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In this paper, sufficient conditions are given to investigate the existence of mild solutions on a semi-infinite interval for two classes of first order semilinear functional and neutral functional differential evolution inclusions with infinite delay using a recent nonlinear alternative for contractive multivalued maps in Fréchet spaces due to Frigon, combined with semigroup theory. [ABSTRACT FROM AUTHOR]

Many applications in real-time signal, image, and video processing require automatic algorithms for rapid characterizations of signals and images through fast estimation of their underlying statistical distributions. We present fast and globally convergent algorithms for estimating the three-parameter generalized gamma distribution (G Γ D). The proposed method is based on novel scale-independent shape estimation (SISE) equations. We show that the SISE equations have a unique global root in their semi-infinite domains and the probability that the sample SISE equations have a unique global root tends to one. The consistency of the global root, its scale, and index shape estimators is obtained. Furthermore, we establish that, with probability tending to one, Newton-Raphson (NR) algorithms for solving the sample SISE equations converge globally to the unique root from any initial value in its given domain. In contrast to .existing methods, another remarkable novelty is that the sample SISE equations are completely independent of gamma and polygamma functions and involve only elementary mathematical operations, making the algorithms well suited for real-time both hardware and software implementations. The SISE estimators also allow the maximum likelihood (ML) ratio procedure to be carried out for testing the generalized Gaussian distribution (GGD) versus the G Γ D. Finally, the fast global convergence and accuracy of our algorithms for finite samples are demonstrated by both simulation studies and real image analysis. [ABSTRACT FROM AUTHOR]

The paper proposes a new fixed-point method for solving time-stepping hysteretic field problems. The method is aimed to speed up the convergence of the fixed-point solution and enhance the applicability of the fixed-point iteration. The method makes use of the differential reluctivity and produces a locally convergent solution. A 1-D finite-element procedure is performed to test the method by computing the magnetic field in a ferromagnetic laminated steel. The efficiency, stability, and applicability of the method are assessed in which the method is proven simple and remarkably fast. [ABSTRACT FROM AUTHOR]

Abstract: The Bayesian Ying–Yang (BYY) harmony learning theory has brought about a new mechanism that model selection on Gaussian mixture can be made automatically during parameter learning via maximization of a harmony function on finite mixture defined through a specific bidirectional architecture (BI-architecture) of the BYY learning system. In this paper, we propose a fast fixed-point learning algorithm for efficiently implementing maximization of the harmony function on Gaussian mixture with automated model selection. Several simulation experiments are performed to compare its effectiveness in automated model selection as well as its efficiency in parameter learning with other existing learning algorithms. The experimental results reveal that the performance of the proposed algorithm is superior to its counterparts in these aspects. Moreover, the proposed algorithm is further tested with three typical real-world data sets and successfully applied to unsupervised color image segmentation. [Copyright &y& Elsevier]

Float-point to fixed-point conversion is required by many communication, voice and image applications, in order to achieve acceptable levels of performance and cost. This is particularly crucial in real-time applications that have strict timeline requirement on processing throughput and latency. Therefore, fixed-point conversion from float-point computation brings great challenges with the improvement at the same time: How to evaluate the accuracy of the fixed-point system quickly? This paper proposes a novel method for the float-point to fixed-point conversion and evaluates the precision of complex signal systems from statistical perspective. The proposed approach greatly reduces the complexity of the evaluation, and achieves optimum fixed-point implementation in a short time. The experiments in MP3 and the AAC decoding algorithm demonstrate that the accuracy of the fixed-point system is greatly improved by this method. [ABSTRACT FROM AUTHOR]

This paper proposes and evaluates compile time and instruction-set techniques for improving the accuracy of signal-processing algorithms run on fixed-point embedded processors. These techniques are proposed in the context of a profile guided floating- to fixed-point compiler-based conversion process. A novel fixed-point scaling algorithm (IRP) is introduced that exploits correlations between values in a program by applying fixed-point scaling, retaining as much precision as possible without causing overflow. This approach is extended into a more aggressive scaling algorithm (IRP-SA) by leveraging the modulo nature of 2's complement addition and subtraction to discard most significant bits that may not be redundant sign-extension bits. A complementary scaling technique (IDS) is then proposed that enables the fixed-point scaling of a variable to be parameterized, depending upon the context of its definitions and uses. Finally, a novel instruction-set enhancement--fractional multiplication with internal left shift (FMLS)--is proposed to further leverage interoperand correlations uncovered by the IRP-SA scaling algorithm. FMLS preserves a different subset of the full product's bits than traditional fractional fixed-point or integer multiplication. On average, FMLS combined with IRP-SA improves accuracy on processors with uniform bitwidth register architectures by the equivalent of 0.61 bits of additional precision for a set of signal-processing benchmarks (up to 2 bits). Even without employing FMLS, the IRP-SA scaling algorithm achieves additional accuracy over two previous fixed-point scaling algorithms by averages of 1.71 and 0.49 bits. Furthermore, as FMLS combines multiplication with a scaling shift, it reduces execution time by an average of 9.8%. An implementation of IDS, specialized to single-nested loops, is found to improve accuracy of a lattice filter benchmark by the equivalent of more than 16-bits of precision. [ABSTRACT FROM AUTHOR]

In this article, we deal with the uniqueness problems on meromorphic functions concerning differential polynomials that share fixed-points. Moreover we extend former results of W. C. Lin and H. X. Yi. [ABSTRACT FROM AUTHOR]

Inversion of deformation fields is applied frequently to map images, dose, and contours between the reference frame and the study frame. A prevailing approach that takes the negative of the forward deformation as the inverse deformation is oversimplified and can cause large errors for large deformations or deformations that are composites of several deformations. Other approaches, including Newton’s method and scatter data interpolation, either require the first derivative or are very inefficient. Here we propose an iterative approach that is easy to implement, converges quickly to the inverse when it does, and works for a majority of cases in practice. Our approach is rooted in fixed-point theory. We build a sequence to approximate the inverse deformation through iterative evaluation of the forward deformation. A sufficient but not necessary convergence condition (Lipschitz condition) and its proof are also given. Though this condition guarantees the convergence, it may not be met for an arbitrary deformation field. One should always check whether the inverse exists for the given forward deformation field by calculating its Jacobian. If nonpositive values of the Jacobian occur only for few voxels, this method will usually converge to a pseudoinverse. In case the iteration fails to converge, one should switch to other means of finding the inverse. We tested the proposed method on simulated 2D data and real 3D computed tomography data of a lung patient and compared our method with two implementations in the Insight Segmentation and Registration Toolkit (ITK). Typically less than ten iterations are needed for our method to get an inverse deformation field with clinically relevant accuracy. Based on the test results, our method is about ten times faster and yet ten times more accurate than ITK’s iterative method for the same number of iterations. Simulations and real data tests demonstrated the efficacy and the accuracy of the proposed algorithm. [ABSTRACT FROM AUTHOR]

Abstract: When a digital filter is realized with floating-point or fixed-point arithmetics, errors and constraints due to finite word length are unavoidable. In this paper, we show how these errors can be mechanically analysed using the HOL theorem prover. We first model the ideal real filter specification and the corresponding floating-point and fixed-point implementations as predicates in higher-order logic. We use valuation functions to find the real values of the floating-point and fixed-point filter outputs and define the error as the difference between these values and the corresponding output of the ideal real specification. Fundamental analysis lemmas have been established to derive expressions for the accumulation of roundoff error in parametric Lth-order digital filters, for each of the three canonical forms of realization: direct, parallel, and cascade. The HOL formalization and proofs are found to be in a good agreement with existing theoretical paper-and-pencil counterparts. [Copyright &y& Elsevier]

Abstract: In this paper, the second-order four-point boundary value problem is studied, where , , and , are nonnegative continuous functions. By the use of the property of the corresponding Green''s function, fixed-point index theory, Leray–Schauder degree and upper and lower solution method, some existence, nonexistence, and multiplicity results of positive solutions are acquired. [Copyright &y& Elsevier]

MIMO has been proposed as an extension to 3G and Wireless LANs. As an implementation scheme of MIMO systems, V-BLAST is suitable for the applications with very high data rates. The square root algorithm for V-BLAST detection is attractive to hardware implementations due to its low computational complexity and numerical stability. In this paper, the fixed-point implementation of the square root algorithm is analyzed, and a low complexity VLSI architecture is proposed. The proposed architecture is scalable for various configurations, and implemented for a 4 × 4 QPSK V-BLAST system in a 0.35 $\mu$m CMOS technology. The chip core covers 9 $mm^2$ and 190 K gates. The detection throughput of the chip depends on the received symbol packet length. When the packet length is larger than or equal to 100 bytes, it can achieve a maximal detection throughput of 128 $\sim$ 160 Mb/s at a maximal clock frequency of 80 MHz. The core power consumption, measured at 2.7 V and room temperature, is about 608 mW for 160 Mb/s data rate at 80 MHz, and 81 mW for 20 Mb/s at 10 MHz. The proposed architecture is shown to meet the requirements for emerging MIMO applications, such as 3G HSDPA and IEEE 802.11n. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we consider and analyze some new projection-proximal methods for solving general variational inequalities. The modified methods converge for pseudomonotone operators which is a weaker condition than monotonicity. The proposed methods include several new and known methods as special cases. Our results can be considered as a novel and important extension of the previously known results. Since the general variational inequalities include the quasi-variational inequalities and implicit complementarity problems as special cases, results proved in this paper continue to hold for these problems. [Copyright &y& Elsevier]

We argue that the essence of thirdness in computing is self-reference. Our discussion is grounded on the theories of Church and Curry, which have been studied in the domain of theoretical computing. Using their theories, we show that any program can be transformed into a program consisting only of three-term relations, where the essence of the three-term relations lies in self-reference. [ABSTRACT FROM AUTHOR]

Taking Löb's Axiom in modal provability logic as a running thread, we discuss some general methods for extending modal frame correspondences, mainly by adding fixed-point operators to modal languages as well as their correspondence languages. Our suggestions are backed up by some new results – while we also refer to relevant work by earlier authors. But our main aim is advertizing the perspective, showing how modal languages with fixed-point operators are a natural medium to work with. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we consider some classes of merit functions for general variational inequalities. Using these functions, we obtain error bounds for the solution of general variational inequalities under some mild conditions. Since the general variational inequalities include variational inequalities, quasivariational inequalities and complementarity problems as special cases, results proved in this paper hold for these problems. In this respect, results obtained in this paper represent a refinement of previously known results for classical variational inequalities. [Copyright &y& Elsevier]

A procedure for obtaining tighter bounds on zero-input limit cycles is presented. The proposed new bounds are applicable to digital filters of arbitrary order, described in state-space formulation and implemented with fixed-point arithmetic. For the most part, we obtain smaller bounds than those reported in the literature, using a computationally efficient algorithm that is easy to implement and has a comparatively short execution time. Simulation results show the validity of the proposed theory. [ABSTRACT FROM AUTHOR]

We propose a novel methodology for estimating the shape parameter of a generalized Gaussian distribution (GGD). This new method is based on a simple estimating equation derived from a convex shape equation. The estimating equation is completely independent of gamma and polygamma functions. Thus, no lookup table, interpolation, or additional subroutine to evaluate these functions are required for real-time implementations of the proposed method, which is in contrast to all existing methods. Furthermore, we establish that the has a unique global root on the positive real line and the Newton-Raphson root-finding algorithm converges to the unique global root from any starting point in a semi-infinite interval Θmin. More importantly, we show that the sample-based shape estimating equation has a unique global root with probability tending to one and the root is consistent for the true shape parameter. we prove via fixed point arguments that, with probability tending to one, the Newton-Raphson algorithm converges to the unique global root of the sample shape estimating equation from any starting point in Θmin. Some numerical experiments are also provided to demonstrate the global convergence and the excellent finite sample performance of the proposed method. [ABSTRACT FROM AUTHOR]

This paper presents a 64-bit fixed-point vector multiply-accumulator (MAC) architecture capable of supporting multiple precisions. The vector MAC can perform one 64 x 64, two 32 x 32, four 16 x 16, or eight 8 x 8 bit signed/unsigned multiply-accumulates using essentially the same hardware as a scalar 64-bit MAC and with only a small increase in delay. The scalar MAC architecture is "vectorized" by inserting mode-dependent multiplexing into the partial product generation and by inserting mode-dependent kills in the carry chain of the reduction tree and the final carry-propagate adder. This is an example of "shared segmentation" in which the existing scalar structure is segmented and then shared between vector modes. The vector MAC is area efficient and can be fully pipelined, which makes it suitable for high-performance processors and, possibly, dynamically reconfigurable processors. The "shared segmentation" method is compared to an alternative method, referred to as the "shared subtree" method, by implementing vector MAC designs using two different technologies and three different vector widths. [ABSTRACT FROM AUTHOR]

Abstract: This paper is concerned with the nonlinear fractional differential equation L(D)u=f(x,u), u(0)=0, 0<x<1, where L(D) = Ds n − a n−1 D s n−1 − … − a 1 D s 1 1 < s 2 < … < sn < 1, and aj > 0, j = 1,2,…, n − 1. Some results are obtained for the existence, nonexistence, and multiplicity of positive solutions of the above equation by using Krasnoselskii''s fixed-point theorem in a cone. In particular, it is proved that the above equation has N positive solutions under suitable conditions, where N is an arbitrary positive integer. [Copyright &y& Elsevier]

In this article, we deal with the uniqueness problems on meromorphic functions concerning differential polynomials that share fixed-points. Moreover, we greatly improve a former result. [ABSTRACT FROM AUTHOR]

In this paper, we consider and analyze a new class of self-adaptive projection algorithms for solving general variational inequalities by using the technique of updating the solution. We prove that the convergence of these new methods only requires the pseudomonotonicity, which is a weaker condition than monotonicity. These new methods differ from the previously known splitting methods for solving variational inequalities and related complementarity problems. Proof of convergence is very simple. As special cases, we can obtain a number of four-step forward–backward splitting methods of Noor for solving variational inequalities. [Copyright &y& Elsevier]

In this paper, we consider and analyze a new class of extragradient-type methods for solving general variational inequalities. The modified methods converge for pseudomonotone operators which is weaker condition than monotonicity. Our proof of convergence is very simple as compared with other methods. The proposed methods include several new and known methods as special cases. Our results present a significant improvement of previously known methods for solving variational inequalities and related optimization problems. [Copyright &y& Elsevier]

Support Vector Machine (SVM) has become a very effective method in statistical machine learning and it has proved that training SMV is to solve Nearest Point pair Problem (NPP) between two disjoint closed convex sets. Later Keerthi pointed out that it is difficult to apply classical excellent geometric algorithms direcly to SVM and so designed a new geometric algorithm for SVM. In this article, a new algorithm for geometrically solving SVM, Kernel Projection Algorithm, is presented based on the theorem on fixed-points of projection mapping. This new algorithm makes it easy to apply classical geometric algorithms to solving SVM and is more understandable than Keerthi’s. Experiments show that the new algorithm can also handle large-scale SVM problems. Geometric algorithms for SVM, such as Keerthi’s algorithm, require that two closed convex sets be disjoint and otherwise the algorithms are meaningless. In this article, this requirement will be guaranteed in theory by using the theoretic result on universal kernel functions. [ABSTRACT FROM AUTHOR]

This paper presents a reduced-complexity, fixed-point algorithm and efficient real-time VLSI architectures for multiuser channel estimation, one of the core baseband processing operations in wireless base-station receivers for CDMA. Future wireless base-station receivers will need to use sophisticated algorithms to support extremely high data rates and multimedia. Current DSP implementations of these algorithms are unable to meet real-time requirements. However, there exists massive parallelism and bit level arithmetic present in these algorithms than can be revealed and efficiently implemented in a VLSI architecture. We re-design an existing channel estimation algorithm from an implementation perspective for a reduced complexity, fixed-point hardware implementation. Fixed point simulations are presented to evaluate the precision requirements of the algorithm. A dependence graph of the algorithm is presented and area-time trade-offs are developed. An area-constrained architecture achieves low data rates with minimum hardware, which may be used in pico-cell base-stations. A time-constrained solution exploits the entire available parallelism and determines the maximum theoretical data processing rates. An area-time efficient architecture meets real-time requirements with minimum area overhead. [ABSTRACT FROM AUTHOR]

I use modal logic and transfinite set-theory to define metaphysical foundations for a general theory of computation. A possible universe is a certain kind of situation; a situation is a set of facts. An algorithm is a certain kind of inductively defined property. A machine is a series of situations that instantiates an algorithm in a certain way. There are finite as well as transfinite algorithms and machines of any degree of complexity (e.g., Turing and super-Turing machines and more). There are physically and metaphysically possible machines. There is an iterative hierarchy of logically possible machines in the iterative hierarchy of sets. Some algorithms are such that machines that instantiate them are minds. So there is an iterative hierarchy of finitely and transfinitely complex minds. [ABSTRACT FROM AUTHOR]

In this paper, we prove the following result: Let f(z) and g(z) be two nonconstant meromorphic(entire) functions, n ≥ 11(n ≥ 6) a positive integer. If fn(z)f′(z) and gn(z)g′(z) have the same fixed-points, then either f(z) = c1ecz2, g(z) = c2e− cz2, where c1, c2, and c are three constants satisfying 4(c1c2)n + 1c2 = −1, or f(z) ≡ tg(z) for a constant t such that tn + 1 = 1. [Copyright &y& Elsevier]

The intent of this manuscript is to present new rational symmetric ϖ − ξ -contractions and infer some fixed-points for such contractions in the setting of Θ -metric spaces. Furthermore, some related results such as Suzuki-type rational symmetric contractions, orbitally Υ -complete, and orbitally continuous mappings in Θ -metric spaces are introduced. Ultimately, the theoretical results are shared to study the existence of the solution to a fractional-order differential equation with one boundary stipulation. [ABSTRACT FROM AUTHOR]

It is well known that dismantling a finite poset P leads to a retract, called the core of P, which has the fixed-point property if and only if P itself has this property. The PT-order, or passing through order, of a poset P is the quasi order ⊴ defined on P so that a⊴ b holds if and only if every maximal chain of P which passes through a also passes through b. This leads to a generalization of the dismantling procedure which works for arbitrary chain complete posets which have no infinite antichain. We prove that such a poset also has a finite core, i.e. a finite retract which reflects the fixed-point property for P. [ABSTRACT FROM AUTHOR]

In recent years, complex-valued fuzzy metric spaces (in short CVFMS) were introduced by Shukla et al. (Fixed Point Theory 32 (2018)). This setting is a valuable extension of fuzzy metric spaces with the complex grade of membership function. They also established fixed-point results under contractive condition in the aforementioned spaces and generalized some essential existence results in fixed-point theory. The purpose of this manuscript is to derive some fixed-point results for multivalued mappings enjoying the least upper bound property in CVFMS. Furthermore, we studied the existence theorem for a unique solution to the Fuzzy fractional Volterra–Fredholm integro-differential equations (FCFVFIDEs) as an application to our derived result involving the Caputo derivative. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to introduce a new type of contraction called fuzzy F-contraction. As compared to the F-contraction in the existing literature, our fuzzy F-contraction is much simpler and more straightforward, since it contains only one condition—that is, the function F is strictly increasing. Moreover, some fixed-point theorems for fuzzy F-contraction are presented. Further, some examples are given to illustrate its validity and superiority. In addition, by applying a very significant lemma, we show that our proofs of most fixed-point theorems are shorter and more elegant than ones in the literature. [ABSTRACT FROM AUTHOR]

The main result of this paper is a fixed-point theorem for multivalued contractions obtained through an inequality with rational terms. The contraction is an F-type contraction. The results are obtained in a metric space endowed with a graph. The main theorem is supported by illustrative examples. Several results as special cases are obtained by specific choices of the control functions involved in the inequality. The study is broadly in the domain of setvalued analysis. The methodology of the paper is a blending of both graph theoretic and analytic methods. [ABSTRACT FROM AUTHOR]

In the present work, a spar-buoy scaled model was designed and built through a "Lab-on-Sea" unit, equipped with an energy harvesting system. Such a system is based on deformable bands, which are loyal to the unit, to convert wave motion energy into electricity by means of piezo patch transducers. In a preliminary stage, the scaled model, suitable for tests in a controlled ripples-type wave motion channel, was tested in order to verify the "fixed-point" assumption in pitch and roll motions and, consequently, to optimize energy harvesting. A special type of structure was designed, numerically simulated, and experimentally verified. The proposed solution represents an advantageous compromise between the lightness of the used materials and the amount of recoverable energy. The energy, which was obtained from the piezo patch transducers during the simulations in the laboratory, was found to be enough to self-sustain the feasible on-board sensors and the remote data transmission system. [ABSTRACT FROM AUTHOR]