Miracle-dz/UniFAR-FTUs huggingface dataset:
A regularized representation of the fractional Laplacian in n dimensions and its relation to Weierstrass–Mandelbrot-type fractal functions

We demonstrate that the fractional Laplacian (FL) is the principal characteristic operator of harmonic systems with {\it self-similar} interparticle interactions. We show that the FL represents the ``{\it fractional continuum limit}'' of a discrete ``self-similar Laplacian" which is obtained by Hamilton's variational principle from a discrete spring model. We deduce from generalized self-similar elastic potentials regular representations for the FL which involve convolutions of symmetric finite difference operators of even orders extending the standard representation of the FL. Further we deduce a regularized representation for the FL $-(-\Delta)^{\frac{\alpha}{2}}$ holding for $\alpha\in \R \geq 0$. We give an explicit proof that the regularized representation of the FL gives for integer powers $\frac{\alpha}{2} \in \N_0$ a distributional representation of the standard Laplacian operator $\Delta$ including the trivial unity operator for $\alpha\rightarrow 0$. We demonstrate that self-similar {\it harmonic} systems are {\it all} governed in a distributional sense by this {\it regularized representation of the FL} which therefore can be conceived as characteristic footprint of self-similarity.
MODEL THEORY AND MACHINE LEARNING

Abstract About 25 years ago, it came to light that a single combinatorial property determines both an important dividing line in model theory (NIP) and machine learning (PAC-learnability). The following years saw a fruitful exchange of ideas between PAC-learning and the model theory of NIP structures. In this article, we point out a new and similar connection between model theory and machine learning, this time developing a correspondence between stability and learnability in various settings of online learning. In particular, this gives many new examples of mathematically interesting classes which are learnable in the online setting.
The safety loading of reinsurance premiums

Abstract 1. Introduction 1.1. In the older forms of reinsurance, often referred to as “proportional” reinsurance, there is no real problem involved in determining the correct safety loading of premiums. It seems natural, in fact almost obvious, that reinsurance should take place on “original terms”, and that any departure from this procedure would need special justification. The only problem which may be troublesome is to determine the three components of the gross premium, i.e. net premium, safety loading and loading for expenses. The last of these components is calculated to cover costs connected with the direct underwriting, such as agent's commission, and does not, in principle concern the reinsurer.
Investigation of Radiation Properties of CO2 Reacted Portland

In this study we explored the radiation properties of CO2-reacted Portland which take place in kiln process of cement production. The use of CO2 can change Portland density via chemical process to obtain CaCO3. When the CO2 capture rate of Portland cement is zero, the density is 2.3 g/cm3, while the CO2 capture rate is 100%, the density is reached to 2.705 g/cm3. The radiation shielding properties were explored using FLUKA code. To define the radiation shielding properties of the CO2-reacted Portland, four types of beams (photons, electrons, protons and neutrons) were used. These beams have been used to explain the leptonic and hadronic interactions. The CO2-reacted Portland radiation length and density have been calculated and presented. The energy depositions of four beams with various beam energies were examined by considering density variation of the cement. It has been found that CO2-reacted Portland has more efficient radiation shielding than traditional Portland materials. The carbonization of Portland will be carried out during the kiln process, not by the CO2 diffusion process, which is a very slow process, but by the faster and more convenient spray method.
Adapting the minimum variance beamformer to a graphics processing unit for active sonar imaging systems

The MVDR beamformer has been shown to improve active sonar image quality compared to conventional methods. Unfortunately, it is also significantly more computationally expensive because a spatial covariance matrix must be estimated and inverted for each image pixel. We target this challenge by altering and mapping the MVDR beamformer to a GPU, and suggest three different solutions depending on the system size. For systems with relatively few channels, we suggest arithmetic optimizations for the estimation step, and show how a GPU can be used to yield image creation rates of more than 1 Mpx/s. For larger systems we show that frequency domain processing is preferable, as this promotes high processing rates at a negligible reduction in image quality. These GPU implementations consistently reduced the runtime by 2 orders of magnitude compared to our reference C implementation. For even larger systems we suggest employing the LCA beamformer. It does not calculate a weightset, but merely computes the beamformer.
Optical see-through head-mounted display with occlusion capability

Lack of mutual occlusion capability between computer-rendered and real objects is one of fundamental problems for most existing optical see-through head-mounted displays (OST-HMD). Without the proper occlusion management, the virtual view through an OST-HMD appears “ghost-like”, floating in the real world. To address this challenge, we have developed an innovative optical scheme that uniquely combines the eyepiece and see-through relay optics to achieve an occlusion-capable OST-HMD system with a very compelling form factor and high optical performances. The proposed display system was based on emerging freeform optical design technologies and was designed for highly efficient liquid crystal on silicon (LCoS) type spatial light modulator (SLM) and bright Organic LED (OLED) microdisplay. The proposed display technology was capable of working in both indoor and outdoor environments. Our current design offered a 1280x1024 color resolution based on 0.8" microdisplay and SLM. The MTF values for the majority of the fields at the cutoff frequency of 40lps/mm, which is determined by the pixel size of the microdisplay, are better than 15%. The design achieved a diagonal FOV of 40 degrees, 31.7 degrees horizontally and 25.6 degrees vertically, an exit pupil diameter of 8mm (non-vignetted), and an eye clearance of 18mm. The optics weights about 20 grams per eye. Our proposed occlusion capable OST-HMD system can easily find myriads of applications in various military and commercial sectors such as military training, gaming and entertainment.
Elemental abundances in a Type I supernova remnant

The solid-state spectrometer (SSS) on the HEAO 2 (Einstein) X-ray observatory observed the X-ray spectrum of Tycho's SNR. The observations show a relative excess of line emission from Si, S, and Ar by not less than 6 compared to that expected from a plasma of solar composition in collisional equilibrium and by a factor of not less than 3 compared to Cas A. Similar excesses are not found for line emission from Mg and Fe. The data suggest that the SN observed by Tycho in 1572 produced significant amounts of Si group elements but did not eject large amounts of Fe as predicted by some models of Type I SN events.
Large-Scale Patterns Associated with Severe Summertime Thunderstorms over Central Arizona

Abstract Severe thunderstorms are relatively rare over Arizona and occur most frequently during the summer monsoon period, that is, July, August, and early September. Forecasting in Arizona during the summertime is quite difficult and skill scores are low for both precipitation and severe thunderstorm watches and warnings. In the past, due to the sparse population of Arizona, severe thunderstorms usually impacted few people and were considered relatively insignificant events. However, over the last 20 years, the population of central Arizona has grown dramatically, and the impact of severe thunderstorm and flash flood occurrences has also increased. Synoptic conditions associated with 27 severe thunderstorm events that occurred in central Arizona during the summer monsoon have been examined systematically and compared to long-term mean July conditions. The period of study covered 1978 to 1990, and cases selected were limited to the high population area of central Arizona. McCollum subjectively identified .
Quasi‐periodic behavior of ion events and wave activity upstream from Jupiter's Bow Shock: Ulysses' observations

A new insight into the ways that the Jovian magnetosphere influences the near Jupiter interplanetary space becomes possible thanks to Ulysses' collection of magnetic field, plasma and energetic ion (HI‐SCALE) data during its inbound trajectory (d22–d34, 1992). The most striking new results from the analysis of those data are the following: a) presence of large amplitude (ΔB⟂/B≈1) near plane polarized Alfvén waves upstream from the Jovian bow shock with a period equal to the planet's rotation (∼10h) at times when the Interplanetary Magnetic Field (IMF) was in contact with the bow shock/magnetopause and lay well outside the ecliptic; b) observation of ∼10h quasi‐periodic variation in the ion plasma and energetic ion data up to energies of ∼2 MeV, c) existence of a variation with a period 2.5 h ≤T ≤6.5 h in the magnetic field and the ion data, in several cases, d) detection of magnetic waves and charged particle modulation with a period of ∼40min, e) observation of an ∼10 h inward/outward motion of the Jovian magnetopause. The observations are consistent with generation of the low frequency upstream (Alfvén) waves through periodic injection of plasma/energetic ions from within the magnetosphere into the upstream region.
Performance Optimization of SSHC Rectifiers for Piezoelectric Energy Harvesting

In the past decades, inductor-based synchronized switch harvesting on inductor (SSHI) rectifiers have been widely employed in many active rectification systems for piezoelectric energy harvesting. Although SSHI rectifiers achieve high energy extraction performance compared to passive full-bridge rectifier (FBR), the performance greatly depends on the inductor employed. While a larger inductor can achieve higher performance, the system form factor is also increased, which is counter to system miniaturization in many applications. To solve this issue, an efficient synchronized switch harvesting on capacitors (SSHC) rectifier was proposed recently. Instead of using large inductors, the SSHC rectifier employs on-chip or off-chip flying capacitors to achieve comparable or higher performance. In previous studies, the flying capacitors are chosen equal to the inherent capacitance of the piezoelectric transducer (PT) to achieve 1/3 voltage flipping efficiency $(\eta _{F})$ for a 1-stage SSHC rectifier and 4/5 flipping efficiency for a 8-stage SSHC rectifier. This brief presents that the flipping efficiency can be further increased to 1/2 for a 1-stage SSHC rectifier if the flying capacitor is chosen to be much larger than $C_{P}$ and the 4/5 flipping efficiency can be achieved by employing only 4 flying capacitors.
Bias dependent tunneling in ferromagnetic junctions and inversion of the tunneling magnetoresistance from a quantum mechanical point of view

In the framework of the free-electron approximation, we have developed a quantum mechanical treatment for describing the bias dependent tunneling in FM/I/FM ferromagnetic junctions. In our theory, the Slonczewski model is extended to include the bias effect. In the barrier region, the Wentzel–Kramers–Brillouin wave function is used following Harrison. The main point of our treatment is to match the wave functions at both sides of the electrode/barrier interfaces quantum mechanically. We find that apart from the usual density of states effect, there exists a quantum coherent factor D(Ex,V)=κR2(Ex,V)−kR↑(Ex,V)kR↓(Ex,V), which decreases monotonously with the increasing applied bias and could change its sign at a sufficiently high bias. The characteristic of this coherent factor can explain the observed rapid decrease of tunneling magnetoresistance (TMR) with increasing bias and the sign change of TMR in some ferromagnetic junctions. Furthermore, numerical results for asymmetry barrier junctions provide a goo.
Finite Modules over $\Bbb Z[t,t^{-1}]$

Let $\Lambda=\Bbb Z[t,t^{-1}]$ be the ring of Laurent polynomials over $\Bbb Z$. We classify all $\Lambda$-modules $M$ with $|M|=p^n$, where $p$ is a primes and $n\le 4$. Consequently, we have a classification of Alexander quandles of order $p^n$ for $n\le 4$.
Nucleating Techniques in Forest Restoration of a Degraded Area in a Seasonally Dry Tropical Forest, Brazil

The nucleator techniques have specific and very particular functions, helping the reoccupation of some animals in the area, besides the natural succession. The objective of this study was to evaluate the use of the nucleator techniques of artificial perches and branch windrowing for the establishment of forest restoration in a seasonally dry tropical forest, Brazil. The research was conducted at Experimental Farm Cachoeira de São Porfírio, municipality of Santa Luzia, Paraíba, Brazil, in the period from August 2017 to July 2018. Two nucleator techniques were used, the artificial perches and branch windrowing. For both, the randomized block design was employed, with five treatments composed of the spacing between the structures that composed the respective techniques (5x5m; 10x10m; 15x15m; 20x20m and control treatment), in four repetitions. For the artificial perches the number of seeds and excreta were evaluated, and for the branched perches the height of the branches and their decomposition over time was evaluated. in addition, the water content and temperature of the soil in the experimental area were also analyzed. The artificial perches provided insertion of seeds distributed in three botanical families and excreta to the degraded area, thus incorporating organic matter and enriching the seed bank of the experimental site. The largest site. The largest number of excreta was obtained on perches with greater distance between them, proving that the spacing of 15x15m is the most suitable. The volumes of branches were altered throughout the experimental period, with a faster decomposition of the branches in the control treatment compared to the other treatments, and their cover provided lower temperatures compared to soil exposed to full sun. Both techniques have high potential for forest restoration in degraded areas in seasonally dry tropical forests.
In both directions: Expansions of European land snails to the north and south from glacial refugia

Were postglacial recolonizations facilitated by persistence close to the colonized areas rather than by dispersal ability allowing for colonization from distant sources? This question is particularly relevant for organisms with low active dispersal abilities and lacking specialized propagules. Here we identified glacial refugia of four Central European land snail species, including one for which a northern glacial refugium in the region was indicated by indirectly dated fossils.
A comparison of stochastic models for spatial rainfall downscaling

We explore the performance of three types of stochastic models used for spatial rainfall downscaling and assess their ability to reproduce the statistics of precipitation fields observed during the GATE radar experiment. We consider a bounded multifractal cascade, an autoregressive linear process passed through a nonlinear static filter (sometimes called a meta‐Gaussian model), and a model based on the presence of individual rainfall cells with power law profile. As test statistics we use the low‐order moments of the amplitude distribution, the distribution of generalized fractal dimensions, the generalized scaling exponents, the slope of the power spectrum, and the properties of the spatial autocorrelation. The results of the analysis indicate that all models provide, on average, a satisfactory representation of the statistical properties of the GATE rainfall fields (including the anomalous scaling behavior), with a slightly better performance of the model based on individual rainfall cells. All models, however, display large scatter in the field‐to‐field comparison with the data. These results indicate that data analysis alone does not allow, at the moment, for preferring one downscaling approach over another.
Polymer Quantum Mechanics and its Continuum Limit

A rather nonstandard quantum representation of the canonical commutation relations of quantum mechanics systems, known as the polymer representation, has gained some attention in recent years, due to its possible relation with Planck scale physics. In particular, this approach has been followed in a symmetric sector of loop quantum gravity known as loop quantum cosmology. Here we explore different aspects of the relation between the ordinary Schroedinger theory and the polymer description. The paper has two parts. In the first one, we derive the polymer quantum mechanics starting from the ordinary Schroedinger theory and show that the polymer description arises as an appropriate limit. In the second part we consider the continuum limit of this theory, namely, the reverse process in which one starts from the discrete theory and tries to recover back the ordinary Schroedinger quantum mechanics. We consider several examples of interest, including the harmonic oscillator, the free particle, and a simple cosmological model.
High-intensity therapeutic ultrasound: metrological requirements versus clinical usage

High-intensity therapeutic ultrasound (HITU) is an appealing non-invasive, non-ionizing therapeutic modality with a wide range of tissue interactions ranging from transient permeabilization of cell membranes to thermal ablation. The ability to guide and monitor the treatment with an associated ultrasonic or magnetic resonance imaging device has resulted in a dramatic rise in the clinical use of therapeutic ultrasound in the past two decades. Nevertheless, the range of clinical applications and the number of patients treated has grown at a much higher pace than the definition of standards. In this paper the metrological requirements of the therapeutic beams are reviewed and are compared with the current clinical use of image-guided HITU mostly based on a practical approach. Liver therapy, a particularly challenging clinical application, is discussed to highlight the differences between some complex clinical situations and the experimental conditions of the metrological characterization of ultrasonic transducers.
Camera calibration with a near-parallel imaging system based on geometric moments

This paper presents a novel approach of camera calibration under the near-parallel condition based on geometric moments. The near-parallel condition means that the calibration board is near parallel (or parallel) to the imaging plane. A camera calibration model for the near-parallel condition and a calibration board with arranged rectangular features are suggested. Before calibration, feature regions on the image of calibration board are extracted, and centroid and rotation of each feature are detected using geometric moments. These centroids are used for feature points, and meanwhile mean value of rotations is used for the rotation around axis Z. Then, the closed-form solutions to the translations, other two angles and effective focal length are provided by combining Gauss lens model with camera model. Subsequently, principal point is received by radial alignment constraint (RAC), and distortion coefficients are calculated. Finally, all camera parameters are refined by a nonlinear minimization procedure according to the distortion coefficients. Simulations and experiments are performed to verify the proposed camera calibration algorithm. The precision of detecting feature points and calibrating camera parameters are analyzed. The precision of camera calibration results is also evaluated.
Closed orbits in homology classes for Anosov flows

Abstract We consider transitive Anosov flows φ: M → M and give necessary and sufficient conditions for every homology class in H1(M,ℤ) to contain a closed φ-orbit. Under these conditions, we derive an asymptotic formula for the number of closed φ-orbits in a fixed homology class, generalizing a result of Katsuda and Sunada.
On Komlós’ tiling theorem in random graphs

Abstract Given graphs G and H, a family of vertex-disjoint copies of H in G is called an H-tiling. Conlon, Gowers, Samotij and Schacht showed that for a given graph H and a constant γ >0, there exists C>0 such that if $p \ge C{n^{ - 1/{m_2}(H)}}$ , then asymptotically almost surely every spanning subgraph G of the random graph 𝒢(n, p) with minimum degree at least $\delta (G) \ge (1 - \frac{1}{{{\chi _{{\rm{cr}}}}(H)}} + \gamma )np$ contains an H-tiling that covers all but at most γn vertices. Here, χ cr(H) denotes the critical chromatic number, a parameter introduced by Komlós, and m 2(H) is the 2-density of H. We show that this theorem can be bootstrapped to obtain an H-tiling covering all but at most $\gamma {(C/p)^{{m_2}(H)}}$ vertices, which is strictly smaller when $p \ge C{n^{ - 1/{m_2}(H)}}$ . In the case where H = K3, this answers the question of Balogh, Lee and Samotij. Furthermore, for an arbitrary graph H we give an upper bound on p for which some leftover is unavoidable and a bound on the size of a largest H -tiling for p below this value.
Dynamics of postcritically bounded polynomial semigroups

We investigate the dynamics of semigroups generated by polynomial maps on the Riemann sphere such that the postcritical set in the complex plane is bounded. Moreover, we investigate the associated random dynamics of polynomials. We show that for such a polynomial semigroup, if A and B are two connected components of the Julia set, then one of A and B surrounds the other. Moreover, we show that for any n 2 [{@0}, there exists a finitely generated polynomial semigroup with bounded planar postcritical set such that the cardinality of the set of all connected components of the Julia set is equal to n. Furthermore, we show that under a certain condition, a random Julia set is almost surely a Jordan curve, but not a quasicircle. Many phenomena of polynomial semigroups and random dynamics of polynomials that do not occur in the usual dynamics of polynomials are found and investigated.
Batalin-Vilkovisky Structures on Ext and Tor

This article studies the algebraic structure of homology theories defined by a left Hopf algebroid U over a possibly noncommutative base algebra A, such as for example Hochschild, Lie algebroid (in particular Lie algebra and Poisson), or group and etale groupoid (co)homology. Explicit formulae for the canonical Gerstenhaber algebra structure on Ext_U(A,A) are given. The main technical result constructs a Lie derivative satisfying a generalised Cartan-Rinehart homotopy formula whose essence is that Tor^U(M,A) becomes for suitable right U-modules M a Batalin-Vilkovisky module over Ext_U(A,A), or in the words of Nest, Tamarkin, Tsygan and others, that Ext_U(A,A) and Tor^U(M,A) form a differential calculus. As an illustration, we show how the well-known operators from differential geometry in the classical Cartan homotopy formula can be obtained. Another application consists in generalising Ginzburg's result that the cohomology ring of a Calabi-Yau algebra is a Batalin-Vilkovisky algebra to twisted Calabi-Yau algebras.
High resolution entropy stable scheme for shallow water equations

A high resolution entropy stable scheme is proposed for solving shallow water equations in this paper. The scheme contains two parts: entropy conservative flux and numerical diffusion operator. To achieve high resolution, a limiter is employed to guarantee the numerical diffusion term being added around the discontinuities automatically. Numerical experiments are presented to demonstrate the proposed scheme’s capacity.