Energy in Yang-Mills on a Riemann Surface

Sengupta's lower bound for the Yang-Mills action on smooth connections on a bundle over a Riemann surface generalizes to the space of connections whose action is finite. In this larger space the inequality can always be saturated. The Yang-Mills critical sets correspond to critical sets of the energy action on a space of paths. This may shed light on Atiyah and Bott's conjecture concerning Morse theory for the space of connections modulo gauge transformations.Comment: 7 pages, 2 figures, Latex2e with epsfig, submitted to Journal of Mathematical Physic

Complex Line Bundles over Simplicial Complexes and their Applications

Discrete vector bundles are important in Physics and recently found remarkable applications in Computer Graphics. This article approaches discrete bundles from the viewpoint of Discrete Differential Geometry, including a complete classification of discrete vector bundles over finite simplicial complexes. In particular, we obtain a discrete analogue of a theorem of Andr\'e Weil on the classification of hermitian line bundles. Moreover, we associate to each discrete hermitian line bundle with curvature a unique piecewise-smooth hermitian line bundle of piecewise constant curvature. This is then used to define a discrete Dirichlet energy which generalizes the well-known cotangent Laplace operator to discrete hermitian line bundles over Euclidean simplicial manifolds of arbitrary dimension

Haemoglobin and size dependent constraints on swimbladder inflation in fish larvae

In developmental studies of fish species (especially physostomians) it could be demonstrated, that the lack of haemoglobin during larval and juvenile stages is a relatively common phenomenon. Generally it is linked with body translucency. In representatives of the families Galaxiidae, Osmeridae and Clupeidae, partly reared, partly observed immediately after being caught in the wild, it turned out, that this condition coincides with a considerable delay in swimbladder inflation. To determine the moment of its first inflation, larvae placed in a hermetic chamber were observed under a dissecting microscope. While lowering the pressure, the expanding swimbladder showed whether or not its content is really gaseous. The reason postulated to be responsible for the delayed inflation is that larvae lacking haemoglobin do not have the possibility of oxygen transport to their buoyancy organ by means of the blood. Apart of this, capillarity force calculations and body force estimations show that with decreasing size the constraints linked with surface tension increase overproportionally. While in larger sized larvae like trout we could demonstrate inflation by swallowing air, in species with small larvae this was not the case. Below a certain size, even in physostomians, the ductus pneumaticus is no alternative to the blood pathway for swimbladder inflation

Exact ground states of a staggered supersymmetric model for lattice fermions

We study a supersymmetric model for strongly interacting lattice fermions in the presence of a staggering parameter. The staggering is introduced as a tunable parameter in the manifestly supersymmetric Hamiltonian. We obtain analytic expressions for the ground states in the limit of small and large staggering for the model on the class of doubly decorated lattices. On this type of lattice there are two ground states, each with a different density. In one limit we find these ground states to be a simple Wigner crystal and a valence bond solid (VBS) state. In the other limit we find two types of quantum liquids. As a special case, we investigate the quantum liquid state on the one dimensional chain in detail. It is characterized by a massless kink that separates two types of order.Comment: 21 pages, 6 figures, v2: largely rewritten version with more emphasis on physical interpretatio

Optical absorption of non-interacting tight-binding electrons in a Peierls-distorted chain at half band-filling

In this first of three articles on the optical absorption of electrons in half-filled Peierls-distorted chains we present analytical results for non-interacting tight-binding electrons. We carefully derive explicit expressions for the current operator, the dipole transition matrix elements, and the optical absorption for electrons with a cosine dispersion relation of band width $W$ and dimerization parameter $\delta$. New correction (``$\eta$''-)terms to the current operator are identified. A broad band-to-band transition is found in the frequency range $W\delta < \omega < W$ whose shape is determined by the joint density of states for the upper and lower Peierls subbands and the strong momentum dependence of the transition matrix elements.Comment: 17 pages REVTEX 3.0, 2 postscript figures; hardcopy versions before May 96 are obsolete; accepted for publication in The Philosophical Magazine

Asymptotically Free Yang-Mills Classical Mechanics with Self-Linked Orbits

We construct a classical mechanics Hamiltonian which exhibits spontaneous symmetry breaking akin the Coleman-Weinberg mechanism, dimensional transmutation, and asymptotically free self-similarity congruent with the beta-function of four dimensional Yang-Mills theory. Its classical equations of motion support stable periodic orbits and in a three dimensional projection these orbits are self-linked into topologically nontrivial, toroidal knots.Comment: 9 pages incl. 5 fig

The Error is the Feature: how to Forecast Lightning using a Model Prediction Error

Despite the progress within the last decades, weather forecasting is still a challenging and computationally expensive task. Current satellite-based approaches to predict thunderstorms are usually based on the analysis of the observed brightness temperatures in different spectral channels and emit a warning if a critical threshold is reached. Recent progress in data science however demonstrates that machine learning can be successfully applied to many research fields in science, especially in areas dealing with large datasets. We therefore present a new approach to the problem of predicting thunderstorms based on machine learning. The core idea of our work is to use the error of two-dimensional optical flow algorithms applied to images of meteorological satellites as a feature for machine learning models. We interpret that optical flow error as an indication of convection potentially leading to thunderstorms and lightning. To factor in spatial proximity we use various manual convolution steps. We also consider effects such as the time of day or the geographic location. We train different tree classifier models as well as a neural network to predict lightning within the next few hours (called nowcasting in meteorology) based on these features. In our evaluation section we compare the predictive power of the different models and the impact of different features on the classification result. Our results show a high accuracy of 96% for predictions over the next 15 minutes which slightly decreases with increasing forecast period but still remains above 83% for forecasts of up to five hours. The high false positive rate of nearly 6% however needs further investigation to allow for an operational use of our approach.Comment: 10 pages, 7 figure

Chern-kernels and anomaly cancellation in M-theory

This paper deals with magnetic equations of the type dH=J where the current J is a delta-function on a brane worldvolume and H a p-form field strength. In many situations in M-theory this equation needs to be solved for H in terms of a potential. A standard universality class of solutions, involving Dirac-branes, gives rise to strong intermediate singularities in H which in many physically relevant cases lead to inconsistencies. In this paper we present an alternative universality class of solutions for magnetic equations in terms of Chern-kernels, and provide relevant applications, among which the anomaly-free effective action for open M2-branes ending on M5-branes. The unobservability of the Dirac-brane requires a Dirac quantization condition; we show that the requirement of ``unobservability'' of the Chern-kernel leads in M-theory to classical gravitational anomalies which cancel precisely their quantum counterparts.Comment: LaTex, 39 pages, references and comments adde

A super-analogue of Kontsevich's theorem on graph homology

In this paper we will prove a super-analogue of a well-known result by Kontsevich which states that the homology of a certain complex which is generated by isomorphism classes of oriented graphs can be calculated as the Lie algebra homology of an infinite-dimensional Lie algebra of symplectic vector fields.Comment: 15 page

How do HMOs Achieve Savings? The Effectiveness of One Organization\u27s Strategies.

To examine how a group practice used organizational strategies rather than provider-level incentives to achieve savings for health maintenance organization (HMO) compared to fee-for-service (FFS) patients. A large group practice with a group model HMO also treating FFS patients. Data sources were all patient encounter records, demographic files, and clinic records covering 3.5 years (1986-1989). The clinic\u27s procedures to record services and charges were identical for FFS and HMO patients. All FFS and HMO patients under age 65 who received any outpatient services during approximately 100,000 episodes of the seven study illnesses were eligible