Notes on Euclidean Wilson loops and Riemann Theta functions

The AdS/CFT correspondence relates Wilson loops in N=4 SYM theory to minimal area surfaces in AdS5 space. In this paper we consider the case of Euclidean flat Wilson loops which are related to minimal area surfaces in Euclidean AdS3 space. Using known mathematical results for such minimal area surfaces we describe an infinite parameter family of analytic solutions for closed Wilson loops. The solutions are given in terms of Riemann theta functions and the validity of the equations of motion is proven based on the trisecant identity. The world-sheet has the topology of a disk and the renormalized area is written as a finite, one-dimensional contour integral over the world-sheet boundary. An example is discussed in detail with plots of the corresponding surfaces. Further, for each Wilson loops we explicitly construct a one parameter family of deformations that preserve the area. The parameter is the so called spectral parameter. Finally, for genus three we find a map between these Wilson loops and closed curves inside the Riemann surface.Comment: 35 pages, 7 figures, pdflatex. V2: References added. Typos corrected. Some points clarifie

Quantization of Fayet-Iliopoulos Parameters in Supergravity

In this short note we discuss quantization of the Fayet-Iliopoulos parameter in supergravity theories. We argue that in supergravity, the Fayet-Iliopoulos parameter determines a lift of the group action to a line bundle, and such lifts are quantized. Just as D-terms in rigid N=1 supersymmetry are interpreted in terms of moment maps and symplectic reductions, we argue that in supergravity the quantization of the Fayet-Iliopoulos parameter has a natural understanding in terms of linearizations in geometric invariant theory (GIT) quotients, the algebro-geometric version of symplectic quotients.Comment: 21 pages, utarticle class; v2: typos and tex issue fixe

Power calculation for gravitational radiation: oversimplification and the importance of time scale

A simplified formula for gravitational-radiation power is examined. It is shown to give completely erroneous answers in three situations, making it useless even for rough estimates. It is emphasized that short timescales, as well as fast speeds, make classical approximations to relativistic calculations untenable.Comment: Three pages, no figures, accepted for publication in Astronomische Nachrichte

The Bethe ansatz in a periodic box-ball system and the ultradiscrete Riemann theta function

Vertex models with quantum group symmetry give rise to integrable cellular automata at q=0. We study a prototype example known as the periodic box-ball system. The initial value problem is solved in terms of an ultradiscrete analogue of the Riemann theta function whose period matrix originates in the Bethe ansatz at q=0.Comment: 11 pages, 1 figur

Mumford dendrograms and discrete p-adic symmetries

In this article, we present an effective encoding of dendrograms by embedding them into the Bruhat-Tits trees associated to $p$-adic number fields. As an application, we show how strings over a finite alphabet can be encoded in cyclotomic extensions of $\mathbb{Q}_p$ and discuss $p$-adic DNA encoding. The application leads to fast $p$-adic agglomerative hierarchic algorithms similar to the ones recently used e.g. by A. Khrennikov and others. From the viewpoint of $p$-adic geometry, to encode a dendrogram $X$ in a $p$-adic field $K$ means to fix a set $S$ of $K$-rational punctures on the $p$-adic projective line $\mathbb{P}^1$. To $\mathbb{P}^1\setminus S$ is associated in a natural way a subtree inside the Bruhat-Tits tree which recovers $X$, a method first used by F. Kato in 1999 in the classification of discrete subgroups of $\textrm{PGL}_2(K)$. Next, we show how the $p$-adic moduli space $\mathfrak{M}_{0,n}$ of $\mathbb{P}^1$ with $n$ punctures can be applied to the study of time series of dendrograms and those symmetries arising from hyperbolic actions on $\mathbb{P}^1$. In this way, we can associate to certain classes of dynamical systems a Mumford curve, i.e. a $p$-adic algebraic curve with totally degenerate reduction modulo $p$. Finally, we indicate some of our results in the study of general discrete actions on $\mathbb{P}^1$, and their relation to $p$-adic Hurwitz spaces.Comment: 14 pages, 6 figure

EFSA guidelines on environmental risk assessment of GM animals, including insects

Future applications for the marketing of genetically modified organisms (GMOs) in the EU may include food/feed products derived from genetically modified (GM) animals, and the release of GM animals, including insects, into the environment. Efforts towards the development of GM insects to control insect vectors of human diseases and manage agricultural pests have progressed substantially with various GM insect × trait combinations in the development pipeline. As a proactive measure, the scientific GMO Panel of the European Food Safety Authority (EFSA) has developed guidelines on: (1) the risk assessment of food/feed derived from GM animals including animal health and welfare aspects; and (2) the environmental risk assessment (ERA) of living GM animals, including insects, released into the environment for commercial purposes. The latter assists applicants in the preparation and presentation of their applications by describing the elements and data requirements for a structured ERA of GM insects consistent with the current Directive 2001/18/EC. A dedicated Working Group (WG) was involved in the elaboration of the ERA guidelines on GM insects, which underwent a public consultation before their finalisation. Relevant comments received were considered by the WG. The WG also took into account the external scientific report on GM insects commissioned by EFSA (Benedict et al., 2010). This report provided background information by mapping relevant fields of expertise and identified essential elements to be considered when performing an ERA of GM insects. Content and stakeholder involvement for the EFSA guidelines are presented

European Non-native Species in Aquaculture Risk Analysis Scheme - a summary of assessment protocols and decision support tools for use of alien species in aquaculture

The European Non-native Species in Aquaculture Risk Analysis Scheme (ENSARS) was developed in response to European 'Council Regulation No. 708/2007 of 11 June 2007 concerning use of alien and locally absent species in aquaculture' to provide protocols for identifying and evaluating the potential risks of using non-native species in aquaculture. ENSARS is modular in structure and adapted from non-native species risk assessment schemes developed by the European and Mediterranean Plant Protection Organisation and for the UK. Seven of the eight ENSARS modules contain protocols for evaluating the risks of escape, introduction to and establishment in open waters, of any non-native aquatic organism being used (or associated with those used) in aquaculture, that is, transport pathways, rearing facilities, infectious agents, and the potential organism, ecosystem and socio-economic impacts. A concluding module is designed to summarise the risks and consider management options. During the assessments, each question requires the assessor to provide a response and confidence ranking for that response based on expert opinion. Each module can also be used individually, and each requires a specific form of expertise. Therefore, a multidisciplinary assessment team is recommended for its completion

On the numerical evaluation of algebro-geometric solutions to integrable equations

Physically meaningful periodic solutions to certain integrable partial differential equations are given in terms of multi-dimensional theta functions associated to real Riemann surfaces. Typical analytical problems in the numerical evaluation of these solutions are studied. In the case of hyperelliptic surfaces efficient algorithms exist even for almost degenerate surfaces. This allows the numerical study of solitonic limits. For general real Riemann surfaces, the choice of a homology basis adapted to the anti-holomorphic involution is important for a convenient formulation of the solutions and smoothness conditions. Since existing algorithms for algebraic curves produce a homology basis not related to automorphisms of the curve, we study symplectic transformations to an adapted basis and give explicit formulae for M-curves. As examples we discuss solutions of the Davey-Stewartson and the multi-component nonlinear Schr\"odinger equations.Comment: 29 pages, 20 figure

Developing Leadership for Creative Efforts: A Preface

Michael D. Mumford is the George Lynn Cross distinguished research professor of psychology at the University of Oklahoma where he directs the Center for Applied Social Research. He received his doctoral degree from the University of Georgia in 1983 in the fields of industrial and organizational psychology and psychometrics. He is a fellow of the American Psychological Association (Divisions 3, 5, 10, 14), the Society for Industrial and Organizational Psychology, and the American Psychological Society. He has written more than 270 articles on leadership, creativity, innovation, planning, and ethics. He has served as senior editor of The Leadership Quarterly, and he sits on the editorial boards of the Creativity Research Journal, The Journal of Creative Behavior, IEEE Transactions on Engineering Management, and Ethics and Behavior, among other journals. He has served as principal investor on grants totaling more than US$30 million from the National Science Foundation, The National Institute of Health, the Department of Defense, the Department of Labor, and the Department of State. He is a recipient of the Society for Industrial and Organizational Psychology’s M. Scott Myers Award for Applied Research in the Workplace.Yeshttps://us.sagepub.com/en-us/nam/manuscript-submission-guideline