Ephemeral point-events: is there a last remnant of physical objectivity?

For the past two decades, Einstein's Hole Argument (which deals with the apparent indeterminateness of general relativity due to the general covariance of the field equations) and its resolution in terms of Leibniz equivalence (the statement that Riemannian geometries related by active diffeomorphisms represent the same physical solution) have been the starting point for a lively philosophical debate on the objectivity of the point-events of space-time. It seems that Leibniz equivalence makes it impossible to consider the points of the space-time manifold as physically individuated without recourse to dynamical individuating fields. Various authors have posited that the metric field itself can be used in this way, but nobody so far has considered the problem of explicitly distilling the metrical fingerprint of point-events from the gauge-dependent components of the metric field. Working in the Hamiltonian formulation of general relativity, and building on the results of Lusanna and Pauri (2002), we show how Bergmann and Komar's intrinsic pseudo-coordinates (based on the value of curvature invariants) can be used to provide a physical individuation of point-events in terms of the true degrees of freedom (the Dirac observables) of the gravitational field, and we suggest how this conceptual individuation could in principle be implemented with a well-defined empirical procedure. We argue from these results that point-events retain a significant kind of physical objectivity.Comment: LaTeX, natbib, 34 pages. Final journal versio

Vision technology/algorithms for space robotics applications

The thrust of automation and robotics for space applications has been proposed for increased productivity, improved reliability, increased flexibility, higher safety, and for the performance of automating time-consuming tasks, increasing productivity/performance of crew-accomplished tasks, and performing tasks beyond the capability of the crew. This paper provides a review of efforts currently in progress in the area of robotic vision. Both systems and algorithms are discussed. The evolution of future vision/sensing is projected to include the fusion of multisensors ranging from microwave to optical with multimode capability to include position, attitude, recognition, and motion parameters. The key feature of the overall system design will be small size and weight, fast signal processing, robust algorithms, and accurate parameter determination. These aspects of vision/sensing are also discussed

Torus knots and mirror symmetry

We propose a spectral curve describing torus knots and links in the B-model. In particular, the application of the topological recursion to this curve generates all their colored HOMFLY invariants. The curve is obtained by exploiting the full Sl(2, Z) symmetry of the spectral curve of the resolved conifold, and should be regarded as the mirror of the topological D-brane associated to torus knots in the large N Gopakumar-Vafa duality. Moreover, we derive the curve as the large N limit of the matrix model computing torus knot invariants.Comment: 30 pages + appendix, 3 figure

Nonlinear Invariants of Planar Point Clouds Transformed by Matrices

The goal of this paper is to present invariants of planar point clouds, that is functions which take the same value before and after a linear transformation of a planar point cloud via a $2 \times 2$ invertible matrix. In the approach we adopt here, these invariants are functions of two variables derived from the least squares straight line of the planar point cloud under consideration. A linear transformation of a point cloud induces a nonlinear transformation of these variables. The said invariants are solutions to certain Partial Differential Equations, which are obtained by employing Lie theory. We find cloud invariants in the general case of a four$-$parameter transformation matrix, as well as, cloud invariants of various one$-$parameter sets of transformations which can be practically implemented. Case studies and simulations which verify our findings are also provided

High-pressure phase and transition phenomena in ammonia borane NH3BH3 from X-ray diffraction, Landau theory, and ab initio calculations

Structural evolution of a prospective hydrogen storage material, ammonia borane NH3BH3, has been studied at high pressures up to 12 GPa and at low temperatures by synchrotron powder diffraction. At 293 K and above 1.1 GPa a disordered I4mm structure reversibly transforms into a new ordered phase. Its Cmc21 structure was solved from the diffraction data, the positions of N and B atoms and the orientation of NH3 and BH3 groups were finally assigned with the help of density functional theory calculations. Group-theoretical analysis identifies a single two-component order parameter, combining ordering and atomic displacement mechanisms, which link an orientationally disordered parent phase I4mm with ordered distorted Cmc21, Pmn21 and P21 structures. We propose a generic phase diagram for NH3BH3, mapping three experimentally found and one predicted (P21) phases as a function of temperature and pressure, along with the evolution of the corresponding structural distortions. Ammonia borane belongs to the class of improper ferroelastics and we show that both temperature- and pressure-induced phase transitions can be driven to be of the second order. The role of N-H...H-B dihydrogen bonds and other intermolecular interactions in the stability of NH3BH3 polymorphs is examined.Comment: 23 pages, 7 figure

Advances in Manipulation and Recognition of Digital Ink

Handwriting is one of the most natural ways for a human to record knowledge. Recently, this type of human-computer interaction has received increasing attention due to the rapid evolution of touch-based hardware and software. While hardware support for digital ink reached its maturity, algorithms for recognition of handwriting in certain domains, including mathematics, are lacking robustness. Simultaneously, users may possess several pen-based devices and sharing of training data in adaptive recognition setting can be challenging. In addition, resolution of pen-based devices keeps improving making the ink cumbersome to process and store. This thesis develops several advances for efficient processing, storage and recognition of handwriting, which are applicable to the classification methods based on functional approximation. In particular, we propose improvements to classification of isolated characters and groups of rotated characters, as well as symbols of substantially different size. We then develop an algorithm for adaptive classification of handwritten mathematical characters of a user. The adaptive algorithm can be especially useful in the cloud-based recognition framework, which is described further in the thesis. We investigate whether the training data available in the cloud can be useful to a new writer during the training phase by extracting styles of individuals with similar handwriting and recommending styles to the writer. We also perform factorial analysis of the algorithm for recognition of n-grams of rotated characters. Finally, we show a fast method for compression of linear pieces of handwritten strokes and compare it with an enhanced version of the algorithm based on functional approximation of strokes. Experimental results demonstrate validity of the theoretical contributions, which form a solid foundation for the next generation handwriting recognition systems

Inflation and topological phase transition driven by exotic smoothness

In this paper we will discuss a model which describes the cause of inflation by a topological transition. The guiding principle is the choice of an exotic smoothness structure for the space-time. Here we consider a space-time with topology $S^{3}\times\mathbb{R}$. In case of an exotic $S^{3}\times\mathbb{R}$, there is a change in the spatial topology from a 3-sphere to a homology 3-sphere which can carry a hyperbolic structure. From the physical point of view, we will discuss the path integral for the Einstein-Hilbert action with respect to a decomposition of the space-time. The inclusion of the boundary terms produces fermionic contributions to the partition function. The expectation value of an area (with respect to some surface) shows an exponential increase, i.e. we obtain inflationary behavior. We will calculate the amount of this increase to be a topological invariant. Then we will describe this transition by an effective model, the Starobinski or $R^{2}$ model which is consistent with the current measurement of the Planck satellite. The spectral index and other observables are also calculated. Finally we obtain a realistic cosmological constant.Comment: 21 pages, no figures, iopart styla, accepted in Advances in High Energy Physics, special issue "Experimental Tests of Quantum Gravity and Exotic Quantum Field Theory Effects (QGEQ)