A combinatorial approach to the set-theoretic solutions of the Yang-Baxter equation

A bijective map $r: X^2 \longrightarrow X^2$, where $X = \{x_1, ..., x_n \}$ is a finite set, is called a \emph{set-theoretic solution of the Yang-Baxter equation} (YBE) if the braid relation $r_{12}r_{23}r_{12} = r_{23}r_{12}r_{23}$ holds in $X^3.$ A non-degenerate involutive solution $(X,r)$ satisfying $r(xx)=xx$, for all $x \in X$, is called \emph{square-free solution}. There exist close relations between the square-free set-theoretic solutions of YBE, the semigroups of I-type, the semigroups of skew polynomial type, and the Bieberbach groups, as it was first shown in a joint paper with Michel Van den Bergh. In this paper we continue the study of square-free solutions $(X,r)$ and the associated Yang-Baxter algebraic structures -- the semigroup $S(X,r)$, the group $G(X,r)$ and the $k$- algebra $A(k, X,r)$ over a field $k$, generated by $X$ and with quadratic defining relations naturally arising and uniquely determined by $r$. We study the properties of the associated Yang-Baxter structures and prove a conjecture of the present author that the three notions: a square-free solution of (set-theoretic) YBE, a semigroup of I type, and a semigroup of skew-polynomial type, are equivalent. This implies that the Yang-Baxter algebra $A(k, X,r)$ is Poincar\'{e}-Birkhoff-Witt type algebra, with respect to some appropriate ordering of $X$. We conjecture that every square-free solution of YBE is retractable, in the sense of Etingof-Schedler.Comment: 34 page

Arthroscopic rotator cuff repair with a fibrin scaffold containing growth factors and autologous progenitor cells derived from humeral cBMA improves clinical outcomes in high risk patients

PURPOSE: To report the clinical outcomes after biologically augmented rotator cuff repair (RCR) with a fibrin scaffold derived from autologous whole blood and supplemented with concentrated bone marrow aspirate (cBMA) harvested at the proximal humerus. METHODS: Patients who underwent arthroscopic RCR with biologic augmentation using a fibrin clot scaffold (“Mega- Clot”) containing progenitor cells and growth factors from proximal humerus BMA and autologous whole blood between April 2015 and January 2018 were prospectively followed. Only high-risk patients in primary and revision cases that possessed relevant comorbidities or physically demanding occupation were included. Minimum follow-up for inclusion was 1 year. The visual analog score for pain (VAS), American Shoulder and Elbow Surgeons (ASES), Simple Shoulder Test (SST), Single Assessment Numerical Evaluation (SANE), and Constant-Murley scores were collected preoperatively and at final follow-up. In vitro analyses of the cBMA and fibrin clot using nucleated cell count, colony forming units, and live/dead assays were used to quantify the substrates. RESULTS: Thirteen patients (56.9 ± 7.7 years) were included. The mean follow-up was 26.9 ± 17.7 months (n = 13). There were significant improvements in all outcome scores from the preoperative to the postoperative state: VAS (5.6 ± 2.5 to 3.1 ± 3.2; P < .001), ASES (42.0 ± 17.1 to 65.5 ± 30.6; P < .001), SST (3.2 ± 2.8 to 6.5 ± 4.7; P = .002), SANE (11.5 ± 15.6 to 50.3 ± 36.5; P < .001), and Constant-Murley (38.9 ± 17.5 to 58.1 ± 26.3; P < .001). Six patients (46%) had retears on postoperative MRI, despite all having improvements in pain and function except one. All failures were chronic rotator cuff tears, and all were revision cases except one (1.6 ± 0.5 previous RCRs). The representative sample of harvested cBMA showed an average of 28.5 ± 9.1 × 10(6) nucleated cells per mL. CONCLUSIONS: Arthroscopic rotator cuff repairs that are biologically augmented with a fibrin scaffold containing growth factors and autologous progenitor cells derived from autologous whole blood and humeral cBMA can improve clinical outcomes in primary, as well as revision cases in high-risk patients. However, the incidence of retears remains a concern in this population, demanding further improvements in biologic augmentation. LEVEL OF EVIDENCE: IV, therapeutic case series

SMART-1 Impact Ground-based campaign

Based on predictions of impact magnitude and cloud ejecta dynamics, we organized a SMART-1 ground-based observation campaign to perform coordinated measurements of the impact. Results from the coordinated multi-site campaign will be discussed

Primordial fluctuations and non-Gaussianities from multifield DBI Galileon inflation

We study a cosmological scenario in which the DBI action governing the motion of a D3-brane in a higher-dimensional spacetime is supplemented with an induced gravity term. The latter reduces to the quartic Galileon Lagrangian when the motion of the brane is non-relativistic and we show that it tends to violate the null energy condition and to render cosmological fluctuations ghosts. There nonetheless exists an interesting parameter space in which a stable phase of quasi-exponential expansion can be achieved while the induced gravity leaves non trivial imprints. We derive the exact second-order action governing the dynamics of linear perturbations and we show that it can be simply understood through a bimetric perspective. In the relativistic regime, we also calculate the dominant contribution to the primordial bispectrum and demonstrate that large non-Gaussianities of orthogonal shape can be generated, for the first time in a concrete model. More generally, we find that the sign and the shape of the bispectrum offer powerful diagnostics of the precise strength of the induced gravity.Comment: 34 pages including 9 figures, plus appendices and bibliography. Wordings changed and references added; matches version published in JCA

Determinants of impact : towards a better understanding of encounters with the arts

The article argues that current methods for assessing the impact of the arts are largely based on a fragmented and incomplete understanding of the cognitive, psychological and socio-cultural dynamics that govern the aesthetic experience. It postulates that a better grasp of the interaction between the individual and the work of art is the necessary foundation for a genuine understanding of how the arts can affect people. Through a critique of philosophical and empirical attempts to capture the main features of the aesthetic encounter, the article draws attention to the gaps in our current understanding of the responses to art. It proposes a classification and exploration of the factors—social, cultural and psychological—that contribute to shaping the aesthetic experience, thus determining the possibility of impact. The ‘determinants of impact’ identified are distinguished into three groups: those that are inherent to the individual who interacts with the artwork; those that are inherent to the artwork; and ‘environmental factors’, which are extrinsic to both the individual and the artwork. The article concludes that any meaningful attempt to assess the impact of the arts would need to take these ‘determinants of impact’ into account, in order to capture the multidimensional and subjective nature of the aesthetic experience

PhyloPattern: regular expressions to identify complex patterns in phylogenetic trees

<p>Abstract</p> <p>Background</p> <p>To effectively apply evolutionary concepts in genome-scale studies, large numbers of phylogenetic trees have to be automatically analysed, at a level approaching human expertise. Complex architectures must be recognized within the trees, so that associated information can be extracted.</p> <p>Results</p> <p>Here, we present a new software library, PhyloPattern, for automating tree manipulations and analysis. PhyloPattern includes three main modules, which address essential tasks in high-throughput phylogenetic tree analysis: node annotation, pattern matching, and tree comparison. PhyloPattern thus allows the programmer to focus on: i) the use of predefined or user defined annotation functions to perform immediate or deferred evaluation of node properties, ii) the search for user-defined patterns in large phylogenetic trees, iii) the pairwise comparison of trees by dynamically generating patterns from one tree and applying them to the other.</p> <p>Conclusion</p> <p>PhyloPattern greatly simplifies and accelerates the work of the computer scientist in the evolutionary biology field. The library has been used to automatically identify phylogenetic evidence for domain shuffling or gene loss events in the evolutionary histories of protein sequences. However any workflow that relies on phylogenetic tree analysis, could be automated with PhyloPattern.</p

Unconventional Cosmology

I review two cosmological paradigms which are alternative to the current inflationary scenario. The first alternative is the "matter bounce", a non-singular bouncing cosmology with a matter-dominated phase of contraction. The second is an "emergent" scenario, which can be implemented in the context of "string gas cosmology". I will compare these scenarios with the inflationary one and demonstrate that all three lead to an approximately scale-invariant spectrum of cosmological perturbations.Comment: 45 pages, 10 figures; invited lectures at the 6th Aegean Summer School "Quantum Gravity and Quantum Cosmology", Chora, Naxos, Greece, Sept. 12 - 17 2012, to be publ. in the proceedings; these lecture notes form an updated version of arXiv:1003.1745 and arXiv:1103.227

Release of Histone H3K4-reading transcription factors from chromosomes in mitosis is independent of adjacent H3 phosphorylation

Histone modifications influence the recruitment of reader proteins to chromosomes to regulate events including transcription and cell division. The idea of a histone code, where combinations of modifications specify unique downstream functions, is widely accepted and can be demonstrated in vitro. For example, on synthetic peptides, phosphorylation of Histone H3 at threonine-3 (H3T3ph) prevents the binding of reader proteins that recognize trimethylation of the adjacent lysine-4 (H3K4me3), including the TAF3 component of TFIID. To study these combinatorial effects in cells, we analyzed the genome-wide distribution of H3T3ph and H3K4me2/3 during mitosis. We find that H3T3ph anti-correlates with adjacent H3K4me2/3 in cells, and that the PHD domain of TAF3 can bind H3K4me2/3 in isolated mitotic chromatin despite the presence of H3T3ph. Unlike in vitro, H3K4 readers are still displaced from chromosomes in mitosis in Haspin-depleted cells lacking H3T3ph. H3T3ph is therefore unlikely to be responsible for transcriptional downregulation during cell division.This study was funded by a Wellcome Trust Investigator Award (106951/Z/15/Z) and a Royal Society Wolfson Research Merit Award (WM130089) to J.M.G.H., an EPSRC DTP (Biological Informatics) PhD Studentship to M.H., a Barbour Foundation PhD Studentship to J.L.M., and by a J.G.W. Patterson Foundation grant to L.G.Peer reviewe

The appropriateness of gatekeeping in the provision of reproductive health care for adolescents in Lithuania:the general practice perspective

BACKGROUND: Adolescents' consultation of primary health care services remains problematic despite their accessibility. The reproductive health service seeking behavior of adolescents is the object of much research but little is known about how this behavior is influenced by the gatekeeping system. This study aimed to explore general practitioners' perceptions of the appropriateness of gatekeeping in adolescent reproductive health care. METHODS: Twenty in-depth interviews regarding factors affecting adolescent reproductive health care were carried out on a diverse sample of general practitioners and analyzed using grounded theory. RESULTS: The analysis identified several factors that shaped GPs' negative attitude to gatekeeping in adolescent reproductive health care. Its appropriateness in this field was questionable due to a lack of willingness on the part of GPs to provide reproductive health services for teenagers, their insufficient training, inadequately equipped surgeries and low perceived support for reproductive health service provision. CONCLUSION: Since factors for improving adolescent reproductive health concern not only physicians but also the health system and policy levels, complex measures should be designed to overcome these barriers. Discussion of a flexible model of gatekeeping, encompassing both co-ordination of care provided by GPs and the possibility of patients' self-referral, should be included in the political agenda. Adolescents tend to under-use rather than over-use reproductive health services and every effort should be made to facilitate the accessibility of such services