共查询到20条相似文献,搜索用时 31 毫秒
1.
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
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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
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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
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A widely used clustering algorithm, density peak clustering (DPC), assigns different attribute values to data points through the distance between data points, and then determines the number and range of clustering by attribute values. However, DPC is inefficient when dealing with scenes with a large amount of data, and the range of parameters is not easy to determine. To fix these problems, we propose a quantum DPC (QDPC) algorithm based on a quantum circuit and a Grover circuit. The time complexity is reduced to , whereas that of the traditional algorithm is . The space complexity is also decreased from to . 相似文献
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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
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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
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The discrepancy among one-electron and two-electron densities for diverse N-electron atomss, enclosing neutral systems (with nuclear charge ) and charge-one ions (), is quantified by means of mutual information, I, and Quantum Similarity Index, , in the conjugate spaces position/momentum. These differences can be interpreted as a measure of the electron correlation of the system. The analysis is carried out by considering systems with a nuclear charge up to and singly charged ions (cations and anions) as far as . The interelectronic correlation, for any given system, is quantified through the comparison of its double-variable electron pair density and the product of the respective one-particle densities. An in-depth study along the Periodic Table reveals the importance, far beyond the weight of the systems considered, of their shell structure. 相似文献
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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
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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
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The quantum search algorithm is one of the milestones of quantum algorithms. Compared with classical algorithms, it shows quadratic speed-up when searching marked states in an unsorted database. However, the success rates of quantum search algorithms are sensitive to the number of marked states. In this paper, we study the relation between the success rate and the number of iterations in a quantum search algorithm of given , where M is the number of marked state and N is the number of items in the dataset. We develop a robust quantum search algorithm based on Grover–Long algorithm with some uncertainty in the number of marked states. The proposed algorithm has the same query complexity as the Grover’s algorithm, and shows high tolerance of the uncertainty in the ratio . In particular, for a database with an uncertainty in the ratio , our algorithm will find the target states with a success rate no less than . 相似文献
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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
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Humaira Kalsoom Miguel Vivas-Cortez Muhammad Idrees Praveen Agarwal 《Entropy (Basel, Switzerland)》2021,23(11)
In this work, first, we consider novel parameterized identities for the left and right part of the -analogue of Hermite–Hadamard inequality. Second, using these new parameterized identities, we give new parameterized -trapezoid and parameterized -midpoint type integral inequalities via -quasiconvex function. By changing values of parameter , some new special cases from the main results are obtained and some known results are recaptured as well. Finally, at the end, an application to special means is given as well. This new research has the potential to establish new boundaries in comparative literature and some well-known implications. From an application perspective, the proposed research on the -quasiconvex function has interesting results that illustrate the applicability and superiority of the results obtained. 相似文献
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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
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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
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We use an m-vicinity method to examine Ising models on hypercube lattices of high dimensions . This method is applicable for both short-range and long-range interactions. We introduce a small parameter, which determines whether the method can be used when calculating the free energy. When we account for interaction with the nearest neighbors only, the value of this parameter depends on the dimension of the lattice . We obtain an expression for the critical temperature in terms of the interaction constants that is in a good agreement with the results of computer simulations. For , our theoretical estimates match the numerical results both qualitatively and quantitatively. For , our method is sufficiently accurate for the calculation of the critical temperatures; however, it predicts a finite jump of the heat capacity at the critical point. In the case of the three-dimensional lattice (), this contradicts the commonly accepted ideas of the type of the singularity at the critical point. For the four-dimensional lattice (), the character of the singularity is under current discussion. For the dimensions the m-vicinity method is not applicable. 相似文献
18.
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
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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