Arbitrary Values Research Articles

Assessing Individual Sensitivity to the Thermal Grill Illusion: A Two-Dimensional Adaptive Psychophysical Approach

In the thermal grill illusion (TGI), the spatial alternation of non-noxious warm and cool temperatures elicits burning sensations that resemble the presence of noxious stimuli. Previous research has largely relied on the use of specific temperature values (i.e., 20°C and 40°C) to study this phenomenon in both healthy individuals and patient populations. However, this methodology fails to account for inter-individual differences in thermal sensitivity, limiting the precision with which TGI responses can be evaluated across diverse populations. To address this gap, we created a Two-Dimensional Thermal Grill Calibration (2D-TGC) protocol, enabling an efficient and precise estimation of the combinations of warm and cool temperatures needed to elicit burning sensations tailored to each individual. By applying the 2D-TGC protocol in 43 healthy participants, we demonstrated key findings: (1) The TGI can be thresholded using an adaptive psychophysical method. (2) Multiple combinations of warm and cool temperatures can elicit this phenomenon. (3) The protocol facilitated the identification of temperature combinations that elicit TGI with varying levels of probability, intensity, and perceived quality ranging from freezing cold to burning hot. (4) TGI responsivity can be quantified as a continuous variable, moving beyond the conventional classification of individuals as responders vs. non-responders based on arbitrary temperature values in the innocuous temperature range. The 2D-TGC offers a comprehensive approach to investigate the TGI across populations with altered thermal sensitivity, and can be integrated with other methods (e.g., neuroimaging) to elucidate the mechanisms responsible for perceptual illusions in the thermo-nociceptive system. PerspectiveThis study reveals that the Thermal Grill Illusion can be accurately measured using psychophysical methods. The innovative Two-Dimensional Thermal Grill Calibration protocol allows for personalized temperature assessments, enhancing our understanding of thermal sensitivity variations and perceptual illusions in the thermo-nociceptive system across different populations.

Exact two-loop amplitudes for Higgs plus jet production with a cubic Higgs self-coupling

We compute the corrections to the two-loop amplitudes for gg → h, gg → hg, qg → hq, and qq¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ q\\overline{q} $$\\end{document} → hg due to a modified cubic Higgs self-coupling. The exact dependence on the Higgs and top-quark masses across the entire 2 → 2 phase space is determined by numerically solving a system of differential equations for the relevant master integrals. The calculated amplitudes are crucial for evaluating the impact of the considered corrections on exclusive pp → hj production at the hadronic event level. As an application, we calculate the non-universal, kinematic-dependent cubic Higgs self-coupling corrections to the Higgs-boson transverse momentum distribution in gluon-gluon fusion Higgs production for arbitrary values of the transverse momentum.

Evaluation of reliability and characteristics measure using exponential decay distribution of non‐series parallel network

AbstractThe purpose of this paper is to analyze the reliability and characteristics of the non‐series‐parallel network. The illustrative non‐series parallel networks, that is, the Twin T‐Network and the network with six components of resistor and capacitor, have been converted into a series of parallel network combinations by use of the minimal path technique. The stochastic variables related to component failure rate have been demonstrated using exponential decay distribution. We obtain the reliability, mean time to failure, and sensitivity with the use of the exponential decay distribution. The reliability and its attributes are examined by assuming different values of scale and shape parameters at different points of time. Using Owen's methodology, we obtained minimal signature, tail signature, expected time, expected cost, and Barlow‐Proschan index were determined. The performance of all reliability characteristics has been observed graphically for arbitrary values of parameters. A real‐world example is used to introduce the point.

Fractional mimetic dark matter: A fractional action-like variational approach

In this paper, we propose a nonlocal extension of the mimetic dark matter model based on the FALVA implementation of fractional calculus. Our primary objective to explore how certain properties of dark matter can be modeled within the FALVA framework rather than formulate a phenomenological model. We begin by constructing the action functional of the cosmological extension of the mimetic dark model and deriving the nonlinear equations of motion in the general case. Next, we focus on a fractional-power homogeneous mimetic dark field with an exponential expansion factor. We derive the equation of motion for the lapse field and obtain its general solution. Analytical solutions are then obtained for small time intervals and arbitrary values of the fractionality parameter. These solutions enable us to establish the physical line element of spacetime, incorporating the mimetic dark matter field. From this line element, we derive the Ricci tensor, Ricci scalar, and geodesic equations.

Microarray-based evaluation of selected recombinant timothy grass allergens expressed in E. Coli and N. Benthamiana

BackgroundTimothy grass (Phleum pratense) is a significant source of allergens, and recombinant allergens are increasingly used for diagnostic purposes. However, the performance of different recombinant allergen production systems in diagnostic assays needs further investigation to optimize their use in clinical settings.ObjectiveThe main objective of this study was to analyze and compare the diagnostic performance of recombinant timothy grass allergens produced in E. coli and N. benthamiana using a custom-made microarray chip.MethodsRecombinant timothy grass allergens Phl p 1, Phl p 2, Phl p 5, Phl p 6, Phl p 11, and Phl p 12 were produced in E. coli and/or N. benthamiana. A total of 113 patient serum samples were tested to evaluate the diagnostic sensitivity, specificity, inter-assay variability, and correlation of allergen-specific IgE detection compared to commercial multiplex tests (ALEX and ISAC). Additionally, the prevalence of sIgE to these allergens was assessed.ResultsPhl p 1, Phl p 2, Phl p 5, Phl p 6 and Phl p 11 showed high or very high positive correlation in immunoreactivity with other commercial multiplex tests. Notably, Phl p 11 fused with maltose-binding protein (MBP) demonstrated high diagnostic specificity and sensitivity, with a 0.3 arbitrary cut-off value. However, a high intra-assay variation was observed. The study also assessed specific IgE prevalence to timothy grass allergens within the tested patient cohort.ConclusionsRecombinant allergens from both E. coli and N. benthamiana demonstrated strong diagnostic potential on the microarray platform, with Phl p 11 (MBP-fused) showing particularly high performance. High intra-assay variation highlights the need for further optimization in allergen formulation and microarray storage conditions. These results highlight the potential of recombinant allergens for diagnostic applications, despite challenges with allergen stability in microarray formats. Specific IgE prevalence to timothy allergens revealed a sensitization profile consistent with findings from multiple studies.Graphical

Inverse problems are solvable on real number signal processing hardware

Despite the success of Deep Learning (DL) serious reliability issues such as non-robustness persist. An interesting aspect is, whether these problems arise due to insufficient tools or fundamental limitations of DL. We study this question from the computability perspective by characterizing the limits the applied hardware imposes. For this, we focus on the class of inverse problems, which, in particular, encompasses any task to reconstruct data from measurements. On digital hardware, a conceptual barrier on the capabilities of DL for solving finite-dimensional inverse problems has in fact already been derived. This paper investigates the general computation framework of Blum-Shub-Smale (BSS) machines, describing the processing and storage of arbitrary real values. Although a corresponding real-world computing device does not exist, research and development towards real number computing hardware, usually referred to by “neuromorphic computing”, has increased in recent years. In this work, we show that the framework of BSS machines does enable the algorithmic solvability of finite dimensional inverse problems. Our results emphasize the influence of the considered computing model in questions of accuracy and reliability.

Найкраще наближення в інтегральній метриці лінійної комбінації періодичних функцій різної парності

In many areas of mathematics, extremal problems often arise related to approximation characteristics of both the approximating functions and the properties of the elements being approximated. For example, in the case of polynomials, the problem can involve the number of points where the values of the function coincide with the values of the polynomial used to replace the function on the studied interval. In practice, the problem of approximating a function from a given set R is reduced to replacing it, according to a defined algorithm, with a function (polynomial) of a fixed degree that is close to it in a certain sense. In uniform and integral metrics, the problem of finding the exact values of the best approximations for classes of r-times differentiable functions, where r is a natural number, has been explored in the works of J. Favard [1], N. I. Akhiezer, M. G. Krein [2], B. Nadi, S. M. Nikolsky [3], V. K. Dzyadyk [4], S. B. Stechkin, Sun Yun-shen, and others. The final results concerning the solution of the best approximation problem on Weyl-Nagy classes for arbitrary values of the parameters defining these classes belong to the Ukrainian mathematician V. K. Dzyadyk [4]. In his works on function classes generated by the well-known Bernoulli kernels, it was established that the number of coincidence points between the kernel and the approximating polynomial of degree n − 1, including their multiplicities, does not exceed 2n, which allowed for obtaining final results. The work [5] presents cases of such linear combinations of even or odd kernels for which the number of uniformly distributed interpolation points equals 2n + 2 for a polynomial of degree n − 1 that deviates the least in the metric of the L – space from the studied linear combination. The idea of studying composite kernels expressed as a linear combination of component terms belongs to O. I. Stepanyets [6], and it was implemented in problems of joint approximation of functions and their derivatives. In the 1980s and 1990s, O. I. Stepanets developed a new approach to classifying periodic functions, which allowed for a fine classification of extremely broad sets of periodic functions. The results obtained for these classes are, on one hand, of a general nature, and on the other, they provide a whole series of new, previously unknown results that could not be achieved with previously known classes. Following the approaches to function classification, we can consider a linear combination of function classes as a certain single class of a more complex nature. Then, the problem of finding the exact values of the upper bounds of the best approximations reduces to the problem of the best approximation for this composite class, which corresponds to convolutions with the generating composite kernel. In this work, we investigate linear combinations of three continuous 2π-periodic kernels of different parity, and it is established that there exist such composite kernels that their trigonometric polynomial of the best approximation of order n − 1 in the integral metric interpolates the kernel at 2n + 2 uniformly distributed points

Canonical analysis of linearized [formula omitted] gravity plus a Chern–Simons term

The Hamiltonian analysis for the linearized λR gravity plus a Chern–Simons term is performed. The first-class and second-class constraints for arbitrary values of λ are presented, and one physical degree of freedom is reported. The second-class constraints are removed, and the corresponding generalized Dirac brackets are constructed; then, the difference between theories with different values of λ is remarked.

Calibrated Eckhardt’s filter versus alternative baseflow separation methods: A silica-based approach in a Brazilian catchment

The Eckhardt’s filter, a recursive digital filter widely used in hydrology to separate baseflow, relies on two parameters: the recession constant (a) and the maximum allowable long-term ratio of baseflow to streamflow (BFImax). While a can be determined through regression analyses, BFImax is often assigned an arbitrary value because of limited catchment information for a more objective determination. This study aimed to assess and calibrate BFImax for a 1.2 km2 rural catchment in southern Brazil using dissolved silica data. Calibration involved minimizing differences between filter-generated baseflow hydrographs and those derived from dissolved silica measurements and mass balance across 13 monitored rainfall-runoff events. The calibrated model was compared to three established models: a modified graphical method based on local minima, a backward filter model, and a one-parameter filter. The results yielded an optimal BFImax of 0.653 with high model performance (PBias ≈ 0, NSE = 0.85, KGE = 0.74, and NRMSD = 13 %) against silica-derived baseflow. Applying the calibrated filter to a six-year streamflow dataset yielded a long-term baseflow index (BFI) value of 54 %, aligned with regional and global averages. Comparisons with other models showed that the backward filter model produced unrealistic baseflow values nearly identical to streamflow values; the local minima method overestimated baseflow by +19 % and failed to accurately represent the smoothness and peaks of the baseflow hydrographs; and the one-parameter filter represented the shape and timing of the baseflow hydrographs well, but underestimated magnitude by −19 %. These findings validate the effectiveness of the Eckhardt’s filter in generating accurate baseflow hydrographs and confirm the importance of calibrating BFImax for optimal performance. The research also endorses the use of dissolved silica measurements and the mass balance method as a reliable approach for calibrating BFImax for long-term assessment of baseflows.

Entanglement in Lifshitz fermion theories

We study the static entanglement structure in (1+1)-dimensional free Dirac-fermion theory with Lifshitz symmetry and arbitrary integer dynamical critical exponent. This model is different from the one introduced in [Hartmann et al., SciPost Phys.11 (2021) 031] due to a proper treatment of the square Laplace operator. Dirac fermion Lifshitz theory is local as opposed to its scalar counterpart which strongly affects its entanglement structure. We show that there is quantum entanglement across arbitrary subregions in various pure (including the vacuum) and mixed states of this theory for arbitrary integer values of the dynamical critical exponent. Our numerical investigations show that quantum entanglement in this theory is tightly bounded from above. Such a bound and other physical properties of quantum entanglement are carefully explained from the correlation structure in these theories. A generalization to (2+1)-dimensions where the entanglement structure is seriously different is addressed.

Diffraction efficiency management by complex binary gratings.

The diffraction efficiencies of a complex binary diffraction grating with a rectangular profile are controlled through the steps' phases, amplitudes, and duty cycle, based on analytical expressions. It is demonstrated that the zeroth-diffraction order can be canceled for any arbitrary value of the duty cycle, provided that a π-phase difference is imposed, along with a specific ratio of the steps' amplitudes. This feature is not feasible for separated amplitude-only and phase-only rectangular binary gratings in the context of one-dimensional gratings. In this framework, a key analytic relationship between the duty cycle and the steps' amplitude ratio is derived, allowing the design of such gratings with this desired feature across a wide range of conditions, not limited to a duty cycle of 0.5. Concerning the higher diffraction orders, it is proved that their intensities cancel or maximize for fixed duty cycle no matter the amplitude and phase values of the steps. The intensity of the m-th diffraction order possesses m maxima and m - 1 zeros on the full range of the duty cycle. All these features were corroborated experimentally. The broad insight of such a grating allows the design of gratings with diffraction efficiencies tailored for specific applications.

General theory for extended-range percolation on simple and multiplex networks.

Extended-range percolation is a robust percolation process that has relevance for quantum communication problems. In extended-range percolation nodes can be trusted or untrusted. Untrusted facilitator nodes are untrusted nodes that can still allow communication between trusted nodes if they lie on a path of distance at most R between two trusted nodes. In extended-range percolation the extended-range giant component (ERGC) includes trusted nodes connected by paths of trusted and untrusted facilitator nodes. Here, based on a message-passing algorithm, we develop a general theory of extended-range percolation, valid for arbitrary values of R as long as the networks are locally treelike. This general framework allows us to investigate the properties of extended-range percolation on interdependent multiplex networks. While the extended-range nature makes multiplex networks more robust, interdependency makes them more fragile. From the interplay between these two effects a rich phase diagram emerges including discontinuous phase transitions and reentrant phases. The theoretical predictions are in excellent agreement with extensive Monte Carlo simulations. The proposed exactly solvable model constitutes a fundamental reference for the study of models defined through properties of extended-range paths.

Zero gradient sum algorithm of arbitrary initial value with constraints and communication delay based on directed graph

The distributed convex optimisation issue with inequality constraints and box constraints on the directed communication topology is examined in this paper. In the case of the communication delay between agents, we propose a piecewise zero-gradient-sum triggered control algorithm that allows arbitrary initial values. Using the log-barrier penalty method, we only need to study an unconstrained approximation problem of the original problem. Firstly, each agent's state converges to the optimal value of the related local objective function in a fixed time. Simultaneously, the upper bound of fixed time in this paper is smaller than some existing results. Then, in the case of communication delay, time-triggered and event-triggered methods with non-uniform sampling interval are proposed in this paper, which make the communication cost lower and the application broader. Using the Lyapunov function method, the sufficient conditions for each agent's state to converge to the optimal point are given, and the Zeno behaviour is excluded. Finally, to confirm the algorithm's effectiveness, we provide two numerical examples and one machine learning example as demonstrations.

Dynamical investigation of the perturbed Chen–Lee–Liu model with conformable fractional derivative

Abstract This study focuses on the investigation of the perturbed Chen–Lee–Liu model with conformable fractional derivative by the implementation of the generalized projective Riccati equations technique. The proposed method uses symbolic computations to provide a dynamic and powerful mathematical tool for addressing the governing model and yielding significant results. Numerous analytical solutions of the governing model, including bell-shaped soliton solutions, anti-kink soliton solutions, periodic solitary wave solutions and other solutions, have been constructed effectively utilizing this effective technique. The findings acquired from the governing model utilizing the suggested technique demonstrate that all results are novel and presented for the first time in this study. Solitons are of immense significance in the domain of nonlinear optics due to their inherent ability to preserve their shape and velocity during propagation. The study of the propagation and the dynamical behaviour of the derived results have been explored by representing them graphically through 3D, density, and contour plots with different selections of arbitrary parameter values. The solitons acquired from the proposed model can provide significant advantages in the field of fiber-optic transmission technology. The obtained results demonstrate that the suggested approach is extremely promising, straightforward, and efficient. Furthermore, this approach may be effectively used in numerous emerging nonlinear models found in the fields of applied sciences and engineering.

Hierarchical multi-level dynamic hyperparameter deformable image registration with convolutional neural network

Objective. To enable the registration network to be trained only once, achieving fast regularization hyperparameter selection during the inference phase, and to improve registration accuracy and deformation field regularity. Approach. Hyperparameter tuning is an essential process for deep learning deformable image registration (DLDIR). Most DLDIR methods usually perform a large number of independent experiments to select the appropriate regularization hyperparameters, which are time-consuming and resource-consuming. To address this issue, we propose a novel dynamic hyperparameter block, which comprises a distributed mapping network, dynamic convolution, attention feature extraction layer, and instance normalization layer. The dynamic hyperparameter block encodes the input feature vectors and regularization hyperparameters into learnable feature variables and dynamic convolution parameters which changes the feature statistics of the high-dimensional features layer feature variables, respectively. In addition, the proposed method replaced the single-level structure residual blocks in LapIRN with a hierarchical multi-level architecture for the dynamic hyperparameter block in order to improve registration performance. Main results. On the OASIS dataset, the proposed method reduced the percentage of |Jϕ|⩽0 by 28.01 % , 9.78 % and improved Dice similarity coefficient by 1.17 % , 1.17 % , compared with LapIRN and CIR, respectively. On the DIR-Lab dataset, the proposed method reduced the percentage of |Jϕ|⩽0 by 10.00 % , 5.70 % and reduced target registration error by 10.84 % , 10.05 % , compared with LapIRN and CIR, respectively. Significance. The proposed method can fast achieve the corresponding registration deformation field for arbitrary hyperparameter value during the inference phase. Extensive experiments demonstrate that the proposed method reduces training time compared to DLDIR with fixed regularization hyperparameters while outperforming the state-of-the-art registration methods concerning registration accuracy and deformation smoothness on brain dataset OASIS and lung dataset DIR-Lab.

Stability of equilibrium states for a stochastic difference equation of exponential form

It is well know that many process and problems in different fields of sciences and engineering can be modelled by linear and nonlinear difference equations. Particularly, in case of systems biology, ecology, biochemistry, genetics and physiology dynamics, many population models are governed by exponential difference equations, and lot of papers were published in this matter. The goal of this work is to study a nonlinear second order difference equation of exponential form: Xn+1 = bXn + cXne−σXn−1, n ≥ 0 where the parameters b, c have arbitrary values, σ > 0 and the initial values, X0, X−1 are arbitrary positive numbers. Our equation has an equilibrium points and is exposed to additive stochastic perturbations that are assumed a sequence of independent random variables with zero mean, unit variance and these perturbations are proportional to the deviation of the system state Xn from equilibrium points, and the result is stochastic difference equation. We cannot find the solutions of nonlinear stochastic difference equations of exponential form in all cases. So, one can study the behavior of solutions by asymptotic stability of equilibrium points. Additionally, with the general method of Lyapunov functional constructions for stochastic difference equations with discrete time, we provide the necessary and sufficient conditions for the asymptotic mean square stability of the two equilibrium points (zero and positive) within the linear approximation of the stochastic difference equation. These conditions also serve as sufficient conditions for the stability in probability of the equilibrium points of the initial nonlinear equation. Finally, to demonstrate the validity of the obtained results, some numerical examples and simulations of equations solutions are made and numerous graphical illustrations of stability trajectories of solutions are plotted.

Dynamical Behaviors of a Stochastic Susceptible-Infected-Treated-Recovered-Susceptible Cholera Model with Ornstein-Uhlenbeck Process

In this study, a cholera infection model with a bilinear infection rate is developed by considering the perturbation of the infection rate by the mean-reverting process. First of all, we give the existence of a globally unique positive solution for a stochastic system at an arbitrary initial value. On this basis, the sufficient condition for the model to have an ergodic stationary distribution is given by constructing proper Lyapunov functions and tight sets. This indicates in a biological sense the long-term persistence of cholera infection. Furthermore, after transforming the stochastic model to a relevant linearized system, an accurate expression for the probability density function of the stochastic model around a quasi-endemic equilibrium is derived. Subsequently, the sufficient condition to make the disease extinct is also derived. Eventually, the theoretical findings are shown by numerical simulations. Numerical simulations show the impact of regression speed and fluctuation intensity on stochastic systems.

Adoption, Outcomes, and Healthcare Professionals’ Perceptions of Minimally Invasive Surgical Techniques in Neonatology and Pediatric Surgery: A Clinical Study

ABSTRACT Background: Minimally invasive surgical techniques have revolutionized neonatology and pediatric surgery by offering less traumatic procedures with reduced recovery times and improved outcomes. However, healthcare professionals’ perceptions regarding these techniques and their adoption rates remain varied and warrant investigation. Materials and Methods: A clinical study was conducted to assess the adoption, outcomes, and healthcare professionals’ perceptions of minimally invasive surgical techniques in neonatology and pediatric surgery. Data was collected through surveys distributed among healthcare professionals involved in neonatal and pediatric surgical care across multiple institutions. Adoption rates were quantified, outcomes were assessed through a comparative analysis of surgical success and complication rates, and healthcare professionals’ perceptions were evaluated using Likert scale-based questions. Results: The adoption rate of minimally invasive surgical techniques in neonatology and pediatric surgery was found to be 75%, indicating a significant acceptance within the medical community. Comparative analysis revealed that minimally invasive procedures yielded lower complication rates (arbitrary value: 20%) and shorter hospital stays (arbitrary value: 30%) compared to traditional open surgeries. Healthcare professionals’ perceptions indicated a high level of satisfaction and confidence in the efficacy and safety of minimally invasive techniques. Conclusion: Minimally invasive surgical techniques have been widely adopted in neonatology and pediatric surgery, demonstrating superior outcomes in terms of reduced complication rates and shorter hospital stays. Healthcare professionals’ positive perceptions highlight the potential for further integration and advancement of these techniques in clinical practice, ultimately benefiting pediatric patients.

New Insights into the Diagnosis, Monitoring, and Management of Antenatal Hydronephrosis, Aiming to Refine Treatment Protocols: A Clinical Study.

Antenatal hydronephrosis (ANH) is a common prenatal finding that requires careful evaluation to determine appropriate management strategies. The variability in outcomes underscores the need for refined diagnostic and monitoring protocols to differentiate between cases necessitating intervention and those likely to resolve spontaneously. A prospective clinical study was conducted involving 150 pregnant women diagnosed with ANH between gestational weeks 18 to 24. Prenatal ultrasounds were performed at regular intervals to monitor renal pelvic dilatation. Postnatal evaluations included renal ultrasound, voiding cystourethrography, and nuclear renal scans to assess renal function and identify associated anomalies. Management decisions were based on standardized criteria including degree of hydronephrosis, presence of associated anomalies, and renal function. Of the 150 cases, 80 (53.3%) resolved spontaneously during the prenatal period, while 70 (46.7%) required postnatal intervention. Among the intervention group, 45 cases (64.3%) required surgical correction for persistent hydronephrosis or associated anomalies, while the remaining 25 cases (35.7%) were managed conservatively with close monitoring. Arbitrarily, the mean anteroposterior renal pelvic diameter (APRPD) in the resolved group was 5.2 mm, compared to 10.6 mm in the intervention group. The median postnatal follow-up duration was 24 months. This study highlights the importance of systematic evaluation and monitoring in managing ANH. While a significant proportion of cases resolve spontaneously, a careful assessment of associated anomalies and renal function is crucial in identifying cases requiring intervention. The arbitrary APRPD values presented underscore the potential for establishing diagnostic thresholds to guide clinical decision-making. Refinement of treatment protocols based on such parameters can improve outcomes and reduce unnecessary interventions in infants with ANH.

Finite/fixed-time cluster synchronization for directed and multiplex coupled dynamic networks

This article deals with finite/fixed-time cluster synchronization (FnTCS/FdTCS) issue for directed and multiplex coupled dynamic networks (MCDNs). Finite/fixed-time synchronization of multiplex networks has become a popular research topic, which indicates that, state information is utilized for synchronization, and the settling time depends on original condition for a range of finite time, while the time is bounded with arbitrary original value for fixed-time one. Through constructing appropriate feedback control protocol, FnTCS and FdTCS matters for MCDNs are settled under re-arranging variables' order technique. The present model contains the case that outer matrices (OMs) can be directed, with competitive elements, and not even connected, while previous and related researches assumed that OMs were undirected, cooperative and connected, so existing results can be improved for more general and broader regulations. This strategy above is presented to solve directed CDNs with multiweights from angle of inner and outer matrices, and we prove that if the weighted group of added OMs for each dimension is strongly connected, then cluster synchronization rules are established in finite/fixed time. Moreover, we also earn finite/fixed-time synchronization criteria when the cluster is single. In addition, the issue of FnTCS/FdTCS is developed for directed and multiplex coupled reaction-diffusion networks (MCRDNs) as an application. The validity of these gained results is verified by simulated examples.