Post-Lie Algebras, Factorization Theorems and Isospectral-Flows

In these notes we review and further explore the Lie enveloping algebra of a post-Lie algebra. From a Hopf algebra point of view, one of the central results, which will be recalled in detail, is the existence of a second Hopf algebra structure. By comparing group-like elements in suitable completions of these two Hopf algebras, we derive a particular map which we dub post-Lie Magnus expansion. These results are then considered in the case of Semenov-Tian-Shansky's double Lie algebra, where a post-Lie algebra is defined in terms of solutions of modified classical Yang-Baxter equation. In this context, we prove a factorization theorem for group-like elements. An explicit exponential solution of the corresponding Lie bracket flow is presented, which is based on the aforementioned post-Lie Magnus expansion.Comment: 49 pages, no-figures, review articl

Predicting protein linkages in bacteria: Which method is best depends on task

<p>Abstract</p> <p>Background</p> <p>Applications of computational methods for predicting protein functional linkages are increasing. In recent years, several bacteria-specific methods for predicting linkages have been developed. The four major genomic context methods are: Gene cluster, Gene neighbor, Rosetta Stone, and Phylogenetic profiles. These methods have been shown to be powerful tools and this paper provides guidelines for when each method is appropriate by exploring different features of each method and potential improvements offered by their combination. We also review many previous treatments of these prediction methods, use the latest available annotations, and offer a number of new observations.</p> <p>Results</p> <p>Using <it>Escherichia coli </it>K12 and <it>Bacillus subtilis</it>, linkage predictions made by each of these methods were evaluated against three benchmarks: functional categories defined by COG and KEGG, known pathways listed in EcoCyc, and known operons listed in RegulonDB. Each evaluated method had strengths and weaknesses, with no one method dominating all aspects of predictive ability studied. For functional categories, as previous studies have shown, the Rosetta Stone method was individually best at detecting linkages and predicting functions among proteins with shared KEGG categories while the Phylogenetic profile method was best for linkage detection and function prediction among proteins with common COG functions. Differences in performance under COG versus KEGG may be attributable to the presence of paralogs. Better function prediction was observed when using a weighted combination of linkages based on reliability versus using a simple unweighted union of the linkage sets. For pathway reconstruction, 99 complete metabolic pathways in <it>E. coli </it>K12 (out of the 209 known, non-trivial pathways) and 193 pathways with 50% of their proteins were covered by linkages from at least one method. Gene neighbor was most effective individually on pathway reconstruction, with 48 complete pathways reconstructed. For operon prediction, Gene cluster predicted completely 59% of the known operons in <it>E. coli </it>K12 and 88% (333/418)in <it>B. subtilis</it>. Comparing two versions of the <it>E. coli </it>K12 operon database, many of the unannotated predictions in the earlier version were updated to true predictions in the later version. Using only linkages found by both Gene Cluster and Gene Neighbor improved the precision of operon predictions. Additionally, as previous studies have shown, combining features based on intergenic region and protein function improved the specificity of operon prediction.</p> <p>Conclusion</p> <p>A common problem for computational methods is the generation of a large number of false positives that might be caused by an incomplete source of validation. By comparing two versions of a database, we demonstrated the dramatic differences on reported results. We used several benchmarks on which we have shown the comparative effectiveness of each prediction method, as well as provided guidelines as to which method is most appropriate for a given prediction task.</p

Room temperature magnetic phase transition in an electrically-tuned van der Waals ferromagnet

Finding tunable van der Waals (vdW) ferromagnets that operate at above room temperature is an important research focus in physics and materials science. Most vdW magnets are only intrinsically magnetic far below room temperature and magnetism with square-shaped hysteresis at room-temperature has yet to be observed. Here, we report magnetism in a quasi-2D magnet Cr1.2Te2 observed at room temperature (290 K). This magnetism was tuned via a protonic gate with an electron doping concentration up to 3.8 * 10^21 cm^-3. We observed non-monotonic evolutions in both coercivity and anomalous Hall resistivity. Under increased electron doping, the coercivities and anomalous Hall effects (AHEs) vanished, indicating a doping-induced magnetic phase transition. This occurred up to room temperature. DFT calculations showed the formation of an antiferromagnetic (AFM) phase caused by the intercalation of protons which induced significant electron doping in the Cr1.2Te2. The tunability of the magnetic properties and phase in room temperature magnetic vdW Cr1.2Te2 is a significant step towards practical spintronic devices.Comment: 18 pages, 4 figure

Young Adults With Anterior Ischemic Optic Neuropathy: A Multicenter Optic Disc Drusen Study.

PURPOSE: Optic disc drusen (ODD), present in 2% of the general population, have occasionally been reported in patients with nonarteritic anterior ischemic optic neuropathy (NA-AION). The purpose of this study was to examine the prevalence of ODD in young patients with NA-AION. DESIGN: Retrospective, cross-sectional multicenter study. METHODS: All patients with NA-AION 50 years old or younger, seen in neuro-ophthalmology clinics of the international ODDS (Optic Disc Drusen Studies) Consortium between April 1, 2017, and March 31, 2019, were identified. Patients were included if ODD were diagnosed by any method, or if ODD were excluded by enhanced-depth imaging optical coherence tomography (EDI-OCT) using ODDS Consortium guidelines. NA-AION eyes with ODD were termed "ODD-AION"; those without were termed "NODD-AION". RESULTS: A total of 65 patients (127 eyes) with NA-AION were included (mean 41 years old). Of the 74 eyes with NA-AION, 51% had ODD-AION, whereas 43% of fellow eyes without NA-AION had ODD (P = .36). No significant differences were found between ODD-AION and NODD-AION eyes in terms of Snellen best-corrected VA or perimetric mean deviation. According to EDI-OCT results, 28% of eyes with NODD-AION had peripapillary hyperreflective ovoid mass-like structures (PHOMS); 7% had hyperreflective lines, whereas 54% with ODD-AION had PHOMS; and 66% had hyperreflective lines (P = .006 and P < .001, respectively). CONCLUSIONS: Most of these young NA-AION patients had ODD. This indicates that ODD may be an independent risk factor for the development of NA-AION, at least in younger patients. This study suggests ODD-AION be recognized as a novel diagnosis

On the analysis of the contact angle for impacting droplets using a polynomial fitting approach

ractical considerations on the measurement of the dynamic contact angle and the spreading diameter of impacting droplets are discussed in this paper. The contact angle of a liquid is commonly obtained either by a polynomial or a linear fitting to the droplet profile around the triple phase point. Previous works have focused on quasi-static or sessile droplets, or in cases where inertia does not play a major role on the contact angle dynamics. Here, we study the effect of droplet shape, the order of the fitting polynomial, and the fitting domain, on the measurement of the contact angle on various stages following droplet impact where the contact line is moving. Our results, presented in terms of the optical resolution and the droplet size, show that a quadratic fitting provides the most consistent results for a range of various droplet shapes. As expected, our results show that contact angle values are less sensitive to the fitting conditions for the cases where the droplet can be approximated to a spherical cap. Our experimental conditions include impact events with liquid droplets of different sizes and viscosities on various substrates. In addition, validating past works, our results show that the maximum spreading diameter can be parameterised by the Weber number and the rapidly advancing contact angle

Adsorption of choline benzoate ionic liquid on graphene, silicene, germanene and boron-nitride nanosheets: a DFT perspective

The adsorption of choline benzoate ([CH][BE]) ionic liquid (IL) on the surface of different hexagonal nanosheets has been studied using Density Functional Theory (DFT) methods. For this, the interaction mechanism, binding energies and electronic structure of [CH][BE] ionic liquid on four types of nanosheets, i.e., graphene, silicene, germanene and boron-nitride, were estimated and compared. The adsorption of [CH][BE] ionic liquid on different nanosheets is mainly featured by van der Waals forces, leading to strong benzoate ion–surface π-stacking. Likewise, there is also an important charge transfer from the anion to the sheet. The electronic structure analysis shows that Si- and Ge-based sheets lead to the largest changes in the HOMO and LUMO levels of choline benzoate. This paper provides new insights into the capability of DFT methods to provide useful information about the adsorption of ionic liquids on nanosheets and how ionic liquid features could be tuned through the adsorption on the suitable nanosheet.Ministerio de Economı´a y Competitividad (Spain, project CTQ2013-40476-R) and Junta de Castilla y León (Spain, project BU324U14)

A scattering and repulsive swarm intelligence algorithm for solving global optimization problems

The firefly algorithm (FA), as a metaheuristic search method, is useful for solving diverse optimization problems. However, it is challenging to use FA in tackling high dimensional optimization problems, and the random movement of FA has a high likelihood to be trapped in local optima. In this research, we propose three improved algorithms, i.e., Repulsive Firefly Algorithm (RFA), Scattering Repulsive Firefly Algorithm (SRFA), and Enhanced SRFA (ESRFA), to mitigate the premature convergence problem of the original FA model. RFA adopts a repulsive force strategy to accelerate fireflies (i.e. solutions) to move away from unpromising search regions, in order to reach global optimality in fewer iterations. SRFA employs a scattering mechanism along with the repulsive force strategy to divert weak neighbouring solutions to new search regions, in order to increase global exploration. Motivated by the survival tactics of hawk-moths, ESRFA incorporates a hovering-driven attractiveness operation, an exploration-driven evading mechanism, and a learning scheme based on the historical best experience in the neighbourhood to further enhance SRFA. Standard and CEC2014 benchmark optimization functions are used for evaluation of the proposed FA-based models. The empirical results indicate that ESRFA, SRFA and RFA significantly outperform the original FA model, a number of state-of-the-art FA variants, and other swarm-based algorithms, which include Simulated Annealing, Cuckoo Search, Particle Swarm, Bat Swarm, Dragonfly, and Ant-Lion Optimization, in diverse challenging benchmark functions

Stratification of co-evolving genomic groups using ranked phylogenetic profiles

<p>Abstract</p> <p>Background</p> <p>Previous methods of detecting the taxonomic origins of arbitrary sequence collections, with a significant impact to genome analysis and in particular metagenomics, have primarily focused on compositional features of genomes. The evolutionary patterns of phylogenetic distribution of genes or proteins, represented by phylogenetic profiles, provide an alternative approach for the detection of taxonomic origins, but typically suffer from low accuracy. Herein, we present <it>rank-BLAST</it>, a novel approach for the assignment of protein sequences into genomic groups of the same taxonomic origin, based on the ranking order of phylogenetic profiles of target genes or proteins across the reference database.</p> <p>Results</p> <p>The rank-BLAST approach is validated by computing the phylogenetic profiles of all sequences for five distinct microbial species of varying degrees of phylogenetic proximity, against a reference database of 243 fully sequenced genomes. The approach - a combination of sequence searches, statistical estimation and clustering - analyses the degree of sequence divergence between sets of protein sequences and allows the classification of protein sequences according to the species of origin with high accuracy, allowing taxonomic classification of 64% of the proteins studied. In most cases, a main cluster is detected, representing the corresponding species. Secondary, functionally distinct and species-specific clusters exhibit different patterns of phylogenetic distribution, thus flagging gene groups of interest. Detailed analyses of such cases are provided as examples.</p> <p>Conclusion</p> <p>Our results indicate that the rank-BLAST approach can capture the taxonomic origins of sequence collections in an accurate and efficient manner. The approach can be useful both for the analysis of genome evolution and the detection of species groups in metagenomics samples.</p

Sprouty4 Is an Endogenous Negative Modulator of TrkA Signaling and Neuronal Differentiation Induced by NGF

The Sprouty (Spry) family of proteins represents endogenous regulators of downstream signaling pathways induced by receptor tyrosine kinases (RTKs). Using real time PCR, we detect a significant increase in the expression of Spry4 mRNA in response to NGF, indicating that Spry4 could modulate intracellular signaling pathways and biological processes induced by NGF and its receptor TrkA. In this work, we demonstrate that overexpression of wild-type Spry4 causes a significant reduction in MAPK and Rac1 activation and neurite outgrowth induced by NGF. At molecular level, our findings indicate that ectopic expression of a mutated form of Spry4 (Y53A), in which a conserved tyrosine residue was replaced, fail to block both TrkA-mediated Erk/MAPK activation and neurite outgrowth induced by NGF, suggesting that an intact tyrosine 53 site is required for the inhibitory effect of Spry4 on NGF signaling. Downregulation of Spry4 using small interference RNA knockdown experiments potentiates PC12 cell differentiation and MAPK activation in response to NGF. Together, these findings establish a new physiological mechanism through which Spry4 regulates neurite outgrowth reducing not only the MAPK pathway but also restricting Rac1 activation in response to NGF

Frequency and severity of myocardial perfusion abnormalities using Tc-99m MIBI SPECT in cardiac syndrome X

BACKGROUND: Cardiac syndrome X is defined by a typical angina pectoris with normal or near normal (stenosis <40%) coronary angiogram with or without electrocardiogram (ECG) change or atypical angina pectoris with normal or near normal coronary angiogram plus a positive none-invasive test (exercise tolerance test or myocardial perfusion scan) with or without ECG change. Studies with myocardial perfusion imaging on this syndrome have indicated some abnormal perfusion scan. We evaluated the role of myocardial perfusion imaging (MPI) and also the severity and extent of perfusion abnormality using Tc-99m MIBI Single Photon Emission Computed Tomography (SPECT) in these patients. METHODS: The study group consisted of 36 patients with cardiac syndrome X. The semiquantitative perfusion analysis was performed using exercise Tc-99m MIBI SPECT. The MPI results were analyzed by the number, location and severity of perfusion defects. RESULTS: Abnormal perfusion defects were detected in 13 (36.10%) cases, while the remaining 23 (63.90%) had normal cardiac imaging. Five of 13 (38.4%) abnormal studies showed multiple perfusion defects. The defects were localized in the apex in 3, apical segments in 4, midventricular segments in 12 and basal segments in 6 cases. Fourteen (56%) of all abnormal segments revealed mild, 7(28%) moderate and 4 (16%) severe reduction of tracer uptake. No fixed defects were identified. The vessel territories were approximately the same in all subjects. The Exercise treadmill test (ETT) was positive in 25(69%) and negative in 11(30%) patients. There was no consistent pattern as related to the extent of MPI defects or exercise test results. CONCLUSION: Our study suggests that multiple perfusion abnormalities with different levels of severity are common in cardiac syndrome X, with more than 30 % of these patients having at least one abnormal perfusion segment. Our findings suggest that in these patients microvascular angina is probably more common than is generally believed