The Hamiltonian Approach to Yang-Mills (2+1): An Expansion Scheme and Corrections to String Tension

We carry out further analysis of the Hamiltonian approach to Yang-Mills theory in 2+1 dimensions which helps to place the calculation of the vacuum wave function and the string tension in the context of a systematic expansion scheme. The solution of the Schrodinger equation is carried out recursively. The computation of correlators is re-expressed in terms of a two-dimensional chiral boson theory. The effective action for this theory is calculated to first order in our expansion scheme and to the fourth order in a kinematic expansion parameter. The resulting corrections to the string tension are shown to be very small, in the range -0.3% to -2.8%, moving our prediction closer to the recent lattice estimates.Comment: 33 pages, 10 figure

On the Recognition of Fan-Planar and Maximal Outer-Fan-Planar Graphs

Fan-planar graphs were recently introduced as a generalization of 1-planar graphs. A graph is fan-planar if it can be embedded in the plane, such that each edge that is crossed more than once, is crossed by a bundle of two or more edges incident to a common vertex. A graph is outer-fan-planar if it has a fan-planar embedding in which every vertex is on the outer face. If, in addition, the insertion of an edge destroys its outer-fan-planarity, then it is maximal outer-fan-planar. In this paper, we present a polynomial-time algorithm to test whether a given graph is maximal outer-fan-planar. The algorithm can also be employed to produce an outer-fan-planar embedding, if one exists. On the negative side, we show that testing fan-planarity of a graph is NP-hard, for the case where the rotation system (i.e., the cyclic order of the edges around each vertex) is given

Yang-Mills Theory in 2+1 Dimensions: Coupling of Matter Fields and String-breaking Effects

We explore further the Hamiltonian formulation of Yang-Mills theory in 2+1 dimensions in terms of gauge-invariant matrix variables. Coupling to scalar matter fields is discussed in terms of gauge-invariant fields. We analyze how the screening of adjoint (and other screenable) representations can arise in this formalism. A Schrodinger equation is then derived for the gluelump states which are the daughter states when an adjoint string breaks. A variational solution of this Schrodinger equation leads to an analytic estimate of the string-breaking energy which is within 8.8% of the latest lattice estimates.Comment: 31 pages, 1 figure, minor comments, references added, final version to appear in Nucl.Phys.

Matrix Models

Matrix models and their connections to String Theory and noncommutative geometry are discussed. Various types of matrix models are reviewed. Most of interest are IKKT and BFSS models. They are introduced as 0+0 and 1+0 dimensional reduction of Yang--Mills model respectively. They are obtained via the deformations of string/membrane worldsheet/worldvolume. Classical solutions leading to noncommutative gauge models are considered.Comment: Lectures given at the Winter School on Modern Trends in Supersymmetric Mechanics, March 2005 Frascati; 38p

Why decision support systems are important for medical education

During the last decades the inclusion of digital tools in health education has rapidly lead to a continuously enlarging digital era. All the online interactions between learners and tutors, the description, creation, reuse and sharing of educational digital resources and the interlinkage between them in conjunction with cheap storage technology has led to an enormous amount of educational data. Medical education is a unique type of education due to accuracy of information needed, continuous changing competences required and alternative methods of education used. Nowadays medical education standards provide the ground for organizing the educational data and the paradata. Analysis of such education data through education data mining techniques is in its infancy, but decision support systems for medical education need further research. To the best of our knowledge, there is a gap and a clear need for identifying the challenges for decision support systems in medical education in the era of medical education standards. Thus, in this paper the role and the attributes of such a decision support system for medical education are delineated and the challenges and vision for future actions are identified

Stokes-operator-squeezed continuous-variable polarization states

We investigate nonclassical Stokes-operator variances in continuous-wave polarization-squeezed laser light generated from one and two optical parametric amplifiers. A general expression of how Stokes-operator variances decompose into two-mode quadrature operator variances is given. Stokes parameter variance spectra for four different polarization-squeezed states have been measured and compared with a coherent state. Our measurement results are visualized by three-dimensional Stokes-operator noise volumes mapped on the quantum Poincare sphere. We quantitatively compare the channel capacity of the different continuous-variable polarization states for communication protocols. It is shown that squeezed polarization states provide 33% higher channel capacities than the optimum coherent beam protocol

Evaluation of sesamum gum as an excipient in matrix tablets

In developing countries modern medicines are often beyond the affordability of the majority of the population. This is due to the reliance on expensive imported raw materials despite the abundance of natural resources which could provide an equivalent or even an improved function. The aim of this study was to investigate the potential of sesamum gum (SG) extracted from the leaves of Sesamum radiatum (readily cultivated in sub-Saharan Africa) as a matrix former. Directly compressed matrix tablets were prepared from the extract and compared with similar matrices of HPMC (K4M) using theophylline as a model water soluble drug. The compaction, swelling, erosion and drug release from the matrices were studied in deionized water, 0.1 N HCl (pH 1.2) and phosphate buffer (pH 6.8) using USP apparatus II. The data from the swelling, erosion and drug release studies were also fitted into the respective mathematical models. Results showed that the matrices underwent a combination of swelling and erosion, with the swelling action being controlled by the rate of hydration in the medium. SG also controlled the release of theophylline similar to the HPMC and therefore may have use as an alternative excipient in regions where Sesamum radiatum can be easily cultivated

Search for Tensor, Vector, and Scalar Polarizations in the Stochastic Gravitational-Wave Background

The detection of gravitational waves with Advanced LIGO and Advanced Virgo has enabled novel tests of general relativity, including direct study of the polarization of gravitational waves. While general relativity allows for only two tensor gravitational-wave polarizations, general metric theories can additionally predict two vector and two scalar polarizations. The polarization of gravitational waves is encoded in the spectral shape of the stochastic gravitational-wave background, formed by the superposition of cosmological and individually unresolved astrophysical sources. Using data recorded by Advanced LIGO during its first observing run, we search for a stochastic background of generically polarized gravitational waves. We find no evidence for a background of any polarization, and place the first direct bounds on the contributions of vector and scalar polarizations to the stochastic background. Under log-uniform priors for the energy in each polarization, we limit the energy densities of tensor, vector, and scalar modes at 95% credibility to Ω0T<5.58×10-8, Ω0V<6.35×10-8, and Ω0S<1.08×10-7 at a reference frequency f0=25 Hz. © 2018 American Physical Society

Search for Gravitational Waves Associated with Gamma-Ray Bursts Detected by Fermi and Swift during the LIGO-Virgo Run O3b

We search for gravitational-wave signals associated with gamma-ray bursts (GRBs) detected by the Fermi and Swift satellites during the second half of the third observing run of Advanced LIGO and Advanced Virgo (2019 November 1 15:00 UTC-2020 March 27 17:00 UTC). We conduct two independent searches: A generic gravitational-wave transients search to analyze 86 GRBs and an analysis to target binary mergers with at least one neutron star as short GRB progenitors for 17 events. We find no significant evidence for gravitational-wave signals associated with any of these GRBs. A weighted binomial test of the combined results finds no evidence for subthreshold gravitational-wave signals associated with this GRB ensemble either. We use several source types and signal morphologies during the searches, resulting in lower bounds on the estimated distance to each GRB. Finally, we constrain the population of low-luminosity short GRBs using results from the first to the third observing runs of Advanced LIGO and Advanced Virgo. The resulting population is in accordance with the local binary neutron star merger rate. © 2022. The Author(s). Published by the American Astronomical Society