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In this paper we study arithmetic correlations of sequences. Arithmetic correlations are the with-carry analogs of classical correlations. We analyze the arithmetic autocorrelations of non-binary ℓ-sequences, showing that they are nearly optimal. We analyze the expected auto- and cross-correlations of sequences with fixed shift, averaged over all sequences with a fixed period. We analyze the expected autocorrelations of a fixed sequence, averaged over all shifts.

The scaling ranges of time correlations in the cloud base height records of marine boundary layer stratocumulus are studied applying the Detrended Fluctuation Analysis statistical method. We have found that time dependent variations in the evolution of the α exponent reflect the diurnal dynamics of cloud base height fluctuations in the marine boundary layer. In general, a more stable structure of the boundary layer corresponds to a lower value of the α-indicator, i.e., larger anti-persistence, thus a set of fluctuations tending to induce a greater stability of the stratocumulus. In contrast, during the periods of higher instability in the marine boundary, less anti-persistent (more persistent like) behavior of the system drags it out of equilibrium, corresponding to larger α values. From an analysis of the frequency spectrum, the stratocumulus base height evolution is found to be a nonstationary process with stationary increments. The occurrence of these statistics in cloud base height fluctuations suggests the usefulness of similar studies for the radiation transfer dynamics modeling.

We examine the application of the Variational Monte Carlo (VMC) method to a cluster model for halo nuclei. Particular attention is paid to the error estimate in the presence of correlations in the underlying random walk. We analyze the required steps for a reliable application of the VMC in the case of a complicated many-body problem, such as the direct solution of the nuclear Hamiltonian with realistic interactions. We also examine the possibility of variance reduction through the "zero variance principle", paying particular attention to the complexity of the many-body problem.

We show how the connection structure of a loopless communication network may be discovered using only ubiquitous echo requests or as a byproduct of normal two-way transport. The key factor is the correlation effect in waiting times of successively sent messages, which is caused by background traffic on the routers.

We propose a simple network growth process where the preferential attachment contains two essential parameters: homophily, namely, the tendency of sites to link with similar ones, and the number of attaching neighbors. It jointly generalizes the Barabási–Albert model and the scale-free homophilic model with a control parameter which tunes the importance of the homophily on preferential attachment process. Our results support a detailed discussion about different kinds of correlation, in special a fitness correlation introduced in this paper, and comparisons between BA model, scale-free homophilic model, and our present model considering its topological properties: degree distribution, time dependence of the connectivity and clustering coefficient.

We consider lattice-gas automata where the lack of semi-detailed balance results from node occupation redistribution ruled by distant configurations; such models with nonlocal interactions are interesting because they exhibit non-ideal gas properties and can undergo phase transitions. For this class of automata, mean-field theory provides a correct evaluation of properties such as compressibility and viscosity (away from the phase transition), despite the fact that no H-theorem strictly holds. We introduce the notion of locality — necessary to define quantities accessible to measurements — by treating the coupling between nonlocal bits as a perturbation. Then if we define operationally "local" states of the automaton — whether the system is in a homogeneous or in an inhomogeneous state — we can compute an estimator of the entropy and measure the local channel occupation correlations. These considerations are applied to a simple model with nonlocal interactions.

Deterministic models, even if used repeatedly, will not capture the essence of planning in an uncertain world. Flexibility and robustness can only be properly valued in models that use stochastics explicitly, such as stochastic optimization models. However, it may also be very important to capture how the random phenomena are related to one another. In this article we show how the solution to a stochastic service network design model depends heavily on the correlation structure among the random demands. The major goal of this paper is to discuss why this happens, and to provide insights into the effects of correlations on solution structures. We illustrate by an example.

Correlation functions measured in heavy-ion collisions are used to extract information about the space-time extent of the emitting sources. Similar techniques can be applied to study some spectroscopic properties of unbound states produced during the dynamical evolution of the colliding system.

Lowest-order cumulants provide important information on the shape of the emission source in femtoscopy. For the simple case of noninteracting identical particles, we show how the fourth-order source cumulant can be determined from measured cumulants in momentum space. The textbook Gram–Charlier series is found to be highly inaccurate, while the related Edgeworth series provides increasingly accurate estimates. Ordering of terms compatible with the Central Limit Theorem appears to play a crucial role even for non-Gaussian distributions.

In this paper, we introduce a family of correlation measures relative to a local channel in terms of the metric-adjusted skew information for a global state and reveal their fundamental properties. We quantify the correlation of quantum states with respect to several typical channels, including unitary channels, twirling channels, and weak measurements, and illustrate that the correlation with respect to the twirling channel induced by the fully unitary group is consistent with that relative to the completely depolarizing channel. In particular, we further evaluate the correlations of the Bell diagonal states, Werner states, and isotropic states and make a comparative study for this family of correlation measures with different operator monotone functions of the two-qubit Werner states and isotropic states, respectively.

The small collision systems like p+p and p+A collisions have shown new features like A+A collisions in the relativistic regime. These new aspects in small systems which have altered our research and understanding on the two-particle correlation measurements have been provided. Additionally, a critical observation of the fluctuation measurements provides new ways to infer such novel happening in the small collision systems. The ongoing and future endeavors towards the new measurements are also discussed.

We present a brief review of our recent results concerning non-mean-field effects of laser-induced dipole–dipole interactions on static and dynamical properties of atomic Bose–Einstein condensates.

The single-particle spectral functions in asymmetric nuclear matter are computed using the ladder approximation within the theory of finite temperature Green's functions. The internal energy and the momentum distributions of protons and neutrons are studied as a function of the density and the asymmetry of the system. The proton states are more strongly depleted when the asymmetry increases, whereas the occupation of the neutron states is enhanced compared to the symmetric case. Preliminary results for the entropy and the free energy are also presented.

In a particular exactly solvable model of an interacting system, the Boltzmann equation predicts a constant single particle density operator, whereas the exact solution gives a single particle density operator with a nontrivial time dependence. All of the time dependence of the single particle density operator is generated by the correlations.

In this paper, we proposed a new one-parameter correlation for the surface tension of saturated fluids. This new correlation requires only the critical temperature as inputs and is tested by using the REFPROP data for 72 saturated fluids including refrigerants, alkanes and some other simple fluids such as argon, carbon dioxide, etc. It is found that this correlation well stands in the whole temperature range from the triple point to the critical point with high accuracy for 59 liquids with average absolute deviations (AADs) less than 5%, 50 liquids with AADs less than 3%, and 13 liquids with AADs less than 1%. These results are clearly better than those of the other available correlations. This correlation can be used to estimate the value of the surface tension of the corresponding liquids at any temperature point from the triple point to the critical point.

In this study, the analytical elucidation for a generalized rotational harmonic system that possesses coherence and periodically excited force is reported. The methods of multiple scales within the interferometry are applied to evaluate the proposed problem and certain distinguishable cases for the rotational oscillators including normal harmonic oscillators without damped rotating are explored and discussed in detail. The distinctive computations for all mentioned chaotic cases about source peculiarities are deduced in detail. The acquired results are demonstrated in concrete graphical and numerical examples. Also, the coherence and the corresponding chaotic characteristics are discussed to probe the system intrinsic configurations. We can differentiate between correlations that result from particular multi-particle formation dynamics and even those caused by the influences of quantum symmetrization. We specifically demonstrate periodic flows and the interferences within the symmetrization for the partially chaotic systems obtained with the smashing of particles that is significant compared to the particle mass m. The partially chaotic system exhibits the coherence components which suppress the correlation intercept significantly and thus the current technique measures the degree of coherence precisely. The contemplated methodology can be applied to evaluating and analyzing many strong nonlinear oscillatory equations. Such an innovative approach can compute the problems of celestial mechanics and chemical reactions in engineering and medical fields.

This work investigates the nonlinear differential equations which have emerged as a substantial concentration of research within a multifariousness of nonlinear disciplines of science and the model computations elucidate the chaotic-coherence radiations with their corresponding convection parameters. The solution for droplets, temperature and chaotic properties of the systems is drawn using the nonlinear dynamics procedure and thus the graphical interpretation is carried out for the system controlling parameters. The significance of pertinent chaotic systems with correlations and their parameters is visualized graphically through the hybrid granular model. In particular, the chaotic-coherent profile is described with the statistical analysis for various system peculiarities and certain nonlinear equations explored in the current methodology through the feasible interferences transformation approach. The discussion part provides a detailed explanation of the schematic methods and certain conclusion observations based on the results of the present research. The findings of this research probe the new specific perceptiveness which commensurable to the system performance of incoherent material with peculiar aspects and such contemplation divulges the remunerative significance in engineering fields.

Based on the recent progress on both the temperature dependence of surface tension [H. L. Yi, J. X. Tian, A. Mulero and I. Cachading, J. Therm. Anal. Calorim.126 (2016) 1603, and the correlation between surface tension and viscosity of liquids [J. X. Tian and A. Mulero, Ind. Eng. Chem. Res.53 (2014) 9499], we derived a new multiple parameter correlation to describe the temperature-dependent viscosity of liquids. This correlation is verified by comparing with data from NIST Webbook for 35 saturated liquids including refrigerants, hydrocarbons and others, in a wide temperature range from the triple point temperature to the one very near to the critical temperature. Results show that this correlation predicts the NIST data with high accuracy with absolute average deviation (AAD) less than 1% for 21 liquids and more than 3% for only four liquids, and is clearly better than the popularly used Vogel–Fulcher–Tamman (VFT) correlation.

Based on the recent progresses on the corresponding state-based correlations for the temperature-dependent surface tension of saturated fluids [I. Cachadiña, A. Mulero and J. X. Tian, Fluid Phase Equilibr.442 (2017) 68; J. X. Tian, M. M. Zheng, H. L. Yi, L. B. Zhang and S. Z. Liu, Mod. Phys. Lett. B31 (2017) 1750110], we proposed a new correlation for saturated hydrocarbons. This correlation includes three fluid-independent parameters and inquires the critical temperature, the triple-point temperature and the surface tension at the triple-point temperature as inputs for each hydrocarbon. Results show that this correlation can reproduce NIST data with absolute average deviation (AAD) less than 1% for 10 out of 19 hydrocarbons and AAD less than 5% for 17 out of 19 hydrocarbons, clearly better than other correlations.

Backpropagation is one of the most widely used methods for training multilayer neural networks, yet questions still exist regarding how the networks organize internally during (raining to represent the external training environment. This paper presents empirical measurements showing that feedforward networks, when trained on many separable and non-separable problems, learn a characteristic internal representation, herein called the Network Linear Transform (NLT), that is independent of: (a) the initial weights and cell biases, and (b) the number of hidden units. The internal decomposition (defined as the values of cell weights and biases) of the trained nets, however, is greatly dependent upon these quantities. For the case of orthogonal input patterns, the NLT captures a literal image of the training environment, while for linearly-independent and separable linearly-dependent training sets, the NLT: (a) captures characteristic features of the correct input patterns, (b) captures inverted versions of characteristic features of incorrect patterns, and (c) rejects features common to all pattern classes. For non-separable problems, the NLT captures statistical ensemble information about patterns in each training class. The hidden units act as difference detectors and thus convey information that distinguishes input patterns from one another. They separate the patterns into groups that are easily discriminated by the output cells. A linearized mathematical network model is developed that accurately reproduces weight matrices and cell responses for certain separable learning situations, and which supports the experimental findings given above.