Semiring and semimodule issues in MV-algebras

In this paper we propose a semiring-theoretic approach to MV-algebras based on the connection between such algebras and idempotent semirings - such an approach naturally imposing the introduction and study of a suitable corresponding class of semimodules, called MV-semimodules. We present several results addressed toward a semiring theory for MV-algebras. In particular we show a representation of MV-algebras as a subsemiring of the endomorphism semiring of a semilattice, the construction of the Grothendieck group of a semiring and its functorial nature, and the effect of Mundici categorical equivalence between MV-algebras and lattice-ordered Abelian groups with a distinguished strong order unit upon the relationship between MV-semimodules and semimodules over idempotent semifields.Comment: This version contains some corrections to some results at the end of Section

Surface layering of liquids: The role of surface tension

Recent measurements show that the free surfaces of liquid metals and alloys are always layered, regardless of composition and surface tension; a result supported by three decades of simulations and theory. Recent theoretical work claims, however, that at low enough temperatures the free surfaces of all liquids should become layered, unless preempted by bulk freezing. Using x-ray reflectivity and diffuse scattering measurements we show that there is no observable surface-induced layering in water at T=298 K, thus highlighting a fundamental difference between dielectric and metallic liquids. The implications of this result for the question in the title are discussed.Comment: 5 pages, 4 figures, to appear in Phys. Rev. B. 69 (2004

Hard-Sphere Fluids in Contact with Curved Substrates

The properties of a hard-sphere fluid in contact with hard spherical and cylindrical walls are studied. Rosenfeld's density functional theory (DFT) is applied to determine the density profile and surface tension $\gamma$ for wide ranges of radii of the curved walls and densities of the hard-sphere fluid. Particular attention is paid to investigate the curvature dependence and the possible existence of a contribution to $\gamma$ that is proportional to the logarithm of the radius of curvature. Moreover, by treating the curved wall as a second component at infinite dilution we provide an analytical expression for the surface tension of a hard-sphere fluid close to arbitrary hard convex walls. The agreement between the analytical expression and DFT is good. Our results show no signs for the existence of a logarithmic term in the curvature dependence of $\gamma$.Comment: 15 pages, 6 figure

Intrinsic activity in the fly brain gates visual information during behavioral choices

The small insect brain is often described as an input/output system that executes reflex-like behaviors. It can also initiate neural activity and behaviors intrinsically, seen as spontaneous behaviors, different arousal states and sleep. However, less is known about how intrinsic activity in neural circuits affects sensory information processing in the insect brain and variability in behavior. Here, by simultaneously monitoring Drosophila's behavioral choices and brain activity in a flight simulator system, we identify intrinsic activity that is associated with the act of selecting between visual stimuli. We recorded neural output (multiunit action potentials and local field potentials) in the left and right optic lobes of a tethered flying Drosophila, while its attempts to follow visual motion (yaw torque) were measured by a torque meter. We show that when facing competing motion stimuli on its left and right, Drosophila typically generate large torque responses that flip from side to side. The delayed onset (0.1-1 s) and spontaneous switch-like dynamics of these responses, and the fact that the flies sometimes oppose the stimuli by flying straight, make this behavior different from the classic steering reflexes. Drosophila, thus, seem to choose one stimulus at a time and attempt to rotate toward its direction. With this behavior, the neural output of the optic lobes alternates; being augmented on the side chosen for body rotation and suppressed on the opposite side, even though the visual input to the fly eyes stays the same. Thus, the flow of information from the fly eyes is gated intrinsically. Such modulation can be noise-induced or intentional; with one possibility being that the fly brain highlights chosen information while ignoring the irrelevant, similar to what we know to occur in higher animals

An Automated Paradigm for Drosophila Visual Psychophysics

Background: Mutations that cause learning and memory defects in Drosophila melanogaster have been found to also compromise visual responsiveness and attention. A better understanding of attention-like defects in such Drosophila mutants therefore requires a more detailed characterization of visual responsiveness across a range of visual parameters. Methodology/Principal Findings: We designed an automated behavioral paradigm for efficiently dissecting visual responsiveness in Drosophila. Populations of flies walk through multiplexed serial choice mazes while being exposed to moving visuals displayed on computer monitors, and infra-red fly counters at the end of each maze automatically score the responsiveness of a strain. To test our new design, we performed a detailed comparison between wild-type flies and a learning and memory mutant, dunce. We first confirmed that the learning mutant dunce displays increased responsiveness to a black/green moving grating compared to wild type in this new design. We then extended this result to explore responses to a wide range of psychophysical parameters for moving gratings (e.g., luminosity, contrast, spatial frequency, velocity) as well as to a different stimulus, moving dots. Finally, we combined these visuals (gratings versus dots) in competition to investigate how dunce and wild-type flies respond to more complex and conflicting motion effects. Conclusions/Significance: We found that dunce responds more strongly than wild type to high contrast and highly structured motion. This effect was found for simple gratings, dots, and combinations of both stimuli presented in competition

Global and local sea level during the Last Interglacial: A probabilistic assessment

The Last Interglacial (LIG) stage, with polar temperatures likely 3-5 C warmer than today, serves as a partial analogue for low-end future warming scenarios. Based upon a small set of local sea level indicators, the Intergovernmental Panel on Climate Change (IPCC) inferred that LIG global sea level (GSL) was about 4-6 m higher than today. However, because local sea levels differ from GSL, accurately reconstructing past GSL requires an integrated analysis of globally distributed data sets. Here we compile an extensive database of sea level indicators and apply a novel statistical approach that couples Gaussian process regression of sea level to Markov Chain Monte Carlo modeling of geochronological errors. Our analysis strongly supports the hypothesis that LIG GSL was higher than today, probably peaking at 6-9 m. Our results highlight the sea level hazard associated with even relatively low levels of sustained global warming.Comment: Preprint version of what has since been published in Natur

Oscillatory stimuli differentiate adapting circuit topologies

This is the author accepted manuscript. The final version is available from Springer Nature via the DOI in this record.Biology emerges from interactions between molecules, which are challenging to elucidate with current techniques. An orthogonal approach is to probe for 'response signatures' that identify specific circuit motifs. For example, bistability, hysteresis, or irreversibility are used to detect positive feedback loops. For adapting systems, such signatures are not known. Only two circuit motifs generate adaptation: negative feedback loops (NFLs) and incoherent feed-forward loops (IFFLs). On the basis of computational testing and mathematical proofs, we propose differential signatures: in response to oscillatory stimulation, NFLs but not IFFLs show refractory-period stabilization (robustness to changes in stimulus duration) or period skipping. Applying this approach to yeast, we identified the circuit dominating cell cycle timing. In Caenorhabditis elegans AWA neurons, which are crucial for chemotaxis, we uncovered a Ca2+ NFL leading to adaptation that would be difficult to find by other means. These response signatures allow direct access to the outlines of the wiring diagrams of adapting systems.The work was supported by US National Institutes of Health grant 5RO1-GM078153-07 (F.R.C.), NRSA Training Grant CA009673-36A1 (S.J.R.), a Merck Postdoctoral Fellowship at The Rockefeller University (S.J.R.), and the Simons Foundation (S.J.R.). J.L. was supported by a fellowship from the Boehringer Ingelheim Fonds. E.D.S. was partially supported by the US Office of Naval Research (ONR N00014-13-1-0074) and the US Air Force Office of Scientific Research (AFOSR FA9550-14-1-0060)