Principal bundle structure of matrix manifolds

In this paper, we introduce a new geometric description of the manifolds of matrices of fixed rank. The starting point is a geometric description of the Grassmann manifold $\mathbb{G}_r(\mathbb{R}^k)$ of linear subspaces of dimension $r<k$ in $\mathbb{R}^k$ which avoids the use of equivalence classes. The set $\mathbb{G}_r(\mathbb{R}^k)$ is equipped with an atlas which provides it with the structure of an analytic manifold modelled on $\mathbb{R}^{(k-r)\times r}$. Then we define an atlas for the set $\mathcal{M}_r(\mathbb{R}^{k \times r})$ of full rank matrices and prove that the resulting manifold is an analytic principal bundle with base $\mathbb{G}_r(\mathbb{R}^k)$ and typical fibre $\mathrm{GL}_r$, the general linear group of invertible matrices in $\mathbb{R}^{k\times k}$. Finally, we define an atlas for the set $\mathcal{M}_r(\mathbb{R}^{n \times m})$ of non-full rank matrices and prove that the resulting manifold is an analytic principal bundle with base $\mathbb{G}_r(\mathbb{R}^n) \times \mathbb{G}_r(\mathbb{R}^m)$ and typical fibre $\mathrm{GL}_r$. The atlas of $\mathcal{M}_r(\mathbb{R}^{n \times m})$ is indexed on the manifold itself, which allows a natural definition of a neighbourhood for a given matrix, this neighbourhood being proved to possess the structure of a Lie group. Moreover, the set $\mathcal{M}_r(\mathbb{R}^{n \times m})$ equipped with the topology induced by the atlas is proven to be an embedded submanifold of the matrix space $\mathbb{R}^{n \times m}$ equipped with the subspace topology. The proposed geometric description then results in a description of the matrix space $\mathbb{R}^{n \times m}$, seen as the union of manifolds $\mathcal{M}_r(\mathbb{R}^{n \times m})$, as an analytic manifold equipped with a topology for which the matrix rank is a continuous map

A tensor approximation method based on ideal minimal residual formulations for the solution of high-dimensional problems

In this paper, we propose a method for the approximation of the solution of high-dimensional weakly coercive problems formulated in tensor spaces using low-rank approximation formats. The method can be seen as a perturbation of a minimal residual method with residual norm corresponding to the error in a specified solution norm. We introduce and analyze an iterative algorithm that is able to provide a controlled approximation of the optimal approximation of the solution in a given low-rank subset, without any a priori information on this solution. We also introduce a weak greedy algorithm which uses this perturbed minimal residual method for the computation of successive greedy corrections in small tensor subsets. We prove its convergence under some conditions on the parameters of the algorithm. The residual norm can be designed such that the resulting low-rank approximations are quasi-optimal with respect to particular norms of interest, thus yielding to goal-oriented order reduction strategies for the approximation of high-dimensional problems. The proposed numerical method is applied to the solution of a stochastic partial differential equation which is discretized using standard Galerkin methods in tensor product spaces

Sumbangan Power Otot Tungkai, Keseimbangan, Koordinasi dan Kepercayaan Diri terhadap Prestasi Poomsae Taekwondo (Studi Korelasional Prestasi Poomsae Altet Taekwondoin di Surakarta)

ABSTRAK Binuko Amarseto. A121308003. 2016. “Sumbangan Power Otot Tungkai, Keseimbangan, Koordinasi dan Kepercayaan Diri terhadap Prestasi Poomsae Taekwondo (Studi Korelasional Prestasi Poomsae Altet Taekwondoin di Surakarta)”. TESIS. Program Studi Ilmu Keolahragaan Pascasarjana Universitas Sebelas Maret Surakarta. Pembimbing: Prof. Dr. Sugiyanto (Pembimbing I), dan Prof. Dr. Agus Kristiyanto, M.Pd. (Pembimbing II). Prestasi Poomsae Taekwondo tidak hanya dicapai dengan hanya mengandalkan faktor ketrampilan teknik, tetapi juga haruslah memperhatikan faktor kondisi fisik dan psikis. Kondisi fisik baik berupa power otot tungkai, keseimbangan, dan koordinasi akan menentukan gerakan dalam setiap teknik Poomsae Taekwondo. Selain itu penilaian prestasi Poomsae Taekwondo terdapat penilaian lainnya yang berupa presentasi daripada ekspresi yang mencerminkan kepercayaan diri seorang atlet. Penelitian ini bertujuan untuk menemukan kebenaran tentang sumbangan power otot tungkai, keseimbangan, koordinasi dan kepercayaan diri terhadap prestasi Poomsae Taekwondo. Penelitian ini menggunakan pendekatan kuantitatif dengan metode penelitian korelasional, populasi dalam penelitian ini adalah atlet usia 13-15 tahun pada dojang se-Surakarta, jumlah sampel yang didapatkan berjumlah 40 responden. Variabel dalam penelitian ini terdiri dari 4 variabel independent yaitu power otot tungkai, keseimbangan, koordinasi dan kepercayaan diri dan 1 variabel dependent yaitu prestasi Poomsae Taekwondo. Teknik analisis data menggunakan analisis korelasi regresi dengan melakukan pengujian prasyarat uji normalitas dan linieritas. Pengujian hipotesis menggunakan analisis regresi dan korelasi masingmasing prediktor dan analisis regresi ganda serta korelasi ganda. Hasil penelitian menunjukkan bahwa power otot tungkai, keseimbangan, koordinasi dan kepercayaan diri berhubungan baik secara parsial dan secara simultan membentuk persamaan regresi. Dimana setiap power otot tungkai meningkat maka akan mengakibatkan peningkatan prestasi Poomsae Taekwondo sebesar 0,018, setiap peningkatan keseimbangan akan mengakibatkan peningkatan prestasi Poomsae Taekwondo sebesar 0,027, setiap peningkatan koordinasi akan mengakibatkan peningkatan prestasi Poomsae Taekwondo sebesar 0,042, setiap peningkatan kepercayaan diri akan mengakibatkan peningkatan prestasi Poomsae Taekwondo sebesar 0,054. Kesimpulan dari penelitian ini adalah power otot tungkai, keseimbangan, koordinasi dan kepercayaan diri berhubungan dan memiliki sumbangan baik secara parsial maupaun simultan terhadap prestasi Poomsae Taekwondo. Kata kunci : Kondisi fisik, Psikologis, Prestasi Poomsae Taekwondo

Psychological adjustment to cleft lip and/or palate: A narrative review of the literature

© 2016 Informa UK Limited, trading as Taylor & Francis Group. Objective: Adjustment to cleft lip and/or palate (CL/P) is multifaceted, involving several domains of psychological and social functioning. A substantial increase in research in this area has been evident in recent years, along with a preliminary shift in how adjustment to CL/P is conceptualised and measured. An updated and comprehensive review of the literature is needed in light of the rapidly expanding and changing field. Design: A narrative review of 148 quantitative and qualitative studies published between January 2004 and July 2015. Main outcome measures: Findings are presented according to five key domains of adjustment: Developmental Trajectory, Behaviour, Emotional Well-being, Social Experiences and Satisfaction with Appearance and Treatment. Data pertaining to General Psychological Well-being were also examined. Results: The overall impact of CL/P on psychological adjustment appears to be low. Nonetheless, the review demonstrates the complexity of findings both within and across domains, and highlights recurring methodological challenges. Conclusions: Research findings from the last decade are considered to be largely inconclusive, although some areas of emerging consensus and improvements in the approaches used were identified. Efforts to collect data from large, representative and longitudinal samples, which are comparable across studies and encompassing of the patient perspective, should be doubled

Psychological adjustment to craniofacial conditions (excluding oral clefts): A review of the literature

© 2016 Informa UK Limited, trading as Taylor & Francis Group. Objective: A congenital craniofacial anomaly (CFA) is expected to impact upon several domains of psychological, emotional and social functioning, yet no recent reviews have comprehensively summarised the available literature. Further, existing reviews tend to draw upon literature in the field of cleft lip and palate, and do not give substantive attention to other types of CFAs. Design: A review of 41 papers published between January 2000 and March 2016 pertaining to psychological adjustment to CFAs. Main outcome measures: Findings are presented according to key psychological domains: General Psychological Well-being, Quality of Life, Behaviour, Emotional Well-being, Social Experiences, Appearance, and Treatment-Related Experiences. Results: Current literature offers a contradictory picture of adjustment to CFAs. Psychological adjustment appeared to be comparable to norms and reference groups in approximately half of the papers related to non-syndromic CFAs, while more variation was found across domains among samples with syndromic CFAs. Associations were found between adjustment, physical health and cognitive function in several papers. The review identified a number of gaps in the literature, such as the inclusion of a wide range of diagnoses within research samples. Conclusions: This review demonstrates the complexity of findings, both within and across domains, and highlights a number of methodological challenges

Mechanisms of ATP release and signalling in the blood vessel wall

The nucleotide adenosine 5′-triphosphate (ATP) has classically been considered the cell's primary energy currency. Importantly, a novel role for ATP as an extracellular autocrine and/or paracrine signalling molecule has evolved over the past century and extensive work has been conducted to characterize the ATP-sensitive purinergic receptors expressed on almost all cell types in the body. Extracellular ATP elicits potent effects on vascular cells to regulate blood vessel tone but can also be involved in vascular pathologies such as atherosclerosis. While the effects of purinergic signalling in the vasculature have been well documented, the mechanism(s) mediating the regulated release of ATP from cells in the blood vessel wall and circulation are now a key target of investigation. The aim of this review is to examine the current proposed mechanisms of ATP release from vascular cells, with a special emphasis on the transporters and channels involved in ATP release from vascular smooth muscle cells, endothelial cells, circulating red blood cells, and perivascular sympathetic nerves, including vesicular exocytosis, plasma membrane F1/F0-ATP synthase, ATP-binding cassette (ABC) transporters, connexin hemichannels, and pannexin channel