Internet-based cognitive behavioral therapy (ICBT) has been found to be effective for tinnitus management, although there is limited understanding about who will benefit the most from ICBT. Traditional statistical models have largely failed to identify the nonlinear associations and hence find strong predictors of success with ICBT. This study aimed at examining the use of an artificial neural network (ANN) and support vector machine (SVM) to identify variables associated with treatment success in ICBT for tinnitus.

The study involved a secondary analysis of data from 228 individuals who had completed ICBT in previous intervention studies. A 13-point reduction in Tinnitus Functional Index (TFI) was defined as a successful outcome. There were 33 predictor variables, including demographic, tinnitus, hearing-related and treatment-related variables, and clinical factors (anxiety, depression, insomnia, hyperacusis, hearing disability, cognitive function, and life satisfaction). Predictive models using ANN and SVM were developed and evaluated for classification accuracy. SHapley Additive exPlanations (SHAP) analysis was used to identify the relative predictor variable importance using the best predictive model for a successful treatment outcome.

The best predictive model was achieved with the ANN with an average area under the receiver operating characteristic value of 0.73 ± 0.03. The SHAP analysis revealed that having a higher education level and a greater baseline tinnitus severity were the most critical factors that influence treatment outcome positively.

Predictive models such as ANN and SVM help predict ICBT treatment outcomes and identify predictors of outcome. However, further work is needed to examine predictors that were not considered in this study as well as to improve the predictive power of these models.

]]>For m ≤ 4 and ℓ = 3 , simple combinatorial statistics called "cranks" witness these congruences. We prove this analytically for m = 4 , and then both analytically and combinatorially for m = 3 . Our combinatorial proof relies upon explicit dissections of convex lattice polygons.

For m ≤ 4 and ℓ = 3 , simple combinatorial statistics called cranks" witness these congruences. We prove this analytically for m = 4 , and then both analytically and combinatorially for m = 3 . Our combinatorial proof relies upon explicit dissections of convex lattice polygons.

]]>where b is an arbitrary real constant. %By applying ∂¯-steepest descent method, l Long-time asymptotics of the equation is obtained through the ∂¯-steepest descent method. Firstly, based on the spectral analysis of the Lax pair and scattering matrix, the solution of the equation is able to be constructed %can be expressed by %the solution of via solving the corresponding Riemann-Hilbert problem (RHP). Then, we present %obtain different long time asymptotic expansions of the solution u(y,t) in different space-time solitonic regions of ξ=y/t. The half-plane (y,t):−∞0 is divided into four asymptotic regions: ξ∈(−∞,−1), ξ∈(−1,0), ξ∈(0,18) and ξ∈(18,+∞). When ξ falls in (−∞,−1)∪(18,+∞), no stationary phase point of the phase function θ(z) exists on the jump profile in the space-time region. In this case, corresponding asymptotic approximations can be characterized with an N(Λ)-solitons with diverse residual error order O(t−1+2ε). %While There are four stationary phase points and eight stationary phase points on the jump curve as ξ∈(−1,0) and ξ∈(0,18), respectively. The corresponding asymptotic form is accompanied by a residual error order O(t−34).

]]>With the innovation and integration of the Internet and the financial industry, the third-party payment market has developed greatly and has great potential. This paper discusses the duopoly game between third-party payment service providers and banks, which are the main participants in the mobile payment market. By constructing Nash game model, the conditions of equilibrium point, stability and bifurcation are analyzed. The effects of adjusting parameters and cooperation coefficient on business volume and profit are discussed. The conclusions are as follows: excessive investment will lead to unpredictable fluctuations in the market and fall into chaos; By strengthening cooperation, all participants in the mobile payment industry chain can improve business volume and profits while curbing chaos in the mobile payment market.

]]>We prove the complex polynomial plank covering theorem for not necessarily homogeneous polynomials. As the consequence of this result, we extend the complex plank theorem of Ball to the case of planks that are not necessarily centrally symmetric and not necessarily round. We also prove a weaker version of the spherical polynomial plank covering conjecture for planks of different widths.]]>

Heat and mass transfer rates play a significant role in achieving a high-efficiency, low-cost wire coating process. Therefore, the flow analysis of molten polymer (polyvinyl chloride) carrying nanoparticles inside a pressure-type die is presented. The third-grade liquid model is used for the constitutive equation of the polyvinyl chloride (PVC), while the non-homogeneous biphasic model is used for nanoparticles. The properties of PVC are temperature-dependent. The melt flow is governed by the modified Navier-Stokes equation for the third-grade fluid, energy conservation, and nanoparticles' continuity equation. The finite difference method-based routine is applied to solve the nonlinear differential equations that include nine physical parameters. The Response Surface Method (RSM) is implemented to optimize the heat/mass transfer rate coated wire's eminence depends on the coating material's rheological characteristics of PVC. Full quadratic correlation models for heat/mass transfer rate of melt are proposed through central-composite-design (CCD). The optimal level of third-grade fluid factor and nanofluid factors was determined to achieve an optimum heat/mass transfer rate of the melt. The rheological characteristics of PVC have been improved due to the temperature-dependent viscosity and shear thickening/thinning property of the melt. The nanofluid factors improve the thermal field and subsequently reduce the Nusselt number. Maximum heat transfer occurs for a low level of Brownian factor, a high level of thermophoresis factor, and a third-grade fluid factor of 0.2177, also reaching the maximum mass transfer simultaneously.

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