Loop models on random maps via nested loops: case of domain symmetry breaking and application to the Potts model

We use the nested loop approach to investigate loop models on random planar maps where the domains delimited by the loops are given two alternating colors, which can be assigned different local weights, hence allowing for an explicit Z_2 domain symmetry breaking. Each loop receives a non local weight n, as well as a local bending energy which controls loop turns. By a standard cluster construction that we review, the Q = n^2 Potts model on general random maps is mapped to a particular instance of this problem with domain-non-symmetric weights. We derive in full generality a set of coupled functional relations for a pair of generating series which encode the enumeration of loop configurations on maps with a boundary of a given color, and solve it by extending well-known complex analytic techniques. In the case where loops are fully-packed, we analyze in details the phase diagram of the model and derive exact equations for the position of its non-generic critical points. In particular, we underline that the critical Potts model on general random maps is not self-dual whenever Q \neq 1. In a model with domain-symmetric weights, we also show the possibility of a spontaneous domain symmetry breaking driven by the bending energy.Comment: 44 pages, 13 figure

Random tree growth by vertex splitting

We study a model of growing planar tree graphs where in each time step we separate the tree into two components by splitting a vertex and then connect the two pieces by inserting a new link between the daughter vertices. This model generalises the preferential attachment model and Ford's $\alpha$-model for phylogenetic trees. We develop a mean field theory for the vertex degree distribution, prove that the mean field theory is exact in some special cases and check that it agrees with numerical simulations in general. We calculate various correlation functions and show that the intrinsic Hausdorff dimension can vary from one to infinity, depending on the parameters of the model.Comment: 47 page

M87, Globular Clusters, and Galactic Winds: Issues in Giant Galaxy Formation

New VRI photometry is presented for the globular clusters in the innermost 140'' of the M87 halo. The results are used to discuss several issues concerning the formation and evolution of globular cluster systems in supergiant ellipticals like M87. (1) we find no significant change in the globular cluster luminosity function (GCLF) with galactocentric radius, for cluster masses M < 10^5 solar masses, indicating that the main effects of dynamical evolution may be only on lower-mass clusters. (2) Within the core radius (1') of the globular cluster system, the metallicity distribution is uniform, but at larger radii the mean metallicity declines steadily as Z ~ r^-0.9. (3) The various options for explaining the existence of high specific frequency galaxies like M87 are evaluated, and scaling laws for the GCSs in these galaxies are given. Interpretations involving secondary evolution (formation of many globular clusters during mergers, intergalactic globular clusters, etc.) are unlikely to be the primary explanation for high-S_N galaxies. (4) We suggest that central-supergiant E galaxies may have formed in an exceptionally turbulent or high-density environment in which an early, powerful galactic wind drove out a high fraction of the protogalactic gas, thus artificially boosting the specificComment: 67 pages, 17 figures. To appear in Astronomical Journal, in press for May 1998. Preprints also available from W.Harris; send e-mail request to [email protected]

Molecular mechanistic origin of the toughness of natural adhesives, fibres and composites

Natural materials are renowned for their strength and toughness(1-5). Spider dragline silk has a breakage energy per unit weight two orders of magnitude greater than high tensile steel(1,6), and is representative of many other strong natural fibres(3,7,8). The abalone shell, a composite of calcium carbonate plates sandwiched between organic material, is 3,000 times more fracture resistant than a single crystal of the pure mineral(4,5). The organic component, comprising just a few per cent of the composite by weight(9), is thought to hold the key to nacre's fracture toughness(10,11). Ceramics laminated with organic material are more fracture resistant than non-laminated ceramics(11,12), but synthetic materials made of interlocking ceramic tablets bound by a few weight per cent of ordinary adhesives do not have a toughness comparable to nacre(13). We believe that the key to nacre's fracture resistance resides in the polymer adhesive, and here we reveal the properties of this adhesive by using the atomic force microscope(14) to stretch the organic molecules exposed on the surface of freshly cleaved nacre. The adhesive fibres elongate in a stepwise manner as folded domains or loops are pulled open. The elongation events occur for forces of a few hundred piconewtons, which are smaller than the forces of over a nanonewton required to break the polymer backbone in the threads. We suggest that this 'modular' elongation mechanism might prove to be quite general for conveying toughness to natural fibres and adhesives, and we predict that it might be found also in dragline silk

Three-year tracking of fatty acid composition of plasma phospholipids in healthy children

Objectives: The fatty acid composition of plasma phospholipids reflects the dietary fatty acid intake as well as endogenous turnover. We aimed at investigating the potential tracking of plasma phospholipid fatty acid composition in children that participated in a prospective cohort study. Methods: 26 healthy children participated in a longitudinal study on health risks and had been enrolled after birth. All children were born at term with birth weights appropriate for gestational age. Follow-up took place at ages 24, 36 and 60 months. At each time point a 24-hour dietary recall was obtained, anthropometric parameters were measured and a blood sample for phospholipid fatty acid analysis was taken. Results: Dietary intake of saturated (SFA), monounsaturated (MUFA) and polyunsaturated (PUFA) fatty acids at the three time points were not correlated. We found lower values for plasma MUFA and the MUFA/SFA ratio at 60 months compared to 24 months. In contrast, total PUFA, total n-6 and n-6 long-chain polyunsaturated fatty acids (LC-PUFA) were higher at 60 months. Significant averaged correlation coefficients (average of Pearson's R for 24 versus 36 months and 36 versus 60 months) were found for n-6 LC-PUFA (r = 0.67), n-6/n-3 LC-PUFA ratio (r = 0.59) and arachidonic acid/linoleic acid ratio (r = 0.64). Partial tracking was found for the docosahexaenoic acid/alpha-linolenic acid ratio (r = 0.33). Body mass index and sum of skinfolds Z-scores were similar in the three evaluations. Conclusions: A significant tracking of n-6 LC-PUFA, n-6 LC-PUFA/n-3 LC-PUFA ratio, arachidonic acid/ linoleic acid ratio and docosahexaenoic acid/alpha-linolenic acid ratio may reflect an influence of individual endogenous fatty acid metabolism on plasma concentrations of some, but not all, fatty acids. Copyright (c) 2007 S. Karger AG, Basel

Force distribution in a scalar model for non-cohesive granular material

We study a scalar lattice model for inter-grain forces in static, non-cohesive, granular materials, obtaining two primary results. (i) The applied stress as a function of overall strain shows a power law dependence with a nontrivial exponent, which moreover varies with system geometry. (ii) Probability distributions for forces on individual grains appear Gaussian at all stages of compression, showing no evidence of exponential tails. With regard to both results, we identify correlations responsible for deviations from previously suggested theories.Comment: 16 pages, 9 figures, Submitted to PR

Searching for network modules

When analyzing complex networks a key target is to uncover their modular structure, which means searching for a family of modules, namely node subsets spanning each a subnetwork more densely connected than the average. This work proposes a novel type of objective function for graph clustering, in the form of a multilinear polynomial whose coefficients are determined by network topology. It may be thought of as a potential function, to be maximized, taking its values on fuzzy clusterings or families of fuzzy subsets of nodes over which every node distributes a unit membership. When suitably parametrized, this potential is shown to attain its maximum when every node concentrates its all unit membership on some module. The output thus is a partition, while the original discrete optimization problem is turned into a continuous version allowing to conceive alternative search strategies. The instance of the problem being a pseudo-Boolean function assigning real-valued cluster scores to node subsets, modularity maximization is employed to exemplify a so-called quadratic form, in that the scores of singletons and pairs also fully determine the scores of larger clusters, while the resulting multilinear polynomial potential function has degree 2. After considering further quadratic instances, different from modularity and obtained by interpreting network topology in alternative manners, a greedy local-search strategy for the continuous framework is analytically compared with an existing greedy agglomerative procedure for the discrete case. Overlapping is finally discussed in terms of multiple runs, i.e. several local searches with different initializations.Comment: 10 page

Mejora de sensores vítreos sol-gel para la conservación preventiva de materiales históricos frente a la acidez

[ES] Los sensores a base de recubrimientos vítreos sol-gel dopados con ácido 2[4-(dimetil-amino) fenilazo] benzoico son capaces de cambiar su absorción óptica cuando se someten a distintas concentraciones de iones H3O+ y OH-. La respuesta de los sensores en ensayos de campo se estudió en Cracovia (Polonia) variando el procedimiento normal de uso, con el fin de mejorar su respuesta. Se midieron tanto los parámetros ópticos de los sensores como las condiciones ambientales (temperatura, humedad, presión y concentraciones de SO2 y de NOx). La respuesta de los sensores se analizó en términos de los cambios de su absorción visible. Dichos cambios se deben a reacciones locales de neutralización que tienen lugar en la superficie de los sensores, debido al efecto conjunto de los contaminantes de carácter ácido y a la humedad ambiental. Se establecieron correlaciones entre la concentración del contaminante principal (SO2) y la respuesta de los sensores para elaborar una calibración directa entre la absorción óptica y el pH ambiental. Los sensores pueden detectar y evaluar la acidez ambiental, así como alertar sobre la concentración de contaminantes ácidos que pueden dañar a la mayoría de los materiales históricos.[EN] Sensors based on sol-gel glassy coatings doped with 2[4-(dimethyl-amino) phenylazo] benzoic acid are able to change their optical absorption when they are submitted to different concentration of H3O+ and OH-. The sensors behaviour in field tests was studied in Cracow (Poland), varying the normal procedure of operation to improve their response. Both the sensors optical parameters and the environmental conditions (temperature, humidity, pressure, SO2 and NOx concentrations) were measured. The sensors response was analysed in terms of their visible absorbance changes, which are due to local neutralisation reactions in the sensors surface by the join effect of acid pollutants and humidity. Correlations between the main acid pollutant (SO2) concentration and the sensors response are established to provide a relation between the optical absorption and the environmental pH. The sensors are able to detect and monitorise environmental acidity, as well as to alert on the pollutant concentration that may damage most of the historical materials.The authors wish to acknowledge bilateral Polish-Spanish project Ref. PAN-CSIC 2003PL0011, European Marie Curie project Ref. MERG-CT-2004-516436 and Spanish project Ref. CICYT-MAT-2003-03231 for financing support. N.C. acknowledges CSIC-ESF for an I3P postdoctoral contract.Peer reviewe

Material Symmetry to Partition Endgame Tables

Many games display some kind of material symmetry . That is, some sets of game elements can be exchanged for another set of game elements, so that the resulting position will be equivalent to the original one, no matter how the elements were arranged on the board. Material symmetry is routinely used in card game engines when they normalize their internal representation of the cards. Other games such as chinese dark chess also feature some form of material symmetry, but it is much less clear what the normal form of a position should be. We propose a principled approach to detect material symmetry. Our approach is generic and is based on solving multiple rel- atively small sub-graph isomorphism problems. We show how it can be applied to chinese dark chess , dominoes , and skat . In the latter case, the mappings we obtain are equivalent to the ones resulting from the standard normalization process. In the two former cases, we show that the material symmetry allows for impressive savings in memory requirements when building endgame tables. We also show that those savings are relatively independent of the representation of the tables

Primary solitary retro-clival amyloidoma.

Amyloidosis encompasses a group of disorders sharing the common feature of intercellular deposition of amyloid protein by several different pathogenetic mechanisms. Primary solitary amyloidosis, or amyloidoma, is a rare subset of amyloidosis in which amyloid deposition is focal and not secondary to a systemic process or plasma cell dyscrasia.This 84-year-old female presented with history of multiple syncopal episodes, dysphagia, and ataxia. Motor strength was 3+/5 in the right upper extremity. Rheumatoid factor, cyclic citrullinated peptide (CCP), and anti-nuclear antibody (ANA) were normal. Serum and urine immune-electrophoresis detected no abnormal bands. Computed tomography (CT) and magnetic resonance imaging (MRI) demonstrated a non-enhancing soft-tissue mass extending from the retro-clivus to C2 posteriorly, eccentric to the right with severe mass effect on the upper cervical medullary junction. Endoscopic trans-nasal debulking of the retro-clival mass was performed with occiput to C5 posterior instrumentation for spinal stabilization.Primary solitary amyloidosis, unlike other forms of amyloidosis, has an excellent prognosis with local resection. Diagnosis requires special stains and a degree of suspicion for the disease. This is the first report to document an endoscopic trans-nasal approach for removal of a primary solitary amyloidosis of the retro-clivus. Management of vertebral amyloidoma involves aggressive local resection of the tumor when feasible and spine stabilization as the degree of tumor involvement mandates. Complete evaluation for the diagnosis of systemic amyloidosis is essential for the management and prognostication. Surgeons encountering such lesions must maintain high suspicion for this rare disease and advise pathologists accordingly to establish the correct diagnosis