**Abstract: **Many statistical models over a discrete sample space often face the computational difficulty of the normalization constant. Because of that, the maximum likelihood estimator does not work. In order to circumvent the computation difficulty, alternative estimators such as pseudo-likelihood and composite likelihood that require only a local computation over the sample space have been proposed. In this paper, we present a theoretical analysis of such localized estimators. The asymptotic variance of localized estimators depends on the neighborhood system on the sample space. We investigate the relation between the neighborhood system and estimation accuracy of localized estimators. Moreover, we derive the efficiency bound. The theoretical results are applied to investigate the statistical properties of existing estimators and some extended ones.

**Abstract: **The discovery of the entropy production paradox (Hoffmann et al., 1998) raised basic questions about the nature of irreversibility in the regime between diffusion and waves. First studied in the form of spatial movements of moments of H functions, pseudo propagation is the pre-limit propagation-like movements of skewed probability density function (PDFs) in the domain between the wave and diffusion equations that goes over to classical partial differential equation propagation of characteristics in the wave limit. Many of the strange properties that occur in this extraordinary regime were thought to be connected in some manner to this form of proto-movement. This paper eliminates pseudo propagation by employing a similar evolution equation that imposes spatial unimodal symmetry on evolving PDFs. Contrary to initial expectations, familiar peculiarities emerge despite the imposed symmetry, but they have a distinct character.

**Abstract: **The year 2015 marked the 150th anniversary of “entropy” as a concept in classical thermodynamics. Despite its central role in the mathematical formulation of the Second Law and most of classical thermodynamics, its physical meaning continues to be elusive and confusing. This is especially true when we seek a reconstruction of the classical thermodynamics of a system from the statistical behavior of its constituent microscopic particles or vice versa. This paper sketches the classical definition by Clausius and offers a modified mathematical definition that is intended to improve its conceptual meaning. In the modified version, the differential of specific entropy appears as a non-dimensional energy term that captures the invigoration or reduction of microscopic motion upon addition or withdrawal of heat from the system. It is also argued that heat transfer is a better model process to illustrate entropy; the canonical heat engines and refrigerators often used to illustrate this concept are not very relevant to new areas of thermodynamics (e.g., thermodynamics of biological systems). It is emphasized that entropy changes, as invoked in the Second Law, are necessarily related to the non-equilibrium interactions of two or more systems that might have initially been in thermal equilibrium but at different temperatures. The overall direction of entropy increase indicates the direction of naturally occurring heat transfer processes in an isolated system that consists of internally interacting (non-isolated) sub systems. We discuss the implication of the proposed modification on statements of the Second Law, interpretation of entropy in statistical thermodynamics, and the Third Law.

**Abstract: **With the recent emergence of wireless sensor networks (WSNs) in the cloud computing environment, it is now possible to monitor and gather physical information via lots of sensor nodes to meet the requirements of cloud services. Generally, those sensor nodes collect data and send data to sink node where end-users can query all the information and achieve cloud applications. Currently, one of the main disadvantages in the sensor nodes is that they are with limited physical performance relating to less memory for storage and less source of power. Therefore, in order to avoid such limitation, it is necessary to develop an efficient data prediction method in WSN. To serve this purpose, by reducing the redundant data transmission between sensor nodes and sink node while maintaining the required acceptable errors, this article proposes an entropy-based learning scheme for data prediction through the use of kernel least mean square (KLMS) algorithm. The proposed scheme called E-KLMS develops a mechanism to maintain the predicted data synchronous at both sides. Specifically, the kernel-based method is able to adjust the coefficients adaptively in accordance with every input, which will achieve a better performance with smaller prediction errors, while employing information entropy to remove these data which may cause relatively large errors. E-KLMS can effectively solve the tradeoff problem between prediction accuracy and computational efforts while greatly simplifying the training structure compared with some other data prediction approaches. What’s more, the kernel-based method and entropy technique could ensure the prediction effect by both improving the accuracy and reducing errors. Experiments with some real data sets have been carried out to validate the efficiency and effectiveness of E-KLMS learning scheme, and the experiment results show advantages of the our method in prediction accuracy and computational time.

**Abstract: **In this paper, a thermo-mechanical coupling analysis model of the spindle-bearing system based on Hertz’s contact theory and a point contact non-Newtonian thermal elastohydrodynamic lubrication (EHL) theory are developed. In this model, the effect of preload, centrifugal force, the gyroscopic moment, and the lubrication state of the spindle-bearing system are considered. According to the heat transfer theory, the mathematical model for the temperature field of the spindle system is developed and the effect of the spindle cooling system on the spindle temperature distribution is analyzed. The theoretical simulations and the experimental results indicate that the bearing preload has great effect on the frictional heat generation; the cooling fluid has great effect on the heat balance of the spindle system. If a steady-state heat balance between the friction heat generation and the cooling system cannot be reached, thermally-induced preload will lead to a further increase of the frictional heat generation and then cause the thermal failure of the spindle.

**Abstract: **In this paper, our concern is to design some criteria for deterministic remote state preparation for preparing an arbitrary three-particle state via a genuinely entangled six-qubit state. First, we put forward two schemes in both the real and complex Hilbert space, respectively. Using an appropriate set of eight-qubit measurement basis, the remote three-qubit preparation is completed with unit success probability. Departing from previous research, our protocol has a salient feature in that the serviceable measurement basis only contains the initial coefficients and their conjugate values. By utilizing the permutation group, it is convenient to provide the permutation relationship between coefficients. Second, our ideas and methods can also be generalized to the situation of preparing an arbitrary *N*-particle state in complex case by taking advantage of Bell states as quantum resources. More importantly, criteria satisfied conditions for preparation with 100% success probability in complex Hilbert space is summarized. Third, the classical communication costs of our scheme are calculated to determine the classical recourses required. It is also worth mentioning that our protocol has higher efficiency and lower resource costs compared with the other papers.