Automatic structures for semigroup constructions

We survey results concerning automatic structures for semigroup constructions, providing references and describing the corresponding automatic structures. The constructions we consider are: free products, direct products, Rees matrix semigroups, Bruck-Reilly extensions and wreath products.Comment: 22 page

The monoid of queue actions

We investigate the monoid of transformations that are induced by sequences of writing to and reading from a queue storage. We describe this monoid by means of a confluent and terminating semi-Thue system and study some of its basic algebraic properties, e.g., conjugacy. Moreover, we show that while several properties concerning its rational subsets are undecidable, their uniform membership problem is NL-complete. Furthermore, we present an algebraic characterization of this monoid's recognizable subsets. Finally, we prove that it is not Thurston-automatic

Redress in terms of the National Credit Act and the Consumer Protection Act for defective goods sold and financed in terms of an instalment agreement

We will attempt to answer the vexing question that arises in the context of the consumer’s remedies where he has been sold defective goods after 31 March 2011 (the date on which the CPA came into general effective operation) under an instalment agreement governed by the NCA. We will therefore also focus on the nature of an instalment sale agreement, and the rights and obligations of all the parties involved in the sale of the vehicle and the eventual conclusion of an instalment agreement in terms of the NCA. Further, we will examine the interplay, if any, between those rights and obligations in terms of the NCA in the case of an instalment agreement, and the rights and obligations of a supplier and a consumer under the CPA as regards the issue of defective goods.http://reference.sabinet.co.za/sa_epublication/ju_samljhb201

Atypical periosteal osteoid osteoma: a case report

Osteoid osteoma is a benign osteoblastic tumor usually seen in adolescent and young males. In the paediatric age group, since the history may be difficult to elicit, there are often problems in early diagnosis. The author reports an unusual presentation of osteoid osteoma in a ten-year-old girl, which could not be diagnosed by conventional X-rays and CT scan

Special fast diffusion with slow asymptotics. Entropy method and flow on a Riemannian manifold

We consider the asymptotic behaviour of positive solutions $u(t,x)$ of the fast diffusion equation $u_t=\Delta (u^{m}/m)={\rm div} (u^{m-1}\nabla u)$ posed for x\in\RR^d, $t>0$, with a precise value for the exponent $m=(d-4)/(d-2)$. The space dimension is $d\ge 3$ so that $m<1$, and even $m=-1$ for $d=3$. This case had been left open in the general study \cite{BBDGV} since it requires quite different functional analytic methods, due in particular to the absence of a spectral gap for the operator generating the linearized evolution. The linearization of this flow is interpreted here as the heat flow of the Laplace-Beltrami operator of a suitable Riemannian Manifold (\RR^d,{\bf g}), with a metric ${\bf g}$ which is conformal to the standard \RR^d metric. Studying the pointwise heat kernel behaviour allows to prove {suitable Gagliardo-Nirenberg} inequalities associated to the generator. Such inequalities in turn allow to study the nonlinear evolution as well, and to determine its asymptotics, which is identical to the one satisfied by the linearization. In terms of the rescaled representation, which is a nonlinear Fokker--Planck equation, the convergence rate turns out to be polynomial in time. This result is in contrast with the known exponential decay of such representation for all other values of $m$.Comment: 37 page

Machine learning approaches classify clinical malaria outcomes based on haematological parameters

Background Malaria is still a major global health burden, with more than 3.2 billion people in 91 countries remaining at risk of the disease. Accurately distinguishing malaria from other diseases, especially uncomplicated malaria (UM) from non-malarial infections (nMI), remains a challenge. Furthermore, the success of rapid diagnostic tests (RDTs) is threatened by Pfhrp2/3 deletions and decreased sensitivity at low parasitaemia. Analysis of haematological indices can be used to support the identification of possible malaria cases for further diagnosis, especially in travellers returning from endemic areas. As a new application for precision medicine, we aimed to evaluate machine learning (ML) approaches that can accurately classify nMI, UM, and severe malaria (SM) using haematological parameters. Methods We obtained haematological data from 2,207 participants collected in Ghana: nMI (n = 978), SM (n = 526), and UM (n = 703). Six different ML approaches were tested, to select the best approach. An artificial neural network (ANN) with three hidden layers was used for multi-classification of UM, SM, and uMI. Binary classifiers were developed to further identify the parameters that can distinguish UM or SM from nMI. Local interpretable model-agnostic explanations (LIME) were used to explain the binary classifiers. Results The multi-classification model had greater than 85% training and testing accuracy to distinguish clinical malaria from nMI. To distinguish UM from nMI, our approach identified platelet counts, red blood cell (RBC) counts, lymphocyte counts, and percentages as the top classifiers of UM with 0.801 test accuracy (AUC = 0.866 and F1 score = 0.747). To distinguish SM from nMI, the classifier had a test accuracy of 0.96 (AUC = 0.983 and F1 score = 0.944) with mean platelet volume and mean cell volume being the unique classifiers of SM. Random forest was used to confirm the classifications, and it showed that platelet and RBC counts were the major classifiers of UM, regardless of possible confounders such as patient age and sampling location. Conclusion The study provides proof of concept methods that classify UM and SM from nMI, showing that the ML approach is a feasible tool for clinical decision support. In the future, ML approaches could be incorporated into clinical decision-support algorithms for the diagnosis of acute febrile illness and monitoring response to acute SM treatment particularly in endemic settings

Measurement of the B0-anti-B0-Oscillation Frequency with Inclusive Dilepton Events

The $B^0$-$\bar B^0$ oscillation frequency has been measured with a sample of 23 million \B\bar B pairs collected with the BABAR detector at the PEP-II asymmetric B Factory at SLAC. In this sample, we select events in which both B mesons decay semileptonically and use the charge of the leptons to identify the flavor of each B meson. A simultaneous fit to the decay time difference distributions for opposite- and same-sign dilepton events gives $\Delta m_d = 0.493 \pm 0.012{(stat)}\pm 0.009{(syst)}$ ps$^{-1}$.Comment: 7 pages, 1 figure, submitted to Physical Review Letter

d-Methionine protects against cisplatin-induced neurotoxicity in cortical networks

Article discussing D-Methionine protecting against cisplatin-induced neurotoxicity in cortical networks