Constrained Non-Monotone Submodular Maximization: Offline and Secretary Algorithms

Constrained submodular maximization problems have long been studied, with near-optimal results known under a variety of constraints when the submodular function is monotone. The case of non-monotone submodular maximization is less understood: the first approximation algorithms even for the unconstrainted setting were given by Feige et al. (FOCS '07). More recently, Lee et al. (STOC '09, APPROX '09) show how to approximately maximize non-monotone submodular functions when the constraints are given by the intersection of p matroid constraints; their algorithm is based on local-search procedures that consider p-swaps, and hence the running time may be n^Omega(p), implying their algorithm is polynomial-time only for constantly many matroids. In this paper, we give algorithms that work for p-independence systems (which generalize constraints given by the intersection of p matroids), where the running time is poly(n,p). Our algorithm essentially reduces the non-monotone maximization problem to multiple runs of the greedy algorithm previously used in the monotone case. Our idea of using existing algorithms for monotone functions to solve the non-monotone case also works for maximizing a submodular function with respect to a knapsack constraint: we get a simple greedy-based constant-factor approximation for this problem. With these simpler algorithms, we are able to adapt our approach to constrained non-monotone submodular maximization to the (online) secretary setting, where elements arrive one at a time in random order, and the algorithm must make irrevocable decisions about whether or not to select each element as it arrives. We give constant approximations in this secretary setting when the algorithm is constrained subject to a uniform matroid or a partition matroid, and give an O(log k) approximation when it is constrained by a general matroid of rank k.Comment: In the Proceedings of WINE 201

High resolution infrared absorption spectra, crystal field, and relaxation processes in CsCdBr_3:Pr^3+

High resolution low-temperature absorption spectra of 0.2% Pr^3+ doped CsCdBr_3 were measured in the spectral region 2000--7000 cm-1. Positions and widths of the crystal field levels within the 3H5, 3H4, 3F2, and 3F3 multiplets of the Pr^3+ main center have been determined. Hyperfine structure of several spectral lines has been found. Crystal field calculations were carried out in the framework of the semiphenomenological exchange charge model (ECM). Parameters of the ECM were determined by fitting to the measured total splittings of the 3H4 and 3H6 multiplets and to the observed in this work hyperfine splittings of the crystal field levels. One- and two-phonon relaxation rates were calculated using the phonon Green's functions of the perfect (CsCdBr_3) and locally perturbed (impurity dimer centers in CsCdBr_3:Pr^3+) crystal lattice. Comparison with the measured linewidths confirmed an essential redistribution of the phonon density of states in CsCdBr_3 crystals doped with rare-earth ions.Comment: 16 pages, 5 tables, 3 figure

Theory of Coexistence of Superconductivity and Ferroelectricity : A Dynamical Symmetry Model

We propose and investigate a model for the coexistence of Superconductivity (SC) and Ferroelectricity (FE) based on the dynamical symmetries $su(2)$ for the pseudo-spin SC sector, $h(4)$ for the displaced oscillator FE sector, and $su(2) \otimes h(4)$ for the composite system. We assume a minimal symmetry-allowed coupling, and simplify the hamiltonian using a double mean field approximation (DMFA). A variational coherent state (VCS) trial wave-function is used for the ground state: the energy, and the relevant order parameters for SC and FE are obtained. For positive sign of the SC-FE coupling coefficient, a non-zero value of either order parameter can suppress the other (FE polarization suppresses SC and vice versa). This gives some support to "Matthias' Conjecture" [1964], that SC and FE tend to be mutually exclusive. For such a Ferroelectric Superconductor we predict: a) the SC gap $\Delta$ (and $T_c$) will increase with increasing applied pressure when pressure quenches FE as in many ferroelectrics, and b) the FE polarization will increase with increaesing magnetic field up to $H_c$. The last result is equivalent to the prediction of a new type of Magneto-Electric Effect in a coexistent SC-FE material. Some discussion will be given of the relation of these results to the cuprate superconductors.Comment: 46 page

Clostridioides difficile canonical L,D-transpeptidases catalyze a novel type of peptidoglycan cross-links and are not required for beta-lactam resistance

Clostridioides difficile is the leading cause of antibiotic-associated diarrhea worldwide with significant morbidity and mortality. This organism is naturally resistant to several beta-lactam antibiotics that inhibit the polymerization of peptidoglycan, an essential component of the bacteria cell envelope. Previous work has revealed that C. difficile peptidoglycan has an unusual composition. It mostly contains 3-3 cross-links, catalyzed by enzymes called L,D-transpeptidases (Ldts) that are poorly inhibited by beta-lactams. It was therefore hypothesized that peptidoglycan polymerization by these enzymes could underpin antibiotic resistance. Here, we investigated the catalytic activity of the three canonical Ldts encoded by C. difficile (LdtCd1, LdtCd2, and LdtCd3) in vitro and explored their contribution to growth and antibiotic resistance. We show that two of these enzymes catalyze the formation of novel types of peptidoglycan cross-links using meso-diaminopimelic acid both as a donor and an acceptor, also observed in peptidoglycan sacculi. We demonstrate that the simultaneous deletion of these three genes only has a minor impact on both peptidoglycan structure and resistance to beta-lactams. This unexpected result therefore implies that the formation of 3-3 peptidoglycan cross-links in C. difficile is catalyzed by as yet unidentified noncanonical Ldt enzymes

Evolution of the nuclear spin-orbit splitting explored via the ³²Si<i>(d,p)</i>³³Si reaction using SOLARIS

The spin-orbit splitting between neutron 1p orbitals at 33Si has been deduced using the single-neutron-adding (d,p) reaction in inverse kinematics with a beam of 32Si, a long-lived radioisotope. Reaction products were analyzed by the newly implemented SOLARIS spectrometer at the reaccelerated-beam facility at the National Superconducting Cyclotron Laboratory. The measurements show reasonable agreement with shell-model calculations that incorporate modern cross-shell interactions, but they contradict the prediction of proton density depletion based on relativistic mean-field theory. The evolution of the neutron 1p-shell orbitals is systematically studied using the present and existing data in the isotonic chains of = 17, 19, and 21. In each case, a smooth decrease in the separation of the - orbitals is seen as the respective p-orbitals approach zero binding, suggesting that the finite nuclear potential strongly influences the evolution of nuclear structure in this region

Democracy and governance networks: compatible or not?

The relationship between representative democracy and governance networks is investigated at a theoretical level. Four conjectures about the relationship are defined. The incompatibility conjectures rests on the primacy of politics and sees governance networks as a threat. The complementarity conjecture presents governance networks as a means of enabling greater participation in the policy process and sensitivity in programme implementation. The transitional conjecture posits a wider evolution of governance forms towards network relationships. The instrumental conjecture views governance networks as a powerful means through which dominant interests can achieve their goals. Illustrative implications for theory and practice are identified, in relation to power in the policy process, the public interest, and the role of public managers. The heuristic potential of the conjectures is demonstrated through the identification of an outline research agenda

Using verbal autopsy to measure causes of death: the comparative performance of existing methods

Background: Monitoring progress with disease and injury reduction in many populations will require widespread use of verbal autopsy (VA). Multiple methods have been developed for assigning cause of death from a VA but their application is restricted by uncertainty about their reliability. Methods: We investigated the validity of five automated VA methods for assigning cause of death: InterVA-4, Random Forest (RF), Simplified Symptom Pattern (SSP), Tariff method (Tariff), and King-Lu (KL), in addition to physician review of VA forms (PCVA), based on 12,535 cases from diverse populations for which the true cause of death had been reliably established. For adults, children, neonates and stillbirths, performance was assessed separately for individuals using sensitivity, specificity, Kappa, and chance-corrected concordance (CCC) and for populations using cause specific mortality fraction (CSMF) accuracy, with and without additional diagnostic information from prior contact with health services. A total of 500 train-test splits were used to ensure that results are robust to variation in the underlying cause of death distribution. Results: Three automated diagnostic methods, Tariff, SSP, and RF, but not InterVA-4, performed better than physician review in all age groups, study sites, and for the majority of causes of death studied. For adults, CSMF accuracy ranged from 0.764 to 0.770, compared with 0.680 for PCVA and 0.625 for InterVA; CCC varied from 49.2% to 54.1%, compared with 42.2% for PCVA, and 23.8% for InterVA. For children, CSMF accuracy was 0.783 for Tariff, 0.678 for PCVA, and 0.520 for InterVA; CCC was 52.5% for Tariff, 44.5% for PCVA, and 30.3% for InterVA. For neonates, CSMF accuracy was 0.817 for Tariff, 0.719 for PCVA, and 0.629 for InterVA; CCC varied from 47.3% to 50.3% for the three automated methods, 29.3% for PCVA, and 19.4% for InterVA. The method with the highest sensitivity for a specific cause varied by cause. Conclusions: Physician review of verbal autopsy questionnaires is less accurate than automated methods in determining both individual and population causes of death. Overall, Tariff performs as well or better than other methods and should be widely applied in routine mortality surveillance systems with poor cause of death certification practices. © 2014 Murray et al.; licensee BioMed Central Ltd