A simple explanation for taxon abundance patterns

For taxonomic levels higher than species, the abundance distributions of the number of subtaxa per taxon tend to approximate power laws but often show strong deviations from such laws. Previously, these deviations were attributed to finite-time effects in a continuous-time branching process at the generic level. Instead, we describe herein a simple discrete branching process that generates the observed distributions and find that the distribution's deviation from power law form is not caused by disequilibration, but rather that it is time independent and determined by the evolutionary properties of the taxa of interest. Our model predicts—with no free parameters—the rank-frequency distribution of the number of families in fossil marine animal orders obtained from the fossil record. We find that near power law distributions are statistically almost inevitable for taxa higher than species. The branching model also sheds light on species-abundance patterns, as well as on links between evolutionary processes, self-organized criticality, and fractals.

On representations of finite type

Representations of the (infinite) canonical anticommutation relations and the associated operator algebra, the fermion algebra, are studied. A “coupling constant” (in (0,1]) is defined for primary states of “finite type” of that algebra. Primary, faithful states of finite type with arbitrary coupling are constructed and classified. Their physical significance for quantum thermodynamical systems at high temperatures is discussed. The scope of this study is broadened to include a large class of operator algebras sharing some of the structural properties of the fermion algebra.

Using three-dimensional microfluidic networks for solving computationally hard problems

This paper describes the design of a parallel algorithm that uses moving fluids in a three-dimensional microfluidic system to solve a nondeterministically polynomial complete problem (the maximal clique problem) in polynomial time. This algorithm relies on (i) parallel fabrication of the microfluidic system, (ii) parallel searching of all potential solutions by using fluid flow, and (iii) parallel optical readout of all solutions. This algorithm was implemented to solve the maximal clique problem for a simple graph with six vertices. The successful implementation of this algorithm to compute solutions for small-size graphs with fluids in microchannels is not useful, per se, but does suggest broader application for microfluidics in computation and control.

Prediction of protein deamidation rates from primary and three-dimensional structure

A method for the quantitative estimation of instability with respect to deamidation of the asparaginyl (Asn) residues in proteins is described. The procedure involves the observation of several simple aspects of the three-dimensional environment of each Asn residue in the protein and a calculation that includes these observations, the primary amino acid residue sequence, and the previously reported complete set of sequence-dependent rates of deamidation for Asn pentapeptides. This method is demonstrated and evaluated for 23 proteins in which 31 unstable and 167 stable Asn residues have been reported and for 7 unstable and 63 stable Asn residues that have been reported in 61 human hemoglobin variants. The relative importance of primary structure and three-dimensional structure in Asn deamidation is estimated.

The operator algebra approach to quantum groups

A relatively simple definition of a locally compact quantum group in the C*-algebra setting will be explained as it was recently obtained by the authors. At the same time, we put this definition in the historical and mathematical context of locally compact groups, compact quantum groups, Kac algebras, multiplicative unitaries, and duality theory.

The three-dimensional structure of NAD(P)H:quinone reductase, a flavoprotein involved in cancer chemoprotection and chemotherapy: mechanism of the two-electron reduction.

Quinone reductase [NAD(P)H:(quinone acceptor) oxidoreductase, EC 1.6.99.2], also called DT diaphorase, is a homodimeric FAD-containing enzyme that catalyzes obligatory NAD(P)H-dependent two-electron reductions of quinones and protects cells against the toxic and neoplastic effects of free radicals and reactive oxygen species arising from one-electron reductions. These two-electron reductions participate in the reductive bioactivation of cancer chemotherapeutic agents such as mitomycin C in tumor cells. Thus, surprisingly, the same enzymatic reaction that protects normal cells activates cytotoxic drugs used in cancer chemotherapy. The 2.1-A crystal structure of rat liver quinone reductase reveals that the folding of a portion of each monomer is similar to that of flavodoxin, a bacterial FMN-containing protein. Two additional portions of the polypeptide chains are involved in dimerization and in formation of the two identical catalytic sites to which both monomers contribute. The crystallographic structures of two FAD-containing enzyme complexes (one containing NADP+, the other containing duroquinone) suggest that direct hydride transfers from NAD(P)H to FAD and from FADH2 to the quinone [which occupies the site vacated by NAD(P)H] provide a simple rationale for the obligatory two-electron reductions involving a ping-pong mechanism.

Three-dimensional scroll waves of cAMP could direct cell movement and gene expression in Dictyostelium slugs.

Complex three-dimensional waves of excitation can explain the observed cell movement pattern in Dictyostelium slugs. Here we show that these three-dimensional waves can be produced by a realistic model for the cAMP relay system [Martiel, J. L. & Goldbeter, A. (1987) Biophys J. 52, 807-828]. The conversion of scroll waves in the prestalk zone of the slug into planar wave fronts in the prespore zone can result from a smaller fraction of relaying cells in the prespore zone. Further, we show that the cAMP concentrations to which cells in a slug are exposed over time display a simple pattern, despite the complex spatial geometry of the waves. This cAMP distribution agrees well with observed patterns of cAMP-regulated cell type-specific gene expression. The core of the spiral, which is a region of low cAMP concentration, might direct expression of stalk-specific genes during culmination.

Sample-to-sample fluctuations of the overlap distributions in the three-dimensional Edwards-Anderson spin glass

We study the sample-to-sample fluctuations of the overlap probability densities from large-scale equilibrium simulations of the three-dimensional Edwards-Anderson spin glass below the critical temperature. Ultrametricity, stochastic stability, and overlap equivalence impose constraints on the moments of the overlap probability densities that can be tested against numerical data. We found small deviations from the Ghirlanda Guerra predictions, which get smaller as system size increases. We also focus on the shape of the overlap distribution, comparing the numerical data to a mean-field-like prediction in which finite-size effects are taken into account by substituting delta functions with broad peaks.

Finite-size scaling analysis of the distributions of pseudo-critical temperatures in spin glasses

Using the results of large scale numerical simulations we study the probability distribution of the pseudo critical temperature for the three dimensional Edwards Anderson Ising spin glass and for the fully connected Sherrington-Kirkpatrick model. We find that the behaviour of our data is nicely described by straightforward finitesize scaling relations.

Microcanonical finite-size scaling in second-order phase transitions with diverging specific heat

A microcanonical finite-size ansatz in terms of quantities measurable in a finite lattice allows extending phenomenological renormalization the so-called quotients method to the microcanonical ensemble. The ansatz is tested numerically in two models where the canonical specific heat diverges at criticality, thus implying Fisher renormalization of the critical exponents: the three-dimensional ferromagnetic Ising model and the two-dimensional four-state Potts model (where large logarithmic corrections are known to occur in the canonical ensemble). A recently proposed microcanonical cluster method allows simulating systems as large as L = 1024 Potts or L= 128 (Ising). The quotients method provides accurate determinations of the anomalous dimension, η, and of the (Fisher-renormalized) thermal ν exponent. While in the Ising model the numerical agreement with our theoretical expectations is very good, in the Potts case, we need to carefully incorporate logarithmic corrections to the microcanonical ansatz in order to rationalize our data.

First-order transition in a three-dimensional disordered system

We present the first detailed numerical study in three dimensions of a first-order phase transition that remains first order in the presence of quenched disorder (specifically, the ferromagnetic-paramagnetic transition of the site-diluted four states Potts model). A tricritical point, which lies surprisingly near the pure-system limit and is studied by means of finite-size scaling, separates the first-order and second-order parts of the critical line. This investigation has been made possible by a new definition of the disorder average that avoids the diverging-variance probability distributions that plague the standard approach. Entropy, rather than free energy, is the basic object in this approach that exploits a recently introduced microcanonical Monte Carlo method.

Equações de quarta ordem na modelagem de oscilações de pontes

Equações diferenciais de quarta ordem aparecem naturalmente na modelagem de oscilações de estruturas elásticas, como aquelas observadas em pontes pênseis. São considerados dois modelos que descrevem as oscilações no tabuleiro de uma ponte. No modelo unidimensional estudamos blow up em espaço finito de soluções de uma classe de equações diferenciais de quarta ordem. Os resultados apresentados solucionam uma conjectura apresentada em [F. Gazzola and R. Pavani. Wide oscillation finite time blow up for solutions to nonlinear fourth order differential equations. Arch. Ration. Mech. Anal., 207(2):717752, 2013] e implicam a não existência de ondas viajantes com baixa velocidade de propagação em uma viga. No modelo bidimensional analisamos uma equação não local para uma placa longa e fina, suportada nas extremidades menores, livre nas demais e sujeita a protensão. Provamos existência e unicidade de solução fraca e estudamos o seu comportamento assintótico sob amortecimento viscoso. Estudamos ainda a estabilidade de modos simples de oscilação, os quais são classificados como longitudinais ou torcionais.

The Finite Embeddability Property for some noncommutative knotted varieties of RL and DRL.

Residuated lattices, although originally considered in the realm of algebra providing a general setting for studying ideals in ring theory, were later shown to form algebraic models for substructural logics. The latter are non-classical logics that include intuitionistic, relevance, many-valued, and linear logic, among others. Most of the important examples of substructural logics are obtained by adding structural rules to the basic logical calculus

Flexible ruthenium oxide-activated carbon cloth composites prepared by simple electrodeposition methods

This work focuses on the preparation of flexible ruthenium oxide containing activated carbon cloth by electrodeposition. Different electrodeposition methods have been used, including chronoamperometry, chronopotentiometry and cyclic voltammetry. The electrochemical properties of the obtained materials have been measured. The results show that the potentiostatic method allows preparing composites with higher specific capacitance than the pristine activated carbon cloth. The capacitance values measured by cyclic voltammetry at 10 mV s−1 and 1 V of potential window were up to 160 and 180 F g−1. This means an improvement of 82% and 100% with respect to the capacitance of the pristine activated carbon cloth. This excellent capacitance enhancement is attributed to the small particle size (4–5 nm) and the three-dimensional nanoporous network of the ruthenium oxide film which allows reaching very high degree of oxide utilization without blocking the pore structure of the activated carbon cloth. In addition, the electrodes maintain the mechanical properties of the carbon cloth and can be useful for flexible devices.

A simple method to predict elastic settlements in foundations resting on two soils of differing deformability

This paper shows the analysis results obtained from more than 200 finite element method (FEM) models used to calculate the settlement of a foundation resting on two soils of differing deformability. The analysis considers such different parameters as the foundation geometry, the percentage of each soil in contact with the foundation base and the ratio of the soils’ elastic moduli. From the described analysis, it is concluded that the maximum settlement of the foundation, calculated by assuming that the foundation is completely resting on the most deformable soil, can be correlated with the settlement calculated by FEM models through a correction coefficient named “settlement reduction factor” (α). As a consequence, a novel expression is proposed for calculating the real settlement of a foundation resting on two soils of different deformability with maximum errors lower than 1.57%, as demonstrated by the statistical analysis carried out. A guide for the application of the proposed simple method is also explained in the paper. Finally, the proposed methodology has been validated using settlement data from an instrumented foundation, indicating that this is a simple, reliable and quick method which allows the computation of the maximum elastic settlement of a raft foundation, evaluates its suitability and optimises its selection process.