Strong Products of Hypergraphs: Unique Prime Factorization Theorems and Algorithms

It is well-known that all finite connected graphs have a unique prime factor decomposition (PFD) with respect to the strong graph product which can be computed in polynomial time. Essential for the PFD computation is the construction of the so-called Cartesian skeleton of the graphs under investigation. In this contribution, we show that every connected thin hypergraph H has a unique prime factorization with respect to the normal and strong (hypergraph) product. Both products coincide with the usual strong graph product whenever H is a graph. We introduce the notion of the Cartesian skeleton of hypergraphs as a natural generalization of the Cartesian skeleton of graphs and prove that it is uniquely defined for thin hypergraphs. Moreover, we show that the Cartesian skeleton of hypergraphs can be determined in O(|E|^2) time and that the PFD can be computed in O(|V|^2|E|) time, for hypergraphs H = (V,E) with bounded degree and bounded rank

Square Property, Equitable Partitions, and Product-like Graphs

Equivalence relations on the edge set of a graph $G$ that satisfy restrictive conditions on chordless squares play a crucial role in the theory of Cartesian graph products and graph bundles. We show here that such relations in a natural way induce equitable partitions on the vertex set of $G$, which in turn give rise to quotient graphs that can have a rich product structure even if $G$ itself is prime.Comment: 20 pages, 6 figure

Texas sea breeze: fact or fiction? : an investigation of Texas climate records for a sea-land breeze signature

Due to the character of the original source materials and the nature of batch digitization, quality control issues may be present in this document. Please report any quality issues you encounter to [email protected], referencing the URI of the item.Includes bibliographical references: leaves 54-55.An analysis of the climatic averages from a number of locations in Texas is performed to ascertain whether they contain a sea-land breeze signature. Theory and previous research dictates that if any such signature exists, it should be confined to the region near the coast. The manner in which temperature, humidity, and wind should behave is influenced by the sea-land breeze on the climatic scale is first established. As a whole the coastal stations show varying amounts of evidence of a signature compared to the inland set of stations where it is presumed there is no sea-land breeze influence. Temperature and humidity data offers no conclusive evidence, but a clear indication the sea-land breeze is indeed present in the climate record comes from certain manifestations of the wind data. It is concluded there apparently is some kind of sea-land breeze signature in the climate records of the coastal set of stations. However, that signature is greatly concealed meaning the sea-land breeze is a minor factor in Texas climate compared to the large-scale synoptic weather pattern

Localisation and characterisation of thylakoid membrane-shaping factors in Synechocystis sp. PCC 6803

Oxygenic photosynthesis converts light energy to chemical energy and releases molecular oxygen as a byproduct. Furthermore, the energy fixed during photosynthesis is the source for the main production of biomass on earth. Its evolutionary development goes back more than 2700 million years and has shaped a large part of life on our earth. Photosynthesis is a highly complex process involving a large number of factors. The most important photosynthetic complexes are photosystem I, photosystem II, cytochrome b6f and the ATP synthase. A co-evoled endomembrane system called thylakoids serves as carrier and reaction space for photosynthesis. While the photosynthetic complexes were relatively conserved in the course of evolution and differentiation of species, the shape and arrangement of the thylakoids were subject to constant change in adaptation to the respective environmental circumstances. This ranges from simple circular or star-shaped arrangements in cyanobacteria to the clear discrimination of stroma and grana lamellae in chloroplasts of today’s plants. In the cyanobacterium Synechocystis sp. PCC 6803 (hereafter Synechocystis 6803) the individual thylakoids are arranged in layers parallel to the plasma membrane and interrupted by convergence zones. These are regions where the thylakoid membranes partially fuse and curve towards the plasma membrane forming contact sites called thylapses. Due to the very high number of ribosomes in these areas, they have been shown to be biogenic regions. CurT, the cyanobacterial homolog of the CURVATURE THYLAKOID1 protein family, is essential for the curvature of thylakoids in cyanobacteria as well as in chloroplasts of green algae and higher plants. A lack of CurT triggers dramatic alterations in the thylakoid architecture of Synechocystis 6803 including the loss of convergence zones. Moreover, photosynthetic activity and growth are reduced. By whole-genome sequencing of a strain partially suppressing the photosynthetic curT- phenotype, the protein AncM (anchor of convergence membranes) was identified. AncM is an integral membrane protein located at thylakoid membrane convergence zones that form thylapses. An ancM- mutant is shown to exhibit an altered thylakoid ultrastructure with converged membranes detached from the plasma membrane and reduced photosynthetic performance. Furthermore, reduction in one protein, CurT or AncM, effects the other, which suggests an antagonistic function. Another important factor for thylakoid architecture and maintenance is VIPP1. It has been shown that it belongs to a highly conserved superfamily of stabilizing and stress-counteracting proteins. Despite its essential role and apparent coevolution with thylakoids, the exact mechanism and action of VIPP1 has not been fully deciphered. However, by means of high-resolution microscopic techniques, the structure of homooligomeric supercomplexes could be shown in detail. Amphiphilic structures were identified and thereby a potential mechanism of how VIPP1 builds large hydrophobic columns to bind and curve membranes. In summary, the present work represents an extension of the previous knowledge about factors shaping the thylakoid membrane, their effects on photosynthesis and an expanded understanding of this important process

Role competition in Central Asia? Network analysis, role theory and great power regionalism: a framework for analysis

The present thesis develops an analytical framework that rests on three pillars: 1. Network Analysis; 2. Role Theory; 3. Neorealism. These theoretical and analytical approaches have been hitherto disconnected in IR and FPA, despite their potential for synthesis. Through a critical appreciation of each approach, the author highlights their interoperability and reconceptualizes central themes in international relations such as the agency-structure debate, the concept of power, interdependence and institutions, and the security dilemma. It comes to the conclusion that the analysis of real-world phenomena needs to take into account both material and ideational factors, since ideational and material structures are inextricably interlinked in the conduct of foreign policy. The second part of the thesis applies this analytical framework to the regional case of Central Asia, and traces how great powers have engaged in role competition between 2007 and 2022. In an interpretative content analysis, it finds 13 roles conceptualized by the United States and Russia respectively; five of them are the most salient ones. In addition, it explores the roles enacted by the European Union and China. The main finding is that the great powers engage in competitive role-play and reject each other’s role conceptions; create conflicting role expectations; and eventually find themselves in ideational security dilemmas that are partially characterized by capacity-identity gaps. Importantly, the case demonstrates the interdependence of regional subsystems through international feedback loops. Role location processes in the Central Asian network cluster contributed to the deterioration of great power relations – and conflictual great power relations shaped the regional context