Resource Allocation with Sigmoidal Demands: Mobile Healthcare Units and Service Adoption

Problem definition: Achieving broad access to health services (a target within the sustainable development goals) requires reaching rural populations. Mobile healthcare units (MHUs) visit remote sites to offer health services to these populations. However, limited exposure, health literacy, and trust can lead to sigmoidal (S-shaped) adoption dynamics, presenting a difficult obstacle in allocating limited MHU resources. It is tempting to allocate resources in line with current demand, as seen in practice. However, to maximize access in the long term, this may be far from optimal, and insights into allocation decisions are limited. Academic/practical relevance: We present a formal model of the long-term allocation of MHU resources as the optimization of a sum of sigmoidal functions. We develop insights into optimal allocation decisions and propose pragmatic methods for estimating our model’s parameters from data available in practice. We demonstrate the potential of our approach by applying our methods to family planning MHUs in Uganda. Methodology: Nonlinear optimization of sigmoidal functions and machine learning, especially gradient boosting, are used. Results: Although the problem is NP-hard, we provide closed form solutions to particular cases of the model that elucidate insights into the optimal allocation. Operationalizable heuristic allocations, grounded in these insights, outperform allocations based on current demand. Our estimation approach, designed for interpretability, achieves better predictions than standard methods in the application. Managerial implications: Incorporating the future evolution of demand, driven by community interaction and saturation effects, is key to maximizing access with limited resources. Instead of proportionally assigning more visits to sites with high current demand, a group of sites should be prioritized. Optimal allocation among prioritized sites aims at equalizing demand at the end of the planning horizon. Therefore, more visits should generally be allocated to sites where the cumulative demand potential is higher and counterintuitively, often those where demand is currently lower.

Asymptotic Expansion for Neural Network Operators of the Kantorovich Type and High Order of Approximation

In this paper, we study the rate of pointwise approximation for the neural network operators of the Kantorovich type. This result is obtained proving a certain asymptotic expansion for the above operators and then by establishing a Voronovskaja type formula. A central role in the above resuts is played by the truncated algebraic moments of the density functions generated by suitable sigmoidal functions. Furthermore, to improve the rate of convergence, we consider finite linear combinations of the above neural network type operators, and also in the latter case, we obtain a Voronovskaja type theorem. Finally, concrete examples of sigmoidal activation functions have been deeply discussed, together with the case of rectified linear unit (ReLu) activation function, very used in connection with deep neural networks.

Blue-Light Hazard of Light-Emitting Diodes Assessed with Gaussian Functions

The high blue proportion of phosphor-conversion white-light emitting diodes (pc-LEDs), especially of those with higher correlated color temperatures (CCT), raises concern about photochemically induced retinal damages. Although almost all general lighting service LEDs are safe, other applications exist, like spotlights for theatres or at construction sites, that can pose a severe blue-light hazard (BLH) risk, and their photobiological safety must be assessed. Because of required but challenging radiance measurements, a calculative approach can be supportive for risk assessment. It is the aim of this work to exploit Gaussian functions to study LED parameter variations affecting BLH exposure. Gaussian curve approximations for color LEDs, the BLH action spectrum, and the spectral luminous efficiency for photopic vision enabled analytically solving the BLH efficiency, ηB, and the BLH efficacy of luminous radiation, KB,v. It was found that sigmoidal functions describe the CCT dependence of ηB and KB,v for different color LEDs with equal spectral bandwidth. Regarding pc-LEDs, variations of peak wavelengths, intensities, and bandwidths led to linear or parabolic shaped chromaticity coordinate correlations. ηB and KB,v showed pronounced CCT dependent extrema that might be exploited to reduce BLH. Finally, an experimental test of the presented Gaussian approach yielded its successful applicability for color and pc-LEDs but a minor accuracy for blue and green LEDs.

Modeling the Methane Production Kinetics of Anaerobic Co-Digestion of Agricultural Wastes Using Sigmoidal Functions

The modified sigmoidal bacteria growth functions (the modified Gompertz, logistic, and Richards) were used to evaluate the methane production process kinetics of agricultural wastes. The mesophilic anaerobic co-digestion experiments were conducted with various agricultural wastes as feedstocks, including cow manure, corn straw, grape leaves, vines, wine residue, strawberry leaves, and tomato leaves. The results showed that anaerobic co-digestion of cow manure and other agricultural wastes increased the methane yields while it prolonged the lag phase time. Compared with the modified Gompertz and logistic models, the modified Richards model obtained higher correlation coefficients and was able to fit experimental data better. The results of this study were expected to determine a suitable model to simulate and study the kinetic process of anaerobic co-digestion with mixed agricultural wastes as feedstocks.

Fuzzy-Neuro Network in a CO-OFDM system: Various Membership Functions Comparison

Fuzzy-Neuro Network based nonlinear equalizer (FNN-NLE) has been used for the extenuation of nonlinearities in optical communication systems. Until now, many membership functions with resilient backpropagation activation function was used for making FNN-NLE in a coherent optical orthogonal frequency division multiplexing (CO-OFDM) systems. Despite this, no research is reflecting the comparison of different membership functions (MFs). In this paper, various membership functions such as gaussian MF, gaussian combination MF, triangular MF, difference between two sigmoidal functions MF, pi shaped MF, generalized bell shaped MF, trapezoidal MF and product of two sigmoid functions MF has been compared. From this study, the maximum performance in terms of BER is achieved with gaussian membership function has been concluded.

Representation of discontinuous seismic velocity fields by sigmoidal functions for ray tracing and traveltime modelling

SUMMARY Wave-modelling methods based on asymptotic ray theory have a lower computational cost than full wave-equation methods but require a smooth velocity field, though discontinuities may be handled by imposing interface conditions between adjacent blocks. We propose to approximate discontinuous velocity fields with model parametrizations based on smooth, rapidly varying functions known as sigmoidal functions. We have implemented the proposed technique on Cartesian grids using the wavelet theory formalism. Numerical experiments with 2-D and 3-D initial-value and two-point ray tracing in heterogeneous media show that the ray paths and traveltimes produced with the sigmoidal representation are consistent with the results produced by conventional ray tracing in block structures, broadening the scope of classical algorithms based on smooth velocity fields.

The spatial–temporal total friction coefficient of the fault viewed from the perspective of seismo-electromagnetic theory

Recently, it has been shown theoretically how the lithospheric stress changes could be linked with magnetic anomalies, frequencies, spatial distribution and the magnetic-moment magnitude relation using the electrification of microfractures in the semibrittle–plastic rock regime (Venegas-Aravena et al., 2019). However, this seismo-electromagnetic theory has not been connected with the fault's properties in order to be linked with the onset of the seismic rupture process itself. In this work we provide a simple theoretical approach to two of the key parameters for seismic ruptures which are the friction coefficient and the stress drop. We use sigmoidal functions to model the stress changes in the nonelastic regime within the lithosphere. We determine the temporal changes in frictional properties of faults. We also use a long-term friction coefficient approximation that depends on the fault dip angle and four additional parameters that weigh the first and second stress derivative, the spatial distribution of the nonconstant stress changes, and the stress drop. We found that the friction coefficient is not constant in time and evolves prior to and after the earthquake occurrence regardless of the (nonzero) weight used. When we use a dip angle close to 30∘ and the contribution of the second derivative is more significant than that of the first derivative, the friction coefficient increases prior to the earthquake. During the earthquake event the friction drops. Finally, the friction coefficient increases and decreases again after the earthquake occurrence. It is important to mention that, when there is no contribution of stress changes in the semibrittle–plastic regime, no changes are expected in the friction coefficient.