共查询到20条相似文献,搜索用时 62 毫秒
1.
Martin Lindberg Andris Vaivads Savvas Raptis Per-Arne Lindqvist Barbara L. Giles Daniel Jonathan Gershman 《Entropy (Basel, Switzerland)》2022,24(6)
We use Magnetospheric Multiscale (MMS) data to study electron kinetic entropy per particle across Earth’s quasi-perpendicular bow shock. We have selected 22 shock crossings covering a wide range of shock conditions. Measured distribution functions are calibrated and corrected for spacecraft potential, secondary electron contamination, lack of measurements at the lowest energies and electron density measurements based on plasma frequency measurements. All crossings display an increase in electron kinetic entropy across the shock being positive or zero within their error margin. There is a strong dependence of on the change in electron temperature, , and the upstream electron plasma beta, . Shocks with large have large . Shocks with smaller are associated with larger . We use the values of , and density change to determine the effective adiabatic index of electrons for each shock crossing. The average effective adiabatic index is . 相似文献
2.
Anas D. Khalaf Tareq Saeed Reman Abu-Shanab Waleed Almutiry Mahmoud Abouagwa 《Entropy (Basel, Switzerland)》2022,24(5)
This study deals with drift parameters estimation problems in the sub-fractional Vasicek process given by , with , being unknown and ; here, represents a sub-fractional Brownian motion (sfBm). We introduce new estimators for and for based on discrete time observations and use techniques from Nordin–Peccati analysis. For the proposed estimators and , strong consistency and the asymptotic normality were established by employing the properties of . Moreover, we provide numerical simulations for sfBm and related Vasicek-type process with different values of the Hurst index H. 相似文献
3.
A possible detection of sub-solar mass ultra-compact objects would lead to new perspectives on the existence of black holes that are not of astrophysical origin and/or pertain to formation scenarios of exotic ultra-compact objects. Both possibilities open new perspectives for better understanding of our universe. In this work, we investigate the significance of detection of sub-solar mass binaries with components mass in the range: up to 1, within the expected sensitivity of the ground-based gravitational waves detectors of third generation, viz., the Einstein Telescope (ET) and the Cosmic Explorer (CE). Assuming a minimum of amplitude signal-to-noise ratio for detection, viz., , we find that the maximum horizon distances for an ultra-compact binary system with components mass and 1 are 40 Mpc and 1.89 Gpc, respectively, for ET, and 125 Mpc and 5.8 Gpc, respectively, for CE. Other cases are also presented in the text. We derive the merger rate and discuss consequences on the abundances of primordial black hole (PBH), . Considering the entire mass range [–1], we find (<) for ET (CE), respectively. 相似文献
4.
Pedro Carpena Manuel Gmez-Extremera Pedro A. Bernaola-Galvn 《Entropy (Basel, Switzerland)》2022,24(1)
Detrended Fluctuation Analysis (DFA) has become a standard method to quantify the correlations and scaling properties of real-world complex time series. For a given scale ℓ of observation, DFA provides the function , which quantifies the fluctuations of the time series around the local trend, which is substracted (detrended). If the time series exhibits scaling properties, then asymptotically, and the scaling exponent is typically estimated as the slope of a linear fitting in the vs. plot. In this way, measures the strength of the correlations and characterizes the underlying dynamical system. However, in many cases, and especially in a physiological time series, the scaling behavior is different at short and long scales, resulting in vs. plots with two different slopes, at short scales and at large scales of observation. These two exponents are usually associated with the existence of different mechanisms that work at distinct time scales acting on the underlying dynamical system. Here, however, and since the power-law behavior of is asymptotic, we question the use of to characterize the correlations at short scales. To this end, we show first that, even for artificial time series with perfect scaling, i.e., with a single exponent valid for all scales, DFA provides an value that systematically overestimates the true exponent . In addition, second, when artificial time series with two different scaling exponents at short and large scales are considered, the value provided by DFA not only can severely underestimate or overestimate the true short-scale exponent, but also depends on the value of the large scale exponent. This behavior should prevent the use of to describe the scaling properties at short scales: if DFA is used in two time series with the same scaling behavior at short scales but very different scaling properties at large scales, very different values of will be obtained, although the short scale properties are identical. These artifacts may lead to wrong interpretations when analyzing real-world time series: on the one hand, for time series with truly perfect scaling, the spurious value of could lead to wrongly thinking that there exists some specific mechanism acting only at short time scales in the dynamical system. On the other hand, for time series with true different scaling at short and large scales, the incorrect value would not characterize properly the short scale behavior of the dynamical system. 相似文献
5.
In this paper, we present a new method for the construction of maximally entangled states in when . A systematic way of constructing a set of maximally entangled bases (MEBs) in was established. Both cases when is divisible by d and not divisible by d are discussed. We give two examples of maximally entangled bases in , which are mutually unbiased bases. Finally, we found a new example of an unextendible maximally entangled basis (UMEB) in . 相似文献
6.
Private Information Retrieval (PIR) protocols, which allow the client to obtain data from servers without revealing its request, have many applications such as anonymous communication, media streaming, blockchain security, advertisement, etc. Multi-server PIR protocols, where the database is replicated among the non-colluding servers, provide high efficiency in the information-theoretic setting. Beimel et al. in CCC 12’ (further referred to as BIKO) put forward a paradigm for constructing multi-server PIR, capturing several previous constructions for servers, as well as improving the best-known share complexity for 3-server PIR. A key component there is a share conversion scheme from corresponding linear three-party secret sharing schemes with respect to a certain type of “modified universal” relation. In a useful particular instantiation of the paradigm, they used a share conversion from -CNF over to three-additive sharing over for primes where and , and the relation is modified universal relation . They reduced the question of the existence of the share conversion for a triple to the (in)solvability of a certain linear system over , and provided an efficient (in ) construction of such a sharing scheme. Unfortunately, the size of the system is which entails the infeasibility of a direct solution for big m’s in practice. Paskin-Cherniavsky and Schmerler in 2019 proved the existence of the conversion for the case of odd , when , obtaining in this way infinitely many parameters for which the conversion exists, but also for infinitely many of them it remained open. In this work, using some algebraic techniques from the work of Paskin-Cherniavsky and Schmerler, we prove the existence of the conversion for even m’s in case (we computed in this case) and the absence of the conversion for even m’s in case . This does not improve the concrete efficiency of 3-server PIR; however, our result is promising in a broader context of constructing PIR through composition techniques with servers, using the relation where m has more than two prime divisors. Another our suggestion about 3-server PIR is that it’s possible to achieve a shorter server’s response using the relation for extended . By computer search, in BIKO framework we found several such sets for small m’s which result in share conversion from -CNF over to 3-additive secret sharing over , where is several times less than , which implies several times shorter server’s response. We also suggest that such extended sets can result in better PIR due to the potential existence of matching vector families with the higher Vapnik-Chervonenkis dimension. 相似文献
7.
Kornelia M. Batko Izabella
lzak-Prochazka Andrzej
lzak Wioletta M. Bajdur Radomir
urek 《Entropy (Basel, Switzerland)》2022,24(1)
Based on Kedem–Katchalsky formalism, the model equation of the membrane potential () generated in a membrane system was derived for the conditions of concentration polarization. In this system, a horizontally oriented electro-neutral biomembrane separates solutions of the same electrolytes at different concentrations. The consequence of concentration polarization is the creation, on both sides of the membrane, of concentration boundary layers. The basic equation of this model includes the unknown ratio of solution concentrations ( at the membrane/concentration boundary layers. We present the calculation procedure ( based on novel equations derived in the paper containing the transport parameters of the membrane (, , and ), solutions (, ), concentration boundary layer thicknesses (, ), concentration Raileigh number (), concentration polarization factor (), volume flux (), mechanical pressure difference (), and ratio of known solution concentrations (). From the resulting equation, was calculated for various combinations of the solution concentration ratio (), the Rayleigh concentration number (), the concentration polarization coefficient (), and the hydrostatic pressure difference ). Calculations were performed for a case where an aqueous NaCl solution with a fixed concentration of 1 mol m−3 () was on one side of the membrane and on the other side an aqueous NaCl solution with a concentration between 1 and 15 mol m−3 (). It is shown that () depends on the value of one of the factors (i.e., , , and ) at a fixed value of the other three. 相似文献
8.
Recently, Savaré-Toscani proved that the Rényi entropy power of general probability densities solving the p-nonlinear heat equation in is a concave function of time under certain conditions of three parameters , which extends Costa’s concavity inequality for Shannon’s entropy power to the Rényi entropy power. In this paper, we give a condition of under which the concavity of the Rényi entropy power is valid. The condition contains Savaré-Toscani’s condition as a special case and much more cases. Precisely, the points satisfying Savaré-Toscani’s condition consist of a two-dimensional subset of , and the points satisfying the condition consist a three-dimensional subset of . Furthermore, gives the necessary and sufficient condition in a certain sense. Finally, the conditions are obtained with a systematic approach. 相似文献
9.
We study the viable Starobinsky dark energy model in spatially non-flat FLRW backgrounds, where with and representing the characteristic curvature scale and model parameter, respectively. We modify CAMB and CosmoMC packages with the recent observational data to constrain Starobinsky gravity and the density parameter of curvature . In particular, we find the model and density parameters to be at 68% C.L. and at 95% C.L., respectively. The best fitting result shows that , indicating that the viable gravity model is consistent with CDM when is set as a free parameter. We also evaluate the values of AIC, BIC and DIC for the best fitting results of and CDM models in the non-flat universe. 相似文献
10.
This paper systematically presents the -deformation as the canonical framework of deformation to the dually flat (Hessian) geometry, which has been well established in information geometry. We show that, based on deforming the Legendre duality, all objects in the Hessian case have their correspondence in the -deformed case: -convexity, -conjugation, -biorthogonality, -logarithmic divergence, -exponential and -mixture families, etc. In particular, -deformation unifies Tsallis and Rényi deformations by relating them to two manifestations of an identical -exponential family, under subtractive or divisive probability normalization, respectively. Unlike the different Hessian geometries of the exponential and mixture families, the -exponential family, in turn, coincides with the -mixture family after a change of random variables. The resulting statistical manifolds, while still carrying a dualistic structure, replace the Hessian metric and a pair of dually flat conjugate affine connections with a conformal Hessian metric and a pair of projectively flat connections carrying constant (nonzero) curvature. Thus, -deformation is a canonical framework in generalizing the well-known dually flat Hessian structure of information geometry. 相似文献
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12.
Kai Li Ming Zhang Xiaowen Liu Yong Liu Hongyi Dai Yijun Zhang Chen Dong 《Entropy (Basel, Switzerland)》2022,24(7)
Solving linear systems of equations is one of the most common and basic problems in classical identification systems. Given a coefficient matrix A and a vector b, the ultimate task is to find the solution x such that . Based on the technique of the singular value estimation, the paper proposes a modified quantum scheme to obtain the quantum state corresponding to the solution of the linear system of equations in poly time for a general dimensional A, which is superior to existing quantum algorithms, where is the condition number, r is the rank of matrix A and is the precision parameter. Meanwhile, we also design a quantum circuit for the homogeneous linear equations and achieve an exponential improvement. The coefficient matrix A in our scheme is a sparsity-independent and non-square matrix, which can be applied in more general situations. Our research provides a universal quantum linear system solver and can enrich the research scope of quantum computation. 相似文献
13.
This article estimates several integral inequalities involving -convexity via the quantum calculus, through which Important integral inequalities including Simpson-like, midpoint-like, averaged midpoint-trapezoid-like and trapezoid-like are extended. We generalized some quantum integral inequalities for q-differentiable -convexity. Our results could serve as the refinement and the unification of some classical results existing in the literature by taking the limit . 相似文献
14.
The transverse momentum spectra of different types of particles, , , p and , produced at mid-(pseudo)rapidity in different centrality lead–lead (Pb–Pb) collisions at 2.76 TeV; proton–lead (p–Pb) collisions at 5.02 TeV; xenon–xenon (Xe–Xe) collisions at 5.44 TeV; and proton–proton (p–p) collisions at 0.9, 2.76, 5.02, 7 and 13 TeV, were analyzed by the blast-wave model with fluctuations. With the experimental data measured by the ALICE and CMS Collaborations at the Large Hadron Collider (LHC), the kinetic freeze-out temperature, transverse flow velocity and proper time were extracted from fitting the transverse momentum spectra. In nucleus–nucleus (A–A) and proton–nucleus (p–A) collisions, the three parameters decrease with the decrease of event centrality from central to peripheral, indicating higher degrees of excitation, quicker expansion velocities and longer evolution times for central collisions. In p–p collisions, the kinetic freeze-out temperature is nearly invariant with the increase of energy, though the transverse flow velocity and proper time increase slightly, in the considered energy range. 相似文献
15.
Yinnian He 《Entropy (Basel, Switzerland)》2021,23(12)
In this work, a finite element (FE) method is discussed for the 3D steady Navier–Stokes equations by using the finite element pair . The method consists of transmitting the finite element solution of the 3D steady Navier–Stokes equations into the finite element solution pairs based on the finite element space pair of the 3D steady linearized Navier–Stokes equations by using the Stokes, Newton and Oseen iterative methods, where the finite element space pair satisfies the discrete inf-sup condition in a 3D domain . Here, we present the weak formulations of the FE method for solving the 3D steady Stokes, Newton and Oseen iterative equations, provide the existence and uniqueness of the FE solution of the 3D steady Stokes, Newton and Oseen iterative equations, and deduce the convergence with respect to of the FE solution to the exact solution of the 3D steady Navier–Stokes equations in the norm. Finally, we also give the convergence order with respect to of the FE velocity to the exact velocity u of the 3D steady Navier–Stokes equations in the norm. 相似文献
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17.
Gilles Cohen-Tannoudji Jean-Pierre Gazeau Clestin Habonimana Juma Shabani 《Entropy (Basel, Switzerland)》2022,24(6)
As an extension of Gabor signal processing, the covariant Weyl-Heisenberg integral quantization is implemented to transform functions on the eight-dimensional phase space into Hilbertian operators. The values are space-time variables, and the values are their conjugate frequency-wave vector variables. The procedure is first applied to the variables and produces essentially canonically conjugate self-adjoint operators. It is next applied to the metric field of general relativity and yields regularized semi-classical phase space portraits . The latter give rise to modified tensor energy density. Examples are given with the uniformly accelerated reference system and the Schwarzschild metric. Interesting probabilistic aspects are discussed. 相似文献
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19.
We present a coupled variational autoencoder (VAE) method, which improves the accuracy and robustness of the model representation of handwritten numeral images. The improvement is measured in both increasing the likelihood of the reconstructed images and in reducing divergence between the posterior and a prior latent distribution. The new method weighs outlier samples with a higher penalty by generalizing the original evidence lower bound function using a coupled entropy function based on the principles of nonlinear statistical coupling. We evaluated the performance of the coupled VAE model using the Modified National Institute of Standards and Technology (MNIST) dataset and its corrupted modification C-MNIST. Histograms of the likelihood that the reconstruction matches the original image show that the coupled VAE improves the reconstruction and this improvement is more substantial when seeded with corrupted images. All five corruptions evaluated showed improvement. For instance, with the Gaussian corruption seed the accuracy improves by (from to ) and robustness improves by (from to ). Furthermore, the divergence between the posterior and prior distribution of the latent distribution is reduced. Thus, in contrast to the -VAE design, the coupled VAE algorithm improves model representation, rather than trading off the performance of the reconstruction and latent distribution divergence. 相似文献
20.
In this paper, a methodology for a non-linear system state estimation is demonstrated, exploiting the input and parameter observability. For this purpose, the initial system is transformed into the canonical observability form, and the function that aggregates the non-linear dynamics of the system, which may be unknown or difficult to be computed, is approximated by a linear combination of Laguerre polynomials. Hence, the system identification translates into the estimation of the parameters involved in the linear combination in order for the system to be observable. For the validation of the elaborated observer, we consider a biological model from the literature, investigating whether it is practically possible to infer its states, taking into account the new coordinates to design the appropriate observer of the system states. Through simulations, we investigate the parameter settings under which the new observer can identify the state of the system. More specifically, as the parameter increases, the system converges more quickly to the steady-state, decreasing the respective distance from the system’s initial state. As for the first state, the estimation error is in the order of for , and assuming . Under the same conditions, the estimation error of the system’s second state is in the order of , setting a performance difference of in relation to the first state. The outcomes show that the proposed observer’s performance can be further improved by selecting even higher values of . Hence, the system is observable through the measurement output. 相似文献