A mathematical excursion: From the three-door problem to a Cantor-type perfect set

We start with a generalization of the well-known three-door problem:the n-door problem. The solution of this new problem leads us toa beautiful representation system for real numbers in (0,1] as alternated series, known in the literature as Pierce expansions. A closer look to Pierce expansions will take us to some metrical properties of sets defined through the Pierce expansions of its elements. Finally, these metrical properties will enable us to present 'strange' sets, similar to the classical Cantor set.

Phylogenetic relationships among four species of the guarani group of Drosophila (Diptera, Drosophilidae) as inferred by molecular and morphological analyses

Traditionally, the Drosophila guarani species group has been divided into two subgroups: the guarani and the guaramunu subgroups. Two, out of the four species included in this research, are members of the guarani subgroup (D. ornatifrons Duda, 1927 and D. subbadia Paterson & Mainland, 1943) and two are included in the guaramunu subgroup (D. maculifrons Duda, 1927 and D. griseolineata Duda, 1927). However, some authors have suggested that D. maculifrons and D. griseolineata are much closer to some species of the Drosophila tripunctata group than to some of the species of the guarani group. To add new data to the matter under dispute, Polyacrylamide Gel Eletrophoresis (PAGE-SDS) was used for the analysis and comparison of protein composition and Random Amplified Polymorphic DNA (RAPD) analysis to find differences in genomic DNA, in addition to the analysis of quantitative morphological characters previously described. Analysis of PAGE-SDS results in a dendrogram that pointed out D. subbadia as being the most distant within the Drosophila guarani group. However, these results were not supported either by RAPD analysis or by the analysis of continuous morphological characters, which supplied the clustering of D. subbadia with D. ornatifrons. Although our data give strong support to the clustering of D. subbadia and D. ornatifrons, none of the dendrograms provided a clade comprising D. maculifrons and D. griseolineata. Thus, this research does not support the traditional subdivision of the D. guarani group into those two subgroups.

In vitro compatibility of remifentanil hydrochloride and sufentanil citrate with selected drugs

: Objectives Physicochemical incompatibilities between intravenous drugs are a recurrent problem in intensive care units. The present study was aimed at investigating the physical compatibility of remifentanil and sufentanil with other drugs (insulin, midazolam, propofol, potassium chloride, magnesium sulfate, furosemide, heparin, monobasic potassium phosphate) that are frequently administered together intravenously. In addition, the physicochemical compatibility of three common associations of drugs was evaluated in glass tube tests and during dynamic simulated Y site administrations (remifentanil-insulin-midazolam; remifentanil-insulin-propofol; sufentanil-insulin-midazolam). Methods Physical compatibility was verified by visual inspection of the various mixtures (two, three or four drugs) in glass tubes and by pH determination of the mixtures collected during simulated Y site administrations. Solutions were considered as compatible in the absence of any visual change in the solution and of any significant variation in pH value. In addition, chemical stability was checked during in vitro dynamic simulations. The solutions were prepared in 50 ml syringes, placed on syringe pumps and connected to a Swan-Ganz catheter; the liquid collected at the tip was assayed by high performance liquid chromatography. Results In the visual examinations, only the associations of remifentanil and furosemide were incompatible. The three assayed associations were compatible in the tested proportion range over 24 h. Conclusions Remifentanil was physically compatible with the tested drugs, except for furosemide (Lasix; Sanofi-Aventis, 250 mg/25 ml) and physicochemically compatible with insulin and midazolam and insulin and propofol. Sufentanil was physically compatible with all tested drugs and physicochemically compatible with insulin and midazolam

Revising the Cannabis Use Disorders Identification Test (CUDIT) by means of Item Response Theory.

Cannabis use among adolescents and young adults has become a major public health challenge. Several European countries are currently developing short screening instruments to identify 'problematic' forms of cannabis use in general population surveys. One such instrument is the Cannabis Use Disorders Identification Test (CUDIT), a 10-item questionnaire based on the Alcohol Use Disorders Identification Test. Previous research found that some CUDIT items did not perform well psychometrically. In the interests of improving the psychometric properties of the CUDIT, this study replaces the poorly performing items with new items that specifically address cannabis use. Analyses are based on a sub-sample of 558 recent cannabis users from a representative population sample of 5722 individuals (aged 13-32) who were surveyed in the 2007 Swiss Cannabis Monitoring Study. Four new items were added to the original CUDIT. Psychometric properties of all 14 items, as well as the dimensionality of the supplemented CUDIT were then examined using Item Response Theory. Results indicate the unidimensionality of CUDIT and an improvement in its psychometric performance when three original items (usual hours being stoned; injuries; guilt) are replaced by new ones (motives for using cannabis; missing out leisure time activities; difficulties at work/school). However, improvements were limited to cannabis users with a high problem score. For epidemiological purposes, any further revision of CUDIT should therefore include a greater number of 'easier' items.

Locating emergency services with priority rules: The priority queuing covering location problem

One of the assumptions of the Capacitated Facility Location Problem (CFLP) is thatdemand is known and fixed. Most often, this is not the case when managers take somestrategic decisions such as locating facilities and assigning demand points to thosefacilities. In this paper we consider demand as stochastic and we model each of thefacilities as an independent queue. Stochastic models of manufacturing systems anddeterministic location models are put together in order to obtain a formula for thebacklogging probability at a potential facility location.Several solution techniques have been proposed to solve the CFLP. One of the mostrecently proposed heuristics, a Reactive Greedy Adaptive Search Procedure, isimplemented in order to solve the model formulated. We present some computationalexperiments in order to evaluate the heuristics performance and to illustrate the use ofthis new formulation for the CFLP. The paper finishes with a simple simulationexercise.

A multi-objective model for a multi-period distribution management problem

The problems arising in commercial distribution are complex and involve several players and decision levels. One important decision is relatedwith the design of the routes to distribute the products, in an efficient and inexpensive way.This article deals with a complex vehicle routing problem that can beseen as a new extension of the basic vehicle routing problem. The proposed model is a multi-objective combinatorial optimization problemthat considers three objectives and multiple periods, which models in a closer way the real distribution problems. The first objective is costminimization, the second is balancing work levels and the third is amarketing objective. An application of the model on a small example, with5 clients and 3 days, is presented. The results of the model show the complexity of solving multi-objective combinatorial optimization problems and the contradiction between the several distribution management objective.

Deposits of transforming growth factor-beta-induced protein in granular corneal dystrophy type II after LASIK.

PURPOSE: To analyze components of the deposits in the corneal flap interface of granular corneal dystrophy type II (GCD II) patients after laser in situ keratomileusis (LASIK). METHODS: Four corneal GCD II specimens displaying disease exacerbation after LASIK were analyzed. Three of these specimens included the recipient corneal button after penetrating keratoplasty or deep lamellar keratoplasty for advanced GCD II after LASIK. The fourth specimen, a similar case of GCD II after LASIK, included the amputated corneal flap. Specimens were processed for histopathologic and immunohistochemical analyses. RESULTS: Corneal stromal deposits in the LASIK flaps of all specimens were stained with 3 anti-transforming growth factor-beta-induced protein (TGFBIp) antibodies. The deposits displayed bright red color staining with Masson trichrome; however, negative staining was seen with Congo red, suggesting that hyaline is the main component localizing to the TGFBIp deposits rather than amyloid. CONCLUSIONS: Amorphous granular material deposited along the interface of the LASIK flap in GCD II corneas is composed mainly of hyaline deposits.

Multiparametric brainstem segmentation using a modified multivariate mixture of Gaussians

The human brainstem is a densely packed, complex but highly organised structure. It not only serves as a conduit for long projecting axons conveying motor and sensory information, but also is the location of multiple primary nuclei that control or modulate a vast array of functions, including homeostasis, consciousness, locomotion, and reflexive and emotive behaviours. Despite its importance, both in understanding normal brain function as well as neurodegenerative processes, it remains a sparsely studied structure in the neuroimaging literature. In part, this is due to the difficulties in imaging the internal architecture of the brainstem in vivo in a reliable and repeatable fashion. A modified multivariate mixture of Gaussians (mmMoG) was applied to the problem of multichannel tissue segmentation. By using quantitative magnetisation transfer and proton density maps acquired at 3 T with 0.8 mm isotropic resolution, tissue probability maps for four distinct tissue classes within the human brainstem were created. These were compared against an ex vivo fixated human brain, imaged at 0.5 mm, with excellent anatomical correspondence. These probability maps were used within SPM8 to create accurate individual subject segmentations, which were then used for further quantitative analysis. As an example, brainstem asymmetries were assessed across 34 right-handed individuals using voxel based morphometry (VBM) and tensor based morphometry (TBM), demonstrating highly significant differences within localised regions that corresponded to motor and vocalisation networks. This method may have important implications for future research into MRI biomarkers of pre-clinical neurodegenerative diseases such as Parkinson's disease.

Regions of rationality: Maps for bounded agents

An important problem in descriptive and prescriptive research in decision making is to identify regions of rationality, i.e., the areas for which heuristics are and are not effective. To map the contours of such regions, we derive probabilities that heuristics identify the best of m alternatives (m > 2) characterized by k attributes or cues (k > 1). The heuristics include a single variable (lexicographic), variations of elimination-by-aspects, equal weighting, hybrids of the preceding, and models exploiting dominance. We use twenty simulated and four empirical datasets for illustration. We further provide an overview by regressing heuristic performance on factors characterizing environments. Overall, sensible heuristics generally yield similar choices in many environments. However, selection of the appropriate heuristic can be important in some regions (e.g., if there is low inter-correlation among attributes/cues). Since our work assumes a hit or miss decision criterion, we conclude by outlining extensions for exploring the effects of different loss functions.

Minimax lower bounds for the two-armed bandit problem

We obtain minimax lower bounds on the regret for the classicaltwo--armed bandit problem. We provide a finite--sample minimax version of the well--known log $n$ asymptotic lower bound of Lai and Robbins. Also, in contrast to the log $n$ asymptotic results on the regret, we show that the minimax regret is achieved by mere random guessing under fairly mild conditions on the set of allowable configurations of the two arms. That is, we show that for {\sl every} allocation rule and for {\sl every} $n$, there is a configuration such that the regret at time $n$ is at least 1 -- $\epsilon$ times the regret of random guessing, where $\epsilon$ is any small positive constant.

The Conversion of Four Lane Undivded Urban Roadways to Three Lane Facilities, 2007

In recent years, many traffic engineers have advocated converting four-lane undivided urban streets to threelane two-way left-turn facilities. A number of these conversions have been successfully implemented. Accident rates have decreased while corridor and intersection levels of service remained acceptable. This conversion concept is yet another viable alternative “tool” to place in our urban safety/congestion toolbox.

Modeling the forensic two-trace problem with Bayesian networks

The forensic two-trace problem is a perplexing inference problem introduced by Evett (J Forensic Sci Soc 27:375-381, 1987). Different possible ways of wording the competing pair of propositions (i.e., one proposition advanced by the prosecution and one proposition advanced by the defence) led to different quantifications of the value of the evidence (Meester and Sjerps in Biometrics 59:727-732, 2003). Here, we re-examine this scenario with the aim of clarifying the interrelationships that exist between the different solutions, and in this way, produce a global vision of the problem. We propose to investigate the different expressions for evaluating the value of the evidence by using a graphical approach, i.e. Bayesian networks, to model the rationale behind each of the proposed solutions and the assumptions made on the unknown parameters in this problem.

Four new species of Neotropical spittlebugs (Hemiptera, Cercopidae, Tomaspidinae)

The following new species of South American Cercopidae, are described: Ischnorhina quadrimelasma sp. nov. (Bolivia), Laccogrypota quadrilineata sp. nov. (Bolivia), (Neolaccogrypota youngi sp. nov. (Peru), and Neosphenorhina schombergi sp. nov. (Brazil).