Statistical mechanics of the vertex-cover problem

We review recent progress in the study of the vertex-cover problem (VC). VC belongs to the class of NP-complete graph theoretical problems, which plays a central role in theoretical computer science. On ensembles of random graphs, VC exhibits an coverable-uncoverable phase transition. Very close to this transition, depending on the solution algorithm, easy-hard transitions in the typical running time of the algorithms occur. We explain a statistical mechanics approach, which works by mapping VC to a hard-core lattice gas, and then applying techniques like the replica trick or the cavity approach. Using these methods, the phase diagram of VC could be obtained exactly for connectivities $c<e$, where VC is replica symmetric. Recently, this result could be confirmed using traditional mathematical techniques. For $c>e$, the solution of VC exhibits full replica symmetry breaking. The statistical mechanics approach can also be used to study analytically the typical running time of simple complete and incomplete algorithms for VC. Finally, we describe recent results for VC when studied on other ensembles of finite- and infinite-dimensional graphs.Comment: review article, 26 pages, 9 figures, to appear in J. Phys. A: Math. Ge

Comparative proteome and peptidome analysis of the cephalic fluid secreted by Arapaima gigas (Teleostei: Osteoglossidae) during and outside parental care

Parental investment in Arapaima gigas includes nest building and guarding, followed by a care provision when a cephalic fluid is released from the parents&rsquo; head to the offspring. This fluid has presumably important functions for the offspring but so far its composition has not been characterised. In this study the proteome and peptidome of the cephalic secretion was studied in parental and non-parental fish using capillary electrophoresis coupled to mass spectrometry (CE-MS) and GeLC-MS/MS analyses. Multiple comparisons revealed 28 peptides were significantly different between males and parental males (PC-males), 126 between females and parental females (PC-females), 51 between males and females and 9 between PC-males and PC-females. Identification revealed peptides were produced in the inner ear (pcdh15b), eyes (tetraspanin and ppp2r3a), central nervous system (otud4, ribeye a, tjp1b and syn1) among others. A total of 422 proteins were also identified and gene ontology analysis revealed 28 secreted extracellular proteins. From these, 2 hormones (prolactin and stanniocalcin) and 12 proteins associated to immunological processes (serotransferrin, &alpha;-1-antitrypsin homolog, apolipoprotein A-I, and others) were identified. This study provides novel biochemical data on the lateral line fluid which will enable future hypotheses-driven experiments to better understand the physiological roles of the lateral line in chemical communication

A spitting image: specializations in archerfish eyes for vision at the interface between air and water

Archerfish are famous for spitting jets of water to capture terrestrial insects, a task that not only requires oral dexterity, but also the ability to detect small camouflaged prey against a visually complex background of overhanging foliage. Because detection of olfactory, auditory and tactile cues is diminished at air–water interfaces, archerfish must depend almost entirely on visual cues to mediate their sensory interactions with the aerial world. During spitting, their eyes remain below the water's surface and must adapt to the optical demands of both aquatic and aerial fields of view. These challenges suggest that archerfish eyes may be specially adapted to life at the interface between air and water. Using microspectrophotometry to characterize the spectral absorbance of photoreceptors, we find that archerfish have differentially tuned their rods and cones across their retina, correlated with spectral differences in aquatic and aerial fields of view. Spatial resolving power also differs for aquatic and aerial fields of view with maximum visual resolution (6.9 cycles per degree) aligned with their preferred spitting angle. These measurements provide insight into the functional significance of intraretinal variability in archerfish and infer intraretinal variability may be expected among surface fishes or vertebrates where different fields of view vary markedly

Poissons characoïdes de l'Amazonie péruvienne

Description of 64 species of fresh‐water Fishes of the suborder Characoidei (Cypriniformes), collected by Dr. K. H. Lüling during his 1959/60 Expedition in lower Ucayali and Iquitos regions. New forms for science (about 10 per cent of the collected species) are: a new genus, Oxybrycon, which seems to be close to Leptobrycon and Macropsobrycon; a Hemigrammus‐species and 2 Hyphessobrycon‐species; a Cheirodon (the genus was not signaled from Peruvian Amazon); and a Serrasalmus. Besides, 10 species seem to be new for the concerned territory, whereas 2 other forms have been described in former papers (see References). Some identification‐Keys are given, concerning Amazonian Triportheus and Schizodon, as well as concerning one Curimatus‐group of species. Finally a list of the characoid Fishes, known to occur in the Iquitos surroundings and in the lower Ucayali, is given