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We give a combinatorial model for the bounded derived category of graded modules over the dual numbers in terms of arcs on the integer line with a point at infinity. Using this model we describe the lattice of thick subcategories of the…
Biological networks provide insight into the complex organization of biological processes in a cell at the system level. They are an effective tool for understanding the comprehensive map of functional interactions, finding the functional…
We review Grover's algorithm by means of a detailed geometrical interpretation and a worked out example. Some basic concepts of Quantum Mechanics and quantum circuits are also reviewed. This work is intended for non-specialists which have…
This paper aims to identify whether different weighted PageRank algorithms can be applied to author citation networks to measure the popularity and prestige of a scholar from a citation perspective. Information Retrieval (IR) was selected…
We prove the Categorified Wrapping Number Conjecture for large classes of annular links, including alternating annular links and tangle closures exhibiting plumbed link phenomena. We do so by characterizing when a resolution is sufficient…
Circumscription is one of the main approaches for defining non-monotonic description logics (DLs). While the decidability and complexity of traditional reasoning tasks such as satisfiability of circumscribed DL knowledge bases (KBs) is well…
Structures and properties of many inorganic compounds have been collected historically. However, it only covers a very small portion of possible inorganic crystals, which implies the presence of numerous currently unknown compounds. A…
Based on the column pivoted QR decomposition, we propose some randomized algorithms including pass-efficient ones for the generalized CUR decompositions of matrix pair and matrix triplet. Detailed error analyses of these algorithms are…
Can a Web crawler efficiently locate an unknown relevant page? While this question is receiving much empirical attention due to its considerable commercial value in the search engine community [Cho98,Chakrabarti99,Menczer00,Menczer01],…
We construct a fundamental theory of the derived category of non-finite bi-filtered complexes.
We consider skew ruled surfaces in the three-dimensional Euclidean space and some geometrically distinguished families of curves on them whose normal curvature has a concrete form. The aim of this paper is to find and classify all ruled…
Parameterized complexity theory was developed in the 1990s to enrich the complexity-theoretic analysis of problems that depend on a range of parameters. In this paper we establish a quantum equivalent of classical parameterized complexity…
These notes loosely follow an introductory course on graph complexes, held at Humboldt-Universit\"at zu Berlin in summer 23. Instead of simply typing up my lecture notes I decided to give here an overview over (parts of) the topic (lecture…
We develop estimation for potentially high-dimensional additive structural equation models. A key component of our approach is to decouple order search among the variables from feature or edge selection in a directed acyclic graph encoding…
LWF chain graphs combine directed acyclic graphs and undirected graphs. We present a PC-like algorithm that finds the structure of chain graphs under the faithfulness assumption to resolve the problem of scalability of the proposed…
This article advances the prerequisite network as a means to visualize the hidden structure in an academic curriculum. Network technologies have been used for some time now in social analyses and more recently in biology in the areas of…
Proximal nested sampling was introduced recently to open up Bayesian model selection for high-dimensional problems such as computational imaging. The framework is suitable for models with a log-convex likelihood, which are ubiquitous in the…
This is an informal survey of progress in Weihrauch complexity (cf arXiv:1707.03202) in the period 2018-2020. Open questions are emphasised.
We classify certain non-symmetric commutative association schemes. As an application, we determine all the primitive weakly distance-regular circulant digraphs.
Analyzing and understanding the structure of complex relational data is important in many applications including analysis of the connectivity in the human brain. Such networks can have prominent patterns on different scales, calling for a…