Approximating the minimum directed tree cover

Given a directed graph $G$ with non negative cost on the arcs, a directed tree cover of $G$ is a rooted directed tree such that either head or tail (or both of them) of every arc in $G$ is touched by $T$. The minimum directed tree cover problem (DTCP) is to find a directed tree cover of minimum cost. The problem is known to be $NP$-hard. In this paper, we show that the weighted Set Cover Problem (SCP) is a special case of DTCP. Hence, one can expect at best to approximate DTCP with the same ratio as for SCP. We show that this expectation can be satisfied in some way by designing a purely combinatorial approximation algorithm for the DTCP and proving that the approximation ratio of the algorithm is $\max\{2, \ln(D^+)\}$ with $D^+$ is the maximum outgoing degree of the nodes in $G$.Comment: 13 page

Spin-density-functional theory of circular and elliptical quantum dots

Using spin-density-functional theory, we study the electronic states of a two-dimensional parabolic quantum dot with up to N=58 electrons. We observe a shell structure for the filling of the dot with electrons. Hund's rule determines the spin configuration of the ground state, but only up to 22 electrons. At specific N, the ground state is degenerate, and a small elliptical deformation of the external potential induces a rotational charge-density-wave (CDW) state. Previously identified spin-density-wave (SDW) states are shown to be artifacts of broken spin symmetry in density-functional theory.Comment: 10 pages, 3 figure

Covering problems in edge- and node-weighted graphs

This paper discusses the graph covering problem in which a set of edges in an edge- and node-weighted graph is chosen to satisfy some covering constraints while minimizing the sum of the weights. In this problem, because of the large integrality gap of a natural linear programming (LP) relaxation, LP rounding algorithms based on the relaxation yield poor performance. Here we propose a stronger LP relaxation for the graph covering problem. The proposed relaxation is applied to designing primal-dual algorithms for two fundamental graph covering problems: the prize-collecting edge dominating set problem and the multicut problem in trees. Our algorithms are an exact polynomial-time algorithm for the former problem, and a 2-approximation algorithm for the latter problem, respectively. These results match the currently known best results for purely edge-weighted graphs.Comment: To appear in SWAT 201

Probing the Shape of Quantum Dots with Magnetic Fields

A tool for the identification of the shape of quantum dots is developed. By preparing a two-electron quantum dot, the response of the low-lying excited states to a homogeneous magnetic field, i.e. their spin and parity oscillations, is studied for a large variety of dot shapes. For any geometric configuration of the confinement we encounter characteristic spin singlet - triplet crossovers. The magnetization is shown to be a complementary tool for probing the shape of the dot.Comment: 11 pages, 4 figure

Diffusion Monte Carlo study of circular quantum dots

We present ground and excited state energies obtained from Diffusion Monte Carlo (DMC) calculations, using accurate multiconfiguration wave functions, for $N$ electrons ($N\le13$) confined to a circular quantum dot. We analyze the electron-electron pair correlation functions and compare the density and correlation energies to the predictions of local spin density approximation theory (LSDA). The DMC estimated change in electrochemical potential as function of the number of electrons in the dot is compared to that from LSDA and Hartree-Fock (HF) calculations.Comment: 7 pages, 4 eps figures. To be published in Phys. Rev. B, September 15th 2000. See erratum cond-mat/030571

The origins and properties of intrinsic nonradiative recombination centers in wide bandgap GaN and AlGaN

The nonradiative lifetime (τNR) of the near-band-edge emission in various quality GaN samples is compared with the results of positron annihilation measurement, in order to identify the origin and to determine the capture-cross-section of the major intrinsic nonradiative recombination centers (NRCs). The room-temperature τNR of various n-type GaN samples increased with decreasing the concentration of divacancies composed of a Ga vacancy (VGa) and a N vacancy (VN), namely, VGaVN. The τNR value also increased with increasing the diffusion length of positrons, which is almost proportional to the inverse third root of the gross concentration of all point defects. The results indicate that major intrinsic NRC in n-type GaN is VGaVN. From the relationship between its concentration and τNR, its hole capture-cross-section is estimated to be about 7 × 10−14 cm2. Different from the case of 4H-SiC, the major NRCs in p-type and n-type GaN are different: the major NRCs in Mg-doped p-type GaN epilayers are assigned to multiple vacancies containing a VGa and two (or three) VNs, namely, VGa(VN)n (n = 2 or 3). The ion-implanted Mg-doped GaN films are found to contain larger size vacancy complexes such as (VGa)3(VN)3. In analogy with GaN, major NRCs in Al0.6Ga0.4N alloys are assigned to vacancy complexes containing an Al vacancy or a VGa

Analysis of C3 Suggests Three Periods of Positive Selection Events and Different Evolutionary Patterns between Fish and Mammals

BACKGROUND: The third complement component (C3) is a central protein of the complement system conserved from fish to mammals. It also showed distinct characteristics in different animal groups. Striking features of the fish complement system were unveiled, including prominent levels of extrahepatic expression and isotypic diversity of the complement components. The evidences of the involvement of complement system in the enhancement of B and T cell responses found in mammals indicated that the complement system also serves as a bridge between the innate and adaptive responses. For the reasons mentioned above, it is interesting to explore the evolutionary process of C3 genes and to investigate whether the huge differences between aquatic and terrestrial environments affected the C3 evolution between fish and mammals. METHODOLOGY/PRINCIPAL FINDINGS: Analysis revealed that these two groups of animals had experienced different evolution patterns. The mammalian C3 genes were under purifying selection pressure while the positive selection pressure was detected in fish C3 genes. Three periods of positive selection events of C3 genes were also detected. Two happened on the ancestral lineages to all vertebrates and mammals, respectively, one happened on early period of fish evolutionary history. CONCLUSIONS/SIGNIFICANCE: Three periods of positive selection events had happened on C3 genes during history and the fish and mammals C3 genes experience different evolutionary patterns for their distinct living environments

Extreme Heterogeneity in Sex Chromosome Differentiation and Dosage Compensation in Livebearers

Once recombination is halted between the X and Y chromosomes, sex chromosomes begin to differentiate and transition to heteromorphism. While there is a remarkable variation across clades in the degree of sex chromosome divergence, far less is known about the variation in sex chromosome differentiation within clades. Here, we combined whole-genome and transcriptome sequencing data to characterize the structure and conservation of sex chromosome systems across Poeciliidae, the livebearing clade that includes guppies. We found that the Poecilia reticulata XY system is much older than previously thought, being shared not only with its sister species, Poecilia wingei, but also with Poecilia picta, which diverged roughly 20 million years ago. Despite the shared ancestry, we uncovered an extreme heterogeneity across these species in the proportion of the sex chromosome with suppressed recombination, and the degree of Y chromosome decay. The sex chromosomes in P. reticulata and P. wingei are largely homomorphic, with recombination in the former persisting over a substantial fraction. However, the sex chromosomes in P. picta are completely nonrecombining and strikingly heteromorphic. Remarkably, the profound degradation of the ancestral Y chromosome in P. picta is counterbalanced by the evolution of functional chromosome-wide dosage compensation in this species, which has not been previously observed in teleost fish. Our results offer important insight into the initial stages of sex chromosome evolution and dosage compensation

Expanding frontiers in materials chemistry and physics with multiple anions

During the last century, inorganic oxide compounds laid foundations for materials synthesis, characterization, and technology translation by adding new functions into devices previously dominated by main-group element semiconductor compounds. Today, compounds with multiple anions beyond the single-oxide ion, such as oxyhalides and oxyhydrides, offer a new materials platform from which superior functionality may arise. Here we review the recent progress, status, and future prospects and challenges facing the development and deployment of mixed-anion compounds, focusing mainly on oxide-derived materials. We devote attention to the crucial roles that multiple anions play during synthesis, characterization, and in the physical properties of these materials. We discuss the opportunities enabled by recent advances in synthetic approaches for design of both local and overall structure, state-of-the-art characterization techniques to distinguish unique structural and chemical states, and chemical/physical properties emerging from the synergy of multiple anions for catalysis, energy conversion, and electronic materials