The radiating part of circular sources

An analysis is developed linking the form of the sound field from a circular source to the radial structure of the source, without recourse to far-field or other approximations. It is found that the information radiated into the field is limited, with the limit fixed by the wavenumber of source multiplied by the source radius (Helmholtz number). The acoustic field is found in terms of the elementary fields generated by a set of line sources whose form is given by Chebyshev polynomials of the second kind, and whose amplitude is found to be given by weighted integrals of the radial source term. The analysis is developed for tonal sources, such as rotors, and, for Helmholtz number less than two, for random disk sources. In this case, the analysis yields the cross-spectrum between two points in the acoustic field. The analysis is applied to the problems of tonal radiation, random source radiation as a model problem for jet noise, and to noise cancellation, as in active control of noise from rotors. It is found that the approach gives an accurate model for the radiation problem and explicitly identifies those parts of a source which radiate.Comment: Submitted to Journal of the Acoustical Society of Americ

Equilibrium properties of realistic random heteropolymers and their relevance for globular and naturally unfolded proteins

Random heteropolymers do not display the typical equilibrium properties of globular proteins, but are the starting point to understand the physics of proteins and, in particular, to describe their non-native states. So far, they have been studied only with mean-field models in the thermodynamic limit, or with computer simulations of very small chains on lattice. After describing a self-adjusting parallel-tempering technique to sample efficiently the low-energy states of frustrated systems without the need of tuning the system-dependent parameters of the algorithm, we apply it to random heteropolymers moving in continuous space. We show that if the mean interaction between monomers is negative, the usual description through the random energy model is nearly correct, provided that it is extended to account for non-compact conformations. If the mean interaction is positive, such a simple description breaks out and the system behaves in a way more similar to Ising spin glasses. The former case is a model for the denatured state of glob- ular proteins, the latter of naturally-unfolded proteins, whose equilibrium properties thus result qualitatively different

Deviations from the mean field predictions for the phase behaviour of random copolymers melts

We investigate the phase behaviour of random copolymers melts via large scale Monte Carlo simulations. We observe macrophase separation into A and B--rich phases as predicted by mean field theory only for systems with a very large correlation lambda of blocks along the polymer chains, far away from the Lifshitz point. For smaller values of lambda, we find that a locally segregated, disordered microemulsion--like structure gradually forms as the temperature decreases. As we increase the number of blocks in the polymers, the region of macrophase separation further shrinks. The results of our Monte Carlo simulation are in agreement with a Ginzburg criterium, which suggests that mean field theory becomes worse as the number of blocks in polymers increases.Comment: 6 pages, 4 figures, Late

Optimal General Matchings

Given a graph $G=(V,E)$ and for each vertex $v \in V$ a subset $B(v)$ of the set $\{0,1,\ldots, d_G(v)\}$, where $d_G(v)$ denotes the degree of vertex $v$ in the graph $G$, a $B$-factor of $G$ is any set $F \subseteq E$ such that $d_F(v) \in B(v)$ for each vertex $v$, where $d_F(v)$ denotes the number of edges of $F$ incident to $v$. The general factor problem asks the existence of a $B$-factor in a given graph. A set $B(v)$ is said to have a {\em gap of length} $p$ if there exists a natural number $k \in B(v)$ such that $k+1, \ldots, k+p \notin B(v)$ and $k+p+1 \in B(v)$. Without any restrictions the general factor problem is NP-complete. However, if no set $B(v)$ contains a gap of length greater than $1$, then the problem can be solved in polynomial time and Cornuejols \cite{Cor} presented an algorithm for finding a $B$-factor, if it exists. In this paper we consider a weighted version of the general factor problem, in which each edge has a nonnegative weight and we are interested in finding a $B$-factor of maximum (or minimum) weight. In particular, this version comprises the minimum/maximum cardinality variant of the general factor problem, where we want to find a $B$-factor having a minimum/maximum number of edges. We present an algorithm for the maximum/minimum weight $B$-factor for the case when no set $B(v)$ contains a gap of length greater than $1$. This also yields the first polynomial time algorithm for the maximum/minimum cardinality $B$-factor for this case

An Analytical Approach to the Protein Designability Problem

We present an analytical method for determining the designability of protein structures. We apply our method to the case of two-dimensional lattice structures, and give a systematic solution for the spectrum of any structure. Using this spectrum, the designability of a structure can be estimated. We outline a heirarchy of structures, from most to least designable, and show that this heirarchy depends on the potential that is used.Comment: 16 pages 4 figure

A classification of locally semicomplete digraphs

Recently, Huang (1995) gave a characterization of local tournaments. His characterization involves arc-reversals and therefore may not be easily used to solve other structural problems on locally semicomplete digraphs (where one deals with a fixed locally semicomplete digraph). In this paper we derive a classification of locally semicomplete digraphs which is very useful for studying structural properties of locally semicomplete digraphs and which does not depend on Huang's characterization. An advantage of this new classification of locally semicomplete digraphs is that it allows one to prove results for locally semicomplete digraphs without reproving the same statement for tournaments. We use our result to characterize pancyclic and vertex pancyclic locally semicomplete digraphs and to show the existence of a polynomial algorithm to decide whether a given locally semicomplete digraph has a kernel

Nucleation phenomena in protein folding: The modulating role of protein sequence

For the vast majority of naturally occurring, small, single domain proteins folding is often described as a two-state process that lacks detectable intermediates. This observation has often been rationalized on the basis of a nucleation mechanism for protein folding whose basic premise is the idea that after completion of a specific set of contacts forming the so-called folding nucleus the native state is achieved promptly. Here we propose a methodology to identify folding nuclei in small lattice polymers and apply it to the study of protein molecules with chain length N=48. To investigate the extent to which protein topology is a robust determinant of the nucleation mechanism we compare the nucleation scenario of a native-centric model with that of a sequence specific model sharing the same native fold. To evaluate the impact of the sequence's finner details in the nucleation mechanism we consider the folding of two non- homologous sequences. We conclude that in a sequence-specific model the folding nucleus is, to some extent, formed by the most stable contacts in the protein and that the less stable linkages in the folding nucleus are solely determined by the fold's topology. We have also found that independently of protein sequence the folding nucleus performs the same `topological' function. This unifying feature of the nucleation mechanism results from the residues forming the folding nucleus being distributed along the protein chain in a similar and well-defined manner that is determined by the fold's topological features.Comment: 10 Figures. J. Physics: Condensed Matter (to appear

Time series irreversibility: a visibility graph approach

We propose a method to measure real-valued time series irreversibility which combines two differ- ent tools: the horizontal visibility algorithm and the Kullback-Leibler divergence. This method maps a time series to a directed network according to a geometric criterion. The degree of irreversibility of the series is then estimated by the Kullback-Leibler divergence (i.e. the distinguishability) between the in and out degree distributions of the associated graph. The method is computationally effi- cient, does not require any ad hoc symbolization process, and naturally takes into account multiple scales. We find that the method correctly distinguishes between reversible and irreversible station- ary time series, including analytical and numerical studies of its performance for: (i) reversible stochastic processes (uncorrelated and Gaussian linearly correlated), (ii) irreversible stochastic pro- cesses (a discrete flashing ratchet in an asymmetric potential), (iii) reversible (conservative) and irreversible (dissipative) chaotic maps, and (iv) dissipative chaotic maps in the presence of noise. Two alternative graph functionals, the degree and the degree-degree distributions, can be used as the Kullback-Leibler divergence argument. The former is simpler and more intuitive and can be used as a benchmark, but in the case of an irreversible process with null net current, the degree-degree distribution has to be considered to identifiy the irreversible nature of the series.Comment: submitted for publicatio

Cardiorespiratory fitness is associated with hard and light intensity physical activity but not time spent sedentary in 10–14 year old schoolchildren: the HAPPY study

Sedentary behaviour is a major risk factor for developing chronic diseases and is associated with low cardiorespiratory fitness in adults. It remains unclear how sedentary behaviour and different physical activity subcomponents are related to cardiorespiratory fitness in children. The purpose of this study was to assess how sedentary behaviour and different physical activity subcomponents are associated with 10–14 year-old schoolchildren's cardiorespiratory fitness

Macrophage Ontogeny Underlies Differences in Tumor-Specific Education in Brain Malignancies.

Extensive transcriptional and ontogenetic diversity exists among normal tissue-resident macrophages, with unique transcriptional profiles endowing the cells with tissue-specific functions. However, it is unknown whether the origins of different macrophage populations affect their roles in malignancy. Given potential artifacts associated with irradiation-based lineage tracing, it remains unclear if bone-marrow-derived macrophages (BMDMs) are present in tumors of the brain, a tissue with no homeostatic involvement of BMDMs. Here, we employed multiple models of murine brain malignancy and genetic lineage tracing to demonstrate that BMDMs are abundant in primary and metastatic brain tumors. Our data indicate that distinct transcriptional networks in brain-resident microglia and recruited BMDMs are associated with tumor-mediated education yet are also influenced by chromatin landscapes established before tumor initiation. Furthermore, we demonstrate that microglia specifically repress Itga4 (CD49D), enabling its utility as a discriminatory marker between microglia and BMDMs in primary and metastatic disease in mouse and human