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We know that space and time are treated almost equally in classical physics, but we also know that this is not the case for quantum mechanics. A quantum description of both space and time is important to really understand the quantum nature of reality. The Page–Wootters mechanism of quantum time is a promising starting point, according to which the evolution of the quantum system is described by the entanglement between it and quantum temporal degrees of freedom. In this paper, we consider a qubit clock that is entangled with a quantum system due to the Wigner rotation induced by Lorentz transformation. We study how this time-system entanglement depends on the rapidity of the Lorentz boost. We consider the case of a spin-1/2 particle with Gaussian momentum distribution as a concrete example. We also compare the time-system entanglement entropy with the spin-momentum entanglement entropy and find that the former is smaller than the latter. [ABSTRACT FROM AUTHOR]

If we interpret the Bekenstein–Hawking entropy of the Hubble horizon as thermodynamic entropy, then the entanglement entropy of the superhorizon modes of curvature perturbation entangled with the subhorizon modes will exceed the Bekenstein–Hawking bound at some point; we call this the unitary paradox of cosmological perturbations by analogy with black hole. In order to avoid a fine-tuned problem, the paradox must occur during the inflationary era at the critical time t c = ln (3 π / 2 H H inf ) / 2 H inf (in Planck units), where H = − Ḣ / H 2 is the first Hubble slow-roll parameter and H inf is the Hubble rate during inflation. If we instead accept the fine-tuned problem, then the paradox will occur during the dark energy era at the critical time t c ′ = ln (3 π H inf / 2 f e 2 N H Λ 2) / 2 H Λ , where H Λ is the Hubble rate dominated by dark energy, N is the total number of e-folds of inflation and f is a purification factor that takes the range 0 < f < 3 π H inf / 2 e 2 N H Λ 2 . [ABSTRACT FROM AUTHOR]

Within the S P 2 , R symmetry, the two-time model (2T model) has six dimensions with two dimensions of time and the dilaton field that can be identified as inflaton in a warm inflation scenario with potential of the form ~ ϕ 4 . From that consideration, we derive the range of parameters for the Higgs-Dilaton potential, the coupling constant between Higgs and Dilaton (α) is larger than 0.0053 and the mass of Dilaton is smaller than 1 0 − 7 GeV. Therefore, the 2T model indirectly suggests that extra dimension can also be a source of inflation. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the problem of dominant point detection on digital curves which consists in finding points with local maximum curvature. Thanks to previous studies of the decomposition of curves into sequence of discrete structures [1–3] , namely maximal blurred segments of width ν [4] , an initial algorithm has been proposed in [5] to detect dominant points. However, an heuristic strategy is used to identify the dominant points. We now propose a modified algorithm without heuristics but a simple measure of angle. In addition, two applications are as well presented: (1) polygonal simplification to reduce the number of detected dominant points by associating a weight to each of them, and (2) classification using the polygon issued from the reduced dominant points. The experimental results demonstrate the efficiency and robustness of the proposed method. [ABSTRACT FROM AUTHOR]

We investigate inflation with a class of concave inflaton potentials of the form ∼ ϕ n (0 < n < 1) in the Randall–Sundrum model with an infinite extra spatial dimension. We show that this class of models is much more in good agreement with observations compared to the standard inflation. We also find the range of the five-dimensional Planck scale ( M 5 ) and show that large tensor-to-scalar ratios do not eliminate small-field inflation in braneworld cosmology. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of timber board positioning within the log where they were sawn from. The method takes as input log and board end cross-section images. It uses a two-step image matching method based on scale invariant feature transform and normalized correlation coefficient (NCC). In the first step, the scale factor and rotation angle of board end images are estimated from the board images that are correctly identified on the log end image by SIFT. Then, the accurate position of each board within the log end image is achieved by the NCC method. The method has been tested on 70 different log images and the 798 corresponding board images of various visual aspects and coming from three different species (Douglas fir, Norway spruce, and oak). The results fully demonstrate that the proposed method is not only rotation and scale invariant, but also has high accuracy properties. [ABSTRACT FROM AUTHOR]

Image registration has become a crucial step in a wide range of imaging domains, from computer vision to computer graphics. The core of image registration consists of determining the transformation that induces the best mapping between two images. This problem is ill-posed; it is also difficult to handle, due to the high size of the images and the high dimension of the transformation parameter spaces. Computing an actually optimal solution is practically impossible when transformations are assumed continuous (i.e., defined on R n ). In this article, we initiate the exploration of a new way of considering image registration. Since digital images are basically defined in a discrete framework (i.e., in Z n ), the transformation spaces–despite a potentially high complexity–actually remain finite, allowing for the development of explicit exploration of the parameter space via discrete optimization schemes. We propose an analysis of the very basis of registration, by considering rigid registration between 2D images. We show, in particular, how this problem can be handled in a fully discrete fashion, by computing locally the combinatorial structure of the parameter space of discrete rigid transformations, and by navigating on-the-flight within this space via gradient descent paradigms. This registration framework is applied in real imaging cases, emphasizing the relevance of our approach, and the potential usefulness of its further extension to higher dimension images and richer transformations. [ABSTRACT FROM AUTHOR]

Rigid transformations are involved in a wide range of digital image processing applications. In such a context, they are generally considered as continuous processes, followed by a digitization of the results. Recently, rigid transformations on ℤ have been alternatively formulated as a fully discrete process. Following this paradigm, we investigate - from a combinatorial point of view - the effects of pixel-invariance constraints on such transformations. In particular we describe the impact of these constraints on both the combinatorial structure of the transformation space and the algorithm leading to its generation. [ABSTRACT FROM AUTHOR]