Critical Line in Random Threshold Networks with Inhomogeneous Thresholds

We calculate analytically the critical connectivity $K_c$ of Random Threshold Networks (RTN) for homogeneous and inhomogeneous thresholds, and confirm the results by numerical simulations. We find a super-linear increase of $K_c$ with the (average) absolute threshold $|h|$, which approaches $K_c(|h|) \sim h^2/(2\ln{|h|})$ for large $|h|$, and show that this asymptotic scaling is universal for RTN with Poissonian distributed connectivity and threshold distributions with a variance that grows slower than $h^2$. Interestingly, we find that inhomogeneous distribution of thresholds leads to increased propagation of perturbations for sparsely connected networks, while for densely connected networks damage is reduced; the cross-over point yields a novel, characteristic connectivity $K_d$, that has no counterpart in Boolean networks. Last, local correlations between node thresholds and in-degree are introduced. Here, numerical simulations show that even weak (anti-)correlations can lead to a transition from ordered to chaotic dynamics, and vice versa. It is shown that the naive mean-field assumption typical for the annealed approximation leads to false predictions in this case, since correlations between thresholds and out-degree that emerge as a side-effect strongly modify damage propagation behavior.Comment: 18 figures, 17 pages revte

Self-organization of heterogeneous topology and symmetry breaking in networks with adaptive thresholds and rewiring

We study an evolutionary algorithm that locally adapts thresholds and wiring in Random Threshold Networks, based on measurements of a dynamical order parameter. A control parameter $p$ determines the probability of threshold adaptations vs. link rewiring. For any $p < 1$, we find spontaneous symmetry breaking into a new class of self-organized networks, characterized by a much higher average connectivity $\bar{K}_{evo}$ than networks without threshold adaptation ($p =1$). While $\bar{K}_{evo}$ and evolved out-degree distributions are independent from $p$ for $p <1$, in-degree distributions become broader when $p \to 1$, approaching a power-law. In this limit, time scale separation between threshold adaptions and rewiring also leads to strong correlations between thresholds and in-degree. Finally, evidence is presented that networks converge to self-organized criticality for large $N$.Comment: 4 pages revtex, 6 figure

Damage Spreading and Criticality in Finite Random Dynamical Networks

We systematically study and compare damage spreading at the sparse percolation (SP) limit for random boolean and threshold networks with perturbations that are independent of the network size $N$. This limit is relevant to information and damage propagation in many technological and natural networks. Using finite size scaling, we identify a new characteristic connectivity $K_s$, at which the average number of damaged nodes $\bar d$, after a large number of dynamical updates, is independent of $N$. Based on marginal damage spreading, we determine the critical connectivity $K_c^{sparse}(N)$ for finite $N$ at the SP limit and show that it systematically deviates from $K_c$, established by the annealed approximation, even for large system sizes. Our findings can potentially explain the results recently obtained for gene regulatory networks and have important implications for the evolution of dynamical networks that solve specific computational or functional tasks.Comment: 4 pages, 4 eps figure

Are geometric morphometric analyses replicable? Evaluating landmark measurement error and its impact on extant and fossil Microtus classification.

Geometric morphometric analyses are frequently employed to quantify biological shape and shape variation. Despite the popularity of this technique, quantification of measurement error in geometric morphometric datasets and its impact on statistical results is seldom assessed in the literature. Here, we evaluate error on 2D landmark coordinate configurations of the lower first molar of five North American Microtus (vole) species. We acquired data from the same specimens several times to quantify error from four data acquisition sources: specimen presentation, imaging devices, interobserver variation, and intraobserver variation. We then evaluated the impact of those errors on linear discriminant analysis-based classifications of the five species using recent specimens of known species affinity and fossil specimens of unknown species affinity. Results indicate that data acquisition error can be substantial, sometimes explaining &gt;30% of the total variation among datasets. Comparisons of datasets digitized by different individuals exhibit the greatest discrepancies in landmark precision, and comparison of datasets photographed from different presentation angles yields the greatest discrepancies in species classification results. All error sources impact statistical classification to some extent. For example, no two landmark dataset replicates exhibit the same predicted group memberships of recent or fossil specimens. Our findings emphasize the need to mitigate error as much as possible during geometric morphometric data collection. Though the impact of measurement error on statistical fidelity is likely analysis-specific, we recommend that all geometric morphometric studies standardize specimen imaging equipment, specimen presentations (if analyses are 2D), and landmark digitizers to reduce error and subsequent analytical misinterpretations

Allometric trajectories of body and head morphology in three sympatric Arctic charr (Salvelinus alpinus (L.)) morphs

A study of body and head development in three sympatric reproductively isolated Arctic charr (Salvelinus alpinus (L.)) morphs from a subarctic lake (Skogsfjordvatn, northern Norway) revealed allometric trajectories that resulted in morphological differences. The three morphs were ecologically assigned to a littoral omnivore, a profundal benthivore and a profundal piscivore, and this was confirmed by genetic analyses (microsatellites). Principal component analysis was used to identify the variables responsible for most of the morphological variation of the body and head shape. The littoral omnivore and the profundal piscivore morph had convergent allometric trajectories for the most important head shape variables, developing bigger mouths and relatively smaller eyes with increasing head size. The two profundal morphs shared common trajectories for the variables explaining most of the body and head shape variation, namely head size relative to body size, placement of the dorsal and pelvic fins, eye size and mouth size. In contrast, the littoral omnivore and the profundal benthivore morphs were not on common allometric trajectories for any of the examined variables. The findings suggest that different selective pressures could have been working on traits related to their trophic niche such as habitat and diet utilization of the three morphs, with the two profundal morphs experiencing almost identical environmental conditions

Radiation Damage Studies of Silicon Photomultipliers

We report on the measurement of the radiation hardness of silicon photomultipliers (SiPMs) manufactured by Fondazione Bruno Kessler in Italy (1 mm$^2$ and 6.2 mm$^2$), Center of Perspective Technology and Apparatus in Russia (1 mm$^2$ and 4.4 mm$^2$), and Hamamatsu Corporation in Japan (1 mm$^2$). The SiPMs were irradiated using a beam of 212 MeV protons at Massachusetts General Hospital, receiving fluences of up to $3 \times 10^{10}$ protons per cm$^2$ with the SiPMs at operating voltage. Leakage currents were read continuously during the irradiation. The delivery of the protons was paused periodically to record scope traces in response to calibrated light pulses to monitor the gains, photon detection efficiencies, and dark counts of the SiPMs. The leakage current and dark noise are found to increase with fluence. Te leakage current is found to be proportional to the mean square deviation of the noise distribution, indicating the dark counts are due to increased random individual pixel activation, while SiPMs remain fully functional as photon detectors. The SiPMs are found to anneal at room temperature with a reduction in the leakage current by a factor of 2 in about 100 days.Comment: 35 pages, 25 figure

Jets Produced in π^-, π^+, and Proton Interactions at 200 GeV on Hydrogen and Aluminum Targets

This paper presents results from an experiment on the production of jets (groups of particles) with high p_⊥ produced in 200-GeV/c interactions. Results are presented on the comparison of jet cross sections on aluminum and hydrogen targets. The jet fragmentation distributions are also examined. Both the cross section and the jet structure are found to depend strongly on the beam and target types

Measurement of Forward Jets Produced in High-Transverse-Momentum Hadron-Proton Collisions

A measurement of charged-particle production is reported for the forward region in events triggered by high-transverse-momentum (p⊥) jets and single particles. The momentum distributions of forward-going particles are observed to scale in a simple p⊥-dependent longitudinal variable. Forward-going (beam) jets are observed to be tilted away from the original direction by an amount which agrees with muon-pair data when interpreted in a parton (quantum-chromodynamics) model