Tropical secant graphs of monomial curves

The first secant variety of a projective monomial curve is a threefold with an action by a one-dimensional torus. Its tropicalization is a three-dimensional fan with a one-dimensional lineality space, so the tropical threefold is represented by a balanced graph. Our main result is an explicit construction of that graph. As a consequence, we obtain algorithms to effectively compute the multidegree and Chow polytope of an arbitrary projective monomial curve. This generalizes an earlier degree formula due to Ranestad. The combinatorics underlying our construction is rather delicate, and it is based on a refinement of the theory of geometric tropicalization due to Hacking, Keel and Tevelev.Comment: 30 pages, 8 figures. Major revision of the exposition. In particular, old Sections 4 and 5 are merged into a single section. Also, added Figure 3 and discussed Chow polytopes of rational normal curves in Section

Erratum : Existence of 3D Skyrmions. Complete version

This erratum corrects the proof given in \cite{E1,E2} about the existence of $3D$ Skyrmions. This is done by changing the arguments of the proof while remaining in the same framework of concentration-compactness. Note however that the use of this method is here different of most of what has been done with it so far. In that sense, this new proof has some interest by itself. The proof given here is self-contained. I thank F. Lin and Y. Yang for having pointed out to me that there were gaps in my proofs.Comment: 10 page

Structural health monitoring of offshore wind turbines: A review through the Statistical Pattern Recognition Paradigm

Offshore Wind has become the most profitable renewable energy source due to the remarkable development it has experienced in Europe over the last decade. In this paper, a review of Structural Health Monitoring Systems (SHMS) for offshore wind turbines (OWT) has been carried out considering the topic as a Statistical Pattern Recognition problem. Therefore, each one of the stages of this paradigm has been reviewed focusing on OWT application. These stages are: Operational Evaluation; Data Acquisition, Normalization and Cleansing; Feature Extraction and Information Condensation; and Statistical Model Development. It is expected that optimizing each stage, SHMS can contribute to the development of efficient Condition-Based Maintenance Strategies. Optimizing this strategy will help reduce labor costs of OWTs׳ inspection, avoid unnecessary maintenance, identify design weaknesses before failure, improve the availability of power production while preventing wind turbines׳ overloading, therefore, maximizing the investments׳ return. In the forthcoming years, a growing interest in SHM technologies for OWT is expected, enhancing the potential of offshore wind farm deployments further offshore. Increasing efficiency in operational management will contribute towards achieving UK׳s 2020 and 2050 targets, through ultimately reducing the Levelised Cost of Energy (LCOE)

The role of self-concept and expectations in academic achievement: A preliminary study

As early career students face new challenges at university, the relationship between L2 skills and academic success depends upon self-perception to a greater extent than previously assumed. Up to the moment, most levelling courses have focused on developing students’ skills in specific subjects in order to bridge the gap between the knowledge that the high school alumni have and university teachers expect them to possess. Yet, early academic failure remains elevated. For this reason, we have decided to focus our English Degree levelling course on academic strategies, expectations and procedures with the aim to disclose the role of students’ self-perception on L2 performance in an academic context. We have designed a two-staged method consisting of a survey and a standardized placement test to measure learners’ self-perception. The results of both stages are measured by following a mixed method procedure, combining quantitative and qualitative analyses. Results show that there is a close relationship between students’ self-concepts, academic expectations, and final outcomes. When the learning of new contents occurs by means of a foreign language, the implications of learners’ confidence and their academic awareness are even clearer. Therefore, we conclude that learners’ self-concepts, and awareness of their academic expectations should play a key role in initial undergraduate training.Universidad de Málaga. Campus de Excelencia Internacional Andalucía TEC

Algorithms for purchasing AIDS vaccines

The authors delineate two different algorithms for the purchase of AIDS vaccines, to show how differences in policy objectives can greatly affect projections of the number of courses of vaccine that will be needed. They consider a hypothetical vaccine costing ten dollars to produce, and offering sixty percent, seventy five percent, and ninety percent reductions in the risk of HIV for ten years. For each of the world's ten major geographic divisions, they sue published estimates of the risk of AIDS, the value of medical costs averted, and the value of potential productivity losses. Under the"health sector"algorithm - in which purchases are made to minimize the impact of AIDS/HIV on government health spending - 766 million courses of vaccine would be purchased. Under the"societal"algorithm - in which purchases are made to minimize the impact of AIDS/HIV on health spending and GDP - more than 3.7 billion courses of vaccine would be purchased. Under an"equity"model - allocating vaccines to everyone in the world at high risk, as if they had the financial resources of Western Europeans - vaccine would be offered to 4.7 billion people. For a Western European man, reducing the risk of AIDS/HIV would be a $789 concern; in Africa,the comparable risk would be a$48,577 crisis. The authors conclude that financing AIDS vaccines solely on the fixed budget of a ministry of health, means large vulnerable populations wouldn't receive the vaccine. Allocating the vaccine based on society's ability to pay would still exclude many poor infants who would probably be immunized if they were born in more developed regions. Policymakers concerned about equity in health care must redouble efforts to making the financing of development, and distribution of AIDS vaccines, a global, not a regional concern.Disease Control&Prevention,Public Health Promotion,Health Monitoring&Evaluation,Early Child and Children's Health,HIV AIDS,HIV AIDS,Health Monitoring&Evaluation,Health Economics&Finance,Adolescent Health,Environmental Economics&Policies

The Fourier estimation method with positive semi-definite estimators

In this paper we present a slight modification of the Fourier estimation method of the spot volatility (matrix) process of a continuous It\^o semimartingale where the estimators are always non-negative definite. Since the estimators are factorized, computational cost will be saved a lot

Gauge coupling Unification and SO(10) in 5D

We analyze the gauge unification in minimal supersymmetric SO(10) grand unified theories in 5 dimensions. The single extra spatial dimension is compactified on the orbifold S^1/(Z_2 x Z_2') reducing the gauge group to that of Pati-Salam SU(4)_c x SU(2)_L x SU(2)_R. The Standard Model gauge group is achieved by the further brane-localized Higgs mechanism on one of the fixed points. There are two main different approaches developed in literature. Higgs mechanism can take place on the Pati Salam brane, or on the SO(10) preserving brane. We show, both analytically and numerically, that in the first case a natural and succesfull gauge coupling unification can be achieved, while the second case is highly disfavoured. For completeness, we consider either the case in which the brane breaking scale is near the cutoff scale or the case in which it is lower than the compactification scale.Comment: 18 Pages and 8 PostScript Figure

Local Defects in colloidal quantum dot thin films measured via spatially resolved multi-modal optoelectronic spectroscopy.

The morphology, chemical composition, and electronic uniformity of thin-film solution-processed optoelectronics are believed to greatly affect device performance. Although scanning probe microscopies can address variations on the micrometer scale, the field of view is still limited to well under the typical device area, as well as the size of extrinsic defects introduced during fabrication. Herein, a micrometer-resolution 2D characterization method with millimeter-scale field of view is demonstrated, which simultaneously collects photoluminescence spectra, photocurrent transients, and photovoltage transients. This high-resolution morphology mapping is used to quantify the distribution and strength of the local optoelectronic property variations in colloidal quantum dot solar cells due to film defects, physical damage, and contaminants across nearly the entire test device area, and the extent to which these variations account for overall performance losses. It is found that macroscopic defects have effects that are confined to their localized areas, rarely prove fatal for device performance, and are largely not responsible for device shunting. Moreover, quantitative analysis based on statistical partitioning methods of such data is used to show how defect identification can be automated while identifying variations in underlying properties such as mobilities and recombination strengths and the mechanisms by which they govern device behavior.DMR-1807342 - National Science Foundation; Hopkins Extreme Materials InstituteAccepted manuscrip

Bayesian Implications of Current LHC Supersymmetry and Dark Matter Detection Searches for the Constrained MSSM

We investigate the impact of recent limits from LHC searches for supersymmetry and from direct and indirect searches for dark matter on global Bayesian inferences of the parameter space of the Constrained Minimal Supersymmetric Standard Model (CMSSM). In particular we apply recent exclusion limits from the CMS \alpha_T analysis of 1.1/fb of integrated luminosity, the current direct detection dark matter limit from XENON100, as well as recent experimental constraints on \gamma-ray fluxes from dwarf spheroidal satellite galaxies of the Milky Way from the FermiLAT telescope, in addition to updating values for other non-LHC experimental constraints. We extend the range of scanned parameters to include a significant fraction of the focus point/hyperbolic branch region. While we confirm earlier conclusions that at present LHC limits provide the strongest constraints on the model's parameters, we also find that when the uncertainties are not treated in an excessively conservative way, the new bounds from dwarf spheroidal have the power to significantly constrain the focus point/hyperbolic branch region. Their effect is then comparable, if not stronger, to that from XENON100. We further analyze the effects of one-year projected sensitivities on the neutrino flux from the Sun in the 86-string IceCube+DeepCore configuration at the South Pole. We show that data on neutrinos from the Sun, expected for the next few months at IceCube and DeepCore, have the potential to further constrain the same region of parameter space independently of the LHC and can yield additional investigating power for the model.Comment: 27 pages, 7 figures, version published in PR