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The problem of phase retrieval, i.e., the problem of recovering a function from the magnitudes of its Fourier transform, naturally arises in various fields of physics, such as astronomy, radar, speech recognition, quantum mechanics, and, perhaps most prominently, diffraction imaging. The mathematical study of phase retrieval problems possesses a long history with a number of beautiful and deep results drawing from different mathematical fields, such as harmonic analysis, complex analysis, and Riemannian geometry. The present paper aims to present a summary of some of these results with an emphasis on recent activities. In particular we aim to summarize our current understanding of uniqueness and stability properties of phase retrieval problems.

At the onset of COVID-19, regulating mass gatherings that were potential superspreader events was a key challenge for public administration. Before the national COVID-19 restrictions, decisions about mass events were debated at the local level, with team sensemaking a crucial tool in the decision-making process. This study uses data-frame theory to examine team sensemaking activities during the incubation period before a decision to allow a superspreader event in early March 2020 in Saaremaa, Estonia. By mapping the team sensemaking network, analyzing 17 media articles and conducting five stakeholder interviews, this article explores the team sensemaking activities behind the erroneous decision to allow the mass event. The results suggest that during the incubation period, errors in team-level sensemaking may stem not only from dysfunctional dynamics but also from a limited scope of team sensemaking activities. Team sensemaking during the incubation period seems limited to mapping data and elaborating on existing frames, reinforcing prevailing interpretations rather than reassessing them. Individuals engage in a broader range of sensemaking activities, such as questioning the frame or re-framing, but these insights do not translate to the team level. This study uncovers the complex dynamics of the incubation period team sensemaking and its crucial role in the early phases of crisis.

This article examines ideology and motivation in terrorism through a psychological lens, responding to a debate about the analytic value of ideology. Drawing on Peters’ concept of reason-guided, socially embedded action, and integrating rule-governed behaviour and Relational Frame Theory, it argues that terrorist behaviour is shaped by verbally mediated rules rather than simple causal mechanisms. This perspective aligns partially with social-movement framing theory, but highlights individual level processes. Conceptualising ideology as a dynamic process of rule governance offers a workable framework for understanding terrorist motivation and may help address the low base-rate problem in terrorism research.

There exists a vast literature on affect and emotion in psychological disciplines, yet contemporary conceptualizations and technologies to predict and influence emotion have been slower to emerge in behavior analysis. The current article is an attempt to conceptualize emotional experiencing through a radical behavioral lens using relational frame theory (RFT) and contemporary extensions. RFT provides a behavioral approach to cognitive appraisal within existing models of human emotion by emphasizing derived relational responding, transformation of stimulus function, and generalized reinforcement learning. Relational density theory (RDT) and the hyperdimensional multilevel (HDML) framework both expand upon RFT and may allow for a more complete account of emotional experiencing within complex networks. Synthesizing these two approaches yields multiple testable predictions that are consistent with RDT across levels of the HDML. Moreover, the ROE-M (relating, orienting, and evoking functions within a motivational context) is a dynamical unit that may be readily evident within emotional experiencing as it is generally described within the psychological literature, and compatible with the synthesized model. Taken together, these approaches and emerging research on affective dynamics may provide a starting point to develop a robust and comprehensive analysis of human emotion that can strengthen behavior analysis and therapies

Este artículo analiza el modo en que los movimientos sociales adaptan sus marcos de referencia cuando deciden participar en la arena electoral y la política institucional. Para ello, se estudia el caso de una agrupación de electores que en 2015 llegó al gobierno local en un municipio gaditano. El artículo propone el concepto de marcos espaciales de motivación, diagnóstico y pronóstico para estudiar la acción colectiva, combinando así la teoría del enmarcamiento y la teoría espacial. Este enfoque permite identificar las transformaciones de marco y las tensiones que experimentan los activistas cuando se enfrentan a la participación institucional, así como el papel de los discursos y prácticas espaciales en estas tensiones. This article analyses the way in which social movements adapt their reference frames when they decide to participate in the electoral arena and institutional politics. For this purpose, it studies the case of a citizens' candidature that came to municipal government of a city of Cádiz in 2015. The article proposes the concept of spatial frames of motivation, diagnosis and prognosis in order to study collective action, combining frame theory and spatial theory. This approach permits to identify frame transformations and the tensions experienced by activists when they face institutional participation, and the role of spatial practices and discourses in these tensions.

Relational models theory predicts that social relationships are formed from four underlying psychological models: communal sharing, authority ranking, equality matching, and market pricing. Here, in four studies, we test this four-factor model using the 33-item Modes of Relationships Questionnaire (MORQ). In Study 1, we administered the MORQ to N = 347 subjects. A parallel analysis supported the four-factor structure, but several items failed to load on their predicted target factors. In Study 2 (N = 617), we developed a well-fitting four-factor model of the MORQ with a total of 20 items (five items retained for each factor). This model replicated across multiple relationships reported by each subject. In Study 3, we replicated the model in an independent dataset (N = 615). A general factor associated with relationship type was required in both Study 2 and Study 3. In Study 4, we tested the nature of this general factor, finding that it was associated with the closeness of the relationship. The results support the Relational Models four-factor structure of social relationships. Given the mature theory and applications in a wide range of disciplines, from social to organisational psychology, we hope that this compact, valid, and interpretable instrument leads to increased usage of the scale.

Process-based behavior therapy (PBBT®) is a recently developed therapeutic approach based almost entirely on the core behavioral process of arbitrarily applicable relational responding (AARR), as postulated by relational frame theory (RFT), and in particular on advances in the theory made in recent years. In particular, PBBT directs its attention towards the hyper-dimensional multi-level (HDML) framework for conceptualizing relational responding and the basic behavioral unit that emerged from that framework, called the ROE unit (i.e., the ongoing dynamic interaction of Relating, Orienting, and Evoking), for conceptualizing human psychological events. The current article seeks to outline and provide an introduction to PBBT as a contemporary behavioral therapeutic approach to psychological suffering and mental well-being. Toward this aim, the ROE unit and related RFT concepts will first be summarized followed by presentation of three key components of PBBT. Clinical examples are provided throughout to help illustrate the tight links between updated RFT and its clinical application in PBBT.

The integration of photovoltaic (PV) systems and renewable energy sources into modern utility grids presents substantial opportunities for sustainable energy, yet also introduces critical power quality challenges due to the proliferation of nonlinear and unbalanced loads. This paper proposes a dynamic multi-function reference frame control (DMRFC) strategy for a multifunctional bidirectional grid-interactive converter (µG-MPGIC), designed for PV-grid interconnection with enhanced power quality assistance. Built upon the Synchronous Reference Frame (SRF) theory, the DMRFC approach enables autonomous multifunctionality: (i) dynamic regulation of active power transfer based on load demands and available DC-side energy, (ii) bidirectional energy flow between AC and DC interfaces considering the battery's state of charge (SOC), (iii) harmonic current mitigation, reactive power compensation, and (iv) neutral current suppression under unbalanced load conditions. A small-signal transfer function model is developed for stability analysis using frequency-domain methods. Simulation studies conducted in MATLAB/SIMULINK demonstrate that the proposed DMRFC control achieves a total harmonic distortion (THD) reduction in grid currents to 1.25% , compared to 1.79% with conventional symmetrical component theory (SCT)-based control and 2.80% with Instantaneous Power Theory (IPT)-based control under identical conditions. Furthermore, the system achieves unity power factor operation under highly nonlinear loading, superior to the 0.96 and 0.93 power factors achieved with SCT and IPT, respectively. Under dynamic loading and fluctuating irradiation, the converter maintains a near-constant DC-link voltage, demonstrating robust grid synchronization and operational stability. The system also effectively supports bidirectional power flow, handling battery charging at −4.96 kW and discharging at +4.95 kW with seamless transitions, validated through grid current magnitude variations between 32 A and 42 A. The proposed DMRFC strategy offers a significant enhancement over conventional methods, delivering superior power quality improvement, intelligent energy management, and adaptive multifunctional operation in grid-connected PV systems.

Ehlers’ Frame Theory is a class of geometric theories parameterized by λ:=1/c2 and identical to the General Theory of Relativity for λ≠0. The limit λ→0 does not recover Newtonian gravity, as one might expect, but yields the so-called Newton–Cartan theory of gravity, which is characterized by a second gravitational field ω, called the Coriolis field. Such a field encodes at a non-relativistic level the dragging feature of general spacetimes, as we show explicitly for the case of the (η,H) geometries. Taking advantage of the Coriolis field, we apply Ehlers’ theory to an axially symmetric distribution of matter, mimicking, for example, a disc galaxy, and show how its dynamics might reproduce a flattish rotation curve. In the same setting, we further exploit the formal simplicity of Ehlers’ formalism in addressing non-stationary cases, which are remarkably difficult to treat with the General Theory of Relativity. We show that the time derivative of the Coriolis field gives rise to a tangential acceleration which allows for studying a possible formation in time of the rotation curve’s flattish feature.

The purpose of the current study was to evaluate the effects of behavioral procedures, including relational training and multiple exemplar training on empathic responding of individuals who display racial bias. In particular, this study used a multielement design with five adult participants to evaluate whether the presentation of relational frames of coordination and distinction between the participants’ values and the values of a person belonging to a group for which a bias existed altered empathic responses toward people belonging to such groups. The results showed empathic responding was higher when relational frames of coordination were presented and lower when relational frames of distinction were presented. This study provides preliminary data suggesting that relational training may result in altered patterns of empathic responses toward people belonging to different racial groups for which a bias previously was observed.