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We report our experience in enhancing automated grading in a functional programming course using formal verification. In our approach, we deploy a verifier for Scala programs to check equivalences between student submissions and reference solutions. Conseq ...
Maximal subgraph mining is increasingly important in various domains, including bioinformatics, genomics, and chemistry, as it helps identify common characteristics among a set of graphs and enables their classification into different categories. Existing ...
In this thesis, we investigate the inverse problem of trees and barcodes from a combinatorial, geometric, probabilistic and statistical point of view.Computing the persistent homology of a merge tree yields a barcode B. Reconstructing a tree from B involve ...
The field of computational topology has developed many powerful tools to describe the shape of data, offering an alternative point of view from classical statistics. This results in a variety of complex structures that are not always directly amenable for ...
We define filter quotients of -categories and prove that filter quotients preserve the structure of an elementary -topos and in particular lift the filter quotient of the underlying elementary topos. We then specialize to the case of filter products of -ca ...
Dynamical systems are topologically equivalent when their orbits can be mapped onto each other via a homeomorphic change of coordinates. We will show that in general, closed-loop systems resulting from Linear Quadratic Optimal Control problems are all topo ...
We prove that four different ways of defining Cartesian fibrations and the Cartesian model structure are all Quillen equivalent: 1.On marked simplicial sets (due to Lurie [31]), 2.On bisimplicial spaces (due to deBrito [12]), 3.On bisimplicial sets, 4.On m ...
Spectral techniques for Boolean and multiple-valued functions have been well studied and found to be useful in logic design and testing for conventional circuits. Spectral techniques also have potential application for reversible and quantum circuits. This ...
Blockchain systems need to solve consensus despite the presence of rational users and failures. The notion of (k, t)-robustness is key to derive impossibility results with k rational players and t faulty players. However, these t faulty players are always ...
In this article, we investigate the possibility to model a metasurface, defined as a zero-thickness sheet of surface polarization currents and described by generalized sheet transition conditions (GSTCs), by a thin slab with a subwavelength thickness and u ...