Representations of the homotopy surface category of a simply connected space

We introduce the homotopy surface category of a space which generalizes the 1+1-dimensional cobordism category of circles and surfaces to the situation where one introduces a background space. We explain how for a simply connected background space, monoidal functors from this category to vector spaces can be interpreted in terms of Frobenius algebras with additional structure.Comment: 9 pages, 2 figure

Homotopy Quantum Field Theories and Related Ideas

In this short note we provide a review of some developments in the area of homotopy quantum field theories, loosely based on a talk given by the second author at the Xth Oporto Meeting on Geometry, Topology and Physics.Comment: 8 pages, 2 figures; correcte

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

The Neurological Morbidity of Carotid Revascularisation: Using Markers of Cellular Brain Injury to Compare CEA and CAS

AimThis comparative study attempts to evaluate the profile of S-100β and Neuron-Specific Enolase (NSE), biomarkers of brain injury, in patients undergoing carotid endarterectomy (CEA) and carotid artery stenting (CAS) and to correlate this with haemodynamic and embolic events detected using trans-cranial Doppler (TCD).Methods52 patients with internal carotid artery stenosis requiring intervention were recruited. 24 patients underwent CAS, and 28 underwent CEA. TCD was performed peri-operatively to record mean Middle Cerebral Artery (MCA) velocity and number of High Intensity Transient Signals (HITS) in the MCA of the operated side. Serum was drawn pre-operatively and at six time points in a 48 hour post-operative period, and then assayed using automated commercial equipment. Within and between group variability in markers were assessed by Generalized Estimation Equations modelling.ResultsCAS caused more HITS (p=0.028) but less haemodynamic disturbance (p=0.0001) than CEA. Treatment modality (CAS versus CEA) had no direct effect on S-100 changes (p=0.467). NSE levels declined after revascularisation in the CAS group but not after CEA (p=0.002). S-100β levels rose in patients who had higher numbers of HITS (p=0.002). S-100β and NSE were not associated with changes in MCA velocity (p>0.5). S-100β alone increased significantly at 24 hours in those patients with a post-operative neurological deficit (p=0.015).ConclusionsTrans-cranial Doppler findings suggest that the mechanisms of rise in S-100β and NSE levels may differ and may be due to increased peri-operative micro-embolisation and cerebral hypoperfusion respectively. Further studies are required to assess the clinical significance of these observed changes

Pattern Avoidance in Poset Permutations

We extend the concept of pattern avoidance in permutations on a totally ordered set to pattern avoidance in permutations on partially ordered sets. The number of permutations on $P$ that avoid the pattern $\pi$ is denoted $Av_P(\pi)$. We extend a proof of Simion and Schmidt to show that $Av_P(132) \leq Av_P(123)$ for any poset $P$, and we exactly classify the posets for which equality holds.Comment: 13 pages, 1 figure; v2: corrected typos; v3: corrected typos and improved formatting; v4: to appear in Order; v5: corrected typos; v6: updated author email addresse

The Random Discrete Action for 2-Dimensional Spacetime

A one-parameter family of random variables, called the Discrete Action, is defined for a 2-dimensional Lorentzian spacetime of finite volume. The single parameter is a discreteness scale. The expectation value of this Discrete Action is calculated for various regions of 2D Minkowski spacetime. When a causally convex region of 2D Minkowski spacetime is divided into subregions using null lines the mean of the Discrete Action is equal to the alternating sum of the numbers of vertices, edges and faces of the null tiling, up to corrections that tend to zero as the discreteness scale is taken to zero. This result is used to predict that the mean of the Discrete Action of the flat Lorentzian cylinder is zero up to corrections, which is verified. The ``topological'' character of the Discrete Action breaks down for causally convex regions of the flat trousers spacetime that contain the singularity and for non-causally convex rectangles.Comment: 20 pages, 10 figures, Typos correcte

Spacetime topology from the tomographic histories approach: Part II

As an inverse problem, we recover the topology of the effective spacetime that a system lies in, in an operational way. This means that from a series of experiments we get a set of points corresponding to events. This continues the previous work done by the authors. Here we use the existence of upper bound in the speed of transfer of matter and information to induce a partial order on the set of events. While the actual partial order is not known in our operational set up, the grouping of events to (unordered) subsets corresponding to possible histories, is given. From this we recover the partial order up to certain ambiguities that are then classified. Finally two different ways to recover the topology are sketched and their interpretation is discussed.Comment: 21 pages, slight change in title and certain minor corrections in this second version. To apear in IJT

Spacelike distance from discrete causal order

Any discrete approach to quantum gravity must provide some prescription as to how to deduce continuum properties from the discrete substructure. In the causal set approach it is straightforward to deduce timelike distances, but surprisingly difficult to extract spacelike distances, because of the unique combination of discreteness with local Lorentz invariance in that approach. We propose a number of methods to overcome this difficulty, one of which reproduces the spatial distance between two points in a finite region of Minkowski space. We provide numerical evidence that this definition can be used to define a `spatial nearest neighbor' relation on a causal set, and conjecture that this can be exploited to define the length of `continuous curves' in causal sets which are approximated by curved spacetime. This provides evidence in support of the ``Hauptvermutung'' of causal sets.Comment: 32 pages, 16 figures, revtex4; journal versio