Search results for "TOP"
showing 10 items of 17685 documents
The link of a finitely determined map germ from R 2 to R 2
2010
Let f: (R2, 0) → (R2, 0) be a finitely determined map germ. The link of f is obtained by taking a small enough representative f: U ⊂ R2 → R2 and the intersection of its image with a small enough sphere Sε1 centered at the origin in R2. We will describe the topology of f in terms of the Gauss word associated to its link.
Eksperimenti ar topoloģisko datu analīzi
2022
Maģistra darba mērķis ir iepazīstināt ar topoloģisko datu analīzi, kas ir pieeja datu kopu analīzei, izmantojot topoloģijas, kā matemātikas novirziena, metodes. Šī inovatīvā datu analīzes metode pasaulē pēdējos gados strauji attīstās un ar vien plašāk tiek pielietota, lai iegūtu informāciju no sarežģītiem, liela apjoma, daudzdimensionāliem datiem. Pašreiz nekur nav atrodams topoloģiskās datu analīzes apraksts un pielietojamība, latviešu valodā. Darbā tiek apskatīti divi dažādi uz topoloģiskās datu analīzes balstīti algoritmi - Mapper un ToMATo, kuru veiksmīgā izmantošanā noteicošais ir pareizu parametru izvēle. Darbā tiek pētītas un piedāvātas šo algoritmu parametru optimizācijas metodes un…
The resonant state at filling factor {\nu} = 1/2 in chiral fermionic ladders
2017
Helical liquids have been experimentally detected in both nanowires and ultracold atomic chains as the result of strong spin-orbit interactions. In both cases the inner degrees of freedom can be considered as an additional space dimension, providing an interpretation of these systems as synthetic ladders, with artificial magnetic fluxes determined by the spin-orbit terms. In this work, we characterize the helical state which appears at filling $\nu=1/2$: this state is generated by a gap arising in the spin sector of the corresponding Luttinger liquid and it can be interpreted as the one-dimensional (1D) limit of a fractional quantum Hall state of bosonic pairs of fermions. We study its main…
Momentum-space structure of surface states in a topological semimetal with a nexus point of Dirac lines
2016
Three-dimensional topological semimetals come in different variants, either containing Weyl points or Dirac lines. Here we describe a more complicated momentum-space topological defect where several separate Dirac lines connect with each other, forming a momentum-space equivalent of the real-space nexus considered before for helium-3. Close to the nexus the Dirac lines exhibit a transition from type I to type II lines. We consider a general model of stacked honeycomb lattices with the symmetry of Bernal (AB) stacked graphite and show that the structural mirror symmetries in such systems protect the presence of the Dirac lines, and also naturally lead to the formation of the nexus. By the bu…
Dirakův kužel a pseudogapped hustota stavů v topologické polovině Heuslerovy sloučeniny YPtBi
2016
Topologické izolátory (Tis) jsou zajímavé materiály, které vykazují nebývalé vlastnosti. . Zde jsme prozkoumali sloučeniny YPtBi jako příklad ze třídy polovu-Heuslerových materiálů. Topological insulators (TIs) are exciting materials, which exhibit unprecedented properties, such as helical spinmomentum locking, which leads to large torques for magnetic switching and highly efficient spin current detection. Here we explore the compound YPtBi, an example from the class of half-Heusler materials, for which the typical band inversion of topological insulators was predicted. We prepared this material as thin films by conventional cosputtering from elementary targets. By in situ time-of-flight mo…
Some Remarks about Product Spaces
2018
Summary This article covers some technical aspects about the product topology which are usually not given much of a thought in mathematics and standard literature like [7] and [6], not even by Bourbaki in [4]. Let {Ti}i∈I be a family of topological spaces. The prebasis of the product space T = ∏ i∈I Ti is defined in [5] as the set of all π −1 i (V) with i ∈ I and V open in Ti . Here it is shown that the basis generated by this prebasis consists exactly of the sets ∏ i∈I Vi with Vi open in Ti and for all but finitely many i ∈ I holds Vi = Ti . Given I = {a} we have T ≅ Ta , given I = {a, b} with a≠ b we have T ≅ Ta ×Tb . Given another family of topological spaces {Si}i∈I such that Si ≅ Ti fo…
Anonymization as homeomorphic data space transformation for privacy-preserving deep learning
2021
Industry 4.0 is largely data-driven nowadays. Owners of the data, on the one hand, want to get added value from the data by using remote artificial intelligence tools as services, on the other hand, they concern on privacy of their data within external premises. Ideal solution for this challenge would be such anonymization of the data, which makes the data safe in remote servers and, at the same time, leaves the opportunity for the machine learning algorithms to capture useful patterns from the data. In this paper, we take the problem of supervised machine learning with deep feedforward neural nets and provide an anonymization algorithm (based on the homeomorphic data space transformation),…
Modeling the mechanical behavior of carbon nanostructures
2016
Low-dimensional nanostructures are expected to have vast number of applications in the future. Particularly large amount of research has been invested in the atomthick carbon membrane called graphene, which has become popular due to its unique electronic and mechanical properties. This thesis presents studies of the mechanical and electromechanical properties of several different types of graphene nanostructures. In addition, short detours are performed in order to study the elasticity of gold nanostructures and topology effects in graphene nanoribbons. The research is performed by using several different simulation methods. In simulations the system parameters and environment can be chosen…
Skeleton-Based Multiview Reconstruction
2016
International audience; The advantage of skeleton-based 3D reconstruction is to completely generate a single 3D object from well chosen views. Having numerous views is necessary for a reliable reconstruction but projections of skeletons lead to different topologies. We reconstruct 3D objects with curved medial axis (whose topology is a tree) from the perspective skeletons on an arbitrary number of calibrated acquisitions. The main contribution is to estimate the 3D skeleton, from multiple images: its topology is chosen as the closest to those of the perspective skeletons on the set of images, which means that the number of topology changes to map the 3D skeleton topology to topologies on im…
Zemākās atdalāmības aksiomas nestriktajā topoloģijā
2016
Darbs veltīts nestrikto punktu atdalāmības problemātikai nestriktās topoloģiskās telpās. Darbā tiek aplūkotas dažādu autoru atšķirīgās pieejas definējot nestriktā punkta jēdzienu, nestriktās topoloģijas un zemākās atdalāmības aksiomas tajās. Darbā konstruēti vairāki nestriktu topoloģisku telpu piemēri un pārbaudītas zemākās atdalāmības aksiomas šajās telpās.