Normal frames for non-Riemannian connections

The principal properties of geodesic normal coordinates are the vanishing of the connection components and first derivatives of the metric components at some point. It is well-known that these hold only at points where the connection has vanishing torsion and non-metricity. However, it is shown that normal frames, possessing the essential features of normal coordinates, can still be constructed when the connection is non-Riemannian.Comment: 4 pages, plain TeX. To appear in Class. Quantum Gra

Coframe teleparallel models of gravity. Exact solutions

The superstring and superbrane theories which include gravity as a necessary and fundamental part renew an interest to alternative representations of general relativity as well as the alternative models of gravity. We study the coframe teleparallel theory of gravity with a most general quadratic Lagrangian. The coframe field on a differentiable manifold is a basic dynamical variable. A metric tensor as well as a metric compatible connection is generated by a coframe in a unique manner. The Lagrangian is a general linear combination of Weitzenb\"{o}ck's quadratic invariants with free dimensionless parameters \r_1,\r_2,\r_3. Every independent term of the Lagrangian is a global SO(1,3)-invariant 4-form. For a special choice of parameters which confirms with the local SO(1,3) invariance this theory gives an alternative description of Einsteinian gravity - teleparallel equivalent of GR. We prove that the sign of the scalar curvature of a metric generated by a static spherical-symmetric solution depends only on a relation between the free parameters. The scalar curvature vanishes only for a subclass of models with \r_1=0. This subclass includes the teleparallel equivalent of GR. We obtain the explicit form of all spherically symmetric static solutions of the ``diagonal'' type to the field equations for an arbitrary choice of free parameters. We prove that the unique asymptotic-flat solution with Newtonian limit is the Schwarzschild solution that holds for a subclass of teleparallel models with \r_1=0. Thus the Yang-Mills-type term of the general quadratic coframe Lagrangian should be rejected.Comment: 28 pages, Latex error is fixe

Do Visual Cues Influence the Perception of Earth Vertical?

Accurate perception of the direction of earth vertical can be achieved by sensing the direction of gravity in body coordinates. This is equivalent to knowing body orientation in world coordinates. There are a number of visual and non-visual cues we can use to estimate earth vertical relative to the body. Non-visual cues include the sensation of gravity and forces due to acceleration, and they can be measured by the somatosensory and vestibular systems. These systems cannot always tell us directly about the direction of gravity because they signal gravito-inertial (GI) force, which is the sum of all forces acting on the body at a given time. For example, if one is accelerating, the GI force is the sum of the force due to acceleration and the force due to gravity. In these situations, the direction of GI force does not indicate the direction of earth vertical, but visual cues may be used to resolve the ambiguity. We conducted an experiment in which the direction of GI force was manipulated by pitching observers (rotation about the body’s x-axis) on a motion platform. Their task was to indicate the direction of earth vertical using a pointing device. In some conditions, no visual stimulus was presented. In other conditions, observers were presented with a visual scene depicting acceleration over a flat, textured ground plane. Two cues in the visual display contained information relevant to judging the direction of earth vertical: 1) the location and orientation of the horizon and 2) the rate of acceleration over the ground plane. We present a model of how these visual and non-visual cues might be used to generate an estimate of the direction of earth vertical. Observer responses are compared with the predictions of this model. Results suggest that under the conditions of the present experiment, visual cues had very little effect, and perception of earth vertical was estimated primarily on the basis of vestibular and somatosensory cues

Normal frames and the validity of the equivalence principle

We investigate the validity of the equivalence principle along paths in gravitational theories based on derivations of the tensor algebra over a differentiable manifold. We prove the existence of local bases, called normal, in which the components of the derivations vanish along arbitrary paths. All such bases are explicitly described. The holonomicity of the normal bases is considered. The results obtained are applied to the important case of linear connections and their relationship with the equivalence principle is described. In particular, any gravitational theory based on tensor derivations which obeys the equivalence principle along all paths, must be based on a linear connection.Comment: 14 pages, LaTeX 2e, the package amsfonts is neede

Normal frames and the validity of the equivalence principle. I. Cases in a neighborhood and at a point

A treatment in a neighborhood and at a point of the equivalence principle on the basis of derivations of the tensor algebra over a manifold is given. Necessary and sufficient conditions are given for the existence of local bases, called normal frames, in which the components of derivations vanish in a neighborhood or at a point. These frames (bases), if any, are explicitly described and the problem of their holonomicity is considered. In particular, the obtained results concern symmetric as well as nonsymmetric linear connections.Comment: LaTeX2e, 9 pages, to be published in Journal of Physics A: Mathematical and Genera

Hamiltonian Poincar\'e Gauge Theory of Gravitation

We develop a Hamiltonian formalism suitable to be applied to gauge theories in the presence of Gravitation, and to Gravity itself when considered as a gauge theory. It is based on a nonlinear realization of the Poincar\'e group, taken as the local spacetime group of the gravitational gauge theory, with $SO(3)$ as the classification subgroup. The Wigner--like rotation induced by the nonlinear approach singularizes out the role of time and allows to deal with ordinary $SO(3)$ vectors. We apply the general results to the Einstein--Cartan action. We study the constraints and we obtain Einstein's classical equations in the extremely simple form of time evolution equations of the coframe. As a consequence of our approach, we identify the gauge--theoretical origin of the Ashtekar variables.Comment: 38 pages, plainTe

Plane torsion waves in quadratic gravitational theories

The definition of the Riemann-Cartan space of the plane wave type is given. The condition under which the torsion plane waves exist is found. It is expressed in the form of the restriction imposed on the coupling constants of the 10-parametric quadratic gravitational Lagrangian. In the mathematical appendix the formula for commutator of the variation operator and Hodge operator is proved. This formula is applied for the variational procedure when the gravitational field equations are obtained in terms of the exterior differential forms.Comment: 3 May 1998. - 11

A quantum Monte-Carlo method for fermions, free of discretization errors

In this work we present a novel quantum Monte-Carlo method for fermions, based on an exact decomposition of the Boltzmann operator $exp(-\beta H)$. It can be seen as a synthesis of several related methods. It has the advantage that it is free of discretization errors, and applicable to general interactions, both for ground-state and finite-temperature calculations. The decomposition is based on low-rank matrices, which allows faster calculations. As an illustration, the method is applied to an analytically solvable model (pairing in a degenerate shell) and to the Hubbard model.Comment: 5 pages, 4 figures, submitted to Phys. Rev. Let

A new analysis approach of epidermal growth factor receptor pathway activation patterns provides insights into cetuximab resistance mechanisms in head and neck cancer

The pathways downstream of the epidermal growth factor receptor (EGFR) have often been implicated to play crucial roles in the development and progression of various cancer types. Different authors have proposed models in cell lines in which they study the modes of pathway activities after perturbation experiments. It is prudent to believe that a better understanding of these pathway activation patterns might lead to novel treatment concepts for cancer patients or at least allow a better stratification of patient collectives into different risk groups or into groups that might respond to different treatments. Traditionally, such analyses focused on the individual players of the pathways. More recently in the field of systems biology, a plethora of approaches that take a more holistic view on the signaling pathways and their downstream transcriptional targets has been developed. Fertig et al. have recently developed a new method to identify patterns and biological process activity from transcriptomics data, and they demonstrate the utility of this methodology to analyze gene expression activity downstream of the EGFR in head and neck squamous cell carcinoma to study cetuximab resistance. Please see related article: http://www.biomedcentral.com/1471-2164/13/16