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This study used knee MR imaging features to quantify the severity of knee injury in patients and analyzed the predictive value of knee MR imaging features in their risk of knee replacement. A total of 120 patients with knee arthritis were included from a public knee arthritis database FNIH OAI. First, univariate logistic regression was used to screen clinical features to obtain the clinical risk factors. Then the minimum redundancy maximum correlation (mRMR) method was used to reduce the image features, and the LASSO method was used to further screen the retained image features to construct a Rad model. Next, the multivariate logistic regression method was used to combine the Rad model and the screened clinical risk factors to construct a combined model and its corresponding nomogram. Finally, ROC curve and its related metrics, Hosmer–Lemeshow test and Delong test were used to evaluate and compare the accuracy and consistency of the model performance. Age and body mass index (BMI) were found as significant clinical risk factors for knee replacement. After using mRMR and LASSO methods, 147 image features were reduced to 30 and 7 features, respectively, then these 7 features were linearly combined to construct the Rad model. Age, BMI, and the Rad model were combined to establish the combined model and its corresponding nomogram. The resulted two models showed high accuracy (AUC ∼ 0. 8) and consistency (H-L test: p > 0. 0 5) on both the training set and test set. Finally, the comparison results showed that the prediction performance of the combined model was better than that of the Rad model, but their difference was not significant (Delong test: p > 0. 0 5). This paper studied the predictive performance of MR imaging features on the risk of knee replacement and built a model that can be used to predict the potential risk of knee replacement in patients with knee arthritis. The resulting models showed good predictive accuracy and consistency. The drawn nomogram could be used as a useful tool to personalize the prognosis of patients with knee arthritis and guide clinical decisions on knee replacement. [ABSTRACT FROM AUTHOR]

We first give a q -analogue of a supercongruence of Sun, which is a generalization of Van Hamme's (H.2) supercongruence for any prime p ≡ 3 (mod 4). We also give a further generalization of this q -supercongruence, which may also be considered as a generalization of a q -supercongruence recently conjectured by the second author and Zudilin. Then, by combining these two q -supercongruences, we obtain q -analogues of the following two results: for any integer d > 1 and prime p with p ≡ − 1 (mod 2 d) ∑ k = 0 (p 2 − 1) / d 1 d k 3 k ! 3 ≡ p 2 (mod p 4) , ∑ k = 0 p 2 − 1 1 d k 3 k ! 3 ≡ p 2 (mod p 4) , which are generalizations of Swisher's (H.3) conjecture modulo p 4 for r = 2. The key ingredients in our proof are the 'creative microscoping' method, the q -Dixon sum, Watson's terminating 8 ϕ 7 transformation, and properties of the p -adic Gamma function. [ABSTRACT FROM AUTHOR]

We study the existence of traveling wave solutions and spreading properties for single-layer delayed neural field equations. We focus on the case where the kinetic dynamics are of monostable type and characterize the invasion speeds as a function of the asymptotic decay of the connectivity kernel. More precisely, we show that for exponentially bounded kernels the minimal speed of traveling waves exists and coincides with the spreading speed, which further can be explicitly characterized under a KPP type condition. We also investigate the case of algebraically decaying kernels where we prove the non-existence of traveling wave solutions and show the level sets of the solutions eventually locate in-between two exponential functions of time. The uniqueness of traveling waves modulo translation is also obtained. [ABSTRACT FROM AUTHOR]

Let be an umbilical free hypersurface in the unit sphere . Four basic invariants of , under the Möbius transformation group of are the Möbius metric , the Möbius second fundamental form , the Blaschke tensor and the Möbius form . In this paper, we study complete hypersurfaces with constant normalized Möbius scalar curvature and vanishing Möbius form . By computing the Laplacian of the funtion , where the trace-free Blaschke tensor , and applying the well known generalized maximum principle of Omori-Yau, we obtain the following result: must be either Möbius equivalent to a minimal hypersurface with constant Möbius scalar curvature, when ; in , when ; the pre-image of the stereographic projection of the circular cylinder in , when ; or the pre-image of the projection of the hypersurface in , when . [ABSTRACT FROM AUTHOR]

The free vibration of rotating tapered Timoshenko beams (TBs) made of the axially functionally graded materials (FGMs) is studied. The Chebyshev polynomials multiplied by the boundary functions are selected as the admissible functions in the Ritz minimization procedure, which is called the Chebyshev-Ritz method. As such, the geometric boundary conditions are satisfied, while the numerical robustness is guaranteed through use of the Chebyshev polynomials. The Ritz approach provides an upper bound of the exact frequencies. The effectiveness of the method is confirmed in the convergence and comparison studies. The effects of hub radius ratio, rotational speed ratio, taper ratios, rotary inertia and material gradient on the natural frequencies of the TBs for six different sets of boundary conditions are studied in detail. [ABSTRACT FROM AUTHOR]

In this paper, lag full state hybrid projective synchronization (LFSHPS) in fractional-order chaotic systems is first studied. We show that LFSHPS does exist in fractional-order chaotic systems. Based on active control theory, synchronization schemes for LFSHPS of the fractional-order chaotic systems are given. Numerical simulations are provided to illustrate and verify the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

The large eddy simulation (LES) of compressible turbulent channel flow controlled by active spanwise wall fluctuations (ASWF) is carried out in this paper. Heat transport and its relation with the momentum transport are paid with great attentions. In all the flow cases of present study, the changes of temperature fluctuation, heat transport and temperature streaks are in consistence with streamwise velocity fluctuation, momentum transport and velocity streaks respectively. This demonstrates the existence of same mechanism in heat transport and momentum transport in turbulent boundary layer, which gives the theoretical support for using the drag reduction technology to control wall heat flux. [ABSTRACT FROM AUTHOR]

In this paper, the problem of adaptive synchronization for a class of stochastic neural networks (SNNs) which involve both mixed delays and Markovian jumping parameters is investigated. The mixed delays comprise the time-varying delays and distributed delays, both of which are mode-dependent. The stochastic perturbations are described in terms of Browian motion. By the adaptive feedback technique, several sufficient criteria have been proposed to ensure the synchronization of SNNs in mean square. Moreover, the proposed adaptive feedback scheme is applied to the secure communication. Finally, the corresponding simulation results are given to demonstrate the usefulness of the main results obtained. [ABSTRACT FROM AUTHOR]

In this paper, a simple and systematic adaptive feedback method for achieving lag projective stochastic perturbed synchronization of a new four-wing chaotic system with unknown parameters is presented. Moreover, a secure communication scheme based on the adaptive feedback lag projective synchronization of the new chaotic systems with stochastic perturbation and unknown parameters is presented. The simulation results show the feasibility of the proposed method. [ABSTRACT FROM AUTHOR]

This paper is concerned with the synchronization problem for a class of stochastic neural networks with unknown parameters and mixed time-delays via output coupling. The mixed time-delays comprise the time-varying delay and distributed delay, and the neural networks are subjected to stochastic disturbances described in terms of a Brownian motion. Firstly, we use Lyapunov functions to establish general theoretical conditions for designing the output coupling matrix. Secondly, by using the adaptive feedback technique, a simple, analytical and rigorous approach is proposed to synchronize the stochastic neural networks with unknown parameters and mixed time-delays. Finally, numerical simulation results are given to show the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

The WSe2/g-C3N4 (graphite carbon nitride) composite with photocatalytic properties was synthesized using a hydrothermal method. This synthesis pathway can be characterized by being simple, inexpensive and nonpolluting, integrating the concept of green chemistry. The WSe2/g-C3N4 composite could effectively degrade methyl orange solution under visible light irradiation. The decolorization experiment of methyl orange solution shows that the degradation rate of the 30 wt.% WSe2/g-C3N4 composite can reach 98.7% after 100 min of illumination, while the degradation rate of pure g-C3N4 was only 87.6% under the same conditions. This can be attributed to the fact that the combination of WSe2 and g-C3N4 nanosheets can increase the number of active binding sites, increasing the rate of charge separation and transport ability, decreasing the recombination rate of the photogenerated electron–hole pairs. Therefore, the WSe2/g-C3N4 composite will have potential development as a new material with low cost, easy synthesis and excellent performance in photocatalytic degradation of water pollution. The present research shown that WSe2/g-C3N4 composite has excellent photocatalytic properties for the degradation of MO in visible light. Photogenerated electron–hole pairs promote the degradation of MO into CO2, water and other minerals in acidic environment. Furthermore, the unique two-dimensional layered structure of WSe2 increases the active sites of the reaction, and the photocatalytic degradation efficiency is improved. [ABSTRACT FROM AUTHOR]

The effect of spanwise alternatively distributed strips (SADS) control on turbulent flow in a plane channel has been studied by direct numerical simulations to investigate the characteristics of large-scale streamwise vortices (LSSVs) induced by small-scale active wall actuation, and their potential in suppressing flow separation. SADS control is realized by alternatively arranging out-of-phase control (OPC) and in-phase control (IPC) wall actuations on the lower channel wall surface, in the spanwise direction. It is found that the coherent structures are suppressed or enhanced alternatively by OPC or IPC, respectively, leading to the formation of a vertical shear layer, which is responsible for the LSSVs' presence. Large-scale low-speed region can also be observed above the OPC strips, which resemble large-scale low-speed streaks. LSSVs are found to be in a statistically-converged steady state and their cores are located between two neighboring OPC and IPC strips. Their motions contribute significantly to the momentum transport in the wall-normal and spanwise directions, demonstrating their potential ability to suppress flow separation. [ABSTRACT FROM AUTHOR]

The thermal quantum discord (QD) is investigated in the two-qubit anisotropic Heisenberg XXZ model under an external non-uniform magnetic field along the Z-axis. We obtain the analytical expressions of the thermal QD and thermal entanglement measured by concurrence (C). It shows that for any temperature T, QD gradually decreases with the increase of non-uniform magnetic field |b|, in some regions where C increases while QD decreases. It is also found that thermal quantum discord does not vanish at finite temperatures, but concurrence vanishes completely at a critical temperature. It is shown that for a higher value of JZ, the system has a stronger QD. There is a critical magnetic field Bc, which increases with the increasing b. QD decay monotonically (for B < Bc) when temperature T increases, or initially increases to some peaks and then decrease (for B > Bc). [ABSTRACT FROM AUTHOR]

Excitement and synchronization of electrically and chemically coupled Newman-Watts (NW) small-world neuronal networks with a short-term synaptic plasticity described by a modified Oja learning rule are investigated. For each type of neuronal network, the variation properties of synaptic weights are examined first. Then the effects of the learning rate, the coupling strength and the shortcut-adding probability on excitement and synchronization of the neuronal network are studied. It is shown that the synaptic learning suppresses the over-excitement, helps synchronization for the electrically coupled network but impairs synchronization for the chemically coupled one. Both the introduction of shortcuts and the increase of the coupling strength improve synchronization and they are helpful in increasing the excitement for the chemically coupled network, but have little effect on the excitement of the electrically coupled one. [ABSTRACT FROM AUTHOR]

In this letter, a general model of an array of N linearly coupled chaotic neural networks with hybrid coupling is proposed, which is composed of constant coupling, time-varying delay coupling and distributed delay coupling. The complex network jumps from one mode to another according to a Markovian chain with known transition probability. Both the coupling time-varying delays and the coupling distributed delays terms are mode-dependent. By the adaptive feedback technique, several sufficient criteria have been proposed to ensure the synchronization in an array of jump chaotic neural networks with mode-dependent hybrid coupling and mixed delays in mean square. Finally, numerical simulations illustrated by mode switching between two complex networks of different structure dependent on mode switching verify the effectiveness of the proposed results. [ABSTRACT FROM AUTHOR]

With the aid of an extended projective method and a variable separation approach, new families of variable separation solutions (including solitary wave solutions, periodic wave solutions and rational function solutions) with arbitrary functions for (2+1)-dimensional general Korteweg–de Vries (GKdV) system are derived. Analytical investigation of the (2+1)-dimensional GKdV system shows the existence of abundant stable localized coherent excitations such as dromions, lumps, peakons, compactons and ring soliton solutions as well as rich fractal and chaotic localized patterns in terms of the derived solitary solutions or the variable separation solutions when we consider appropriate boundary conditions and/or initial qualifications. [ABSTRACT FROM AUTHOR]

With the help of a mapping approach, a new type of variable separation solution with two arbitrary functions to (2+1)-dimensional Boiti–Leon–Pempinelli system (BLP) is derived. Based on the derived variable separation solution, some single valued and multiple valued localized excitations such as dromions, peakons and foldons, etc. with novel evolutional properties are revealed by introducing appropriate initial conditions in this paper. [ABSTRACT FROM AUTHOR]