Fast Dynamic Graph Algorithms for Parameterized Problems

Fully dynamic graph is a data structure that (1) supports edge insertions and deletions and (2) answers problem specific queries. The time complexity of (1) and (2) are referred to as the update time and the query time respectively. There are many researches on dynamic graphs whose update time and query time are $o(|G|)$, that is, sublinear in the graph size. However, almost all such researches are for problems in P. In this paper, we investigate dynamic graphs for NP-hard problems exploiting the notion of fixed parameter tractability (FPT). We give dynamic graphs for Vertex Cover and Cluster Vertex Deletion parameterized by the solution size $k$. These dynamic graphs achieve almost the best possible update time $O(\mathrm{poly}(k)\log n)$ and the query time $O(f(\mathrm{poly}(k),k))$, where $f(n,k)$ is the time complexity of any static graph algorithm for the problems. We obtain these results by dynamically maintaining an approximate solution which can be used to construct a small problem kernel. Exploiting the dynamic graph for Cluster Vertex Deletion, as a corollary, we obtain a quasilinear-time (polynomial) kernelization algorithm for Cluster Vertex Deletion. Until now, only quadratic time kernelization algorithms are known for this problem. We also give a dynamic graph for Chromatic Number parameterized by the solution size of Cluster Vertex Deletion, and a dynamic graph for bounded-degree Feedback Vertex Set parameterized by the solution size. Assuming the parameter is a constant, each dynamic graph can be updated in $O(\log n)$ time and can compute a solution in $O(1)$ time. These results are obtained by another approach.Comment: SWAT 2014 to appea

Conditionally autoregressive models improve occupancy analyses of autocorrelated data : an example with environmental DNA

Site occupancy-detection models (SODMs) are statistical models widely used for biodiversity surveys where imperfect detection of species occurs. For instance, SODMs are increasingly used to analyse environmental DNA (eDNA) data, taking into account the occurrence of both false-positive and false-negative errors. However, species occurrence data are often characterized by spatial and temporal autocorrelation, which might challenge the use of standard SODMs. Here we reviewed the literature of eDNA biodiversity surveys and found that most of studies do not take into account spatial or temporal autocorrelation. We then demonstrated how the analysis of data with spatial or temporal autocorrelation can be improved by using a conditionally autoregressive SODM, and show its application to environmental DNA data. We tested the autoregressive model on both simulated and real data sets, including chronosequences with different degrees of autocorrelation, and a spatial data set on a virtual landscape. Analyses of simulated data showed that autoregressive SODMs perform better than traditional SODMs in the estimation of key parameters such as true-/false-positive rates and show a better discrimination capacity (e.g., higher true skill statistics). The usefulness of autoregressive SODMs was particularly high in data sets with strong autocorrelation. When applied to real eDNA data sets (eDNA from lake sediment cores and freshwater), autoregressive SODM provided more precise estimation of true-/false-positive rates, resulting in more reasonable inference of occupancy states. Our results suggest that analyses of occurrence data, such as many applications of eDNA, can be largely improved by applying conditionally autoregressive specifications to SODMs

Magnetic enhancement of Co0.2_{0.2}Zn0.8_{0.8}Fe2_2O4_4 spinel oxide by mechanical milling

We report the magnetic properties of mechanically milled Co$_{0.2}$Zn$_{0.8}$Fe$_2$O$_4$ spinel oxide. After 24 hours milling of the bulk sample, the XRD spectra show nanostructure with average particle size $\approx$ 20 nm. The as milled sample shows an enhancement in magnetization and ordering temperature compared to the bulk sample. If the as milled sample is annealed at different temperatures for the same duration, recrystallization process occurs and approaches to the bulk structure on increasing the annealing temperatures. The magnetization of the annealed samples first increases and then decreases. At higher annealing temperature ($\sim$ 1000$^{0}$C) the system shows two coexisting magnetic phases {\it i.e.}, spin glass state and ferrimagnetic state, similar to the as prepared bulk sample. The room temperature M\"{o}ssbauer spectra of the as milled sample, annealed at 300$^{0}$C for different durations (upto 575 hours), suggest that the observed change in magnetic behaviour is strongly related with cations redistribution between tetrahedral (A) and octahedral (O) sites in the spinel structure. Apart from the cation redistribution, we suggest that the enhancement of magnetization and ordering temperature is related with the reduction of B site spin canting and increase of strain induced anisotropic energy during mechanical milling.Comment: 14 pages LaTeX, 10 ps figure

Analysis and design of power management scheme for an on-board solar energy storage system

This paper investigates the power management issues in a mobile solar energy storage system. A multi-converter based energy storage system is proposed, in which solar power is the primary source while the grid or the diesel generator is selected as the secondary source. The existence of the secondary source facilitates the battery state of charge detection by providing a constant battery charging current. Converter modeling, multi-converter control system design, digital implementation and experimental verification are introduced and discussed in details. The prototype experiment indicates that the converter system can provide a constant charging current during solar converter maximum power tracking operation, especially during large solar power output variation, which proves the feasibility of the proposed design

DD-dimensions Dirac fermions BEC-BCS cross-over thermodynamics

An effective Proca Lagrangian action is used to address the vector condensation Lorentz violation effects on the equation of state of the strongly interacting fermions system. The interior quantum fluctuation effects are incorporated as an external field approximation indirectly through a fictive generalized Thomson Problem counterterm background. The general analytical formulas for the $d$-dimensions thermodynamics are given near the unitary limit region. In the non-relativistic limit for $d=3$, the universal dimensionless coefficient $\xi ={4}/{9}$ and energy gap $\Delta/\epsilon_f ={5}/{18}$ are reasonably consistent with the existed theoretical and experimental results. In the unitary limit for $d=2$ and T=0, the universal coefficient can even approach the extreme occasion $\xi=0$ corresponding to the infinite effective fermion mass $m^*=\infty$ which can be mapped to the strongly coupled two-dimensions electrons and is quite similar to the three-dimensions Bose-Einstein Condensation of ideal boson gas. Instead, for $d=1$, the universal coefficient $\xi$ is negative, implying the non-existence of phase transition from superfluidity to normal state. The solutions manifest the quantum Ising universal class characteristic of the strongly coupled unitary fermions gas.Comment: Improved versio

Spin instabilities and quantum phase transitions in integral and fractional quantum Hall states

The inter-Landau-level spin excitations of quantum Hall states at filling factors nu=2 and 4/3 are investigated by exact numerical diagonalization for the situation in which the cyclotron (hbar*omega_c) and Zeeman (E_Z) splittings are comparable. The relevant quasiparticles and their interactions are studied, including stable spin wave and skyrmion bound states. For nu=2, a spin instability at a finite value of epsilon=hbar*omega_c-E_Z leads to an abrupt paramagnetic to ferromagnetic transition, in agreement with the mean-field approximation. However, for nu=4/3 a new and unexpected quantum phase transition is found which involves a gradual change from paramagnetic to ferromagnetic occupancy of the partially filled Landau level as epsilon is decreased.Comment: 4 pages, 5 figures, submitted to Phys.Rev.Let

Band-dependent quasiparticle dynamics in the hole-doped Ba-122 iron pnictides

We report on band-dependent quasiparticle dynamics in the hole-doped Ba-122 pnictides measured by ultrafast pump-probe spectroscopy. In the superconducting state of the optimal and over hole-doped samples, we observe two distinct relaxation processes: a fast component whose decay rate increases linearly with excitation density and a slow component whose relaxation is independent of excitation strength. We argue that these two components reflect the recombination of quasiparticles in the two hole bands through intraband and interband processes. We also find that the thermal recombination rate of quasiparticles increases quadratically with temperature in all samples. The temperature and excitation density dependence of the decays indicates fully gapped hole bands and nodal or very anisotropic electron bands.United States. Department of Energy (Grant No. DE-FG02-08ER46521)National Science Foundation (U.S.). Materials Research Science and Engineering Centers (Program) (award number DMR - 0819762

Scanning electron microscopy image representativeness: morphological data on nanoparticles.

A sample of a nanomaterial contains a distribution of nanoparticles of various shapes and/or sizes. A scanning electron microscopy image of such a sample often captures only a fragment of the morphological variety present in the sample. In order to quantitatively analyse the sample using scanning electron microscope digital images, and, in particular, to derive numerical representations of the sample morphology, image content has to be assessed. In this work, we present a framework for extracting morphological information contained in scanning electron microscopy images using computer vision algorithms, and for converting them into numerical particle descriptors. We explore the concept of image representativeness and provide a set of protocols for selecting optimal scanning electron microscopy images as well as determining the smallest representative image set for each of the morphological features. We demonstrate the practical aspects of our methodology by investigating tricalcium phosphate, Ca3 (PO4 )2 , and calcium hydroxyphosphate, Ca5 (PO4 )3 (OH), both naturally occurring minerals with a wide range of biomedical applications

Censored Glauber Dynamics for the mean field Ising Model

We study Glauber dynamics for the Ising model on the complete graph on $n$ vertices, known as the Curie-Weiss Model. It is well known that at high temperature ($\beta < 1$) the mixing time is $\Theta(n\log n)$, whereas at low temperature ($\beta > 1$) it is $\exp(\Theta(n))$. Recently, Levin, Luczak and Peres considered a censored version of this dynamics, which is restricted to non-negative magnetization. They proved that for fixed $\beta > 1$, the mixing-time of this model is $\Theta(n\log n)$, analogous to the high-temperature regime of the original dynamics. Furthermore, they showed \emph{cutoff} for the original dynamics for fixed $\beta<1$. The question whether the censored dynamics also exhibits cutoff remained unsettled. In a companion paper, we extended the results of Levin et al. into a complete characterization of the mixing-time for the Currie-Weiss model. Namely, we found a scaling window of order $1/\sqrt{n}$ around the critical temperature $\beta_c=1$, beyond which there is cutoff at high temperature. However, determining the behavior of the censored dynamics outside this critical window seemed significantly more challenging. In this work we answer the above question in the affirmative, and establish the cutoff point and its window for the censored dynamics beyond the critical window, thus completing its analogy to the original dynamics at high temperature. Namely, if $\beta = 1 + \delta$ for some $\delta > 0$ with $\delta^2 n \to \infty$, then the mixing-time has order $(n / \delta)\log(\delta^2 n)$. The cutoff constant is $(1/2+[2(\zeta^2 \beta / \delta - 1)]^{-1})$, where $\zeta$ is the unique positive root of $g(x)=\tanh(\beta x)-x$, and the cutoff window has order $n / \delta$.Comment: 55 pages, 4 figure

Bhabha Scattering with Radiated Gravitons at Linear Colliders

We study the process e+- e- -> e+- e- +- missing energy at a high-energy e+- e- collider, where the missing energy arises from the radiation of Kaluza-Klein gravitons in a model with large extra dimensions. It is shown that at a high-energy linear collider, this process can not only confirm the signature of such theories but can also sometimes be comparable in effectiveness to the commonly discussed channel e+- e- -> gamma +- missing energy, especially for a large number of extra dimensions and with polarized beams. We also suggest some ways of distinguishing the signals of a graviton tower from other types of new physics signals by combining data on our suggested channel with those on the photon-graviton channel.Comment: 16 pages, LaTex, 8 figures embedded, typos, report no and references correcte