Rank Maximal Matchings -- Structure and Algorithms

Let G = (A U P, E) be a bipartite graph where A denotes a set of agents, P denotes a set of posts and ranks on the edges denote preferences of the agents over posts. A matching M in G is rank-maximal if it matches the maximum number of applicants to their top-rank post, subject to this, the maximum number of applicants to their second rank post and so on. In this paper, we develop a switching graph characterization of rank-maximal matchings, which is a useful tool that encodes all rank-maximal matchings in an instance. The characterization leads to simple and efficient algorithms for several interesting problems. In particular, we give an efficient algorithm to compute the set of rank-maximal pairs in an instance. We show that the problem of counting the number of rank-maximal matchings is #P-Complete and also give an FPRAS for the problem. Finally, we consider the problem of deciding whether a rank-maximal matching is popular among all the rank-maximal matchings in a given instance, and give an efficient algorithm for the problem

Continuous feedback on a quantum gas coupled to an optical cavity

We present an active feedback scheme acting continuously on the state of a quantum gas dispersively coupled to a high-finesse optical cavity. The quantum gas is subject to a transverse pump laser field inducing a self-organization phase transition, where the gas acquires a density modulation and photons are scattered into the resonator. Photons leaking from the cavity allow for a real-time and non-destructive readout of the system. We stabilize the mean intra-cavity photon number through a micro-processor controlled feedback architecture acting on the intensity of the transverse pump field. The feedback scheme can keep the mean intra-cavity photon number $n_\text{ph}$ constant, in a range between $n_\text{ph}=0.17\pm 0.04$ and $n_\text{ph}=27.6\pm 0.5$, and for up to 4 s. Thus we can engage the stabilization in a regime where the system is very close to criticality as well as deep in the self-organized phase. The presented scheme allows us to approach the self-organization phase transition in a highly controlled manner and is a first step on the path towards the realization of many-body phases driven by tailored feedback mechanisms

Dielectric spectroscopy studies of 4-cyano-3-fluorophenyl 4-butylbenzoate liquid crystal at high pressure

For 4-cyano-3- uorophenyl 4-butylbenzoate, nematic glassformer at ambient pressure, dielectric relaxation studies were performed under elevated pressure. In the isobaric experiment, on cooling the nematic phase two superarrhenius -relaxations, ascribed to the reorientations of molecules around short axes and precession of long molecular axes were found and the Arrhenius -relaxation related to intramolecular motions. Complexity of dynamics at elevated and ambient pressure is similar. Shift towards lower frequencies was found for both-relaxations

Physical Stability and Viscoelastic Properties of Co-Amorphous Ezetimibe/Simvastatin System

The purpose of this paper is to examine the physical stability as well as viscoelastic properties of the binary amorphous ezetimibe–simvastatin system. According to our knowledge, this is the first time that such an amorphous composition is prepared and investigated. The tendency toward re-crystallization of the amorphous ezetimibe–simvastatin system, at both standard storage and elevated temperature conditions, have been studied by means of X-ray diffraction (XRD). Our investigations have revealed that simvastatin remarkably improves the physical stability of ezetimibe, despite the fact that it works as a plasticizer. Pure amorphous ezetimibe, when stored at room temperature, begins to re-crystallize after 14 days after amorphization. On the other hand, the ezetimibe-simvastatin binary mixture (at the same storage conditions) is physically stable for at least 1 year. However, the devitrification of the binary amorphous composition was observed at elevated temperature conditions (T = 373 K). Therefore, we used a third compound to hinder the re-crystallization. Finally, both the physical stability as well as viscoelastic properties of the ternary systems containing different concentrations of the latter component have been thoroughly investigated

Bull Trout (Salvelinus confluentus) can detect conspecific pheromones in a two choice Y-maze

Two stocks of Bull Trout (Salvelinus confluentus) were tested in a two choice Y-maze to determine if they could detect pheromones from the same natal population (population specific pheromones PSP) or from a different (conspecific) population of Bull Trout (CSP). Fish from the Pack River (PR), Idaho and the Metolius River (MR), Oregon were transferred to a fish hatchery where Y-maze studies were conducted. The Y-maze was constructed to supply well water at 12°C (blank) to both arms with the temperature and discharge of each arm matched to within 0.1°C and 0.01 l/s. One arm was randomly selected to be supplied with pheromones from fish held in stock tanks. Four types of tests were conducted with each stock: 1) blank supplied to both arms; 2) PSP + blank in one arm; 3) CSP + blank in one arm; 4) PSP + blank in one arm and CSP + blank in the other. Chi Square (χ²) Goodness of Fit tests with two degrees of freedom were used to compare the frequency at which fish entered each arm to the theoretical distribution that assumed they randomly selected an arm. Both stocks exhibited no preference when blank water only was present [PR: (χ²=4.79; p=0.091; n=28); MR: (χ²=4.67; p=.097; n=27)]. Both stocks preferred the PSP arm over the blank arm during PSP tests [PR: (χ²=14.00; p\u3c0.001; n=27); MR: (χ²=21.94; p\u3c0.001; n=28)]. Both stocks preferred the CSP arm over the blank arm during CSP tests [PR: (χ²=15.07; p\u3c0.001; n=26); MR: (χ²=16.72; p\u3c0.001; n=31)]. During the PSP vs. CSP tests, both PR and MR spent equivalent frequency in PSP and CSP arms therefore exhibited no preference [PR: (χ²=2.96; p=0.227; n=29); MR: (χ²=4.90; p=0.086; n=31)]. These results showed Bull Trout could detect pheromones from other Bull Trout but could not differentiate between PSPs and CSPs

Impact of alternative solid state forms and specific surface area of high-dose, hydrophilic active pharmaceutical ingredients on tabletability

YesIn order to investigate the effect of using different solid state forms and specific surface area (TBET) of active pharmaceutical ingredients on tabletability and dissolution performance, the mono- and dihydrated crystalline forms of chlorothiazide sodium and chlorothiazide potassium (CTZK) salts were compared to alternative anhydrous and amorphous forms, as well as to amorphous microparticles of chlorothiazide sodium and potassium which were produced by spray drying and had a large specific surface area. The tablet hardness and tensile strength, porosity, and specific surface area of single-component, convex tablets prepared at different compression pressures were characterized. Results confirmed the complexity of the compressibility mechanisms. In general it may be concluded that factors such as solid-state form (crystalline vs amorphous), type of hydration (presence of interstitial molecules of water, dehydrates), or specific surface area of the material have a direct impact on the tabletability of the powder. It was observed that, for powders of the same solid state form, those with a larger specific surface area compacted well, and better than powders of a lower surface area, even at relatively low compression pressures. Compacts prepared at lower compression pressures from high surface area porous microparticles presented the shortest times to dissolve, when compared with compacts made of equivalent materials, which had to be compressed at higher compression pressures in order to obtain satisfactory compacts. Therefore, materials composed of nanoparticulate microparticles (NPMPs) may be considered as suitable for direct compaction and possibly for inclusion in tablet formulations as bulking agents, APIs, carriers, or binders due to their good compactibility performanceSolid State Pharmaceutical Cluster (SSPC), supported by Science Foundation Ireland under Grant No. 07/SRC/B1158

The clustering instability of inertial particles spatial distribution in turbulent flows

A theory of clustering of inertial particles advected by a turbulent velocity field caused by an instability of their spatial distribution is suggested. The reason for the clustering instability is a combined effect of the particles inertia and a finite correlation time of the velocity field. The crucial parameter for the clustering instability is a size of the particles. The critical size is estimated for a strong clustering (with a finite fraction of particles in clusters) associated with the growth of the mean absolute value of the particles number density and for a weak clustering associated with the growth of the second and higher moments. A new concept of compressibility of the turbulent diffusion tensor caused by a finite correlation time of an incompressible velocity field is introduced. In this model of the velocity field, the field of Lagrangian trajectories is not divergence-free. A mechanism of saturation of the clustering instability associated with the particles collisions in the clusters is suggested. Applications of the analyzed effects to the dynamics of droplets in the turbulent atmosphere are discussed. An estimated nonlinear level of the saturation of the droplets number density in clouds exceeds by the orders of magnitude their mean number density. The critical size of cloud droplets required for clusters formation is more than $20 \mu$m.Comment: REVTeX 4, 15 pages, 2 figures(included), PRE submitte

Manipulation Strategies for the Rank Maximal Matching Problem

We consider manipulation strategies for the rank-maximal matching problem. In the rank-maximal matching problem we are given a bipartite graph $G = (A \cup P, E)$ such that $A$ denotes a set of applicants and $P$ a set of posts. Each applicant $a \in A$ has a preference list over the set of his neighbours in $G$, possibly involving ties. Preference lists are represented by ranks on the edges - an edge $(a,p)$ has rank $i$, denoted as $rank(a,p)=i$, if post $p$ belongs to one of $a$'s $i$-th choices. A rank-maximal matching is one in which the maximum number of applicants is matched to their rank one posts and subject to this condition, the maximum number of applicants is matched to their rank two posts, and so on. A rank-maximal matching can be computed in $O(\min(c \sqrt{n},n) m)$ time, where $n$ denotes the number of applicants, $m$ the number of edges and $c$ the maximum rank of an edge in an optimal solution. A central authority matches applicants to posts. It does so using one of the rank-maximal matchings. Since there may be more than one rank- maximal matching of $G$, we assume that the central authority chooses any one of them randomly. Let $a_1$ be a manipulative applicant, who knows the preference lists of all the other applicants and wants to falsify his preference list so that he has a chance of getting better posts than if he were truthful. In the first problem addressed in this paper the manipulative applicant $a_1$ wants to ensure that he is never matched to any post worse than the most preferred among those of rank greater than one and obtainable when he is truthful. In the second problem the manipulator wants to construct such a preference list that the worst post he can become matched to by the central authority is best possible or in other words, $a_1$ wants to minimize the maximal rank of a post he can become matched to