Improved bounds for the number of forests and acyclic orientations in the square lattice

In a recent paper Merino and Welsh (1999) studied several counting problems on the square lattice $L_n$. The authors gave the following bounds for the asymptotics of $f(n)$, the number of forests of $L_n$, and $\alpha(n)$, the number of acyclic orientations of $L_n$: $3.209912 \leq \lim_{n\rightarrow\infty} f(n)^{1/n^2} \leq 3.84161$ and $22/7 \leq \lim_{n\rightarrow\infty} \alpha(n) \leq 3.70925$. In this paper we improve these bounds as follows: $3.64497 \leq \lim_{n\rightarrow\infty} f(n)^{1/n^2} \leq 3.74101$ and $3.41358 \leq \lim_{n\rightarrow\infty} \alpha(n) \leq 3.55449$. We obtain this by developing a method for computing the Tutte polynomial of the square lattice and other related graphs based on transfer matrices

Conflict-Free Coloring Made Stronger

In FOCS 2002, Even et al. showed that any set of $n$ discs in the plane can be Conflict-Free colored with a total of at most $O(\log n)$ colors. That is, it can be colored with $O(\log n)$ colors such that for any (covered) point $p$ there is some disc whose color is distinct from all other colors of discs containing $p$. They also showed that this bound is asymptotically tight. In this paper we prove the following stronger results: \begin{enumerate} \item [(i)] Any set of $n$ discs in the plane can be colored with a total of at most $O(k \log n)$ colors such that (a) for any point $p$ that is covered by at least $k$ discs, there are at least $k$ distinct discs each of which is colored by a color distinct from all other discs containing $p$ and (b) for any point $p$ covered by at most $k$ discs, all discs covering $p$ are colored distinctively. We call such a coloring a {\em $k$-Strong Conflict-Free} coloring. We extend this result to pseudo-discs and arbitrary regions with linear union-complexity. \item [(ii)] More generally, for families of $n$ simple closed Jordan regions with union-complexity bounded by $O(n^{1+\alpha})$, we prove that there exists a $k$-Strong Conflict-Free coloring with at most $O(k n^\alpha)$ colors. \item [(iii)] We prove that any set of $n$ axis-parallel rectangles can be $k$-Strong Conflict-Free colored with at most $O(k \log^2 n)$ colors. \item [(iv)] We provide a general framework for $k$-Strong Conflict-Free coloring arbitrary hypergraphs. This framework relates the notion of $k$-Strong Conflict-Free coloring and the recently studied notion of $k$-colorful coloring. \end{enumerate} All of our proofs are constructive. That is, there exist polynomial time algorithms for computing such colorings

Is PPARβ/δ a Retinoid Receptor?

The broad ligand-binding characteristic of PPARβ/δ has long hampered identification of physiologically-meaningful ligands for the receptor. The observations that the activity of PPARβ/δ is supported by fatty acid binding protein 5 (FABP5), which directly delivers ligands from the cytosol to the receptor, suggest that bona fide PPARβ/δ ligands both activate the receptor, and trigger the nuclear translocation of FABP5. Using these criteria, it was recently demonstrated that all-trans-retinoic acid (RA), the activator of the classical retinoic acid receptor RAR, also serves as a ligand for PPARβ/δ. Partitioning of RA between its two receptors was found to be regulated by FABP5, which delivers it to PPARβ/δ, and cellular RA binding protein II (CRABP-II), which targets it to RAR. Consequently, RA activates PPARβ/δ in cells that display a high FABP5/CRABP-II expression ratio. It remains to be clarified whether compounds other than RA may also serve as endogenous activators for this highly promiscuous protein

The measurement of disaster risk: An example from tropical cyclones in the Philippines

What shapes people’s disaster risk exposure? Using a sub-national (provincial) panel econometric and deductive approach we answer this question by focussing on tropical cyclones, and using the Philippines as a case study for our measurement approach. We construct a new provincial level panel dataset, and use panel estimation methods to assess the influence of socioeconomic (vulnerability), geographic, demographic, topographic (exposure), and meteorological (hazard) characteristics on the resulting fatalities and affected persons from recent tropical cyclones. We find strong evidence that socioeconomic development reduces people’s vulnerability and loss of human lives. Further, good local governance is associated with fewer fatalities. Rapid and unplanned urbanization generates vulnerabilities and increases harm. Exposure, including topography, and hazard strength are likewise important determinants. However, disaster impacts on people appear to be influenced much more by vulnerability and exposure, than by the hazard itself. We quantify this difference in order to contribute to policy planning at national and sub-national scales

Short cavity InGaAsP/InP lasers with dielectric mirrors

Short cavity length (38 µm) lasers have been fabricated using a recently developed microcleavage technique. SiO2-amorphous Si multilayer coatings have been evaported on the lasers to obtain high reflectivity mirrors. The lasers have current thresholds as low as 3.8 mA with 85% reflecting front mirror and high reflectivity rear mirror and 2.9 mA with two high reflectivity mirrors. Single longitudinal mode operation is observed over a wide range of driving currents and temperatures

An Infrastructure for acquiring high quality semantic metadata

Because metadata that underlies semantic web applications is gathered from distributed and heterogeneous data sources, it is important to ensure its quality (i.e., reduce duplicates, spelling errors, ambiguities). However, current infrastructures that acquire and integrate semantic data have only marginally addressed the issue of metadata quality. In this paper we present our metadata acquisition infrastructure, ASDI, which pays special attention to ensuring that high quality metadata is derived. Central to the architecture of ASDI is a erification engine that relies on several semantic web tools to check the quality of the derived data. We tested our prototype in the context of building a semantic web portal for our lab, KMi. An experimental evaluation omparing the automatically extracted data against manual annotations indicates that the verification engine enhances the quality of the extracted semantic metadata

Utilising semantic technologies for intelligent indexing and retrieval of digital images

The proliferation of digital media has led to a huge interest in classifying and indexing media objects for generic search and usage. In particular, we are witnessing colossal growth in digital image repositories that are difficult to navigate using free-text search mechanisms, which often return inaccurate matches as they in principle rely on statistical analysis of query keyword recurrence in the image annotation or surrounding text. In this paper we present a semantically-enabled image annotation and retrieval engine that is designed to satisfy the requirements of the commercial image collections market in terms of both accuracy and efficiency of the retrieval process. Our search engine relies on methodically structured ontologies for image annotation, thus allowing for more intelligent reasoning about the image content and subsequently obtaining a more accurate set of results and a richer set of alternatives matchmaking the original query. We also show how our well-analysed and designed domain ontology contributes to the implicit expansion of user queries as well as the exploitation of lexical databases for explicit semantic-based query expansion

Acute military psychiatric casualties from the war in Iraq

Background: The view that most military personnel evacuated from war zones are suffering from combat stress reactions, or are otherwise traumatised by the horrors of war, has an impact on all aspects of military psychiatry. Aims: To delineate the reasons for psychiatric aeromedical evacuation from Iraq from the start of build-up of UK forces in January 2003 until the end of October that year, 6 months after the end of formal hostilities. Method: A retrospective study was conducted of field and in-patient psychiatric assessments of 116 military personnel evacuated to the UK military psychiatric in-patient facility in Catterick Garrison. Results: Evacuees were mainly non-combatants (69%). A significant proportion were in reserve service (21%) and had a history of contact with mental health services (37%). Only 3% had a combat stress reaction. In over 85% of cases evacuation was for low mood attributed to separation from friends or family, or difficulties adjusting to the environment. Conclusions: These findings have implications especially for screening for suitability for deployment, and for understanding any longer-term mental health problems arising in veterans from Iraq