Uncertainty in a mixed duopoly with quadratic costs

In this paper, we consider a mixed market with uncertain demand, involving one private firm and one public firm with quadratic costs. The model is a two-stage game in which players choose to make their output decisions either in stage 1 or stage 2. We assume that the demand is unknown until the end of the first stage. We compute the output levels at equilibrium in each possible role. We also determine ex-ante and ex-post firms’ payoff functions.

Vertex component analysis: a geometric-based approach to unmix hyperspectral data

Hyperspectral remote sensing exploits the electromagnetic scattering patterns of the different materials at specific wavelengths [2, 3]. Hyperspectral sensors have been developed to sample the scattered portion of the electromagnetic spectrum extending from the visible region through the near-infrared and mid-infrared, in hundreds of narrow contiguous bands [4, 5]. The number and variety of potential civilian and military applications of hyperspectral remote sensing is enormous [6, 7]. Very often, the resolution cell corresponding to a single pixel in an image contains several substances (endmembers) [4]. In this situation, the scattered energy is a mixing of the endmember spectra. A challenging task underlying many hyperspectral imagery applications is then decomposing a mixed pixel into a collection of reflectance spectra, called endmember signatures, and the corresponding abundance fractions [8–10]. Depending on the mixing scales at each pixel, the observed mixture is either linear or nonlinear [11, 12]. Linear mixing model holds approximately when the mixing scale is macroscopic [13] and there is negligible interaction among distinct endmembers [3, 14]. If, however, the mixing scale is microscopic (or intimate mixtures) [15, 16] and the incident solar radiation is scattered by the scene through multiple bounces involving several endmembers [17], the linear model is no longer accurate. Linear spectral unmixing has been intensively researched in the last years [9, 10, 12, 18–21]. It considers that a mixed pixel is a linear combination of endmember signatures weighted by the correspondent abundance fractions. Under this model, and assuming that the number of substances and their reflectance spectra are known, hyperspectral unmixing is a linear problem for which many solutions have been proposed (e.g., maximum likelihood estimation [8], spectral signature matching [22], spectral angle mapper [23], subspace projection methods [24,25], and constrained least squares [26]). In most cases, the number of substances and their reflectances are not known and, then, hyperspectral unmixing falls into the class of blind source separation problems [27]. Independent component analysis (ICA) has recently been proposed as a tool to blindly unmix hyperspectral data [28–31]. ICA is based on the assumption of mutually independent sources (abundance fractions), which is not the case of hyperspectral data, since the sum of abundance fractions is constant, implying statistical dependence among them. This dependence compromises ICA applicability to hyperspectral images as shown in Refs. [21, 32]. In fact, ICA finds the endmember signatures by multiplying the spectral vectors with an unmixing matrix, which minimizes the mutual information among sources. If sources are independent, ICA provides the correct unmixing, since the minimum of the mutual information is obtained only when sources are independent. This is no longer true for dependent abundance fractions. Nevertheless, some endmembers may be approximately unmixed. These aspects are addressed in Ref. [33]. Under the linear mixing model, the observations from a scene are in a simplex whose vertices correspond to the endmembers. Several approaches [34–36] have exploited this geometric feature of hyperspectral mixtures [35]. Minimum volume transform (MVT) algorithm [36] determines the simplex of minimum volume containing the data. The method presented in Ref. [37] is also of MVT type but, by introducing the notion of bundles, it takes into account the endmember variability usually present in hyperspectral mixtures. The MVT type approaches are complex from the computational point of view. Usually, these algorithms find in the first place the convex hull defined by the observed data and then fit a minimum volume simplex to it. For example, the gift wrapping algorithm [38] computes the convex hull of n data points in a d-dimensional space with a computational complexity of O(nbd=2cþ1), where bxc is the highest integer lower or equal than x and n is the number of samples. The complexity of the method presented in Ref. [37] is even higher, since the temperature of the simulated annealing algorithm used shall follow a log( ) law [39] to assure convergence (in probability) to the desired solution. Aiming at a lower computational complexity, some algorithms such as the pixel purity index (PPI) [35] and the N-FINDR [40] still find the minimum volume simplex containing the data cloud, but they assume the presence of at least one pure pixel of each endmember in the data. This is a strong requisite that may not hold in some data sets. In any case, these algorithms find the set of most pure pixels in the data. PPI algorithm uses the minimum noise fraction (MNF) [41] as a preprocessing step to reduce dimensionality and to improve the signal-to-noise ratio (SNR). The algorithm then projects every spectral vector onto skewers (large number of random vectors) [35, 42,43]. The points corresponding to extremes, for each skewer direction, are stored. A cumulative account records the number of times each pixel (i.e., a given spectral vector) is found to be an extreme. The pixels with the highest scores are the purest ones. N-FINDR algorithm [40] is based on the fact that in p spectral dimensions, the p-volume defined by a simplex formed by the purest pixels is larger than any other volume defined by any other combination of pixels. This algorithm finds the set of pixels defining the largest volume by inflating a simplex inside the data. ORA SIS [44, 45] is a hyperspectral framework developed by the U.S. Naval Research Laboratory consisting of several algorithms organized in six modules: exemplar selector, adaptative learner, demixer, knowledge base or spectral library, and spatial postrocessor. The first step consists in flat-fielding the spectra. Next, the exemplar selection module is used to select spectral vectors that best represent the smaller convex cone containing the data. The other pixels are rejected when the spectral angle distance (SAD) is less than a given thresh old. The procedure finds the basis for a subspace of a lower dimension using a modified Gram–Schmidt orthogonalizati on. The selected vectors are then projected onto this subspace and a simplex is found by an MV T pro cess. ORA SIS is oriented to real-time target detection from uncrewed air vehicles using hyperspectral data [46]. In this chapter we develop a new algorithm to unmix linear mixtures of endmember spectra. First, the algorithm determines the number of endmembers and the signal subspace using a newly developed concept [47, 48]. Second, the algorithm extracts the most pure pixels present in the data. Unlike other methods, this algorithm is completely automatic and unsupervised. To estimate the number of endmembers and the signal subspace in hyperspectral linear mixtures, the proposed scheme begins by estimating sign al and noise correlation matrices. The latter is based on multiple regression theory. The signal subspace is then identified by selectin g the set of signal eigenvalue s that best represents the data, in the least-square sense [48,49 ], we note, however, that VCA works with projected and with unprojected data. The extraction of the end members exploits two facts: (1) the endmembers are the vertices of a simplex and (2) the affine transformation of a simplex is also a simplex. As PPI and N-FIND R algorithms, VCA also assumes the presence of pure pixels in the data. The algorithm iteratively projects data on to a direction orthogonal to the subspace spanned by the endmembers already determined. The new end member signature corresponds to the extreme of the projection. The algorithm iterates until all end members are exhausted. VCA performs much better than PPI and better than or comparable to N-FI NDR; yet it has a computational complexity between on e and two orders of magnitude lower than N-FINDR. The chapter is structure d as follows. Section 19.2 describes the fundamentals of the proposed method. Section 19.3 and Section 19.4 evaluate the proposed algorithm using simulated and real data, respectively. Section 19.5 presents some concluding remarks.

An integer programming framework for sequencing cutting patterns based on interval graph completion

We derived a framework in integer programming, based on the properties of a linear ordering of the vertices in interval graphs, that acts as an edge completion model for obtaining interval graphs. This model can be applied to problems of sequencing cutting patterns, namely the minimization of open stacks problem (MOSP). By making small modifications in the objective function and using only some of the inequalities, the MOSP model is applied to another pattern sequencing problem that aims to minimize, not only the number of stacks, but also the order spread (the minimization of the stack occupation problem), and the model is tested.

Balancing and lot-sizing mixed-model lines in the footwear industry

This report describes the full research proposal for the project \Balancing and lot-sizing mixed-model lines in the footwear industry", to be developed as part of the master program in Engenharia Electrotécnica e de Computadores - Sistemas de Planeamento Industrial of the Instituto Superior de Engenharia do Porto. The Portuguese footwear industry is undergoing a period of great development and innovation. The numbers speak for themselves, Portugal footwear exported 71 million pairs of shoes to over 130 countries in 2012. It is a diverse sector, which covers different categories of women, men and children shoes, each of them with various models. New and technologically advanced mixed-model assembly lines are being projected and installed to replace traditional mass assembly lines. Obviously there is a need to manage them conveniently and to improve their operations. This work focuses on balancing and lot-sizing stitching mixed-model lines in a real world environment. For that purpose it will be fundamental to develop and evaluate adequate effective solution methods. Different objectives may be considered, which are relevant for the companies, such as minimizing the number of workstations, and minimizing the makespan, while taking into account a lot of practical restrictions. The solution approaches will be based on approximate methods, namely by resorting to metaheuristics. To show the impact of having different lots in production the initial maximum amount for each lot is changed and a Tabu Search based procedure is used to improve the solutions. The developed approaches will be evaluated and tested. A special attention will be given to the solution of real applied problems. Future work may include the study of other neighbourhood structures related to Tabu Search and the development of ways to speed up the evaluation of neighbours, as well as improving the balancing solution method.

Factorization of elliptic boundary value problems by invariant embedding and application to overdetermined problems

Dissertação para obtenção do Grau de Doutor em Matemática

Barriers preventing the successful integration of mental health services into Primary Health Care in Nigeria : a mixed methods approach

RESUMO: A Nigéria tem uma população estimada em cerca de 170 milhões de pessoas. O número de profissionais de saúde mental é muito diminuto, contando apenas com 150 psiquiatras o que perfaz aproximadamente um rácio de psiquiatra: população de mais de 1:1 milhão de pessoas. O Plano Nacional de Saúde Mental de 1991 reconheceu esta insuficiência e recomendou a integração dos serviços de saúde mental nos cuidados de saúde primários (CSP). Depois de mais de duas décadas, essa política não foi ainda implementada. Este estudo teve como objetivos mapear a estrutura organizacional dos serviços de saúde mental da Nigéria, e explorar os desafios e barreiras que impedem a integração bem-sucedida dos serviços de saúde mental nos cuidados de saúde primários, isto segundo a perspectiva dos profissionais dos cuidados de saúde primários. Com este objetivo, desenvolveu-se um estudo exploratório sequencial e utilizou-se um modelo misto para a recolha de dados. A aplicação em simultâneo de abordagens qualitativas e quantitativas permitiram compreender os problemas relacionados com a integração dos serviços de saúde mental nos CSP na Nigéria. No estudo qualitativo inicial, foram realizadas entrevistas com listagens abertas a 30 profissionais dos CSP, seguidas de dois grupos focais com profissionais dos CSP de duas zonas governamentais do estado de Oyo de forma a obter uma visão global das perspectivas destes profissionais locais sobre os desafios e barreiras que impedem uma integração bem-sucedida dos serviços de saúde mental nos CSP. Subsequentemente, foram realizadas entrevistas com quatro pessoas-chave, especificamente coordenadores e especialistas em saúde mental. Os resultados do estudo qualitativo foram utilizados para desenvolver um questionário para análise quantitativa das opiniões de uma amostra maior e mais representativa dos profissionais dos CSP do Estado de Oyo, bem como de duas zonas governamentais locais do Estado de Osun. As barreiras mais comummente identificadas a partir deste estudo incluem o estigma e os preconceitos sobre a doença mental, a formação inadequada dos profissionais dos CPS sobre saúde mental, a perceção pela equipa dos CSP de baixa prioridade de ação do Governo, o medo da agressão e violência pela equipa dos CSP, bem como a falta de disponibilidade de fármacos. As recomendações para superar estes desafios incluem a melhoria sustentada dos esforços da advocacia à saúde mental que vise uma maior valorização e apoio governamental, a formação e treino organizados dos profissionais dos cuidados primários, a criação de redes de referência e de apoio com instituições terciárias adjacentes, e o engajamento da comunidade para melhorar o acesso aos serviços e à reabilitação, pelas pessoas com doença mental. Estes resultados fornecem indicações úteis sobre a perceção das barreiras para a integração bem sucedida dos serviços de saúde mental nos CSP, enquanto se recomenda uma abordagem holística e abrangente. Esta informação pode orientar as futuras tentativas de implementação da integração dos serviços de saúde mental nos cuidados primários na Nigéria.------------ABSTRACT: Nigeria has an estimated population of about 170 million people but the number of mental health professionals is very small, with about 150 psychiatrists. This roughly translates to a psychiatrist:population ratio of more than 1:1 million people. The National Mental Health Policy of 1991 recognized this deficiency and recommended the integration of mental health into primary health care (PHC) delivery system. After more than two decades, this policy has yet to be implemented. This study aimed to map out the organizational structure of the mental health systems in Nigeria, and to explore the challenges and barriers preventing the successful integration of mental health into primary health care, from the perspective of the primary health care workers. A mixed methods exploratory sequential study design was employed, which entails the use of sequential timing in the combined methods of data collection. A combination of qualitative and uantitative approaches in sequence, were utilized to understand the problems of mental health services integration into PHC in Nigeria. The initial qualitative phase utilized free listing interviews with 30 PHC workers, followed by two focus group discussions with primary care workers from two Local Government Areas (LGA) of Oyo State to gain useful insight into the local perspectives of PHC workers about the challenges and barriers preventing successful integration of mental health care services into PHC. Subsequently, 4 key informant interviews with PHC co-ordinators and mental health experts were carried out. The findings from the qualitative study were utilized to develop a quantitative study questionnaire to understand the opinions of a larger and more representative sample of PHC staff in two more LGAs of Oyo State, as well as 2 LGAs from Osun State. The common barriers identified from this study include stigma and misconceptions about mental illness, inadequate training of PHC staff about mental health, low government priority, fear of aggression and violence by the PHC staff, as well as non-availability of medications. Recommendations for overcoming these challenges include improved and sustained efforts at mental health advocacy to gain governmental attention and support, organized training and retraining for primary care staff, establishment of referral and supportive networks with neighbouring tertiary facilities and community engagement to improve service utilization and rehabilitation of mentally ill persons. These findings provide useful insight into the barriers to the successful integration of mental health into PHC, while recommending a holistic and comprehensive approach. This information can guide future attempts to implement the integration of mental health into primary care in Nigeria.

A mixed finite element method for nonlinear diffusion equations

We propose a mixed finite element method for a class of nonlinear diffusion equations, which is based on their interpretation as gradient flows in optimal transportation metrics. We introduce an appropriate linearization of the optimal transport problem, which leads to a mixed symmetric formulation. This formulation preserves the maximum principle in case of the semi-discrete scheme as well as the fully discrete scheme for a certain class of problems. In addition solutions of the mixed formulation maintain exponential convergence in the relative entropy towards the steady state in case of a nonlinear Fokker-Planck equation with uniformly convex potential. We demonstrate the behavior of the proposed scheme with 2D simulations of the porous medium equations and blow-up questions in the Patlak-Keller-Segel model.

Social influences on fertility : a comparative mixed methods study in eastern and western Germany

This article uses a mixed methods design to investigate the effects of social influence on family formation in a sample of eastern and western German young adults at an early stage of their family formation. Theoretical propositions on the importance of informal interaction for fertility and family behavior are still rarely supported by systematic empirical evidence. Major problems are the correct identification of salient relationships and the comparability of social networks across population subgroups. This article addresses the two issues through a combination of qualitative and quantitative data collection and analysis. In-depth interviewing, network charts, and network grids are used to map individual personal relationships and their influence on family formation decisions. In addition, an analysis of friendship dyads is provided.

Assessment of inflammatory Bowel Disease patient's needs and problems from a nursing perspective

BACKGROUND: In this study, we aimed at assessing Inflammatory Bowel Disease patients' needs and current nursing practice to investigate to what extent consensus statements (European Crohn's and Colitis Organization) on the nursing roles in caring for patients with IBD concur with local practice. METHODS: We used a mixed-method convergent design to combine quantitative data prospectively collected in the Swiss IBD cohort study and qualitative data from structured interviews with IBD healthcare experts. Symptoms, quality of life, and anxiety and depression scores were retrieved from physician charts and patient self-reported questionnaires. Descriptive analyses were performed based on quantitative and qualitative data. RESULTS: 230 patients of a single center were included, 60% of patients were males, and median age was 40 (range 18-85). The prevalence of abdominal pain was 42%. Self-reported data were obtained from 75 out of 230 patients. General health was perceived significantly lower compared with the general population (p < 0.001). Prevalence of tiredness was 73%; sleep problems, 78%; issues related to work, 20%; sexual constraints, 35%; diarrhea, 67%; being afraid of not finding a bathroom, 42%; depression, 11%; and anxiety symptoms, 23%. According to experts' interviews, the consensus statements are found mostly relevant with many recommendations that are not yet realized in clinical practice. CONCLUSION: Identified prevalence may help clinicians in detecting patients at risk and improve patient management. © 2015 S. Karger AG, Basel.

Psychosexual development in men with congenital hypogonadotropic hypogonadism on long-term treatment: a mixed methods study.

INTRODUCTION: Congenital hypogonadotropic hypogonadism (CHH) is a rare, genetic, reproductive endocrine disorder characterized by absent puberty and infertility. Limited information is available on the psychosocial impact of CHH and psychosexual development in these patients. AIM: The aim of this study was to determine the impact of CHH on psychosexual development in men on long-term treatment. METHODS: A sequential mixed methods explanatory design was used. First, an online survey (quantitative) was used to quantify the frequency of psychosexual problems among CHH men. Second, patient focus groups (qualitative) were conducted to explore survey findings in detail and develop a working model to guide potential nursing and interdisciplinary interventions. MAIN OUTCOME MEASURES: Patient characteristics, frequency of body shame, difficulty with intimate relationships, and never having been sexually active were assessed. Additionally, we collected subjective patient-reported outcomes regarding the impact of CHH on psychological/emotional well-being, intimate relationships, and sexual activity. RESULTS: A total of 101 CHH men on long-term treatment (>1 year) were included for the analysis of the online survey (mean age 37 ± 11 years, range 19-66, median 36). Half (52/101, 51%) of the men had been seen at a specialized academic center and 37/101 (37%) reported having had fertility-inducing treatment. A high percentage of CHH men experience psychosexual problems including difficulty with intimate relationships (70%) and body image concerns/body shame (94/101, 93%), and the percentage of men never having been sexually active is five times the rate in a reference group (26% vs. 5.4%, P < 0.001). Focus groups revealed persisting body shame and low self-esteem despite long-term treatment that has lasting impact on psychosexual functioning. CONCLUSIONS: CHH men frequently experience psychosexual problems that pose barriers to intimate relationships and initiating sexual activity. These lingering effects cause significant distress and are not ameliorated by long-term treatment. Psychosexual assessment in CHH men with appropriate psychological support and treatment should be warranted in these patients. Dwyer AA, Quinton R, Pitteloud N, and Morin D. Psychosexual development in men with congenital hypogonadotropic hypogonadism on long-term treatment: A mixed methods study. Sex Med 2015;3:32-41.

The use of explicit algorithms and episodic context to teach subtraction to students with learning problems in mathematics /

This research attempted to address the question of the role of explicit algorithms and episodic contexts in the acquisition of computational procedures for regrouping in subtraction. Three groups of students having difficulty learning to subtract with regrouping were taught procedures for doing so through either an explicit algorithm, an episodic content or an examples approach. It was hypothesized that the use of an explicit algorithm represented in a flow chart format would facilitate the acquisition and retention of specific procedural steps relative to the other two conditions. On the other hand, the use of paragraph stories to create episodic content was expected to facilitate the retrieval of algorithms, particularly in a mixed presentation format. The subjects were tested on similar, near, and far transfer questions over a four-day period. Near and far transfer algorithms were also introduced on Day Two. The results suggested that both explicit and episodic context facilitate performance on questions requiring subtraction with regrouping. However, the differential effects of these two approaches on near and far transfer questions were not as easy to identify. Explicit algorithms may facilitate the acquisition of specific procedural steps while at the same time inhibiting the application of such steps to transfer questions. Similarly, the value of episodic context in cuing the retrieval of an algorithm may be limited by the ability of a subject to identify and classify a new question as an exemplar of a particular episodically deflned problem type or category. The implications of these findings in relation to the procedures employed in the teaching of Mathematics to students with learning problems are discussed in detail.

The dual role of students with behavioural problems: an analysis of their experiences as bullies and victims /

The present study examined the bullying experiences of a group of students, age 10-14 years, identified as having behaviour problems. A total often students participated in a series of mixed methodology activities, including self-report questionnaires, story telling exercises, and interview style joumaling. The main research questions were related to the prevalence of bully/victims and the type of bullying experiences in this population. Questionnaires gathered information about their involvement in bullying, as well as about psychological risk factors including normative beliefs about antisocial acts, impulsivity, problem solving, and coping strategies. Journal questions expanded on these themes and allowed students to explain their personal experiences as bullies and victims as well as provide suggestions for intervention. The overall results indicated that all of the ten students in this sample have participated in bullying as both a bully and a victim. This high prevalence of bully/victim involvement in students from behavioural classrooms is in sharp contrast with the general population where the prevalence is about 33%. In addition, a common thread was found that indicated that these students who participated in this study demonstrate characteristics of emotionally dysregulated reactive bullies. Theoretical implication and educational practices are discussed.

Zero-sum problems in finite cyclic groups

The purpose of this thesis is to investigate some open problems in the area of combinatorial number theory referred to as zero-sum theory. A zero-sequence in a finite cyclic group G is said to have the basic property if it is equivalent under group automorphism to one which has sum precisely IGI when this sum is viewed as an integer. This thesis investigates two major problems, the first of which is referred to as the basic pair problem. This problem seeks to determine conditions for which every zero-sequence of a given length in a finite abelian group has the basic property. We resolve an open problem regarding basic pairs in cyclic groups by demonstrating that every sequence of length four in Zp has the basic property, and we conjecture on the complete solution of this problem. The second problem is a 1988 conjecture of Kleitman and Lemke, part of which claims that every sequence of length n in Zn has a subsequence with the basic property. If one considers the special case where n is an odd integer we believe this conjecture to hold true. We verify this is the case for all prime integers less than 40, and all odd integers less than 26. In addition, we resolve the Kleitman-Lemke conjecture for general n in the negative. That is, we demonstrate a sequence in any finite abelian group isomorphic to Z2p (for p ~ 11 a prime) containing no subsequence with the basic property. These results, as well as the results found along the way, contribute to many other problems in zero-sum theory.

Problèmes de tournées de véhicules avec contraintes de chargement

Cette thèse s’intéresse aux problèmes de tournées de véhicules où l’on retrouve des contraintes de chargement ayant un impact sur les séquences de livraisons permises. Plus particulièrement, les items placés dans l’espace de chargement d’un véhicule doivent être directement accessibles lors de leur livraison sans qu’il soit nécessaire de déplacer d’autres items. Ces problèmes sont rencontrés dans plusieurs entreprises de transport qui livrent de gros objets (meubles, électroménagers). Le premier article de cette thèse porte sur une méthode exacte pour un problème de confection d’une seule tournée où un véhicule, dont l’aire de chargement est divisée en un certain nombre de piles, doit effectuer des cueillettes et des livraisons respectant une contrainte de type dernier entré, premier sorti. Lors d’une collecte, les items recueillis doivent nécessairement être déposés sur le dessus de l’une des piles. Par ailleurs, lors d’une livraison, les items doivent nécessairement se trouver sur le dessus de l’une des piles. Une méthode de séparation et évaluation avec plans sécants est proposée pour résoudre ce problème. Le second article présente une méthode de résolution exacte, également de type séparation et évaluation avec plans sécants, pour un problème de tournées de véhicules avec chargement d’items rectangulaires en deux dimensions. L’aire de chargement des véhicules correspond aussi à un espace rectangulaire avec une orientation, puisque les items doivent être chargés et déchargés par l’un des côtés. Une contrainte impose que les items d’un client soient directement accessibles au moment de leur livraison. Le dernier article aborde une problème de tournées de véhicules avec chargement d’items rectangulaires, mais où les dimensions de certains items ne sont pas connus avec certitude lors de la planification des tournées. Il est toutefois possible d’associer une distribution de probabilités discrète sur les dimensions possibles de ces items. Le problème est résolu de manière exacte avec la méthode L-Shape en nombres entiers.

Studies On Strength Characteristics Of Soil Mixed With Bio-Waste

Researches are always in quest for finding innovative methods for ground improvement using sustainable and environmental friendly solutions. Theproduction of large quantity of biowastes all over the world faces serious problems of handling and disposal. Coir pith is a biowaste from coir industry and sugarcane baggase is another biowaste obtained after extractingjuice from sugar cane. So the present study is an investigation into the effect of coir pith and sugarcane baggase on some geotechnical properties of red earth. The investigation includes study on variation of properties such as O.M.C, maximum dry density, C.B.R. values,unconfined compressive strength and permeability when these materials are included in soil. Several conclusions are arrived at, on the basis of the experiments conducted and it may be helpful for predicting the behavior of such soil matrix