Sigma models for genuinely non-geometric backgrounds

The existence of genuinely non-geometric backgrounds, i.e. ones without geometric dual, is an important question in string theory. In this paper we examine this question from a sigma model perspective. First we construct a particular class of Courant algebroids as protobialgebroids with all types of geometric and non-geometric fluxes. For such structures we apply the mathematical result that any Courant algebroid gives rise to a 3D topological sigma model of the AKSZ type and we discuss the corresponding 2D field theories. It is found that these models are always geometric, even when both 2-form and 2-vector fields are neither vanishing nor inverse of one another. Taking a further step, we suggest an extended class of 3D sigma models, whose world volume is embedded in phase space, which allow for genuinely non-geometric backgrounds. Adopting the doubled formalism such models can be related to double field theory, albeit from a world sheet perspective.

T-duality without isometry via extended gauge symmetries of 2D sigma models

Target space duality is one of the most profound properties of string theory. However it customarily requires that the background fields satisfy certain invariance conditions in order to perform it consistently; for instance the vector fields along the directions that T-duality is performed have to generate isometries. In the present paper we examine in detail the possibility to perform T-duality along non-isometric directions. In particular, based on a recent work of Kotov and Strobl, we study gauged 2D sigma models where gauge invariance for an extended set of gauge transformations imposes weaker constraints than in the standard case, notably the corresponding vector fields are not Killing. This formulation enables us to follow a procedure analogous to the derivation of the Buscher rules and obtain two dual models, by integrating out once the Lagrange multipliers and once the gauge fields. We show that this construction indeed works in non-trivial cases by examining an explicit class of examples based on step 2 nilmanifolds.

Lie symmetries in cortical inspired CNNs

Our scope in this thesis is to propose architectures of CNNs in such a way to model the early visual pathway, including the Lateral Geniculate Nucleus and the Horizontal Connectivity of the primary visual cortex. Moreover, we will show how cortically inspired architectures allow to perform contrast perceptual invariance as well as grouping and the emergence of visual percepts. Particularly, the LGN is modeled with a first layer l0 containing a single filter Ψ0 that pre-filters the image I. Since the RPs of the LGN cells can be modeled as a LoG, we expect to obtain a radially symmetric filter with a similar shape; to this end, we prove the rotational invariance of Ψ0 and we study the influence of this filter to the subsequent layer. Indeed, we compare the statistic distribution of the filters in the second layer l1 of our architecture with the statistic distribution of the RPs of V1 cells of a macaque. Then, we model the horizontal connectivity of V1 implementing a transition kernel K1 to the layer l1. In this setting, we study the vector fields and the association fields induced by the connectivity kernel K1. To this end, we first approximate the filters bank in l1 with a Gabor function and use the parameters just found to re-parameterize the kernel. Thanks to this step, the kernel is now re-parameterized into a sub-Riemmanian space R2 × S1. Now we are able to compare the vector and association fields induced by K1 with the models of the horizontal connectivity.

Heat kernel and worldline path integrals for the Proca theory

In this thesis we study the heat kernel, a useful tool to analyze various properties of different quantum field theories. In particular, we focus on the study of the one-loop effective action and the application of worldline path integrals to derive perturbatively the heat kernel coefficients for the Proca theory of massive vector fields. It turns out that the worldline path integral method encounters some difficulties if the differential operator of the heat kernel is of non-minimal kind. More precisely, a direct recasting of the differential operator in terms of worldline path integrals, produces in the classical action a non-perturbative vertex and the path integral cannot be solved. In this work we wish to find ways to circumvent this issue and to give a suggestion to solve similar problems in other contexts.

Lipschitz regularity for weak solutions of parabolic p-Laplacian type equations in certain subriemannian structures

The main aim of the thesis is to prove the local Lipschitz regularity of the weak solutions to a class of parabolic PDEs modeled on the parabolic p-Laplacian. This result is well known in the Euclidean case and recently has been extended in the Heisenberg group, while higher regularity results are not known in subriemannian parabolic setting. In this thesis we will consider vector fields more general than those in the Heisenberg setting, introducing some technical difficulties. To obtain our main result we will use a Moser-like iteration. Due to the non linearity of the equation, we replace the usual parabolic cylinders with new ones, whose dimension also depends on the L^p norm of the solution. In addition, we deeply simplify the iterative procedure, using the standard Sobolev inequality, instead of the parabolic one.

Mean anisotropy of homogeneous Gaussian random fields and anisotropic norms of linear translation-invariant operators on multidimensional integer lattices

Sensitivity of output of a linear operator to its input can be quantified in various ways. In Control Theory, the input is usually interpreted as disturbance and the output is to be minimized in some sense. In stochastic worst-case design settings, the disturbance is considered random with imprecisely known probability distribution. The prior set of probability measures can be chosen so as to quantify how far the disturbance deviates from the white-noise hypothesis of Linear Quadratic Gaussian control. Such deviation can be measured by the minimal Kullback-Leibler informational divergence from the Gaussian distributions with zero mean and scalar covariance matrices. The resulting anisotropy functional is defined for finite power random vectors. Originally, anisotropy was introduced for directionally generic random vectors as the relative entropy of the normalized vector with respect to the uniform distribution on the unit sphere. The associated a-anisotropic norm of a matrix is then its maximum root mean square or average energy gain with respect to finite power or directionally generic inputs whose anisotropy is bounded above by a≥0. We give a systematic comparison of the anisotropy functionals and the associated norms. These are considered for unboundedly growing fragments of homogeneous Gaussian random fields on multidimensional integer lattice to yield mean anisotropy. Correspondingly, the anisotropic norms of finite matrices are extended to bounded linear translation invariant operators over such fields.

Trypanosoma cruzi strains isolated from human, vector, and animal reservoir in the same endemic region in Mexico and typed as T. cruzi I, discrete typing unit 1 exhibit considerable biological diversity

In this study, three strains of Trypanosoma cruzi were isolated at the same time and in the same endemic region in Mexico from a human patient with chronic chagasic cardiomyopathy (RyC-H); vector (Triatoma barberi) (RyC-V); and rodent reservoir (Peromyscus peromyscus) (RyC-R). The three strains were characterized by multilocus enzyme electrophoresis, random amplified polymorphic DNA, and by pathological profiles in experimental animals (biodemes). Based on the analysis of genetic markers the three parasite strains were typed as belonging to T. cruzi I major group, discrete typing unit 1. The pathological profile of RyC-H and RyC-V strains indicated medium virulence and low mortality and, accordingly, the strains should be considered as belonging to biodeme Type III. On the other hand, the parasites from RyC-R strain induced more severe inflammatory processes and high mortality (> 40%) and were considered as belonging to biodeme Type II. The relationship between genotypes and biological characteristics in T. cruzi strains is still debated and not clearly understood. An expert committee recommended in 1999 that Biodeme Type III would correspond to T. cruzi I group, whereas Biodeme Type II, to T. cruzi II group. Our findings suggest that, at least for Mexican isolates, this correlation does not stand and that biological characteristics such as pathogenicity and virulence could be determined by factors different from those identified in the genotypic characterization

Results of MDR-1 vector modification trial indicate that granulocyte/macrophage colony-forming unit cells do not contribute to posttransplant hematopoietic recovery following intensive systemic therapy

To formally test the hypothesis that the granulocyte/macrophage colony-forming unit (GM-CFU) cells can contribute to early hematopoietic reconstitution immediately after transplant, the frequency of genetically modified GM-CFU after retroviral vector transduction was measured by a quantitative in situ polymerase chain reaction (PCR), which is specific for the multidrug resistance-1 (MDR-1) vector, and by a quantitative GM-CFU methylcellulose plating assay. The results of this analysis showed no difference between the transduction frequency in the products of two different transduction protocols: “suspension transduction” and “stromal growth factor transduction.” However, when an analysis of the frequency of cells positive for the retroviral MDR-1 vector posttransplantation was carried out, 0 of 10 patients transplanted with cells transduced by the suspension method were positive for the vector MDR-1 posttransplant, whereas 5 of 8 patients transplanted with the cells transduced by the stromal growth factor method were positive for the MDR-1 vector transcription unit by in situ or in solution PCR assay (a difference that is significant at the P = 0.0065 level by the Fisher exact test). These data suggest that only very small subsets of the GM-CFU fraction of myeloid cells, if any, contribute to the repopulation of the hematopoietic tissues that occurs following intensive systemic therapy and transplantation of autologous hematopoietic cells.

Experimental investigation of plasma micro-instabilities in crossed magnetic and AC electric fields. Contract no. AF19(628)-5832, Project no. 5635, Task no. 563504, Work Unit no. 56350401.

"AFCRL-68-0044."

Use of the Vector (TM) scaling unit in supportive periodontal therapy: a subjective patient evaluation

Background: Patient discomfort is one reason for poor compliance with supportive periodontal therapy (SPT). The aim of this study was to compare the levels of discomfort during SPT, using the Vector (TM) system and treatment with a conventional ultrasonic scaler. Methods: Forty-six patients with an SPT programme were debrided using both the Vector (TM) system and a conventional piezo-electric scaler (Sirona (TM)) in a split mouth design. A visual analogue scale was used to evaluate of pain scores upon completion of treatment. A verbal response scale(VRS) was used to assess discomfort, vibration and noise associated with the scaling system, as well as the volume and taste of the coolant used by these systems. Results: Patients instrumented with the Vector (TM) system experienced approximately half the amount of pain compared with the conventional ultrasonic scaling system. The VRS showed that the Vector (TM) system caused less discomfort than the conventional ultrasonic scaling system when assessed for pain, vibration, noise and volume of coolant. These findings were all statistically significant. There was, however, no statistically significant difference between the two systems when assessed for taste. Conclusion: During SPT the Vector (TM) system caused reduced discomforting sensations compared with conventional methods and may be useful in improving compliance with SPT programmes.

Dispersive analysis of KL mu 3 and KLe3 scalar and vector form factors using KTeV data

Using the published KTeV samples of K(L) -> pi(+/-)e(-/+)nu and K(L) -> pi(+/-)mu(-/+)nu decays, we perform a reanalysis of the scalar and vector form factors based on the dispersive parametrization. We obtain phase-space integrals I(K)(e) = 0.15446 +/- 0.00025 and I(K)(mu) = 0.10219 +/- 0.00025. For the scalar form factor parametrization, the only free parameter is the normalized form factor value at the Callan-Treiman point (C); our best-fit results in InC = 0.1915 +/- 0.0122. We also study the sensitivity of C to different parametrizations of the vector form factor. The results for the phase-space integrals and C are then used to make tests of the standard model. Finally, we compare our results with lattice QCD calculations of F(K)/F(pi) and f(+)(0).

Heat flow for Yang-Mills-Higgs fields, part I

The Yang-Mills-Higgs field generalizes the Yang-Mills field. The authors establish the local existence and uniqueness of the weak solution to the heat flow for the Yang-Mills-Higgs field in a vector bundle over a compact Riemannian 4-manifold, and show that the weak solution is gauge-equivalent to a smooth solution and there are at most finite singularities at the maximum existing time.

Solar Intensity Forecasting using Artificial Neural Networks and Support Vector Machines

This paper presents several forecasting methodologies based on the application of Artificial Neural Networks (ANN) and Support Vector Machines (SVM), directed to the prediction of the solar radiance intensity. The methodologies differ from each other by using different information in the training of the methods, i.e, different environmental complementary fields such as the wind speed, temperature, and humidity. Additionally, different ways of considering the data series information have been considered. Sensitivity testing has been performed on all methodologies in order to achieve the best parameterizations for the proposed approaches. Results show that the SVM approach using the exponential Radial Basis Function (eRBF) is capable of achieving the best forecasting results, and in half execution time of the ANN based approaches.

Profile of the Trypanosoma cruzi vector infestation in Jaboticatubas, State of Minas Gerais, Brazil

Introduction This work aimed to analyze the triatomine infestation scenario in Jaboticatubas after 30 years of the uninterrupted actions of the Program of Chagas Disease Control. Methods From 2007 to 2010, household unit infestation was researched, and an exploratory analysis of the localities infested with Panstrongylus megistus was performed. Results In total, 613 triatomines were captured in 78 households, the majority of which were Panstrongylus megistus and were captured mainly in chicken houses, but they were also found to be colonizing human houses. Conclusions The epidemiological importance of Panstrongylus megistus was confirmed in Jaboticatubas, and capability to colonize indoors has been demonstrated, as has its proximity to humans. Its distribution is aggregated in the northern and in central-eastern regions of the municipality.

The Multiple-partners assignment game with heterogeneous sales and multi-unit demands: competitive equilibria

A multiple-partners assignment game with heterogeneous sales and multiunit demands consists of a set of sellers that own a given number of indivisible units of (potentially many different) goods and a set of buyers who value those units and want to buy at most an exogenously fixed number of units. We define a competitive equilibrium for this generalized assignment game and prove its existence by using only linear programming. In particular, we show how to compute equilibrium price vectors from the solutions of the dual linear program associated to the primal linear program defined to find optimal assignments. Using only linear programming tools, we also show (i) that the set of competitive equilibria (pairs of price vectors and assignments) has a Cartesian product structure: each equilibrium price vector is part of a competitive equilibrium with all optimal assignments, and vice versa; (ii) that the set of (restricted) equilibrium price vectors has a natural lattice structure; and (iii) how this structure is translated into the set of agents' utilities that are attainable at equilibrium.