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We study the degree to which the coherence of quantum states is affected by noise. We give the definition of the $n$-th decay rate and investigate the coherence of Bell-diagonal states under $n$ iterations of channels. We derive explicit formulas of the $n$-th decay rates based on $l_1$ norm of coherence, relative entropy of coherence and skew information-based coherence. It is found that the larger $n$ is, the faster the $n$-th decay rate decreases as the parameter $p$ of Bell-diagonal states increases. Moreover, for any fixed $n$, with the increase of $p$, Bell-diagonal states can be completely incoherent under generalized amplitude damping (GAD) channels, depolarization (DEP) channels and phase flip (PF) channels, while this is not the case for bit flip (BF) channels and bit-phase flip (BPF) channels. We also investigate the geometry of the relative entropy of coherence and skew information-based coherence of Bell-diagonal states under different channels when the $n$-th decay rate is one, i.e., the coherence is frozen. It is shown that compared with BF and BPF channels, when $n$ is large enough, the coherence of Bell-diagonal states will not be frozen under GAD, DEP and PF channels. For skew information-based coherence, similar properties of coherence freezing are found.

Quantifying the quantumness of ensembles is a vital and practical task in quantum information theory. In this paper, we quantify the quantumness of quantum ensembles based on a quantifier of the coherence of ensembles via generalized α-z-relative Renyi entropy. It is shown that this measure satisfies the intuitive and desirable properties which are required by a measure of quantumness, such as positivity, unitary invariance, monotonicity under any commutativity preserving operations and so on. The relationship between our measure and some existing measures for quantumness of quantum ensembles is discussed. Detailed examples are presented to some important ensembles to illustrate the quantumness given by our measure.

Uncertainty relation is a core issue in quantum mechanics and quantum information theory. We introduce modified generalized Wigner-Yanase-Dyson (MGWYD) skew information and modified weighted generalizedWigner-Yanase-Dyson (MWGWYD) skew information, and establish new uncertainty relations in terms of the MGWYD skew information and MWGWYD skew information., 16 pages

We study an approximate coincidence point and a common fixed point problem for a hybrid pair of mappings with constraints in Menger PM-spaces, and obtain some new results. We derive interesting consequences of the main results by using the properties of a Menger–Hausdorff metric, and analogous results based on graphs instead of partial orders can be similarly formulated. Moreover, we construct two examples to reveal that the main results are valid, and show that the main results can be used to explore the existence of solutions to a system of nonlinear integral equations.

The aim of this paper is to propose a new φ -coupled fixed point theorem for a mixed monotone mapping in a metric space, which is taken no account of the continuity of the mapping. To this end, we introduce the notions of φ -coupled fixed point and modified F -control function. Our obtained results are applied to derive some φ -coupled fixed point theorems in partial metric spaces and quasi-metric spaces, respectively. Some applications to matrix equations and integral equations are also presented so as to illustrate our results.

We study the average skew information-based coherence for both random pure and mixed states. The explicit formulae of the average skew information-based coherence are derived and shown to be the functions of the dimension N of the state space. We demonstrate that as N approaches to infinity, the average coherence is 1 for random pure states, and a positive constant less than 1/2 for random mixed states. We also explore the typicality of average skew information-based coherence of random quantum states. Furthermore, we identify a coherent subspace such that the amount of the skew information-based coherence for each pure state in this subspace can be bounded from below almost always by a fixed number that is arbitrarily close to the typical value of coherence., 24pages

Indoor positioning system plays an important role in smart grid. Although GPS is the predominant outdoor positioning technology, it is unsuitable to be used in many fields of smart grid for three main reasons: first, signals sent from GPS could easily get blocked by solid materials such as metal or brick; second, the complex electromagnetic interference induced by electrical circuits greatly affects GPS signals; third, GPS can only achieve meter-level real time positioning accuracy, which is far from sufficient for many requirements of smart grid applications. Some other indoor positioning technologies, such as Bluetooth, Wi-Fi, ultrasound, infrared and RFID, fail in either the positioning accuracy, the positioning range, or the positioning speed required in many smart grid applications. Therefore, this paper proposes a real time indoor positioning system for smart gird based on a more promising technology, ultra-wideband (UWB). UWB is suitable for real-time localization in smart grid because UWB has short radio frequency pulse duration and wide bandwidth, which can minimize the effects of multipath interference and allow for high-resolution ranging and easier material penetration. In addition, since high-accuracy position information is required in many smart grid fields, a comprehensive framework integrating several artificial intelligence techniques, including outlier detection, line-of-sight/non-line-of-sight classification, filter design, range measurement correction and maximum likelihood localization estimation, is also proposed to further improve the positioning accuracy. At last, the performance of this system is verified through a series of experiments.

We introduce modified generalized Wigner-Yanase-Dyson (MGWYD) skew information and modified weighted generalized Wigner-Yanase-Dyson (MWGWYD) skew information. By revisiting state-channel interaction based on MGWYD skew information, a family of coherence measures with respect to quantum channels is proposed. Furthermore, explicit analytical expressions of these coherence measures of qubit states are derived with respect to different quantum channels. Moreover, complementarity relations based on MGWYD skew information and MWGWYD skew information are also presented. Specifically, the conservation relations are investigated, while two interpretations of them including symmetry-asymmetry complementarity and wave-particle duality have been proposed., 20pages

In this paper, we introduce the concepts of cyclic $$\varphi $$ -contractions in Menger PM-spaces and cyclic weak $$\phi $$ -contractions in generalized Menger PM-spaces. Based on these concepts, some fixed point results for cyclic $$\varphi $$ -contractions in Menger PM-spaces are obtained. Furthermore, some fixed point theorems for cyclic weak $$\phi $$ -contractions and cyclic $$\varphi $$ -contractions in generalized Menger PM-spaces are obtained by assuming that the number of cyclic sets is odd. An example is also given to show the validity of our main results.

In this paper, we obtain some new fixed point theorems for (?,?,?,?) -contractive multi-valued mappings in ?-?-T-complete Menger PM-spaces, which turn out to generalize many results in existing literatures. Some examples are also given to illustrate the definition and support our new results. Moreover, some interesting fixed point results endowed with binary relations or graphs are derived as applications of our main results.

In this paper, we propose some new coupled coincidence point and fixed point theorems for the mappings F and g. Our results are obtained by exploring the corresponding initial value problems for the mapping F and weakening the involved contractive conditions. As an application, we study the existence and uniqueness of solution to integro-differential equations.

We investigate facial expression recognition using state-of-the-art classification models. Recently, CNNs have been extensively used for face recognition. However, CNNs have not been thoroughly evaluated for facial expression recognition. In this paper, we train and test a CNN model for facial expression recognition. The performance of the CNN model is used as benchmark for evaluating other pre-trained deep CNN models. We evaluate the performance of Inception and VGG which are pre-trained for object recognition, and compare these with VGG-Face which is pre-trained for face recognition. All experiments are performed on publicly available face databases, namely, CK+, JAFFE and FACES.

The conflict between the dynamics postulate (unitary evolution) and the measurement postulate (wave-packet collapse) of quantum mechanics has been reconciled by Zurek from an information transfer perspective [Phys. Rev. A 76 (2007) 052110], and has further been extended to a more general scenario [Phys. Rev. A 87 (2013) 052111]. In this paper, we reconsider Zurek's new derivation by using weak repeatability postulate or covariant condition instead of repeatability postulate.

In this paper, the new concepts of \(\alpha \)-admissible mappings with respect to \(\eta \) in single-valued case and \(\alpha _{*}\)-admissible mappings with respect to \(\eta _{*}\) in set-valued case in Menger PM-spaces are introduced, and some new fixed point results for both single-valued and set-valued mappings under certain contractive conditions are studied, which extend and generalize some results in corresponding literatures. Some examples are provided to illustrate the validity of our main results, and an application is also given to discuss the existence of solution for Volterra type integral equations.

Some new coupled coincidence point and coupled fixed point theorems are established in partially ordered metric-like spaces, which generalize many results in corresponding literatures. An example is given to support our main results. As an application, we discuss the existence of the solutions for a class of nonlinear integral equations.

We investigate facial expression recognition based on geometric features, and image appearance, using a range of classifier models. First, we evaluate expression recognition of face images based on geometric features, namely, facial landmarks based on the Active Appearance Model, and Action Units based on the Facial Action Coding System. A generalized linear model and a neural network are used to classify face images based on these geometric features. Second, the classification achieved by facial landmarks and Action Units is compared with the classification achieved by convolutional neural network (CNN) which extracts image features from raw pixels. Finally, we use transfer learning technique to evaluate classification using a pre-trained model. All experiments are performed on the state-of-the-art CK+ face database.

We propose an Otto heat engine that undergoes processes involving a special class of feedback and analyze theoretically its response. We use stochastic thermodynamics to determine the performance characteristics of the heat engine and indicate the possibility that its maximum efficiency can surpass the Carnot value. The analytical expression for efficiency at maximum power, including the effects resulting from feedback, reduces to that previously derived based on an engine without feedback.