By juxtaposing ideas from fractal geometry and dynamical systems, Furstenberg proposed a series of conjectures in the late 1960's that explore the relationship between digit expansions with respect to multiplicatively independent bases. In this work, we in ...
Semantic segmentation datasets often exhibit two types of imbalance: \textit{class imbalance}, where some classes appear more frequently than others and \textit{size imbalance}, where some objects occupy more pixels than others. This causes traditional eva ...
We use birational geometry to show that the existence of rational points on proper rationally connected varieties over fields of characteristic 0 is a consequence of the existence of rational points on terminal Fano varieties. We discuss several consequenc ...
Signalized intersections are a fundamental part of urban networks. Their understanding is crucial to identify congestion patterns, queues, delays, and safety issues in local and network level. In this work, we analyze multimodal vehicle trajectories and pr ...
Traffic congestion constitutes one of the most frequent, yet challenging, problems to address in the urban space. Caused by the concentration of population, whose mobility needs surpass the serving capacity of urban networks, congestion cannot be resolved ...
A toric variety is called fibered if it can be represented as a total space of fibre bundle over toric base and with toric fiber. Fibered toric varieties form a special case of toric variety bundles. In this note we first give an introduction to the class ...
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 ...
In this thesis, original applications of the Density Overlap Region Indicator (DORI), a density dependent bonding descriptor capable of simultaneously capturing covalent and noncovalent interactions, are discussed. The use of scalar fields, such as DORI, w ...
We consider sets L = {l(1),..., l(n)} of n labeled lines in general position in R-3, and study the order types of point sets {p(1),..., p(n)} that stem from the intersections of the lines in L with (directed) planes Pi, not parallel to any line of L, that ...
The fluorescence properties of the BODIPY dye and its two meso-substituted derivatives, tert-butyl- and phenyl-BODIPY, are rationalized. The non emissive behavior of the latter two are attributed to the energetically accessible low-lying conical intersecti ...
