Reciprocal Problem Research Articles

A geometric view of seismic wavefields: implications for imaging dense clusters of events

SUMMARY Imaging dense clusters of seismicity is crucial to many problems in seismology: to delineate complex systems of faults, provide constraints on the causes of volcanic and cryogenic swarms, and to shed light on possible means to prevent damaging induced seismicity in mining, geothermal, and oil and gas extraction activities. Current imaging methods rely upon high-resolution relative location techniques, commonly requiring arrival-time picks for seismic phases. This paper examines an alternative approach, based upon concepts drawn from differential geometry, that images directly from waveform data. It relies upon the common assumption of spatial continuity of seismic wavefield observations, which implies that a differentiable map exists between the source region to be imaged and waveform observations considered as elements of a vector space. The map creates an image of event clusters on a Riemannian manifold embedded in that vector space. The image can be visualized by projecting the observations into a tangent space of the manifold and is a distorted rendering of cluster geometry. However, the distortion can be predicted and removed if a model for wavefield propagation is available. This visualization approach is applicable to clusters of uniform events with highly similar waveforms, such as are commonly acquired with correlation detectors or other pattern matching techniques. To assess its performance, it is applied to the closely related reciprocal problem of imaging the (known) geometry of an array from observations by the array of several regional events. Differences between the original problem and its reciprocal analogue are noted and controlled for in the analysis. Chief among the differences is the necessity for aligning the waveforms in the original problem, which, to maintain consistency with the original problem, is solved in the reciprocal problem by a generalization of the VanDecar–Crosson algorithm. The VanDecar–Crosson algorithm exhibits a bias, shown through an analysis of the situation when the observed wavefields are adequately modelled as plane waves. In that circumstance, the bias can be predicted and removed. In a test using a portion of a large-N array, this imaging approach is shown to successfully reconstruct the array geometry. The method is applicable directly to infinitesimal array apertures, but is extended to a larger aperture by partitioning the image into local, effectively infinitesimal overlapping subsets. These are inverted, then assembled into a global picture of the array geometry using constraints provided by the overlapped regions. Although demonstrated in a reciprocal array context, the method appears viable for imaging clusters of events with highly similar source mechanisms and time histories.

Design of a locally resonant system to reduce noise inside the payload fairing of a launcher during the lift-off

The high sound pressure exerted on the payload during the launch of space vehicles can jeopardize its structural integrity. Given space and weight restrictions, designing fairing noise protection systems is not easy and the number of alternatives is limited, especially for small launchers. This work proposes the design of an acoustic protection based on an simultaneous increase of insulation and absorption in the system tailored to the payload fairing of a space launcher. To this end, the use of a panel made of Helmholtz resonators is investigated. The panel presents a deep subwavelength thickness, as well as a highly efficient acoustic protection (90% of absorption and 13 dB of Transmission Loss) over the frequency range of interest. The panel is designed by considering a reciprocal and non mirror symmetric transmission problem and the acoustic incidence from both sides of the panel. A high Transmission Loss in the frequency range of interest is then obtained when considering an incidence coming from the outside of the payload fairing, whereas the quasi-perfect absorption of acoustic waves is observed in the case where the incidence comes from the inside of the fairing. The panels are subsequently prototyped and their performance is experimentally evaluated. Measurements are correlated and discussed in view of the theoretical and numerical predictions. This mitigation approach sets a new trajectory for innovative noise reduction in small-scale space launchers.

Reciprocal sensitivity kernels for receiver positioning

In their classical formulation, sensitivity kernels aim to evaluate the points where an infinitesimal variation in the properties of the medium would most affect a pressure (or displacement) measurement at a fixed location. These kernels feature typical cigar shapes, with characteristically low sensitivity on the direct path. In this presentation, the same approach is applied to the reciprocal problem, where we want to evaluate, at a constant source position, which points are the most (or least) sensitive to a given model change. These reciprocal kernels exhibit flared shapes centered on the areas where the model is perturbed. Applications to receiver positioning in acoustic are discussed.

Strong reciprocal ratio consensus of modified second-order multi-agent systems with periodically time-varying topologies

The strong reciprocal ratio consensus problem of modified second-order discrete-time multi-agent systems (DTMASs) with periodically time-varying topologies is investigated. The strong reciprocal ratio consensus is a new consensus and covers the strong ratio average-consensus as a special case. Modified second-order DTMAS is a variant of second-order DTMAS. A distributed control protocol is designed to achieve the strong reciprocal ratio consensus and it is the first time that ratio strategy is combined with second-order DTMASs. Furthermore, our work covers several cases where dynamically changing topologies are directed or undirected, connected or disconnected, or even mixed patterns of connected and disconnected graphs.

The reciprocal elastic net

A new penalized likelihood method (reciprocal elastic net) is put forward for regularization and variable selection. Our proposal is based on a new class of reciprocal penalty functions, combining the strengths of the reciprocal LASSO regularization and ridge regression. We formulate the reciprocal elastic net problem as an equivalent reciprocal LASSO problem on augmented data, facilitating a direct utilization of the reciprocal LASSO algorithm to generate the entire reciprocal elastic net solution path. We further present the reciprocal adaptive elastic net, fusing the merits of ridge regression with the adaptively weighted reciprocal LASSO regularization. These methods, illustrated through simulated examples and real data analysis, demonstrate satisfactory performance in various diversified scenarios compared to published methods. Finally, we propose Bayesian methods to solve the reciprocal elastic net and reciprocal adaptive elastic net models using Gibbs samplers.

МАТЕМАТИЧЕСКАЯ МОДЕЛЬ ОПЕРАТИВНОСТИ РЕМОНТА АВТОМОБИЛЬНОЙ ТЕХНИКИ

The use of a probabilistic approach is proposed in the modeling task. Several repeatable groups of the same type of operations are considered - the search for the cause of failure and its elimination. Based on the experience of previous repairs of the same type of car components, the distribution series of values Pm (probability of repair of certain nodes) and Pn (probability of failure of certain nodes) are set. The model takes into account the qualifications of engineers and technicians of the service station, the availability and capabilities of mobile and stationary monitoring and repair facilities. After determining the probability of correct troubleshooting and planning a certain algorithm of maintenance operations, the repair efficiency is estimated as the ratio of the probabilities of performing repairs for a given time and the average repair time. The desired probability density, given the multiphase nature of the process, is determined by the method of multiple convolution. The resulting model allows us to solve two reciprocal problems. Firstly, to determine the optimal repair time, provided that diagnostic and repair tools are equipped, as well as the qualifications of technical workers. Secondly, at a given repair time, determine the required characteristics of diagnostic equipment, maintenance facilities and personnel.

Accurate dipole radiation model for waveguide grating couplers

An analytical theoretical model for the waveguide grating coupler is developed and applicable to practical deep gratings. The grating-assisted input coupling efficiency is calculated by considering the reciprocal out-coupling problem. The deep grating structure is modelled as an optical layer filled with polarization dipole sources, and the scattered fields are then calculated using the associated Green’s functions and taking into account the multiple reflections and interference from the adjacent layers. The joint loss between the grating region and the waveguide is also considered. Comparison with numerical simulations shows very good agreement and validates the accuracy of the analytical model. The model explicitly describes the importance of multilayer interference of the scattered fields and guided-mode joint loss on the total grating-assisted coupling efficiency and can be used for practical waveguide grating coupler design with negligible computation workload.

Subwavelength Broadband Perfect Absorption for Unidimensional Open‐Duct Problems

AbstractPassive metamaterials provide efficient solutions for sound absorption in the low‐frequency regime with deep subwavelength dimensions. They have been extensively applied in unidimensional reciprocal problems considering that an incident wave is either reflected or transmitted at the outlet boundary. However, the generalized problem with impedance boundary condition is not well understood yet. This work presents a general design methodology of metamaterial absorbers for open‐duct problems, which is a special case of impedance outlet boundary encountered in broad practical applications, for example, noise‐attenuation problems in heat ventilation and air conditioning systems. By properly using monopolar point scatterers made of arrays of Helmholtz resonators, the design process is significantly simplified; the transfer matrix modeling is sufficiently accurate to describe the acoustic response of the system. A single monopolar point scatterer is insufficient to attenuate both the reflected and radiated waves; a frequency‐dependent maximum absorption exists and is derived analytically. To go beyond this absorption bound and achieve perfect absorption, at least two point scatterers are necessary. Specific designs are provided and validated experimentally for maximum or perfect absorption, either at single frequencies or over specific frequency bands.

A multiple criteria framework to assess learning methodologies

New job skills required by the professional market have been causing significant changes in the learning process of undergraduate students. Different learning methodologies can be adopted to assist in the development of those skills, and the process of choosing the most suitable learning methodology for each situation may be complex, involving multiple and conflicting criteria. In order to support the choice of learning methodologies for the development of the “4C skills”, i.e, collaboration, communication, creativity and critical thinking, we propose a new framework based on the multiple criteria decision-making approach PROMETHEE II (Preference Ranking Organization Method for Enrichment of Evaluations), considering as criteria the “4C skills”, student motivation, level of learning, student comfort, decision-making capacity and time required for class preparation. Passive methods and active learning methodologies such as Guided Reciprocal Peer Questioning (GRPQ), Think-Pair-Share (TPS), and Problem Based Learning (PBL) are compared. Each methodology was applied to three groups of students of Industrial Engineering of a Brazilian University, totaling 138 students. As a result, PBL obtained the best assessment in the three groups, followed by GRPQ. The proposed framework validates the assessment of learning methodologies, providing a structure and guideline for its replication in other educational institutions.

Unified reciprocal LASSO estimation via least squares approximation

The primary goal of this article is to extend the reciprocal LASSO for applications to binary and survival outcomes. We consider the least squares approximation (LSA) as a solver for the reciprocal LASSO problem. The LSA is a general theoretical framework that includes generalized linear models, Cox regression, and many others as special cases. By applying LSA to reciprocal LASSO regularization, we transfer the original reciprocal LASSO problem into an asymptotically equivalent least squares problem. While the existing literature on reciprocal LASSO has mostly focused on linear models, our algorithm can be easily implemented for general likelihoods, providing a flexible framework for variable selection using reciprocal penalties. To handle the computational burden of implementing the resulting procedure, we employ a scalable stochastic search method called Simplified Shotgun Stochastic Search with Screening (S5), which is easy to implement, without requiring any sophisticated optimization package other than a linear equation solver. We examine the effectiveness of our procedure through Monte Carlo simulations and real data analyses.

Comparison of Mathematical Learning Capabilities Among Students Using the Reciprocal Teaching and Problem Posing Model

The purpose of this study is to ascertain whether students who learn to utilize the reciprocal teaching model have a greater understanding of mathematical topics than students who learn to use the problem posing approach. This research was carried out at SMP Negeri 97 Jakarta for seventh grade students on the subject of Persamaan Linear Satu Variabel (PLSV). This study was conducted using a quasi-experimental design. A two-stage random sampling method was employed for the sampling process.The first stage is purposive sampling, in this case three classes are selected which are taught by the same teacher. Then the second stage is cluster random sampling, from three classes that are normally distributed, homogeneous and have the same average, two classes are randomly selected as experimental class I (reciprocal teaching model) and experimental class II (problem posing model). The research instrument used was the final test of the ability to understand mathematical concepts on the subject of PLSV as many as 6 questions. Validity testing uses content, construct, and empirical validity. Calculation of the reliability of the instrument using the Cronbach Alpha correlation formula and obtained a reliability coefficient of 0.714 which is classified as high. The research hypothesis was tested using t-test statistics.The result show that the ability to understand mathematical concepts of students who learn to use the reciprocal teaching model is higher than problem posing model.

Reinforcement Learned Distributed Multi-Robot Navigation With Reciprocal Velocity Obstacle Shaped Rewards

The challenges to solving the collision avoidance problem lie in adaptively choosing optimal robot velocities in complex scenarios full of interactive obstacles. In this letter, we propose a distributed approach for multi-robot navigation which combines the concept of reciprocal velocity obstacle (RVO) and the scheme of deep reinforcement learning (DRL) to solve the reciprocal collision avoidance problem under limited information. The novelty of this work is threefold: (1) using a set of sequential VO and RVO vectors to represent the interactive environmental states of static and dynamic obstacles, respectively; (2) developing a bidirectional recurrent module based neural network, which maps the states of a varying number of surrounding obstacles to the actions directly; (3) developing a RVO area and expected collision time based reward function to encourage reciprocal collision avoidance behaviors and trade off between collision risk and travel time. The proposed policy is trained through simulated scenarios and updated by the actor-critic based DRL algorithm. We validate the policy in complex environments with various numbers of differential drive robots and obstacles. The experiment results demonstrate that our approach outperforms the state-of-art methods and other learning based approaches in terms of the success rate, travel time, and average speed.

Theories of indirect chiral coupling and proposal of Fabry–Perot resonance as a flexible chiral-coupling interface

The chiral coupling of an emitter to waveguide mode, i.e., the propagation direction of the excited waveguide mode is locked to the transverse spin (T-spin) of a circularly polarized emitter, has exhibited unprecedented applications in nanophotonics and quantum information processing. This chiral coupling can be largely enhanced in terms of unidirectivity, efficiency, and spontaneous emission rate by introducing resonant modes as coupling interfaces. However, this indirect chiral coupling still undergoes limitations in flexibility and miniaturization, and the underlying physical mechanisms are to be clarified. Here, we present an intuitive and rigorous approach for analyzing the direct/indirect chiral coupling, and thereout, derive some general relations between the chiral-coupling directionality and the T-spin of the field or emitter. Based on the theories, we propose an indirect chiral-coupling system on the platform of surface plasmon polariton (SPP), with a nanocavity supporting Fabry–Perot (FP) resonance of dual SPP modes serving as a novel coupling interface. The FP resonance provides flexible design freedoms which can modulate the chirality of the T-spin (and the resultant chiral-coupling directionality) to flip or disappear. A unidirectivity up to 99.9% along with a high coupling efficiency and enhancement of spontaneous emission rate is achieved. Two first-principles-based SPP models for the reciprocal and original problems are built up to verify the decisive role of the FP resonance in achieving the chiral coupling. The proposed theories and novel chiral-coupling interface will be beneficial to the design of more compact and flexible chiral-coupling systems for diverse applications.

Fanon, Hegel, and the Problem of Reciprocity

AbstractIn this article I put forward an interpretation of what is at stake in Frantz Fanon's claim that there is a reciprocity at the basis of G. W. F Hegel's master-servant dialectic. I do this by staging a critique of the ‘shared-humanity’ interpretation of Fanon's claim. Fanon's problem, as this interpretation understands it, is that the master-servant dialectic describes a situation in which two human beings knowingly confront one another as such. Such a situation—because human-to-human confrontation is assumed—does not adequately describe a racially divided situation because of racism's dehumanizing force. Fanon's problem would thus be that Hegel assumed shared humanity. I contest this reading by claiming that Fanon's issue is not reciprocal humanity but reciprocal struggle. To get to this point requires demonstrating that the shared-humanity reading is implausible on a variety of grounds. Thanks to the work of Philippe Van Haute it can already be said that in Hegel's text no shared humanity takes place. But Van Haute nevertheless claims that the shared-humanity problem is present in Kojève. Thus, it first needs to be shown that Kojève's text disallows such a reading. With this result in hand, I move to show the textually unsupportable nature of a subset of the shared-humanity reading—the ‘ontological reading’—whose strategy of reading Fanon's Black Skin, White Masks obscures the Sartrean-Beauvoirian commitments which would in fact allow a more accurate reading of Fanon's claims about reciprocity in Hegel to be made. I then seek to show—with reference to these commitments and a broadly Kojèvean emphasis on the centrality of struggle in human subject-formation—that Fanon's comments about reciprocity take aim at the question of mutual struggle in Hegel and Kojève. ‘The French Negro’, Fanon argues, did not get to experience the cost and value of freedom, unlike Hegel's servant.

Justice Toward God: Piety and the Problem of Human-Divine Reciprocity

Justice Toward God: Piety and the Problem of Human-Divine Reciprocity

Взаимная аккультурация мигрантов и принимающего населения: модели, методики, ключевые исследования и вызовы

Objective. An integrative review of modern models of acculturation, taking into account the problem of reciprocity of acculturation orientations of migrants and the host population, as well as antecedents and psychological consequences of migrants acculturation. Background. Over the past 100 years, more than 13000 scientific articles have been published on the topic of acculturation. Thanks to them we know a lot about how migrants and host population, ethnic minorities and ethnic majority adapt to each other. Today, most of this knowledge is systematized using models (taxonomies) of mutual acculturation of these groups. As a result, there is a great need for conducting a qualitative integrative review of the main and most influential models of mutual acculturation of migrants and the host population, the methods created on their basis, the results of key studies and criticism of these models. The analysis allows us to see the development of the theory of acculturation over the past half century, taking into account the main problems and challenges, that future generations of researchers of acculturation will face. Methodology. Systematic approach, method of comparative and critical analysis. Conclusions. The challenges that acculturation researchers meet open up new perspectives for creating modern systematic models of mutual acculturation of ethnocultural groups. Basically, acculturation should be considered as a life-long development process in changing ecological contexts of different levels, taking into account the consequences of the pandemic, the growing impact of digitalization and cultural globalization.

DYNAMICS OF DESIRE: GIFT GIVING AND RECIPROCITY IN ANCIENT GREEK HOMOEROTIC COURTSHIP COURTSHIP

The article addresses the problem of reciprocity in homoerotic relationships in classical Athens. According to the more traditional approach, the pecking ord er model ’’, these typically a symmetrical relationships almost inevitably involved humiliation of one of the partners, who literally or metaphorically assumed a passive and therefore u n manly role. Although more recent studies tend to underline the arti fici al cha racter of these schola rly reconstructions, they still fail to account for the nuances of ancient homoerotic courtship. I argue that some sources often used by scholars as reflec t ing negative attitudes towards homoeroticism may actually t estify to the existenc e of very clear rules of highly valued and praised behaviours of passive partners. T h ese rules formed an implicit grammar of social actions but were never explicitly codified.

On the orbits of automaton semigroups and groups

We investigate the orbits of automaton semigroups and groups to obtain algorithmic and structural results, both for general automata but also for some special subclasses. First, we show that a more general version of the finiteness problem for automaton groups is undecidable. This problem is equivalent to the finiteness problem for left principal ideals in automaton semigroups generated by complete and reversible automata. Then, we look at w-word (i.\,e.\ right infinite words) with a finite orbit. We show that every automaton yielding an w-word with a finite orbit already yields an ultimately periodic one, which is not periodic in general, however. On the algorithmic side, we observe that it is not possible to decide whether a given periodic w-word has an infinite orbit and that we cannot check whether a given reversible and complete automaton admits an w-word with a finite orbit, a reciprocal problem to the finiteness problem for automaton semigroups in the reversible case. Finally, we look at automaton groups generated by reversible but not bi-reversible automata and show that many words have infinite orbits under the action of such automata.

The Ties that Bind Us

This paper reviews the evolutionary literature on cooperation and the mechanisms proposed to explain the differences we see in the scale, breadth, and intensity of cooperation across societies, over history, and among behavioural domains. The most well-studied mechanisms that help societies sustain cooperation include kinship, reciprocity, reputation, signalling, norms, informal and formal institutions, and the competition between stable equilibria sustained by these mechanisms. I apply each of these mechanisms to the problem of reciprocity across the lifecycle. I then discuss how these same ties also tear us apart and what policies might help tie us back together. JEL Codes: A12, A13, C71, J14, J18, Z1

Impact localization for composite plate using the modified error-outlier algorithm with Pugh’s concept selection under various temperatures

The previous error outlier based impact localization algorithm has a weak point during the impact localization due to a reciprocity problem coupled with the symmetric boundary conditions of target structures. Thus, the modified error outlier based impact localization algorithm was proposed to overcome the improper impact localization due to this reciprocity problem. The previous impact localization method using fiber Bragg grating sensors did not consider the effect of the operating temperature of structures although they were operated under various temperatures. Thus, this study experimentally verified the error outlier impact localization algorithm by performing impact localization for a carbon fiber-reinforced polymer composite plate under various temperatures. It was found that the total average error of 2.0 mm was estimated under the given temperatures, being only 2.5% of the pre-assigned grid size of 80.0 mm on the plate. Therefore, we concluded that the modified algorithm can overcome the reciprocity problems and be sufficiently used for impact localization using fiber Bragg grating sensors under various temperatures.