Scaling limit for a drainage network model

We consider the two dimensional version of a drainage network model introduced by Gangopadhyay, Roy and Sarkar, and show that the appropriately rescaled family of its paths converges in distribution to the Brownian web. We do so by verifying the convergence criteria proposed by Fontes, Isopi, Newman and Ravishankar.Comment: 15 page

Lyubeznik Ideals Minimally Generated by Four or Fewer Elements

Free resolutions for an ideal are constructions that tell us useful information about the structure of the ideal. Every ideal has one minimal free resolution which tells us significantly more about the structure of the ideal. In this thesis, we consider a specific type of resolution, the Lyubeznik resolution, for a monomial ideal I, which is constructed using a total order on the minimal generating set G(I). An ideal is called Lyubeznik if some total order on G(I) produces a minimal Lyubeznik resolution for I. We investigate the problem of characterizing whether an ideal I is Lyubeznik by using covers of generators of I, a construction due to Guo, Wu, and Yu [3] that is distinct from its Lyubeznik resolution. For monomial ideals of a polynomial ring, we characterize all Lyubeznik ideals that are minimally generated by four or fewer generators, and provide the total order that produces the minimal Lyubeznik resolution for all such ideals

Non-Equilibrium Modeling of the Fe XVII 3C/3D ratio for an Intense X-ray Free Electron Laser

We present a review of two methods used to model recent LCLS experimental results for the 3C/3D line intensity ratio of Fe XVII (Bernitt et al. 2012), the time-dependent collisional-radiative method and the density-matrix approach. These are described and applied to a two-level atomic system excited by an X-ray free electron laser. A range of pulse parameters is explored and the effects on the predicted Fe XVII 3C and 3D line intensity ratio are calculated. In order to investigate the behavior of the predicted line intensity ratio, a particular pair of A-values for the 3C and 3D transitions was chosen (2.22 $\times$ 10$^{13}$ s$^{-1}$ and 6.02 $\times$ 10$^{12}$ s$^{-1}$ for the 3C and 3D, respectively), but our conclusions are independent of the precise values. We also reaffirm the conclusions from Oreshkina et al.(2014, 2015): the non-linear effects in the density matrix are important and the reduction in the Fe XVII 3C/3D line intensity ratio is sensitive to the laser pulse parameters, namely pulse duration, pulse intensity, and laser bandwidth. It is also shown that for both models the lowering of the 3C/3D line intensity ratio below the expected time-independent oscillator strength ratio has a significant contribution due to the emission from the plasma after the laser pulse has left the plasma volume. Laser intensities above $\sim 1\times 10^{12}$ W/cm$^{2}$ are required for a reduction in the 3C/3D line intensity ratio below the expected time independent oscillator strength ratio

Policies to Foster the Creation of Research-Based Spin-offs in Portugal

This paper presents a brief overview of the main government and institutional policies and mechanisms that promote and support (directly or indirectly) the creation of research-based spin-offs, as well as of the institutional changes that have been introduced to facilitate the commercial exploitation of results from academic research. In addition, there is an attempt to conduct a very preliminary assessment of some of the results achieved by these policies, within the limitations of the information available. It is concluded that the conditions for creating a firm that brings to the market knowledge or technology originating from academic research substantially improved in the last decade. Technology-based (and sometimes also scientific) entrepreneurship has been the object of several government policies and incentives and have also attracted the attention of other public and private actors, who launched a variety of programs to fund and otherwise support firm creation. This also coincided with institutional changes that facilitated the entrepreneurial initiatives of academic scientists. Although this appeared to have had positive effects in terms of the number of research-based spin-offs supported, the paper concludes, based on the limited data on results, that there is still work to do to improve the quality and effectiveness of the assistance provided. One step in this direction is a greater concentration and coordination of efforts.FC

Contact process under renewals I

Motivated by questions regarding long range percolation, we investigate a non-Markovian analogue of the Harris contact process in $\mathbb{Z}^d$: an individual is attached to each site $x \in \mathbb{Z}^d$, and it can be infected or healthy; the infection propagates to healthy neighbors just as in the usual contact process, according to independent exponential times with a fixed rate $\lambda$; nevertheless, the possible recovery times for an individual are given by the points of a renewal process with heavy tail; the renewal processes are assumed to be independent for different sites. We show that the resulting processes have a critical value equal to zero.Comment: 13 page

Scaling Limit and Critical Exponents for Two-Dimensional Bootstrap Percolation

Consider a cellular automaton with state space $\{0,1 \}^{{\mathbb Z}^2}$ where the initial configuration $\omega_0$ is chosen according to a Bernoulli product measure, 1's are stable, and 0's become 1's if they are surrounded by at least three neighboring 1's. In this paper we show that the configuration $\omega_n$ at time n converges exponentially fast to a final configuration $\bar\omega$, and that the limiting measure corresponding to $\bar\omega$ is in the universality class of Bernoulli (independent) percolation. More precisely, assuming the existence of the critical exponents $\beta$, $\eta$, $\nu$ and $\gamma$, and of the continuum scaling limit of crossing probabilities for independent site percolation on the close-packed version of ${\mathbb Z}^2$ (i.e., for independent $*$-percolation on ${\mathbb Z}^2$), we prove that the bootstrapped percolation model has the same scaling limit and critical exponents. This type of bootstrap percolation can be seen as a paradigm for a class of cellular automata whose evolution is given, at each time step, by a monotonic and nonessential enhancement.Comment: 15 page

Entry strategies in the face of incumbents dominant position: the case of advanced renewable energy technologies

The paper discusses the entry strategies adopted by research-based firms introducing advanced renewable energy technologies in the electricity production sector, which combines strong incumbent power with fast technological change. Drawing on contributions from the literatures on sustainability transitions and on strategic management of technology we build an analytical framework to address the conditions faced by the new entrants and the attitude of established incumbents towards their technologies. This framework is applied through in-depth case studies of new firms in two energy fields that display different levels of technological maturity: wind and wave energy. The paper presents preliminary results from a first set of case studies, which provide some insights into the “commercialisation environment” prevailing in those fields. They suggest that research-based firms tend to depend on the complementary assets possessed by incumbents, but have conditions to protect their technologies; and that the technology is relevant for (at least some) incumbents, which show interest on them, or are directly involved in their development/use. This is, in most cases, conducive to “cooperation” strategies, which assume different forms according to the stage of development of the technology and its proximity to incumbent competences and business modelsFCT QREN – Operational Programme for Competitiveness Factors, the European Union – European Regional Development Fund and National Funds Portuguese Foundation for Science and Technology under Project FCOMP-01-0124-FEDER-011377, Project PEst-C/EGE/UI4105/2011 and Project Project Pest-OE/EME/UI0252/2011 INESC Coimbr