Coadjoint Orbits, Cocycles and Gravitational Wess-Zumino

About 30 years ago, in a joint work with L. Faddeev we introduced a geometric action on coadjoint orbits. This action, in particular, gives rise to a path integral formula for characters of the corresponding group $G$. In this paper, we revisit this topic and observe that the geometric action is a 1-cocycle for the loop group $LG$. In the case of $G$ being a central extension, we construct Wess-Zumino (WZ) type terms and show that the cocycle property of the geometric action gives rise to a Polyakov-Wiegmann (PW) formula. In particular, we obtain a PW type formula for the Polyakov's gravitational WZ action. After quantization, this formula leads to an interesting bulk-boundary decoupling phenomenon previously observed in the WZW model. We explain that this decoupling is a general feature of the Wess-Zumino terms obtained from geometric actions, and that in this case the path integral is expressed in terms of the 2-cocycle which defines the central extension. In memory of our teacher Ludwig Faddeev.Comment: 15 pages, v2: references adde

Zigzag nanoribbons in external electric and magnetic fields

We consider the Schr\"odinger operators on zigzag nanoribbons (quasi-1D tight-binding models) in external magnetic fields and an electric potential $V$. The magnetic field is perpendicular to the plane of the ribbon and the electric field is perpendicular to the axis of the nanoribbon and the magnetic field. If the magnetic and electric fields are absent, then the spectrum of the Schr\"odinger (Laplace) operator consists of two non-flat bands and one flat band (an eigenvalue with infinite multiplicity) between them. If we switch on the magnetic field, then the spectrum of the magnetic Schr\"odinger operator consists of some non-flat bands and one flat band between them. Thus the magnetic field changes the continuous spectrum but does not the flat band. If we switch on a weak electric potential $V\to 0$, then there are two cases: (1) the flat band splits into the small spectral band. We determine the asymptotics of the spectral bands for small fields. (2) the unperturbed flat band remains the flat band. We describe all potentials when the unperturbed flat band remains the flat band and when one splits into the small band of the continuous spectrum. Moreover, we solve inverse spectral problems for small potentials.Comment: 19 pages, 7 figure

Discovery Learning Experiments in a New Machine Design Laboratory

A new Machine Design Laboratory at Marquette University has been created to foster student exploration with hardware and real-world systems. The Laboratory incorporates areas for teaching and training, and has been designed to promote “hands-on” and “minds-on” learning. It reflects the spirit of transformational learning that is a theme in the College of Engineering. The goal was to create discovery learning oriented experiments for a required junior-level “Design of Machine Elements” course in mechanical engineering that would give students practical experiences and expose them to physical hardware, actual tools, and real-world design challenges. In the experiments students face a range of real-world tasks: identify and select components, measure parameters (dimensions, speed, force), distinguish between normal and used (worn) components and between proper and abnormal behavior, reverse engineer systems, and justify design choices. The experiments serve to motivate the theory and spark interest in the subject of machine design. This paper presents details of the experiments and summarizes student reactions and our experiences in the Machine Design Laboratory. In addition, the paper provides some insights for others who may wish to develop similar types of experiments

Seasonal Solow residuals and Christmas: a case for labor hoarding and increasing returns

In aggregate unadjusted data, measured Solow residuals exhibit large seasonal variations. Total Factor Productivity grows rapidly in the fourth quarter at an annual rate of 16 percent and regresses sharply in the first quarter at an annual rate of ?24 percent. This paper considers two potential explanations for the measured seasonal variation in the Solow residual: labor hoarding and increasing returns to scale. Using a specification that allows for no exogenous seasonal variation in technology and a single seasonal demand shift in the fourth quarter, we ask the following question: How much of the total seasonal variation in the measured Solow residual can be explained by Christmas? The answer to this question is surprising. With increasing returns and time varying labor effort, Christmas is sufficient to explain the seasonal variation in the Solow residual, consumption, average productivity, and output in all four quarters. Our analysis of seasonally unadjusted data uncovers important roles for labor hoarding and increasing returns which are difficult to identify in adjusted data.Seasonal variations (Economics)

Challenge Patient Dispatching in Mass Casualty Incidents

Efficient management of mass casualty incidents is complex, since regular emergency medical services struc-tures have to be switched to a temporary “disaster mode” involving additional operational and tactical struc-tures. Most of the relevant decisions have to be taken on-site in a provisional and chaotic environment. Data gathering about affected persons is one side of the coin; the other side is on-site patient dispatching requiring information exchange with the regular emergency call center and destination hospitals. In this paper we extend a previous conference contribution about the research project e-Triage to the aspect of patient data and on-site patient dispatching. Our considerations reflect the situation in Germany, which deserves from our point of view substantial harmonization

Programming Not Only by Example

In recent years, there has been tremendous progress in automated synthesis techniques that are able to automatically generate code based on some intent expressed by the programmer. A major challenge for the adoption of synthesis remains in having the programmer communicate their intent. When the expressed intent is coarse-grained (for example, restriction on the expected type of an expression), the synthesizer often produces a long list of results for the programmer to choose from, shifting the heavy-lifting to the user. An alternative approach, successfully used in end-user synthesis is programming by example (PBE), where the user leverages examples to interactively and iteratively refine the intent. However, using only examples is not expressive enough for programmers, who can observe the generated program and refine the intent by directly relating to parts of the generated program. We present a novel approach to interacting with a synthesizer using a granular interaction model. Our approach employs a rich interaction model where (i) the synthesizer decorates a candidate program with debug information that assists in understanding the program and identifying good or bad parts, and (ii) the user is allowed to provide feedback not only on the expected output of a program, but also on the underlying program itself. That is, when the user identifies a program as (partially) correct or incorrect, they can also explicitly indicate the good or bad parts, to allow the synthesizer to accept or discard parts of the program instead of discarding the program as a whole. We show the value of our approach in a controlled user study. Our study shows that participants have strong preference to using granular feedback instead of examples, and are able to provide granular feedback much faster

Violation of the Holographic Viscosity Bound in a Strongly Coupled Anisotropic Plasma

We study the conductivity and shear viscosity tensors of a strongly coupled N=4 super-Yang-Mills plasma which is kept anisotropic by a theta parameter that depends linearly on one of the spatial dimensions. Its holographic dual is given by an anisotropic axion-dilaton-gravity background and has recently been proposed by Mateos and Trancanelli as a model for the pre-equilibrium stage of quark-gluon plasma in heavy-ion collisions. By applying the membrane paradigm which we also check by numerical evaluation of Kubo formula and lowest lying quasinormal modes, we find that the shear viscosity purely transverse to the direction of anisotropy saturates the holographic viscosity bound, whereas longitudinal shear viscosities are smaller, providing the first such example not involving higher-derivative theories of gravity and, more importantly, with fully known gauge-gravity correspondence.Comment: 4 pages, 2 figures; v3: references added, version to appear in Phys. Rev. Let

Using Remote Access for Sharing Experiences in a Machine Design Laboratory

A new Machine Design Laboratory at Marquette University has been created to foster student exploration and promote “hands-on” and “minds-on” learning. Laboratory experiments have been developed to give students practical experiences and expose them to physical hardware, actual tools, and design challenges. Students face a range of real-world tasks: identify and select components, measure parameters (dimensions, speed, force), distinguish between normal and used (worn) components and between proper and abnormal behavior, reverse engineer systems, and justify design choices. The experiments serve to motivate the theory, spark interest, and promote discovery learning in the subject of machine design. This paper presents details of the experiments in the Machine Design Laboratory and then explores the feasibility of sharing some of the experiences with students at other institutions through remote access technologies. The paper proposes steps towards achieving this goal and raises issues to be addressed for a pilot-study offering machine design experiences to students globally who have access to the internet