Functional Point Research Articles

Estimating thresholds with the adaptive scan method of psychophysical testing

We previously introduced an adaptive psychophysical method called the adaptive scan (AS) that is readily available in the digital app PART. AS presents multiple progressive tracks (e.g., “scans”) each of which comprises a range of stimulus values whose positioning adapts based on a listener´s performance. Each scan is intended to contain trials above and below a listener´s detection or discrimination threshold for an auditory cue, which is anticipated to increase familiarity with the tested cues. Previously, AS was validated against other known adaptive psychophysical methods (e.g., up-down staircases) and the method of constant stimulus using the QUEST algorithm. QUEST allowed for targeting the same point in the psychometric function (e.g., 80% threshold) in all methods tested. However, the QUEST procedure is parametric, requires many trials, and is not easily applied to the diversity of psychophysical tests that AS can be useful for. Here, we examine a variety of alternative approaches to estimate threshold from the AS procedure. This work adds to the usability of AS in particular and psychophysical testing in general.

A Non-Global Traversal Method for Dynamic Load Rapid Localization and Identification

Dynamic load localization and identification technology is very important in the structural design and optimization of aircraft. This paper proposes a non-global traversal method (NTM) for the fast positioning and recognition of dynamic loads on continuous beams. This method separates the load’s position and amplitude information in the modal space. Then, it constructs an interpolation function about position information, and converts load positioning to solving the zero point of the interpolation function. After determining the position of the dynamic load, the amplitude of the dynamic load is recognized. This method does not need to traverse all the position points globally, thereby greatly improving the efficiency of load positioning. Numerical simulations and experiments show that compared with the original variable separation fast positioning method (VSRPM), this method improves the calculation efficiency by more than 80% while maintaining the same recognition accuracy. NTM is a new method of great application value.

The Critical Analysis of the Lesotho Language Planning and Policy and Its Implications on Education

The paper aimed at analysing the Lesotho language policy to unmask how power is assumed to be exercised by the Lesotho policy-makers through linguistic elements and structure .The main analytical tool of this paper was critical sociolinguistics, using IGMs in Systemic Functional Linguistics, rhetorical strategies and the CDA model in which the paper analysed the relationship between discourse and society. The paper unveiled performativity (mode, censorship and interpellation and the grammatical aspects from the point of functions of co-ordination, modality and nominalisation as effective and dominant principles and tropes used by the Lesotho language policy makers to convince the citizens to acknowledge the language policy irrespective of how it overshadows the minority languages in Lesotho.

Allelic Variations in Vernalization (Vrn) Genes in Triticum spp.

Rapid climate changes, with higher warming rates during winter and spring seasons, dramatically affect the vernalization requirements, one of the most critical processes for the induction of wheat reproductive growth, with severe consequences on flowering time, grain filling, and grain yield. Specifically, the Vrn genes play a major role in the transition from vegetative to reproductive growth in wheat. Recent advances in wheat genomics have significantly improved the understanding of the molecular mechanisms of Vrn genes (Vrn-1, Vrn-2, Vrn-3, and Vrn-4), unveiling a diverse array of natural allelic variations. In this review, we have examined the current knowledge of Vrn genes from a functional and structural point of view, considering the studies conducted on Vrn alleles at different ploidy levels (diploid, tetraploid, and hexaploid). The molecular characterization of Vrn-1 alleles has been a focal point, revealing a diverse array of allelic forms with implications for flowering time. We have highlighted the structural complexity of the different allelic forms and the problems linked to the different nomenclature of some Vrn alleles. Addressing these issues will be crucial for harmonizing research efforts and enhancing our understanding of Vrn gene function and evolution. The increasing availability of genome and transcriptome sequences, along with the improvements in bioinformatics and computational biology, offers a versatile range of possibilities for enriching genomic regions surrounding the target sites of Vrn genes, paving the way for innovative approaches to manipulate flowering time and improve wheat productivity.

L-Cysteine and barium titanate co-modified enteromorpha biochar as effective peroxymonosulfate activator for atrazine treatment

In this study, pyrolysis and hydrothermal methods were used for Enteromorpha biochar that was co-modified with l-cysteine and barium titanate (LBCBa). It has great environmental tolerance and can remove 93.0 % of atrazine (ATZ, 10 mg·L−1) within 60 mins of ultrasonic treatment. The enhanced hydrophilicity, electron-donating capability, and piezoelectricity of LBCBa are considered to induce excellent performance. The apparent reaction rate of the LBCBa-2/PMS/ATZ system with ultrasonic was 2.87 times that without ultrasonic. The density functional theory points out that, introducing l-cysteine to carbon edges improves the adsorption of ATZ and peroxymonosulfate (PMS), making PMS easier to activate. This work offered unique insights for fabricating effective catalysts and demonstrated the combination of hydrophilic functional groups and piezoelectricity in improving catalytic performance and stability.

"On-the-fly" : How to reliably and automatically characterize and construct potential energy surfaces.

In this work, the code, developed previously by the authors to find "holes" as well as legitimate transition states in existing potential energy surface (PES) functions [JPC Lett. 11, 6468 (2020)], is retooled to perform on-the-fly "direct dynamics"-type PES explorations, as well as automatic construction of new PES functions. In all of these contexts, the chief advantage of over other methods is its ability to globally map the PES, thereby determining the most relevant regions of configuration space quickly and reliably-even when the dimensionality is rather large. Here, is used to generate a uniformly spaced grid of density functional theory (DFT) or ab initio points, truncated over the relevant regions, which can then be used to either: (a) hone in precisely on PES features such as minima and transition states, or; (b) create a new PES function automatically, via interpolation. Proof of concept is demonstrated via application to three molecular systems: water (H O), (reduced-dimensional) methane (CH ), and methylene imine (CH NH).

On semi-continuity and continuity of the smallest and largest minimizing point of real convex functions with applications in probability and statistics

We prove that the smallest minimizer σ(f)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sigma (f)$$\\end{document} of a real convex function f is less than or equal to a real point x if and only if the right derivative of f at x is non-negative. Similarly, the largest minimizer τ(f)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ au (f)$$\\end{document} is greater than or equal to x if and only if the left derivative of f at x is non-positive. From this simple result we deduce measurability and semi-continuity of the functionals σ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sigma $$\\end{document} and τ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ au $$\\end{document}. Furthermore, if f has a unique minimizing point, so that σ(f)=τ(f)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sigma (f)=\ au (f)$$\\end{document}, then the functional is continuous at f. With these analytical preparations we can apply Continuous Mapping Theorems to obtain several Argmin theorems for convex stochastic processes. The novelty here are statements about classical distributional convergence and almost sure convergence, if the limit process does not have a unique minimum point. This is possible by replacing the natural topology on R\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathbb {R}$$\\end{document} with the order topologies. Another new feature is that not only sequences but more generally nets of convex stochastic processes are allowed.

A Nonconvex Proximal Bundle Method for Nonsmooth Constrained Optimization

An implementable algorithm for solving nonsmooth nonconvex constrained optimization is proposed by combining bundle ideas, proximity control, and the exact penalty function. We construct two kinds of approximations to nonconvex objective function; these two approximations correspond to the convex and concave behaviors of the objective function at the current point, which captures precisely the characteristic of the objective function. The penalty coefficients are increased only a finite number of times under the conditions of Slater constraint qualification and the boundedness of the constrained set, which limit the unnecessary penalty growth. The given algorithm converges to an approximate stationary point of the exact penalty function for constrained nonconvex optimization with weakly semismooth objective function. We also provide the results of some preliminary numerical testing to show the validity and efficiency of the proposed method.

Radical Resection of Malignant Tumors of Major Salivary Glands: Is This Possible?

In primary therapy, a universally recognized surgical indication applies to all tumors of the salivary glands. According to the classic rule, radical resection of a head and neck tumor requires clean margins of at least 5 mm, although recent studies have shown that for certain locations, 1 mm may be sufficient. In the surgical resection of a tumor of the salivary glands, especially of the parotid gland, can these rules be respected? Owing to the complex branching and connections of the facial nerve within the parotid gland, even a medium-sized malignant tumor may be in contact with a branch of the nerve, thus raising the question of its preservation. The facial nerve is so important from a functional and aesthetic point of view that it is commonly believed that it should be preserved unless it is incorporated into the tumor. This is a compromise between an oncological resection, that is, the complete excision of the tumor with no residual cancer cells left behind, and quality of life. Almost all authors try to overcome this lack of radicality by indicating postoperative (chemo)radiotherapy. In this article, the pros and cons of nerve preservation will be analyzed by examining the published studies on this topic.

Comparative Pharmacological Effects of Lisuride and Lysergic Acid Diethylamide Revisited.

Lisuride is a non-psychedelic serotonin (5-HT) 2A receptor (5-HT2A) agonist and analogue of the psychedelic lysergic acid diethylamide (LSD). Lisuride also acts as an agonist at the serotonin 1A receptor (5-HT1A), a property known to counter psychedelic effects. Here, we tested whether lisuride lacks psychedelic activity due to a dual mechanism: (1) partial agonism at 5-HT2A and (2) potent agonism at 5-HT1A. The in vitro effects of lisuride, LSD, and related analogues on 5-HT2A signaling were characterized by using miniGαq and β-arrestin 2 recruitment assays. The 5-HT1A- and 5-HT2A-mediated effects of lisuride and LSD were also compared in male C57BL/6J mice. The in vitro results confirmed that LSD is an agonist at 5-HT2A, with high efficacy and potency for recruiting miniGαq and β-arrestin 2. By contrast, lisuride displayed partial efficacy for both functional end points (6-52% of 5-HT or LSD Emax) and antagonized the effects of LSD. The mouse experiments demonstrated that LSD induces head twitch responses (HTRs)(ED50 = 0.039 mg/kg), while lisuride suppresses HTRs (ED50 = 0.006 mg/kg). Lisuride also produced potent hypothermia and hypolocomotion (ED50 = 0.008-0.023 mg/kg) that was blocked by the 5-HT1A antagonist WAY100635 (3 mg/kg). Blockade of 5-HT1A prior to lisuride restored basal HTRs, but it failed to increase HTRs above baseline levels. HTRs induced by LSD were blocked by lisuride (0.03 mg/kg) or the 5-HT1A agonist 8-OH-DPAT (1 mg/kg). Overall, our findings show that lisuride is an ultrapotent 5-HT1A agonist in C57BL/6J mice, limiting its use as a 5-HT2A ligand in mouse studies examining acute drug effects. Results also indicate that the 5-HT2A partial agonist-antagonist activity of lisuride explains its lack of psychedelic effects.

Near-optimal tensor methods for minimizing the gradient norm of convex functions and accelerated primal–dual tensor methods

Motivated, in particular, by the entropy-regularized optimal transport problem, we consider convex optimization problems with linear equality constraints, where the dual objective has Lipschitz pth order derivatives, and develop two approaches for solving such problems. The first approach is based on the minimization of the norm of the gradient in the dual problem and then the reconstruction of an approximate primal solution. Recently, Grapiglia and Nesterov [Tensor methods for finding approximate stationary points of convex functions, Optim. Methods Softw. (2020), pp. 1–34] showed lower complexity bounds for the problem of minimizing the gradient norm of the function with Lipschitz pth order derivatives. Still, the question of optimal or near-optimal methods remained open as the algorithms presented in [Grapiglia and Nesterov, Tensor methods for finding approximate stationary points of convex functions, Optim. Methods Softw. (2020), pp. 1–34] achieve suboptimal bounds only. We close this gap by proposing two near-optimal (up to logarithmic factors) methods with complexity bounds O ~ ( ε − 2 ( p + 1 ) / ( 3 p + 1 ) ) and O ~ ( ε − 2 / ( 3 p + 1 ) ) with respect to the initial objective residual and the distance between the starting point and solution, respectively. We then apply these results (having independent interest) to our primal–dual setting. As the second approach, we propose a direct accelerated primal–dual tensor method for convex problems with linear equality constraints, where the dual objective has Lipschitz pth order derivatives. For this algorithm, we prove O ~ ( ε − 1 / ( p + 1 ) ) complexity in terms of the duality gap and the residual in the constraints. We illustrate the practical performance of the proposed algorithms in experiments on logistic regression, entropy-regularized optimal transport problem, and the minimal mutual information problem.

Cooperative Multiagent Reinforcement Learning With Partial Observations

In this paper, we propose a distributed zeroth-order policy optimization method for Multi-Agent Reinforcement Learning (MARL). Existing MARL algorithms often assume that every agent can observe the states and actions of all the other agents in the network. This can be impractical in large-scale problems, where sharing the state and action information with multi-hop neighbors may incur significant communication overhead. The advantage of the proposed zeroth-order policy optimization method is that it allows the agents to compute the local policy gradients needed to update their local policy functions using local estimates of the global accumulated rewards that depend on partial state and action information only and can be obtained using consensus. Specifically, to calculate the local policy gradients, we develop a new distributed zeroth-order policy gradient estimator that relies on one-point residual-feedback which, compared to existing zeroth-order estimators that also rely on one-point feedback, significantly reduces the variance of the policy gradient estimates improving, in this way, the learning performance. We show that the proposed distributed zeroth-order policy optimization method with constant stepsize converges to the neighborhood of a policy that is a stationary point of the global objective function. The size of this neighborhood depends on the agents' learning rates, the exploration parameters, and the number of consensus steps used to calculate the local estimates of the global accumulated rewards. Moreover, we provide numerical experiments that demonstrate that our new zeroth-order policy gradient estimator is more sample-efficient compared to other existing one-point estimators.

Evaluating urban mini plant factories: engineering and software cost perspectives for agriculture sustainability

Precision agriculture serves as a crucial solution to address the challenges of food security and agriculture sustainability. It provides significant benefits and enables effective monitoring of agriculture throughout the entire supply chain using a technology-driven approach that prioritizes internet connectivity and leverages big data. A noteworthy application of precision agriculture is the Mini Plant Factory, where plants are cultivated in closed systems with artificial lighting. The development of the Mini Plant Factory requires an economic feasibility analysis as a determinant of technology viability before widespread implementation, aiming to promote agriculture sustainability. The Software Cost Estimation Model (SCEM) assesses software development’s cost and time requirements. Engineering economics evaluates economic feasibility using metrics like NPV, BCR, IRR, PBP, and BEP methods. Function Point Analysis for UMPF software development estimates a cost of Rp 33,052,414, equivalent to 1,311 man-hours. Investment feasibility analysis considers the utilization of UMPF as viable, with an NPV of IDR 46,938,615, BCR of 1.08, IRR of 28%, and projected profitability within four years. Precision agriculture strategically addresses complex agricultural challenges, fostering sustainability with innovations such as the UMPF. The SCEM and engineering economics confirm the feasibility and rationale for implementing UMPF technology, providing essential insights for sustainable agricultural practices.

Complex Function Solution of Stratum Displacements and Stresses in Shallow Rectangular Pipe Jacking Excavation Considering the Convergence Boundary

The construction of pipe jacking has little impact on the environment and is usually used to build underground passages with shallow buried depths and short lengths. Compared with circular pipe jacking, rectangular pipe jacking has the advantages of shallow buried depth and high space utilization. Therefore, research on the excavation of rectangular pipe jacking is necessary. This paper establishes a cross-section model of shallow buried rectangular pipe jacking excavation. Taking advantage of complex functions for solving problems involving non-circular tunnels, an analytical solution is obtained using an approximate mapping function and potential functions in series forms for the stress and displacement of the stratum with a displacement condition at the excavation boundary and a stress condition at the ground surface boundary. The finite element simulation results and the engineering-measured data are used for comparisons and verifications. With the analytical solution of the complex function, the influence of selecting control points for the mapping function on the accuracy is calculated and analyzed, as well as the influence of the stratum loss rate, span, buried depth, and stratum unit weight on surface subsidence and major principal stress of the excavation boundary. The proposed analytical solution can be applied to the construction of rectangular pipe jacking tunnels.

Nonparametric Bayesian functional clustering with applications to racial disparities in breast cancer

AbstractAs we have easier access to massive data sets, functional analyses have gained more interest. However, such data sets often contain large heterogeneities, noises, and dimensionalities. When generalizing the analyses from vectors to functions, classical methods might not work directly. This paper considers noisy information reduction in functional analyses from two perspectives: functional clustering to group similar observations and thus reduce the sample size and functional variable selection to reduce the dimensionality. The complicated data structures and relations can be easily modeled by a Bayesian hierarchical model due to its flexibility. Hence, this paper proposes a nonparametric Bayesian functional clustering and peak point selection method via weighted Dirichlet process mixture (WDPM) modeling that automatically clusters and provides accurate estimations, together with conditional Laplace prior, which is a conjugate variable selection prior. The proposed method is named WDPM‐VS for short, and is able to simultaneously perform the following tasks: (1) Automatic cluster without specifying the number of clusters or cluster centers beforehand; (2) Cluster for heterogeneously behaved functions; (3) Select vibrational peak points; and (4) Reduce noisy information from the two perspectives: sample size and dimensionality. The method will greatly outperform its comparison methods in root mean squared errors. Based on this proposed method, we are able to identify biological factors that can explain the breast cancer racial disparities.

FORMATION OF THE ADMINISTRATIVE MANAGEMENT SYSTEM OF ASSETS AND LIABILITIES OF A BANKING INSTITUTION IN THE STRATEGIC ASPECT

The article examines the essence of the process of managing assets and liabilities of a banking institution. The works of ukrainian and foreign scientists devoted to issues of asset and liability management systems were studied and analyzed. The essence of the concept of the structure of assets and liabilities is determined. The main strategies for managing the bank's assets and liabilities have been identified - the asset management strategy, the liability management strategy, and the combined strategy.
 The purpose of the article is the formation of the formation of the system of administrative management of assets and liabilities of a banking institution. The main tasks of a comprehensive strategy and its important elements are defined. Two basic groups of asset and liability management methods are highlighted - methods of managing a certain risk and methods of modeling the optimal balance sheet structure. The shortcomings inherent in both groups were analyzed.
 It is proposed to use, in addition to classic digital methods, tools for influencing the structure of the bank's assets and liabilities. A diagram of the asset and liability management system from a functional point of view has been created. In order to effectively manage a banking institution, it is proposed to include digital tools for influencing the structure of assets and liabilities to the tools of the asset and liability management system in order to obtain maximum profit while maintaining reliability. For the formation of the MAL system, it is proposed to implement the following digital elements: implementation of the biometric system of online banking; integration with the Diya platform; distribution and promotion of the use of Visa pay-Wave cards; expansion and adaptation of POS lending (including biometric identification of the recipient) using POS terminals; expansion of online banking functionality. Their influence on the three main factors determining the degree of profit of a banking institution is determined.
 In the course of the analytical work, it was found that an important tool in the asset and liability management strategy is bank digitalization. Using digital technologies, banking institutions have the opportunity to reach a completely new level, providing innovative services and services to clients. Despite the fact that these directions have received active development in recent years, their potential has not yet been exhausted. The impact of digitalization provides significant benefits to banks and improves their attractiveness. This, in turn, provides stability to the banking institution and the ability to quickly adapt to unpredictable changes in the market. Thus, using digital tools as part of the formation of the asset and liability management system, it is possible to directly influence their structure and attract a larger number of customers, which directly affects the bank's profitability.

Untrained neural network embedded Fourier phase retrieval from few measurements

Fourier phase retrieval (FPR) is a challenging task used in various applications to recover an unknown signal from its Fourier phaseless measurements. FPR with few measurements helps reduce time and hardware costs but suffers from severe ill-posedness. Recently, untrained neural networks have offered new approaches by introducing learned priors to alleviate ill-posedness without requiring external data. However, they are computationally expensive and not ideal for reconstructing high-frequency structures in images. This paper proposes an untrained neural network (NN) embedded FPR algorithm, based on the alternating direction method of multipliers. Specifically, we use a generative network to represent the image to be recovered, which confines the image to the space defined by the network structure. Additionally, total variation regularization is imposed to facilitate the preservation of image edges and local structures. Furthermore, to reduce the computational cost mainly caused by the updates of NN’s parameters, we develop an accelerated algorithm that adaptively trades off between explicit and implicit regularization. We theoretically analyze that the proposed algorithm can converge to a stationary point of the objective function under mild conditions. Experimental results indicate that the proposed algorithm outperforms existing untrained-NN-based algorithms with fewer computational resources and even performs competitively against trained-NN-based algorithms.

Preference-based multi-objective evolutionary algorithm with linear combination scalarizing function and reference point adjustment

In practice, the decision-maker (DM) may be only interested in a particular part of Pareto optimal front (PF). For this reason, many preference-based multi-objective evolutionary algorithms (MOEA) have been proposed to find a solution set that approximates the region of the interest (ROI). Most existing preference-based methods focus on selecting solutions in the ROI. Nevertheless, the enhancement of convergence in preference-based MOEAs has been neglected. Most decomposition-based approaches often employ the achievement scalarizing function (ASF) as their scalarizing function. However, it holds a weaker search ability than the weighted sum function (WSF) despite its capability to tackle problems with arbitrary PF geometries. In order to strengthen the selective pressure toward the PF, this paper proposes a new scalarizing function, LSF, which is a linear combination of the WSF and the ASF. Then, a simple adaptive penalty scheme is employed in LSF to balance the search ability and robustness. To focus the search on the ROI, we develop a reference point adjustment method that dynamically adjusts the position of the reference point according to the distance from the approximated target point. We apply the above two innovations to the MOEA/D framework and propose a new preference-based MOEA, namely RAMOEAD. Experimental results show that RAMOEAD is highly competitive when compared with five state-of-the-art preference-based MOEAs. Finally, the proposed algorithm is extended to double reference points for solving the problems in which the ROIs are defined by the reservation and aspiration points.

MULTI-OBJECTIVE OPTIMIZATION AND PERFORMANCE ANALYSIS OF BIMORPH MAGNETO-ELECTRO-ELASTIC ENERGY HARVESTERS

This study thoroughly investigates the multi-objective optimization of a magneto-electro-elastic (MEE) harvester in bimorph configurations and by the new method of Harris Hawk’s optimization (HHO). The harvesters are configured in both series and parallel connections and under harmonic excitation to explore the effects of various parameters on the performance of the harvesting system. The primary objective is to maximize the total harvested power. Optimization involves various parameters, including dimensions, relative displacement changes, voltage, and current values. The Pareto fronts from the HHO method reveal optimal points in different configurations and scenarios. Notably, the optimal points are selected based on the criterion of maximum total power. The results reveal distinct optimal points for each objective function, demonstrating trade-offs between performance metrics. These findings provide valuable insights into the design and operation of efficient energy harvesters in MEE systems. The parallel configuration outperforms the series connection in terms of the current generation. Moreover, the evaluation of the overall performance of the energy harvesters in terms of total harvested power indicated that both series and parallel connections could lead to promising outcomes. However, the series connection exhibited a more dominant effect on maximizing the total harvested power, proving its relevance in pursuing the highest possible power output.

Regression Depth for Statistical Depth Function

The statistical depth function is one of the modern approaches that can be used for developing multivariate robust regression based on robust estimates of the location and dispersion matrix. One merit advantage of the depth concept is that it can be used directly to provide deeper estimation functions for data location and regression parameters in a multidimensional environment. The deeper estimation functions induced by depth are expected to inherit the desired and inherent robustness properties (such as limited maximum bias, impact function, and high breaking point) as do their counterparts at univariate sites. Investigation. The main objective of this article is to check the power of the statistical depth function throw the depth regression, it turns out that the deepest functional projection possesses a finite effect function and the best possible asymptotic breakpoint as well as the best breaking point of a finite sample compared with some classical and robust existed method.