Infinity structures and higher products in rational homotopy theory

Fecha de Lectura de Tesis: 22 de Marzo de 2018.Rational homotopy theory classically studies the torsion free phenomena in the homotopy category of topological spaces and continuous maps. Its success is mainly due to the existence of relatively simple algebraic models that faithfully capture this non-torsion homotopical information. Infinity structures are algebraic gadgets in which some axioms hold up to a hierarchy of coherent homotopies. We will work particularly with two of the most important of these, namely, A-infinity and L-infinity algebras. The former can be thought of as a differential graded algebra (DGA, henceforth, or CDGA if it is commutative) where the associativity law holds up to a homotopy which is determined by a 3-product whose associativity up to homotopy is again given by a 4-product, and so on. The latter can be seen as a differential graded Lie algebra (DGL, henceforth) where similarly, the Jacobi identity holds up to a homotopy which is determined by a 3-product, and so on. In this work, we use infinity structures to shed light on classical matters of rational homotopy theory, and beyond. When attempting to classify (or, more modestly, just to distinguish) rational homotopy types, one is naturally led to consider secondary operations in homotopy or cohomology. Among these, we focus on the higher Whitehead and Massey products, complementing the usual Whitehead product in homotopy andcup product in cohomology, respectively. These fundamental homotopical invariantsare at the very heart of the theory, but their manipulation can be difficult at times. Infinity structures also classify rational homotopy types and are sometimes more amenable to computations or better adapted to the problem at hand than are the secondary operations. The main achievement of this thesis is the description of the precise relationship between the higher arity operations of an infinity structure governing a given rational homotopy type and the higher products in homotopy and cohomology of it

The complex dust formation zone of the AGB star IRC+10216 probed with CARMA 0.25 arcsec angular resolution molecular observations

We present low spectral resolution molecular interferometric observations at 1.2 mm obtained with the Combined Array for Research in Millimetre-wave Astronomy (CARMA) towards the C-rich AGB star IRC+10216. We have mapped the emission of several lines of SiS, H13CN, SiO, and SiC2 in the ground and first excited vibrational states with a high angular resolution of 0.25 arcsec. These observations have allowed us to partially resolve the emission of the envelope at distances from the star <50 stellar radii (R*), where the stellar wind is mainly accelerated. The structure of the molecular emission has been modelled with a 3D radiation transfer code. The emission of line SiS(v=0,J=14-13) is best reproduced with a set of maser emitting arcs arranged between 5 and 20 R*. The abundance of H13CN with respect to H2 decreases from 8e-7 at 1-5 R* to 3e-7 at 20 R*. The SiO observations are explained with an abundance <2e-8 in the shell-like region between 1 and 5 R*. At this point, the SiO abundance sharply increases up to (2-3)e-7. The vibrational temperature of SiO increases by a factor of 2 due North-East between 20 and 50 R*. SiC2 is formed at the stellar surface with an abundance of 8e-7 decreasing down to 8e-8 at 20 R* probably due to depletion on to dust grains. Several asymmetries are found in the abundance distributions of H13CN, SiO, and SiC2 which define three remarkable directions (North-East, South-Southwest, and South-East) in the explored region of the envelope. There are some differences between the red- and blue-shifted emissions of these molecules suggesting the existence of additional asymmetries in their abundance distributions along the line-of-sight.Comment: 22 pages, 16 figures, 9 tables, accepted for publication in MNRA

An Algorithm for the Decentralized Market Coupling Problem

In this communication a conceptual algorithm is proposed for the market coupling process in the presence of block orders. The basic idea is to use the Lagrangian relaxation to get a decomposition of the problem that emulates the necessary decentralization process. The feasibility of this procedure misanalyses using a simplified model of the problem. In particular, the solution obtained in this decentralized way is contrasted with the numerically exact solution of the problem by evaluating the duality gap. The examples presented suggest that in this way reasonably approximate solutions can be obtained, to improve those obtained through empirical procedures used by the market operators

Functional Glyconanomaterials

Nanotechnology provides a new array of techniques and platforms to study biological processes including glycosystems [...

Magnetization pinning in modulated nanowires: from topological protection to the "corkscrew" mechanism

Diameter-modulated nanowires offer an important paradigm to design the magnetization response of 3D magnetic nanostructures by engineering the domain wall pinning. With the aim to understand its nature and to control the process, we analyze the magnetization response in FeCo modulated polycrystalline two-segment nanowires varying the minor diameter. Our modelling indicates a very complex behavior with a strong dependence on the disorder distribution and an important role of topologically non-trivial magnetization structures. We demonstrate that modulated nanowires with a small diameter difference are characterized by an increased coercive field in comparison to the straight ones which is explained by a formation of topologically protected walls formed by two 3D skyrmions with opposite chiralities. For a large diameter difference we report the occurrence of a novel pinning type called here the "corkscrew": the magnetization of the large diameter segment forms a skyrmion tube with a core position in a helical modulation along the nanowire. This structure is pinned at the constriction and in order to penetrate the narrow segments the vortex/skyrmion core size should be reduced

Definition of a labelling code for the noise emitted by machines

It has been increasingly realised that traditional parameters, such as A-weighted sound levels, sound power and noise spectra in octaves or third octaves are not enough to describe a sound and that machine labels should show more subjective information about the emitted noise. A new labelling system based on empirical data is proposed. The methodology of the study used as the basis for the proposal is explained, as well as the objective and subjective characteristics to be included in the new label. The uses and applications of the label are discussed briefly

Development of an Operational System for a Coastal Area on the German North Sea using Artificial Intelligence

This thesis presents a methodology of developing a quasi real time flow model in a coastal area. This model improves the water level conditions along the boundary of the flow model by the implementation of a set of neural network short term forecast