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.

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 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.

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.

J2 effect and elliptic inclined periodic orbits in the collision three-body problem

The existence of a new class of inclined periodic orbits of the collision restricted three-body problem is shown. The symmetric periodic solutions found are perturbations of elliptic kepler orbits and they exist only for special values of the inclination and are related to the motion of a satellite around an oblate planet

Bayesian Networks and the Value of the Evidence for the Forensic Two-Trace Transfer Problem

Forensic scientists face increasingly complex inference problems for evaluating likelihood ratios (LRs) for an appropriate pair of propositions. Up to now, scientists and statisticians have derived LR formulae using an algebraic approach. However, this approach reaches its limits when addressing cases with an increasing number of variables and dependence relationships between these variables. In this study, we suggest using a graphical approach, based on the construction of Bayesian networks (BNs). We first construct a BN that captures the problem, and then deduce the expression for calculating the LR from this model to compare it with existing LR formulae. We illustrate this idea by applying it to the evaluation of an activity level LR in the context of the two-trace transfer problem. Our approach allows us to relax assumptions made in previous LR developments, produce a new LR formula for the two-trace transfer problem and generalize this scenario to n traces.

The problem of nitrogen disposal in the obese

Amino-N is preserved because of the scarcity and nutritional importance of protein. Excretion requires its conversion to ammonia, later incorporated into urea. Under conditions of excess dietary energy, the body cannot easily dispose of the excess amino-N against the evolutively adapted schemes that prevent its wastage; thus ammonia and glutamine formation (and urea excretion) are decreased. High lipid (and energy) availability limits the utilisation of glucose, and high glucose spares the production of ammonium from amino acids, limiting the synthesis of glutamine and its utilisation by the intestine and kidney. The amino acid composition of the diet affects the production of ammonium depending on its composition and the individual amino acid catabolic pathways. Surplus amino acids enhance protein synthesis and growth, and the synthesis of non-protein-N-containing compounds. But these outlets are not enough; consequently, less-conventional mechanisms are activated, such as increased synthesis of NO∙ followed by higher nitrite (and nitrate) excretion and changes in the microbiota. There is also a significant production of N(2) gas, through unknown mechanisms. Health consequences of amino-N surplus are difficult to fathom because of the sparse data available, but it can be speculated that the effects may be negative, largely because the fundamental N homeostasis is stretched out of normalcy, forcing the N removal through pathways unprepared for that task. The unreliable results of hyperproteic diets, and part of the dysregulation found in the metabolic syndrome may be an unwanted consequence of this N disposal conflict.

Generating a raster map presentation of a forest resource by solving a transportation problem

Abstract

An Improved Hybrid Model for the Generic Hoist Scheduling Problem

Peer-reviewed