On the gravitational stability of D1-D5-P black holes

We examine the stability of the nonextremal D1-D5-P black hole solutions. In particular, we look for the appearance of a superradiant instability for the spinning black holes but we find no evidence of such an instability. We compare this situation with that for the smooth soliton geometries, which were recently observed to suffer from an ergoregion instability, and consider the implications for the fuzzball proposal.Comment: 18 pages, 3 figures. Minor comments added to match published versio

Wave Equations for Classical Two-Component Proca Fields in Curved Spacetimes with Torsionless Affinities

The world formulation of the full theory of classical Proca fields in generally relativistic spacetimes is concisely reviewed and the entire set of pertinent field equations is transcribed in a straightforward way into the framework of one of the Infeld-van der Waerden formalisms. Some well-known calculational techniques are then utilized for deriving the wave equations that control the propagation of the fields allowed for. It appears that no interaction couplings between such fields and electromagnetic curvatures are carried by the wave equations at issue. What results is, in effect, that the only interactions which ultimately occur in the theoretical context under consideration involve strictly Proca fields and wave functions for gravitons.Comment: Many improvements on the paper have still been made. In particular, its title has been modified so as to conform further to one of its main aim

A Neural Network model with Bidirectional Whitening

We present here a new model and algorithm which performs an efficient Natural gradient descent for Multilayer Perceptrons. Natural gradient descent was originally proposed from a point of view of information geometry, and it performs the steepest descent updates on manifolds in a Riemannian space. In particular, we extend an approach taken by the "Whitened neural networks" model. We make the whitening process not only in feed-forward direction as in the original model, but also in the back-propagation phase. Its efficacy is shown by an application of this "Bidirectional whitened neural networks" model to a handwritten character recognition data (MNIST data).Comment: 16page

Ultrarelativistic boost of spinning black rings

We study the D=5 Emparan-Reall spinning black ring under an ultrarelativistic boost along an arbitrary direction. We analytically determine the resulting shock pp-wave, in particular for boosts along axes orthogonal and parallel to the plane of rotation. The solution becomes physically more interesting and simpler if one enforces equilibrium between the forces on the ring. We also comment on the ultrarelativistic limit of recently found supersymmetric black rings with two independent angular momenta. Essential distinct features with respect to the boosted Myers-Perry black holes are pointed out.Comment: 15 pages, 2 figures. v2: added multipole expansions at spatial infinity, and a comparison with the boosted Myers-Perry solution in a new appendix. To appear in JHE

BPS black holes, the Hesse potential, and the topological string

The Hesse potential is constructed for a class of four-dimensional N=2 supersymmetric effective actions with S- and T-duality by performing the relevant Legendre transform by iteration. It is a function of fields that transform under duality according to an arithmetic subgroup of the classical dualities reflecting the monodromies of the underlying string compactification. These transformations are not subject to corrections, unlike the transformations of the fields that appear in the effective action which are affected by the presence of higher-derivative couplings. The class of actions that are considered includes those of the FHSV and the STU model. We also consider heterotic N=4 supersymmetric compactifications. The Hesse potential, which is equal to the free energy function for BPS black holes, is manifestly duality invariant. Generically it can be expanded in terms of powers of the modulus that represents the inverse topological string coupling constant, $g_s$, and its complex conjugate. The terms depending holomorphically on $g_s$ are expected to correspond to the topological string partition function and this expectation is explicitly verified in two cases. Terms proportional to mixed powers of $g_s$ and $\bar g_s$ are in principle present.Comment: 28 pages, LaTeX, added comment

The influence of institutional environment on venture capital development in emerging economies: the example of Nigeria

The aim of the study is to investigate the development of venture capital (VC) in an emerging economy lacking the fully-developed legal and financial institutions necessary to support private-equity financing. This study, undertaken in Nigeria, included extended interviews with venture capitalists (VCs), entrepreneurs who were able to secure VC funding and those who were not, a government minister and their key policy staff. The findings suggest that VCs require stable trusted institutional frameworks, regulations and tax regimes, alongside clear exit strategies. They also suggest that informal institution such as networking is important for VC development. These findings have major implications for VC policy and for the development of technology-based industrial start-ups. The paper contributes to the literature on the impact of institutions on VC development processes in emerging economies

Beyond the global financial crisis: challenges facing venture capitalists operating in an emerging economy such as Nigeria

Objectives: The study investigates the challenges faced by venture capitalists (VCs) when operating in an emerging market, as well as problems in dealing with the entrepreneurs themselves. This is to gain a deeper understanding of the environmental and governmental policy factors that are hindering the growth of the industry in Nigeria. Prior Work: In light of the recent global financial downturn where people are being made redundant, many could see it as an opportunity to start up their own business. However, the smooth operation of the finance escalator has proved difficult to achieve under recent financial conditions (North et al. 2013; Gill 2010; Mason et al 2010; NESTA 2009. Moreover, in an emerging economy, small business owners are more likely to secure funding for their new business venture from traditional sources rather than venture capital (VC) since they do not know much about it (Gupta and Sapienza, 2001). Jiang et al. (2014) argue that although the role of VCs is well documented in western developed economies, limited attention has been paid to it by SMEs in emerging markets. Approach: The data was collected using qualitative method involving interviews with 4 VCs who operate in Nigeria, 5 entrepreneurs who were not able to secure venture capital (VC) funding for their ventures and a government minister and a member of staff as key informants. Results: The results show that VCs who operate in Nigeria face challenges which are unique to an emerging economy. The findings suggest that people do not fully understand what VCs look for in a business, the benefits they bring to a business, how they work and the time it takes to get things done from a bureaucratic and legal perspective. Implications: The implication of the study is that the Nigerian government should take steps to improve the country’s VC industry by setting up of a VC fund for technology-based starts-ups. The government should also meet with the heads of the major financial houses in Nigeria in an effort to create a positive public relation campaign to highlight the benefits VCs bring to businesses. This will help significantly towards the development of the industry in Nigeria. Value: This study makes contribution to the growing body of literature on venture capital and the effect of global financial crisis. A better understanding of the decision making process of deal structuring will help VCs to make better decisions regarding investments and stages of funding. Understanding how VCs decide when and where to invest, might benefit entrepreneurs and SMEs with respect to attracting VC as well as increasing the likelihood of receiving higher levels of funding, because a higher level of financing gives them a bigger level of flexibility (Payne et al. (2009)

Learning with a neural network based on similarity measures

Currently, in machine learning, there is a growing interest in finding new and better predictive models that can deal with heterogeneous data and missing values. In this thesis, two learning algorithms are proposed that can deal with both issues. The first learning algorithm that is studied consists of a neural network based on similarity measures, the Similarity Neural Network (SNN). It is a two-layer network, where the hidden layer computes the similarity between the input data and a set of prototypes, and the output layer gathers these results and predicts the output. In this thesis, several variants of this algorithm are proposed and it is analyzed which one performs better. Some of these variants are the way to choose the prototypes or how to set the parameters of the activation function. A full analysis is performed in the experiments section. Secondly, an Ensemble of SNNs is also proposed. The purpose of using an ensemble is to increase predictive performance, reduce variability and reduce learning time complexity. This second learning algorithm combines the predictions of a set of SNNs and gives the response of the ensemble based on these predictions. For this algorithm, several ensemble learners are proposed (in other words, different ways to combined these predictions). These variants are analyzed with a set of experiments. The main goal of this thesis is to understand these two methods, derive training algorithms and compare them with traditional learning algorithms, such as the classical Random Forest. The results of the experiments show a competitive performance of both methods, obtaining similar results than the Random Forest and improving it in some problems. 16 datasets with heterogeneous data and missing values are tested, some of them large and difficult problems. About the SNN, with these experiments, it is found that adding regularization to the network has a high influence on the model. About the ensemble, the experiment results suggest that the simplest ensemble learner (mean or majority vote of the SNNs) is the one that performs better. Among the two proposals, both get similar and quite good performance metrics but the ensemble obtains slightly better predictions

Impact of a Realistic Density Stratification on a Simple Solar Dynamo Calculation

In our Sun, the magnetic cycle is driven by the dynamo action occurring inside the convection zone, beneath the surface. Rotation couples with plasma turbulent motions to produce organized magnetic fields that erupt at the surface and undergo relatively regular cycles of polarity reversal. Among others, the axisymmetric dynamo models have been proved to be a quite useful tool to understand the dynamical processes responsible for the evolution of the solar magnetic cycle and the formation of the sunspots. Here, we discuss the role played by the radial density stratification on the critical layers of the Sun on the solar dynamo. The current view is that a polytropic description of the density stratification from beneath the tachocline region up to the Sun's surface is sufficient for the current precision of axisymmetric dynamo models. In this work, by using an up-to-date density profile obtained from a standard solar model, which is itself consistent with helioseismic data, we show that the detailed peculiarities of the density in critical regions of the Sun's interior, such as the tachocline, the base of the convection zone, the layers of partial ionization of hydrogen and helium, and the super-adiabatic layer, play a non-negligible role on the evolution of the solar magnetic cycle. Furthermore, we found that the chemical composition of the solar model plays a minor role in the formation and evolution of the solar magnetic cycle

Necessary and sufficient conditions for a Hamiltonian graph

A graph is singular if the zero eigenvalue is in the spectrum of its 0-1 adjacency matrix A. If an eigenvector belonging to the zero eigenspace of A has no zero entries, then the singular graph is said to be a core graph. A ( k,t)-regular set is a subset of the vertices inducing a k -regular subgraph such that every vertex not in the subset has t neighbours in it. We consider the case when k=t which relates to the eigenvalue zero under certain conditions. We show that if a regular graph has a ( k,k )-regular set, then it is a core graph. By considering the walk matrix we develop an algorithm to extract ( k,k )-regular sets and formulate a necessary and sufficient condition for a graph to be Hamiltonian