Separatrix Reconnections in Chaotic Regimes

In this paper we extend the concept of separatrix reconnection into chaotic regimes. We show that even under chaotic conditions one can still understand abrupt jumps of diffusive-like processes in the relevant phase-space in terms of relatively smooth realignments of stable and unstable manifolds of unstable fixed points.Comment: 4 pages, 5 figures, submitted do Phys. Rev. E (1998

Hopf-Galois structures on extensions of degree p2qp^{2} q and skew braces of order p2qp^{2} q: the elementary abelian Sylow pp-subgroup case

Let $p, q$ be distinct primes, with $p > 2$. In a previous paper we classified the Hopf-Galois structures on Galois extensions of degree $p^{2} q$, when the Sylow $p$-subgroups of the Galois group are cyclic. This is equivalent to classifying the skew braces of order $p^2q$, for which the Sylow $p$-subgroups of the multiplicative group is cyclic. In this paper we complete the classification by dealing with the case when the Sylow $p$-subgroups of the Galois group are elementary abelian. According to Greither and Pareigis, and Byott, we will do this by classifying the regular subgroups of the holomorphs of the groups $(G, \cdot)$ of order $p^{2} q$, in the case when the Sylow $p$-subgroups of $G$ are elementary abelian. We rely on the use of certain gamma functions $\gamma:G\to \operatorname{Aut}(G)$. These functions are in one-to-one correspondence with the regular subgroups of the holomorph of $G$, and are characterised by the functional equation $\gamma(g^{\gamma(h)} \cdot h) = \gamma(g) \gamma(h)$, for $g, h \in G$. We develop methods to deal with these functions, with the aim of making their enumeration easier and more conceptual.Comment: 95 page

Hopf-Galois structures on extensions of degree p2qp^{2} q and skew braces of order p2qp^{2} q: the cyclic Sylow pp-subgroup case

\DeclareMathOperator{\Aut}{Aut}Let $p, q$ be distinct primes, with $p > 2$. We classify the Hopf-Galois structures on Galois extensions of degree $p^{2} q$, such that the Sylow $p$-subgroups of the Galois group are cyclic. This we do, according to Greither and Pareigis, and Byott, by classifying the regular subgroups of the holomorphs of the groups $(G, \cdot)$ of order $p^{2} q$, in the case when the Sylow $p$-subgroups of $G$ are cyclic. This is equivalent to classifying the skew braces $(G, \cdot, \circ)$. Furthermore, we prove that if $G$ and $\Gamma$ are groups of order $p^{2} q$ with non-isomorphic Sylow $p$-subgroups, then there are no regular subgroups of the holomorph of $G$ which are isomorphic to $\Gamma$. Equivalently, a Galois extension with Galois group $\Gamma$ has no Hopf-Galois structures of type $G$. Our method relies on the alternate brace operation $\circ$ on $G$, which we use mainly indirectly, that is, in terms of the functions \gamma : G \to \Aut(G) defined by $g \mapsto (x \mapsto (x \circ g) \cdot g^{-1})$. These functions are in one-to-one correspondence with the regular subgroups of the holomorph of $G$, and are characterised by the functional equation $\gamma(g^{\gamma(h)} \cdot h) = \gamma(g) \gamma(h)$, for $g, h \in G$. We develop methods to deal with these functions, with the aim of making their enumeration easier, and more conceptual.Comment: 43 page

Hough Transform Proposal and Simulations for Particle Track Recognition for LHC Phase-II Upgrade

In the near future, LHC experiments will continue future upgrades by overcoming the technological obsolescence of the detectors and the readout capabilities. Therefore, after the conclusion of a data collection period, CERN will have to face a long shutdown to improve overall performance, by updating the experiments, and implementing more advanced technologies and infrastructures. In particular, the largest LHC experiment, i.e., ATLAS, will upgrade parts of the detector, the trigger, and the data acquisition system. In addition, the ATLAS experiment will complete the implementation of new strategies, algorithms for data handling, and transmission to the final storage apparatus. This paper presents an overview of an upgrade planned for the second half of this decade for the ATLAS experiment. In particular, we show a study of a novel pattern recognition algorithm used in the trigger system, which is a device designed to provide the information needed to select physical events from unnecessary background data. The idea is to use a well known mathematical transform, the Hough transform, as the algorithm for the detection of particle trajectories. The effectiveness of the algorithm has already been validated in the past, regardless of particle physics applications, to recognize generic shapes within images. On the contrary, here, we first propose a software emulation tool, and a subsequent hardware implementation of the Hough transform, for particle physics applications. Until now, the Hough transform has never been implemented on electronics in particle physics experiments, and since a hardware implementation would provide benefits in terms of overall Latency, we complete the studies by comparing the simulated data with a physical system implemented on a Xilinx hardware accelerator (FELIX-II card). In more detail, we have implemented a low-abstraction RTL design of the Hough transform on Xilinx UltraScale+ FPGAs as target devices for filtering applications

In Search of Differential Inhibitors of Aldose Reductase

Aldose reductase, classified within the aldo-keto reductase family as AKR1B1, is an NADPH dependent enzyme that catalyzes the reduction of hydrophilic as well as hydrophobic aldehydes. AKR1B1 is the first enzyme of the so-called polyol pathway that allows the conversion of glucose into sorbitol, which in turn is oxidized to fructose by sorbitol dehydrogenase. The activation of the polyol pathway in hyperglycemic conditions is generally accepted as the event that is responsible for a series of long-term complications of diabetes such as retinopathy, cataract, nephropathy and neuropathy. The role of AKR1B1 in the onset of diabetic complications has made this enzyme the target for the development of molecules capable of inhibiting its activity. Virtually all synthesized compounds have so far failed as drugs for the treatment of diabetic complications. This failure may be partly due to the ability of AKR1B1 to reduce alkenals and alkanals, produced in oxidative stress conditions, thus acting as a detoxifying agent. In recent years we have proposed an alternative approach to the inhibition of AKR1B1, suggesting the possibility of a differential inhibition of the enzyme through molecules able to preferentially inhibit the reduction of either hydrophilic or hydrophobic substrates. The rationale and examples of this new generation of aldose reductase differential inhibitors (ARDIs) are presented

Gershgorin disks for multiple eigenvalues of non-negative matrices

Gershgorin's famous circle theorem states that all eigenvalues of a square matrix lie in disks (called Gershgorin disks) around the diagonal elements. Here we show that if the matrix entries are non-negative and an eigenvalue has geometric multiplicity at least two, then this eigenvalue lies in a smaller disk. The proof uses geometric rearrangement inequalities on sums of higher dimensional real vectors which is another new result of this paper

Pathways of 4-hydroxy-2-nonenal detoxification in a human astrocytoma cell line

One of the consequences of the increased level of oxidative stress that often characterizes the cancer cell environment is the abnormal generation of lipid peroxidation products, above all 4-hydroxynonenal. The contribution of this aldehyde to the pathogenesis of several diseases is well known. In this study, we characterized the ADF astrocytoma cell line both in terms of its pattern of enzymatic activities devoted to 4-hydroxynonenal removal and its resistance to oxidative stress induced by exposure to hydrogen peroxide. A comparison with lens cell lines, which, due to the ocular function, are normally exposed to oxidative conditions is reported. Our results show that, overall, ADF cells counteract oxidative stress conditions better than normal cells, thus confirming the redox adaptation demonstrated for several cancer cells. In addition, the markedly high level of NADP+-dependent dehydrogenase activity acting on the glutahionyl-hydroxynonanal adduct detected in ADF cells may promote, at the same time, the detoxification and recovery of cell-reducing power in these cells

Rupture Of Abdominal Aortic Aneurysm Due To Endograft Infection After Endovascular Aneurysm Repair (EVAR): A Case Report

Endograft infection is a rare event, with few reports in the literature. This report describes delayed infection of an aortic endoprosthesis that eventually resulted in abdominal aortic aneurysm (AAA) rupture. The procedure was performed in an angiographic suite. In the postoperative period the patient developed a central venous line infection. This appears to be the first recognized and reported case in which the infected aortic neck completely dilated due to the radial force of the stent graft

Flight Performance of the Inflatable Reentry Vehicle Experiment II

The Inflatable Reentry Vehicle Experiment II launched August 17, 2009, from NASA Wallops Flight Facility. The three mission objectives were to demonstrate inflation and re-entry survivability, assess the thermal and drag performance of the reentry vehicle, and to collect flight data for comparison with analysis and design techniques used in vehicle development. The flight was a complete success, with the re-entry vehicle separating cleanly from the launcher, inflating as planned, and demonstrating stable flight through reentry and descent while on-board systems telemetered video and flight performance data to the ground