Multiple Functions Research Articles

Algorithms for optimizing systems with multiple extremum functionals

The problem of minimizing (maximizing) multiple extremum functionals (infinite-dimensional optimization) is considered. This problem cannot be solved by conventional gradient methods. New gradient methods with adaptive relaxation of steps in the vicinity of local extrema are proposed. The efficiency of the proposed methods is demonstrated by the example of optimizing the shape of a hydraulic gun nozzle with respect to the objective functional, which is the average force of the hydraulic pulse jet momentum acting on an obstacle. Two local maxima are found, the second of which is global; in the second maximum, the average force of the jet momentum is three times higher than in the first maximum. The corresponding nozzle shape is optimal. Conventional gradient methods have not found any maximum; i.e., they were unable to solve the problem.

Constructing non-AMNM weighted convolution algebras for every semilattice of infinite breadth

The AMNM property for commutative Banach algebras is a form of Ulam stability for multiplicative linear functionals. We show that on any semilattice of infinite breadth, one may construct a weight for which the resulting weighted convolution algebra fails to have the AMNM property. Our work is the culmination of a trilogy started in [4] and continued in [5]. In particular, we obtain a refinement of the main result of [5], by establishing a dichotomy for union-closed set systems that has a Ramsey-theoretic flavour.

A hybrid summation and multiplication displacement amplification mechanism for piezoelectric actuators

Abstract This paper reports a novel amplified piezoelectric actuator featuring compliant displacement amplification mechanism of hybrid summation and multiplication. The hybrid amplification mechanism uses the concept of nesting a pair of Scott-Russell linkages into a toggle linkage to realize the hybrid amplification functions of summation and multiplication. Also, compliant amplification mechanisms with double output ports are designed, enhancing the flexibility of designs and applications. The hybrid displacement amplification principle is mathematically explained in detail. It is demonstrated based on finite element simulations that the displacement amplification ratio, output stiffness and resonance frequency of the proposed hybrid amplification mechanism of summation and multiplication outperform those of the classic rhombus-type and bridge-type compliant mechanisms. The experimental testing results of a prototype show that the amplified piezoelectric actuator is capable of providing 315 μm strokes with the displacement amplification ratio of 16.2. The fundamental resonance frequency with piezoelectric stacks mounted is 1218 Hz. Comparison to typical designs in literature shows well comprehensive performances of statics and dynamics, verifying the advantages of such a hybrid amplification mechanism of summation and multiplication.

Novel Stability Criteria of Asynchronously Switched Nonlinear Neutral Time-Delay Systems.

This article investigates the input-to-state stability and integral input-to-state stability for the switched nonlinear neutral systems (SNNSs) with multiple time-varying delays (MTVDs) and asynchronous switching. According to the fact that the switching signals of the controllers and the subsystems are inconsistent, novel stability criteria on the input-to-state stability and integral input-to-state stability properties for SNNSs with MTVDs and the asynchronous switching phenomenon are presented by multiple Lyapunov-Krasovskii functionals, the merging switching signal, and the mode-dependent average dwell time technique. Compared with the existing related works, our results are less conservative. Meanwhile, our proposed works not only investigate the effects of switches and neutral terms on the stability property for SNNSs but also study the case of the systems with MTVDs and asynchronous switching. Finally, two practical examples, including the practical coupled mass-spring-damper-pendulum system, are presented to show the effectiveness of our results.

Research on Image Encryption Method based on the Chaotic Iteration of a Ternary Nonlinear Function

Objective: Considering that some image encryption algorithms have the disadvantages of complex structure and high computational cost, and there are not many commonly used chaotic systems, which are easy to crack by attacks, to solve these problems, this paper proposes an image encryption algorithm based on three-dimensional nonlinear functions to solve these problems. Methods: The algorithm mainly combines the sinusoidal chaotic map with the ternary nonlinear function system to encrypt the image. Firstly, multiple ternary nonlinear function chaotic systems are designed. Then, the function iteration system is changed to invoke the computation of a specific expression under a random number; it is a chaotic sequence generated according to a chaotic mapping such as sine, and then the value of this chaotic sequence is used to select a ternary nonlinear function for iteration to obtain a chaotic sequence. Finally, the chaotic sequence performs the XOR and scrambling operations on the grey image Results: The algorithm has a simple structure, a better encryption effect, and more incredible difficulty deciphering. Moreover, through the phase diagram and bifurcation diagram, it can be seen that the system has good chaotic characteristics Conclusion: The method in this paper is novel; this method is a random variable order composite operation, which can not only be applied to image encryption but also can be used for fractal map generation and so on, and in some other chaotic fields will have a wide range of applications. It has essential research value.

Interpolating Between Rényi Entanglement Entropies for Arbitrary Bipartitions via Operator Geometric Means

AbstractThe asymptotic restriction problem for tensors can be reduced to finding all parameters that are normalized, monotone under restrictions, additive under direct sums and multiplicative under tensor products, the simplest of which are the flattening ranks. Over the complex numbers, a refinement of this problem, originating in the theory of quantum entanglement, is to find the optimal rate of entanglement transformations as a function of the error exponent. This trade-off can also be characterized in terms of the set of normalized, additive, multiplicative functionals that are monotone in a suitable sense, which includes the restriction-monotones as well. For example, the flattening ranks generalize to the (exponentiated) Rényi entanglement entropies of order $$\alpha \in [0,1]$$ α ∈ [ 0 , 1 ] . More complicated parameters of this type are known, which interpolate between the flattening ranks or Rényi entropies for special bipartitions, with one of the parts being a single tensor factor. We introduce a new construction of subadditive and submultiplicative monotones in terms of a regularized Rényi divergence between many copies of the pure state represented by the tensor and a suitable sequence of positive operators. We give explicit families of operators that correspond to the flattening-based functionals, and show that they can be combined in a nontrivial way using weighted operator geometric means. This leads to a new characterization of the previously known additive and multiplicative monotones, and gives new submultiplicative and subadditive monotones that interpolate between the Rényi entropies for all bipartitions. We show that for each such monotone there exist pointwise smaller multiplicative and additive ones as well. In addition, we find lower bounds on the new functionals that are superadditive and supermultiplicative.

A - 13 Cognitive Correlates of Technology-Based Instrumental Activities of Daily Living Performance in Older Adults Presenting for Cognitive Evaluations

Abstract Objective Rapid advances in technology have altered how daily activities are performed. Accumulating evidence suggests technology-based instrumental activities of daily living (iADLs) are increasingly common in older adults’ lives, and assessing these skills may improve diagnostic identification of individuals with Alzheimer’s disease and related dementias (ADRD). While iADLs are complex tasks reliant on multiple cognitive processes, prior work suggests memory and executive functioning are the cognitive processes most strongly predictive of iADL performance in ADRD. However, whether similar associations exist with technology-based iADLs has not been established. The goal of the present study was to evaluate the cognitive correlates of technology-based compared to traditional iADL items. Method One hundred seventy-eight individuals (mean age: 75.35 ± 7.30) presenting for evaluation of cognitive status completed tests of memory, executive functioning, language, and processing speed. Care partners completed the Functional Activities Questionnaire (FAQ) and 11 technology-based iADL items. Associations between cognition and traditional and technology-based FAQ items were examined through Pearson’s correlations and multiple regression analyses. Results Cognition was significantly correlated with both traditional and technology-based iADLs (|r’s| > 0.30, p’s.44). In multiple regression models, executive functioning and processing speed but not memory were the strongest predictors of traditional iADL performance (p’s < 0.02), but for independence with technology-based iADLs, executive functioning alone (p < 0.001) emerged. Conclusions Relations between cognition and daily functioning are similar for both traditional and technology-based FAQ items, with executive functioning particularly relevant for both types of tasks. Implications for clinical practice and technology-based interventions are discussed.

Heterogeneous network of 2D MOFs decorated 1D CNTs imparting multiple functionalities to composite phase change materials

Heterogeneous network of 2D MOFs decorated 1D CNTs imparting multiple functionalities to composite phase change materials

Efficient large-scale 3D gravity modeling using a fast evaluate kernel matrix combined with compressed matrix techniques

A fast calculated kernel matrix method is coupled with a compressed matrix technique to solve the large-scale gravity forward-modeling problem. This method accelerates the coefficient matrix computation by reducing the arctangent, logarithm, and multiplication functions in the prismatic gravity analytical expression. In addition, the use of the compressed matrix technique presents a significant advantage in that it does not require the storage of redundant kernel matrices, further reducing the memory requirements and computation time. Moreover, the discrete convolution of the compressed matrix with density is executed through the 2D fast Fourier transform (FFT). Two typical synthetic models are used to test the performance of the novel algorithm. The results demonstrate that the developed algorithm is approximately 15 times faster than the traditional algorithm. Concurrently, it demands almost 1/7th of the memory while ensuring equivalent computational accuracy. To further illustrate the capability of the algorithm, we apply our method to the terrain correction of an airborne gravity data set using a real digital elevation model. Our approach efficiently calculates 250,000 observation points across 25 million cells in only 5.42 s, compared with 234.81 s for the latest 2D Gauss-FFT method.

Predicting the entire pyrolysis process of representative charring material infiltrated with kerosene using an improved artificial neural network

It is crucial to predict the entire pyrolysis process of charring materials infiltrated with flammable liquids to provide guidance for reducing the fire hazards and implementing numerical simulations of fire accidents caused by the leakage of flammable liquids. In the present study, pyrolysis data obtained from the thermogravimetric experiments were preprocessed using linear interpolation and data normalization methods. The processed data set was then used to train the artificial neural network (ANN) framework to predict the pyrolysis behaviors of typical charring material (Mongolian Scots pine) infiltrated with typical flammable liquid (kerosene) under three different conditions: (1) pyrolysis at a constant mass fraction of kerosene with multiple heating rates; (2) pyrolysis at multiple mass fractions of kerosene with a constant heating rate; and (3) pyrolysis at multiple mass fractions of kerosene and multiple heating rates. The ANN, with the double hidden layer structure (6−3), was capable to well predict the entire pyrolysis behaviors of Mongolian Scots pine under all the three scenarios. Besides, five data transformation function (multiplication, exponential function with base e, logarithmic function with base e, square root, and exponentiation function) were applied to the present three input variables (temperature, mass fraction of kerosene, and heating rate) to generate new input variables in order to extract more characteristics among the pyrolysis data. Therein, the ANN utilizing the data transformation functions of multiplication and exponential function with base e exhibited the best predictive ability. Among the three input variables in the ANN (temperature, mass fraction of kerosene, and heating rate), temperature was identified as the most sensitive one to the prediction performance, followed by mass fraction of kerosene, with heating rate being the least sensitive.

Design and FPGA Implementation of Signal Strength Measurement Techniques for Satellite Communication Systems

Communication receivers perform three major functions, frequency down conversion, IF demodulation and subcarrier demodulation. The functioning of a receiver is mainly controlled by input signal strength and relative dynamics. Signal strength is measured in terms of Signal to Noise ratio (SNR) and Carrier to Noise power density (C/No). Any measure of signal strength indirectly gives information about receiver performance for that period. Apart from this, SNR measurement in close loop with Phase Locked Loop (PLL) parameter forms the adaptive PLL system, which is one of the driving forces for this paper. The focus of this paper is to find suitable signal strength measurement techniques and their implementation for satellite communication systems. Signal to Noise Variance method (SNV) and Narrow band Wide band Power Ratio (NWPR) methods are considered based on the performance and realization aspects. All techniques require division, logarithm, and multiplication functions for their realization in hardware. CO-ordinate Rotation Digital Computer (CORDIC) algorithm is considered for realizing logarithm function. A comparison study is done for developed algorithm with Intellectual Property (IP) core. Developed SNR techniques are simulated for Binary Phase Shift Keying (BPSK) demodulator system and performance is evaluated for Additive White Gaussian Noise (AWGN). The paper describes the FPGA design and simulations of these techniques. Developed design is targeted to commercial and space qualified FPGA platforms. FPGA implementations results are compared with system level simulation results, and both are found to be satisfactory. Application of developed system in adaptive BPSK demodulator is also presented.

Event-triggered quasi-time-varying [formula omitted] filtering for switched systems via multiple trigger-dependent Lyapunov functionals

This paper investigates the event-triggered filtering problem for switched systems from the perspective of switched impulsive systems (SISs) by exploiting the characteristics of trigger and impulse behavior. By constructing multiple trigger-dependent Lyapunov functionals (MTDLFs), an event-triggered quasi-time-varying (ET-QTV) H∞ filtering scheme is developed. Since the MTDLFs properly capture the event-induced impulse property of SISs, they release less conservatism. The filtering stability in the scenario of frequent plant switching during an interevent interval is also guaranteed by incorporating the average dwell time switching. The filtering synthesis condition is formulated as a set of QTV matrix inequalities defined over a finite time horizon, based on which a sum of squares-based filter design algorithm is presented further. Additionally, the derivation of a lower bound on interevent intervals is clarified for the event-triggering mechanism (ETM) to exclude the Zeno phenomenon. Finally, the effectiveness and potential practicability of the proposed filtering scheme are validated using a morphing aircraft model.

Switched Neural Networks for Simultaneous Learning of Multiple Functions

Switched Neural Networks for Simultaneous Learning of Multiple Functions

H∞ control of delayed switched systems under asynchronous switching: New results without the constraint between the switching delay and the dwell time of submodes

AbstractThis article investigates the control problem of switched systems with time‐varying delays under asynchronous switching. By reconstructing the switching rule of local controllers and empolying multiple Lyapunov functionals and integral inequalities, sufficient conditions without the constraint between the switching delay and the dwell time of submodes to solve the control problem are derived. The control gain matrices can be conveniently obtained by the proposed linear search algorithm.

Continuous multiplicative spectral functionals on Hermitian Banach algebras

Continuous multiplicative spectral functionals on Hermitian Banach algebras

Switching Anti-Windup Synthesis for Linear Systems With Asymmetric Actuator Saturation.

This article proposes a switching anti-windup strategy for linear, time-invariant (LTI) systems subject to asymmetric actuator saturation and L2 -disturbances, the core idea behind which is to make full use of the available range of control input space by switching among multiple anti-windup gains. The asymmetrically saturated LTI system is converted to a switched system with symmetrically saturated subsystems, and a dwell time switching rule is presented to govern the switching between different antiwindup gains. Based on multiple Lyapunov functions, we derive sufficient conditions for guaranteeing the regional stability and weighted L2 performance of the closed-loop system. The switching anti-windup synthesis that designs a separate anti-windup gain for each subsystem is cast as a convex optimization problem. In comparison with the design of a single anti-windup gain, our method can induce less conservative results since the asymmetric character of the saturation constraint is fully utilized in the switching anti-windup design. Two numerical examples, and an application to aeroengine control (the experiments are conducted on a semiphysical test bench), demonstrate the superiority and practicality of the proposed scheme.

The Expectation of a Multiplicative Functional under the Sine-Process

The Expectation of a Multiplicative Functional under the Sine-Process

Longitudinal associations between attachment representations coded in the adult attachment interview in late adolescence and perceptions of romantic relationship adjustment in adulthood

AbstractIncreasingly, researchers have operationalized Adult Attachment Interview (AAI)‐derived attachment representations as reflecting individual differences in secure base script knowledge (AAIsbs) – the degree to which individuals show awareness of the temporal‐causal schema that summarizes the basic features of seeking and receiving effective support from caregivers when in distress. In a series of pre‐registered analyses, we used AAI transcripts recently re‐coded for AAIsbs and leveraged a new follow‐up assessment of the NICHD Study of Early Child Care and Youth Development cohort at around age 30 years (479 currently partnered participants; 59% female; 82% White/non‐Hispanic) to assess and compare the links between AAIsbs and traditional AAI coding measures at around age 18 years and self‐reported romantic relationship quality in adulthood. Higher AAIsbs predicted better dyadic adjustment scores in adulthood (r = 0.17) and this association remained significant controlling for other AAI‐derived coding measures, as well as sociodemographic and cognitive functioning covariates. Findings extend previous evidence pointing to the predictive significance of AAIsbs for multiple adult functioning domains.

Triple Action of Lignosulfonic Acid Sodium: Anti-protease, Antioxidant, and Anti-inflammatory Effects of a Polymeric Heparin Mimetic.

Heparins are sulfated glycosaminoglycans that are used as anticoagulants to treat thrombosis. Heparins exhibit other potential therapeutic effects, such as anti-inflammatory, anti-viral, and anti-malarial effects. However, the strong anticoagulant activity of heparins poses a risk of life-threatening bleeding, limiting their therapeutic use for other diseases beyond thrombosis. To exploit the other effects of heparins and eliminate the bleeding risk, we explored an alternative polymer called lignosulfonic acid sodium (LSAS), which acts as a sulfonated heparin mimetic. LSAS targets factor XIa to exert an anticoagulant effect, and thus, unlike heparins, it is unlikely to cause bleeding. This study investigated the multiple effects of LSAS to identify potential leads for complex pathologies treatment. A series of chromogenic substrate hydrolysis assays were used to evaluate the inhibition of three inflammation-related proteases by LSAS. Its chemical antioxidant activity against the system of ABTS/hydrogen peroxide/metmyoglobin was also determined. Lastly, the effect of LSAS on TNFα-induced activation of the NF-κB pathway in HEK-293 cells was also tested to determine its cellular anti-inflammatory activity. The results showed that LSAS effectively inhibited human neutrophil elastase, cathepsin G, and plasmin, with IC50 values ranging from 0.73 to 212.5 μg/mL. Additionally, LSAS demonstrated a significant chemical antioxidant effect, with an IC50 value of 44.1 μg/mL. Furthermore, at a concentration of approximately 530 μg/mL, LSAS inhibited the TNFα-induced activation of the NF-κB pathway in HEK-293 cells, indicating a substantial anti-inflammatory effect. An essential advantage of LSAS is its high water solubility and virtual non-toxicity, making it a safe and readily available polymer. Based on these findings, LSAS is put forward as a polymeric heparin mimetic with multiple functions, serving as a potential platform for developing novel therapeutics to treat complex pathologies.

Effect of XC functionals and dispersion corrections on the DFT‐computed structural and vibrational properties of SrCl2–NaCl and ZrF4–LiF

AbstractDensity functional theory (DFT) calculations were performed to examine the impact of exchange–correlation (XC) functionals and van der Waals corrections (specifically the D3 method) on the structural and vibrational properties of the SrCl2–NaCl and ZrF4–LiF salt systems. Multiple XC functionals, including the local density approximation (LDA), the generalized gradient approximation using the Perdew–Burke–Ernzerhof (PBE) model, and its modified form suitable for solids (PBEsol), the dispersion‐corrected PBE‐D3 and PBEsol‐D3, were considered. Of these functionals, LDA was found to exhibit the highest degree of error, while PBEsol and PBE‐D3 displayed the least error. Underestimated lattice parameters compared with experimental values were observed to result in higher force constants, leading to an overprediction of vibrational frequencies. Conversely, an overestimation of lattice parameters was associated with lower vibrational frequencies. The methodology presented in this study yielded results that are in good agreement with experiment, irrespective of the method (finite differences vs. density functional perturbation theory) employed for calculating infrared and Raman spectra. It was further demonstrated that for alkali halides with weak Raman scattering, utilizing a supercell constructed from primitive cells better predicts Raman features than does the use of conventional cells.