Projection Technique Research Articles

Projective Psychological Tests from the Point of View of Neural Network Theory of Society

It is shown that the issues raised by the international expert community in the discussion regarding the legality of using projective techniques (in particular, tests such as the Luscher test, the Szondi test and the Dellinger test) can be resolved on the basis of an adequate interpretation of the concept of “archetype” and an analogy with neural networks. At the same time, the interpretation of the concept “archetype” is based on the neural network theory of society, which allows us to remove the difficulties that arise with the traditional interpretation of this concept. It is shown that there is an equivalent scheme for the testing procedure, in which the testing itself can be reduced to the functioning of the external (output) layer of the general neural network, which also includes a neural network formed by the human brain. This approach makes it possible to remove many of the criticisms put forward against the use of projective techniques (even declaring them pseudoscientific), but it implies a significant change in existing approaches to the interpretation of results obtained when using tests of the type in question. Namely, within the framework of the proposed approach, not every possible combination of images on which the test is built makes sense. Such a meaning can be given only to some of them, specifically to those that are most often encountered in experiments. Such combinations, which can be interpreted as basic, are interpreted on the basis of an analogy with images recognized by a neural network. The remaining combinations are treated as images containing errors; they are reduced to the basic ones based on an analogy with the methods used in constructing error-resistant codes.

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.

An improved Dai‐Liao‐style hybrid conjugate gradient‐based method for solving unconstrained nonconvex optimization and extension to constrained nonlinear monotone equations

In this work, for unconstrained optimization, we introduce an improved Dai‐Liao‐style hybrid conjugate gradient method based on the hybridization‐based self‐adaptive technique, and the search direction generated fulfills the sufficient descent and trust region properties regardless of any line search. The global convergence is established under standard Wolfe line search and common assumptions. Then, combining the hyperplane projection technique and a new self‐adaptive line search, we extend the proposed conjugate gradient method and obtain an improved Dai‐Liao‐style hybrid conjugate gradient projection method to solve constrained nonlinear monotone equations. Under mild conditions, we obtain its global convergence without Lipschitz continuity. In addition, the convergence rates for the two proposed methods are analyzed, respectively. Finally, numerical experiments are conducted to demonstrate the effectiveness of the proposed methods.

Fabrication tolerant multi-layer integrated photonic topology optimization

Optimal multi-layer device design requires consideration of fabrication uncertainties associated with inter-layer alignment and conformal layering. We present layer-restricted topology optimization (TO), which we believe to be a novel technique which mitigates the effects of unwanted conformal layering for multi-layer structures and enables TO in multi-etch material platforms. We explore several approaches to achieve this result compatible with density-based TO projection techniques and geometric constraints. Then, we present a robust TO formulation to design devices resilient to inter-layer misalignment. The novel constraint and robust formulation are demonstrated in 2D grating couplers and a 3D polarization rotator.

Gauss-Seidel Type Iterative Algorithm for a Generalized System of Extended Non-linear Variational Inequalities

This study is focused on a new generalized system of extended non-linear variational inequalities (GSENVI, for short) involving 3k-distinct non-linear relaxed cocoercive operators. We give the equivalent formulation of GSENVI in a more convenient form by using auxiliary principal technique. Through the projection technique, we demonstrate that the non-linear projection equations are analogous to equivalent form of GSENVI. By the use of alternative fixed point formulations, we proposed the k-steps Gauss-Seidel type iterative algorithms to obtain an approximate solution of the GSENVI. Further, we discuss the convergence of proposed k-step Gauss Seidel type iterative algorithms. Several special cases of GSENVI are discussed for the reliability of our findings.

Inertial subgradient projection techniques for solving a class of bilevel equilibrium problems

ABSTRACT In this paper, we introduce a new algorithm for solving bilevel equilibrium problems with nonexpansive and pseudocontractive mappings in a real Hilbert space. The proposed algorithm is based on subgradient method with Armijo-type linesearch process, subgradient method, and inertial projection techniques. By choosing the suitable regular parameters, we prove strong convergence of the algorithm under classical conditions of the cost bifunctions.

Spatial coding strategy for dual-frequency phase-shifting profilometry

Dual-frequency fringe projection techniques have been broadly utilized for three-dimensional (3D) shape recovery. However, a pervasive challenge across these methodologies lies in the precise implementation of high-speed measurements. This paper explores a spatial coding strategy designed for the dual-frequency phase unwrapping method to tackle this. The strategy mandates the utilization of only four patterns, encapsulating the phase information of both high and low frequencies. The codewords are strategically embedded within the low-frequency phase, facilitating the acquisition of an accurate absolute phase map. A robust decoding algorithm engineered to ensure dependable phase unwrapping, particularly in scenarios characterized by a substantial number of high-frequency cycles. The proposed method exhibits superior noise immunity and enhances accuracy when compared with the previous dual-frequency phase-shifting methodology. Simulations and experiments demonstrate the robustness and efficiency of the proposed strategy.

Drawn Stories Technique: Method and Concluding TherapeuticTurn

Summary The developmental age is often characterized by problems of somatization of psychological problems and conflicts: Anorexia, enuresis, encopresis and persistent constipation. The Drawn-Story (DS) technique presented in this article was developed to enhance and support the narrative-dialogic relationship in the psychodiagnostic and psychotherapeutic context – initially primarily for work with children of developmental age, but later also for other patient groups. It is a projective drawing technique that was developed by Giancarlo Trombini in the 1970s based on his training in Gestalt psychology and psychoanalysis at the University of Bologna and has since been further developed by him, Elena Trombini and their colleagues and also used in other fields of application. This article uses an early case history of DS to explore central aspects of this technique in greater depth. It also explores the question of whether the Concluding Therapeutic Turn observed in therapies with adults can also be observed in developmental age therapy according to the criterion of reconciliation of time perspectives.

Projection superimposition for the generation of high-resolution digital grating.

Fringe projection profilometry based on MEMS micro-vibration mirrors is very promising due to its rapid projection, large depth of field, compact size, and low cost. Although high-frequency fringes can achieve accurate reconstruction, the projector must offer sufficient pixel resolution. In this paper, we proposed a high-resolution projection technique called the delay superposition method. During a single exposure time of the camera, the projector projects a group of low-resolution fringe patterns, which are delayed according to the movement characteristics of the vibration mirror. Then, the camera exposure superimposes these low-resolution images to form a high-resolution image. These two steps effectively subdivide the angle intervals, thereby achieving a pixel interpolation. Finally, experimental results show that the proposed method can significantly improve the projector's pixel resolution and reconstruction accuracy. The proposed method allows the MEMS projector's pixel resolution (along one direction) to far exceed that of common DLP projectors. It holds great application potential for high-frequency fringe projection.

New Parameters of the Conjugate Gradient Method to Solve Nonlinear Systems of Equations

The conjugated gradient methods can solve smooth functions with large-scale variables in the specified number of iterations for that they are highly important methods compared to concerning other iterative methods. In this paper, we propose two new conjugate gradient methods, namely the PMDL-1 and PMDL-2. However, for non-smooth functions, which are called conjugate gradient-free derivative methods depending on the projection technique. The two methods give great results compared to the basic PDL method. Moreover, we provide theorems that prove the global convergence between these two methods.

Projective techniques: in search of an alternative to validity and reliability

Projective techniques: in search of an alternative to validity and reliability

Analysis of Macronutrients in Soil Using Impedimetric Multisensor Arrays.

The need to increase food production to address the world population growth can only be fulfilled with precision agriculture strategies to increase crop yield with minimal expansion of the cultivated area. One example is site-specific fertilization based on accurate monitoring of soil nutrient levels, which can be made more cost-effective using sensors. This study developed an impedimetric multisensor array using ion-selective membranes to analyze soil samples enriched with macronutrients (N, P, and K), which is compared with another array based on layer-by-layer films. The results obtained from both devices are analyzed with multidimensional projection techniques and machine learning methods, where a decision tree model algorithm chooses the calibrations (best frequencies and sensors). The multicalibration space method indicates that both devices effectively distinguished all soil samples tested, with the ion-selective membrane setup presenting a higher sensitivity to K content. These findings pave the way for more environmentally friendly and efficient agricultural practices, facilitating the mapping of cropping areas for precise fertilizer application and optimized crop yield.

Challenges in Integrating Demographic Variables into Local Government Authorities’ Development Plans

This paper examines the Challenges in Integrating Demographic Variables into Local Government Authorities’ Development plans in Chemba and Mpwapwa district councils. The study population was LGA’s development planning officers. The study adopted a cross-sectional research design in which both qualitative and quantitative data from planning officers were collected. Descriptive statistics (Univariate analysis) was done to explore the characteristics and distribution of respondents presented in frequencies and percentages. Cross-tabulation with chi-square (χ2) test tested the association of variables at a 0.05 (95%) significance level. The study findings revealed that LGA planning officers face several challenges in integrating population variables into development plans. Such challenges are Institutional-based (Scarcity of data, lack of political commitment to the goal, limited access to computing facilities, and inadequacy of statistical sources. Resource-based (Unclear relevance of the move among development planners, Continuing discussions on the best ways can use population data in development planning, Lack of clear understanding of demographic variables that can be integrated into the development plans in different sectors, Inadequate conceptualization and understanding of the operation and effects of population variables, lack of sufficient expertise to prepare needed projection inputs). Planning process based (Bureaucratic structures of centralized planning offices; create a barrier between planners and the public) Relying on secondary data from socio-economic profiles, too many directives (central government priories).Technical-based (unclear approaches of integrating population issues into development plans, lack of appropriate methodology, lack of planning and projection techniques, missing manual on the methodology, inadequate research into the many facets of the demographic processes and of their interrelations with other social and economic processes. The chi-square (2) test of the findings revealed no significant (P>0.05) statistical variation by LGAs on the faced challenges in integrating population variables into development plans. The study concludes that institutional setup, resource constraints, the nature of the planning process, and some technical issues affect LGA’s in coming up with effective and comprehensive development plans that cope with the area-specific aging population. The findings require the LGAs to consider putting more effort into the reliable sources of data, knowledge, and skills of planners, planning tools, and planning approaches in order to come up with good and realistic development plans that foster increasing local economic growth and improve the living standard of people; that slow down youth rural-urban migration due to low economic efficiency in their places of origin. The study recommends that LGAs in collaboration with the parent Ministry have to design the means of curbing the encountered planning challenges including improving awareness and sources of data for planning purposes, reviewing the planning approach by making it rather horizontal and comprehensive instead of being vertical from central government policies because obstacles and opportunities for development are area specific, and planners should get acquainted with methodologies for integrating population variables into development plans.

Use of distinct projective techniques in investigating participants' perception of a clean label dairy product: A study on the presence of additives/stabilizers in Ultra high temperature processing milk's label in Brazil

AbstractUsing an online questionnaire, the perception of additives/stabilizers in ultra‐high temperature (UHT) milk was investigated using different projective techniques. Clustering data on the Food Choice Questionnaire (FCQ) identified two groups of participants, Moderates and Judicious, with the latter assigning significantly higher agreement scores for all FCQ items. In the Word Association task, clean label UHT milk was more associated with “Nutrients and Constituents” by the Moderates and less by the Judicious, suggesting that for part of the interviewed participants, the absence of stabilizers increases the general quality of the product. In the Product Personality Profiling task, the same product was related to “young people” and a “balanced diet” by the Moderates. At the same time, the Judicious was designed for a stereotype of healthy living. Finally, the methodologies used provide valuable insights into the dairy sector, holistically highlighting the nuances in consumer preferences and expectations, offering a significant strategic opportunity for developing and promoting new clean‐label products in the segment.Practical ApplicationInvestigating consumer perceptions regarding the absence of additives offers valuable insights for marketing strategies and product development aimed at different consumer market segments, especially the dairy sector, and contributes to consumer psychology and behavioral research. At the same time, the food industry can use these findings to improve attribute communication, build consumer confidence, and adapt products to identified preferences, reflecting a practical intersection between academia and the industry.

Understanding food consumer behavior using projective methods and the big five personality traits model: The case of traditional Mexican cheeses

AbstractThis research aimed to use two projective methods and the Big Five Personality Traits (BFPT) model to study food consumer behavior in the case of traditional Mexican cheeses. Based on an online survey (n = 197), this study employs the Word Association and Mason‐Haire's Shopping List projective techniques with two shopping lists (traditional vs. supermarket). Several factors influencing consumers' perceptions of traditional cheeses were identified, such as hedonism, sensory characteristics, quality and freshness. The shopping list allowed the identification of factors related to food consumption and consumer personality traits. Conscientiousness and Neuroticism were associated with the profile of the consumer who purchases food in supermarkets. In contrast, the personalities of Agreeableness and Openness were associated with the profile of the consumer of traditional Mexican cheeses. The results of this research could be helpful in promoting and marketing traditional foods, considering consumers' personality traits.Practical applicationsThis research identified consumer perceptions of traditional cheeses produced in the central region of Mexico and the personality traits associated with the consumer profile of these food products. The results can be of great use to the cheese‐producing agroindustry, considering that consumers are aware that by purchasing these products, they are contributing to the development and support of the local economy. Therefore, it is essential for producers and sellers to consider the attributes that consumers associate with traditional cheeses, such as artisanal and local characteristics, hedonic value, and consumers' personality traits.

A PROJECTION-BASED ERROR ANALYSIS OF HDG METHODS FOR A NONLINEAR SYSTEM: COUPLED IN BOTH DIRECTIONS

A technique for the error analysis of hybrid discontinuous Galerkin methods (HDG) is applied to a coupled problem. The technique relies on the use of a projection whose design is inspired by the numerical traces of the methods. When this technique appeared in the literature (Cockburn et al., 2010), the authors performed an analysis for an elliptical problem. In this work, we will analyze two coupled elliptical subproblems. The main idea is to apply this projection technique, defined based on the shape of the numerical traces, in the numerical analysis of the HDG method for the coupled problem to verify whether this numerical analysis technique still maintains its main characteristics, such as simplicity and consistency, even with this coupling. The analysis of the coupled problem in two directions was carried out following the strategy of first analyzing the partially coupled problem (De Oliveira, 2024), and then the coupled problem in both directions. The differences between both problems were the analytical development of the coupling and the computation of the approximate solution, which in the problem treated here requires a fixed point algorithm. We expect that the orders of convergence for the approximate solutions correspond to theoretical expectations with the approximation spaces used, which are made up of natural polynomials, that is, order k for vector variables and k+1 for scalar variables. All theoretical and and experimental objectives were achieved, i.e., the convergence in the HDG simulations corresponded to what was theoretically expected.

Dynamic Interferometry With Retrace Error Correction Using Fringe Projection For High-Gradient Fields

This paper introduces an innovative approach aimed at advancing the characterization of high-gradient flow fields through the integration of dynamic interferometry and fringe projection techniques. Traditional interferometry offers a precise tool sensitive to optical path changes, typically used to measure refractive index variations induced by factors such as density changes in fluid flow. Rays are usually considered as straight lines, and refraction can be neglected. However, in scenarios involving high-gradient fields, such as supersonic flow with shock waves, optical path changes due to ray bending become significant. In these high-gradient fields, the trajectory of the ray is altered, leading to longer optical paths (resulting in incorrect values) and geometric distortions of the image (resulting in inaccuracies in position). Although retrace error corrections using numerical models of refractive index distribution can mitigate some effects, complete compensation is often challenging. To address this, our proposed technique integrates fringe projection, which is highly sensitive to ray deflections caused by variations in the index of refraction within a transparent medium. The method involves projecting a precisely defined multiplexed cosine fringe pattern across the measured area. Modifications in the pattern indicate ray bending, providing data for interferometric corrections. Real-time interferometry is seamlessly combined with the fringe projection technique to compensate for optical path length changes and mitigate mapping errors induced by ray deflections. The dynamic nature of this combined approach enables the instantaneous capture of both interferometric and fringe-projection data, making it a suitable tool for real-time measurements. Experimental verification of the technique demonstrates its efficacy, with a comparative study against traditional interferometry showcasing a significant reduction in mapping errors.

Beurling dimension of spectra for a class of random convolutions on [formula omitted]

It is usually difficult to study the structure of the spectra for the measures in R2 and higher dimensions. In this paper, by employing the projective techniques and our previous results on the line we prove that the Beurling dimension of spectra for a class of random convolutions in R2 satisfies an intermediate value property.

Single-frame fringe pattern analysis with synchronous phase-shifting based on polarization interferometry phase measuring deflectometry (PIPMD)

In the domain of phase measuring deflectometry (or fringe projection profilometry), utilizing only a single-frame fringe pattern to achieve high-precision three-dimensional reconstruction has emerged as a focal point of ongoing research. To achieve four-step phase-shifting demodulation from a single-frame fringe pattern, this paper proposes a Polarization Interferometry Phase Measuring Deflectometry (PIPMD). This method primarily relies on a Michelson polarization interferometry structure to produce projected polarization interference fringes, which are then captured by a polarization camera as modulated single-frame deformed fringe patterns. These single-frame fringe patterns enable pixelated four-step phase shifting with adjacent 2 × 2 pixel units. To validate the proposed method, a series of experiments has been conducted, including surface shape detection of a concave spherical mirror and an off-axis parabolic mirror, as well as dynamic deformation measurements of a deformable mirror. All experimental results consistently indicate that the polarization interference-based fringe projection technique can achieve synchronized phase-shifting demodulation of single-frame fringe patterns, thereby facilitating high-precision reconstruction of the fringe patterns captured in a single frame. This synchronous phase-shifting technique can overcome the influence of air disturbances in traditional four-step phase-shifting methods, thereby enhancing the accuracy of phase demodulation. Additionally, this polarization interference-based Phase Measuring Deflectometry exhibits promising application prospects in dynamic measurements.

"Can I Play Too?" A Qualitative Study of Outdoor Play and Participation Among Autistic Preschoolers.

Outdoor play in homes, schools, and communities provides children with unique opportunities to explore their worlds, develop fundamental life skills, and experience belonging. However, few studies have explored outdoor free play among autistic preschoolers in natural settings from a neurodivergent-informed perspective. To explore the play preferences, opportunities, and challenges in outdoor play for autistic preschoolers. In this qualitative study, the authors used a multimethod approach to data collection using visual, verbal, and projective techniques and thematic analysis to identify and describe outdoor play occupation as expressed by autistic preschoolers. Home, community, and preschool environments in a city in Ireland. Seven autistic children and their parents, from seven diverse preschool settings in Ireland. Two overarching themes were identified: (1) outdoor play preferences and meaning and (2) the physical and social environments of outdoor play. The findings suggest that autistic preschoolers demonstrate distinctive play styles and preferences when playing freely outdoors, with physical and social barriers to outdoor play existing in community and educational contexts. The findings suggest that autistic preschoolers' outdoor play styles and preferences require support from adult advocates. Although the importance of relationships and social play cannot be overlooked, infrastructural accommodations for parents and schools are required if we are to create supportive and inclusive outdoor play environments and opportunities for freedom of expression for autistic children. Plain-Language Summary: This study explored the distinctive outdoor play preferences, opportunities, and challenges for autistic preschoolers. The findings show that autistic preschoolers face physical and social barriers to outdoor play and that they need parents, schools, and communities to create supportive and inclusive play environments and opportunities for freedom of expression.