The Cost of Perfection for Matchings in Graphs

Perfect matchings and maximum weight matchings are two fundamental combinatorial structures. We consider the ratio between the maximum weight of a perfect matching and the maximum weight of a general matching. Motivated by the computer graphics application in triangle meshes, where we seek to convert a triangulation into a quadrangulation by merging pairs of adjacent triangles, we focus mainly on bridgeless cubic graphs. First, we characterize graphs that attain the extreme ratios. Second, we present a lower bound for all bridgeless cubic graphs. Third, we present upper bounds for subclasses of bridgeless cubic graphs, most of which are shown to be tight. Additionally, we present tight bounds for the class of regular bipartite graphs

Snarks with total chromatic number 5

A k-total-coloring of G is an assignment of k colors to the edges and vertices of G, so that adjacent and incident elements have different colors. The total chromatic number of G, denoted by chi(T)(G), is the least k for which G has a k-total-coloring. It was proved by Rosenfeld that the total chromatic number of a cubic graph is either 4 or 5. Cubic graphs with chi(T) = 4 are said to be Type 1, and cubic graphs with chi(T) = 5 are said to be Type 2. Snarks are cyclically 4-edge-connected cubic graphs that do not allow a 3-edge-coloring. In 2003, Cavicchioli et al. asked for a Type 2 snark with girth at least 5. As neither Type 2 cubic graphs with girth at least 5 nor Type 2 snarks are known, this is taking two steps at once, and the two requirements of being a snark and having girth at least 5 should better be treated independently. In this paper we will show that the property of being a snark can be combined with being Type 2. We will give a construction that gives Type 2 snarks for each even vertex number n >= 40. We will also give the result of a computer search showing that among all Type 2 cubic graphs on up to 32 vertices, all but three contain an induced chordless cycle of length 4. These three exceptions contain triangles. The question of the existence of a Type 2 cubic graph with girth at least 5 remains open

On the ratio between maximum weight perfect matchings and maximum weight matchings in grids

Given a graph G that admits a perfect matching, we investigate the parameter η(G) (originally motivated by computer graphics applications) which is defined as follows. Among all nonnegative edge weight assignments, η(G) is the minimum ratio between (i) the maximum weight of a perfect matching and (ii) the maximum weight of a general matching. In this paper, we determine the exact value of η for all rectangular grids, all bipartite cylindrical grids, and all bipartite toroidal grids. We introduce several new techniques to this endeavor

The AMPK β2 subunit is required for energy homeostasis during metabolic stress

AMP activated protein kinase (AMPK) plays a key role in the regulatory network responsible for maintaining systemic energy homeostasis during exercise or nutrient deprivation. To understand the function of the regulatory β2 subunit of AMPK in systemic energy metabolism, we characterized β2 subunit-deficient mice. Using these mutant mice, we demonstrated that the β2 subunit plays an important role in regulating glucose, glycogen, and lipid metabolism during metabolic stress. The β2 mutant animals failed to maintain euglycemia and muscle ATP levels during fasting. In addition, β2-deficient animals showed classic symptoms of metabolic syndrome, including hyperglycemia, glucose intolerance, and insulin resistance when maintained on a high-fat diet (HFD), and were unable to maintain muscle ATP levels during exercise. Cell surface-associated glucose transporter levels were reduced in skeletal muscle from β2 mutant animals on an HFD. In addition, they displayed poor exercise performance and impaired muscle glycogen metabolism. These mutant mice had decreased activation of AMPK and deficits in PGC1α-mediated transcription in skeletal muscle. Our results highlight specific roles of AMPK complexes containing the β2 subunit and suggest the potential utility of AMPK isoform-specific pharmacological modulators for treatment of metabolic, cardiac, and neurological disorders

On star and biclique edge-colorings

A biclique of G is a maximal set of vertices that induces a complete bipartite subgraph Kp,q of G with at least one edge, and a star of a graph G is a maximal set of vertices that induces a complete bipartite graph K1,q. A biclique (resp. star) edge-coloring is a coloring of the edges of a graph with no monochromatic bicliques (resp. stars). We prove that the problem of determining whether a graph G has a biclique (resp. star) edgecoloring using two colors is NP-hard. Furthermore, we describe polynomial time algorithms for the problem in restricted classes: K3-free graphs, chordal bipartite graphs, powers of paths, and powers of cycles

Chiral Soliton Model vs Pentaquark Structure for \Theta (1540)

The exotic baryon $\Theta^+$ (1540 MeV)$is visualised as an expected (iso) rotational excitation in the Chiral Soliton Model. It is also argued as a Pentaquark baryon state in a constituent quark model with strong diquark correlations. I contrast the two points of view; the similarities and differences between the two pictures. Collective excitation, characteristic of Chiral Soliton Model points toward small mixing of representations in the wake of SU(3) breaking. In contrast, Constituent quark Models prefer near ``ideal'' mixing, similar to$\omega - \phi$ mixing.Comment: 11 pages, references added, final published versio

Histone deacetylase activity is essential for the expression of HoxA9 and for endothelial commitment of progenitor cells

The regulation of acetylation is central for the epigenetic control of lineage-specific gene expression and determines cell fate decisions. We provide evidence that the inhibition of histone deacetylases (HDACs) blocks the endothelial differentiation of adult progenitor cells. To define the mechanisms by which HDAC inhibition prevents endothelial differentiation, we determined the expression of homeobox transcription factors and demonstrated that HoxA9 expression is down-regulated by HDAC inhibitors. The causal involvement of HoxA9 in the endothelial differentiation of adult progenitor cells is supported by the finding that HoxA9 overexpression partially rescued the endothelial differentiation blockade induced by HDAC inhibitors. Knockdown and overexpression studies revealed that HoxA9 acts as a master switch to regulate the expression of prototypical endothelial-committed genes such as endothelial nitric oxide synthase, VEGF-R2, and VE-cadherin, and mediates the shear stress–induced maturation of endothelial cells. Consistently, HoxA9-deficient mice exhibited lower numbers of endothelial progenitor cells and showed an impaired postnatal neovascularization capacity after the induction of ischemia. Thus, HoxA9 is regulated by HDACs and is critical for postnatal neovascularization

History of exotic Meson (4-quark) and Baryon (5-quark) States

I briefly review the history of exotic meson (4-quark) and baryon (5-quark) states, which is rooted in the formalism of Regge pole and duality. There are robust model-independent predictions for the exchange of 4-quark (Baryonium) Regge trajectories in several processes, which are strongly supported by experiment. On the other hand the predictions for the spectroscopy of 4-quark resonances are based on specific QCD inspired models, with some experimental support. The corresponding predictions for the recently discovered exotic baryon (Pentaquark) state are briefly discussed.Comment: 14 pages Latex including 4 eps figures, final version to appear as a topical review in J. Phys.

Large Scale Immune Profiling of Infected Humans and Goats Reveals Differential Recognition of Brucella melitensis Antigens

Brucellosis is a widespread zoonotic disease that is also a potential agent of bioterrorism. Current serological assays to diagnose human brucellosis in clinical settings are based on detection of agglutinating anti-LPS antibodies. To better understand the universe of antibody responses that develop after B. melitensis infection, a protein microarray was fabricated containing 1,406 predicted B. melitensis proteins. The array was probed with sera from experimentally infected goats and naturally infected humans from an endemic region in Peru. The assay identified 18 antigens differentially recognized by infected and non-infected goats, and 13 serodiagnostic antigens that differentiate human patients proven to have acute brucellosis from syndromically similar patients. There were 31 cross-reactive antigens in healthy goats and 20 cross-reactive antigens in healthy humans. Only two of the serodiagnostic antigens and eight of the cross-reactive antigens overlap between humans and goats. Based on these results, a nitrocellulose line blot containing the human serodiagnostic antigens was fabricated and applied in a simple assay that validated the accuracy of the protein microarray results in the diagnosis of humans. These data demonstrate that an experimentally infected natural reservoir host produces a fundamentally different immune response than a naturally infected accidental human host

A chemical survey of exoplanets with ARIEL

Thousands of exoplanets have now been discovered with a huge range of masses, sizes and orbits: from rocky Earth-like planets to large gas giants grazing the surface of their host star. However, the essential nature of these exoplanets remains largely mysterious: there is no known, discernible pattern linking the presence, size, or orbital parameters of a planet to the nature of its parent star. We have little idea whether the chemistry of a planet is linked to its formation environment, or whether the type of host star drives the physics and chemistry of the planet’s birth, and evolution. ARIEL was conceived to observe a large number (~1000) of transiting planets for statistical understanding, including gas giants, Neptunes, super-Earths and Earth-size planets around a range of host star types using transit spectroscopy in the 1.25–7.8 μm spectral range and multiple narrow-band photometry in the optical. ARIEL will focus on warm and hot planets to take advantage of their well-mixed atmospheres which should show minimal condensation and sequestration of high-Z materials compared to their colder Solar System siblings. Said warm and hot atmospheres are expected to be more representative of the planetary bulk composition. Observations of these warm/hot exoplanets, and in particular of their elemental composition (especially C, O, N, S, Si), will allow the understanding of the early stages of planetary and atmospheric formation during the nebular phase and the following few million years. ARIEL will thus provide a representative picture of the chemical nature of the exoplanets and relate this directly to the type and chemical environment of the host star. ARIEL is designed as a dedicated survey mission for combined-light spectroscopy, capable of observing a large and well-defined planet sample within its 4-year mission lifetime. Transit, eclipse and phase-curve spectroscopy methods, whereby the signal from the star and planet are differentiated using knowledge of the planetary ephemerides, allow us to measure atmospheric signals from the planet at levels of 10–100 part per million (ppm) relative to the star and, given the bright nature of targets, also allows more sophisticated techniques, such as eclipse mapping, to give a deeper insight into the nature of the atmosphere. These types of observations require a stable payload and satellite platform with broad, instantaneous wavelength coverage to detect many molecular species, probe the thermal structure, identify clouds and monitor the stellar activity. The wavelength range proposed covers all the expected major atmospheric gases from e.g. H2O, CO2, CH4 NH3, HCN, H2S through to the more exotic metallic compounds, such as TiO, VO, and condensed species. Simulations of ARIEL performance in conducting exoplanet surveys have been performed – using conservative estimates of mission performance and a full model of all significant noise sources in the measurement – using a list of potential ARIEL targets that incorporates the latest available exoplanet statistics. The conclusion at the end of the Phase A study, is that ARIEL – in line with the stated mission objectives – will be able to observe about 1000 exoplanets depending on the details of the adopted survey strategy, thus confirming the feasibility of the main science objectives.Peer reviewedFinal Published versio