Search Results (29)

We study the approximation of functions by localized shallow neural networks on bounded Lipschitz domains. For a non-polynomial activation, we establish a direct, Jackson-type estimate on the Besov scale ${\displaystyle B_{p,q}^s(\Omega )}$, the approximation error decaying as ${\displaystyle N^{-s/d}}$ in the width ${\displaystyle N}$ with an explicit constant tracked through the activation and the domain. In one spatial variable we prove the corresponding Bernstein-type converse on the nonlinear free-knot Besov scale ${\displaystyle B_{\tau ,\tau }^{\alpha }}$. For coordinate-subset additive classes we refine the direct estimate to the rate ${\displaystyle N^{-s/d_0}}$, in which the effective dimension ${\displaystyle d_0}$ governs the exponent while the ambient dimension enters only through the constant. A deterministic construction corroborates the predicted decay rates, and an effective-dimension reading of educational tabular data is consistent with the additive setting. Full article

We introduce and study a class of multi-composite sigmoid neural network operators for Banach space-valued approximation. The proposed operators are generated by density-type kernels induced by finite compositions of seven standard sigmoid-type activation functions. The approximation is considered for continuous functions on compact intervals of the real line and on the whole real line, with values in an arbitrary Banach space $(X,\parallel ·\parallel )$. We prove quantitative pointwise and uniform convergence results by means of Jackson-type inequalities expressed through the first modulus of continuity. Higher-order and fractional approximation results are also obtained in terms of Banach space-valued derivatives and Caputo–Bochner fractional derivatives. The associated feed-forward neural network representation has one hidden layer and uses the multi-composite sigmoid function as its activation. Numerical experiments are presented to validate the theoretical estimates and to illustrate the approximation behavior of the proposed operators. In particular, we compare classical tanh-based operators, normalized self-composed activation operators, and heterogeneous multi-composite activation operators. The results show that self-composition and heterogeneous composition may improve the uniform approximation error for certain activation families and parameter choices, while also indicating that the observed improvement is activation-dependent and influenced by the composition order, kernel localization, and the regularity of the target function. Full article

Efficient resource utilization and low response times are critical challenges in storage area network (SAN) systems, especially as data-intensive applications like those driven by the Internet of Things and Artificial Intelligence place increasing demands on reliable, high-performance data storage solutions. Addressing these challenges, this paper contributes by proposing a proactive, utilization-driven traffic redistribution strategy to achieve balanced load distribution across switches, thereby improving the overall SAN performance and alleviating the risk of overload-incurred cascading failures. The proposed approach incorporates a Jackson Queueing Network-based method to evaluate both utilization and response time of individual switches, as well as the overall system response time. Based on a comprehensive case study of a mesh SAN system, two key parameters—the transition probability adjustment step size and the node selection window size—are analyzed for their impact on the effectiveness of the proposed strategy, revealing several valuable insights into fine-tuning traffic redistribution parameters. Full article

This work takes up the task of the determination of the rate of pointwise and uniform convergences to the unit operator of the “normalized cusp neural network operators”. The cusp is a compact support activation function, which is the composition of two general activation functions having as domain the whole real line. These convergences are given via the modulus of continuity of the engaged function or its derivative in the form of Jackson type inequalities. The composition of activation functions aims to more flexible and powerful neural networks, introducing for the first time the reduction in infinite domains to the one domain of compact support. Full article

The paper advances the theory of queuing networks by presenting generalized product-form solutions that explicitly take into account the service intensity depending on the number of customers in the network nodes, including the presence of multiple service channels and multi-threaded nodes. This represents a significant extension of the classical results on the Jackson network by integrating graph-theoretic methods, including basic subgraphs with service rates depending on the number of requests. The originality of the article is in the combination of stationary and non-stationary approaches to modeling service networks within a single approach. In particular, acyclic networks with deterministic service time and non-stationary Poisson input flow are considered. Such systems present a significant difficulty, which is noted in well-known works. A stationary model of an open queuing network with service intensity depending on the number of customers in the network nodes is constructed. The stationary network model is related to the problem of marine linear navigation along a strictly defined route and schedule. A generalization of the product theorem with a new form of stationary distribution is developed for it. It is shown that even a small increase in the service intensity with a large number of requests in a queuing network node can significantly reduce its average value. A non-stationary model of an acyclic queuing network with deterministic service time in network nodes and a non-stationary Poisson input flow is constructed. The non-stationary model is associated with irregular (tramp) sea transportation. The intensities of non-stationary Poisson flows in acyclic networks are represented by product formulas using paths between the initial node and other network nodes. The parameters of Poisson distributions of the number of customers in network nodes are calculated. The simplest formulas for calculating such queuing networks are obtained for networks in the form of trees. Full article

Intelligent transport systems are a major component of smart cities because their deployment should result in reduced journey times, less traffic congestion and a significant reduction in road deaths, which will greatly improve the quality of life of their citizens. New technologies such as vehicular networks allow more information be available in realtime, and this information can be used with new analytical models to obtain more accurate estimates of journey times. This would be extremely useful to drivers and will also enable transport authorities to optimise the transport network. This paper addresses these issues using a model-based approach to provide a new way of estimating the delay along specified routes. A journey is defined as the traversal of several road links and junctions from source to destination. The delay at the junctions is analysed using the zero-server Markov chain technique. This is then combined with the Jackson network to analyse the delay across multiple junctions. The delay at road links is analysed using an M/M/K/K model. The results were validated using two simulators: SUMO and VISSIM. A real scenario is also examined to determine the best route. The preliminary results of this model-based analysis look promising but more work is needed to make it useful for wide-scale deployment. Full article

This study proposes a balanced truck dispatching strategy for inter-terminal transportation (ITT) in large ports, incorporating proactive demand outsourcing to address stochastic and imbalanced ITT demand. A portion of ITT tasks are intentionally outsourced to third-party public trucks at a higher cost, so that self-owned trucks can be reserved for more critical tasks. The ITT system is modeled as a closed Jackson network, in which self-owned trucks circulate among terminals and routes. An optimization model is developed to determine the optimal proactive outsourcing ratios for origin–destination terminal pairs and the appropriate fleet size of self-owned trucks, aiming to minimize total transportation costs. Reactive outsourcing is also included to handle occasional truck shortages. A mean value analysis method is used to evaluate system performance with given decisions, and a differential evolution algorithm is employed for optimization. The case study of Shanghai Yangshan Port demonstrates that the proposed strategy reduces total system cost by 9.8% compared to reactive outsourcing. The results also highlight the importance of jointly optimizing outsourcing decisions and fleet size. This study provides theoretical insights and practical guidance for ITT system management under demand uncertainty. Full article

In this study, we research the univariate quantitative symmetrized approximation of complex-valued continuous functions on a compact interval by complex-valued symmetrized and perturbed neural network operators. These approximations are derived by establishing Jackson-type inequalities involving the modulus of continuity of the used function’s high order derivatives. The kinds of our approximations are trigonometric and hyperbolic. Our symmetrized operators are defined by using a density function generated by a q-deformed and $\lambda$-parametrized hyperbolic tangent function, which is a sigmoid function. These accelerated approximations are pointwise and of the uniform norm. The related complex-valued feed-forward neural networks have one hidden layer. Full article

The efficiency of an electrolyzer is significantly influenced by mass, heat, and charge transport within its porous transport layer (PTL). The infeasibility of measuring them in-situ makes it challenging to study their influence experimentally, leading to the adoption of various modeling approaches. This study applies pore network (PN) modeling to investigate mass transport properties and capillary invasion behavior in three commercial titanium felt PTLs commonly used in proton exchange membrane water electrolyzers (PEMWEs). One PTL has a graded structure. Reconstructed PNs were derived from microcomputed X-ray tomography (µ-CT) data, allowing for a detailed analysis of pore size distributions, absolute and relative permeabilities, capillary pressure curves, and residual liquid saturations. The results from the PN approach are compared to literature correlations. The absolute permeability of all PTLs is between 1.1 × 10⁻¹⁰ m² and 1.5 × 10⁻¹⁰ m², with good agreement between PNM results and predictions from the Jackson and James model and the Tomadakis and Sotirchos model, the two latter involving the fiber diameter as a model parameter. The graded PTL, with fiber diameters varying between 25 µm and 40 µm, showed the best agreement with literature correlations. However, the capillary pressure curves exhibited significant deviations from the Leverett and Brooks–Corey equations at low and high liquid saturations, emphasizing the limitations of these correlations. In addition, residual liquid saturation varied strongly with PTL structure. The thicker PTL with a slightly narrower pore size distribution, demonstrated a lower residual liquid saturation (19%) and a more homogeneous invasion compared to the graded PTL (64%), which exhibited significant gas fingering. The results suggest that higher gas saturation could enhance gas removal, with much higher relative permeabilities, despite the greater PTL thickness. In contrast, the graded PTL achieves the highest relative liquid permeability (~70%) while maintaining a relative gas permeability of ~30%. These findings highlight the impact of microstructure on invasion and transport properties and suggest PN modeling as a powerful tool for their study. Full article

We investigate the equilibrium strategies for customers arriving at overtaking-free queueing networks and receiving partial information about the system’s state. In an overtaking-free network, customers cannot be overtaken by others arriving after them. We assume that customer arrivals follow a Poisson process and that service times at any queue are independent and exponentially distributed. Upon arrival, the received partial information is the total number of customers already in the network; however, the distribution of these among the queues is left unknown. Adding rewards for being served and costs for waiting, we analyze the economic behavior of this system, looking for equilibrium threshold strategies. The overtaking-free characteristic allows for coupling of its dynamics with those of corresponding closed Jackson networks, for which an algorithm to compute the expected sojourn times is known. We exploit this feature to compute the profit function and prove the existence of equilibrium threshold strategies. We also illustrate the results by analyzing and comparing two simple network structures. Full article

Here we study the quantitative multivariate approximation of perturbed hyperbolic tangent-activated singular integral operators to the unit operator. The engaged neural network activation function is both parametrized and deformed, and the related kernel is a density function on ${\mathbb{R}}^N$. We exhibit uniform and $L_p$, $p\ge 1$ approximations via Jackson-type inequalities involving the first $L_p$ modulus of smoothness, $1\le p\le \infty$. The differentiability of our multivariate functions is covered extensively in our approximations. We continue by detailing the global smoothness preservation results of our operators. We conclude the paper with the simultaneous approximation and the simultaneous global smoothness preservation by our multivariate perturbed activated singular integrals. Full article

This article is based on chapters 9 and 19 of the new neural network approximation monograph written by the first author. We use the approximation properties coming from the parametrized and deformed neural networks based on the parametrized error and q-deformed and $\beta$-parametrized half-hyperbolic tangent activation functions. So, we implement a univariate theory on a compact interval that is ordinary and fractional. The result is the quantitative approximation of Brownian motion on simple graphs: in particular over a system S of semiaxes emanating from a common origin radially arranged and a particle moving randomly on S. We produce a large variety of Jackson-type inequalities, calculating the degree of approximation of the engaged neural network operators to a general expectation function of this kind of Brownian motion. We finish with a detailed list of approximation applications related to the expectation of important functions of this Brownian motion. The differentiability of our functions is taken into account, producing higher speeds of approximation. Full article

The COVE trial randomized participants to receive two doses of mRNA-1273 vaccine or placebo on Days 1 and 29 (D1, D29). Anti-SARS-CoV-2 Spike IgG binding antibodies (bAbs), anti-receptor binding domain IgG bAbs, 50% inhibitory dilution neutralizing antibody (nAb) titers, and 80% inhibitory dilution nAb titers were measured at D29 and D57. We assessed these markers as correlates of protection (CoPs) against COVID-19 using stochastic interventional vaccine efficacy (SVE) analysis and principal surrogate (PS) analysis, frameworks not used in our previous COVE immune correlates analyses. By SVE analysis, hypothetical shifts of the D57 Spike IgG distribution from a geometric mean concentration (GMC) of 2737 binding antibody units (BAU)/mL (estimated vaccine efficacy (VE): 92.9% (95% CI: 91.7%, 93.9%)) to 274 BAU/mL or to 27,368 BAU/mL resulted in an overall estimated VE of 84.2% (79.0%, 88.1%) and 97.6% (97.4%, 97.7%), respectively. By binary marker PS analysis of Low and High subgroups (cut-point: 2094 BAU/mL), the ignorance interval (IGI) and estimated uncertainty interval (EUI) for VE were [85%, 90%] and (78%, 93%) for Low compared to [95%, 96%] and (92%, 97%) for High. By continuous marker PS analysis, the IGI and 95% EUI for VE at the 2.5th percentile (519.4 BAU/mL) vs. at the 97.5th percentile (9262.9 BAU/mL) of D57 Spike IgG concentration were [92.6%, 93.4%] and (89.2%, 95.7%) vs. [94.3%, 94.6%] and (89.7%, 97.0%). Results were similar for other D29 and D57 markers. Thus, the SVE and PS analyses additionally support all four markers at both time points as CoPs. Full article

A fog-based IoT platform model involving three layers, i.e., IoT devices, fog nodes, and the cloud, was proposed using an open Jackson network with feedback. The system performance was analyzed for individual subsystems, and the overall system was based on different input parameters. Interesting performance metrics were derived from analytical results. A resource optimization problem was developed and solved to determine the optimal service rates at individual fog nodes under some constraint conditions. Numerical evaluations for the performance and the optimization problem are provided for further understanding of the analysis. The modeling and analysis, as well as the optimization design method, are expected to provide a useful reference for the design and evaluation of fog computing systems. Full article

In this article we present the multivariate approximation of time splitting random functions defined on a box or ${\mathbb{R}}^N,N\in \mathbb{N},$ by neural network operators of quasi-interpolation type. We achieve these approximations by obtaining quantitative-type Jackson inequalities engaging the multivariate modulus of continuity of a related random function or its partial high-order derivatives. We use density functions to define our operators. These derive from the logistic and hyperbolic tangent sigmoid activation functions. Our convergences are both point-wise and uniform. The engaged feed-forward neural networks possess one hidden layer. We finish the article with a great variety of applications. Full article