Fusion of implementers for spinors on the circle

We consider the space of odd spinors on the circle, and a decomposition into spinors supported on either the top or on the bottom half of the circle. If an operator preserves this decomposition, and acts on the bottom half in the same way as a second operator acts on the top half, then the fusion of both operators is a third operator acting on the top half like the first, and on the bottom half like the second. Fusion restricts to the Banach Lie group of restricted orthogonal operators, which supports a central extension of implementers on a Fock space. In this article, we construct a lift of fusion to this central extension. Our construction uses Tomita-Takesaki theory for the Clifford-von Neumann algebras of the decomposed space of spinors. Our motivation is to obtain an operator-algebraic model for the basic central extension of the loop group of the spin group, on which the fusion of implementers induces a fusion product in the sense considered in the context of transgression and string geometry. In upcoming work we will use this model to construct a fusion product on a spinor bundle on the loop space of a string manifold, completing a construction proposed by Stolz and Teichner.Comment: 49 page

Universal scaling dependence of QCD energy loss from data driven studies

In this paper we study the energy loss of jets in the QGP via the nuclear modification factor $R_{\textrm{AA}}$ for unidentified particles at high $p_{\textrm{T}}$ ($\gtrsim 10 \textrm{GeV}/c$) in and out of the reaction plane of the collision. We argue that at such a high $p_{\textrm{T}}$ there are no genuine flow effects and, assuming that the energy loss is only sensitive to initial characteristics such as the density and geometry, find that $R_{\textrm{AA}}$ depends linearly on the (RMS) length extracted from Glauber simulations. Furthermore we observe that for different centrality classes the density dependence of the energy loss enters as the square root of the charged particle multiplicity normalized to the initial overlap area. The energy loss extracted for RHIC and LHC data from the $R_{\textrm{AA}}$ is found to exhibit a universal behavior.Comment: 15 pages, 5 figures, version to be published in Phys. Rev.

A two-scale Stefan problem arising in a model for tree sap exudation

The study of tree sap exudation, in which a (leafless) tree generates elevated stem pressure in response to repeated daily freeze-thaw cycles, gives rise to an interesting multi-scale problem involving heat and multiphase liquid/gas transport. The pressure generation mechanism is a cellular-level process that is governed by differential equations for sap transport through porous cell membranes, phase change, heat transport, and generation of osmotic pressure. By assuming a periodic cellular structure based on an appropriate reference cell, we derive an homogenized heat equation governing the global temperature on the scale of the tree stem, with all the remaining physics relegated to equations defined on the reference cell. We derive a corresponding strong formulation of the limit problem and use it to design an efficient numerical solution algorithm. Numerical simulations are then performed to validate the results and draw conclusions regarding the phenomenon of sap exudation, which is of great importance in trees such as sugar maple and a few other related species. The particular form of our homogenized temperature equation is obtained using periodic homogenization techniques with two-scale convergence, which we investigate theoretically in the context of a simpler two-phase Stefan-type problem corresponding to a periodic array of melting cylindrical ice bars with a constant thermal diffusion coefficient. For this reduced model, we prove results on existence, uniqueness and convergence of the two-scale limit solution in the weak form, clearly identifying the missing pieces required to extend the proofs to the fully nonlinear sap exudation model. Numerical simulations of the reduced equations are then compared with results from the complete sap exudation model.Comment: 35 pages, 8 figures. arXiv admin note: text overlap with arXiv:1411.303

Rohstoffspekulation und Nahrungsmittelmarkt

Es wird wissenschaftlich kontrovers diskutiert, ob kausal schlüssige und empirisch robuste Befunde für die Beeinflussung der "realen" Lebensmittelpreise durch Spekulanten vorliegen. Die korrelative Koinzidenz von ansteigender Terminmarktspekulation und einem steigenden Preisniveau lässt auf den ersten Blick einen kausalen Zusammenhang logisch erscheinen. Die Auswertung von wissenschaftlicher Literatur sowie eine eigens durchgeführte Analyse im vorliegenden Beitrag können die Gedankenkette der Spekulationsgegner jedoch nicht bestätigen. Nach aktuellem Stand der Forschung kann die Annahme nicht erhärtet werden, dass die erhöhte Terminmarktspekulation das Niveau und die Volatilität der Agrarrohstoffpreise hat signifikant ansteigen lassen.The existence of causal and empirical robust findings for the speculator's impact on food prices is an omnipresent issue in the academic discussion. The correlative coincidence of increasing speculative activity on the futures market and rising food prices make a causal relationship appear consistent. The review of academic literature and studies as well as a specific analysis in this paper cannot confirm this position. In fact, the findings cast considerable doubt on the belief that higher speculator's activity caused the rise in level and volatility of food prices

Deficits in high- (>60 Hz) gamma-band oscillations during visual processing in schizophrenia

Current theories of the pathophysiology of schizophrenia have focused on abnormal temporal coordination of neural activity. Oscillations in the gamma-band range (>25 Hz) are of particular interest as they establish synchronization with great precision in local cortical networks. However, the contribution of high gamma (>60 Hz) oscillations toward the pathophysiology is less established. To address this issue, we recorded magnetoencephalographic (MEG) data from 16 medicated patients with chronic schizophrenia and 16 controls during the perception of Mooney faces. MEG data were analysed in the 25–150 Hz frequency range. Patients showed elevated reaction times and reduced detection rates during the perception of upright Mooney faces while responses to inverted stimuli were intact. Impaired processing of Mooney faces in schizophrenia patients was accompanied by a pronounced reduction in spectral power between 60–120 Hz (effect size: d = 1.26) which was correlated with disorganized symptoms (r = −0.72). Our findings demonstrate that deficits in high gamma-band oscillations as measured by MEG are a sensitive marker for aberrant cortical functioning in schizophrenia, suggesting an important aspect of the pathophysiology of the disorder