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Living Reviews in Relativity 2010Over the past decade, () theories have been extensively studied as one of the simplest modifications to General Relativity. In this article we review various... (Review)
Review
Over the past decade, () theories have been extensively studied as one of the simplest modifications to General Relativity. In this article we review various applications of () theories to cosmology and gravity - such as inflation, dark energy, local gravity constraints, cosmological perturbations, and spherically symmetric solutions in weak and strong gravitational backgrounds. We present a number of ways to distinguish those theories from General Relativity observationally and experimentally. We also discuss the extension to other modified gravity theories such as Brans-Dicke theory and Gauss-Bonnet gravity, and address models that can satisfy both cosmological and local gravity constraints.
PubMed: 28179828
DOI: 10.12942/lrr-2010-3 -
Optics Express Dec 2008A very general beam solution of the paraxial wave equation in elliptic cylindrical coordinates is presented. We call such a field an elliptic beam (EB). The complex...
A very general beam solution of the paraxial wave equation in elliptic cylindrical coordinates is presented. We call such a field an elliptic beam (EB). The complex amplitude of the EB is described by either the generalized Ince functions or the Whittaker-Hill functions and is characterized by four parameters that are complex in the most general situation. The propagation through complex ABCD optical systems and the conditions for square integrability are studied in detail. Special cases of the EB are the standard, elegant, and generalized Ince-Gauss beams, Mathieu-Gauss beams, among others.
Topics: Computer Simulation; Light; Models, Theoretical; Refractometry; Scattering, Radiation
PubMed: 19065249
DOI: 10.1364/oe.16.021087 -
Bioinformation 2017The antifreeze protein (AFP) activity is explained using two models. The first model is using ice binding and the second is using antiice structuralization of water...
The antifreeze protein (AFP) activity is explained using two models. The first model is using ice binding and the second is using antiice structuralization of water molecules. The description of AFP function using anti-ice structuralization of water molecules is less explored. Therefore, it is of interest to explain AFP function using this model. Protein folding is often described using models where hydrophobic residues move away from water getting buried and hydrophilic residues are exposed to the surface. Thus, the 3D Gauss function stretched on the protein molecule describes the hydrophobicity distribution in a protein molecule. Small antifreeze proteins (less than 150 residues) are often represented by structures with hydrophobic core. Large antifreeze proteins (above 200 residues) contain solenoid (modular repeats). The hydrophobic field of solenoid show different distribution with linear propagation of the bands of different hydrophobicity level having high and low hydrophobicity that is propagated parallel to the long axis of solenoid. This specific ordering of hydrophobicity implies water molecules ordering different from ice. We illustrate this phenomenon using two antifreeze proteins to describe the hypothesis.
PubMed: 29379256
DOI: 10.6026/97320630013400 -
Scientific Reports May 2016That the speed of light in free space c is constant has been a pillar of modern physics since the derivation of Maxwell and in Einstein's postulate in special...
That the speed of light in free space c is constant has been a pillar of modern physics since the derivation of Maxwell and in Einstein's postulate in special relativity. This has been a basic assumption in light's various applications. However, a physical beam of light has a finite extent such that even in free space it is by nature dispersive. The field confinement changes its wavevector, hence, altering the light's group velocity vg. Here, we report the subluminal vg and consequently the dispersion in free space of Laguerre-Gauss (LG) beam, a beam known to carry orbital angular momentum. The vg of LG beam, calculated in the paraxial regime, is observed to be inversely proportional to the beam's divergence θ0, the orbital order ℓ and the radial order p. LG beams of higher orders travel relatively slower than that of lower orders. As a consequence, LG beams of different orders separate in the temporal domain along propagation. This is an added effect to the dispersion due to field confinement. Our results are useful for treating information embedded in LG beams from astronomical sources and/or data transmission in free space.
PubMed: 27231195
DOI: 10.1038/srep26842 -
The AAPS Journal Oct 2021Ordinary differential equation (ODE)-based models of signal transduction pathways often contain parameters that are unidentifiable or unmeasurable by experimental data,...
Ordinary differential equation (ODE)-based models of signal transduction pathways often contain parameters that are unidentifiable or unmeasurable by experimental data, and calibrating such models to data remains challenging. Here, two efficient parameter estimation methods, cluster Gauss-Newton (CGN) and CellNOpt (CNO), were applied to fit a signaling network model of U266 multiple myeloma cells to the activity dynamics of key proteins in response to vorinostat and/or bortezomib. A logic-based network model was constructed and transformed to 17 ODEs with 79 parameters estimated within broad ranges of biologically plausible values. The top 10% best-fit parameters by both methods had high uncertainties with CV > 50% for the majority of parameters. The root mean square and prediction errors were comparable without statistically significant differences between the two methods. Despite uncertain parameter estimation, protein dynamics after the sequential combination of bortezomib and vorinostat was predicted with reasonable accuracy and precision. Global sensitivity analyses of partial rank correlation coefficients and Sobol sensitivity demonstrated that apoptosis induction was most sensitive to parameters governing the activity of the proteasome-JNK-caspase-8 axis. Simulations revealed that the greatest magnitude of pharmacodynamic drug interactions between bortezomib and vorinostat occurred at caspase-9, AKT, and Bcl-2. Two sequential combinations were explored in silico, and the outcome matched qualitatively with an empirical evaluation of the pharmacodynamic interaction based on cell viability. Overall, the CGN and CNO algorithms performed similarly for this ODE-based network model calibration, and the calibrated model provided meaningful insights into cellular signaling mechanisms in response to pharmacological perturbations.
Topics: Algorithms; Antineoplastic Agents; Bortezomib; Cell Line, Tumor; Computer Simulation; Drug Interactions; Humans; Models, Theoretical; Multiple Myeloma; Signal Transduction; Vorinostat
PubMed: 34622346
DOI: 10.1208/s12248-021-00640-7 -
Optics Letters Mar 2023We propose the deep Gauss-Newton (DGN) algorithm. The DGN allows one to take into account the knowledge of the forward model in a deep neural network by unrolling a...
We propose the deep Gauss-Newton (DGN) algorithm. The DGN allows one to take into account the knowledge of the forward model in a deep neural network by unrolling a Gauss-Newton optimization method. No regularization or step size needs to be chosen; they are learned through convolutional neural networks. The proposed algorithm does not require an initial reconstruction and is able to retrieve simultaneously the phase and absorption from a single-distance diffraction pattern. The DGN method was applied to both simulated and experimental data and permitted large improvements of the reconstruction error and of the resolution compared with a state-of-the-art iterative method and another neural-network-based reconstruction algorithm.
PubMed: 36857232
DOI: 10.1364/OL.484862 -
Optics Express Mar 2024The application of a conical wavefront in the near field of the tiled aperture coherent beam combination (CBC) produces a segmented, similar to Bessel-Gauss irradiance...
The application of a conical wavefront in the near field of the tiled aperture coherent beam combination (CBC) produces a segmented, similar to Bessel-Gauss irradiance pattern (BG-CBC), in the far field. The properties of such a structured optical field were numerically investigated. In contrast to that for the classical CBC, the power diffracted beyond the 'zero' BG-CBC diffraction order is more smoothly and homogenously distributed, not evidencing sharp maxima and dark regions typical for CBC. The novelty of the BG-CBC with segmented conical wavefront is a simple way of caustics elongation and redistribution of power density for the same CBC architecture.
PubMed: 38571227
DOI: 10.1364/OE.518686 -
Sensors (Basel, Switzerland) Aug 2022Hexagonal grids have many advantages over square grids and could be successfully used in mobile robotics as a map representation. However, there is a lack of an...
Hexagonal grids have many advantages over square grids and could be successfully used in mobile robotics as a map representation. However, there is a lack of an essential algorithm, namely, SLAM (simultaneous localization and mapping), that would generate a map directly on the hexagonal grid. In this paper, this issue is addressed. The solution is based on scan matching and solving the least-square problem with the Gauss-Newton formula, but it is modified with the Lagrange multiplier theorem. This is necessary to fulfill the constraints given by the manifold. The algorithm was tested in the synthetic environment and on a real robot and is entirely fully suitable for the presented task. It generates a very accurate map and generally has even better precision than the similar approach implemented on the square lattice.
Topics: Algorithms; Computer Systems; Robotics
PubMed: 36015980
DOI: 10.3390/s22166221 -
Catastrophe optics theory unveils the localised wave aberration features that generate ghost images.Ophthalmic & Physiological Optics : the... Sep 2022Monocular polyplopia (ghost or multiple images) is a serious visual impediment for some people who report seeing two (diplopia), three (triplopia) or even more images....
Monocular polyplopia (ghost or multiple images) is a serious visual impediment for some people who report seeing two (diplopia), three (triplopia) or even more images. Polyplopia is expected to appear if the point spread function (PSF) has multiple intensity cores (a dense concentration of a large portion of the radiant flux contained in the PSF) relatively separated from each other, each of which contributes to a distinct image. We present a theory that assigns these multiple PSF cores to specific features of aberrated wavefronts, thereby accounting optically for the perceptual phenomenon of monocular polyplopia. The theory provides two major conclusions. First, the most likely event giving rise to multiple PSF cores is the presence of hyperbolic, or less probably elliptical, umbilic caustics (using the terminology of catastrophe optics). Second, those umbilic caustics formed on the retinal surface are associated with certain points of the wave aberration function, called cusps of Gauss, where the gradient of a curvature function vanishes. However, not all cusps of Gauss generate those umbilic caustics. We also provide necessary conditions for those cusps of Gauss to be fertile. To show the potential of this theoretical framework for understanding the nature and origin of polyplopia, we provide specific examples of ocular wave aberration functions that induce diplopia and triplopia. The polyplopia effects in these examples are illustrated by depicting the multi-core PSFs and the convolved retinal images for clinical letter charts, both through computer simulations and through experimental recording using an adaptive optics set-up. The number and location of cores in the PSF is thus a potentially useful metric for the existence and severity of polyplopia in spatial vision. These examples also help explain why physiological pupil constriction might reduce the incidence of ghosting and multiple images of daily objects that affect vision with dilated pupils. This mechanistic explanation suggests a possible role for optical phase-masking as a clinical treatment for polyplopia and ghosting.
Topics: Caustics; Diplopia; Humans; Optics and Photonics; Retina; Vision, Ocular
PubMed: 35620968
DOI: 10.1111/opo.13008 -
Scientific Reports Oct 2020Recently introduced [Formula: see text] theory is generalized by adding dependence on the arbitrary scalar field [Formula: see text] and its kinetic term [Formula: see...
Recently introduced [Formula: see text] theory is generalized by adding dependence on the arbitrary scalar field [Formula: see text] and its kinetic term [Formula: see text], to explore non-minimal interactions between geometry, scalar and matter fields in context of the Gauss-Bonnet theories. The field equations for the resulting [Formula: see text] theory are obtained and show that particles follow non-geodesic trajectories in a perfect fluid surrounding. The energy conditions in the Friedmann-Lemaître-Robertson-Walker (FLRW) spacetime are discussed for the generic function [Formula: see text]. As an application of the introduced extensions, using the reconstruction techniques we obtain functions that satisfy common cosmological models, along with the equations describing energy conditions for the reconstructed [Formula: see text] gravity. The detailed discussion of the energy conditions for the de Sitter and power-law spacetimes is provided in terms of the fixed kinetic term i.e. in the [Formula: see text] case. Moreover, in order to check viability of the reconstructed models, we discuss the energy conditions in the specific cases, namely the [Formula: see text] and [Formula: see text] approaches. We show, that for the appropriate choice of parameters and constants, the energy conditions can be satisfied for the discussed scenarios.
PubMed: 33093583
DOI: 10.1038/s41598-020-75067-9