Approximating k-Forest with Resource Augmentation: A Primal-Dual Approach

In this paper, we study the $k$-forest problem in the model of resource augmentation. In the $k$-forest problem, given an edge-weighted graph $G(V,E)$, a parameter $k$, and a set of $m$ demand pairs $\subseteq V \times V$, the objective is to construct a minimum-cost subgraph that connects at least $k$ demands. The problem is hard to approximate---the best-known approximation ratio is $O(\min\{\sqrt{n}, \sqrt{k}\})$. Furthermore, $k$-forest is as hard to approximate as the notoriously-hard densest $k$-subgraph problem. While the $k$-forest problem is hard to approximate in the worst-case, we show that with the use of resource augmentation, we can efficiently approximate it up to a constant factor. First, we restate the problem in terms of the number of demands that are {\em not} connected. In particular, the objective of the $k$-forest problem can be viewed as to remove at most $m-k$ demands and find a minimum-cost subgraph that connects the remaining demands. We use this perspective of the problem to explain the performance of our algorithm (in terms of the augmentation) in a more intuitive way. Specifically, we present a polynomial-time algorithm for the $k$-forest problem that, for every $\epsilon>0$, removes at most $m-k$ demands and has cost no more than $O(1/\epsilon^{2})$ times the cost of an optimal algorithm that removes at most $(1-\epsilon)(m-k)$ demands

Marburg hemorrhagic fever in Durba and Watsa, Democratic Republic of the Congo: clinical documentation, features of illness, and treatment

The objective of the present study was to describe day of onset and duration of symptoms of Marburg hemorrhagic fever (MHF), to summarize the treatments applied, and to assess the quality of clinical documentation. Surveillance and clinical records of 77 patients with MHF cases were reviewed. Initial symptoms included fever, headache, general pain, nausea, vomiting, and anorexia (median day of onset, day 1-2), followed by hemorrhagic manifestations (day 5-8+), and terminal symptoms included confusion, agitation, coma, anuria, and shock. Treatment in isolation wards was acceptable, but the quality of clinical documentation was unsatisfactory. Improved clinical documentation is necessary for a basic evaluation of supportive treatment

Cancer and thrombosis: Managing the risks and approaches to thromboprophylaxis

Patients with cancer are at increased risk of venous thromboembolism (VTE) compared with patients without cancer. This results from both the prothrombotic effects of the cancer itself and iatrogenic factors, such as chemotherapy, radiotherapy, indwelling central venous devices and surgery, that further increase the risk of VTE. Although cancer-associated thrombosis remains an important cause of morbidity and mortality, it is often underdiagnosed and undertreated. However, evidence is accumulating to support the use of low-molecular-weight heparins (LMWHs) in the secondary prevention of VTE in patients with cancer. Not only have LMWHs been shown to be at least as effective as coumarin derivatives in this setting, but they have a lower incidence of complications, including bleeding, and are not associated with the practical problems of warfarin therapy. Furthermore, a growing number of studies indicate that LMWHs may improve survival among patients with cancer due to a possible antitumor effect. Current evidence suggests that LMWHs should increasingly be considered for the long-term management of VTE in patients with cancer

Compressibility of titanosilicate melts

The effect of composition on the relaxed adiabatic bulk modulus (K0) of a range of alkali- and alkaline earth-titanosilicate [X 2 n/n+ TiSiO5 (X=Li, Na, K, Rb, Cs, Ca, Sr, Ba)] melts has been investigated. The relaxed bulk moduli of these melts have been measured using ultrasonic interferometric methods at frequencies of 3, 5 and 7 MHz in the temperature range of 950 to 1600°C (0.02 Pa s < s < 5 Pa s). The bulk moduli of these melts decrease with increasing cation size from Li to Cs and Ca to Ba, and with increasing temperature. The bulk moduli of the Li-, Na-, Ca- and Ba-bearing metasilicate melts decrease with the addition of both TiO2 and SiO2 whereas those of the K-, Rb- and Cs-bearing melts increase. Linear fits to the bulk modulus versus volume fraction of TiO2 do not converge to a common compressibility of the TiO2 component, indicating that the structural role of TiO2 in these melts is dependent on the identity of the cation. This proposition is supported by a number of other property data for these and related melt compositions including heat capacity and density, as well as structural inferences from X-ray absorption spectroscopy (XANES). The compositional dependence of the compressibility of the TiO2 component in these melts explains the difficulty incurred in previous attempts to incorporate TiO2 in calculation schemes for melt compressibility. The empirical relationship KV-4/3 for isostructural materials has been used to evaluate the compressibility-related structural changes occurring in these melts. The alkali metasilicate and disilicate melts are isostructural, independent of the cation. The addition of Ti to the metasilicate composition (i.e. X2TiSiO5), however, results in a series of melts which are not isostructural. The alkaline-earth metasilicate and disilicate compositions are not isostructural, but the addition of Ti to the metasilicate compositions (i.e. XTiSiO5) would appear, on the basis of modulus-volume systematics, to result in the melts becoming isostructural with respect to compressibility

Fano resonances in plasmonic core-shell particles and the Purcell effect

Despite a long history, light scattering by particles with size comparable with the light wavelength still unveils surprising optical phenomena, and many of them are related to the Fano effect. Originally described in the context of atomic physics, the Fano resonance in light scattering arises from the interference between a narrow subradiant mode and a spectrally broad radiation line. Here, we present an overview of Fano resonances in coated spherical scatterers within the framework of the Lorenz-Mie theory. We briefly introduce the concept of conventional and unconventional Fano resonances in light scattering. These resonances are associated with the interference between electromagnetic modes excited in the particle with different or the same multipole moment, respectively. In addition, we investigate the modification of the spontaneous-emission rate of an optical emitter at the presence of a plasmonic nanoshell. This modification of decay rate due to electromagnetic environment is referred to as the Purcell effect. We analytically show that the Purcell factor related to a dipole emitter oriented orthogonal or tangential to the spherical surface can exhibit Fano or Lorentzian line shapes in the near field, respectively.Comment: 28 pages, 10 figures; invited book chapter to appear in "Fano Resonances in Optics and Microwaves: Physics and Application", Springer Series in Optical Sciences (2018), edited by E. O. Kamenetskii, A. Sadreev, and A. Miroshnichenk

Testing density-functional approximations on a lattice and the applicability of the related Hohenberg-Kohn-like theorem

We present a metric-space approach to quantify the performance of approximations in lattice density-functional theory for interacting many-body systems and to explore the regimes where the Hohenberg-Kohn-type theorem on fermionic lattices is applicable. This theorem demonstrates the existence of one-to-one mappings between particle densities, wave functions and external potentials. We then focus on these quantities, and quantify how far apart in metric space the approximated and exact ones are. We apply our method to the one-dimensional Hubbard model for different types of external potentials, and assess the regimes where it is applicable to one of the most used approximations in density-functional theory, the local density approximation (LDA). We find that the potential distance may have a very different behaviour from the density and wave function distances, in some cases even providing the wrong assessments of the LDA performance trends. We attribute this to the systems reaching behaviours which are borderline for the applicability of the one-to-one correspondence between density and external potential. On the contrary the wave function and density distances behave similarly and are always sensitive to system variations. Our metric-based method correctly predicts the regimes where the LDA performs fairly well and the regimes where it fails. This suggests that our method could be a practical tool for testing the efficiency of density-functional approximations

Spin Caloritronics

This is a brief overview of the state of the art of spin caloritronics, the science and technology of controlling heat currents by the electron spin degree of freedom (and vice versa).Comment: To be published in "Spin Current", edited by S. Maekawa, E. Saitoh, S. Valenzuela and Y. Kimura, Oxford University Pres

Extremal measures maximizing functionals based on simplicial volumes

We consider functionals measuring the dispersion of a d-dimensional distribution which are based on the volumes of simplices of dimension k ≤ d formed by k + 1 independent copies and raised to some power δ. We study properties of extremal measures that maximize these functionals. In particular, for positive δ we characterize their support and for negative δ we establish connection with potential theory and motivate the application to space-filling design for computer experiments. Several illustrative examples are presented

Simulations of events for the LUX-ZEPLIN (LZ) dark matter experiment

The LUX-ZEPLIN dark matter search aims to achieve a sensitivity to the WIMP-nucleon spin-independent cross-section down to (1–2)×10−12 pb at a WIMP mass of 40 GeV/c2. This paper describes the simulations framework that, along with radioactivity measurements, was used to support this projection, and also to provide mock data for validating reconstruction and analysis software. Of particular note are the event generators, which allow us to model the background radiation, and the detector response physics used in the production of raw signals, which can be converted into digitized waveforms similar to data from the operational detector. Inclusion of the detector response allows us to process simulated data using the same analysis routines as developed to process the experimental data

Academic Performance and Behavioral Patterns

Identifying the factors that influence academic performance is an essential part of educational research. Previous studies have documented the importance of personality traits, class attendance, and social network structure. Because most of these analyses were based on a single behavioral aspect and/or small sample sizes, there is currently no quantification of the interplay of these factors. Here, we study the academic performance among a cohort of 538 undergraduate students forming a single, densely connected social network. Our work is based on data collected using smartphones, which the students used as their primary phones for two years. The availability of multi-channel data from a single population allows us to directly compare the explanatory power of individual and social characteristics. We find that the most informative indicators of performance are based on social ties and that network indicators result in better model performance than individual characteristics (including both personality and class attendance). We confirm earlier findings that class attendance is the most important predictor among individual characteristics. Finally, our results suggest the presence of strong homophily and/or peer effects among university students