Knots in the Canonical Book Representation of Complete Graphs

We describe which knots can be obtained as cycles in the canonical book representation of the complete graph Kn, and we conjecture that the canonical book representation of Kn attains the least possible number of knotted cycles for any embedding of Kn. The canonical book representation of Kn contains a Hamiltonian cycle that is a composite knot if and only if n ≥12. When p and q are relatively prime, the (p, q) torus knot is a Hamiltonian cycle in the canonical book representation of K2p+q. For each knotted Hamiltonian cycle in the canonical book representation of Kn, there are at least 2k(n+kk) Hamiltonian cycles that are ambient isotopic to α in the canonical book representation of Kn+k . Finally, we list the number and type of all nontrivial knots that occur as cycles in the canonical book representation of Kn for n ≤ 11

Knots in the canonical book representation of complete graphs

We describe which knots can be obtained as cycles in the canonical book representation of K_n, the complete graph on n vertices. We show that the canonical book representation of K_n contains a Hamiltonian cycle that is a composite knot if and only if n>11 and we show that when p and q are relatively prime, the (p,q) torus knot is a Hamiltonian cycle in the canonical book representation of K_{2p+q}. Finally, we list the number and type of all non-trivial knots that occur as cycles in the canonical book representation of K_n for n<12. We conjecture that the canonical book representation of K_n attains the least possible number of knotted cycles for any embedding of K_n.Comment: 17 pages, 9 figure

Heart transplantation in patients with dystrophinopathic cardiomyopathy: Review of the literature and personal series

Cardiomyopathy associated with dystrophinopathies [Duchenne muscular dystrophy (DMD), Becker muscular dystrophy (BMD), X-linked dilated cardiomyopathy (XL-dCM) and cardiomyopathy of Duchenne/Becker (DMD/BMD) carriers] is an increasing recognized manifestation of these neuromuscular disorders and notably contributes to their morbidity and mortality. Dystrophinopathic cardiomyopathy (DCM) is the result of the dystrophin protein deficiency at the myocardium level, parallel to the deficiency occurring at the skeletal muscle level. It begins as a "presymptomatic" stage in the first decade of life and evolves in a stepwise manner toward pictures of overt cardiomyopathy (hypertrophic stage, arrhythmogenic stage and dilated cardiomyopathy). The final stage caused by the extensive loss of cardiomyocytes results in an irreversible cardiac failure, characterized by frequent episodes of acute congestive heart failure (CHF), despite a correct pharmacological treatment. The picture of a severe dilated cardiomyopathy with intractable heart failure is typical of BMD, XL-dCM and cardiomyopathy of DMD/BMD carriers, while it is less frequently observed in patients with DMD. Heart transplantation (HT) is the only curative therapy for patients with dystrophinopathic end-stage heart failure who remain symptomatic despite an optimal medical therapy. However, no definitive figures exist in literature concerning the number of patients with DCM transplanted, and their outcome. This overview is to summarize the clinical outcomes so far published on the topic, to report the personal series of dystrophinopathic patients receiving heart transplantation and finally to provide evidence that heart transplantation is a safe and effective treatment for selected patients with end-stage DCM

Genetic Modifiers of Duchenne Muscular Dystrophy and Dilated Cardiomyopathy.

OBJECTIVE: Dilated cardiomyopathy (DCM) is a major complication and leading cause of death in Duchenne muscular dystrophy (DMD). DCM onset is variable, suggesting modifier effects of genetic or environmental factors. We aimed to determine if polymorphisms previously associated with age at loss of independent ambulation (LoA) in DMD (rs28357094 in the SPP1 promoter, rs10880 and the VTTT/IAAM haplotype in LTBP4) also modify DCM onset. METHODS: A multicentric cohort of 178 DMD patients was genotyped by TaqMan assays. We performed a time-to-event analysis of DCM onset, with age as time variable, and finding of left ventricular ejection fraction \u3c 50% and/or end diastolic volume \u3e 70 mL/m2 as event (confirmed by a previous normal exam \u3c 12 months prior); DCM-free patients were censored at the age of last echocardiographic follow-up. RESULTS: Patients were followed up to an average age of 15.9 ± 6.7 years. Seventy-one/178 patients developed DCM, and median age at onset was 20.0 years. Glucocorticoid corticosteroid treatment (n = 88 untreated; n = 75 treated; n = 15 unknown) did not have a significant independent effect on DCM onset. Cardiological medications were not administered before DCM onset in this population. We observed trends towards a protective effect of the dominant G allele at SPP1 rs28357094 and recessive T allele at LTBP4 rs10880, which was statistically significant in steroid-treated patients for LTBP4 rs10880 (\u3c 50% T/T patients developing DCM during follow-up [n = 13]; median DCM onset 17.6 years for C/C-C/T, log-rank p = 0.027). CONCLUSIONS: We report a putative protective effect of DMD genetic modifiers on the development of cardiac complications, that might aid in risk stratification if confirmed in independent cohorts

Core Competencies in Civic Engagement

A review and synthesis of key competencies contained in national-level reports on Civic Engagement, academic programs engaged in community-based models of teaching, learning and research, including a review of the literature and almost 30 academic civic engagement programs around the country

Genetic modifiers of Duchenne muscular dystrophy and dilated cardiomyopathy

OBJECTIVE: Dilated cardiomyopathy (DCM) is a major complication and leading cause of death in Duchenne muscular dystrophy (DMD). DCM onset is variable, suggesting modifier effects of genetic or environmental factors. We aimed to determine if polymorphisms previously associated with age at loss of independent ambulation (LoA) in DMD (rs28357094 in the SPP1 promoter, rs10880 and the VTTT/IAAM haplotype in LTBP4) also modify DCM onset. METHODS: A multicentric cohort of 178 DMD patients was genotyped by TaqMan assays. We performed a time-to-event analysis of DCM onset, with age as time variable, and finding of left ventricular ejection fraction 70 mL/m2 as event (confirmed by a previous normal exam < 12 months prior); DCM-free patients were censored at the age of last echocardiographic follow-up. RESULTS: Patients were followed up to an average age of 15.9 \ub1 6.7 years. Seventy-one/178 patients developed DCM, and median age at onset was 20.0 years. Glucocorticoid corticosteroid treatment (n = 88 untreated; n = 75 treated; n = 15 unknown) did not have a significant independent effect on DCM onset. Cardiological medications were not administered before DCM onset in this population. We observed trends towards a protective effect of the dominant G allele at SPP1 rs28357094 and recessive T allele at LTBP4 rs10880, which was statistically significant in steroid-treated patients for LTBP4 rs10880 (< 50% T/T patients developing DCM during follow-up [n = 13]; median DCM onset 17.6 years for C/C-C/T, log-rank p = 0.027). CONCLUSIONS: We report a putative protective effect of DMD genetic modifiers on the development of cardiac complications, that might aid in risk stratification if confirmed in independent cohorts

Mechanical exfoliation and layer number identification of single crystal monoclinic CrCl3

After the recent finding that CrI3, displays ferromagnetic order down to its monolayer, extensive studies have followed to pursue new two-dimensional (2D) magnetic materials. In this article, we report on the growth of single crystal CrCl3 in the layered monoclinic phase. The system after mechanical exfoliation exhibits stability in ambient air (the degradation occurs on a time scale at least four orders of magnitude longer than is observed for CrI3). By means of mechanical cleavage and atomic force microscopy (AFM) combined with optical identification, we demonstrate the systematic isolation of single and few layer flakes onto 270 nm and 285 nm SiO2/Si~(100) substrates with lateral size larger than graphene flakes isolated with the same method. The layer number identification has been carried with statistically significant data, quantifying the optical contrast as a function of the number of layers for up to six layers. Layer dependent optical contrast data have been fitted within the Fresnel equation formalism determining the real and imaginary part of the wavelength dependent refractive index of the material. A layer dependent (532 nm) micro-Raman study has been carried out down to two layers with no detectable spectral shifts as a function of the layer number and with respect to the bulk

Benefits of glucocorticoids in non-ambulant boys/men with Duchenne muscular dystrophy: A multicentric longitudinal study using the Performance of Upper Limb test

The aim of this study was to establish the possible effect of glucocorticoid treatment on upper limb function in a cohort of 91 non-ambulant DMD boys and adults of age between 11 and 26 years. All 91 were assessed using the Performance of Upper Limb test. Forty-eight were still on glucocorticoid after loss of ambulation, 25 stopped steroids at the time they lost ambulation and 18 were GC naive or had steroids while ambulant for less than a year. At baseline the total scores ranged between 0 and 74 (mean 41.20). The mean total scores were 47.92 in the glucocorticoid group, 36 in those who stopped at loss of ambulation and 30.5 in the naive group (p <0.001). The 12-month changes ranged between -20 and 4 (mean -4.4). The mean changes were -3.79 in the glucocorticoid group, -5.52 in those who stopped at loss of ambulation and -4.44 in the naive group. This was more obvious in the patients between 12 and 18 years and at shoulder and elbow levels. Our findings suggest that continuing glucocorticoids throughout teenage years and adulthood after loss of ambulation appears to have a beneficial effect on upper limb function. (C) 2015 The Authors. Published by Elsevier B.V