Unconstrained and Constrained Fault-Tolerant Resource Allocation

First, we study the Unconstrained Fault-Tolerant Resource Allocation (UFTRA) problem (a.k.a. FTFA problem in \cite{shihongftfa}). In the problem, we are given a set of sites equipped with an unconstrained number of facilities as resources, and a set of clients with set $\mathcal{R}$ as corresponding connection requirements, where every facility belonging to the same site has an identical opening (operating) cost and every client-facility pair has a connection cost. The objective is to allocate facilities from sites to satisfy $\mathcal{R}$ at a minimum total cost. Next, we introduce the Constrained Fault-Tolerant Resource Allocation (CFTRA) problem. It differs from UFTRA in that the number of resources available at each site $i$ is limited by $R_{i}$. Both problems are practical extensions of the classical Fault-Tolerant Facility Location (FTFL) problem \cite{Jain00FTFL}. For instance, their solutions provide optimal resource allocation (w.r.t. enterprises) and leasing (w.r.t. clients) strategies for the contemporary cloud platforms. In this paper, we consider the metric version of the problems. For UFTRA with uniform $\mathcal{R}$, we present a star-greedy algorithm. The algorithm achieves the approximation ratio of 1.5186 after combining with the cost scaling and greedy augmentation techniques similar to \cite{Charikar051.7281.853,Mahdian021.52}, which significantly improves the result of \cite{shihongftfa} using a phase-greedy algorithm. We also study the capacitated extension of UFTRA and give a factor of 2.89. For CFTRA with uniform $\mathcal{R}$, we slightly modify the algorithm to achieve 1.5186-approximation. For a more general version of CFTRA, we show that it is reducible to FTFL using linear programming

Detecting three-qubit bound MUB diagonal entangled states via Nonlinear optimal entanglement witnesses

One of the important approaches to detect quantum entanglement is using linear entanglement witnesses EWs. In this paper, by determining the envelope of the boundary hyper-planes defined by a family of linear EWs, a set of powerful nonlinear optimal EWs is manipulated. These EWs enable us to detect some three qubits bound MUB (mutually unbiased bases) diagonal entangled states, i.e., the PPT (positive partial transpose) entangled states. Also, in some particular cases, the introduced nonlinear optimal EWs are powerful enough to separate the bound entangled regions from the separable ones. Finally, we present numerical examples to demonstrate the practical accessibility of this approach. Keywords :nonlinear optimal entanglement witnesses, mutually unbiased bases, MUB diagonal statesComment: 34 pages 11 figure

Effect of plant ethanolic extracts of Rosmarinus officinalis L. and Nerium oleander L. on mortality, biological parameters and reproduction of Aphis gossypii (Hom.: Aphididae)

Aphis gossypii Glover (Hom.: Aphididae( is one of the most important pests in greenhouse and field. Considering the importance of human health and the environmental protection, reduction in pesticide application has to be considered as an essential issue in the pest control program. In the present study, effects of ethanolic extracts of Rosmarinus officinalis L. and Nerium oleander and an insecticide, imidacloprid were evaluated against Aphis gossypii. Leaf dipping method was used in the laboratory conditions (temperature of 25 ± 1 °C, 65 ± 5% relative humidity and 16 h light: 8 h dark). After 72-h, LC50 values of imidacloprid, plant extracts from rosemary and oleander were estimated 0.004, 24.69 and 45.26 mg/ml, respectively. In this study, the effects of sublethal concentration (LC30) of each treatment was evaluated against A. gossypii. Longevity and the number of offspring were estimated per female per day. In this experiment, significant effects were observed on the life table parameters such as survival, intrinsic rate of increase, net reproductive rate, finite rate of population increase and mean generation time, for aphids fed on the leaves treated with ethanolic plant extracts and imidacloprid as compared to the related controls. This information provides further support for plant extracts of R. officinalis and N. oleander having a good potential to control the A. gossypii. However before claiming firm conclusions, trials under glasshouse and field related conditions are needed to verify the applicability of these two plant extracts in control of A. gossypii

Facility Location in Evolving Metrics

Understanding the dynamics of evolving social or infrastructure networks is a challenge in applied areas such as epidemiology, viral marketing, or urban planning. During the past decade, data has been collected on such networks but has yet to be fully analyzed. We propose to use information on the dynamics of the data to find stable partitions of the network into groups. For that purpose, we introduce a time-dependent, dynamic version of the facility location problem, that includes a switching cost when a client's assignment changes from one facility to another. This might provide a better representation of an evolving network, emphasizing the abrupt change of relationships between subjects rather than the continuous evolution of the underlying network. We show that in realistic examples this model yields indeed better fitting solutions than optimizing every snapshot independently. We present an $O(\log nT)$-approximation algorithm and a matching hardness result, where $n$ is the number of clients and $T$ the number of time steps. We also give an other algorithms with approximation ratio $O(\log nT)$ for the variant where one pays at each time step (leasing) for each open facility

Developmental periods of Oenopia conglobata contaminata (Col.: Coccinellidae) reared on eggs of Sitotroga cerealella (Lep.: Gelechiidae) and Ephestia kuehniella (Lep.: Pyralidae) at constant temperatures

The coccinellid Oenopia conglobata contaminata (Menteries) is one of the most important predators of orchard pests in Iran. The effect of eggs of Sitotroga cereallela Olivier (Lep.: Gelechiidae) and Ephestia kuehniella Zeller (Lep.: Pyralidae) on development and survival of this beetle was studied and compared under laboratory conditions (five constant temperatures i.e., 22.5 ± 1, 25 ± 1, 27.5 ± 1, 30 ± 1 and 32.5 ± 1 °C 55 ± 5% relative humidity (R. H.) and a 16:8 h light: dark photoperiod). Total developmental time at the above-mentioned temperatures were 28.83 ± 0.17, 24.52 ± 0.37, 21,39 ± 0.21 17.92 ± 0.16 and 18.22 ± 0.29 days on S. cereallelaand27 ± 0.38, 23.32 ± 0.14, 19.57 ± 0.28, 16.14 ± 0.17 and 16.33 ± 0.05 days on E. kuehniella. The lower developmental thresholds (T0) of egg, larva, pupa and egg to adult on E. kuehniella were estimated15.02, 8.6, 7.48 and 8.55 ºC and the thermal constant for these periods calculated as 38.16, 222.22, 71.9 and 370.37 DD. The lower developmental thresholds on S. cereallela were found to be 13.79, 5.6, 5.82 and 6.54 ºC andthermal constant for the mentioned periods were 41.15, 277.77, 91.7, 454.54 DD, respectively. Although significant differences between developmental times at different temperatures exist, no significant differences was observed between 30 and 32.5 °C for two prey species. The results suggest that E. kuehniella serves as a more effective host than S. cereallela for rearing of coccinellid O. conglobata

Predatory efficiency of Hippodamia variegata (Col.: Coccinellidae) on common pistachio psylla, Agonoscena pistaciae (Hem.: Aphalaridae), under laboratory conditions

Common pistachio psylla, Agonoscena pistaciae Burckhardt & Lauterer, is the most economically important species among the psyllid pests of pistachio in Iran. Hence, the possibility of using nonchemical control methods against A. pistaciae and the existence of its natural enemies need to be investigated. The spotted amber ladybird, Hippodamia variegata (Goeze), is one of the most effective predators in pistachio orchards. It is a highly polyphagous coccinellid that preys mainly on aphid and psyllid pests of pistachio trees. This study is intended to improve the knowledge about the predation capacity of A. pistaciae. The experiment was conducted under laboratory conditions of 25oC and 30oC, 55 ± 5 RH and 16: 8 L: D. Logistic regression was used to determine the type of functional response and nonlinear regression calculated the parameters of the rate of searching efficiency (a) and handling time (Th). The functional response on different density of prey at both temperatures was type II. The attack rate and handling time were 0.088 ± 0.012 h-1 and 0.0647 ± 0.011 h at 25ºC and 0.195 ± 0.031 h-1 and 0.0698 ± 0.056 h at 30ºC, respectively. The density and temperature affected the predation rate significantly. The data suggests that the H. variegata is a viable biological agent against A. pistaciae

Popular matchings in the marriage and roommates problems

Popular matchings have recently been a subject of study in the context of the so-called House Allocation Problem, where the objective is to match applicants to houses over which the applicants have preferences. A matching M is called popular if there is no other matching M′ with the property that more applicants prefer their allocation in M′ to their allocation in M. In this paper we study popular matchings in the context of the Roommates Problem, including its special (bipartite) case, the Marriage Problem. We investigate the relationship between popularity and stability, and describe efficient algorithms to test a matching for popularity in these settings. We also show that, when ties are permitted in the preferences, it is NP-hard to determine whether a popular matching exists in both the Roommates and Marriage cases

Investigating a Class of 2⊗2⊗d2\otimes2\otimes d Chessboard Density Matrices via Linear and Non-linear Entanglement Witnesses Constructed by Exact Convex Optimization

Here we consider a class of $2\otimes2\otimes d$ chessboard density matrices starting with three-qubit ones which have positive partial transposes with respect to all subsystems. To investigate the entanglement of these density matrices, we use the entanglement witness approach. For constructing entanglement witnesses (EWs) detecting these density matrices, we attempt to convert the problem to an exact convex optimization problem. To this aim, we map the convex set of separable states into a convex region, named feasible region, and consider cases that the exact geometrical shape of feasible region can be obtained. In this way, various linear and non-linear EWs are constructed. The optimality and decomposability of some of introduced EWs are also considered. Furthermore, the detection of the density matrices by introduced EWs are discussed analytically and numerically. {\bf Keywords: chessboard density matrices, optimal non-linear entanglement witnesses, convex optimization} {\bf PACs Index: 03.65.Ud}Comment: 35 pages, 1 figure