Three Hopf algebras from number theory, physics & topology, and their common background II: general categorical formulation

We consider three a priori totally different setups for Hopf algebras from number theory, mathematical physics and algebraic topology. These are the Hopf algebra of Goncharov for multiple zeta values, that of Connes-Kreimer for renormalization, and a Hopf algebra constructed by Baues to study double loop spaces. We show that these examples can be successively unified by considering simplicial objects, co-operads with multiplication and Feynman categories at the ultimate level. These considerations open the door to new constructions and reinterpretations of known constructions in a large common framework which is presented step-by-step with examples throughout. In this second part of two papers, we give the general categorical formulation

A Statistical Evaluation of Atmosphere-Ocean General Circulation Models: Complexity vs. Simplicity

The principal tools used to model future climate change are General Circulation Models which are deterministic high resolution bottom-up models of the global atmosphere-ocean system that require large amounts of supercomputer time to generate results. But are these models a cost-effective way of predicting future climate change at the global level? In this paper we use modern econometric techniques to evaluate the statistical adequacy of three general circulation models (GCMs) by testing three aspects of a GCM's ability to reconstruct the historical record for global surface temperature: (1) how well the GCMs track observed temperature; (2) are the residuals from GCM simulations random (white noise) or are they systematic (red noise or a stochastic trend); (3) what is the explanatory power of the GCMs compared to a simple alternative time series model, which assumes that temperature is a linear function of radiative forcing. The results indicate that three of the eight experiments considered fail to reconstruct temperature accurately; the GCM errors are either red noise processes or contain a systematic error, and the radiative forcing variable used to simulate the GCM's have considerable explanatory power relative to GCM simulations of global temperature. The GFDL model is superior to the other models considered. Three out of four Hadley Centre experiments also pass all the tests but show a poorer goodness of fit. The Max Planck model appears to perform poorly relative to the other two models. It does appear that there is a trade-off between the greater spatial detail and number of variables provided by the GCMs and more accurate predictions generated by simple time series models. This is similar to the debate in economics regarding the forecasting accuracy of large macro-economic models versus simple time series models.

Moduli space actions on the Hochschild Co-Chains of a Frobenius algebra I: Cell Operads

This is the first of two papers in which we prove that a cell model of the moduli space of curves with marked points and tangent vectors at the marked points acts on the Hochschild co--chains of a Frobenius algebra. We also prove that a there is dg--PROP action of a version of Sullivan Chord diagrams which acts on the normalized Hochschild co-chains of a Frobenius algebra. These actions lift to operadic correlation functions on the co--cycles. In particular, the PROP action gives an action on the homology of a loop space of a compact simply--connected manifold. In this first part, we set up the topological operads/PROPs and their cell models. The main theorems of this part are that there is a cell model operad for the moduli space of genus $g$ curves with $n$ punctures and a tangent vector at each of these punctures and that there exists a CW complex whose chains are isomorphic to a certain type of Sullivan Chord diagrams and that they form a PROP. Furthermore there exist weak versions of these structures on the topological level which all lie inside an all encompassing cyclic (rational) operad.Comment: 50 pages, 7 figures. Newer version has minor changes. Some material shifted. Typos and small things correcte

Els components de la passiva. Una perspectiva diacrònica

Resum: En aquest article es defensa, a partir d’unes dades del català antic, que «passiva» és un terme paraigua sense capacitat explicativa i que no es pot parlar d’una construcció passiva, sinó de la interacció de fenòmens com l’aspecte verbal i la legitimació de l’argument intern, en definitiva, de les propietats de les diverses categories funcionals presents a l’estructura. La passiva és un epifenomen. Aquesta aproximació construccionista i estrictament composicional permet superar les clàssiques restriccions sobre les passives establertes en funció de la naturalesa lèxica del predicat. S’hi argumenta que les oracions anomenades passives perifràstiques de les llengües romàniques són oracions reduïdes que requereixen d’un verb lleuger (ser o estar) per legitimar la seva temporalitat i la seva independència discursiva. Apuntem també, de manera temptativa, que la teoria de fases del programa minimista ofereix una via d’explicació molt prometedora de les dues capes de les oracions passives: l’aspectual i la temporal-discursiva. L’enfocament diacrònic permet veure la influència del sistema llatí: el paradigma perfectiu, d’una banda, i la morfologia específica de les formes sintètiques, de l’altra. Paraules clau: passiva, sintaxi diacrònica, aspecte, categories funcionals, estructura lèxica.Abstract: In this paper we argue that «passive sentence» is a cover term with no empirical import or explanatory interest, an epiphenomenon. The properties of passives are derived from the interaction of the formal properties of the functional categories involved. This strictly compositional and constructionist view allows us to gain explanatory adequacy compared to previous approaches based on the properties of individual predicates. Our leading idea is that Romance passives are in fact participial absolute constructions with a light verb (ésser or estar) merged into the structure to license its temporal and discourse features. Specifically, two layers are relevant in passive sentences: a lower area headed by an Aspect projection and a higher one in the T-C system. We tentatively explore the possibility that phase theory could account for these facts. Addressing the topic from a diachronic perspective, further support to our view comes from the discussion of the crucial the role of the perfective system and the passivizing morphology of Latin. Key words: passive sentences, diachronic syntax, aspect, functional categories, lexical structure

Sobre unes frases relatives sense antecedent

In this paper a new analysis of some free relative sentences as selected CPs is proposed. These CPs have a [+WH] phrase in [SPEC, C’] which heads an A’ chain. This A’ chain is responsible of the NONSPECIFIC ARGUMENT interpretation of the sentence. I argue that this analysis has several theoretical and descriptive advantages over the classical one, which treats the sentences as headless relatives

Enhanced Anandamide Plasma Levels in Patients with Complex Regional Pain Syndrome following Traumatic Injury: A Preliminary Report

The complex regional pain syndrome (CRPS) is a disabling neuropathic pain condition that may develop following injuries of the extremities. The pathogenesis of this syndrome is not clear; however, it includes complex interactions between the nervous and the immune system resulting in chronic inflammation, pain and trophic changes. This interaction may be mediated by chronic stress which is thought to activate the endogenous cannabinoid (endocannabinoid) system (ECS). We conducted an open, prospective, comparative clinical study to determine plasma level of the endocannabinoid anandamide by high-performance liquid chromatography and a tandem mass spectrometry system in 10 patients with CRPS type I versus 10 age- and sex-matched healthy controls. As compared to healthy controls, CRPS patients showed significantly higher plasma concentrations of anandamide. These results indicate that the peripheral ECS is activated in CRPS. Further studies are warranted to evaluate the role of the ECS in the limitation of inflammation and pain. Copyright (C) 2009 S. Karger AG, Base

Implications of surface noise for the motional coherence of trapped ions

Electric noise from metallic surfaces is a major obstacle towards quantum applications with trapped ions due to motional heating of the ions. Here, we discuss how the same noise source can also lead to pure dephasing of motional quantum states. The mechanism is particularly relevant at small ion-surface distances, thus imposing a new constraint on trap miniaturization. By means of a free induction decay experiment, we measure the dephasing time of the motion of a single ion trapped 50~$\mu$m above a Cu-Al surface. From the dephasing times we extract the integrated noise below the secular frequency of the ion. We find that none of the most commonly discussed surface noise models for ion traps describes both, the observed heating as well as the measured dephasing, satisfactorily. Thus, our measurements provide a benchmark for future models for the electric noise emitted by metallic surfaces.Comment: (5 pages, 4 figures