General pairing interactions and pair truncation approximations for fermions in a single-j shell

We investigate Hamiltonians with attractive interactions between pairs of fermions coupled to angular momentum J. We show that pairs with spin J are reasonable building blocks for the low-lying states. For systems with only a J = Jmax pairing interaction, eigenvalues are found to be approximately integers for a large array of states, in particular for those with total angular momenta I le 2j. For I=0 eigenstates of four fermions in a single-j shell we show that there is only one non-zero eigenvalue. We address these observations using the nucleon pair approximation of the shell model and relate our results with a number of currently interesting problems.Comment: a latex text file and 2 figures, to be publishe

Many-body Systems Interacting via a Two-body Random Ensemble (I): Angular Momentum distribution in the ground states

In this paper, we discuss the angular momentum distribution in the ground states of many-body systems interacting via a two-body random ensemble. Beginning with a few simple examples, a simple approach to predict P(I)'s, angular momenta I ground state (g.s.) probabilities, of a few solvable cases, such as fermions in a small single-j shell and d boson systems, is given. This method is generalized to predict P(I)'s of more complicated cases, such as even or odd number of fermions in a large single-j shell or a many-j shell, d-boson, sd-boson or sdg-boson systems, etc. By this method we are able to tell which interactions are essential to produce a sizable P(I) in a many-body system. The g.s. probability of maximum angular momentum $I_{max}$ is discussed. An argument on the microscopic foundation of our approach, and certain matrix elements which are useful to understand the observed regularities, are also given or addressed in detail. The low seniority chain of 0 g.s. by using the same set of two-body interactions is confirmed but it is noted that contribution to the total 0 g.s. probability beyond this chain may be more important for even fermions in a single-j shell. Preliminary results by taking a displaced two-body random ensemble are presented for the I g.s. probabilities.Comment: 39 pages and 8 figure

Contraction of cross-linked actomyosin bundles

Cross-linked actomyosin bundles retract when severed in vivo by laser ablation, or when isolated from the cell and micromanipulated in vitro in the presence of ATP. We identify the time scale for contraction as a viscoelastic time tau, where the viscosity is due to (internal) protein friction. We obtain an estimate of the order of magnitude of the contraction time tau ~ 10-100 s, consistent with available experimental data for circumferential microfilament bundles and stress fibers. Our results are supported by an exactly solvable, hydrodynamic model of a retracting bundle as a cylinder of isotropic, active matter, from which the order of magnitude of the active stress is estimated.Comment: To be published in Physical Biolog

Classification of states of single-jj fermions with JJ-pairing interaction

In this paper we show that a system of three fermions is exactly solvable for the case of a single-$j$ in the presence of an angular momentum-$J$ pairing interaction. On the basis of the solutions for this system, we obtain new sum rules for six-$j$ symbols. It is also found that the "non-integer" eigenvalues of three fermions with angular momentum $I$ around the maximum appear as "non-integer" eigenvalues of four fermions when $I$ is around (or larger than) $J_{\rm max}$ and the Hamiltonian contains only an interaction between pairs of fermions coupled to spin $J=J_{\rm max}=2j-1$. This pattern is also found in five and six fermion systems. A boson system with spin $l$ exhibits a similar pattern.Comment: to be published in Physical Review

Spike-Train Responses of a Pair of Hodgkin-Huxley Neurons with Time-Delayed Couplings

Model calculations have been performed on the spike-train response of a pair of Hodgkin-Huxley (HH) neurons coupled by recurrent excitatory-excitatory couplings with time delay. The coupled, excitable HH neurons are assumed to receive the two kinds of spike-train inputs: the transient input consisting of $M$ impulses for the finite duration ($M$: integer) and the sequential input with the constant interspike interval (ISI). The distribution of the output ISI $T_{\rm o}$ shows a rich of variety depending on the coupling strength and the time delay. The comparison is made between the dependence of the output ISI for the transient inputs and that for the sequential inputs.Comment: 19 pages, 4 figure

101 Dothideomycetes genomes: A test case for predicting lifestyles and emergence of pathogens.

Dothideomycetes is the largest class of kingdom Fungi and comprises an incredible diversity of lifestyles, many of which have evolved multiple times. Plant pathogens represent a major ecological niche of the class Dothideomycetes and they are known to infect most major food crops and feedstocks for biomass and biofuel production. Studying the ecology and evolution of Dothideomycetes has significant implications for our fundamental understanding of fungal evolution, their adaptation to stress and host specificity, and practical implications with regard to the effects of climate change and on the food, feed, and livestock elements of the agro-economy. In this study, we present the first large-scale, whole-genome comparison of 101 Dothideomycetes introducing 55 newly sequenced species. The availability of whole-genome data produced a high-confidence phylogeny leading to reclassification of 25 organisms, provided a clearer picture of the relationships among the various families, and indicated that pathogenicity evolved multiple times within this class. We also identified gene family expansions and contractions across the Dothideomycetes phylogeny linked to ecological niches providing insights into genome evolution and adaptation across this group. Using machine-learning methods we classified fungi into lifestyle classes with >95 % accuracy and identified a small number of gene families that positively correlated with these distinctions. This can become a valuable tool for genome-based prediction of species lifestyle, especially for rarely seen and poorly studied species

Quantification of myocardial blood flow with 82Rb positron emission tomography: clinical validation with 15O-water

PURPOSE: Quantification of myocardial blood flow (MBF) with generator-produced (82)Rb is an attractive alternative for centres without an on-site cyclotron. Our aim was to validate (82)Rb-measured MBF in relation to that measured using (15)O-water, as a tracer 100% of which can be extracted from the circulation even at high flow rates, in healthy control subject and patients with mild coronary artery disease (CAD). METHODS: MBF was measured at rest and during adenosine-induced hyperaemia with (82)Rb and (15)O-water PET in 33 participants (22 control subjects, aged 30 ± 13 years; 11 CAD patients without transmural infarction, aged 60 ± 13 years). A one-tissue compartment (82)Rb model with ventricular spillover correction was used. The (82)Rb flow-dependent extraction rate was derived from (15)O-water measurements in a subset of 11 control subjects. Myocardial flow reserve (MFR) was defined as the hyperaemic/rest MBF. Pearson's correlation r, Bland-Altman 95% limits of agreement (LoA), and Lin's concordance correlation ρ (c) (measuring both precision and accuracy) were used. RESULTS: Over the entire MBF range (0.66-4.7 ml/min/g), concordance was excellent for MBF (r = 0.90, [(82)Rb-(15)O-water] mean difference ± SD = 0.04 ± 0.66 ml/min/g, LoA = -1.26 to 1.33 ml/min/g, ρ(c) = 0.88) and MFR (range 1.79-5.81, r = 0.83, mean difference = 0.14 ± 0.58, LoA = -0.99 to 1.28, ρ(c) = 0.82). Hyperaemic MBF was reduced in CAD patients compared with the subset of 11 control subjects (2.53 ± 0.74 vs. 3.62 ± 0.68 ml/min/g, p = 0.002, for (15)O-water; 2.53 ± 1.01 vs. 3.82 ± 1.21 ml/min/g, p = 0.013, for (82)Rb) and this was paralleled by a lower MFR (2.65 ± 0.62 vs. 3.79 ± 0.98, p = 0.004, for (15)O-water; 2.85 ± 0.91 vs. 3.88 ± 0.91, p = 0.012, for (82)Rb). Myocardial perfusion was homogeneous in 1,114 of 1,122 segments (99.3%) and there were no differences in MBF among the coronary artery territories (p > 0.31). CONCLUSION: Quantification of MBF with (82)Rb with a newly derived correction for the nonlinear extraction function was validated against MBF measured using (15)O-water in control subjects and patients with mild CAD, where it was found to be accurate at high flow rates. (82)Rb-derived MBF estimates seem robust for clinical research, advancing a step further towards its implementation in clinical routine

Effect of Trends on Detrended Fluctuation Analysis

Detrended fluctuation analysis (DFA) is a scaling analysis method used to estimate long-range power-law correlation exponents in noisy signals. Many noisy signals in real systems display trends, so that the scaling results obtained from the DFA method become difficult to analyze. We systematically study the effects of three types of trends -- linear, periodic, and power-law trends, and offer examples where these trends are likely to occur in real data. We compare the difference between the scaling results for artificially generated correlated noise and correlated noise with a trend, and study how trends lead to the appearance of crossovers in the scaling behavior. We find that crossovers result from the competition between the scaling of the noise and the ``apparent'' scaling of the trend. We study how the characteristics of these crossovers depend on (i) the slope of the linear trend; (ii) the amplitude and period of the periodic trend; (iii) the amplitude and power of the power-law trend and (iv) the length as well as the correlation properties of the noise. Surprisingly, we find that the crossovers in the scaling of noisy signals with trends also follow scaling laws -- i.e. long-range power-law dependence of the position of the crossover on the parameters of the trends. We show that the DFA result of noise with a trend can be exactly determined by the superposition of the separate results of the DFA on the noise and on the trend, assuming that the noise and the trend are not correlated. If this superposition rule is not followed, this is an indication that the noise and the superimposed trend are not independent, so that removing the trend could lead to changes in the correlation properties of the noise.Comment: 20 pages, 16 figure