. Under these criteria a fast (or O(n)) pre-conditioner in principle creates a fast convex hull (approximately O(n)) for an arbitrary set of points. The paper empirically evaluates and quantifies the acceleration generated by the method against the most common convex hull algorithms. An extra acceleration of at least four times when compared to previous existing preconditioning methods is found from experiments on a dataset.

An Empirical Evaluation of Preconditioning Data for Accelerating Convex Hull Computations

The convex hull describes the extent or shape of a set of data and is used ubiquitously in computational geometry. Common algorithms to construct the convex hull on a finite set of n points (x,y) range from O(nlogn) time to O(n) time. However, it is often the case that a heuristic procedure is applied to reduce the original set of n points to a set of s < n points which contains the hull and so accelerates the final hull finding procedure. We present an algorithm to precondition data before building a 2D convex hull with integer coordinates, with three distinct advantages. First, for all practical purposes, it is linear; second, no explicit sorting of data is required and third, the reduced set of s points is constructed such that it forms an ordered set that can be directly pipelined into an O(n) time convex hull algorithm. Under these criteria a fast (or O(n)) pre-conditioner in principle creates a fast convex hull (approximately O(n)) for an arbitrary set of points. The paper empirically evaluates and quantifies the acceleration generated by the method against the most common convex hull algorithms. An extra acceleration of at least four times when compared to previous existing preconditioning methods is found from experiments on a dataset.

Data-Adaptive Modeling using Convex Regression

Thesis (Ph.D.)--University of Washington, 2016-08

Convex Optimization Algorithms and Statistical Bounds for Learning Structured Models

Thesis (Ph.D.)--University of Washington, 2016-08

On the Set of Locally Convex Topologies Compatible with a Given Topology on a Vector Space: Cardinality Aspects

For a topological vector space (X, τ ), we consider the family LCT (X, τ ) of all locally convex topologies defined on X, which give rise to the same continuous linear functionals as the original topology τ . We prove that for an infinite-dimensional reflexive Banach space (X, τ ), the cardinality of LCT (X, τ ) is at least c.

Mackey topology on locally convex spaces and on locally quasi-convex groups. Similarities and historical remarks

A counterpart of the Mackey–Arens Theorem for the class of locally quasi-convex topological Abelian groups (LQC-groups) was initiated in Chasco et al. (Stud Math 132(3):257–284, 1999). Several authors have been interested in the problems posed there and have done clarifying contributions, although the main question of that source remains open. Some differences between the Mackey Theory for locally convex spaces and for locally quasi-convex groups, stem from the following fact: The supremum of all compatible locally quasi-convex topologies for a topological abelian group G may not coincide with the topology of uniform convergence on the weak quasi-convex compact subsets of the dual groupG∧. Thus, a substantial part of the classical Mackey–Arens Theorem cannot be generalized to LQC-groups. Furthermore, the mentioned fact gives rise to a grading in the property of “being a Mackey group”, as defined and thoroughly studied in Díaz Nieto and Martín-Peinador (Proceedings in Mathematics and Statistics 80:119–144, 2014). At present it is not known—and this is the main open question—if the supremum of all the compatible locally quasi-convex topologies on a topological group is in fact a compatible topology. In the present paper we do a sort of historical review on the Mackey Theory, and we compare it in the two settings of locally convex spaces and of locally quasi-convex groups. We point out some general questions which are still open, under the name of Problems.

Corrigendum to “The envelope theorem for multiobjective convex programming via contingent derivatives” [J. Math. Anal. Appl. 372 (1) (2010) 197–207]

The aim of this note is to formulate an envelope theorem for vector convex programs. This version corrects an earlier work, “The envelope theorem for multiobjective convex programming via contingent derivatives” by Jiménez Guerra et al. (2010) [3]. We first propose a necessary and sufficient condition allowing to restate the main result proved in the alluded paper. Second, we introduce a new Lagrange multiplier in order to obtain an envelope theorem avoiding the aforementioned error.