How training and testing histories affect generalization: a test of simple neural networks

We show that a simple network model of associative learning can\ud reproduce three findings that arise from particular training and\ud testing procedures in generalization experiments: the effect of 1)\ud ``errorless learning'' and 2) extinction testing on peak shift, and\ud 3) the central tendency effect. These findings provide a true test\ud of the network model, which was developed to account for other\ud penhomena, and highlight the potential of neural networks to study\ud phenomena that depend on sequences of experiences with many stimuli.\ud Our results suggest that at least some such phenomena, e.g.,\ud stimulus range effects, may derive from basic mechanisms of\ud associative memory rather than from more complex memory processes

Branching principles of animal and plant networks identified by combining extensive data, machine learning, and modeling

Branching in vascular networks and in overall organismic form is one of the most common and ancient features of multicellular plants, fungi, and animals. By combining machine-learning techniques with new theory that relates vascular form to metabolic function, we enable novel classification of diverse branching networks--mouse lung, human head and torso, angiosperm and gymnosperm plants. We find that ratios of limb radii--which dictate essential biologic functions related to resource transport and supply--are best at distinguishing branching networks. We also show how variation in vascular and branching geometry persists despite observing a convergent relationship across organisms for how metabolic rate depends on body mass.Comment: 55 pages, 8 figures, 8 table

Leonardo's rule, self-similarity and wind-induced stresses in trees

Examining botanical trees, Leonardo da Vinci noted that the total cross-section of branches is conserved across branching nodes. In this Letter, it is proposed that this rule is a consequence of the tree skeleton having a self-similar structure and the branch diameters being adjusted to resist wind-induced loads

Signature of relic heavy stable neutrinos in underground experiments

Considering heavy stable neutrinos of 4th generation we calculate the relic density of such neutrinos in the Universe. Taking into account the condensation of heavy neutrinos in the Galaxy and applying the results of calculations to experimental data from underground experiments on search for WIMPs in elastic neutral current scattering on nuclei we found an exclusion region of neutrino mass 60 GeV < m < 290 GeV. The bounds obtained from present underground experiments while confirming the previous bounds derived from analysis of cosmic ray spectra are more relible ones. We discuss also the first indication of elastic scattering induced by WIMP in DAMA experiment finding a very narrow window of neutrino mass 45 GeV < m < 50 GeV compatible with the possible signal rate in the detector.Comment: 12 pages, 3 figure

Lepton Flavor Violation and the Tau Neutrino Mass

We point out that, in the left-right symmetric model of weak interaction, if $\nu_\tau$ mass is in the keV to MeV range, there is a strong correlation between rare decays such as $\tau \rightarrow 3 \mu, \tau \rightarrow 3 e$ and the $\nu_\tau$ mass. In particular, we point out that a large range of $\nu_\tau$ masses are forbidden by the cosmological constraints on $m_{\nu_\tau}$ in combination with the present upper limits on these processes.Comment: UMDHEP 94-30, 14 pages, TeX file, (some new references added

Ward-Takahashi Identity with External Field in Ladder QED

We derive the Ward-Takahashi identity obeyed by the fermion-antifermion-gauge boson vertex in ladder QED in the presence of a constant magnetic field. The general structure in momentum space of the fermion mass operator with external electromagnetic field is discussed. Using it we find the solutions of the ladder WT identity with magnetic field. The consistency of our results with the solutions of the corresponding Schwinger-Dyson equation ensures the gauge invariance of the magnetic field induced chiral symmetry breaking recently found in ladder QED.Comment: new references(refs.10,11) added, 18 pages, Late

Statistical mechanics of complex networks

Complex networks describe a wide range of systems in nature and society, much quoted examples including the cell, a network of chemicals linked by chemical reactions, or the Internet, a network of routers and computers connected by physical links. While traditionally these systems were modeled as random graphs, it is increasingly recognized that the topology and evolution of real networks is governed by robust organizing principles. Here we review the recent advances in the field of complex networks, focusing on the statistical mechanics of network topology and dynamics. After reviewing the empirical data that motivated the recent interest in networks, we discuss the main models and analytical tools, covering random graphs, small-world and scale-free networks, as well as the interplay between topology and the network's robustness against failures and attacks.Comment: 54 pages, submitted to Reviews of Modern Physic

Biogeographic patterns of soil diazotrophic communities across six forests in North America.

Soil diazotrophs play important roles in ecosystem functioning by converting atmospheric N2 into biologically available ammonium. However, the diversity and distribution of soil diazotrophic communities in different forests and whether they follow biogeographic patterns similar to macroorganisms still remain unclear. By sequencing nifH gene amplicons, we surveyed the diversity, structure and biogeographic patterns of soil diazotrophic communities across six North American forests (126 nested samples). Our results showed that each forest harboured markedly different soil diazotrophic communities and that these communities followed traditional biogeographic patterns similar to plant and animal communities, including the taxa-area relationship (TAR) and latitudinal diversity gradient. Significantly higher community diversity and lower microbial spatial turnover rates (i.e. z-values) were found for rainforests (~0.06) than temperate forests (~0.1). The gradient pattern of TARs and community diversity was strongly correlated (r(2) &nbsp;&gt;&nbsp;0.5) with latitude, annual mean temperature, plant species richness and precipitation, and weakly correlated (r(2) &nbsp;&lt;&nbsp;0.25) with pH and soil moisture. This study suggests that even microbial subcommunities (e.g. soil diazotrophs) follow general biogeographic patterns (e.g. TAR, latitudinal diversity gradient), and indicates that the metabolic theory of ecology and habitat heterogeneity may be the major underlying ecological mechanisms shaping the biogeographic patterns of soil diazotrophic communities