The Submodular Secretary Problem Goes Linear

During the last decade, the matroid secretary problem (MSP) became one of the most prominent classes of online selection problems. Partially linked to its numerous applications in mechanism design, substantial interest arose also in the study of nonlinear versions of MSP, with a focus on the submodular matroid secretary problem (SMSP). So far, O(1)-competitive algorithms have been obtained for SMSP over some basic matroid classes. This created some hope that, analogously to the matroid secretary conjecture, one may even obtain O(1)-competitive algorithms for SMSP over any matroid. However, up to now, most questions related to SMSP remained open, including whether SMSP may be substantially more difficult than MSP; and more generally, to what extend MSP and SMSP are related. Our goal is to address these points by presenting general black-box reductions from SMSP to MSP. In particular, we show that any O(1)-competitive algorithm for MSP, even restricted to a particular matroid class, can be transformed in a black-box way to an O(1)-competitive algorithm for SMSP over the same matroid class. This implies that the matroid secretary conjecture is equivalent to the same conjecture for SMSP. Hence, in this sense SMSP is not harder than MSP. Also, to find O(1)-competitive algorithms for SMSP over a particular matroid class, it suffices to consider MSP over the same matroid class. Using our reductions we obtain many first and improved O(1)-competitive algorithms for SMSP over various matroid classes by leveraging known algorithms for MSP. Moreover, our reductions imply an O(loglog(rank))-competitive algorithm for SMSP, thus, matching the currently best asymptotic algorithm for MSP, and substantially improving on the previously best O(log(rank))-competitive algorithm for SMSP

Millisecond pulsars around intermediate-mass black holes in globular clusters

We study the process of dynamical capture of a millisecond pulsar (MSP) by a single or binary IMBH, simulating various types of single-binary and binary-binary encounters. It is found that [IMBH,MSP] binaries form over cosmic time in a cluster, via encounters of wide--orbit binary MSPs off the single IMBH, and at a lower pace, via interactions of (binary or single) MSPs with the IMBH orbited by a typical cluster star. The formation of an [IMBH,MSP] system is strongly inhibited if the IMBH is orbited by a stellar mass black hole. The [IMBH,MSP] binaries that form are relatively short-lived, \lsim 10^{8-9} yr, since their orbits decay via emission of gravitational waves. The detection of an [IMBH,MSP] system has a low probability of occurrence, when inferred from the current sample of MSPs in GCs. If next generation radio telescopes, like SKA, will detect an order of magnitude larger population of MSP in GCs, at least one [IMBH,MSP] is expected. Therefore, a complete search for low-luminosity MSPs in the GCs of the Milky Way with SKA will have the potential of testing the hypothesis that IMBHs of order 100 \msun are commonly hosted in GCs.Comment: 14 pages, 11 figures, 4 tables, to be published in MNRA

Dynamically formed black hole+millisecond pulsar binaries in globular clusters

The discovery of a binary comprising a black hole (BH) and a millisecond pulsar (MSP) would yield insights into stellar evolution and facilitate exquisitely sensitive tests of general relativity. Globular clusters (GCs) are known to harbor large MSP populations and recent studies suggest that GCs may also retain a substantial population of stellar mass BHs. We modeled the formation of BH+MSP binaries in GCs through exchange interactions between binary and single stars. We found that in dense, massive clusters most of the dynamically formed BH+MSP binaries will have orbital periods of 2 to 10 days, regardless of the mass of the BH, the number of BHs retained by the cluster, and the nature of the GC's binary population. The size of the BH+MSP population is sensitive to several uncertain parameters, including the BH mass function, the BH retention fraction, and the binary fraction in GCs. Based on our models, we estimate that there are $0.6\pm0.2$ dynamically formed BH+MSP binaries in the Milky Way GC system, and place an upper limit on the size of this population of $\sim 10$. Interestingly, we find that BH+MSP binaries will be rare even if GCs retain large BH populations.Comment: 15 pages, 5 figures, 2 tables, accepted for publication in MNRAS, updated to match published versio

Allelic forms of merozoite surface protein-3 in Plasmodium falciparum isolates from southeast of Iran

Background: Genetic diversity has provided Plasmodium falciparum with the potential capacity of avoiding the immune response, and possibly supported the natural selection of drug or vaccine-resistant parasites. Merozoite surface protein-3 (MSP-3) has been used to develop vaccines and investigate the genetic diversity regarding P. falciparum malaria in Iran. Objectives: The main goal of this study was to analyze the polymorphic antigen MSP-3 genes across southeast of Iran among four different districts, to identify the differences in the allele frequency and genetic diversity. Materials and Methods: Nested polymerase chain reaction amplification was used to determine polymorphisms of N-terminal region of the MSP-3 gene. A total of 85 microscopically positive P. falciparum infected individuals from southeast of Iran were included in this study. Results: Of the 85 confirmed P. falciparum samples obtained from four different districts, 72 were successfully scored for MSP-3.The MSP-3 allele classes (K1 and 3D7 types) showed comparable prevalence in all districts. Overall frequencies of K1 and 3D7 allele classes were 94.5 % for both. Conclusions: Since no study has yet looked at the extent of P. falciparum MSP-3 in this geographic region, these data can be helpful to support development of a vaccine based on MSP-3 against malaria. There should be a comparative analysis in different seasonal peaks to indicate the allelic polymorphism of MSP-3 over a period. © 2014, Ahvaz Jundishapur University of Medical Sciences; Published by Kowsar Corp

Purely non-atomic weak L^p spaces

Let \msp be a purely non-atomic measure space, and let $1 < p < \infty$. If \weakLp\msp is isomorphic, as a Banach space, to \weakLp\mspp for some purely atomic measure space \mspp, then there is a measurable partition $\Omega = \Omega_1\cup\Omega_2$ such that $(\Omega_1,\Sigma\cap\Omega_1,\mu_{|\Sigma\cap\Omega_1})$ is countably generated and $\sigma$-finite, and that $\mu(\sigma) = 0$ or $\infty$ for every measurable $\sigma \subseteq \Omega_2$. In particular, \weakLp\msp is isomorphic to $\ell^{p,\infty}$

Glutamatergic transmission in the central nucleus of the amygdala is selectively altered in Marchigian Sardinian alcohol-preferring rats: Alcohol and CRF effects

The CRF system of the central nucleus of the amygdala (CeA) is important for the processing of anxiety, stress, and effects of acute and chronic ethanol. We previously reported that ethanol decreases evoked glutamate transmission in the CeA of Sprague Dawley rats and that ethanol dependence alters glutamate release in the CeA. Here, we examined the effects of ethanol, CRF and a CRF1 receptor antagonist on spontaneous and evoked glutamatergic transmission in CeA neurons from Wistar and Marchigian Sardinian Preferring (msP) rats, a rodent line genetically selected for excessive alcohol drinking and characterized by heightened activity of the CRF1 system. Basal spontaneous and evoked glutamate transmission in CeA neurons from msP rats was increased compared to Wistar rats. Ethanol had divergent effects, either increasing or decreasing spontaneous glutamate release in the CeA of Wistar rats. This bidirectional effect was retained in msP rats, but the magnitude of the ethanol-induced increase in glutamate release was significantly smaller. The inhibitory effect of ethanol on evoked glutamatergic transmission was similar in both strains. CRF also either increased or decreased spontaneous glutamate release in CeA neurons of Wistar rats, however, in msP rats CRF only increased glutamate release. The inhibitory effect of CRF on evoked glutamatergic transmission was also lost in neurons from msP rats. A CRF1 antagonist produced only minor effects on spontaneous glutamate transmission, which were consistent across strains, and no effects on evoked glutamate transmission. These results demonstrate that the genetically altered CRF system of msP rats results in alterations in spontaneous and stimulated glutamate signaling in the CeA that may contribute to both the anxiety and drinking behavioral phenotypes