Manifold dimension of a causal set: Tests in conformally flat spacetimes

This paper describes an approach that uses flat-spacetime dimension estimators to estimate the manifold dimension of causal sets that can be faithfully embedded into curved spacetimes. The approach is invariant under coarse graining and can be implemented independently of any specific curved spacetime. Results are given based on causal sets generated by random sprinklings into conformally flat spacetimes in 2, 3, and 4 dimensions, as well as one generated by a percolation dynamics.Comment: 8 pages, 8 figure

Universal homogeneous causal sets

Causal sets are particular partially ordered sets which have been proposed as a basic model for discrete space-time in quantum gravity. We show that the class C of all countable past-finite causal sets contains a unique causal set (U,<) which is universal (i.e., any member of C can be embedded into (U,<)) and homogeneous (i.e., (U,<) has maximal degree of symmetry). Moreover, (U,<) can be constructed both probabilistically and explicitly. In contrast, the larger class of all countable causal sets does not contain a universal object.Comment: 14 page

Whole genome sequence analysis of ESBL-producing Escherichia coli recovered from New Zealand freshwater sites.

CAUL read and publish agreement 2023Extended-spectrum beta lactamase (ESBL)-producing Escherichia coli are often isolated from humans with urinary tract infections and may display a multidrug-resistant phenotype. These pathogens represent a target for a One Health surveillance approach to investigate transmission between humans, animals and the environment. This study examines the multidrug-resistant phenotype and whole genome sequence data of four ESBL-producing E. coli isolated from freshwater in New Zealand. All four isolates were obtained from a catchment with a mixed urban and pastoral farming land-use. Three isolates were sequence type (ST) 131 (CTX-M-27-positive) and the other ST69 (CTX-M-15-positive); a phylogenetic comparison with other locally isolated strains demonstrated a close relationship with New Zealand clinical isolates. Genes associated with resistance to antifolates, tetracyclines, aminoglycosides and macrolides were identified in all four isolates, together with fluoroquinolone resistance in two isolates. The ST69 isolate harboured the bla CTX-M-15 gene on a IncHI2A plasmid, and two of the three ST131 isolates harboured the bla CTX-M-27 genes on IncF plasmids. The last ST131 isolate harboured bla CTX-M-27 on the chromosome in a unique site between gspC and gspD. These data highlight a probable human origin of the isolates with subsequent transmission from urban centres through wastewater to the wider environment.Publishe

Fluctuations in a general preferential attachment model via Stein's method

We consider a general preferential attachment model, where the probability that a newly arriving vertex connects to an older vertex is proportional to a sublinear function of the indegree of the older vertex at that time. It is well known that the distribution of a uniformly chosen vertex converges to a limiting distribution. Depending on the parameters, this model can show power law, but also stretched exponential behaviour. Using Stein's method we provide rates of convergence for the total variation distance. Our proof uses the fact that the limiting distribution is the stationary distribution of a Markov chain together with the generator method of Barbour

The Galois Complexity of Graph Drawing: Why Numerical Solutions are Ubiquitous for Force-Directed, Spectral, and Circle Packing Drawings

Many well-known graph drawing techniques, including force directed drawings, spectral graph layouts, multidimensional scaling, and circle packings, have algebraic formulations. However, practical methods for producing such drawings ubiquitously use iterative numerical approximations rather than constructing and then solving algebraic expressions representing their exact solutions. To explain this phenomenon, we use Galois theory to show that many variants of these problems have solutions that cannot be expressed by nested radicals or nested roots of low-degree polynomials. Hence, such solutions cannot be computed exactly even in extended computational models that include such operations.Comment: Graph Drawing 201

Occurrence of genes encoding spore germination in Clostridium species that cause meat spoilage

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Finding Short Paths on Polytopes by the Shadow Vertex Algorithm

We show that the shadow vertex algorithm can be used to compute a short path between a given pair of vertices of a polytope P = {x : Ax \leq b} along the edges of P, where A \in R^{m \times n} is a real-valued matrix. Both, the length of the path and the running time of the algorithm, are polynomial in m, n, and a parameter 1/delta that is a measure for the flatness of the vertices of P. For integer matrices A \in Z^{m \times n} we show a connection between delta and the largest absolute value Delta of any sub-determinant of A, yielding a bound of O(Delta^4 m n^4) for the length of the computed path. This bound is expressed in the same parameter Delta as the recent non-constructive bound of O(Delta^2 n^4 \log (n Delta)) by Bonifas et al. For the special case of totally unimodular matrices, the length of the computed path simplifies to O(m n^4), which significantly improves the previously best known constructive bound of O(m^{16} n^3 \log^3(mn)) by Dyer and Frieze