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 $\ell^{p,\infty}$

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

Low-Complexity OFDM Spectral Precoding

This paper proposes a new large-scale mask-compliant spectral precoder (LS-MSP) for orthogonal frequency division multiplexing systems. In this paper, we first consider a previously proposed mask-compliant spectral precoding scheme that utilizes a generic convex optimization solver which suffers from high computational complexity, notably in large-scale systems. To mitigate the complexity of computing the LS-MSP, we propose a divide-and-conquer approach that breaks the original problem into smaller rank 1 quadratic-constraint problems and each small problem yields closed-form solution. Based on these solutions, we develop three specialized first-order low-complexity algorithms, based on 1) projection on convex sets and 2) the alternating direction method of multipliers. We also develop an algorithm that capitalizes on the closed-form solutions for the rank 1 quadratic constraints, which is referred to as 3) semi-analytical spectral precoding. Numerical results show that the proposed LS-MSP techniques outperform previously proposed techniques in terms of the computational burden while complying with the spectrum mask. The results also indicate that 3) typically needs 3 iterations to achieve similar results as 1) and 2) at the expense of a slightly increased computational complexity.Comment: Accepted in IEEE International Workshop on Signal Processing Advances in Wireless Communications (SPAWC), 201

Multi-Step Perturbation Solution of Nonlinear Rational Expectations Models

This paper develops and illustrates the multi-step generalization of the standard single-step perturbation (SSP) method or MSP. In SSP, we can think of evaluating at x the computed approximate solution based on x0, as moving from x0 to x in "one big step" along the straight-line vector x-x0. By contrast, in MSP we move from x0 to x along any chosen path, continuous, curved-line or connected-straight-line, in h steps of equal length 1/h. If at each step we apply SSP, Taylor-series theory says that the approximation error per step is 0(e) = h^(-k-1), so that the total approximation error in moving from x0 to x in h steps is 0(e) = h^(-k). Thus, MSP has two major advantages over SSP. First, both SSP and MSP accuracy declines as the approximation point, x, moves from the initial point, x0, although only in MSP can the decline be countered by increasing h. Increasing k is much more costly than increasing h, because increasing k requires new derivations of derivatives, more computer programming, more computer storage, and more computer run time. By contrast, increasing h generally requires only more computer run time and often only slightly more. Second, in SSP the initial point is usually a nonstochastic steady state but can sometimes also be set up in function space as the known exact solution of a close but simpler model. This "closeness" of a related, simpler, and known solution can be exploited much more explicitly by MSP, when moving from x0 to x. In MSP, the state space could include parameters, so that the initial point, x0, would represent the simpler model with the known solution, and the final point, x, would continue to represent the model of interest. Then, as we would move from the initial x0 to the final x in h steps, the state variables and parameters would move together from their initial to final values and the model being solved would vary continuously from the simple model to the model of interest. Both advantages of MSP facilitate repeatedly, accurately, and quickly solving a NLRE model in an econometric analysis, over a range of data values, which could differ enough from nonstochastic steady states of the model of interest to render computed SSP solutions, for a given k, inadequately accurate. In the present paper, we extend the derivation of SSP to MSP for k = 4. As we did before, we use a mixture of gradient and differential-form differentiations to derive the MSP computational equations in conventional linear-algebraic form and illustrate them with a version of the stochastic optimal one-sector growth model.numerical solution of dynamic stochastic equilibrium models

A novel malaria vaccine candidate antigen expressed in Tetrahymena thermophila

Development of effective malaria vaccines is hampered by the problem of producing correctly folded Plasmodium proteins for use as vaccine components. We have investigated the use of a novel ciliate expression system, Tetrahymena thermophila, as a P. falciparum vaccine antigen platform. A synthetic vaccine antigen composed of N-terminal and C-terminal regions of merozoite surface protein-1 (MSP-1) was expressed in Tetrahymena thermophila. The recombinant antigen was secreted into the culture medium and purified by monoclonal antibody (mAb) affinity chromatography. The vaccine was immunogenic in MF1 mice, eliciting high antibody titers against both N- and C-terminal components. Sera from immunized animals reacted strongly with P. falciparum parasites from three antigenically different strains by immunofluorescence assays, confirming that the antibodies produced are able to recognize parasite antigens in their native form. Epitope mapping of serum reactivity with a peptide library derived from all three MSP-1 Block 2 serotypes confirmed that the MSP-1 Block 2 hybrid component of the vaccine had effectively targeted all three serotypes of this polymorphic region of MSP-1. This study has successfully demonstrated the use of Tetrahymena thermophila as a recombinant protein expression platform for the production of malaria vaccine antigens

Influence of infection on malaria-specific antibody dynamics in a cohort exposed to intense malaria transmission in northern Uganda.

The role of submicroscopic infections in modulating malaria antibody responses is poorly understood and requires longitudinal studies. A cohort of 249 children ≤5 years of age, 126 children between 6 and 10 years and 134 adults ≥20 years was recruited in an area of intense malaria transmission in Apac, Uganda and treated with artemether/lumefantrine at enrolment. Parasite carriage was determined at enrolment and after 6 and 16 weeks using microscopy and PCR. Antibody prevalence and titres to circumsporozoite protein, apical membrane antigen-1 (AMA-1), merozoite surface protein-1 (MSP-119 ), merozoite surface protein-2 (MSP-2) and Anopheles gambiae salivary gland protein 6 (gSG6) were determined by ELISA. Plasmodium falciparum infections were detected in 38·1% (194/509) of the individuals by microscopy and in 57·1% (284/493) of the individuals by PCR at enrolment. Antibody prevalence and titre against AMA-1, MSP-119 , MSP-2 and gSG6 were related to concurrent (sub-)microscopic parasitaemia. Responses were stable in children who were continuously infected with malaria parasites but declined in children who were never parasitaemic during the study or were not re-infected after treatment. These findings indicate that continued malaria infections are required to maintain antibody titres in an area of intense malaria transmission

Study of measured pulsar masses and their possible conclusions

We study the statistics of 61 measured masses of neutron stars (NSs) in binary pulsar systems, including 18 double NS (DNS) systems, 26 radio pulsars (10 in our Galaxy) with white dwarf (WD) companions, 3 NSs with main-sequence companions, 13 NSs in X-ray binaries, and one undetermined system. We derive a mean value of M = 1.46 +/- 0.30 solar masses. When the 46 NSs with measured spin periods are divided into two groups at 20 milliseconds, i.e., the millisecond pulsar (MSP) group and others, we find that their mass averages are, respectively, M=1.57 +/- 0.35 solar masses and M=1.37+/- 0.23 solar masses. In the framework of the pulsar recycling hypothesis, this suggests that an accretion of approximately 0.2 solar mass is sufficient to spin up a neutron star and place it in the millisecond pulsar group. An empirical relation between the accreting mass and MSP spin period is \Delta M=0.43 (solar mass)(P/1 ms)^{-2/3}. UNlike the standard recycling process, if a MSP is formed by the accretion induced collapse (AIC) of a white dwarf with a mass less than Chandrasekha limit, e.g. 1.35 solar mass, then the binary MSPs involved in AICs is not be higher than 20%, which imposes a constraint on the AIC origin of MSPs.Comment: 6 pages, 5 figures, in press, Astronomy and Astrophysics 2011, 527, 8