Gravity and compactified branes in matrix models

A mechanism for emergent gravity on brane solutions in Yang-Mills matrix models is exhibited. Newtonian gravity and a partial relation between the Einstein tensor and the energy-momentum tensor can arise from the basic matrix model action, without invoking an Einstein-Hilbert-type term. The key requirements are compactified extra dimensions with extrinsic curvature M^4 x K \subset R^D and split noncommutativity, with a Poisson tensor \theta^{ab} linking the compact with the noncompact directions. The moduli of the compactification provide the dominant degrees of freedom for gravity, which are transmitted to the 4 noncompact directions via the Poisson tensor. The effective Newton constant is determined by the scale of noncommutativity and the compactification. This gravity theory is well suited for quantization, and argued to be perturbatively finite for the IKKT model. Since no compactification of the target space is needed, it might provide a way to avoid the landscape problem in string theory.Comment: 35 pages. V2: substantially revised and improved, conclusion weakened. V3: some clarifications, published version. V4: minor correctio

Matrix geometries and Matrix Models

We study a two parameter single trace 3-matrix model with SO(3) global symmetry. The model has two phases, a fuzzy sphere phase and a matrix phase. Configurations in the matrix phase are consistent with fluctuations around a background of commuting matrices whose eigenvalues are confined to the interior of a ball of radius R=2.0. We study the co-existence curve of the model and find evidence that it has two distinct portions one with a discontinuous internal energy yet critical fluctuations of the specific heat but only on the low temperature side of the transition and the other portion has a continuous internal energy with a discontinuous specific heat of finite jump. We study in detail the eigenvalue distributions of different observables.Comment: 20 page

An Efficient Representation of Euclidean Gravity I

We explore how the topology of spacetime fabric is encoded into the local structure of Riemannian metrics using the gauge theory formulation of Euclidean gravity. In part I, we provide a rigorous mathematical foundation to prove that a general Einstein manifold arises as the sum of SU(2)_L Yang-Mills instantons and SU(2)_R anti-instantons where SU(2)_L and SU(2)_R are normal subgroups of the four-dimensional Lorentz group Spin(4) = SU(2)_L x SU(2)_R. Our proof relies only on the general properties in four dimensions: The Lorentz group Spin(4) is isomorphic to SU(2)_L x SU(2)_R and the six-dimensional vector space of two-forms splits canonically into the sum of three-dimensional vector spaces of self-dual and anti-self-dual two-forms. Consolidating these two, it turns out that the splitting of Spin(4) is deeply correlated with the decomposition of two-forms on four-manifold which occupies a central position in the theory of four-manifolds.Comment: 31 pages, 1 figur

Fascial tissue research in sports medicine: from molecules to tissue adaptation, injury and diagnostics.

The fascial system builds a three-dimensional continuum of soft, collagen-containing, loose and dense fibrous connective tissue that permeates the body and enables all body systems to operate in an integrated manner. Injuries to the fascial system cause a significant loss of performance in recreational exercise as well as high-performance sports, and could have a potential role in the development and perpetuation of musculoskeletal disorders, including lower back pain. Fascial tissues deserve more detailed attention in the field of sports medicine. A better understanding of their adaptation dynamics to mechanical loading as well as to biochemical conditions promises valuable improvements in terms of injury prevention, athletic performance and sports-related rehabilitation. This consensus statement reflects the state of knowledge regarding the role of fascial tissues in the discipline of sports medicine. It aims to (1) provide an overview of the contemporary state of knowledge regarding the fascial system from the microlevel (molecular and cellular responses) to the macrolevel (mechanical properties), (2) summarise the responses of the fascial system to altered loading (physical exercise), to injury and other physiological challenges including ageing, (3) outline the methods available to study the fascial system, and (4) highlight the contemporary view of interventions that target fascial tissue in sport and exercise medicine. Advancing this field will require a coordinated effort of researchers and clinicians combining mechanobiology, exercise physiology and improved assessment technologies

Assessing quality of life in a clinical study on heart rehabilitation patients: how well do value sets based on given or experienced health states reflect patients' valuations?

Background: Quality of life as an endpoint in a clinical study may be sensitive to the value set used to derive a single score. Focusing on patients' actual valuations in a clinical study, we compare different value sets for the EQ-5D-3L and assess how well they reproduce patients' reported results. Methods: A clinical study comparing inpatient (n = 98) and outpatient (n = 47) rehabilitation of patients after an acute coronary event is re-analyzed. Value sets include: 1. Given health states and time-trade-off valuation (GHS-TTO) rendering economic utilities;2. Experienced health states and valuation by visual analog scale (EHS-VAS). Valuations are compared with patient-reported VAS rating. Accuracy is assessed by mean absolute error (MAE) and by Pearson's correlation.. External validity is tested by correlation with established MacNew global scores. Drivers of differences between value sets and VAS are analyzed using repeated measures regression. Results: EHS-VAS had smaller MAEs and higher. in all patients and in the inpatient group, and correlated best with MacNew global score. Quality-adjusted survival was more accurately reflected by EHS-VAS. Younger, better educated patients reported lower VAS at admission than the EHS-based value set. EHS-based estimates were mostly able to reproduce patient-reported valuation. Economic utility measurement is conceptually different, produced results less strongly related to patients' reports, and resulted in about 20 % longer quality-adjusted survival. Conclusion: Decision makers should take into account the impact of choosing value sets on effectiveness results. For transferring the results of heart rehabilitation patients from another country or from another valuation method, the EHS-based value set offers a promising estimation option for those decision makers who prioritize patient-reported valuation. Yet, EHS-based estimates may not fully reflect patient-reported VAS in all situations

Renormalization group approach to matrix models via noncommutative space

We develop a new renormalization group approach to the large-N limit of matrix models. It has been proposed that a procedure, in which a matrix model of size (N-1) \times (N-1) is obtained by integrating out one row and column of an N \times N matrix model, can be regarded as a renormalization group and that its fixed point reveals critical behavior in the large-N limit. We instead utilize the fuzzy sphere structure based on which we construct a new map (renormalization group) from N \times N matrix model to that of rank N-1. Our renormalization group has great advantage of being a nice analog of the standard renormalization group in field theory. It is naturally endowed with the concept of high/low energy, and consequently it is in a sense local and admits derivative expansions in the space of matrices. In construction we also find that our renormalization in general generates multi-trace operators, and that nonplanar diagrams yield a nonlocal operation on a matrix, whose action is to transport the matrix to the antipode on the sphere. Furthermore the noncommutativity of the fuzzy sphere is renormalized in our formalism. We then analyze our renormalization group equation, and Gaussian and nontrivial fixed points are found. We further clarify how to read off scaling dimensions from our renormalization group equation. Finally the critical exponent of the model of two-dimensional gravity based on our formalism is examined.Comment: 1+42 pages, 4 figure

Endoscopic treatment of prepatellar bursitis

Operative treatment of prepatellar bursitis is indicated in intractable bursitis. The most common complication of surgical treatment for prepatellar bursitis is skin problems. For traumatic prepatellar bursitis, we propose a protocol of outpatient endoscopic surgery under local anaesthesia. From September 1996 to February 2001, 60 cases of failed nonoperative treatment for prepatellar bursitis were included. The average age was 33.5 ± 11.1 years (range 21–55). The average operation duration was 18 minutes. Two to three mini-arthroscopic portals were used in our series. No sutures or a simple suture was needed for the portals after operation. After follow-up for an average of 36.3 months, all patients are were symptom-free and had regained knee function. None of the population had local tenderness or hypo-aesthesia around their wound. Their radiographic and sonographic examinations showed no recurrence of bursitis. Outpatient arthroscopic bursectomy under local anaesthesia is an effective procedure for the treatment of post-traumatic prepatellar bursitis after failed conservative treatments. Both the cosmetic results and functional results were satisfactory

Evidence for F(uzz) Theory

We show that in the decoupling limit of an F-theory compactification, the internal directions of the seven-branes must wrap a non-commutative four-cycle S. We introduce a general method for obtaining fuzzy geometric spaces via toric geometry, and develop tools for engineering four-dimensional GUT models from this non-commutative setup. We obtain the chiral matter content and Yukawa couplings, and show that the theory has a finite Kaluza-Klein spectrum. The value of 1/alpha_(GUT) is predicted to be equal to the number of fuzzy points on the internal four-cycle S. This relation puts a non-trivial restriction on the space of gauge theories that can arise as a limit of F-theory. By viewing the seven-brane as tiled by D3-branes sitting at the N fuzzy points of the geometry, we argue that this theory admits a holographic dual description in the large N limit. We also entertain the possibility of constructing string models with large fuzzy extra dimensions, but with a high scale for quantum gravity.Comment: v2: 66 pages, 3 figures, references and clarifications adde

Soluble Beta-Amyloid Precursor Protein Is Related to Disease Progression in Amyotrophic Lateral Sclerosis

Background: Biomarkers of disease progression in amyotrophic lateral sclerosis (ALS) could support the identification of beneficial drugs in clinical trials. We aimed to test whether soluble fragments of beta-amyloid precursor protein (sAPPa and sAPPß) correlated with clinical subtypes of ALS and were of prognostic value. Methodology/Principal Findings: In a cross-sectional study including patients with ALS (N = 68) with clinical follow-up data over 6 months, Parkinson’s disease (PD, N = 20), and age-matched controls (N = 40), cerebrospinal fluid (CSF) levels of sAPPa a, sAPPß and neurofilaments (NfH SMI35) were measured by multiplex assay, Progranulin by ELISA. CSF sAPPa and sAPPß levels were lower in ALS with a rapidly-progressive disease course (p = 0.03, and p = 0.02) and with longer disease duration (p = 0.01 and p = 0.01, respectively). CSF NfH SMI35 was elevated in ALS compared to PD and controls, with highest concentrations found in patients with rapid disease progression (p,0.01). High CSF NfH SMI3 was linked to low CSF sAPPa and sAPPß (p = 0.001, and p = 0.007, respectively). The ratios CSF NfH SMI35 /CSF sAPPa,-ß were elevated in patients with fast progression of disease (p = 0.002 each). CSF Progranulin decreased with ongoing disease (p = 0.04). Conclusions: This study provides new CSF candidate markers associated with progression of disease in ALS. The data suggest that a deficiency of cellular neuroprotective mechanisms (decrease of sAPP) is linked to progressive neuro-axona