We develop a very general version of the hyperbola method which extends the known method by Blomer and Brudern for products of projective spaces to complete smooth split toric varieties. We use it to count Campana points of bounded log-anticanonical height ...
In this thesis we explore the applications of projective geometry, a mathematical theory of the relation between 3D scenes and their 2D images, in modern learning-based computer vision systems. This is an interesting research question which contradicts the ...
We construct a modular desingularisation of (M) over bar (2,n)(P-r, d)(main). The geometry of Gorenstein singularities of genus two leads us to consider maps from prestable admissible covers; with this enhanced logarithmic structure, it is possible to desi ...
We generalize the class vectors found in neural networks to linear subspaces (i.e., points in the Grassmann manifold) and show that the Grassmann Class Representation (GCR) enables simultaneous improvement in accuracy and feature transferability. In GCR, e ...
We prove that the real cohomology of semi-simple Lie groups admits boundary values, which are measurable cocycles on the Furstenberg boundary. This generalises known invariants such as the Maslov index on Shilov boundaries, the Euler class on projective sp ...
We discuss criteria for a stable map of genus two and degree 4 to the projective plane to be smoothable, as an application of our modular desingularisation of (M) over bar (2,n)(P-r, d)(main) via logarithmic geometry and Gorenstein singularities. ...
Collapsing cell complexes was first introduced in the 1930's as a way to deform a space into a topological-equivalent subspace with a sequence of elementary moves. Recently, discrete Morse theory techniques provided an efficient way to construct deformatio ...
Conjugation spaces are equipped with an involution such that the fixed points have the same mod 2 cohomology (as a graded vector space, a ring, and even an unstable algebra) but with all degrees divided by 2, generalizing the classical examples of complex ...
Conjugation spaces are topological spaces equipped with an involution such that their fixed points have the same mod 2 cohomology (as a graded vector space, a ring and even an unstable algebra) but with all degrees divided by two, generalizing the classica ...
While over fields of characteristic at least 5, a normal, projective and Gorenstein del Pezzo surface is geometrically normal, this does not hold for characteristic 2 and 3. There is no characterization of all such non-geometrically normal surfaces, but th ...
We formulate a conjecture characterizing smooth projective varieties in positive characteristic whose Frobenius morphism can be lifted modulo p(2)-we expect that such varieties, after a finite stale cover, admit a toric fibration over an ordinary abelian v ...
A strong coupling of the lattice to functional properties is observed in many transition metal oxide systems, such as the ABO(3) perovskites. In the quest for tailor-made materials, it is essential to be able to control the structural properties of the com ...
Though deep learning (DL) algorithms are very powerful for image processing tasks, they generally require a lot of data to reach their full potential. Furthermore, there is no straightforward way to impose various properties, given by the prior knowledge a ...
A correspondence functor is a functor from the category of finite sets and correspondences to the category of k-modules, where k is a commutative ring. We determine exactly which simple correspondence functors are projective. We also determine which simple ...
Gas lubricated Herringbone-Grooved Journal Bearings (HGJB) are a promising solution to support high-speed rotors in oil-free turbo-machinery due to their compactness, relatively low losses, no need for lubrication and low wear.
Gas lubricated bearings, how ...
A correspondence functor is a functor from the category of finite sets and correspondences to the category of k-modules, where k is a commutative ring. A main tool for this study is the construction of a correspondence functor associated to any finite latt ...
The measurement results of various nitrile butadiene rubber (NBR) O-Ring sizes are pre-sented, and reduced-order models are developed in order to predict the stiffness and damping coefficient as a function of O-Ring geometry, Shore hardness, squeeze, and e ...
Artists often take advantage of the limitations of the human visual system to create art that provides new experiences for the observers. Similarly, in this thesis, we explore new computational artistic compositions that create new visual experiences by re ...
In the enriched setting, the notions of injective and projective model structures on a category of enriched diagrams also make sense. In this paper, we prove the existence of these model structures on enriched diagram categories under local presentability, ...
In the context of next-generation radio interferometers, we are facing a big challenge of how to economically process data. The classical dimensionality reduction technique, averaging visibilities on time, may dilute fast radio transients (FRT). We propose ...
