Zonoids, Linear Dependence, and Size-Biased Distributions on the Simplex.

The zonoid of a d-dimensional random vector is used as a tool for measuring linear dependence among its components. A preorder of linear dependence is defined through inclusion of the zonoids. The zonoid of a random vector does not characterize its distribution, but it characterizes the size biased distribution of its compositional variables. This fact will allow a characterization of our linear dependence order in terms of a linear-convex order for the size-biased compositional variables. In dimension 2 the linear dependence preorder will be shown to be weaker than the concordance order. Some examples related to the Marshall-Olkin distribution and to a copula model will be presented, and a class of measures of linear dependence will be proposed.zonoid, zonotope, linear dependence, compositional variables, multivariate size biased distribution, concordance order, Marshall-Olkin distribution.

Finding maxmin allocations in cooperative and competitive fair division

We consider upper and lower bounds for maxmin allocations of a completely divisible good in both competitive and cooperative strategic contexts. We then derive a subgradient algorithm to compute the exact value up to any fixed degree of precision.Comment: 20 pages, 3 figures. This third version improves the overll presentation; Optimization and Control (math.OC), Computer Science and Game Theory (cs.GT), Probability (math.PR

Fair division of goods in the shadow of market values

Inheritances, divorces or liquidations of companies require common assets to be divided among the entitled parties. Legal methods usually consider the market value of goods, while fair division theory takes into account the parties’ preferences expressed as utilities. I combine the two practices to define a procedure that optimally allocates divisible goods with market values to people with easily elicited preferences. Imposing an exact equality on the bundles’ monetary values may produce unacceptable solutions. I drop the tight requirement and suggest a procedure in which the differences in the monetary values are explained in terms of satisfaction per monetary share as perceived by the agents. A robustness study shows the consequences of misspecification in the model parameters

Minimal winning coalitions and orders of criticality

In this paper, we analyze the order of criticality in simple games, under the light of minimal winning coalitions.The order of criticality of a player in a simple game is based on the minimal number of other players that have to leave so that the player in question becomes pivotal.We showthat this definition can be formulated referring to the cardinality of theminimal blocking coalitions or minimal hitting sets for the family of minimal winning coalitions; moreover, the blocking coalitions are related to the winning coalitions of the dual game. Finally,we propose to rank all the players lexicographically accounting the number of coalitions for which they are critical of each order, and we characterize this ranking using four independent axioms

Study and Optimization of a CO2 Sparger for Carbonated Beverages and Beer by Means of CFD Modeling

In the present work, two different geometries of spargers for beverage carbonation were modeled by means of CFD technique, taking into consideration three different flow rates. The first geometry presented a radial inlet of liquid food while the second one a tangential one. Calculation allowed to study the effect of fluid velocities on mixing and to identify the best solution; mathematical results were then confirmed from a qualitative point of view by experimental tests with both water and apple juice. CFD resulted a very useful technique for in-silico designing, not only for technically-simple parts of plants but also for very complicated ones such as carbon dioxide spargers in which gas and liquid are mixed together

Post-Mortem Computed Tomographic Features of the Most Caudal Lumbar Vertebrae, Anatomical Variations and Acquired Osseous Pathological Changes, in a Mixed Population of Horses

The radiographic, ultrasonographic, and scintigraphic findings of horses with thoracolumbosacral pain have been previously reported. In this study, the computed tomographic appearance of anatomical variations and pathological changes of the equine caudal lumbar region through a post-mortem examination were investigated. A total of 40 horses that had died or were submitted for euthanasia, for reasons unrelated to the study, were included in the study. From all the specimens, the modified vertebral system was adopted to evaluate and describe the four most caudal lumbar vertebrae, which were numbered from a caudal reference point (lumbosacral junction), with the segment number designated within parentheses (i.e., L(i)-L(iv)). Contact of the spinous processes was detected in 21 specimens (54%) and fusion in 6 specimens (15%). Lumbar spondylosis was seen in 17 specimens (42.5%), more commonly on the lateral aspect or on both ventral and lateral aspects in 12 specimens (71%). The presence of spondylosis was found more commonly in older horses (p < 0.001). There was no difference in bony density in specimens with spondylosis or spinous processes contact compared to specimens without. The highest prevalence of bony changes was found at L(ii)-L(i) intertransverse joints in 28 specimens (97%) on the left and in 22 specimens (96%) on the right side. Spondylolisthesis and partial fusion of the L(ii)-L(i) vertebral disc were found in association with degenerative pathologies. This study showed a high frequency of several anatomical variations and acquired osseous pathological changes in the most caudal lumbar vertebrae via a CT examination

Exercícios passivos na reabilitação de pacientes com dor, edema e limitação articular: estudo piloto

Imobilização parcial ou completa leva a diferentes processos de ajuste como perda de força muscular, diminuição do desempenho geral e edema. Objetivo: Avaliar a melhora da dor utilizando de um dispositivo eletromecânico que realiza movimentos passivo nos pacientes com dor, limitação da mobilidade e uso de dispositivos auxiliadores da marcha. Método: Foram avaliados em ensaio clinico prospectivo 20 pacientes, a melhora da dor, fazendo uso de dispositivos auxiliares de locomoção, em pacientes que faziam tratamento convencional por quatro a 12 meses, mas que passaram a fazer diariamente por uma hora e, comparando com exercício passivo realizado com o dispositivo, por duas horas/dia,  por cinco dias, e avaliados pela escala analógica de dor antes e depois no Hospital de Base da Fundação Faculdade de Medicina de São Jose do Rio Preto - FUNFARME de março de 2019 a janeiro de 2020. Resultados: Quando compara a diferença de redução do grupo realizou dispositivo eletromecânico passivo com o grupo convencional houve uma redução de 6,6 na escala analógica de dor e em relação ao grupo convencional de 2, sendo diferente estatisticamente teste t pareado valor p= 0,0001. Conclusão: Exercícios passivos mecânicos, que realizam a drenagem linfática é uma nova opção de tratamento aos pacientes que tem dor e limitação crônica da marcha.Partial or complete immobilization leads to different adjustment processes such as loss of muscle strength, decreased overall performance and edema. Objective: Was to assess pain improvement using an electromechanical passive device in patients with pain, limited mobility and use of gait assistive devices. Method: 20 patients were evaluated in a prospective clinical trial, pain improvement, using auxiliary locomotion devices, in patients who underwent conventional treatment for four to 12 months, but who started doing it daily for an hour and, compared with exercise passive performed with electromechanical passive device, for two hours/day, for five days, and evaluated by the pain scale before and after in Hospital de Base - Fundação Faculdade de Medicina de Sao Jose do Rio Preto - FUNFARME from march 2019 to january 2020. Results: When comparing the difference in reduction of the electromechanical passive device group with the conventional group, there was a reduction of 6.6 in the analogue pain scale and in relation to the conventional group of 2, with a statistically different paired t-test p= 0.0001. Conclusion: Passive mechanical exercises that perform lymphatic drainage are a new treatment option for patients who have pain and chronic gait limitatio

PDGFA in Cashmere Goat: A Motivation for the Hair Follicle Stem Cells to Activate

The cashmere hair follicle (HF) perpetually goes through cycles of growth, involution and rest. The photoperiod is the main factor in the control of seasonal coat change in cashmere goats while stem cells play a crucial role in the HF growth. Several factors, including Platelet-Derived Growth Factor A (PDGFA), Bone Morphogenetic Protein 2 (BMP2) and Lim-Homeobox gene 2 (LHX2) are implicated in HF morphogenesis and cycle. In this work, the mentioned molecules were investigated to evaluate their role in follicular cycle activation. The study was performed on skin samples collected at different periods of HF cycle and the molecular expression of PDGFA, BMP2 and LHX2 was evaluated by Real-Time PCR (qPCR) at each time point. Since PDGFA showed the most variation, the goat PDGFA gene was sequenced and the protein localization was investigated by immunohistochemistry together with PDGF receptor &#945; (PDGFR&#945;). PDGFA immunostaining was observed in the basal layer of the HF outer root sheath and the immunoreaction appeared stronger in the regressive HFs compared to those in the anagen phase according to qPCR analysis. PDGFR&#945; was observed in the HF epithelium, proving the effect of PDGFA on the follicular structure. The data obtained suggest that PDGFA and BMP2 are both implicated in HF cycle in goat. In particular, PDGFA secreted by the HF is involved in the anagen activation

Some positive dependence stochastic orders

International audienceIn this paper we study some stochastic orders of positive dependence that arise when the underlying random vectors are ordered with respect to some multivariate hazard rate stochastic orders, and have the same univariate marginal distributions. We show how the orders can be studied by restricting them to copulae, we give a number of examples, and we study some positive dependence concepts that arise from the new positive dependence orders. We also discuss the relationship of the new orders to other positive dependence orders that have appeared in the literature