On hyperlogarithms and Feynman integrals with divergences and many scales

It was observed that hyperlogarithms provide a tool to carry out Feynman integrals. So far, this method has been applied successfully to finite single-scale processes. However, it can be employed in more general situations. We give examples of integrations of three- and four-point integrals in Schwinger parameters with non-trivial kinematic dependence, involving setups with off-shell external momenta and differently massive internal propagators. The full set of Feynman graphs admissible to parametric integration is not yet understood and we discuss some counterexamples to the crucial property of linear reducibility. Furthermore we clarify how divergent integrals can be approached in dimensional regularization with this algorithm.Comment: 26 pages, 11 figures, 2 tables, explicit results in ancillary file "results" and on http://www.math.hu-berlin.de/~panzer/ (version as in JHEP; link corrected

Feynman integrals via hyperlogarithms

This talk summarizes recent developments in the evaluation of Feynman integrals using hyperlogarithms. We discuss extensions of the original method, new results that were obtained with this approach and point out current problems and future directions.Comment: 8 pages, 5 figures, Proceedings of "Loops & Legs 2014", Weimar (Germany), April 27 -- May

Graphical functions in parametric space

Graphical functions are positive functions on the punctured complex plane $\mathbb{C}\setminus\{0,1\}$ which arise in quantum field theory. We generalize a parametric integral representation for graphical functions due to Lam, Lebrun and Nakanishi, which implies the real analyticity of graphical functions. Moreover we prove a formula that relates graphical functions of planar dual graphs.Comment: v2: extended introduction, minor changes in notation and correction of misprint

Feynman integral relations from parametric annihilators

We study shift relations between Feynman integrals via the Mellin transform through parametric annihilation operators. These contain the momentum space IBP relations, which are well-known in the physics literature. Applying a result of Loeser and Sabbah, we conclude that the number of master integrals is computed by the Euler characteristic of the Lee-Pomeransky polynomial. We illustrate techniques to compute this Euler characteristic in various examples and compare it with numbers of master integrals obtained in previous works.Comment: v2: new section 3.1 added, several misprints corrected and additional remark

Childhood Obesity: The Role of the Mental Health Professional

This work consists of two major components: understanding the nature of childhood obesity and providing clinical services. Factors responsible for the current epidemic will be outlined, as will the current definition of the disorder. Statistical data regarding the epidemiology of weight disorders in childhood will be provided in order to give a perspective of the problem. Various obesity trajectories and their differential diagnostic and treatment issues will be thoroughly explored. The intervention section intends to help clinicians to evaluate salient factors in assessing the obese child and to identify appropriate goals and treatment methods. The course will provide vital information for all mental health professionals involved in the care of overweight or obese children

Development of an Electrically Small Vivaldi Antenna: The CReSIS Aerial Vivaldi (CAV-A)

Radar operation from the CReSIS Meridian UAV requires a broadband antenna array composed of lightweight, thin, end-fire antenna elements. Toward this goal four Vivaldi antenna designs were simulated, fabricated, and characterized. The final design, dubbed the CReSIS Aerial Vivaldi - Revision A (CAV-A) provides operation over a band extending from 162 MHz to 1.121 GHz. The CAV-A measures 40 cm long, 51 cm wide, and 0.125 inch thick with a weight of 3.22 lbs., thus satisfying the requirements for UAV operation. Due to size, weight, and bandwidth requirements, a simple frequency scaling of a previously published design was unachievable. Most published single-element Vivaldi antenna designs were constrained by traditional thought that says the antenna length should be multiple free-space wavelengths and the antenna width should be a half free-space wavelength, both at the lowest frequency of interest. Contrary to convention, the CAV-A is an electrically small antenna, with an antenna width and length on the order of a quarter free-space wavelength at the lowest frequency of operation