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In this paper we show that under general resonance the classical piecewise linear Fermi-Ulam accelerator behaves substantially different from its quantization in the sense that the classical accelerator exhibits typical recurrence and non-escaping while the quantum version enjoys quadratic energy growth in general. We also describe a procedure to locate the escaping orbits, though exceptionally rare in the infinite-volume phase space, for the classical accelerators, which in particular include Ulam's very original proposal and the linearly escaping orbits therein in the existing literature, and hence provide a complete (modulo a null set) answer to Ulam's original question. For the quantum accelerators, we reveal under resonance the direct and explicit connection between the energy growth and the shape of the quasi-energy spectra.

We revisit Hawking's original derivation of the evaporation process in a non-stationary spacetime, presenting it in a clear and pedagogical manner, with a focus on the spherical collapse of a star into a black hole. Our analysis highlights the underlying assumptions in the calculations, clarifying their physical significance, potential implications, and the limitations of this approach.

We compute 1/2-derivations on the extended Schrödinger-Virasoro algebras and the original deformative Schrödinger-Virasoro algebras. The extended Schrödinger-Virasoro algebras have neither nontrivial 1/2-derivations nor nontrivial transposed Poisson algebra structures. We demonstrate that the original deformative Schrödinger-Virasoro algebras have nontrivial 1/2-derivations, indicating that they possess nontrivial transposed Poisson structures.

Euler derived the differential equations of elastica by the variational method in 1744, but his original derivation has never been properly interpreted or explained in terms of modern mathematics. We elaborate Euler's original derivation of elastica and show that Euler used Noether's theorem concerning the translational symmetry of elastica, although Noether published her theorem in 1918. It is also shown that his equation is essentially the static modified KdV equation which is obtained by the isometric and isoenergy conditions, known as the Goldstein-Petrich scheme.

Pile-up signals are frequently produced in experimental physics. They create inaccurate physics data with high uncertainty and cause various problems. Therefore, the correction to pile-up signals is crucially required. In this study, we implemented a deep learning method to restore the original signals from the pile-up signals. We showed that a deep learning model could accurately reconstruct the original signal waveforms from the pile-up waveforms. By substituting the pile-up signals with the original signals predicted by the model, the energy and timing resolutions of the data are notably enhanced. The model implementation significantly improved the quality of the particle identification plot and particle tracks. This method is applicable to similar problems, such as separating multiple signals or correcting pile-up signals with other types of noises and backgrounds.

Two mechanisms of changes from 2D to 3D (D = dimensionality) involving 2D C(sp2) trigonal paving to C(sp3) tetrahedral stacking are proposed through puckering of the 2D layers on one hand and interlayer insertion of extra C on the other hand. Such transformations, led to original 3D hexagonal C12 and C18 allotropes respectively characterized by lon and bac topologies. Using density functional theory DFT calculations, the two allotropes were found cohesive and stable both mechanically (elastic properties) and dynamically (phonons). Comparisons of the physical properties with known uni C6 were established letting identify ranges of large Vickers hardness: HV (uni C6) = 89 GPa, HV (lon C12) = 97 GPa, and HV (bac C18) = 70 GPa. Whilst C6 was identified with acoustic phonons instability, C12 and C18 were found stable dynamically throughout the acoustic and optic frequency ranges. Furthering on the thermal properties the allotropes were characterized with a temperature dependence curve of the specific heat CV close to experimental data of diamond with best fit for novel C18. The electronic band structures reveal a small band gap of 1 eV for uni C6 and larger direct band gap of 3 eV for t

Private and public actors increasingly encounter use cases where they need to implement sensitive operations on mass-market peripherals for which they have little or no control. They are sometimes inclined to attempt this without using hardware-assisted equipment, such as secure elements. In this case, the white-box attack model is particularly relevant and includes access to every asset, retro-engineering, and binary instrumentation by attackers. At the same time, quantum attacks are becoming more and more of a threat and challenge traditional asymmetrical ciphers, which are treasured by private and public actors. The McEliece cryptosystem is a code-based public key algorithm introduced in 1978 that is not subject to well-known quantum attacks and that could be implemented in an uncontrolled environment. During the NIST post-quantum cryptography standardization process, a derived candidate commonly refer to as classic McEliece was selected. This algorithm is however vulnerable to some fault injection attacks while a priori, this does not apply to the original McEliece. In this article, we thus focus on the original McEliece cryptosystem and we study its resilience against fault in

The original and amplitude permutations are two basic ordinal patterns; however, their relationship has received little attention. This paper compares the original and amplitude permutations used to characterize vector structures. To accurately convey the vector structure, we modify indexes of equal values in the permutations to be the same ones in each group of equalities. Comparative analysis suggests that the amplitude permutation, comprising the positions of the original values in the reordered vector, directly reflects the vector's temporal structure, whereas the original permutation, consisting of the indexes of reorganized values in the original vector, conveys the structural pattern of the reorganized vector. Moreover, we clarify the association of the original and amplitude permutations with timeand amplitude-symmetric vectors, thus contributing to the fields of symbolic analysis, topological data analysis, and so on.

In current applied research the most-used route to an analysis of composition is through log-ratios -- that is, contrasts among log-transformed measurements. Here we argue instead for a more direct approach, using a statistical model for the arithmetic mean on the original scale of measurement. Central to the approach is a general variance-covariance function, derived by assuming multiplicative measurement error. Quasi-likelihood analysis of logit models for composition is then a general alternative to the use of multivariate linear models for log-ratio transformed measurements, and it has important advantages. These include robustness to secondary aspects of model specification, stability when there are zero-valued or near-zero measurements in the data, and more direct interpretation. The usual efficiency property of quasi-likelihood estimation applies even when the error covariance matrix is unspecified. We also indicate how the derived variance-covariance function can be used, instead of the variance-covariance matrix of log-ratios, with more general multivariate methods for the analysis of composition. A specific feature is that the notion of `null correlation' -- for compositi

In this paper we propose a kernel based COBRA which is a direct approximation of the original COBRA. We propose a novel tuning procedure for original COBRA parameters based on this kernel approximation. We show that our proposed algorithm provides much better accuracy than other COBRAs and faster than usual Gridsearch COBRA. We use two datasets to illustrate our proposed methodology over existing COBRAs.

Masking methods for the safe dissemination of microdata consist of distorting the original data while preserving a pre-defined set of statistical properties in the microdata. For continuous variables, available methodologies rely essentially on matrix masking and in particular on adding noise to the original values, using more or less refined procedures depending on the extent of information that one seeks to preserve. Almost all of these methods make use of the critical assumption that the original datasets follow a normal distribution and/or that the noise has such a distribution. This assumption is, however, restrictive in the sense that few variables follow empirically a Gaussian pattern: the distribution of household income, for example, is positively skewed, and this skewness is essential information that has to be considered and preserved. This paper addresses these issues by presenting a simple multiplicative masking method that preserves skewness of the original data while offering a sufficient level of disclosure risk control. Numerical examples are provided, leading to the suggestion that this method could be well-suited for the dissemination of a broad range of microdat

An asteroid family forms as a result of a collision between an impactor and a parent body. The fragments with ejection speeds higher than the escape velocity from the parent body can escape its gravitational pull. The cloud of escaping debris can be identified by the proximity of orbits in proper element, or frequency, domains. Obtaining estimates of the original ejection speed can provide valuable constraints on the physical processes occurring during collision, and used to calibrate impact simulations. Unfortunately, proper elements of asteroids families are modified by gravitational and non-gravitational effects, such as resonant dynamics, encounters with massive bodies, and the Yarkovsky effect, such that information on the original ejection speeds is often lost, especially for older, more evolved families. It has been recently suggested that the distribution in proper inclination of the Koronis family may have not been significantly perturbed by local dynamics, and that information on the component of the ejection velocity that is perpendicular to the orbital plane ($v_W$), may still be available, at least in part. In this work we estimate the magnitude of the original ejectio

Since images are used as evidence in many cases, validation of digital images is essential. Copy-move forgery is a special kind of manipulation in which some parts of an image is copied and pasted into another part of the same image. Various methods have been proposed to detect copy-move forgery, which have achieved promising results. In previous methods, a binary mask determining the original and forged region is presented as the final result. However, it is not specified which part of the mask is the forged region. It should be noted that discriminating the original region from the duplicated one is not usually feasible by human visual system(HVS). On the other hand, exact localizing the forged region can be helpful for automatic forgery detection especially in combined forgeries. In real-world forgeries, some manipulations are performed in order to provide a visibly realistic scene. These modifications are usually applied on the boundary of the duplicated snippets. In this research, the texture information of the border regions of both the original and copied patches have been statistically investigated. Based on this analysis, we propose a method to discriminated copied snippet

The original Deutsch-Jozsa (oDJ) problem is for an oracle (realized here as a database) of size N, where, according to their claim, the deterministic solution of the problem on a classical Turing computer requires O(N) computational complexity. They produced the famous Deutsch-Jozsa quantum algorithm that offered an exponential speedup over the classical computer, namely O[log(N)] complexity for the solution in a quantum computer. In this paper, the problem is implemented on an instantaneous noise-based logic processor. It is shown that, similarly to the quantum algorithm, the oDJ problem can deterministically be solved with O[log(N)] complexity. The implication is that by adding a truly random coin to a classical Turing machine and using this classical-physical algorithm can also speed up the deterministic solution of the Deutsch-Jozsa problem exponentially, similarly to the quantum algorithm. Then it is realized that the same database and the solution of the Deutsch-Jozsa problem can also be realized by using an identical algorithmic structure in a simpler way, even without noise/random coin. The only lost function in this new system, as compared to noise-based logic, is the abil

The 19-dimensional TP06 cardiac muscle cell model is reduced to a 17-dimensional version, which satisfies the required conditions for performing an analysis of its dynamics by means of bifurcation theory. The reformulated model is shown to be a good approximation of the original one. As a consequence, one can extract fairly precise predictions of the behaviour of the original model from the bifurcation analysis of the modified model. Thus, the findings of bifurcations linked to complex dynamics in the modified model - like early afterdepolarisations (EADs), which can be precursors to cardiac death - predicts the occurrence of the same dynamics in the original model. It is shown that bifurcations linked to EADs in the modified model accurately predicts EADs in the original model at the single cell level. Finally, these bifurcations are linked to cardiac death at the tissue level by example.

The use of quantitative indicators of scientific productivity seems now quite widespread for assessing researchers and research institutions. There is a general perception, however, that these indicators are not necessarily representative of the originality of the research carried out, being primarily indicative of a more or less prolific scientific activity and of the size of the targeted scientific subcommunity. We first discuss some of the drawbacks of the broadly adopted $h$-index and of the fact that it represents, in an average sense, an indicator derivable from the total number of citations. Then we propose an indicator which, although not immune from biases, seems more in line with the general expectations for quantifying what is typically considered original work. Qualitative arguments on how different indicators may shape the future of science are finally discussed.

This submission consists of two papers: 1) an erratum that corrects an error in the proof of Proposition 4.3 in my paper "The Homogeneous Coordinate Ring of a Toric Variety", and 2) the original (unchanged) version of the paper, published in 1995. The original paper introduced the homogeneous coordinate ring of a toric variety (now called the total coordinate ring or Cox ring) and gave a quotient construction. The paper also studied sheaves on a toric variety, and in Section 4 described its automorphism group. The error in the proof of Proposition 4.3 resulted from the faulty assumption that a certain set of graded endomorphisms forms a ring; rather, it is a monoid under composition. The erratum notes this error and gives a correct proof of the proposition.

PP-waves have recently been of interest to string theorists. This is the original, hard to find, original article on plane polarized gravitational waves.

In this paper we give Kummer's original type congruence relation modulo a prime power for the universal Bernoulli numbers. Although the index of the power is half of original congruence, this estimate is best possible.