Sufficient Conditions for Tuza's Conjecture on Packing and Covering Triangles

Given a simple graph $G=(V,E)$, a subset of $E$ is called a triangle cover if it intersects each triangle of $G$. Let $\nu_t(G)$ and $\tau_t(G)$ denote the maximum number of pairwise edge-disjoint triangles in $G$ and the minimum cardinality of a triangle cover of $G$, respectively. Tuza conjectured in 1981 that $\tau_t(G)/\nu_t(G)\le2$ holds for every graph $G$. In this paper, using a hypergraph approach, we design polynomial-time combinatorial algorithms for finding small triangle covers. These algorithms imply new sufficient conditions for Tuza's conjecture on covering and packing triangles. More precisely, suppose that the set $\mathscr T_G$ of triangles covers all edges in $G$. We show that a triangle cover of $G$ with cardinality at most $2\nu_t(G)$ can be found in polynomial time if one of the following conditions is satisfied: (i) $\nu_t(G)/|\mathscr T_G|\ge\frac13$, (ii) $\nu_t(G)/|E|\ge\frac14$, (iii) $|E|/|\mathscr T_G|\ge2$. Keywords: Triangle cover, Triangle packing, Linear 3-uniform hypergraphs, Combinatorial algorithm

EF+EX Forest Algebras

We examine languages of unranked forests definable using the temporal operators EF and EX. We characterize the languages definable in this logic, and various fragments thereof, using the syntactic forest algebras introduced by Bojanczyk and Walukiewicz. Our algebraic characterizations yield efficient algorithms for deciding when a given language of forests is definable in this logic. The proofs are based on understanding the wreath product closures of a few small algebras, for which we introduce a general ideal theory for forest algebras. This combines ideas from the work of Bojanczyk and Walukiewicz for the analogous logics on binary trees and from early work of Stiffler on wreath product of finite semigroups

Simulating an Airborne Lidar Bathymetry (ALB) System

This study’s focus is on the horizontal and vertical uncertainties associated with ALB measurements due to scattering through the water column. A lidar simulator was constructed and we present its design and preliminary results

Lymphatic Filariasis Control in Tanzania: Effect of Six Rounds of Mass Drug Administration with Ivermectin and Albendazole on Infection and Transmission.

Control of lymphatic filariasis (LF) in most countries of sub-Saharan Africa is based on annual mass drug administration (MDA) with a combination of ivermectin and albendazole, in order to interrupt transmission. We present findings from a detailed study on the effect of six rounds of MDA with this drug combination as implemented by the National Lymphatic Filariasis Elimination Programme (NLFEP) in a highly endemic rural area of north-eastern Tanzania.\ud The effect of treatment on transmission and human infection was monitored in a community- and a school-based study during an 8-year period (one pre-intervention and 7 post-intervention years) from 2003 to 2011. Before intervention, 24.5% of the community population had microfilariae (mf) in the blood, 53.3% had circulating filarial antigens (CFA) and 78.9% had specific antibodies to the recombinant filarial antigen Bm14. One year after the sixth MDA, these values had decreased considerably to 2.7%, 19.6% and 27.5%, respectively. During the same period, the CFA prevalence among new intakes of Standard 1 pupils in 10 primary schools decreased from 25.2% to 5.6%. In line with this, transmission by the three vectors (Anopheles gambiae, An. funestus and Culex quinquefasciatus) as determined by dissection declined sharply (overall vector infectivity rate by 99.3% and mean monthly transmission potential by 99.2% between pre-intervention and fifth post-intervention period). A major shift in vector species composition, from predominantly anopheline to almost exclusively culicine was observed over the years. This may be largely unrelated to the MDAs but may have important implications for the epidemiology of LF in the area. Six MDAs caused considerable decrease in all the measured indices for transmission and human infection. In spite of this, indices were still relatively high in the late period of the study, and it may take a long time to reach the recommended cut-off levels for interruption of transmission unless extra efforts are made. These should include increased engagement of the target population in the control activities, to ensure higher treatment coverage. It is expected that the recent initiative to distribute insecticide impregnated bed nets to every household in the area will also contribute towards reaching the goal of successful LF elimination

Satellite-Derived Bathymetry Using Multiple Images: The Alaska North Slope Case Study

Currently, charting data in much of the U.S. Arctic North Slope is inadequate or nonexistent and most of its areas have not been updated since the early-1950s. Although the charting infrastructure is out of date, ship transportation (such as, fishing and transit between the towns) has increased. NOAA conducted a preliminary multibeam survey in 2013 that reached Point Barrow, AK. However, all the Arctic North Slope remained untouched. Previous studies have shown that satellite-derived bathymetry (SDB) is a useful reconnaissance tool in tropical and sub-tropical waters in clear water conditions, especially over sandy seafloor. However, it is very difficult to extract good information over the Arctic using a single satellite image, especially over the U.S. North Slope. The glacial powder from land reduces the water clarity that limits the light penetration depth. Also, this turbidity is not uniform along the coast line and may affect the calculations. In this paper, a new SDB approach was developed that compiles multiple satellite images to extract only areas that were identified clear by comparison (i.e., minimum water clarity change between two satellite images). Preliminary results using Landsat 7 imagery from 1999-2002 and Landsat 8 imagery from 2013 are presented

Nautical Chart Adequacy Evaluation Using Publicly-Available Data

The International Hydrographic Office (IHO) C-55 publication communicates the need to improve the collection, quality and availability of hydrographic data world-wide, while also monitoring and rectifying possible deficiencies and shortcomings that are presented on the chart. This task of evaluating the adequacy of nautical chart products poses a challenge to many national hydrographic offices. This stems from the dearth of readily available spatial information: namely, the lack of reliable and accessible vessel traffic data, and little means to assess the changing nature of both near-shore bathymetry and shoreline in a simple and reliable manner. In this paper, we present the potential use of automatic-identification system (AIS) data, satellite-derived bathymetry (SDB), and airborne-lidar bathymetry (ALB) to provide an operational procedure for evaluating the adequacy and completeness of information of NOAA charts. Preliminary results from three U.S. study sites are presented in this paper: Nantucket Sound, MA; Barnegat Bay Inlet, NJ; and Barataria Bay, LA. Based on the publically-available datasets it was possible to identify changes in the charts and develop a reconnaissance procedure to monitor these changes on a yearly basis

Relationships between riparian buffer widths and the effects of logging on stream habitat, invertebrate community composition and fish abundance

Impacts from the logging of Eucalyptus forest on stream habitat, macroinvertebrate abundance and diversity, and fish abundance were surveyed in Tasmania, Australia. Forty-five pairs of sites from 34 streams of greater than or equal to 2.5 km squared of catchment area were each sampled once during summer in the period 1990-92. Each site pair consisted of an 'impacted' site downstream of a logging treatment and an upstream or closely matched 'paired control' site. Site pair treatments encompassed two logging methods (cable and conventional) with a range of riparian buffer strip widths (0-50 m) and included unlogged controls. Differences between site pair variables were used as test statistics for the detection of logging impacts. Logging significantly increased riffle sediment, length of open stream, periphytic algal cover, water temperature and snag volume. Logging also significantly decreased riffle macroinvertebrate abundance, particularly of stoneflies and leptophlebiid mayflies, and brown trout abundance. All effects of logging were dependent on buffer strip width and were not significantly affected by coupe slope, soil erodibility or time (over one to five years) since logging. All impacts of logging were significant only at buffer widths of <30 m. Minimum buffer widths for eliminating logging impacts on stream habitats and biota are discussed

Strategies for estimating human exposure to mycotoxins via food

In this review, five strategies to estimate mycotoxin exposure of a (sub-) population via food, including data collection, are discussed with the aim to identify the added values and limitations of each strategy for risk assessment of these chemicals. The well-established point estimate, observed individual mean, probabilistic and duplicate diet strategies are addressed, as well as the emerging human biomonitoring strategy. All five exposure assessment strategies allow the estimation of chronic (long-term) exposure to mycotoxins, and, with the exception of the observed individual mean strategy, also acute (short-term) exposure. Methods for data collection, i.e. food consumption surveys, food monitoring studies and total diet studies are discussed. In food monitoring studies, the driving force is often enforcement of legal limits, and, consequently, data are often generated with relatively high limits of quantification and targeted at products suspected to contain mycotoxin levels above these legal limits. Total diet studies provide a solid base for chronic exposure assessments since they provide mycotoxin levels in food based on well-defined samples and including the effect of food preparation. Duplicate diet studies and human biomonitoring studies reveal the actual exposure but often involve a restricted group of human volunteers and a limited time period. Human biomonitoring studies may also include exposure to mycotoxins from other sources than food, and exposure to modified mycotoxins that may not be detected with current analytical methods. Low limits of quantification are required for analytical methods applied for data collection to avoid large uncertainties in the exposure due to high numbers of left censored data, i.e. with levels below the limit of quantification

Quantum noise and mixedness of a pumped dissipative non-linear oscillator

Evolutions of quantum noise, characterized by quadrature squeezing parameter and Fano factor, and of mixedness, quantified by quantum von Neumann and linear entropies, of a pumped dissipative non-linear oscillator are studied. The model can describe a signal mode interacting with a thermal reservoir in a parametrically pumped cavity with a Kerr non-linearity. It is discussed that the initial pure states, including coherent states, Fock states, and finite superpositions of coherent states evolve into the same steady mixed state as verified by the quantum relative entropy and the Bures metric. It is shown analytically and verified numerically that the steady state can be well approximated by a nonclassical Gaussian state exhibiting quadrature squeezing and sub-Poissonian statistics for the cold thermal reservoir. A rapid increase is found in the mixedness, especially for the initial Fock states and superpositions of coherent states, during a very short time interval, and then for longer evolution times a decrease in the mixedness to the same, for all the initial states, and relatively low value of the nonclassical Gaussian state.Comment: 10 pages, 12 figure