Papers by Dominic van der Zypen
Schweizerische Zeitschrift für Ganzheitsmedizin / Swiss Journal of Integrative Medicine, 2010
Mathematica Pannonica, Sep 24, 2023
arXiv (Cornell University), Aug 10, 2016
We prove that every digraph has a vertex 4-colouring such that for each vertex v, at most half th... more We prove that every digraph has a vertex 4-colouring such that for each vertex v, at most half the out-neighbours of v receive the same colour as v. We then obtain several results related to the conjecture obtained by replacing 4 by 3. Note that this proof implicitly uses two facts: (1) every digraph has an edge-partition into two acyclic subgraphs, and (2) every acyclic digraph has a majority 2-colouring. The following conjecture naturally arises: Conjecture 2. Every digraph has a majority 3-colouring.
arXiv (Cornell University), Sep 11, 2016
We study some versions of the statement of Hadwiger's conjecture for finite as well as infinite g... more We study some versions of the statement of Hadwiger's conjecture for finite as well as infinite graphs.
arXiv (Cornell University), Oct 22, 2015
Turing Award winner Juris Hartmanis introduced in 1959 [2] lattices of subspaces of generalized p... more Turing Award winner Juris Hartmanis introduced in 1959 [2] lattices of subspaces of generalized partitions ("partitions of type n"; "geometries" if n = 2). Hartmanis states it is "an unsolved problem whether there are any incomplete lattice homomorphisms in" lattices of subspaces of geometries. (He continues, "[I]f so how can these geometries be characterized.") We give a positive answer to this question.
arXiv (Cornell University), Dec 23, 2021
Grätzer and Lakser asked in the 1971 Transactions of the American Mathematical Society if the pse... more Grätzer and Lakser asked in the 1971 Transactions of the American Mathematical Society if the pseudocomplemented distributive lattices in the amalgamation class of the subvariety generated by 2 n ⊕ 1 can be characterized by the property of not having a *-homomorphism onto 2 i ⊕ 1 for 1 < i < n. In this article, this question is answered. If you want to know the answer, you will have to read it (or skip to the last section).
arXiv (Cornell University), May 4, 2022
Purpose Hair has been identified as the causative agent of Pilonidal Sinus Disease (PSD). Stiffer... more Purpose Hair has been identified as the causative agent of Pilonidal Sinus Disease (PSD). Stiffer, dark hair as well as hairiness has been postulated as causative factors. Astonishingly, despite the early clinical significance of this condition (Hodges in Boston Med Surg J 2:485-486, 1880), macroscopic and microscopic examinations of hair inside pilonidal sinus cavities have been scarce. The purpose of this study was to study the morphological aspects of the hair found in PSD in order to determine the origin of the hair. Methods Hair from inside pilonidal sinus cavities was collected intraoperatively from 20 PSD patients. Additionally, occipital, lumbar and intergluteal hair was harvested from the same patients and compared to the hair of volunteermatched pair patients admitted to the hospital at the same time for non-PSD surgery. Intra-and intergroup variations of hair length were characterized with analysis of variance. Numbers and lengths of pilonidal sinus nest hair were recorded. Hair was examined clinically and with light and scanning electron microscopy using surface enhancing gold and carbon dust coating techniques. Results Analysis of 624 pilonidal sinus nest hair samples from 20 independent sinus cavities revealed that hair within pilonidal sinus nests is rootless in 74%. Shorter hair was found inside the pilonidal sinus compared to other sites (length 0.9 ± 0.7 cm p \ 0.0001). Furthermore, hair found inside of the sinus was significantly shorter than hair protruding from pores (p \ 0.000). Hair samples show razor sharp but no broken or split ends. On electron microscopy, these spiky hair ends resemble cut hair ends. Pilonidal hair nests contained between 1 and over 400 hair fragments. Conclusion Short hair fragments with rootless sharp cut ends were found within pilonidal sinus cavities. Morphologically, these fragments resemble short cut rather than intact body hair. Since short cut hair, e.g., derived from the head potentially enters the pilonidal cavity more easily than longer hair, the source of these cut hair fragments needs to be eliminated when aiming to prevent Pilonidal Sinus Disease.
Schweizerische Zeitschrift für Ganzheitsmedizin / Swiss Journal of Integrative Medicine, 2010
Die Kamille ist wohl die bekann teste Heilpflanze hierzulande, seit Langem in Gebrauch, vielfach ... more Die Kamille ist wohl die bekann teste Heilpflanze hierzulande, seit Langem in Gebrauch, vielfach be währt und heute immer noch so gut wie früher. Doch auch in der Phytotherapie steht die Zeit nicht still und die Suche nach neuen Wirkstoffen, neuen Indikationen und vielleicht besseren Darrei chungsformen geht weiter. Mit welchen Methoden und welchem Aufwand Pharmafirmen, die sich mit pflanzlichen Arzneimitteln beschäftigen, nach Innovationen suchen, steht rechts und auf den nächsten beiden Seiten. Die Suche ist vielleicht etwas einfacher als in der klassischen Pharmaindustrie; die Anforderungen, die die Be hörden bei der Zulassung stellen, sind jedoch genauso streng. Einen Biobonus gibt es nicht. Und wie Vertreter der chinesischen, homöo pathischen sowie klassi schen Phytotherapie ihre Disziplin sehen, lesen Sie im Experten gespräch ab der Seite 203.
Grätzer and Lakser asked in the 1971 Transactions of the American Mathematical Society if the pse... more Grätzer and Lakser asked in the 1971 Transactions of the American Mathematical Society if the pseudocomplemented distributive lattices in the amalgamation class of the subvariety generated by 2 ⊕1 can be characterized by the property of not having a ∗-homomorphism onto 2 ⊕ 1 for 1 < i < n. In this article, this question is answered. If you want to know the answer, you will have to read it (or skip to the last section).
For a hypergraph H=(V, E), a subfamily C⊆ E is called a cover of the hypergraph if C= E. A cover ... more For a hypergraph H=(V, E), a subfamily C⊆ E is called a cover of the hypergraph if C= E. A cover C is called minimal if each cover D⊆ C of the hypergraph H coincides with C. We prove that for a hypergraph H the following conditions are equivalent: (i) each countable subhypergraph of H has a minimal cover; (ii) each non-empty subhypergraph of H has a maximal edge; (iii) H contains no isomorphic copy of the hypergraph (ω,ω). This characterization implies that a countable hypergraph (V, E) has a minimal cover if every infinite set I⊆ V contains a finite subset F⊆ I such that the family of edges E_F:={E∈ E:F⊆ E} is finite. Also we prove that a hypergraph (V, E) has a minimal cover if {|E|:E∈ E}<ω or for every v∈ V the family E_v:={E∈ E:v∈ E} is finite.
We introduce the following weak version of Hadwiger's conjecture: If G is a graph and κ is a ... more We introduce the following weak version of Hadwiger's conjecture: If G is a graph and κ is a cardinal such that there is no coloring map c:G →κ, then K_κ is a minor of G. We prove that this statement is true for graphs with infinite chromatic number
We introduce and examine order convergence and the interval topology on partially ordered sets in... more We introduce and examine order convergence and the interval topology on partially ordered sets in general. Problem 76 of Birkhoff's "Lattice Theory" asks whether for complete Boolean algebras the order topology and the interval topology coincide. We answer this question in the negative.
Imagine a website that asks the user to fill in a web form and -- based on the input values -- de... more Imagine a website that asks the user to fill in a web form and -- based on the input values -- derives a relevant figure, for instance an expected salary, a medical diagnosis or the market value of a house. How to deal with missing input values at run-time? Besides using fixed defaults, a more sophisticated approach is to use predefined dependencies (logical or correlational) between different fields to autofill missing values in an iterative way. Directed loopless graphs (in which cycles are allowed) are the ideal mathematical model to formalize these dependencies. We present two new graph-theoretic approaches to filling missing values at run-time.
We solve problems 85 a(nd 87 from Birkhoff's book "Lattice Theory" (3rd edition)
A partially ordered set P is representable if there is a bounded distributive lattice such that i... more A partially ordered set P is representable if there is a bounded distributive lattice such that its ordered set of prime ideals is order-isomorphic to P. We show that if the order components of a poset P are representable, then so is P. Moreover, we provide an example disproving the converse.
Graph embeddings deal with injective maps from a given simple, undirected graph G=(V,E) into a me... more Graph embeddings deal with injective maps from a given simple, undirected graph G=(V,E) into a metric space, such as R^n with the Euclidean metric. This concept is widely studied in computer science, see <cit.>, but also offers attractive research in pure graph theory <cit.>. In this note we show that any graph can be embedded into a particularly simple metric space: {0,1}^n with the Hamming distance, for large enough n.
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Papers by Dominic van der Zypen