Approximating the minimum directed tree cover

Given a directed graph $G$ with non negative cost on the arcs, a directed tree cover of $G$ is a rooted directed tree such that either head or tail (or both of them) of every arc in $G$ is touched by $T$. The minimum directed tree cover problem (DTCP) is to find a directed tree cover of minimum cost. The problem is known to be $NP$-hard. In this paper, we show that the weighted Set Cover Problem (SCP) is a special case of DTCP. Hence, one can expect at best to approximate DTCP with the same ratio as for SCP. We show that this expectation can be satisfied in some way by designing a purely combinatorial approximation algorithm for the DTCP and proving that the approximation ratio of the algorithm is $\max\{2, \ln(D^+)\}$ with $D^+$ is the maximum outgoing degree of the nodes in $G$.Comment: 13 page

Some Further Optimality Conditions for the CM-Embedded Problem

In this paper some new optimality conditions for the C_{M}-embedded problem with the Euclidean norm are presented. Some of them are both necessary and sufficient for certain non-convex regions. The results associated with optimality conditions given here could be used to construct ascent algorithms and in practical calculations

Resolution in Linguistic Propositional Logic based on Linear Symmetrical Hedge Algebra

The paper introduces a propositional linguistic logic that serves as the basis for automated uncertain reasoning with linguistic information. First, we build a linguistic logic system with truth value domain based on a linear symmetrical hedge algebra. Then, we consider G\"{o}del's t-norm and t-conorm to define the logical connectives for our logic. Next, we present a resolution inference rule, in which two clauses having contradictory linguistic truth values can be resolved. We also give the concept of reliability in order to capture the approximative nature of the resolution inference rule. Finally, we propose a resolution procedure with the maximal reliability.Comment: KSE 2013 conferenc

The CM-Embedded Problem and a Sufficient Optimality Condition

In this paper the C_{M}-embedded problem which is also called the design centering problem in other papers will be described, and a sufficient optimality condition and some results associated with optimality conditions will be presented. These results hold for general non-convex regions. To a certain extent they provide the possibility to develop search techniques. It should be pointed out that, in this paper, the only case where the Minkowski norm is just the Euclidean norm is treated, whereas we only mention some results related to the general case a little

Optimal Concentration of Information Content For Log-Concave Densities

An elementary proof is provided of sharp bounds for the varentropy of random vectors with log-concave densities, as well as for deviations of the information content from its mean. These bounds significantly improve on the bounds obtained by Bobkov and Madiman ({\it Ann. Probab.}, 39(4):1528--1543, 2011).Comment: 15 pages. Changes in v2: Remark 2.5 (due to C. Saroglou) added with more general sufficient conditions for equality in Theorem 2.3. Also some minor corrections and added reference

Caractérisation de la Réponse Ultrasonore d'Implant Dentaire : Simulation Numérique et Analyse des Signaux

International audienceThe long-term success of a dental implant is related to the properties of the bone-implant interface. It is important to follow the evolution of bone remodeling phenomena around the implant. To date, there is no satisfactory method for tracking physiological and mechanical properties of this area, and it is difficult for clinicians to qualitatively and quantitatively assess the stability of a dental implant. In this context, methods based on ultrasound wave propagation were already successfully used by our group, in the qualitative and quantitative evaluation of primary and secondary stability of dental implants. In this study we perform numerical simulations, using the finite element method, of wave propagation in a dental implant inserted into bone. To simplify the calculations, an axisymmetric geometry is considered. Given the importance of monitoring of peri-prosthetic area, particular attention is given to the boundary conditions between the implant and the bone. The numerical results are compared with those from experimental tests. These results, numerical and experimental, are then analysed with signal processing tools based on multifractal methods. Analysis of the first results shows that these methods are potentially efficient in this case because they can explore and exploit the multi-scale structure of the signal

Preparative Isolation, Fast Centrifugal Partition Chromatography Purification and Biological Activity of Cajaflavanone from Derris ferruginea Stems

Introduction The Derris genus is known to contain flavonoid derivatives, including prenylated flavanones and isoflavonoids such as rotenoids, which are generally associated with significant biological activity. Objective To develop an efficient preparative isolation procedure for bioactive cajaflavanone. Methodology Fast centrifugal partition chromatography (FCPC) was optimised to purify cajaflavanone from Derris ferruginea stems in a single step as compared to fractionation from the cyclohexane extract by successive conventional solid–liquid chromatography procedures. The purification yield, purity, time and solvent consumption per procedure are described. The anti-fungal, anti-bacterial, anti-leishmanial, anti-plasmodial, anti-oxidant activities and the inhibition of advanced glycation end-products (AGEs) by cajaflavanone accumulation are described. Results FCPC enabled cajaflavanone purification in a single separation step, yielding sufficient quantities to perform in vitro biological screening. Interestingly, cajaflavanone had an inhibitory effect on the formation of AGEs, without displaying any in vitro anti-oxidant activity. Conclusion A simple and efficient procedure, in comparison with other preparative methods, for bioactive cajaflavone purification has been developed using FCPC