22,260 research outputs found
The Universe from Scratch
A fascinating and deep question about nature is what one would see if one
could probe space and time at smaller and smaller distances. Already the
19th-century founders of modern geometry contemplated the possibility that a
piece of empty space that looks completely smooth and structureless to the
naked eye might have an intricate microstructure at a much smaller scale. Our
vastly increased understanding of the physical world acquired during the 20th
century has made this a certainty. The laws of quantum theory tell us that
looking at spacetime at ever smaller scales requires ever larger energies, and,
according to Einstein's theory of general relativity, this will alter spacetime
itself: it will acquire structure in the form of "curvature". What we still
lack is a definitive Theory of Quantum Gravity to give us a detailed and
quantitative description of the highly curved and quantum-fluctuating geometry
of spacetime at this so-called Planck scale. - This article outlines a
particular approach to constructing such a theory, that of Causal Dynamical
Triangulations, and its achievements so far in deriving from first principles
why spacetime is what it is, from the tiniest realms of the quantum to the
large-scale structure of the universe.Comment: 31 pages, 5 figures; review paper commissioned by Contemporary
Physics and aimed at a wider physics audience; minor beautifications,
coincides with journal versio
On the fundamental role of massless form of matter in physics. Quantum gravity
In the article, with the help of various models, the thesis on the fundamental nature of the field form of matter in physics is considered. In the first chapter a model of special relativity is constructed, on the basis of which the priority of the massless form of matter is revealed. In the second chapter, a field model of inert and heavy mass is constructed and on this basis the mechanism of inertia and gravity of weighty bodies is revealed. In the third chapter, the example of geons shows the fundamental nature of a massless form of matter on the Planck scale. The three-dimensionality of the observable space is substantiated. In the fourth chapter, we consider a variant of solving the problem of singularities in general relativity using the example of multidimensional spaces. The last chapter examines the author's approach to quantum gravity. The conclusions do not contradict the main thesis of the article on the fundamental nature of the massless form of matter. We emphasize the qualitative nature of the presentation of the material in the article
Towards retrieving force feedback in robotic-assisted surgery: a supervised neuro-recurrent-vision approach
Robotic-assisted minimally invasive surgeries have gained a lot of popularity over conventional procedures as they offer many benefits to both surgeons and patients. Nonetheless, they still suffer from some limitations that affect their outcome. One of them is the lack of force feedback which restricts the surgeon's sense of touch and might reduce precision during a procedure. To overcome this limitation, we propose a novel force estimation approach that combines a vision based solution with supervised learning to estimate the applied force and provide the surgeon with a suitable representation of it. The proposed solution starts with extracting the geometry of motion of the heart's surface by minimizing an energy functional to recover its 3D deformable structure. A deep network, based on a LSTM-RNN architecture, is then used to learn the relationship between the extracted visual-geometric information and the applied force, and to find accurate mapping between the two. Our proposed force estimation solution avoids the drawbacks usually associated with force sensing devices, such as biocompatibility and integration issues. We evaluate our approach on phantom and realistic tissues in which we report an average root-mean square error of 0.02 N.Peer ReviewedPostprint (author's final draft
Multi-View Face Recognition From Single RGBD Models of the Faces
This work takes important steps towards solving the following problem of current interest: Assuming that each individual in a population can be modeled by a single frontal RGBD face image, is it possible to carry out face recognition for such a population using multiple 2D images captured from arbitrary viewpoints? Although the general problem as stated above is extremely challenging, it encompasses subproblems that can be addressed today. The subproblems addressed in this work relate to: (1) Generating a large set of viewpoint dependent face images from a single RGBD frontal image for each individual; (2) using hierarchical approaches based on view-partitioned subspaces to represent the training data; and (3) based on these hierarchical approaches, using a weighted voting algorithm to integrate the evidence collected from multiple images of the same face as recorded from different viewpoints. We evaluate our methods on three datasets: a dataset of 10 people that we created and two publicly available datasets which include a total of 48 people. In addition to providing important insights into the nature of this problem, our results show that we are able to successfully recognize faces with accuracies of 95% or higher, outperforming existing state-of-the-art face recognition approaches based on deep convolutional neural networks
Bohmian trajectories and the Path Integral Paradigm. Complexified Lagrangian Mechanics
David Bohm shown that the Schr{\"o}dinger equation, that is a "visiting card"
of quantum mechanics, can be decomposed onto two equations for real functions -
action and probability density. The first equation is the Hamilton-Jacobi (HJ)
equation, a "visiting card" of classical mechanics, to be modified by the
Bohmian quantum potential. And the second is the continuity equation. The
latter can be transformed to the entropy balance equation. The Bohmian quantum
potential is transformed to two Bohmian quantum correctors. The first corrector
modifies kinetic energy term of the HJ equation, and the second one modifies
potential energy term. Unification of the quantum HJ equation and the entropy
balance equation gives complexified HJ equation containing complex kinetic and
potential terms. Imaginary parts of these terms have order of smallness about
the Planck constant. The Bohmian quantum corrector is indispensable term
modifying the Feynman's path integral by expanding coordinates and momenta to
imaginary sector.Comment: 14 pages, 3 figures, 46 references, 48 equation
Gaussian processes with linear operator inequality constraints
This paper presents an approach for constrained Gaussian Process (GP)
regression where we assume that a set of linear transformations of the process
are bounded. It is motivated by machine learning applications for
high-consequence engineering systems, where this kind of information is often
made available from phenomenological knowledge. We consider a GP over
functions on taking values in
, where the process is still Gaussian when
is a linear operator. Our goal is to model under the
constraint that realizations of are confined to a convex set of
functions. In particular, we require that , given
two functions and where pointwise. This formulation provides a
consistent way of encoding multiple linear constraints, such as
shape-constraints based on e.g. boundedness, monotonicity or convexity. We
adopt the approach of using a sufficiently dense set of virtual observation
locations where the constraint is required to hold, and derive the exact
posterior for a conjugate likelihood. The results needed for stable numerical
implementation are derived, together with an efficient sampling scheme for
estimating the posterior process.Comment: Published in JMLR: http://jmlr.org/papers/volume20/19-065/19-065.pd
Return of Frustratingly Easy Domain Adaptation
Unlike human learning, machine learning often fails to handle changes between
training (source) and test (target) input distributions. Such domain shifts,
common in practical scenarios, severely damage the performance of conventional
machine learning methods. Supervised domain adaptation methods have been
proposed for the case when the target data have labels, including some that
perform very well despite being "frustratingly easy" to implement. However, in
practice, the target domain is often unlabeled, requiring unsupervised
adaptation. We propose a simple, effective, and efficient method for
unsupervised domain adaptation called CORrelation ALignment (CORAL). CORAL
minimizes domain shift by aligning the second-order statistics of source and
target distributions, without requiring any target labels. Even though it is
extraordinarily simple--it can be implemented in four lines of Matlab
code--CORAL performs remarkably well in extensive evaluations on standard
benchmark datasets.Comment: Fixed typos. Full paper to appear in AAAI-16. Extended Abstract of
the full paper to appear in TASK-CV 2015 worksho
Bond dimension witnesses and the structure of homogeneous matrix product states
For the past twenty years, Matrix Product States (MPS) have been widely used
in solid state physics to approximate the ground state of one-dimensional spin
chains. In this paper, we study homogeneous MPS (hMPS), or MPS constructed via
site-independent tensors and a boundary condition. Exploiting a connection with
the theory of matrix algebras, we derive two structural properties shared by
all hMPS, namely: a) there exist local operators which annihilate all hMPS of a
given bond dimension; and b) there exist local operators which, when applied
over any hMPS of a given bond dimension, decouple (cut) the particles where
they act from the spin chain while at the same time join (glue) the two loose
ends back again into a hMPS. Armed with these tools, we show how to
systematically derive `bond dimension witnesses', or 2-local operators whose
expectation value allows us to lower bound the bond dimension of the underlying
hMPS. We extend some of these results to the ansatz of Projected Entangled
Pairs States (PEPS). As a bonus, we use our insight on the structure of hMPS
to: a) derive some theoretical limitations on the use of hMPS and hPEPS for
ground state energy computations; b) show how to decrease the complexity and
boost the speed of convergence of the semidefinite programming hierarchies
described in [Phys. Rev. Lett. 115, 020501 (2015)] for the characterization of
finite-dimensional quantum correlations.Comment: Accepted for publication in Quantum. We still do not acknowledge
support from the European Research Counci
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