On the Heterotic Effective Action at One-Loop, Gauge Couplings and the Gravitational Sector

We present in detail the procedure for calculating the heterotic one-loop effective action. We focus on gravitational and gauge couplings. We show that the two-derivative couplings of the gravitational sector are not renormalized at one loop when the ground state is supersymmetric. Arguments are presented that this non-renormalization theorem persists to all orders in perturbation theory. We also derive the full one-loop correction to the gauge coupling. For a class of $N=2$ ground states, namely those that are obtained by toroidal compactification to four dimensions of generic six-dimensional $N=1$ models, we give an explicit formula for the gauge-group independent thresholds, and show that these are equal within the whole family.Comment: LateX, 17pp. A minor correction mad

Interplay of linear and nonlinear impurities in the formation of stationary localized states

Formation of stationary localized states in one-dimensional chain as well as in a Cayley tree due to a linear impurity and a nonlinear impurity is studied. Furthermore, a one-dimensional chain with linear and nonlinear site energies at the alternate sites is studied and rich phase diagrams of SL states are obtained for all systems we considered. The results are compared with those of the linear and nonlinear systems.Comment: 7 pages, Latex, 7 figure

R^2 Corrections and Non-perturbative Dualities of N=4 String ground states

We compute and analyse a variety of four-derivative gravitational terms in the effective action of six- and four-dimensional type II string ground states with N=4 supersymmetry. In six dimensions, we compute the relevant perturbative corrections for the type II string compactified on K3. In four dimensions we do analogous computations for several models with (4,0) and (2,2) supersymmetry. Such ground states are related by heterotic-type II duality or type II-type II U-duality. Perturbative computations in one member of a dual pair give a non-perturbative result in the other member. In particular, the exact CP-even R^2 coupling on the (2,2) side reproduces the tree-level term plus NS 5-brane instanton contributions on the (4,0) side. On the other hand, the exact CP-odd coupling yields the one-loop axionic interaction a.R\wedge R together with a similar instanton sum. In a subset of models, the expected breaking of the SL(2,Z)_S S-duality symmetry to a \Gamma(2)_S subgroup is observed on the non-perturbative thresholds. Moreover, we present a duality chain that provides evidence for the existence of heterotic N=4 models in which N=8 supersymmetry appears at strong coupling.Comment: Latex2e, 51 pages, 1 figur

How Do Recessions Affect Colleges’ Costs?

We estimated real total cost functions for private baccalaureate colleges for the academic years of 2003, 2007, 2010, 2014, and 2015. Using data for 242 colleges, collected from IPEDS, our results reveal that following the recessions of 2001 and 2008, the growth rate of colleges’ costs decreased compared to their pre-recession levels. And, we find that in the subsequent expansions, costs increased more rapidly. These results indicate that recessions have depressing effects on colleges’ cost growth in the short-term, but not the long-term

NS5-branes on an ellipsis and novel marginal deformations with parafermions

We consider NS5-branes distributed along the circumference of an ellipsis and explicitly construct the corresponding gravitational background. This provides a continuous line of deformations between the limiting cases, considered before, in which the ellipsis degenerates into a circle or into a bar. We show that a slight deformation of the background corresponding to a circle distribution into an ellipsoidal one is described by a novel non-factorizable marginal perturbation of bilinears of dressed parafermions. The latter are naturally defined for the circle case since, as it was shown in the past, the background corresponds to an orbifold of the exact conformal field theory coset model SU(2)/U(1) times SL(2,R)/U(1). We explore the possibility to define parafermionic objects at generic points of the ellipsoidal families of backgrounds away from the circle point. We also discuss a new limiting case in which the ellipsis degenerates into two infinitely stretched parallel bars and show that the background is related to the Eguchi-Hanson metric, via T-duality.Comment: 24 page

Hierarchies Everywhere -- Managing & Measuring Uncertainty in Hierarchical Time Series

We examine the problem of making reconciled forecasts of large collections of related time series through a behavioural/Bayesian lens. Our approach explicitly acknowledges and exploits the 'connectedness' of the series in terms of time-series characteristics and forecast accuracy as well as hierarchical structure. By making maximal use of the available information, and by significantly reducing the dimensionality of the hierarchical forecasting problem, we show how to improve the accuracy of the reconciled forecasts. In contrast to existing approaches, our structure allows the analysis and assessment of the forecast value added at each hierarchical level. Our reconciled forecasts are inherently probabilistic, whether probabilistic base forecasts are used or not

Improved shaping approach to the preliminary design of low-thrust trajectories

This paper presents a general framework for the development of shape-based approaches to low-thrust trajectory design. A novel shaping method, based on a three-dimensional description of the trajectory in spherical coordinates, is developed within this general framework. Both the exponential sinusoid and the inverse polynomial shaping are demonstrated to be particular two-dimensional cases of the spherical one. The pseudoequinoctial shaping is revisited within the new framework, and the nonosculating nature of the pseudoequinoctial elements is analyzed. A two step approach is introduced to solve the time of flight constraint, related to the design of low-thrust arcs with boundary constraints for both spherical and pseudoequinoctial shaping. The solution derived from the shaping approach is improved with a feedback linear-quadratic controller and compared against a direct collocation method based on finite elements in time. The new shaping approach and the combination of shaping and linear-quadratic controller are tested on three case studies: a mission to Mars, a mission to asteroid 1989ML, a mission to comet Tempel-1, and a mission to Neptune

Computing the set of Epsilon-efficient solutions in multiobjective space mission design

In this work, we consider multiobjective space mission design problems. We will start from the need, from a practical point of view, to consider in addition to the (Pareto) optimal solutions also nearly optimal ones. In fact, extending the set of solutions for a given mission to those nearly optimal significantly increases the number of options for the decision maker and gives a measure of the size of the launch windows corresponding to each optimal solution, i.e., a measure of its robustness. Whereas the possible loss of such approximate solutions compared to optimal—and possibly even ‘better’—ones is dispensable. For this, we will examine several typical problems in space trajectory design—a biimpulsive transfer from the Earth to the asteroid Apophis and two low-thrust multigravity assist transfers—and demonstrate the possible benefit of the novel approach. Further, we will present a multiobjective evolutionary algorithm which is designed for this purpose

Solving the Decompactification Problem in String Theory

We investigate heterotic ground states in four dimensions in which N=4 supersymmetry is spontaneously broken to N=2. N=4 supersymmetry is restored at a decompactification limit corresponding to $m_{3/2}\to 0$. We calculate the full moduli dependent threshold corrections and confirm that they are supressed in the decompactification limit $m_{3/2}\to 0$ as expected from the restoration of N=4 supersymmetry. This should be contrasted with the behavior of the standard N=2 groundstates where the coupling blow up linearly with the volume of the decompactifying manifold. This mechanism provides a solution to the decompactification problem for the gauge coupling constants. We also discuss how the mechanism can be implemented in ground states with lower supersymmetry.Comment: 14pp, LaTeX some typos correcte