Search

We investigate a nonlinear integral equation derived through moment approximation from the individual-based representation of spatial logistic dynamics. The equation describes how the densities of pairs of individuals represented by points in continuous space are expected to equilibrate under spatially explicit birth–death processes characterized by constant fecundity with local natal dispersal and variable mortality determined by local competition. The equation is derived from a moment hierarchy truncated by a moment closure expressing the densities of triplets as a function of the densities of pairs. Focusing on results for individuals inhabiting two-dimensional habitats, we explore the solvability of the equation by introducing a dedicated space of functions that are integrable up to a constant. Using this function space, we establish sufficient conditions for the existence of solutions of the equation within a zero-centered ball. For illustration and further insights, we complement our analytical findings with numerical results. [ABSTRACT FROM AUTHOR]

The qualities of the deformable derivative have been introduced recently. Using the deformable derivative [00] in Banach spaces, we provide adequate requirements in this work for the existence results for perturbed fractional neutral integro-differential systems [PFNIDS]. The use of fixed-point methods allows for the establishment of a number of innovative existence results. In the latter section of the study, we give an example to show our general findings [ABSTRACT FROM AUTHOR]

Summary: We provide rigorous theoretical bounds for Anderson acceleration (AA) that allow for approximate calculations when applied to solve linear problems. We show that, when the approximate calculations satisfy the provided error bounds, the convergence of AA is maintained while the computational time could be reduced. We also provide computable heuristic quantities, guided by the theoretical error bounds, which can be used to automate the tuning of accuracy while performing approximate calculations. For linear problems, the use of heuristics to monitor the error introduced by approximate calculations, combined with the check on monotonicity of the residual, ensures the convergence of the numerical scheme within a prescribed residual tolerance. Motivated by the theoretical studies, we propose a reduced variant of AA, which consists in projecting the least‐squares used to compute the Anderson mixing onto a subspace of reduced dimension. The dimensionality of this subspace adapts dynamically at each iteration as prescribed by the computable heuristic quantities. We numerically show and assess the performance of AA with approximate calculations on: (i) linear deterministic fixed‐point iterations arising from the Richardson's scheme to solve linear systems with open‐source benchmark matrices with various preconditioners and (ii) non‐linear deterministic fixed‐point iterations arising from non‐linear time‐dependent Boltzmann equations. [ABSTRACT FROM AUTHOR]

We are concerned in this paper with the convergence analysis of the primal-dual splitting (PDS) and the split Douglas-Rachford (SDR) algorithms for monotone inclusions by using an operator-oriented approach. We shall show that both PDS and SDR algorithms can be driven by a (firmly) nonexpansive mapping in a product Hilbert space. We are then able to apply the Krasnoselskii-Mann and Halpern fixed point algorithms to PDS and SDR to get weakly and strongly convergent algorithms for finding solutions of the primal and dual monotone inclusions. Moreover, an additional projection technique is used to derive strong convergence of a modified SDR algorithm. [ABSTRACT FROM AUTHOR]

Deep learning hardware achieves high throughput and low power consumption by reducing computing precision and specializing in matrix multiplication. For machine learning inference, fixed-point value computation is commonplace, where the input and output values and the model parameters are quantized. Thus, many processors are now equipped with fast integer matrix multiplication units (IMMU). It is of significant interest to find a way to harness these IMMUs to improve the performance of HPC applications while maintaining accuracy. We focus on computing double-precision equivalent matrix multiplication using the Ozaki scheme, which computes a high-precision matrix multiplication by using lower-precision computing units, and show the advantages and disadvantages of using IMMU. The experiment using integer Tensor Cores shows that we can compute double-precision matrix multiplication faster than cuBLAS and an existing Ozaki scheme implementation on FP16 Tensor Cores on NVIDIA consumer GPUs. Furthermore, we demonstrate accelerating a quantum circuit simulation by up to 4.85 while maintaining the FP64 accuracy. [ABSTRACT FROM AUTHOR]

In this paper, we study discrete-time nonstationary stochastic games with average reward criteria. The state space is denumerable and the action space of players are Borel spaces, while the transition probability and reward functions can be changed with time. Meanwhile, the reward functions are allowed to be non-uniformly bounded. Under the suitable optimality conditions, we establish the average optimality equation and prove the existence of Nash equilibria. Finally, we use a queueing system to illustrate our results. [ABSTRACT FROM AUTHOR]

In this manuscript, we prove the existence and uniqueness of a common best proximity point for a pair of non-self mappings satisfying the iterative mappings in a complete fuzzy multiplicative metric space. We consider the pair of non-self mappings $ X:\mathcal{P}\rightarrow \mathcal{G} $ and $ Z:\mathcal{P }\rightarrow \mathcal{G} $ and the mappings do not necessarily have a common fixed-point. In a complete fuzzy multiplicative metric space, if $ \mathcal{\varphi } $ satisfy the condition $ \mathcal{\varphi } \left(b, Zb, \varsigma \right) = \mathcal{\varphi }\left(\mathcal{P}, \mathcal{ G}, \varsigma \right) = \mathcal{\varphi }\left(b, Xb, \varsigma \right) $, then $ b $ is a common best proximity point. Further, we obtain the common best proximity point for the real valued functions $ \mathcal{L}, \mathcal{M}:(0, 1]\rightarrow \mathbb{R} $ by using a generalized fuzzy multiplicative metric space in the setting of $ (\mathcal{L}, \mathcal{M}) $-iterative mappings. Furthermore, we utilize fuzzy multiplicative versions of the $ (\mathcal{L}, \mathcal{M}) $-proximal contraction, $ (\mathcal{L}, \mathcal{M}) $-interpolative Reich-Rus-Ciric type proximal contractions, $ (\mathcal{L}, \mathcal{M}) $-Kannan type proximal contraction and $ (\mathcal{L}, \mathcal{M}) $-interpolative Hardy-Rogers type proximal contraction to examine the common best proximity points in fuzzy multiplicative metric space. Moreover, we provide differential non-trivial examples to support our results.

In this manuscript, we prove the existence and uniqueness of a common best proximity point for a pair of non-self mappings satisfying the iterative mappings in a complete fuzzy multiplicative metric space. We consider the pair of non-self mappings X: P → G and Z: P → G and the mappings do not necessarily have a common fixed-point. In a complete fuzzy multiplicative metric space, if φ satisfy the condition φ (b, Zb, ς) = φ (P,G, ς) = φ (b, Xb, ς), then b is a common best proximity point. Further, we obtain the common best proximity point for the real valued functions L,M: (0, 1] → R by using a generalized fuzzy multiplicative metric space in the setting of (L,M)- iterative mappings. Furthermore, we utilize fuzzy multiplicative versions of the (L,M)-proximal contraction, (L,M)-interpolative Reich-Rus-Ciric type proximal contractions, (L,M)-Kannan type proximal contraction and (L,M)-interpolative Hardy-Rogers type proximal contraction to examine the common best proximity points in fuzzy multiplicative metric space. Moreover, we provide differential non-trivial examples to support our results. [ABSTRACT FROM AUTHOR]

In this paper we introduce and analyze a Banach spaces-based approach yielding a fully-mixed finite element method for numerically solving the stationary chemotaxis-Navier-Stokes problem. This is a nonlinear coupled model representing the biological process given by the cell movement, driven by either an internal or an external chemical signal, within an incompressible fluid. In addition to the velocity and pressure of the fluid, the velocity gradient and the Bernouilli-type stress tensor are introduced as further unknowns, which allows to eliminate the pressure from the equations and compute it afterwards via a postprocessing formula. In turn, besides the cell density and the chemical signal concentration, the pseudostress associated with the former and the gradient of the latter are introduced as auxiliary unknowns as well. The resulting continuous formulation, posed in suitable Banach spaces, consists of a coupled system of three saddle point-type problems, each one of them perturbed with trilinear forms that depend on data and the unknowns of the other two. The well-posedness of it is analyzed by means of a fixed-point strategy, so that the classical Banach theorem, along with the Babuška-Brezzi theory in Banach spaces, allow to conclude, under a smallness assumption on the data, the existence of a unique solution. Adopting an analogue approach for the associated Galerkin scheme, and under suitable hypotheses on arbitrary finite element subspaces employed, we apply the Brouwer and Banach theorems to show existence and then uniqueness of the discrete solution. General a priori error estimates, including those for the postprocessed pressure, are also derived. Next, a specific set of finite element subspaces satisfying the required stability conditions, and yielding approximate local conservation of momentum, is introduced, which, given an integer k ≥ 0 , is defined in terms of Raviart-Thomas spaces of order k and piecewise polynomials of degree ≤ k only. The respective rates of convergence of the resulting Galerkin method are then provided. Finally, several numerical experiments confirming the latter and illustrating the good performance of the method, are reported. [ABSTRACT FROM AUTHOR]

The aim of this article is to introduce a new type of operator similar to those of A. Petruşel and G. Petruşel type (Fixed point results for decreasing convex orbital operators, J. Fixed Point Theory Appl. 23 (2021), no. 35) and prove some fixed-point theorems which generalize and complement several results in the theory of nonlinear operators.

In this article, we consider the following two-point discrete fractional boundary value problem with constant coefficient associated with Dirichlet boundary conditions. \begin{equation*} \begin{cases} -\big{(}\nabla^{\nu}_{\rho(a)}u\big{)}(t) + \lambda u(t) = f(t, u(t)), \quad t \in \mathbb{N}^{b}_{a + 2}, \\ u(a) = u(b) = 0, \end{cases} \end{equation*} \noindent where $1 < \nu < 2$, $a,b \in \mathbb{R}$ with $b-a\in\mathbb{N}_{3}$, $\mathbb{N}^b_{a+2} = \{a+2,a+3,\hdots,b\}$, $|\lambda| < 1$, $\nabla^{\nu}_{\rho(a)}u$ denotes the $\nu^{\text{th}}$-order Riemann--Liouville nabla difference of $u$ based at $\rho(a)=a-1$, and $f : \mathbb{N}^{b}_{a + 2} \times \mathbb{R} \rightarrow \mathbb{R}^{+}$. \noindent We make use of Guo--Krasnosels'ki\v{\i} and Leggett--Williams fixed-point theorems on suitable cones and under appropriate conditions on the non-linear part of the difference equation. We establish sufficient requirements for at least one, at least two, and at least three positive solutions of the considered boundary value problem. We also provide an example to demonstrate the applicability of established results.

Hardware-in-the-loop (HIL) is a common technique used for testing in power electronics. It draws upon FPGAs (field-programmable gate arrays) because they allow for reaching real-time simulation for mid-high switching frequencies. FPGA area and delay are keys to reaching a compromise between performance and accuracy. To minimize area and delay, signal word length (WL) is critical. Furthermore, the input and output's WL should be carefully chosen because these signals come from ADCs (analog-to-digital converters) or go to DACs (digital-to-analog converters). In other words, the role of ADCs and DACs is the boundary condition when assigning all the signal WLs in an HIL model. This research presents an automatic method for computing the signal WLs in the corresponding model by considering input/output boundary conditions. This automatic method needs a single simulation to decide both the integer and fractional width of every signal. Our method accelerates the process, showing an advantage over manual methods and those requiring multiple simulations. The proposed method is applied to create all the WL assignments to the signals involved in a fixed-point coded buck converter model, which shows its feasibility. [ABSTRACT FROM AUTHOR]

In this paper we introduce and analyze a model of sedimentation based on a solid velocity formulation. A particular feature of the governing equations is given by the fact that the velocity field is non-divergence free. We introduce extra variables such as the pseudostress tensor relating the velocity gradient with the pressure, thus leading to a mixed variational formulation consisting of two systems of equations coupled through their source terms. A result of existence and uniqueness of solutions is shown by means of a fixed-point strategy and the help of the Babuška–Brezzi theory and Banach theorem. Additionally, we employ suitable finite dimensional subspaces to approximate both systems of equations via associated mixed finite element methods. The well-posedness of the resulting coupled scheme is also treated via a fixed-point approach, and hence the discrete version of the existence and uniqueness result is derived analogously to the continuous case. The above is then combined with a finite volume method for the transport equation. Finally, several numerical results illustrating the performance of the proposed model and the full numerical scheme, and confirming the theoretical rates of convergence, are presented. [ABSTRACT FROM AUTHOR]

We consider load controlled quasistatic evolution. Well posedness results for the nonlocal continuum model related to peridynamics are established. We show local existence and uniqueness of quasistatic evolution for load paths originating at stable critical points. These points can be associated with local energy minima among the convex set of deformations belonging to the strength domain of the material. The evolution of the displacements, however, is not constrained to lie inside the strength domain of the material. The load-controlled evolution is shown to exhibit energy balance. [ABSTRACT FROM AUTHOR]

The development of IoT (Internet of Things) calls for circuit designs with energy and area efficiency for edge devices. Approximate computing which trades unnecessary computation precision for hardware cost savings is a promising direction for error-tolerant applications. Multipliers, as frequently invoked basic modules which consume non-trivial hardware costs, have been introduced approximation to achieve distinct energy and area savings for data-intensive applications. In this paper, we propose a fixed-point approximate multiplier that employs a linear mapping technique, which enables the configurability of approximation levels and the unbiasedness of computation errors. We then introduce a dynamic truncation method into the proposed multiplier design to cover a wider and more fine-grained configuration range of approximation for more flexible hardware cost savings. In addition, a novel normalization module is proposed for the required shifting operations, which balances the occupied area and the critical path delay compared with normal shifters. The introduced errors of our proposed design are analyzed and expressed by formulas which are validated by experimental results. Experimental evaluations show that compared with accurate multipliers, our proposed approximate multiplier design provides maximum area and power savings up to 49.70% and 66.39% respectively with acceptable computation errors. [ABSTRACT FROM AUTHOR]

The aim of this article is to study the results of the fixed-point in coupled and tripled measure of noncompactness (MNC). We will use the technique of MNC for coupled and tripled MNC. Also, we tend to prove some results of coupled and tripled MNC for the family of JS-contractive-type mappings. Moreover, an application with an example is provided to illustrate the results.

In this article we would like to present a new type of fuzzy contractive mappings which are called α − ϕ − M0 fuzzy contractive and β − ψ − M0 fuzzy contractive, and then we demonstrate two theorems which ensure the existence of a fixed point for these two types of mappings. And so we combine and generalize some existing notions in the literature ([5], [7]). Proved these theorems in the extended fuzzy metric spaces are in the more general version than the existing in the literature ones. [ABSTRACT FROM AUTHOR]

Copyright of Erzincan University Journal of Science & Technology is the property of Erzincan Binali Yildirim Universitesi and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The sufficiency of electricity market competition and the economy of power system operation require that the economic dispatch should not only preserve the bus privacy but consider network losses. The existing economic dispatch methods, however, can’t preserve the privacy of each bus from leakage and even complicate the solution when they reasonably consider network losses, due to the coupling complexity of network losses. To address these issues, this paper presents a novel distributed economic dispatch (DED) method based on KKT optimality conditions and iteration functions. It focuses on an economic dispatch model that contains bus active power balance equations and generator power limit inequalities. First, the model’s KKT optimality conditions with inequalities are simplified to equivalent pure equality-type optimality conditions. Then a set of iteration functions is created using the Taylor series, which overcomes the difficulty caused by the fact that unknown bus voltage phases are completely contained in the sine and cosine functions of optimality conditions. Finally, a fast fixed-point iteration procedure is proposed for bus agents to solve the economic dispatch model. The proposed method reasonably considers network losses by using the set of bus active power balance equations. It not only preserves the privacy of each bus from leakage but is straightforward in solution (does not complicate the solution). In addition, it is fully bus-level distributed. Numerical simulation results of systems with different sizes verified the effectiveness and advantages of the proposed method.

Closed-loop experiments involving biological and artificial neural networks would improve the understanding of neural cells functioning principles and lead to the development of new generation neuroprosthesis. Several technological challenges require to be faced, as the development of real-time spiking neural network emulators which could bear the increasing amount of data provided by new generation High-Density Multielectrode Arrays. This work focuses on the development of a real-time spiking neural network emulator addressing fully-connected neural networks. This work presents a new way to increase the number of synapses supported by real-time neural network accelerators. The proposed solution has been implemented on the Xilinx Zynq 7020 All-Programmable SoC and can emulate fully connected spiking neural networks counting up to 3,098 Izhikevich neurons and 9.6e6 synapses in real-time, with a resolution of 0.1 ms.

Recently, Karapinar, Aydi and De Hierro introduced the notions of interpolative Kannan-type contractions and interpolative CRR-type contractions and proved that they possess a fixed point when the space is complete. In this paper, we show that the existence of fixed points for interpolative Kannan-type and CRR-type contractions remains true for a metric space which is not necessarily complete and we give a more precise result concerning the behaviour of Picard sequences of arbitrary initial point. We also study some particular classes of interpolative Kannan-type and CRR-type contractions.

The aim of this paper is to prove some existence and uniqueness theorems of the fixed points for Hardy-Rogers type contraction with respect to a wt-distance in b-metric spaces endowed with a graph. These results prepare a more general statement, since we apply the condition of orbitally G-continuity of mappings instead of the condition of continuity, consider b-metric spaces endowed with a graph instead general b-metric spaces and use of control functions instead of constant numbers. [ABSTRACT FROM AUTHOR]

In this paper, we aim to review Meir–Keeler contraction mappings results on various abstract spaces, in particular, on partial metric spaces, dislocated (metric-like) spaces, and M-metric spaces. We collect all significant results in this direction by involving interesting examples. One of the main reasons for this work is to help young researchers by giving a framework for Meir Keeler's contraction. [ABSTRACT FROM AUTHOR]

The paper deals with the abstract model of economic dynamics described by second order discrete inclusions. Then based on the concept of infimal convolution, we construct dual problems for discrete inclusions and prove the duality results. It seems that the Euler-Lagrange type inclusions are "duality relations" for both primal and dual problems. For a set-valued mapping, the graph of which is a cone, the locally adjoint mapping is calculated, and then the necessary and sufficient conditions of optimality are formulated in terms of prices. The Neumann-Gale model is investigated in detail. For the optimal trajectory, there are such prices that when choosing the intensities of the technological capacity of production at a given moment in time, the optimal trajectory corresponds to the one that provides the maximum income in the prices of the next instant time. Finally, in term of prices duality in problems with second order model with polyhedral discrete inclusions are considered. [ABSTRACT FROM AUTHOR]

Abstract This research is conducted for studying some qualitative specifications of solution to a generalized fractional structure of the standard snap boundary problem. We first rewrite the mathematical model of the extended fractional snap problem by means of the G $\mathbb{G}$ -operators. After finding its equivalent solution as a form of the integral equation, we establish the existence criterion of this reformulated model with respect to some known fixed point techniques. Then we analyze its stability and further investigate the inclusion version of the problem with the help of some special contractions. We present numerical simulations for solutions of several examples regarding the fractional G $\mathbb{G}$ -snap system in different structures including the Caputo, Caputo–Hadamard, and Katugampola operators of different orders.

Correct bone screw torque is critical for positive patient outcomes after orthopaedic surgery. Models of the screwing process have been developed to allow a smart screwdriver to optimise the insertion torque. Experimental data is required to test these models, so a test-rig has been developed. Accurate torque measurement is a key part of the test-rig. An FIR filter was designed for this torque signal, implemented on the test-rig, and compared theoretically and experimentally to a mean filter and to no filtering. The FIR and mean filters both performed well, with the FIR achieving better theoretical results, and the mean filter achieving better experimental results. Better understanding of the noise structure and potential signal distortion would be required to improve the FIR filter or to conclusively compare it against the mean filter, however both perform sufficiently well for this application.

In this work, we deal with the following two-point Dirichlet boundary value problem for a finite nabla fractional difference equation: ... Here a, b ∈ ℝ with b - a ∈ ℕ3, 1 < α < 2, f : ℝ → ℝ+ ∪ {0} is a continuous function, and ∇p(a)α denotes the αth- order Riemann-Liouville backward (nabla) difference operator. First, we establish an associated Greens function, and obtain some of its properties. Under suitable conditions on the non-linear part of the difference equation, we deduce some results on at least one and at least three positive solutions of the considered problem. For this purpose, we use a few prominent conical shell fixed-point theorems. [ABSTRACT FROM AUTHOR]

A new zinc fixed-point cell for the dissemination of International Temperature Scale (ITS-90) was realized at the Italian National Metrological Institute (Istituto Nazionale di Ricerca Metrologica, INRiM). This paper presents the results of its characterization, including fabrication details. In particular, immersion effects and influences of impurities on the freezing point of zinc were studied. The new open-type cell was prepared using a high purity sample, chemically analyzed, and the depression of the fixed-point temperature was calculated using the method of Sum of Individual Estimates (SIE). The new cell presents a smaller freezing point depression compared with the national reference for which the Overall Maximum Estimate (OME) method was applied. This behavior was confirmed also by the direct comparison of the two cells. These results provide confidence on the agreement between the experimental comparison and the SIE/OME evaluation. Finally, the improvement of the new zinc cell is reflected also in a lower uncertainty budget for the fixed-point realization. [ABSTRACT FROM AUTHOR]

In this paper, we establish the existence and uniqueness of solution for a nonlinear coupled system of implicit fractional differential equations including ψ-Caputo fractional operator under nonlocal conditions. Schaefer's and Banach fixed-point theorems are applied to obtain the solvability results for the proposed system. Furthermore, we extend the results to investigate several types of Ulam stability for the proposed system by using classical tool of nonlinear analysis. Finally, an example is provided to illustrate the abstract results.

This paper presents a design of digital control based on a fixed-point model for an application of a single phase AC-DC boost Converter with a high power factor and low current distortion. The system uses a simple closed-loop control with a slow voltage loop (outer loop) to stabilize the output DC bus voltage at the required level and a fast current loop (inner loop) to achieve input power factor correction. The digital control uses a fixedpoint structure that improves the control accuracy without increasing the number of arithmetic operations and does not require specific running conditions. The behavior of the system is fully verified by using a digital simulation under Matlab/Simulink environment and experimentally with an implementation in real-time using Xilinx ISE 14.7 software, hardware description language VHDL, Xilinx FPGA ML605 board, and EVAL-AD7656 evaluation board for high-speed analog-to-digital conversion. The obtained results show a good agreement between experiments and simulations for steadystate and transient-responses. [ABSTRACT FROM AUTHOR]

Sparse seismic inversion is wildly utilized for reservoir prediction and resolution improvement. Matching pursuit (MP) is an effective algorithm for solving L0-norm and obtaining sparse inversion results. Sparse seismic inversion based on MP (MPSI) can estimate the sparse parameters of subsurface from observations by controlling the iterations and threshold. However, the low convergence and stability limit the application of MPSI. To accelerate the convergence of MP, the full-time domain matching pursuit (FTMP) algorithm is first proposed. The seismic inversion based on FTMP can realize the multi-point inversion simultaneously instead of searching the inversion results one by one, which is the process of MPSI. Also, the prior model constraint is then involved in the objective function to improve the stability and the layer-boundary fidelity of the inversion results. Furthermore, the empirical mode decomposition (EMD) algorithm is introduced into inversion framework to recover the features of the seismic signal from the noisy seismic signal. The fixed-point (FP) algorithm is adopted to solve the objective function in this study. The optimal inversion results can be estimated after finite iterations by the FP algorithm. Combining the FTMP sparse seismic inversion framework, prior model constraint, EMD and FP algorithms, a complete sparse seismic inversion method named the full-time domain matching pursuit-based sparse fixed-point seismic inversion is ultimately proposed. The synthetic and field examples are utilized to demonstrate the stability and practicality of this approach. Compared with MPSI, the inversion results of the proposed method have higher resolution and fidelity of the layer-boundary. [ABSTRACT FROM AUTHOR]

Shaft is a machine element which is used to transmit rotary motion or torque. During transmission of motion, however, the machine shaft doesn't always rotate with a constant angular velocity. Because of unstable current or due to sudden acceleration and deceleration, the machine shaft will rotate at a variable angular velocity. It is this rotary motion that generates the moment of inertial force, causing the machine shaft to have torsional deformation. However, due to the elasticity of the material, the shaft produces torsional vibration. Therefore, the main objective of this paper is to determine the optimal parameters of dynamic vibration absorber to eliminate torsional vibration of the rotating shaft that varies with time. The new results in this paper are summarized as follows: Firstly, the author determines the optimal parameters by using the minimum quadratic torque method. Secondly, the maximization of equivalent viscous resistance method is used for determining the optimal parameters. Thirdly, the author gives the optimal parameters of dynamic vibration absorber based on the fixed-point method. In this paper, the optimum parameters are found in an explicit analytical solutions, helping the scientists to easily find the optimal parameters for eliminating torsional vibration of the rotating shaft.

In this article, we consider an optimization problem where the objective function is evaluated at the fixed-point of a contraction mapping parameterized by a control variable, and optimization takes place over this control variable. Since the derivative of the fixed-point with respect to the parameter can usually not be evaluated exactly, an adjoint dynamical system can be used to estimate gradients. Using this estimation procedure, the optimization algorithm alternates between derivative estimation and an approximate gradient descent step. We analyze a variant of this approach involving dynamic time-scaling, where after each parameter update the adjoint system is iterated until a convergence threshold is passed. We prove that, under certain conditions, the algorithm can find approximate stationary points of the objective function. We demonstrate the approach in the settings of an inverse problem in chemical kinetics, and learning in attractor networks. [ABSTRACT FROM AUTHOR]

This paper describes three different approaches for the implementation of an online signature verification system on a low-cost FPGA. The system is based on an algorithm, which operates on real numbers using the double-precision floating-point IEEE 754 format. The double-precision computations are replaced by simpler formats, without affecting the biometrics performance, in order to permit efficient implementations on low-cost FPGA families. The first approach is an embedded system based on MicroBlaze, a 32-bit soft-core microprocessor designed for Xilinx FPGAs, which can be configured by including a single-precision floating-point unit (FPU). The second implementation attaches a hardware accelerator to the embedded system to reduce the execution time on floating-point vectors. The last approach is a custom computing system, which is built from a large set of arithmetic circuits that replace the floating-point data with a more efficient representation based on fixed-point format. The latter system provides a very high runtime acceleration factor at the expense of using a large number of FPGA resources, a complex development cycle and no flexibility since it cannot be adapted to other biometric algorithms. By contrast, the first system provides just the opposite features, while the second approach is a mixed solution between both of them. The experimental results show that both the hardware accelerator and the custom computing system reduce the execution time by a factor ×7.6 and ×201 but increase the logic FPGA resources by a factor ×2.3 and ×5.2, respectively, in comparison with the MicroBlaze embedded system. [ABSTRACT FROM AUTHOR]

Bluetooth data sets allow a direct estimation of travel times across sensor pairs; however, the resulting estimations contain noise because of missed detection rate and alternative paths between sensors. Additionally, although Bluetooth data sets allow tracking of vehicles across sensors, they do not provide an exact path (i.e. a sequence of traffic sections). Estimating vehicle paths from Bluetooth records is not a straightforward task. This paper proposes a joint method to simultaneously infer vehicle paths and travel times using Bluetooth records. The methodology is applied in a case study of Bluetooth measurements in Brisbane, Australia. The results are validated against travel time observations, which are collated by creating a testing set out of the whole data set. Travel time estimates are robust to the changes in the size of the available measurements, and the proposed model significantly outperforms a naive model where travel times are estimated via direct matching. [ABSTRACT FROM AUTHOR]

This research is conducted for studying some qualitative specifications of solution to a generalized fractional structure of the standard snap boundary problem. We first rewrite the mathematical model of the extended fractional snap problem by means of the G -operators. After finding its equivalent solution as a form of the integral equation, we establish the existence criterion of this reformulated model with respect to some known fixed point techniques. Then we analyze its stability and further investigate the inclusion version of the problem with the help of some special contractions. We present numerical simulations for solutions of several examples regarding the fractional G -snap system in different structures including the Caputo, Caputo–Hadamard, and Katugampola operators of different orders. [ABSTRACT FROM AUTHOR]

Copyright of Operations Research Transactions / Yunchouxue Xuebao is the property of Editorial office of Operations Research Transactions and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Let F be a family of holomorphic functions on a domain D, and let h (≢ 0) be a holomorphic function on D. If every f ∈ F , f (z) = 0 ⇒ | f ′ (z) | ≤ | h (z) | , and f ′ (z) ≠ h (z) , then F is normal on D. [ABSTRACT FROM AUTHOR]

We introduce Back to Basics (BTB), a fast iterative algorithm for noise reduction. Our method is computationally efficient, does not require training or ground truth data, and can be applied in the presence of independent noise, as well as correlated (coherent) noise, where the noise level is unknown. We examine three study cases: natural image denoising in the presence of additive white Gaussian noise, Poisson-distributed image denoising, and speckle suppression in optical coherence tomography (OCT). Experimental results demonstrate that the proposed approach can effectively improve image quality, in challenging noise settings. Theoretical guarantees are provided for convergence stability. • We introduce Back to Basics (BTB), a fast iterative algorithm for noise reduction. • Our method is computationally efficient and does not require ground truth data. • BTB can mitigate independent or correlated noise with unknown noise level. • Experimental results demonstrate improved image quality, in challenging noise settings. • Theoretical guarantees are provided for convergence stability. [ABSTRACT FROM AUTHOR]

Abstract Constrained independent component analysis (ICA) is an effective method for solving the blind source separation with a prior knowledge. However, most constrained ICA algorithms are proposed for the real-valued sources. In this paper, a novel constrained noncircular complex fast independent component analysis (c-ncFastICA) algorithm based on the fixed-point learning is proposed to address the complex-valued sources. The c-ncFastICA algorithm uses the augmented Lagrangian method to obtain a new cost function and then utilizes the quasi-Newton method to search its optimal solution. Compared with other ICA and constrained ICA algorithms, c-ncFastICA has better separation performance. Simulations confirm the effectiveness and superiority of the c-ncFastICA algorithm.

Many evolutionary processes from various fields of physical and engineering sciences undergo abrupt changes of state at certain moments of time between intervals of continuous evolution. These processes are more suitably modeled by impulsive differential equations. In this paper, we study the controllability of an impulsive fractional differential equation with infinite state‐dependent delay in an arbitrary Banach space. We apply semigroup theory and Schaefer fixed point theorem. As an application, we include an example to illustrate the theory. [ABSTRACT FROM AUTHOR]