On the molecules of numerical semigroups, Puiseux monoids, and Puiseux algebras

A molecule is a nonzero non-unit element of an integral domain (resp., commutative cancellative monoid) having a unique factorization into irreducibles (resp., atoms). Here we study the molecules of Puiseux monoids as well as the molecules of their corresponding semigroup algebras, which we call Puiseux algebras. We begin by presenting, in the context of numerical semigroups, some results on the possible cardinalities of the sets of molecules and the sets of reducible molecules (i.e., molecules that are not irreducibles/atoms). Then we study the molecules in the more general context of Puiseux monoids. We construct infinitely many non-isomorphic atomic Puiseux monoids all whose molecules are atoms. In addition, we characterize the molecules of Puiseux monoids generated by rationals with prime denominators. Finally, we turn to investigate the molecules of Puiseux algebras. We provide a characterization of the molecules of the Puiseux algebras corresponding to root-closed Puiseux monoids. Then we use such a characterization to find an infinite class of Puiseux algebras with infinitely many non-associated reducible molecules.Comment: 21 pages, 2 figure

Biophysical characterization of the inactivation of E. coli transketolase by aqueous co-solvents

Transketolase (TK) has been previously engineered, using semi-rational directed evolution and substrate walking, to accept increasingly aliphatic, cyclic, and then aromatic substrates. This has ultimately led to the poor water solubility of new substrates, as a potential bottleneck to further exploitation of this enzyme in biocatalysis. Here we used a range of biophysical studies to characterise the response of both E. coli apo- and holo-TK activity and structure to a range of polar organic co-solvents: acetonitrile (AcCN), n-butanol (nBuOH), ethyl acetate (EtOAc), isopropanol (iPrOH), and tetrahydrofuran (THF). The mechanism of enzyme deactivation was found to be predominantly via solvent-induced local unfolding. Holo-TK is thermodynamically more stable than apo-TK and yet for four of the five co-solvents it retained less activity than apo-TK after exposure to organic solvents, indicating that solvent tolerance was not simply correlated to global conformational stability. The co-solvent concentrations required for complete enzyme inactivation was inversely proportional to co-solvent log(P), while the unfolding rate was directly proportional, indicating that the solvents interact with and partially unfold the enzyme through hydrophobic contacts. Small amounts of aggregate formed in some cases, but this was not sufficient to explain the enzyme inactivation. TK was found to be tolerant to 15% (v/v) iPrOH, 10% (v/v) AcCN, or 6% (v/v) nBuOH over 3 h. This work indicates that future attempts to engineer the enzyme to better tolerate co-solvents should focus on increasing the stability of the protein to local unfolding, particularly in and around the cofactor-binding loops

Orientation and symmetries of Alexandrov spaces with applications in positive curvature

We develop two new tools for use in Alexandrov geometry: a theory of ramified orientable double covers and a particularly useful version of the Slice Theorem for actions of compact Lie groups. These tools are applied to the classification of compact, positively curved Alexandrov spaces with maximal symmetry rank.Comment: 34 pages. Simplified proofs throughout and a new proof of the Slice Theorem, correcting omissions in the previous versio

Efectividad de los ejercicios nórdicos sobre la incidencia de lesiones de isquiotibiales en futbolistas profesionales y amateur masculinos entre los 15 y 41 años. Revisión sistemática

Introduction: muscular injuries are the most common among soccer players, being hamstring injury the most frequent. Objective: The aim of this study was to analyze the existing evidence on the effects of Nordic exercises on the incidence of hamstring injuries in professional and amateur male soccer players between 15 and 41 years of age. Methods: A systematic review was carried out following the PRISMA guidelines recommendations, a search was carried out for articles in PubMed, BVS, Cochrane, Web OF Science and SCOPUS, in addition Google Scholar was consulted. The search was performed based on the PICO strategy with the following terms: hamstring muscles, exercise, rehabilitation, therapy, athletic injuries, soccer. Results: a total of 257 articles resulted from the search, 5 of which were included in this study. All studies showed positive effects of Nordic exercises for athletes. Conclusions: Nordic exercises reduced the incidence of hamstring injury in 4 of the studies analyzed, the percentage of compliance with the intervention sessions conditioned the quality of the effects while the moment of application of the intervention (pre- or post-training) had no influence.Introducción: Las lesiones musculares son comunes en futbolistas, siendo la lesión de isquiotibiales la más frecuente. Objetivo: Analizar la evidencia existente sobre los efectos de los ejercicios nórdicos en la incidencia de lesiones de isquiotibiales en jugadores de fútbol profesional y amateur masculinos entre los 15 y 41 años. Materiales y métodos: Se llevó a cabo una revisión sistemática siguiendo las recomendaciones de la declaración PRISMA, realizando la búsqueda de artículos en PubMed, BVS, Cochrane, Web OF Science y SCOPUS, además de consultar Google Scholar. La búsqueda se realizó basada en la estrategia PICO con los siguientes términos: hamstring muscles, exercise, rehabilitation, therapy, athletic injuries, soccer. Resultados: un total de 257 artículos resultaron de la búsqueda, siendo 5 los artículos incluidos en este estudio. Todos los estudios evidenciaron efectos positivos de los ejercicios nórdicos para los deportistas. Conclusiones: los ejercicios nórdicos redujeron la incidencia de lesión de isquiotibiales en 4 de los estudios analizados, el porcentaje de cumplimiento de las sesiones de intervención condicionaron la calidad de los efectos mientras que el momento de aplicación de la intervención (pre- o post-entreno) no influy

Kinematic Clues to Bar Evolution for Galaxies in the Local Universe: Why the Fastest Rotating Bars are Rotating Most Slowly

We have used Spitzer images of a sample of 68 barred spiral galaxies in the local universe to make systematic measurements of bar length and bar strength. We combine these with precise determinations of the corotation radii associated with the bars, taken from our previous study, which used the phase change from radial inflow to radial outflow of gas at corotation, based on high-resolution two-dimensional velocity fields in Hα taken with a Fabry-Pérot spectrometer. After presenting the histograms of the derived bar parameters, we study their dependence on the galaxy morphological type and on the total stellar mass of the host galaxy, and then produce a set of parametric plots. These include the bar pattern speed versus bar length, the pattern speed normalized with the characteristic pattern speed of the outer disk versus the bar strength, and the normalized pattern speed versus R, the ratio of corotation radius to bar length. To provide guidelines for our interpretation, we used recently published simulations, including disk and dark matter halo components. Our most striking conclusion is that bars with values of R < 1.4, previously considered dynamically fast rotators, can be among the slowest rotators both in absolute terms and when their pattern speeds are normalized. The simulations confirm that this is because as the bars are braked, they can grow longer more quickly than the outward drift of the corotation radius. We conclude that dark matter halos have indeed slowed down the rotation of bars on Gyr timescales. © 2017. The American Astronomical Society. All rights reserved.

Phylogeny, biogeography and diversification patterns of side-necked turtles (Testudines: Pleurodira)

Pleurodires or side-necked turtles are today restricted to freshwater environments of South America, Africa– Madagascar and Australia, but in the past they were distributed much more broadly, being found also on Eurasia, India and North America, and marine environments. Two hypotheses were proposed to explain this distribution; in the first, vicariance would have shaped the current geographical distribution and, in the second, extinctions constrained a previously widespread distribution. Here, we aim to reconstruct pleurodiran biogeographic history and diversification patterns based on a new phylogenetic hypothesis recovered from the analysis of the largest morphological dataset yet compiled for the lineage, testing which biogeographical process prevailed during its evolutionary history. The resulting topology generally agrees with previous hypotheses of the group and shows that most diversification shifts were related to the exploration of new niches, e.g. littoral or marine radiations. In addition, as other turtles, pleurodires do not seem to have been much affected by either the Cretaceous– Palaeogene or the Eocene–Oligocene mass extinctions. The biogeographic analyses highlight the predominance of both anagenetic and cladogenetic dispersal events and support the importance of transoceanic dispersals as a more common driver of area changes than previously thought, agreeing with previous studies with other non-turtle lineages.Fil: Ferreira, Gabriel S.. Universidade de Sao Paulo; Brasil. Senckenberg Centre For Human Evolution And Palaeoenvironment; Alemania. Universität Tübingen; AlemaniaFil: Bronzati Filho, Mario. Bayerische Staatssammlung für Paläontologie und Geologie; AlemaniaFil: Langer, Max C.. Universidade de Sao Paulo; BrasilFil: Sterli, Juliana. Museo Paleontológico Egidio Feruglio; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin

Hearing the voices of older adult patients: processes and findings to inform health services research

Background Clinical academic research and service improvement is planned using Patient and Public Involvement and Engagement (PPIE) but older PPIE participants are consulted less often due to the perception that they are vulnerable or hard to engage. Objectives To consult frail older adults about a recently adopted service, discharge to assess (D2A), and to prioritise services improvements and research topics associated with the design and delivery of discharge from hospital. To use successive PPIE processes to enable a permanent PPIE panel to be established. Participants Following guidance from an established hospital PPI panel 27 older adult participants were recruited. Participants from Black, Asian and Minority Ethnic (BAME) communities, affluent and non-affluent areas and varied social circumstances were included. Methods Focus groups and individual interviews were conducted in participants own homes or nearby social venues. Results Priorities for discharge included remaining independent despite often feeling lonely at home; to remain in hospital if needed; and for services to ensure effective communication with families. The main research priority identified was facilitating independence, whilst establishing a permanent PPIE panel involving older adults was viewed favourably. Conclusions Taking a structured approach to PPIE enabled varied older peoples’ voices to express their priorities and concerns into early discharge from hospital, as well as enabling the development of health services research into hospital discharge planning and management. Older people as participants identified research priorities after reflecting on their experiences. Listening and reflection enabled researchers to develop a new “Community PPIE Elders Panel” to create an enduring PPIE infrastructure for frail older housebound people to engage in research design, development and dissemination

Controls on gut phosphatisation : the trilobites from the Weeks Formation Lagerstätte (Cambrian; Utah)

Despite being internal organs, digestive structures are frequently preserved in Cambrian Lagerstätten. However, the reasons for their fossilisation and their biological implications remain to be thoroughly explored. This is particularly true with arthropods--typically the most diverse fossilised organisms in Cambrian ecosystems--where digestive structures represent an as-yet underexploited alternative to appendage morphology for inferences on their biology. Here we describe the phosphatised digestive structures of three trilobite species from the Cambrian Weeks Formation Lagerstätte (Utah). Their exquisite, three-dimensional preservation reveals unique details on trilobite internal anatomy, such as the position of the mouth and the absence of a differentiated crop. In addition, the presence of paired pygidial organs of an unknown function is reported for the first time. This exceptional material enables exploration of the relationships between gut phosphatisation and the biology of organisms. Indeed, soft-tissue preservation is unusual in these fossils as it is restricted to the digestive structures, which indicates that the gut played a central role in its own phosphatisation. We hypothesize that the gut provided a microenvironment where special conditions could develop and harboured a source of phosphorus. The fact that gut phosphatization has almost exclusively been observed in arthropods could be explained by their uncommon ability to store ions (including phosphorous) in their digestive tissues. However, in some specimens from the Weeks Formation, the phosphatisation extends to the entire digestive system, suggesting that trilobites might have had some biological particularities not observed in modern arthropods. We speculate that one of them might have been an increased capacity for ion storage in the gut tissues, related to the moulting of their heavily-mineralised carapace

Formation and Propagation of Matter Wave Soliton Trains

Attraction between atoms in a Bose-Einstein-Condensate renders the condensate unstable to collapse. Confinement in an atom trap, however, can stabilize the condensate for a limited number of atoms, as was observed with 7Li, but beyond this number, the condensate collapses. Attractive condensates constrained to one-dimensional motion are predicted to form stable solitons for which the attractive interactions exactly compensate for the wave packet dispersion. Here we report the formation or bright solitons of 7Li atoms created in a quasi-1D optical trap. The solitons are created from a stable Bose-Einstein condensate by magnetically tuning the interactions from repulsive to attractive. We observe a soliton train, containing many solitons. The solitons are set in motion by offsetting the optical potential and are observed to propagate in the potential for many oscillatory cycles without spreading. Repulsive interactions between neighboring solitons are inferred from their motion

Maximal Spontaneous Photon Emission and Energy Loss from Free Electrons

Free electron radiation such as Cerenkov, Smith--Purcell, and transition radiation can be greatly affected by structured optical environments, as has been demonstrated in a variety of polaritonic, photonic-crystal, and metamaterial systems. However, the amount of radiation that can ultimately be extracted from free electrons near an arbitrary material structure has remained elusive. Here we derive a fundamental upper limit to the spontaneous photon emission and energy loss of free electrons, regardless of geometry, which illuminates the effects of material properties and electron velocities. We obtain experimental evidence for our theory with quantitative measurements of Smith--Purcell radiation. Our framework allows us to make two predictions. One is a new regime of radiation operation---at subwavelength separations, slower (nonrelativistic) electrons can achieve stronger radiation than fast (relativistic) electrons. The second is a divergence of the emission probability in the limit of lossless materials. We further reveal that such divergences can be approached by coupling free electrons to photonic bound states in the continuum (BICs). Our findings suggest that compact and efficient free-electron radiation sources from microwaves to the soft X-ray regime may be achievable without requiring ultrahigh accelerating voltages.Comment: 7 pages, 4 figure