Generic optimality conditions for semi-algebraic convex programs

We consider linear optimization over a nonempty convex semi-algebraic feasible region F. Semidefinite programming is an example. If F is compact, then for almost every linear objective there is a unique optimal solution, lying on a unique \active" manifold, around which F is \partly smooth", and the second-order sufficient conditions hold. Perturbing the objective results in smooth variation of the optimal solution. The active manifold consists, locally, of these perturbed optimal solutions; it is independent of the representation of F, and is eventually identified by a variety of iterative algorithms such as proximal and projected gradient schemes. These results extend to unbounded sets F.

On problems of calculating energy expenditure and substrate utilization from respiratory exchange data.

Indirect calorimetry based on respiratory exchange measurement has been successfully used from the beginning of the century to obtain an estimate of heat production (energy expenditure) in human subjects and animals. The errors inherent to this classical technique can stem from various sources: 1) model of calculation and assumptions, 2) calorimetric factors used, 3) technical factors and 4) human factors. The physiological and biochemical factors influencing the interpretation of calorimetric data include a change in the size of the bicarbonate and urea pools and the accumulation or loss (via breath, urine or sweat) of intermediary metabolites (gluconeogenesis, ketogenesis). More recently, respiratory gas exchange data have been used to estimate substrate utilization rates in various physiological and metabolic situations (fasting, post-prandial state, etc.). It should be recalled that indirect calorimetry provides an index of overall substrate disappearance rates. This is incorrectly assumed to be equivalent to substrate "oxidation" rates. Unfortunately, there is no adequate golden standard to validate whole body substrate "oxidation" rates, and this contrasts to the "validation" of heat production by indirect calorimetry, through use of direct calorimetry under strict thermal equilibrium conditions. Tracer techniques using stable (or radioactive) isotopes, represent an independent way of assessing substrate utilization rates. When carbohydrate metabolism is measured with both techniques, indirect calorimetry generally provides consistent glucose "oxidation" rates as compared to isotopic tracers, but only when certain metabolic processes (such as gluconeogenesis and lipogenesis) are minimal or / and when the respiratory quotients are not at the extreme of the physiological range. However, it is believed that the tracer techniques underestimate true glucose "oxidation" rates due to the failure to account for glycogenolysis in the tissue storing glucose, since this escapes the systemic circulation. A major advantage of isotopic techniques is that they are able to estimate (given certain assumptions) various metabolic processes (such as gluconeogenesis) in a noninvasive way. Furthermore when, in addition to the 3 macronutrients, a fourth substrate is administered (such as ethanol), isotopic quantification of substrate "oxidation" allows one to eliminate the inherent assumptions made by indirect calorimetry. In conclusion, isotopic tracers techniques and indirect calorimetry should be considered as complementary techniques, in particular since the tracer techniques require the measurement of carbon dioxide production obtained by indirect calorimetry. However, it should be kept in mind that the assessment of substrate oxidation by indirect calorimetry may involve large errors in particular over a short period of time. By indirect calorimetry, energy expenditure (heat production) is calculated with substantially less error than substrate oxidation rates.

Codis no lineals en Magma: noves construccions

L'objectiu principal d'aquest projecte és ampliar la llibreria BinaryCodes, iniciada al 2007, que ens permet construir i manipular codis binaris lineals i no lineals. Per aquest motiu, s'han desenvolupat una sèrie de funcions, amb els seus corresponents tests i exemples, en l'entorn de programació matemàtica Magma. Aquestes funcions consisteixen bàsicament en la construcció de nous codis a partir d'altres ja existents.

Gaussian estimates for the density of the non-linear stochastic heat equation in any space dimension

In this paper, we establish lower and upper Gaussian bounds for the probability density of the mild solution to the stochastic heat equation with multiplicative noise and in any space dimension. The driving perturbation is a Gaussian noise which is white in time with some spatially homogeneous covariance. These estimates are obtained using tools of the Malliavin calculus. The most challenging part is the lower bound, which is obtained by adapting a general method developed by Kohatsu-Higa to the underlying spatially homogeneous Gaussian setting. Both lower and upper estimates have the same form: a Gaussian density with a variance which is equal to that of the mild solution of the corresponding linear equation with additive noise.

Linear Aggregation In The Social Accounting Matrix Framework

In economic literature, information deficiencies and computational complexities have traditionally been solved through the aggregation of agents and institutions. In inputoutput modelling, researchers have been interested in the aggregation problem since the beginning of 1950s. Extending the conventional input-output aggregation approach to the social accounting matrix (SAM) models may help to identify the effects caused by the information problems and data deficiencies that usually appear in the SAM framework. This paper develops the theory of aggregation and applies it to the social accounting matrix model of multipliers. First, we define the concept of linear aggregation in a SAM database context. Second, we define the aggregated partitioned matrices of multipliers which are characteristic of the SAM approach. Third, we extend the analysis to other related concepts, such as aggregation bias and consistency in aggregation. Finally, we provide an illustrative example that shows the effects of aggregating a social accounting matrix model.

Dietary supplements utilization: an explanatory survey among Swiss consumers

Dietary supplement (DS) use increased rapidly over the last years. However evidence of benefits of many DS for healthy users are scarce and may not equate known risks of overdose, drug interaction and recently discovered negative long-term effects. Therefore this study aimed to investigate perceptions and motivations of DS users in Lausanne, Switzerland. Method A convenience sample was recruited at the entrance of local sales points. Data were collected in on-site semi-structured interviews to assess dietary supplementation habits. Results The 119 participants provided information on 147 users. Among 273 declared products, the majority were mixed products, containing minerals and vitamins (78), mineral products (69), and herbal products (28). 55% of DS users took more than one product simultaneously. Seventy five percent of participants indicated that DS use presents no risk or nearly no risk and about half (49%) of participants did not inform their physician about their consumption. Male participants reported to share this information with their physicians significantly less frequently than female participants (p = 0.008). About half of participants looked for information on potential risks of DS, men significantly more often than women (p=0.001). Discussion According to other studies in the US, our study shows that, in Lausanne (Switzerland), DS are commonly used as mixed products. Risk perception seems generally low among DS users. Implications Physicians should be trained to evaluate patientsʼ health behaviour and needs in order to provide good evidence based information or propose alternatives to DS use.

A linear optimization technique for graph pebbling

Graph pebbling is a network model for studying whether or not a given supply of discrete pebbles can satisfy a given demand via pebbling moves. A pebbling move across an edge of a graph takes two pebbles from one endpoint and places one pebble at the other endpoint; the other pebble is lost in transit as a toll. It has been shown that deciding whether a supply can meet a demand on a graph is NP-complete. The pebbling number of a graph is the smallest t such that every supply of t pebbles can satisfy every demand of one pebble. Deciding if the pebbling number is at most k is NP 2 -complete. In this paper we develop a tool, called theWeight Function Lemma, for computing upper bounds and sometimes exact values for pebbling numbers with the assistance of linear optimization. With this tool we are able to calculate the pebbling numbers of much larger graphs than in previous algorithms, and much more quickly as well. We also obtain results for many families of graphs, in many cases by hand, with much simpler and remarkably shorter proofs than given in previously existing arguments (certificates typically of size at most the number of vertices times the maximum degree), especially for highly symmetric graphs. Here we apply theWeight Function Lemma to several specific graphs, including the Petersen, Lemke, 4th weak Bruhat, Lemke squared, and two random graphs, as well as to a number of infinite families of graphs, such as trees, cycles, graph powers of cycles, cubes, and some generalized Petersen and Coxeter graphs. This partly answers a question of Pachter, et al., by computing the pebbling exponent of cycles to within an asymptotically small range. It is conceivable that this method yields an approximation algorithm for graph pebbling.

Relaxation methods for solving linear inequality systems: Converging results

The problem of finding a feasible solution to a linear inequality system arises in numerous contexts. In [12] an algorithm, called extended relaxation method, that solves the feasibility problem, has been proposed by the authors. Convergence of the algorithm has been proven. In this paper, we onsider a class of extended relaxation methods depending on a parameter and prove their convergence. Numerical experiments have been provided, as well.

Health services utilization associated with cognitive impairment and dementia in older patients undergoing post-acute rehabilitation.

OBJECTIVE: To investigate the relationship between levels of cognitive impairment and health services utilization in older patients undergoing post-acute rehabilitation. DESIGN: Cross-sectional study. SETTING: Post-acute rehabilitation facility. PARTICIPANTS: Patients (N = 1764) aged 70 years and older admitted over 3 years. MEASUREMENTS: Sociodemographic, medical, and functional data were collected upon admission. Based on discharge diagnoses, patients were classified as cognitively intact, cognitively impaired with no dementia (CIND), and demented. RESULTS: Dementia and CIND were diagnosed in 425 (24.1%) and 301 (17.1%) patients, respectively. Gradients from cognitively intact to cognitively impaired to demented patients were observed in median length of stay (19, 22, and 25 days, P < .001), and institutionalization rates at discharge (4.2%, 7.6%, and 28.8%, P < .001). Among patients discharged home, similar gradients were observed in utilization of home care (68.2%, 79.7%, and 83.3%, P < .001) and day care (3.1%, 7.1%, and 14.3%, P < .001). After adjustment, compared with cognitively intact patients, only those with dementia still had longer stays (+2.7 days) and increased odds of institutionalization (adjOR 6.1, 95% CI 4.0-9.3, P < .001). Among patients discharged home, use of home and day care remained higher in those with dementia (adjOR 1.8, 95% CI 1.2-2.7, P = .005, and adjOR 1.8, 95% CI 1.2-2.7, P = .005, respectively), while CIND patients had higher odds of using home care (adjOR 1.6, 95% CI 1.1-2.4, P = .028). CONCLUSION: Among patients undergoing post-acute rehabilitation, those with dementia had increased use of both institutional and community care, whereas those with CIND had increased use of home care services only. Future studies should investigate specific strategies susceptible to reduce the related burden on health care systems.

Off-label utilization of antipsychotics

Résumé Ce travail s'inscrit dans un programme de recherche centré sur la pharmacovigilance en psychiatrie. Buts de l'étude Les nouveaux antipsychotiques atypiques sont prescrits avec beaucoup de succès, parce qu'ils présentent une sécurité dans leur emploi bien supérieure à celle des antipsychotiques classiques. Cette situation a conduit à une large prescription «off-label» (hors indication admise). Le but de ce travail a été d'étudier la pratique en matière de prescription des psychiatres hospitaliers en ce qui concerne les antipsychotiques en comparant des patients traités pour des psychoses ou d'autres indications officielles aux patients recevant un traitement antipsychotique «off-label». Méthode Dans le cadre d'un programme de pharmacovigilance - pharmacoépidemiologie, tous les médicaments prescrits à 5 jours de référence (entre 1999 et 2001) à l'hôpital psychiatrique universitaire de Lausanne (98 lits) ont été enregistrés, avec des données sur l'âge, le sexe et le diagnostic des patients. Les prescriptions de 202 patients ont été évaluées. Les patients ont été classés dans 3 groupes diagnostiques : (1) patient présentant des troubles psychotiques, (2) patient présentant des épisodes maniaques et des épisodes dépressifs avec des symptômes psychotiques, et (3) patient présentant d'autres troubles. Les groupes (1) et (2) forment une classe de patients recevant un antipsychotique pour une indication officielle, et les prescriptions dans le groupe (3) ont été considérées comme «off-label». Résultats principaux Moins de patients psychotiques ont reçu un antidépresseur (p<0.05) ou des hypnotiques non-benzodiazepine (p<0.001) comparés aux patients des deux autres groupes. Les patients présentant des troubles affectifs recevaient seulement exceptionnellement une combinaison d'un antipsychotique atypique et conventionnel, tandis qu'un nombre inférieur de patients avec des indications « off-label » ont reçu moins .souvent des antipsychotiques atypiques que ceux des deux groupes de comparaison (p<0.05). L'analyse statistique (stepwise logistic regression) a révélé que les patients présentant des troubles psychotiques avaient un risque plus élevé de recevoir un médicament antipsychotique d'une dose moyenne ou élevée, (p<0.001) en comparaison aux deux autres groupes. Conclusion Les nouveaux médicaments antipsychotiques semblent être prescrits avec moins d'hésitation principalement pour des indications admises. Les médecins prescrivent de nouveaux médicaments « off-label » seulement après avoir acquis une certaine expérience dans le domaine des indications approuvées, et ils étaient plus prudents en ce qui concerne la dose en traitant sur la base «off-label». Abstract Objective The new brands of atypical antipsychotics are very successfully prescribed because of their enhanced safety profiles and their larger pharmacological profile in comparison to the conventional antipsychotic. This has led to broad off-label utilisation. The aim of the present survey was to study the prescription practice of hospital psychiatrists with regard to antipsychotic drugs, comparing patients treated for psychoses or other registered indications to patients receiving an off-label antipsychotic treatment. Method As part of a pharmacovigilance/pharmacoepidemiology program, all drugs given on 5 reference days (1999 - 2001) in the 98-bed psychiatric hospital of the University of Lausanne, Switzerland, were recorded along with age, sex and diagnosis. The prescriptions of 202 patients were assessed. Patients were classified in 3 diagnostic groups: (1) patient with psychotic disorders, (2) patients with manic episodes and depressive episodes with psychotic symptoms, and (3) patients with other disorders. Group (1) and (2) formed the class of patients receiving an antipsychotic for a registered indication, and the prescriptions in group (3) were considered as off-label. Main results A lesser number of psychotic patients received antidepressant (p<0.05) and nonbenzodiazepine hypnotics (p<0.001) compared to the patients of the other two groups. The patients with affective disorders received only exceptionally a combination of an atypical and a conventional antipsychotic, whereas a lesser number of patients with off-label indications received less often atypical antipsychotics than those of the two comparison groups (p<0.05). Stepwise logistic regression revealed that patients with psychotic disorder were at higher risk of receiving an antipsychotic medication in medium or high dose (p<0.001), in comparison to the two other groups. Conclusions The new antipsychotic drugs seem to be prescribed with less hesitation mainly for approved indications. Physicians prescribe new drugs on off-label application only after having gained some experience in the field of the approved indications, and were more cautious with regard to dose when treating on an off-label basis.

A subspace correction method for discontinuous Galerkin discretizations of linear elasticity equations

We study preconditioning techniques for discontinuous Galerkin discretizations of isotropic linear elasticity problems in primal (displacement) formulation. We propose subspace correction methods based on a splitting of the vector valued piecewise linear discontinuous finite element space, that are optimal with respect to the mesh size and the Lamé parameters. The pure displacement, the mixed and the traction free problems are discussed in detail. We present a convergence analysis of the proposed preconditioners and include numerical examples that validate the theory and assess the performance of the preconditioners.

GLUT4, AMP kinase, but not the insulin receptor, are required for hepatoportal glucose sensor-stimulated muscle glucose utilization.

Recent evidence suggests the existence of a hepatoportal vein glucose sensor, whose activation leads to enhanced glucose use in skeletal muscle, heart, and brown adipose tissue. The mechanism leading to this increase in whole body glucose clearance is not known, but previous data suggest that it is insulin independent. Here, we sought to further determine the portal sensor signaling pathway by selectively evaluating its dependence on muscle GLUT4, insulin receptor, and the evolutionarily conserved sensor of metabolic stress, AMP-activated protein kinase (AMPK). We demonstrate that the increase in muscle glucose use was suppressed in mice lacking the expression of GLUT4 in the organ muscle. In contrast, glucose use was stimulated normally in mice with muscle-specific inactivation of the insulin receptor gene, confirming independence from insulin-signaling pathways. Most importantly, the muscle glucose use in response to activation of the hepatoportal vein glucose sensor was completely dependent on the activity of AMPK, because enhanced hexose disposal was prevented by expression of a dominant negative AMPK in muscle. These data demonstrate that the portal sensor induces glucose use and development of hypoglycemia independently of insulin action, but by a mechanism that requires activation of the AMPK and the presence of GLUT4.