共查询到20条相似文献,搜索用时 46 毫秒
1.
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
2.
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
3.
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
4.
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
5.
We show that neural networks with an absolute value activation function and with network path norm, network sizes and network weights having logarithmic dependence on can -approximate functions that are analytic on certain regions of . 相似文献
6.
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
7.
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
8.
A single master equation governs the behaviour of shear-free neutral perfect fluid distributions arising in gravity theories. In this paper, we study the integrability of find new solutions, and generate a new first integral. The first integral is subject to an integrability condition which is an integral equation which restricts the function We find that the integrability condition can be written as a third order differential equation whose solution can be expressed in terms of elementary functions and elliptic integrals. The solution of the integrability condition is generally given parametrically. A particular form of which corresponds to repeated roots of a cubic equation is given explicitly, which is a new result. Our investigation demonstrates that complexity of a self-gravitating shear-free fluid is related to the existence of a first integral, and this may be extendable to general matter distributions. 相似文献
9.
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
10.
We study the contrarian voter model for opinion formation in a society under the influence of an external oscillating propaganda and stochastic noise. Each agent of the population can hold one of two possible opinions on a given issue—against or in favor—and interacts with its neighbors following either an imitation dynamics (voter behavior) or an anti-alignment dynamics (contrarian behavior): each agent adopts the opinion of a random neighbor with a time-dependent probability , or takes the opposite opinion with probability . The imitation probability is controlled by the social temperature T, and varies in time according to a periodic field that mimics the influence of an external propaganda, so that a voter is more prone to adopt an opinion aligned with the field. We simulate the model in complete graph and in lattices, and find that the system exhibits a rich variety of behaviors as T is varied: opinion consensus for , a bimodal behavior for , an oscillatory behavior where the mean opinion oscillates in time with the field for , and full disorder for . The transition temperature vanishes with the population size N as in complete graph. In addition, the distribution of residence times in the bimodal phase decays approximately as . Within the oscillatory regime, we find a stochastic resonance-like phenomenon at a given temperature . Furthermore, mean-field analytical results show that the opinion oscillations reach a maximum amplitude at an intermediate temperature, and that exhibit a lag with respect to the field that decreases with T. 相似文献
11.
A hyperjerk system described by a single fourth-order ordinary differential equation of the form has been referred to as a snap system. A damping-tunable snap system, capable of an adjustable attractor dimension () ranging from dissipative hyperchaos () to conservative chaos (), is presented for the first time, in particular not only in a snap system, but also in a four-dimensional (4D) system. Such an attractor dimension is adjustable by nonlinear damping of a relatively simple quadratic function of the form , easily tunable by a single parameter A. The proposed snap system is practically implemented and verified by the reconfigurable circuits of field programmable analog arrays (FPAAs). 相似文献
12.
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
13.
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
14.
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
15.
Robert Benkoczi Daya Gaur Naya Nagy Marius Nagy Shahadat Hossain 《Entropy (Basel, Switzerland)》2022,24(3)
This paper studies the effect of quantum computers on Bitcoin mining. The shift in computational paradigm towards quantum computation allows the entire search space of the golden nonce to be queried at once by exploiting quantum superpositions and entanglement. Using Grover’s algorithm, a solution can be extracted in time , where t is the target value for the nonce. This is better using a square root over the classical search algorithm that requires tries. If sufficiently large quantum computers are available for the public, mining activity in the classical sense becomes obsolete, as quantum computers always win. Without considering quantum noise, the size of the quantum computer needs to be qubits. 相似文献
16.
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
17.
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
18.
Sample entropy, an approximation of the Kolmogorov entropy, was proposed to characterize complexity of a time series, which is essentially defined as , where B denotes the number of matched template pairs with length m and A denotes the number of matched template pairs with , for a predetermined positive integer m. It has been widely used to analyze physiological signals. As computing sample entropy is time consuming, the box-assisted, bucket-assisted, x-sort, assisted sliding box, and kd-tree-based algorithms were proposed to accelerate its computation. These algorithms require or computational complexity, where N is the length of the time series analyzed. When N is big, the computational costs of these algorithms are large. We propose a super fast algorithm to estimate sample entropy based on Monte Carlo, with computational costs independent of N (the length of the time series) and the estimation converging to the exact sample entropy as the number of repeating experiments becomes large. The convergence rate of the algorithm is also established. Numerical experiments are performed for electrocardiogram time series, electroencephalogram time series, cardiac inter-beat time series, mechanical vibration signals (MVS), meteorological data (MD), and noise. Numerical results show that the proposed algorithm can gain 100–1000 times speedup compared to the kd-tree and assisted sliding box algorithms while providing satisfactory approximate accuracy. 相似文献
19.
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
20.
In this paper, we establish new -integral and -integral identities. By employing these new identities, we establish new and - trapezoidal integral-type inequalities through strongly convex and quasi-convex functions. Finally, some examples are given to illustrate the investigated results. 相似文献