Jensen's functional equation on the symmetric group Sn\bold{S_n}

Two natural extensions of Jensen's functional equation on the real line are the equations $f(xy)+f(xy^{-1}) = 2f(x)$ and $f(xy)+f(y^{-1}x) = 2f(x)$, where $f$ is a map from a multiplicative group $G$ into an abelian additive group $H$. In a series of papers \cite{Ng1}, \cite{Ng2}, \cite{Ng3}, C. T. Ng has solved these functional equations for the case where $G$ is a free group and the linear group $GL_n(R)$, R=\z,\r, a quadratically closed field or a finite field. He has also mentioned, without detailed proof, in the above papers and in \cite{Ng4} that when $G$ is the symmetric group $S_n$ the group of all solutions of these functional equations coincides with the group of all homomorphisms from $(S_n,\cdot)$ to $(H,+)$. The aim of this paper is to give an elementary and direct proof of this fact.Comment: 8 pages, Abstract changed, the proof of Proposition 2.1 and Lemma 2.4 changed (minor), one reference added, final version, to be published in Aequationes Mathematicae (2011

The impact of COVID-19 on the practice of Oral and Maxillofacial Pathology in the United States and Canada

Background: The COVID-19 pandemic has significantly disrupted the delivery of healthcare, including oral healthcare services. The restrictions imposed for mitigating spread of the virus forced dental practitioners to adopt significant changes in their workflow pattern. The aim of this study was to investigate the impact of the pandemic on the practice of oral and maxillofacial pathology in two countries in regard to educational activities, and clinical and diagnostic pathology services

Congruent families and invariant tensors

Classical results of Chentsov and Campbell state that -- up to constant multiples -- the only $2$-tensor field of a statistical model which is invariant under congruent Markov morphisms is the Fisher metric and the only invariant $3$-tensor field is the Amari-Chentsov tensor. We generalize this result for arbitrary degree $n$, showing that any family of $n$-tensors which is invariant under congruent Markov morphisms is algebraically generated by the canonical tensor fields defined in an earlier paper

Evaluating the potential of hyperpolarised [1-13C] L-lactate as a neuroprotectant metabolic biosensor for stroke.

Cerebral metabolism, which can be monitored by magnetic resonance spectroscopy (MRS), changes rapidly after brain ischaemic injury. Hyperpolarisation techniques boost <sup>13</sup> C MRS sensitivity by several orders of magnitude, thereby enabling in vivo monitoring of biochemical transformations of hyperpolarised (HP) <sup>13</sup> C-labelled precursors with a time resolution of seconds. The exogenous administration of the metabolite L-lactate was shown to decrease lesion size and ameliorate neurological outcome in preclinical studies in rodent stroke models, as well as influencing brain metabolism in clinical pilot studies of acute brain injury patients. The aim of this study was to demonstrate the feasibility of measuring HP [1- <sup>13</sup> C] L-lactate metabolism in real-time in the mouse brain after ischaemic stroke when administered after reperfusion at a therapeutic dose. We showed a rapid, time-after-reperfusion-dependent conversion of [1- <sup>13</sup> C] L-lactate to [1- <sup>13</sup> C] pyruvate and [ <sup>13</sup> C] bicarbonate that brings new insights into the neuroprotection mechanism of L-lactate. Moreover, this study paves the way for the use of HP [1- <sup>13</sup> C] L-lactate as a sensitive molecular-imaging biosensor in ischaemic stroke patients after endovascular clot removal

On the behavior of the algebraic transfer

Let Tr_k : ��_2 (⊗ over GL_k) PH_i(B��_k) → Ext^(k,k+i)_A(��_2,��_2) be the algebraic transfer, which is defined by W. Singer as an algebraic version of the geometrical transfer tr_k : π_∗^S((B��_k)_+) → π_∗^S(S^0). It has been shown that the algebraic transfer is highly nontrivial and, more precisely, that Tr_k is an isomorphism for k = 1,2,3. However, Singer showed that Tr_5 is not an epimorphism. In this paper, we prove that Tr_4 does not detect the non zero element g_s ∈ Ext^(4,12·2^s)_A(��_2,��_2) for every s ≥ 1. As a consequence, the localized (Sq^0)^(−1)Tr_4 given by inverting the squaring operation Sq^0 is not an epimorphism. This gives a negative answer to a prediction by Minami

Singularities and Topology of Meromorphic Functions

We present several aspects of the "topology of meromorphic functions", which we conceive as a general theory which includes the topology of holomorphic functions, the topology of pencils on quasi-projective spaces and the topology of polynomial functions.Comment: 21 pages, 1 figur

Asymptotic diophantine approximation:the multiplicative case

Let $\alpha$ and $\beta$ be irrational real numbers and 0<\F<1/30. We prove a precise estimate for the number of positive integers $q\leq Q$ that satisfy \|q\alpha\|\cdot\|q\beta\|<\F. If we choose \F as a function of $Q$ we get asymptotics as $Q$ gets large, provided \F Q grows quickly enough in terms of the (multiplicative) Diophantine type of $(\alpha,\beta)$, e.g., if $(\alpha,\beta)$ is a counterexample to Littlewood's conjecture then we only need that \F Q tends to infinity. Our result yields a new upper bound on sums of reciprocals of products of fractional parts, and sheds some light on a recent question of L\^{e} and Vaaler.Comment: To appear in Ramanujan Journa

Synchronous colorectal liver metastasis: A network meta-analysis review comparing classical, combined, and liver-first surgical strategies.

BACKGROUND: In recent years, the management of synchronous colorectal liver metastasis has changed significantly. Alternative surgical strategies to the classical colorectal-first approach have been proposed. These include the liver-first and combined resections approaches. The objectives of this review were to compare the short- and long-term outcomes for all three approaches. METHODS: A systematic review of comparative studies was performed. Evaluated endpoints included surgical outcomes (5-year overall survival, 30-day mortality, and post-operative complications). Pair-wise and network meta-analysis (NMA) were performed to compare survival outcomes. RESULTS: Eighteen studies were included in this review, reporting on 3,605 patients. NMA and pair-wise meta-analysis of the 5-year overall survival did not show significant difference between the three surgical approaches: combined versus colorectal-first, mean odds ratio (OR) 1.02 (95% CI 0.8-1.28, P = 0.93); liver-first versus colorectal-first, mean OR 0.81 (95% CI 0.53-1.26, P = 0.37); liver-first versus combined, mean OR 0.80 (95% CI 0.52-1.24, P = 0.41). In addition NMA of the 30-day mortality among the three approaches also did not observe statistical difference. Analysis of variance showed that mean post-operative complications of all approaches were comparable (P = 0.51). CONCLUSION: There are considerable differences in the peri-operative management of synchronous CLM patients. This meta-analysis demonstrated no clear statistical surgical outcome or survival advantage towards any of the three approaches. J. Surg. Oncol. © 2014 Wiley Periodicals, Inc

Estimating landmarks on 2D images of beetle mandibles

Studying links between phenotype/genotype and agricultural practices is one of the main topics in agronomy research. Phenotypes can be characterized by informations like age, sex of animals/plants and more and more often with the help of image analysis of their morphology. From now, getting good quality of images for numerous individuals is easy but that leads to design automatic procedures to replace manual exploration of such amount of images. Several bottlenecks have been identified to analyze automatically images. One of them is segmentation of selected area and/or shapes, and another well-known one is setting automatically morphometric landmarks. Landmarks are points on the object which can be used to identify or to classify the objects. It exists a lot of methods to experiment landmarks setting, depending on the image contents. This work has been initiated by using the article of Palaniswamy et al. "Automatic identification of landmarks in digital images"[6]. They proposed a method based on calculus of a probabilistic Hough transform coupling to a template matching algorithm. They applied their method to the Drosophilia wings. In our study, we have gotten a set of 291 beetles . For each one 2D images of 5 different parts of their anatomy have been taken: mandibles left and right, head, pronotum and elytra. The first part of the project was to test how the Palaniswamy’s method could be used to analyze them. We have implemented all the required algorithms to compute positions of mandibles landmarks and compared the obtained results to landmarks which have been manually set by biologists. We will see that even positions automatically obtained are not fully precised, if we used centroid size to characterize mandibles, the size computed from automatic landmarks is closed to this one computed from the manual ones. Future works will focus on definition of a semi-landmarks procedure which would add some features as the measure of the curve between two landmarks

Exposing errors related to weak memory in GPU applications

© 2016 ACM.We present the systematic design of a testing environment that uses stressing and fuzzing to reveal errors in GPU applications that arise due to weak memory effects. We evaluate our approach on seven GPUS spanning three NVIDIA architectures, across ten CUDA applications that use fine-grained concurrency. Our results show that applications that rarely or never exhibit errors related to weak memory when executed natively can readily exhibit these errors when executed in our testing environment. Our testing environment also provides a means to help identify the root causes of such errors, and automatically suggests how to insert fences that harden an application against weak memory bugs. To understand the cost of GPU fences, we benchmark applications with fences provided by the hardening strategy as well as a more conservative, sound fencing strategy