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The behavior of b = 2 real-space renormalization group (RSRG) maps like the majority rule and the decimation map was examined by numerically applying RSRG steps to critical q = 2 , 3 , 4 Potts spin configurations. While the majority rule is generally believed to work well, a more thorough investigation of the action of the map has yet to be considered in the literature. When fixing the size of the renormalized lattice L g and allowing the source configuration size L 0 to vary, we observed that the RG flow of the spin and energy correlation under the majority rule map appear to converge to a nontrivial model-dependent curve. We denote this property as "faithfulness", because it implies that some information remains preserved by RSRG maps that fall under this class. Furthermore, we show that b = 2 weighted majority-like RSRG maps acting on the q = 2 Potts model can be divided into two categories, maps that behave like decimation and maps that behave like the majority rule. [ABSTRACT FROM AUTHOR]

This paper presents a novel hybrid approach to feature detection designed specifically for enhancing Feature-Based Image Registration (FBIR). Through an extensive evaluation involving state-of-the-art feature detectors such as BRISK, FAST, ORB, Harris, MinEigen, and MSER, the proposed hybrid detector demonstrates superior performance in terms of keypoint detection accuracy and computational efficiency. Three image acquisition methods (i.e., rotation, scene-to-model, and scaling transformations) are considered in the comparison. Applied across a diverse set of remote-sensing images, the proposed hybrid approach has shown marked improvements in match points and match rates, proving its effectiveness in handling varied and complex imaging conditions typical in satellite and aerial imagery. The experimental results have consistently indicated that the hybrid detector outperforms conventional methods, establishing it as a valuable tool for advanced image registration tasks. [ABSTRACT FROM AUTHOR]

The aim of this review paper is to survey the fractal morphology of scale-invariant patterns. We are particularly focusing on the scale and conformal invariance, as well as on the fractal non-uniformity (multifractality), inhomogeneity (lacunarity), and anisotropy (succolarity). We argue that these features can be properly quantified by the following six adimensional numbers: the fractal (e.g., similarity, box-counting, or Assouad) dimension, conformal dimension, degree of multifractal non-uniformity, coefficient of multifractal asymmetry, index of lacunarity, and index of fractal anisotropy. The difference between morphological properties of mathematical and real-world fractals is especially outlined in this review paper. [ABSTRACT FROM AUTHOR]

Two ranges of dielectric permittivity (k) increase in polymer composites upon the modification of BaTiO3 filler with multiwalled carbon nanotubes (MWCNTs) are shown for the first time. The first increase in permittivity is observed at low MWCNT content in the composite (approximately 0.07 vol.%) without a considerable increase in dielectric loss tangent and electrical conductivity. This effect is determined by the intensification of filler–polymer interactions caused by the nanotubes, which introduce Brønsted acidic centers on the modified filler surface and thus promote interactions with the cyanoethyl ester of polyvinyl alcohol (CEPVA) polymer binder. Consequently, the structure of the composites becomes more uniform: the permittivity increase is accompanied by a decrease in the lacunarity (nonuniformity) of the structure and an increase in scale invariance, which characterizes the self-similarity of the composite structure. The permittivity of the composites in the first range follows a modified Lichtenecker equation, including the content of Brønsted acidic centers as a parameter. The second permittivity growth range features a drastic increase in the dielectric loss tangent and conductivity corresponding to the percolation effect with the threshold at 0.3 vol.% of MWCNTs. [ABSTRACT FROM AUTHOR]

As an acute respiratory disease, scarlet fever has great harm to public health. Some evidence indicates that the time distribution pattern of heavy PM2.5 pollution occurrence may have an impact on health risks. This study aims to reveal the relation between scaling features in high-concentrations PM2.5 (HC-PM2.5) evolution and scarlet fever incidence (SFI). Based on the data of Hong Kong from 2012 to 2019, fractal box-counting dimension (D) is introduced to capture the scaling features of HC-PM2.5. It has been found that index D can quantify the time distribution of HC-PM2.5, and lower D values indicate more cluster distribution of HC-PM2.5. Moreover, scale-invariance in HC-PM2.5 at different time scales has been discovered, which indicates that HC-PM2.5 occurrence is not random but follows a typical power-law distribution. Next, the exposure–response relationship between SFI and scale-invariance in HC-PM2.5 is explored by Distributed lag non-linear model, in conjunction with meteorological factors. It has been discovered that scale-invariance in HC-PM2.5 has a nonlinear effect on SFI. Low and moderate D values of HC-PM2.5 are identified as risk factors for SFI at small time-scale. Moreover, relative risk shows a decreasing trend with the increase of exposure time. These results suggest that exposure to short-term clustered HC-PM2.5 makes individual more prone to SFI than exposure to long-term uniform HC-PM2.5. This means that individuals in slightly-polluted regions may face a greater risk of SFI, once the PM2.5 concentration keeps rising. In the future, it is expected that the relative risk of scarlet fever for a specific region can be estimated based on the quantitative analysis of scaling features in high-concentrations PM2.5 evolution. [ABSTRACT FROM AUTHOR]

The twin problems of closure and dissipation have been barriers to the analytical solution of the Navier–Stokes equation for fluid flow by top-down methods for two centuries. Here, the statistical multifractal analysis of airborne observations is used to argue that bottom-up approaches based on the dynamic behaviour of the basic constituent particles are necessary. Contrasts among differing systems will yield scale invariant turbulence, but not with universal analytical solutions to the Navier–Stokes equation. The small number of publications regarding a molecular origin for turbulence are briefly considered. Research approaches using suitable observations are recommended. [ABSTRACT FROM AUTHOR]

Scale invariance of an algorithm refers to its ability to treat objects equally independently of their size. For neural networks, scale invariance is typically achieved by data augmentation. However, when presented with a scale far outside the range covered by the training set, neural networks may fail to generalize. Here, we introduce the Riesz network, a novel scale- invariant neural network. Instead of standard 2d or 3d convolutions for combining spatial information, the Riesz network is based on the Riesz transform which is a scale-equivariant operation. As a consequence, this network naturally generalizes to unseen or even arbitrary scales in a single forward pass. As an application example, we consider detecting and segmenting cracks in tomographic images of concrete. In this context, 'scale' refers to the crack thickness which may vary strongly even within the same sample. To prove its scale invariance, the Riesz network is trained on one fixed crack width. We then validate its performance in segmenting simulated and real tomographic images featuring a wide range of crack widths. An additional experiment is carried out on the MNIST Large Scale data set. [ABSTRACT FROM AUTHOR]

The twin problems of closure and dissipation have been barriers to the analytical solution of the Navier–Stokes equation for fluid flow by top-down methods for two centuries. Here, the statistical multifractal analysis of airborne observations is used to argue that bottom-up approaches based on the dynamic behaviour of the basic constituent particles are necessary. Contrasts among differing systems will yield scale invariant turbulence, but not with universal analytical solutions to the Navier–Stokes equation. The small number of publications regarding a molecular origin for turbulence are briefly considered. Research approaches using suitable observations are recommended.

Scale invariance, which refers to the preservation of geometric properties regardless of observation scale, is a prevalent phenomenon in ecological systems. This concept is closely associated with fractals, and river networks serve as prime examples of fractal systems. Quantifying river network complexity is crucial for unveiling the role of river fractals in riverine ecological dynamics, and researchers have used a metric of "branching probability" to do so. Previous studies showed that this metric reflects the fractal nature of river networks. However, a recent article by Carraro and Altermatt (2022) contradicted this classical observation and concluded that branching probability is "scale dependent." I dispute this claim and argue that their major conclusion is derived merely from their misconception of scale invariance. Their analysis in the original article (fig. 3a) provided evidence that branching probability is scale‐invariant (i.e., branching probability exhibits a power‐law scaling), although the authors erroneously interpreted this result as a sign of scale dependence. In this article, I re‐introduce the definition of scale invariance and show that branching probability meets this definition. This provided an opportunity to address the divergent use of "scale invariance" and "scaling" between fractal theory and ecology. [ABSTRACT FROM AUTHOR]

Detection of small objects with undefined shapes, such as color-stained one or a group of virus-infected cells, i.e. foci, in microscopy images, is challenging due to their size and scale variation. Quantifying the foci numbers manually using light microscope images is a laborious task. On the other hand, state-of-the-art machine learning methods often fail to detect uneven foci due to overfitting because of the unavailability of the required number of training images. This study proposes a Scale-Invariant Object Detection method based on Switchable Atrous Convolution (SIOD_SAC) for detecting foci. The proposed method applies a Switchable Atrous Convolution (SAC) module to extract multi-scale features and maintain scale invariance in object detection. The proposed SAC module adaptively selects different dilation rates to capture features at multiple scales, facilitating the detection of objects of different sizes. Due to the unavailability of a foci image dataset for virus patch detection, we introduce a dataset containing 149 foci images with virus patches of different shapes and sizes. Here, we utilized a dataset comprising 149 images of various shaped and sized foci. The microscopic images in the dataset are obtained from the hepatitis C virus focus-forming assay. We evaluate the proposed method on the introduced dataset for small object detection, and our results show that the proposed method achieves state-of-the-art performance in terms of mean Average Precision (mAP). Specifically, the proposed SIOD_SAC method achieves an mAP of 24.57% for cell patch detection and 76.19% for FFU (focus forming units) detection at the threshold of 25 IOU, outperforming the current state-of-the-art by a significant margin. The dataset can be obtained through https://forms.gle/fbhJrBt9akJkkNz49. The code is available at https://github.com/asAmrita/Virus_Patch_Detection.

The moving vehicles present different scales in the image due to the perspective effect of different viewpoint distances. The premise of advanced driver assistance system (ADAS) system for safety surveillance and safe driving is early identification of vehicle targets in front of the ego vehicle. The recognition of the same vehicle at different scales requires feature learning with scale invariance. Unlike existing feature vector methods, the normalized PCA eigenvalues calculated from feature maps are used to extract scale-invariant features. This study proposed a convolutional neural network (CNN) structure embedded with the module of multi-pooling-PCA for scale variant object recognition. The validation of the proposed network structure is verified by scale variant vehicle image dataset. Compared with scale invariant network algorithms of Scale-invariant feature transform (SIFT) and FSAF as well as miscellaneous networks, the proposed network can achieve the best recognition accuracy tested by the vehicle scale variant dataset. To testify the practicality of this modified network, the testing of public dataset ImageNet is done and the comparable results proved its effectiveness in general purpose of applications.

This paper presents a novel hybrid approach to feature detection designed specifically for enhancing Feature-Based Image Registration (FBIR). Through an extensive evaluation involving state-of-the-art feature detectors such as BRISK, FAST, ORB, Harris, MinEigen, and MSER, the proposed hybrid detector demonstrates superior performance in terms of keypoint detection accuracy and computational efficiency. Three image acquisition methods (i.e., rotation, scene-to-model, and scaling transformations) are considered in the comparison. Applied across a diverse set of remote-sensing images, the proposed hybrid approach has shown marked improvements in match points and match rates, proving its effectiveness in handling varied and complex imaging conditions typical in satellite and aerial imagery. The experimental results have consistently indicated that the hybrid detector outperforms conventional methods, establishing it as a valuable tool for advanced image registration tasks.

This paper presents new classes of exact radial solutions to the nonlinear ordinary differential equation that arises as a saddle-point condition for a Euclidean scalar field theory in D-dimensional spacetime. These solutions are found by exploiting the dimensional consistency of the radial differential equation for a single massless scalar field, which allows it to transform into an autonomous equation. For massive theories, the radial equation is not exactly solvable, but the massless solutions provide useful approximations to the results for the massive case. The solutions presented here depend on the power of the interaction and on the spatial dimension, both of which may be noninteger. Scalar equations arising in the study of conformal invariance fit into this framework, and classes of new solutions are found. These solutions exhibit two distinct behaviors as D → 2 from above. [ABSTRACT FROM AUTHOR]

For a non-relativistic scale invariant system in two spatial dimensions, the quantum scattering amplitude f() is given as a dispersion relation, with a simple closed form for Im f() as well as the integrated cross-section / Im f(= 0). For fixed 6= 0, the ~ ! 0 classical limit is straightforward to obtain. [ABSTRACT FROM AUTHOR]

In many practical situations, we observe a special Burr probability distribution — e.g., Burr distribution describes the distribution of people by income, it describes the rainfall data, etc. In this paper, we provide a theoretical explanation for the ubiquity of Burr distributions: namely, we show that this distribution naturally follows from scale-invariance. To be more precise, the simplest distribution that can be obtained from scale invariance is the Pareto distribution — a frequent particular case of the general Burr family of distributions. Next simplest are all distributions from the Burr family. We also use the scale-invariance approach to come up with a more general class of distributions that will, hopefully, provide an even more accurate description of the corresponding phenomena. [ABSTRACT FROM AUTHOR]

The modeling of sub-daily extreme rainfall has long constituted a challenge for hydrologists in view of the limited availability of data, both in time and space. In this context, the scale invariance principle, which formally links precipitation intensities across a range of time scales under a rigorous theoretical underpin, comprises a useful and parsimonious tool for deriving probabilistic models for the referred stochastic variables. This paper aims at reviewing the history of application of the scale invariance principle to the marginal distributions of intense precipitation, as well as presenting recent developments in this field. We first address the basic concepts and the mathematical formalism of scale invariant models, discussing distinct scaling regimes across durations and estimation procedures. Next, we present a comprehensive review on at-site and regional stationary scaling models applied in several regions of the world, with focus on their underlying assumptions and main limitations. Finally, we address extensions of the rationale for nonstationary models as a means of accommodating potential effects of climate change in extreme short-duration rainfall. While discussing each of these frameworks, we indicate potential research gaps and modeling developments which could further advance the understanding of scaling behavior of extreme precipitation and improve statistical inference. Hence, this review may constitute a useful guide for practitioners and motivate future research in the modeling of short-duration extreme rainfall. [ABSTRACT FROM AUTHOR]

The aim of this review paper is to survey the fractal morphology of scale-invariant patterns. We are particularly focusing on the scale and conformal invariance, as well as on the fractal non-uniformity (multifractality), inhomogeneity (lacunarity), and anisotropy (succolarity). We argue that these features can be properly quantified by the following six adimensional numbers: the fractal (e.g., similarity, box-counting, or Assouad) dimension, conformal dimension, degree of multifractal non-uniformity, coefficient of multifractal asymmetry, index of lacunarity, and index of fractal anisotropy. The difference between morphological properties of mathematical and real-world fractals is especially outlined in this review paper.

Two ranges of dielectric permittivity (k) increase in polymer composites upon the modification of BaTiO3 filler with multiwalled carbon nanotubes (MWCNTs) are shown for the first time. The first increase in permittivity is observed at low MWCNT content in the composite (approximately 0.07 vol.%) without a considerable increase in dielectric loss tangent and electrical conductivity. This effect is determined by the intensification of filler–polymer interactions caused by the nanotubes, which introduce Brønsted acidic centers on the modified filler surface and thus promote interactions with the cyanoethyl ester of polyvinyl alcohol (CEPVA) polymer binder. Consequently, the structure of the composites becomes more uniform: the permittivity increase is accompanied by a decrease in the lacunarity (nonuniformity) of the structure and an increase in scale invariance, which characterizes the self-similarity of the composite structure. The permittivity of the composites in the first range follows a modified Lichtenecker equation, including the content of Brønsted acidic centers as a parameter. The second permittivity growth range features a drastic increase in the dielectric loss tangent and conductivity corresponding to the percolation effect with the threshold at 0.3 vol.% of MWCNTs.

On the basis of a general action principle, we revisit the scale invariant field equation using the cotensor relations by Dirac (1973). This action principle also leads to an expression for the scale factor λ , which corresponds to the one derived from the gauging condition, which assumes that a macroscopic empty space is scale-invariant, homogeneous, and isotropic. These results strengthen the basis of the scale-invariant vacuum (SIV) paradigm. From the field and geodesic equations, we derive, in current time units (years, seconds), the Newton-like equation, the equations of the two-body problem, and its secular variations. In a two-body system, orbits very slightly expand, while the orbital velocity keeps constant during expansion. Interestingly enough, Kepler's third law is a remarkable scale-invariant property. [ABSTRACT FROM AUTHOR]

Beta‐decay half‐lives for the free neutron, for 6He and 8He, and for 8Li are calculated ab initio from geometrical thermodynamics arguments, independently of any quantum mechanics. Half‐lives for the decay of 8Be to two alphas and for the disintegration of the tetraneutron are also calculated. The calculated values are close to those experimentally observed. [ABSTRACT FROM AUTHOR]

The concept of memory is of central importance for characterizing complex systems and phenomena. Presence of long-term memories indicates how their dynamics can be less sensitive to initial conditions compared to the chaotic cases. On the other hand, it is empirically known that the Feller–Pareto distribution, which decays as the power law i.e. the scale-invariant nature, frequently appears as a statistical law generated by the dynamics of complex systems. However, it is generally not a simple task to determine if a system obeying such a power law possesses a high degree of complexity with a long-term memory. Here, a new method is proposed for characterization of memory. In particular, a scaling relation to be satisfied by any memoryless dynamics generating the Feller–Pareto power-law distribution is presented. Then, the method is applied to the real data of energies released by a series of earthquakes and acceleration of ground motion due to a strong earthquake. It is shown in this way that the sequence of the released energy in seismicity is memoryless in the event time, whereas that of acceleration is memoryful in the sampling time. [ABSTRACT FROM AUTHOR]

As an example of the implementation of digital materials science approaches based on statistical processing of electron micrographs with the analysis of fractal parameters, the digital characteristics of microstructure of diamond–silicon carbide ceramic composite material are calculated. The lacunarity parameter characterizing the non-uniform distribution of filler particles in the matrix is found. Based on lacunarity values calculated at different scales, scale invariance parameter characterizing the dependence of lacunarity on the scale is evaluated. Voronoi entropy characterizing the structure based on the quantity of information is also calculated and used to determine the average number of neighboring particles and average distance between them. For the composites with high mechanical properties, the number of nearest neighbors approaches six, indicating an almost closest packing.

The Principle of Indifference ('PI': the simplest non-informative prior in Bayesian probability) has been shown to lead to paradoxes since Bertrand (1889). Von Mises (1928) introduced the 'Wine/Water Paradox' as a resonant example of a 'Bertrand paradox', which has been presented as demonstrating that the PI must be rejected. We now resolve these paradoxes using a Maximum Entropy (MaxEnt) treatment of the PI that also includes information provided by Benford's 'Law of Anomalous Numbers' (1938). We show that the PI should be understood to represent a family of informationally identical MaxEnt solutions, each solution being identified with its own explicitly justified boundary condition. In particular, our solution to the Wine/Water Paradox exploits Benford's Law to construct a non-uniform distribution representing the universal constraint of scale invariance, which is a physical consequence of the Second Law of Thermodynamics. [ABSTRACT FROM AUTHOR]

Optimization in noisy environments arises frequently in applications. Solving this problem quickly, efficiently, and accurately is therefore of great importance. The stochastic gradient descent (SGD) method has proven to be a fundamental and an effective tool which is flexible enough to allow modifications for improving its convergence properties. In this paper we propose a new algorithm for solving an unconstrained optimization problems in noisy environments which combines the SGD with a modified momentum term using a two-point step size estimation in the Barzilai-Borwein (BB) framework. We perform a high probability analysis for the proposed algorithm and we establish its convergence under the standard assumptions. Numerical experiments demonstrate a promising behavior of the proposed method compared to the "vanilla" SGD with momentum in noise-free and in noisy environment when the objective function is scaled. [ABSTRACT FROM AUTHOR]

Intensity-duration-frequency (IDF) relationships are frequently required for hydraulic design and risk assessment in small catchments. Nonetheless, the usual scarcity of subdaily rainfall data may render the derivation of such models unfeasible in the locations of interest. For addressing this problem, in this study, we discuss a regional IDF relationship based on the principle of scale invariance, and apply this model to gauged sites in the metropolitan region of Belo Horizonte, Brazil. Our results indicated that a single regional-scale exponent, as derived from the average of estimates at training sites, is accurate enough (mean absolute error of 15%) for describing the probabilistic behavior of extreme rainfall across a large set of subdaily durations in the study area. In addition, the quantile estimates derived from our model are similar to those obtained with more complex regionalization methods, which suggests that the scale invariance principle may be an effective and parsimonious tool for extreme rainfall frequency analysis in poorly gauged areas. [ABSTRACT FROM AUTHOR]

As an example of the implementation of digital materials science approaches based on statistical processing of electron micrographs with the analysis of fractal parameters, the digital characteristics of microstructure of diamond–silicon carbide ceramic composite material are calculated. The lacunarity parameter characterizing the non-uniform distribution of filler particles in the matrix is found. Based on lacunarity values calculated at different scales, scale invariance parameter characterizing the dependence of lacunarity on the scale is evaluated. Voronoi entropy characterizing the structure based on the quantity of information is also calculated and used to determine the average number of neighboring particles and average distance between them. For the composites with high mechanical properties, the number of nearest neighbors approaches six, indicating an almost closest packing. [ABSTRACT FROM AUTHOR]

Intensity‐duration‐frequency (IDF) curves are useful in water resources engineering for the planning and design of hydrological structures. As opposed to the common use of only extreme data to build IDF curves, here, we use all the non‐zero rainfall intensities, thereby making efficient use of the available information. We use the extended generalized Pareto distribution to model the distribution of the non‐zero rainfall intensities. We consider three commonly used approaches for building IDF curves. The first approach is based on the scale‐invariance property of rainfall, the second relies on the general IDF formulation of Koutsoyiannis et al. (1998, https://doi.org/10.1016/S0022-1694(98)00097-3), and the last approach is purely data‐driven(Overeem et al., 2008, https://doi.org/10.1016/j.jhydrol.2007.09.044). Using these three approaches, and some extensions around them, we build a total of 10 models for the IDF curves, and then we compare them in a split‐sampling cross‐validation framework. We consider a total of 81 stations at 10 min resolution in Switzerland. Due to the marked seasonality of rainfall in the study area, we performed a seasonal‐based analysis. The results reveal the model based on the data‐driven approach as the best model. It is able to correctly model the observed intensities across duration while being reliable and robust. It is also able to reproduce the space and time variability of extreme rainfall across Switzerland. Plain Language Summary: Intensity‐duration‐frequency (IDF) curves are used in water resources engineering for the safe design of hydraulic structures. They summarize the relationship between rainfall intensity, duration, and frequency of occurrence. IDF curves are commonly built using probability distributions that use only extreme data, which can be a drawback in terms of the efficient use of already scarce data. In this study, we use a distribution, the extended generalized Pareto distribution, that uses all the non‐zero rainfall intensities to model IDF curves. We build a total of 10 models, which are based on three commonly used approaches and some extensions around them. We compare them in terms of their reliability and robustness. The best IDF model is able to reproduce the known variability of extreme rainfall across Switzerland. Key Points: We build intensity duration frequency (IDF) curves using all the non‐zero precipitation data and model the intensities with the extended generalized Pareto distributionWe consider three approaches to building IDF curves: scale invariance, IDF formulation of Koutsoyiannis et al. (1998), https://doi.org/10.1016/S0022-1694(98)00097-3 and data‐driven methodWe compare and select the best model in a cross‐validation framework [ABSTRACT FROM AUTHOR]

Background: The non-invasive 3D-imaging and successive 3D-segmentation of plant root systems has gained interest within fundamental plant research and selectively breeding resilient crops. Currently the state of the art consists of computed tomography (CT) scans and reconstruction followed by an adequate 3D-segmentation process. Challenge: Generating an exact 3D-segmentation of the roots becomes challenging due to inhomogeneous soil composition, as well as high scale variance in the root structures themselves. Approach: (1) We address the challenge by combining deep convolutional neural networks (DCNNs) with a weakly supervised learning paradigm. Furthermore, (2) we apply a spatial pyramid pooling (SPP) layer to cope with the scale variance of roots. (3) We generate a fine-tuned training data set with a specialized sub-labeling technique. (4) Finally, to yield fast and high-quality segmentations, we propose a specialized iterative inference algorithm, which locally adapts the field of view (FoV) for the network. Experiments: We compare our segmentation results against an analytical reference algorithm for root segmentation (RootForce) on a set of roots from Cassava plants and show qualitatively that an increased amount of root voxels and root branches can be segmented. Results: Our findings show that with the proposed DCNN approach combined with the dynamic inference, much more, and especially fine, root structures can be detected than with a classical analytical reference method. Conclusion: We show that the application of the proposed DCNN approach leads to better and more robust root segmentation, especially for very small and thin roots. [ABSTRACT FROM AUTHOR]

Inference based on the partial envelope model is variational or nonequivariant under rescaling of the responses, and tends to restrict its use to responses measured in identical or analogous units. The efficiency acquisitions promised by partial envelopes frequently cannot be accomplished when the responses are measured in diverse scales. Here, we extend the partial envelope model to a scaled partial envelope model that overcomes the aforementioned disadvantage and enlarges the scope of partial envelopes. The proposed model maintains the potential of the partial envelope model in terms of efficiency and is invariable to scale changes. Further, we demonstrate the maximum likelihood estimators and their properties. Lastly, simulation studies and a real-data example demonstrate the advantages of the scaled partial envelope estimators, including a comparison with the standard model estimators, partial envelope estimators, and scaled envelope estimators. [ABSTRACT FROM AUTHOR]

In this paper, we use the holographic method to compute the entanglement entropy for different regions in the fourth-order scale-invariant theory of gravity. In four dimensions, the action of scale-invariant gravity contains a parameter where the moduli space has some distinguished points, precisely, the space of solutions contains the Log-gravity and for this specific solution, we compute the entanglement entropy. We also use the numerical method to investigate mutual information and tripartite information. Moreover, we make a comment on the sign of these quantities. [ABSTRACT FROM AUTHOR]

Study region: A network of 25 rain gauges roughly covering an area of 517.2 km2 of Warsaw, in Poland. Study focus: Scaling and intermittency of data series of rainfall intensity are investigated for each of the network rain gauges using five multifractal framework methods: spectral density analysis, functional box-counting, trace moment, probability distribution/multiple scaling, and double trace moment. Synthetic precipitation series are then generated by means of continuous universal random cascade models. Cascade generators are defined by universal parameters calculated for selected Warsaw rain gauges, or rain gauge clusters displaying similarity of multifractal parameters. The generated synthetic precipitation time series are subject to statistical evaluation by comparing the complementary cumulative distribution function and the intermittency calculated for synthetic versus observed data. Finally, a novel filtering algorithm is proposed to correct the intermittency characteristics of synthetic precipitation time series. New hydrological insights: Based on our analyses, the temporal structure of the recorded Warsaw precipitation time series is found to be a multifractal set characterized by a scaling behaviour over a wide range of scales. Furthermore, it has been observed that most Warsaw rain gauges, have a distinct similarity of multifractal properties. It has also been demonstrated that, for the first time in Poland, the universal continuous cascades could be used in practice for the generation of synthetic rainfall series at fine (1-min) temporal resolution

This paper presents new classes of exact radial solutions to the nonlinear ordinary differential equation that arises as a saddle-point condition for a Euclidean scalar field theory in D-dimensional spacetime. These solutions are found by exploiting the dimensional consistency of the radial differential equation for a single massless scalar field, which allows it to transform into an autonomous equation. For massive theories, the radial equation is not exactly solvable, but the massless solutions provide useful approximations to the results for the massive case. The solutions presented here depend on the power of the interaction and on the spatial dimension, both of which may be noninteger. Scalar equations arising in the study of conformal invariance fit into this framework, and classes of new solutions are found. These solutions exhibit two distinct behaviors as D→2 from above.

The causal connection between congestions and velocity changes at different locations induces various statistical features, which we identify and measure in detail. We carry out an empirical analysis of large-scale traffic data on a local motorway network around the Breitscheid intersection in the North Rhine-Westphalia, Germany. We put forward a response function which measures the velocity change at a certain location versus time conditioned on a congestion at another location. We use a novel definition of the corresponding congestion indicator to ensure causality. We find that the response of velocities to the congestion exhibits phase changes in time. A negative response at smaller time lags transforms into positive one at larger time lags, implying a certain traffic mechanism. The response decays as a power law with the distance. We also identify a scaling property leading to a collapse of the response functions on one curve.

We report the observation of a linear magnetoresistance in single crystals and epitaxial thin films of the pyrochlore iridate Bi2Ir2O7. The linear magnetoresistance is positive and isotropic at low temperatures, without any sign of saturation up to 35 T. As temperature increases, the linear field dependence gradually evolves to a quadratic field dependence. The temperature and field dependence of magnetoresistance of Bi2Ir2O7 bears strikingly resemblance to the scale invariant magnetoresistance observed in the strange metal phase in high Tc cuprates. However, the residual resistivity of Bi2Ir2O7 is more than two orders of magnitude higher than the curpates. Our results suggest that the correlation between linear magnetoresistance and quantum fluctuations may exist beyond high temperature superconductors.

BackgroundThe non-invasive 3D-imaging and successive 3D-segmentation of plant root systems has gained interest within fundamental plant research and selectively breeding resilient crops. Currently the state of the art consists of computed tomography (CT) scans and reconstruction followed by an adequate 3D-segmentation process.ChallengeGenerating an exact 3D-segmentation of the roots becomes challenging due to inhomogeneous soil composition, as well as high scale variance in the root structures themselves.Approach(1) We address the challenge by combining deep convolutional neural networks (DCNNs) with a weakly supervised learning paradigm. Furthermore, (2) we apply a spatial pyramid pooling (SPP) layer to cope with the scale variance of roots. (3) We generate a fine-tuned training data set with a specialized sub-labeling technique. (4) Finally, to yield fast and high-quality segmentations, we propose a specialized iterative inference algorithm, which locally adapts the field of view (FoV) for the network.ExperimentsWe compare our segmentation results against an analytical reference algorithm for root segmentation (RootForce) on a set of roots from Cassava plants and show qualitatively that an increased amount of root voxels and root branches can be segmented.ResultsOur findings show that with the proposed DCNN approach combined with the dynamic inference, much more, and especially fine, root structures can be detected than with a classical analytical reference method.ConclusionWe show that the application of the proposed DCNN approach leads to better and more robust root segmentation, especially for very small and thin roots.