11 research outputs found
Elastic Sturmian spirals in the Lorentz-Minkowski plane
No full textMladenov, Ivailo M./0000-0001-5577-5741In this paper we consider some elastic spacelike and timelike curves in the Lorentz-Minkowski plane and obtain the respective vectorial equations of their position vectors in explicit analytical form. We study in more details the generalized Sturmian spirals in the Lorentz-Minkowski plane which simultaneously are elastics in this space.TUBITAKTurkiye Bilimsel ve Teknolojik Arastirma Kurumu (TUBITAK); TUBITAK (The Scientific and Technological Research Council of Turkey)Turkiye Bilimsel ve Teknolojik Arastirma Kurumu (TUBITAK) [2221]The first author would like to thank TUBITAK for the financial support during his PhD study. The third named author is partially supported by TUBITAK (The Scientific and Technological Research Council of Turkey) within the frame of Programme 2221
Erratum: Truncating Mutations in UBAP1 Cause Hereditary Spastic Paraplegia (The American Journal of Human Genetics (2019) 104(4) (767–773), (S0002929719300977), (10.1016/j.ajhg.2019.03.001))
No full text(The American Journal of Human Genetics 104, 767–773; April 4, 2019) In the originally published version of this article, authors Ivailo Tournev and Teodora Chamova were mistakenly omitted from the author list. Their names have been added here. The online version of the full article now appears correctly and includes affiliations for the added authors as well as corrections to some of the other affiliations. The authors regret these omissions
-products and selections of set-valued mappings
No full textsummary:Every lower semi-continuous closed-and-convex valued mapping , where is a -product of metrizable spaces and is a Hilbert space, has a single-valued continuous selection. This improves an earlier result of the author
Refined universality for critical KCM: upper bounds
Full text linkWe study a general class of interacting particle systems called kinetically constrained models (KCM) in two dimensions. They are tightly linked to the monotone cellular automata called bootstrap percolation. Among the three classes of such models, the critical ones are the most studied.
Together with the companion paper by Marêché and the author, our work determines the logarithm of the infection time up to a constant factor for all critical KCM. This was previously known only up to logarithmic corrections. We establish that on this level of precision critical KCM have to be classified into seven categories. This refines the two classes present in bootstrap percolation and the two in previous rougher results. In the present work we establish the upper bounds for the novel five categories and thus complete the universality program for equilibrium critical KCM. Our main innovations are the identification of the dominant relaxation mechanisms and a more sophisticated and robust version of techniques recently developed for the study of the Fredrickson-Andersen 2-spin facilitated model.100 pages, including 3 online-only appendices, 10 figures; comprehensive summary of mechanisms in section 2; changes: none (updated creative commons license
Sharp metastability transition for two-dimensional bootstrap percolation with symmetric isotropic threshold rules
No full textWe study two-dimensional critical bootstrap percolation models. We establish that a class of these models including all isotropic threshold rules with a convex symmetric neighbourhood, undergoes a sharp metastability transition. This extends previous instances proved for several specific rules. The paper supersedes a draft by Alexander Holroyd and the first author from 2012. While it served a role in the subsequent development of bootstrap percolation universality, we have chosen to adopt a more contemporary viewpoint in its present form.37 pages, 6 figures, improved presentation, added section
Universality for critical kinetically constrained models: infinite number of stable directions
No full text31 pages, 6 figuresKinetically constrained models (KCM) are reversible interacting particle systems on with continuous-time constrained Glauber dynamics. They are a natural non-monotone stochastic version of the family of cellular automata with random initial state known as -bootstrap percolation. KCM have an interest in their own right, owing to their use for modelling the liquid-glass transition in condensed matter physics. In two dimensions there are three classes of models with qualitatively different scaling of the infection time of the origin as the density of infected sites vanishes. Here we study in full generality the class termed `critical'. Together with the companion paper by Martinelli and two of the authors we establish the universality classes of critical KCM and determine within each class the critical exponent of the infection time as well as of the spectral gap. In this work we prove that for critical models with an infinite number of stable directions this exponent is twice the one of their bootstrap percolation counterpart. This is due to the occurrence of `energy barriers', which determine the dominant behaviour for these KCM but which do not matter for the monotone bootstrap dynamics. Our result confirms the conjecture of Martinelli, Morris and the last author, who proved a matching upper bound
Excisional hip arthroplasty (case reports)
Full text linkIntroduction: Excisional hip arthroplasty, or femoral head ostectomy, was first described by the English orthopedist Gathorne Girdlestone in 1928 and bears his name. The procedure involves removing the head and neck of the femur. Nowadays, a rather extended variant is usually performed, since, in addition to the classical removal of the head and neck, resection, fenestration, sequestrectomy in the proximal part of the femur is often required. In such cases, it is more correct to speak of a suspended hip joint. Surgery is used as a last resort and often a life-saving procedure in cases of severe, including periprosthetic, infections in the hip joint area.Aim: An attempt is made to answer the question: Does Girdlestone surgery (suspended hip joint) have a place in the modern treatment of severe infections, including periprosthetic ones in the area of the hip joint?Patients and Methods: Four patients are presented—3 women and 1 man, aged 45 to 74 years.Result: A meticulously performed debridement, including excision of the contaminated soft tissues and bony areas, with a removal of the existing endoprosthesis, combined with a closed permanent irrigation system, proved to be the only effective and life-saving procedure for the presented patients.Conclusion: Despite the listed disadvantages, the Girdlestone operation (suspended hip joint), in which the contaminated tissues and all foreign bodies are removed, often combined with a closed permanent irrigation system, has not lost its relevance, since in most cases it leads to complete sanitation of infection, is often a life-saving procedure or an important stage for subsequent repeat endoprosthetics
Catalan percolation
Full text linkIn Catalan percolation, all nearest-neighbor edges along are initially occupied, and all other edges are open independently with
probability . Open edges are occupied if some pair of edges
and , with , become occupied. This model was
introduced by Gravner and the third author, in the context of polluted graph
bootstrap percolation.
We prove that the critical is strictly between that of
oriented site percolation on and the Catalan growth rate .
Our main result shows that an enhanced oriented percolation model, with
non-decaying infinite-range dependency, has a strictly smaller critical
parameter than the classical model. This is reminiscent of the work of
Duminil-Copin, Hil\'ario, Kozma and Sidoravicius on brochette percolation. Our
proof differs, however, in that we do not use Aizenman--Grimmett enhancements
or differential inequalities. Two key ingredients are the work of Hil\'ario,
S\'a, Sanchis and Teixeira on stretched lattices, and the Russo--Seymour--Welsh
result for oriented percolation by Duminil-Copin, Tassion and Teixeira.Comment: 29 pages, 11 figure
Regulation of DNA replication and chromosomal polyploidy by the MLL-WDR5-RBBP5 methyltransferases
No full textDNA replication licensing occurs on chromatin, but how the chromatin template is regulated for replication remains mostly unclear. Here, we have analyzed the requirement of histone methyltransferases for a specific type of replication: the DNA re-replication induced by the downregulation of either Geminin, an inhibitor of replication licensing protein CDT1, or the CRL4CDT2 ubiquitin E3 ligase. We found that siRNA-mediated reduction of essential components of the MLL-WDR5-RBBP5 methyltransferase complexes including WDR5 or RBBP5, which transfer methyl groups to histone H3 at K4 (H3K4), suppressed DNA re-replication and chromosomal polyploidy. Reduction of WDR5/RBBP5 also prevented the activation of H2AX checkpoint caused by re-replication, but not by ultraviolet or X-ray irradiation; and the components of MLL complexes co-localized with the origin recognition complex (ORC) and MCM2-7 replicative helicase complexes at replication origins to control the levels of methylated H3K4. Downregulation of WDR5 or RBBP5 reduced the methylated H3K4 and suppressed the recruitment of MCM2-7 complexes onto replication origins. Our studies indicate that the MLL complexes and H3K4 methylation are required for DNA replication but not for DNA damage repair
Correction to: Eight years after an international workshop on myotonic dystrophy patient registries: case study of a global collaboration for a rare disease
No full textThe original version of this article [1] unfortunately included an error to an author’s name. Author Jordi Díaz-Manera was erroneously presented as Jorge Alberto Diaz Manera. The correct author name has been included in the author list of this Correction article
