Image-Based Angular Distortion Metric of Map Projections by Using Surface Fitting for Noise Reduction

Measuring, analyzing, reducing, and optimizing distortions in map projections is important in cartography. In this study, we introduced a novel image-based angular distortion metric based on the previous spherical great circle arcs-based metric. Images with predefined patterns were used to generate distorted images using mapping software. The generated distorted images with known patterns were then exploited to calculate the proposed angular distortion metric. The mapping software performed the underlying transformation of map projections. Therefore, there was no direct explicit dependence on the forward equations of the map projections in our proposed metric. However, there were fairly large computation errors in the ordinary image-based approach without special correction. To reduce the error, we introduced surface-fitting-based noise reduction in our approach. We established and solved systems of linear equations based on bivariate polynomial functions in the process of noise reduction. Sufficient experiments were made to validate the proposed image-based metric and the accompanying noise reduction approach. In the experiment, the NASA G.Projector was employed as the mapping software for evaluating more than 200 map projections. Experimental results demonstrated that the proposed image-based approach and surface fitting-based noise reduction are feasible and practical for the evaluation of the angular distortion of map projections.

The Refraction Indices and Brewster Law in Stressed Isotropic Materials and Cubic Crystals

We study the elasto-optic behavior of stressed cubic crystals (all classes) and isotropic materials (like e.g., glasses). We obtain the explicit dependence of the refraction indices on the stress (either applied or residual), as well as a mild generalization of the Brewster law for cubic crystals. We show also that the optic indicatrix and the stress ellipsoid are coaxial only in the isotropic case. This theory allows the improvement of the measurement techniques, as photoelasticity, on cubic crystals and optically isotropic materials.

Quantum nonlocality without entanglement: explicit dependence on prior probabilities of nonorthogonal mirror-symmetric states

In the case of a multi-party system, through local operations and classical communication (LOCC), each party may not perform perfect discrimination of quantum states that are separable and orthogonal. This property of quantum ensemble is called “nonlocality without entanglement” since each local party has a limit to full information of given quantum states. When this property is extended to the case of minimum-error discrimination, one can see that it is revealed when a nonlocal measurement provides more information about the unentangled states than LOCC does. One may infer the fact that the property depends on quantum states composing the quantum ensemble. However, an essential but unsettled question about the property is whether an explicit dependence on prior probabilities in terms of minimum-error discrimination could be shown in nonlocality without entanglement. In a simple term, one can ask whether different quantum ensembles made of the same separable quantum states could exhibit explicitly different behavior of the nonlocality. We answer this question in the positive, and we furthermore provide the explicit functional dependence of guessing probability on prior probabilities for the mirror-symmetric ensemble.

Renormalization Scheme and Mass Scale Independence

We demonstrate that in the mass independent renormalization scheme, the renormalization group equations associated with the unphysical parameters that characterize the renormalization scheme and the mass scale leads to summation that results in a cancellation between the implicit and explicit dependence on these parameters. The resulting perturbative expansion is consequently independent of these arbitrary parameters. We illustrate this by considering R, the cross section for e+e− → hadrons.

Fibre-base duality of 5d KK theories

We study circle compactifications of 6d superconformal field theories giving rise to 5d rank 1 and rank 2 Kaluza-Klein theories. We realise the resulting theories as M-theory compactifications on local Calabi-Yau 3-folds and match the prepotentials from geometry and field theory. One novelty in our approach is that we include explicit dependence on bare gauge couplings and mass parameters in the description which in turn leads to an accurate parametrisation of the prepotential including all parameters of the field theory. We find that the resulting geometries admit “fibre-base” duality which relates their six-dimensional origin with the purely five-dimensional quantum field theory interpretation. The fibre-base duality is realised simply by swapping base and fibre curves of compact surfaces in the local Calabi-Yau which can be viewed as the total space of the anti-canonical bundle over such surfaces. Our results show that such swappings precisely occur for surfaces with a zero self-intersection of the base curve and result in an exchange of the 6d and 5d pictures.

A model-independent test of the evolution of gas depletion factor for SPT-SZ and Planck ESZ clusters

The gas mass fraction in galaxy clusters has been widely used to determine cosmological parameters. This method assumes that the ratio of the cluster gas mass fraction to the cosmic baryon fraction ($$\gamma (z)$$ γ ( z ) ) is constant as a function of redshift. In this work, we look for a time evolution of $$\gamma (z)$$ γ ( z ) at $$R_{500}$$ R 500 by using both the SPT-SZ and Planck Early SZ (ESZ) cluster data, in a model-independent fashion without any explicit dependence on the underlying cosmology. For this calculation, we use a non-parametric functional form for the Hubble parameter obtained from Gaussian Process regression using cosmic chronometers. We parameterize $$\gamma (z)$$ γ ( z ) as: $$\gamma (z)= \gamma _0(1+\gamma _1 z)$$ γ ( z ) = γ 0 ( 1 + γ 1 z ) to constrain the redshift evolution. We find contradictory results between both the samples. For SPT-SZ, $$\gamma (z)$$ γ ( z ) decreases as a function of redshift (at more than 5$$\sigma $$ σ ), whereas a positive trend with redshift is found for Planck ESZ data (at more than 4$$\sigma $$ σ ). We however find that the $$\gamma _1$$ γ 1 values for a subset of SPT-SZ and Planck ESZ clusters between the same redshift interval agree to within $$1\sigma $$ 1 σ . When we allow for a dependence on the halo mass in the evolution of the gas depletion factor, the $$4-5\sigma $$ 4 - 5 σ discrepancy reduces to $$2\sigma $$ 2 σ .

Optimization of photo-orientation rate of azobenzene-containing polymer based on a kinetic model of photoinduced ordering

The explicit dependence of the rate of photoinduced ordering (photo-orientation) of azobenzene-containing liquid-crystalline polymer on photostationary concentration of cis-azobenzene has been predicted theoretically and found experimentally. The employed kinetic model...

Statistics of Nascent and Mature RNA Fluctuations in a Stochastic Model of Transcriptional Initiation, Elongation, Pausing, and Termination

Recent advances in fluorescence microscopy have made it possible to measure the fluctuations of nascent (actively transcribed) RNA. These closely reflect transcription kinetics, as opposed to conventional measurements of mature (cellular) RNA, whose kinetics is affected by additional processes downstream of transcription. Here, we formulate a stochastic model which describes promoter switching, initiation, elongation, premature detachment, pausing, and termination while being analytically tractable. We derive exact closed-form expressions for the mean and variance of nascent RNA fluctuations on gene segments, as well as of total nascent RNA on a gene. We also obtain exact expressions for the first two moments of mature RNA fluctuations and approximate distributions for total numbers of nascent and mature RNA. Our results, which are verified by stochastic simulation, uncover the explicit dependence of the statistics of both types of RNA on transcriptional parameters and potentially provide a means to estimate parameter values from experimental data.

Efficient calculation of crossing symmetric BCJ tree numerators

In this paper, we develop an improved method for directly calculating double-copy-compatible tree numerators in (super-)Yang-Mills and Yang-Mills-scalar theories. Our new scheme gets rid of any explicit dependence on reference orderings, restoring a form of crossing symmetry to the numerators. This in turn improves the computational efficiency of the algorithm, allowing us to go well beyond the number of external particles accessible with the reference order based methods. Motivated by a parallel study of one-loop BCJ numerators from forward limits, we explore the generalization to include a pair of fermions. To improve the accessibility of the new algorithm, we provide a Mathematica package that implements the numerator construction. The structure of the computation also provides for a straightforward introduction of minimally-coupled massive particles potentially useful for future computations in both classical and quantum gravity.