Central configurations of nested regular polyhedra for the spatial 2n–body problem

We consider 2n masses located at the vertices of two nested regular polyhedra with the same number of vertices. Assuming that the masses in each polyhedron are equal, we prove that for each ratio of the masses of the inner and the outer polyhedron there exists a unique ratio of the length of the edges of the inner and the outer polyhedron such that the configuration is central.

Central configurations of three nested regular polyhedra for the spatial 3n–body problem

Three regular polyhedra are called nested if they have the same number of vertices n, the same center and the positions of the vertices of the inner polyhedron ri, the ones of the medium polyhedron Ri and the ones of the outer polyhedron Ri satisfy the relation Ri = ri and Ri = Rri for some scale factors R > > 1 and for all i = 1, . . . , n. We consider 3n masses located at the vertices of three nested regular polyhedra. We assume that the masses of the inner polyhedron are equal to m1, the masses of the medium one are equal to m2, and the masses of the outer one are equal to m3. We prove that if the ratios of the masses m2/m1 and m3/m1 and the scale factors and R satisfy two convenient relations, then this configuration is central for the 3n–body problem. Moreover there is some numerical evidence that, first, fixed two values of the ratios m2/m1 and m3/m1, the 3n–body problem has a unique central configuration of this type; and second that the number of nested regular polyhedra with the same number of vertices forming a central configuration for convenient masses and sizes is arbitrary.

Learning about Bayesian networks for forensic interpretation : An example based on the "the problem of multiple propositions"

Both, Bayesian networks and probabilistic evaluation are gaining more and more widespread use within many professional branches, including forensic science. Notwithstanding, they constitute subtle topics with definitional details that require careful study. While many sophisticated developments of probabilistic approaches to evaluation of forensic findings may readily be found in published literature, there remains a gap with respect to writings that focus on foundational aspects and on how these may be acquired by interested scientists new to these topics. This paper takes this as a starting point to report on the learning about Bayesian networks for likelihood ratio based, probabilistic inference procedures in a class of master students in forensic science. The presentation uses an example that relies on a casework scenario drawn from published literature, involving a questioned signature. A complicating aspect of that case study - proposed to students in a teaching scenario - is due to the need of considering multiple competing propositions, which is an outset that may not readily be approached within a likelihood ratio based framework without drawing attention to some additional technical details. Using generic Bayesian networks fragments from existing literature on the topic, course participants were able to track the probabilistic underpinnings of the proposed scenario correctly both in terms of likelihood ratios and of posterior probabilities. In addition, further study of the example by students allowed them to derive an alternative Bayesian network structure with a computational output that is equivalent to existing probabilistic solutions. This practical experience underlines the potential of Bayesian networks to support and clarify foundational principles of probabilistic procedures for forensic evaluation.

Periodic orbits of integrable birational maps on the plane: blending dynamics and algebraic geometry, the Lyness' case

Contingut del Pòster presentat al congrés New Trends in Dynamical Systems

Sub- or intertrochanteric fracture following screw fixation of an intracapsular proximal femoral fracture: true complication or technical error?

PURPOSE: To review, retrospectively, the possible causes of sub- or intertrochanteric fractures after screw fixation of intracapsular fractures of the proximal femur. METHODS: Eighty-four patients with an intracapsular fracture of proximal femur were operated between 1995 and 1998 by using three cannulated 6.25 mm screws. The screws were inserted in a triangular configuration, one screw in the upper part of the femoral neck and two screws in the inferior part. Between 1999 and 2001, we use two screws proximally and one screw distally. RESULTS: In the first series, two patients died within one week after operation. Sixty-four fractures healed without problems. Four patients developed an atrophic non-union; avascular necrosis of the femoral head was found in 11 patients. Three patients (3.6%) suffered a sub- and/or intertrochanteric fracture after a mean postoperative time of 30 days, in one case without obvious trauma. In all three cases surgical revision was necessary. Between 1999 and 2001 we did not observe any fracture after screwing. CONCLUSION: Two screws in the inferior part of the femoral neck create a stress riser in the subtrochanteric region, potentially inducing a fracture in the weakened bone. For internal fixation for proximal intracapsular femoral fracture only one screw must be inserted in the inferior part of neck.

Microstructure and magnetic properties of Ni50 Mn37 Sn13 Heusler alloy ribbons

The Heusler alloy Ni50 Mn37 Sn13 was successfully produced as ribbon flakes of thickness around 7-10 μm melt spinning. Fracture cross section micrographs in the ribbon show the formation of a microcrystalline columnarlike microstructure, with their longer axes perpendicular to the ribbon plane. Phase transition temperatures of the martensite-austenite transformation were found to be MS =218 K, Mf =207 K, AS =224 K, and Af =232 K; the thermal hysteresis of the transformation is 15 K. Ferromagnetic L 21 bcc austenite phase shows a Curie point of 313 K, with cell parameter a=0.5971 (5) nm at 298 K, transforming into a modulated 7M orthorhombic martensite with a=0.6121 (7) nm, b=0.6058 (8) nm, and c=0.5660 (2) nm, at 150 K

Constitution, Diversification and Normalisation of a Health Problem: Organising the Fight against AIDS in Switzerland (1984-2005)

The article traces the formation, diversification and normalization of the AIDS cause in Switzerland. Particular emphasis is placed on interactions between the medical field, public authorities and associative space, the latter being understood as the place where individual and collective actors compete to define the cause. The authors argue that the major phases in the structuring of the struggle, the pace of state intervention and the creation of a multi-organizational field, can only be understood if one adopts a 'configurational perspective' attentive to the manner in which, in a given context and under the effect of particular constraints, key actors strategically interact and contribute to transforming their environment and their chances of reaching their goals. This approach takes into account the changing socio-biological characteristics of those who have committed themselves to the cause. In turn, internal movement divisions about how to respond to the epidemic as well as the changing perceptions of the disease have modified the opportunities for commitment, encouraging certain individual kinds of people and excluding others.

A propos des "small area variations": opérations pour fracture de hanche dans le canton de Vaud. [Small area variations: surgery for hip fractures in the canton of Vaud].

OBJECTIVES: Studies of small area variations of health care utilization are more and more frequent. Such variations are often considered to be an indication of variations in the quality of medical care. The variations in the rate of operations for hip fractures are among the lowest studied to date, due to the fact that a consensus exists concerning this surgery. Our objective is to examine these variations within the context of relatively small and heterogeneous districts. METHOD: Based on anonymous computerized data on public hospital stays, this study describes the variations in population rates (crude and standardized) of operations for hip fracture among the health districts of the Canton of Vaud for the period from 1986 to 1991. District populations vary from 22,000 to 164,000. Using the extremal quotient (EQ), the importance of these variations was determined. RESULTS: The study population consists of 2363 cases, of which 78% are women. Mean age is 80.4 for women and 70.6 for men. Standardized rates of operation for hip fracture per 100,000 in the Canton Vaud for the years 1986 to 1991 are, respectively: 56; 67; 86; 91; 89 and 94. The EQ for the years 1986 to 1991 are respectively: 8.2; 4.0; 3.5; 2.7; 1.9 and 1.9. The high EQ, especially for the earlier years, are contrary to the initial premise of absence of variation. The progressive implementation in the Canton Vaud of VESKA medical statistics could play a role, as could the small size of many of the districts, with resultant instability of rates. CONCLUSIONS: Considering the wide variations shown here for an operation hardly regarded as subject to variations, it is important to exercise caution in interpreting published data of small area variations.

Effect of once-yearly zoledronic acid five milligrams on fracture risk and change in femoral neck bone mineral density.

CONTEXT: In the Health Outcomes and Reduced Incidence with Zoledronic Acid Once Yearly - Pivotal Fracture Trial (HORIZON-PFT), zoledronic acid (ZOL) 5 mg significantly reduced fracture risk. OBJECTIVE: The aim of the study was to identify factors associated with greater efficacy during ZOL 5 mg treatment. DESIGN, SETTING, AND PATIENTS: We conducted a subgroup analysis (preplanned and post hoc) of a multicenter, double-blind, placebo-controlled, 36-month trial in 7765 women with postmenopausal osteoporosis. Intervention: A single infusion of ZOL 5 mg or placebo was administered at baseline, 12, and 24 months. MAIN OUTCOME MEASURES: Primary endpoints were new vertebral fracture and hip fracture. Secondary endpoints were nonvertebral fracture and change in femoral neck bone mineral density (BMD). Baseline risk factor subgroups were age, BMD T-score and vertebral fracture status, total hip BMD, race, weight, geographical region, smoking, height loss, history of falls, physical activity, prior bisphosphonates, creatinine clearance, body mass index, and concomitant osteoporosis medications. RESULTS: Greater ZOL induced effects on vertebral fracture risk were seen with younger age (treatment-by-subgroup interaction, P = 0.05), normal creatinine clearance (P = 0.04), and body mass index >or= 25 kg/m(2) (P = 0.02). There were no significant treatment-factor interactions for hip or nonvertebral fracture or for change in BMD. CONCLUSIONS: ZOL appeared more effective in preventing vertebral fracture in younger women, overweight/obese women, and women with normal renal function. ZOL had similar effects irrespective of fracture risk factors or femoral neck BMD.

Nouveautés dans la prise en charge des fractures vertébrales ostéoporotiques: place de la vertébroplastie et de la kyphoplastie [Trends in the treatment of spinal osteoporic fractures: vertebroplasty and kyphoplasty].

Vertebral osteoporotic fracture (VOF) is a major problem of public health. Surgical treatments such as vertebroplasty and kyphoplasty are interesting adjuvant treatments for the management of osteoporosis. A consensus proposed by the principal contributors of this management is important. Regarding the actual data, we propose a vertebroplasty or a kyphoplasty for all patients suffering of an acute VOF. If a previous kyphosis or an important local kyphosis exists, secondary to the acute VOF or others, we propose a kyphoplasty. If the VOF is older and the conservative treatment is inefficient, we propose a vertebroplasty. In all cases, a specific management and treatment of osteoporosis is proposed.

A hybrid algorithm combining metaheuristic with Monte Carlo simulation for solving the Stochastic Flow Shop problem

In this paper, a hybrid simulation-based algorithm is proposed for the StochasticFlow Shop Problem. The main idea of the methodology is to transform the stochastic problem into a deterministic problem and then apply simulation to the latter. In order to achieve this goal, we rely on Monte Carlo Simulation and an adapted version of a deterministic heuristic. This approach aims to provide flexibility and simplicity due to the fact that it is not constrained by any previous assumption and relies in well-tested heuristics.