On-line learning of non-monotonic rules by simple perceptron

We study the generalization ability of a simple perceptron which learns unlearnable rules. The rules are presented by a teacher perceptron with a non-monotonic transfer function. The student is trained in the on-line mode. The asymptotic behaviour of the generalization error is estimated under various conditions. Several learning strategies are proposed and improved to obtain the theoretical lower bound of the generalization error.Comment: LaTeX 20 pages using IOP LaTeX preprint style file, 14 figure

Fractal Spin Glass Properties of Low Energy Configurations in the Frenkel-Kontorova chain

We study numerically and analytically the classical one-dimensional Frenkel-Kontorova chain in the regime of pinned phase characterized by phonon gap. Our results show the existence of exponentially many static equilibrium configurations which are exponentially close to the energy of the ground state. The energies of these configurations form a fractal quasi-degenerate band structure which is described on the basis of elementary excitations. Contrary to the ground state, the configurations inside these bands are disordered.Comment: revtex, 9 pages, 9 figure

Laser induced breakdown of the magnetic field reversal symmetry in the propagation of unpolarized light

We show how a medium, under the influece of a coherent control field which is resonant or close to resonance to an appropriate atomic transition, can lead to very strong asymmetries in the propagation of unpolarized light when the direction of the magnetic field is reversed. We show how EIT can be used to mimic effects occuring in natural systems and that EIT can produce very large asymmetries as we use electric dipole allowed transitions. Using density matrix calculations we present results for the breakdown of the magnetic field reversal symmetry for two different atomic configurations.Comment: RevTex, 6 pages, 10 figures, Two Column format, submitted to Phys. Rev.

A new glance at the chemosphere of macroalgal–bacterial interactions: In situ profiling of metabolites in symbiosis by mass spectrometry

Symbiosis is a dominant form of life that has been observed numerous times in marine ecosystems. For example, macroalgae coexist with bacteria that produce factors that promote algal growth and morphogenesis. The green macroalga Ulva mutabilis (Chlorophyta) develops into a callus-like phenotype in the absence of its essential bacterial symbionts Roseovarius sp. MS2 and Maribacter sp. MS6. Spatially resolved studies are required to understand symbiont interactions at the microscale level. Therefore, we used mass spectrometry profiling and imaging techniques with high spatial resolution and sensitivity to gain a new perspective on the mutualistic interactions between bacteria and macroalgae. Using atmospheric pressure scanning microprobe matrix-assisted laser desorption/ionisation high-resolution mass spectrometry (AP-SMALDI-HRMS), low-molecular-weight polar compounds were identified by comparative metabolomics in the chemosphere of Ulva. Choline (2-hydroxy-N,N,N-trimethylethan-1-aminium) was only determined in the alga grown under axenic conditions, whereas ectoine (1,4,5,6-tetrahydro-2-methyl-4-pyrimidinecarboxylic acid) was found in bacterial presence. Ectoine was used as a metabolic marker for localisation studies of Roseovarius sp. within the tripartite community because it was produced exclusively by these bacteria. By combining confocal laser scanning microscopy (cLSM) and AP-SMALDI-HRMS, we proved that Roseovarius sp. MS2 settled mainly in the rhizoidal zone (holdfast) of U. mutabilis. Our findings provide the fundament to decipher bacterial symbioses with multicellular hosts in aquatic ecosystems in an ecologically relevant context. As a versatile tool for microbiome research, the combined AP-SMALDI and cLSM imaging analysis with a resolution to level of a single bacterial cell can be easily applied to other microbial consortia and their hosts. The novelty of this contribution is the use of an in situ setup designed to avoid all types of external contamination and interferences while resolving spatial distributions of metabolites and identifying specific symbiotic bacteria

Circumbinary disk evolution in the presence of an outer companion star

We consider a hierarchical triple system consisting of an inner eccentric binary with an outer companion. A highly misaligned circumbinary disk around the inner binary is subject to two competing effects: (i) nodal precession about the inner binary eccentricity vector that leads to an increase in misalignment (polar alignment) and (ii) Kozai-Lidov (KL) oscillations of eccentricity and inclination driven by the outer companion that leads to a reduction in the misalignment. The outcome depends upon the ratio of the timescales of these effects. If the inner binary torque dominates, then the disk aligns to a polar orientation. If the outer companion torque dominates, then the disk undergoes KL oscillations. In that case, the highly eccentric and misaligned disk is disrupted and accreted by the inner binary, while some mass is transferred to the outer companion. However, when the torques are similar, the outer parts of the circumbinary disk can undergo large eccentricity oscillations while the inclination remains close to the polar orientation. The range of initial disk inclinations that evolve to a polar orientation is smaller in the presence of the outer companion. Disk breaking is also more likely, at least temporarily, during the polar alignment process. The stellar orbits in HD 98800 have parameters such that polar alignment of the circumbinary disk is expected. In the absence of the gas, solid particles are unstable at much smaller radii than the gas disk inner tidal truncation radius because KL driven eccentricity leads to close encounters with the binary.Comment: Accepted for publication in ApJ

A two step algorithm for learning from unspecific reinforcement

We study a simple learning model based on the Hebb rule to cope with "delayed", unspecific reinforcement. In spite of the unspecific nature of the information-feedback, convergence to asymptotically perfect generalization is observed, with a rate depending, however, in a non- universal way on learning parameters. Asymptotic convergence can be as fast as that of Hebbian learning, but may be slower. Moreover, for a certain range of parameter settings, it depends on initial conditions whether the system can reach the regime of asymptotically perfect generalization, or rather approaches a stationary state of poor generalization.Comment: 13 pages LaTeX, 4 figures, note on biologically motivated stochastic variant of the algorithm adde