Reciprocity Constraints Research Articles

Nonreciprocal scattering and unidirectional cloaking in nonlinear nanoantennas

Abstract Reciprocal scatterers necessarily extinguish the same amount of incoming power when excited from opposite directions. This property implies that it is not possible to realize scatterers that are transparent when excited from one direction but that scatter and absorb light for the opposite excitation, limiting opportunities in the context of asymmetric imaging and nanophotonic circuits. This reciprocity constraint may be overcome with an external bias that breaks time-reversal symmetry, posing however challenges in terms of practical implementations and integration. Here, we explore the use of tailored nonlinearities combined with geometric asymmetries in suitably tailored resonant nanoantennas. We demonstrate that, under suitable design conditions, a nonlinear scatterer can be cloaked for one excitation direction, yet strongly scatters when excited at the same frequency and intensity from the opposite direction. This nonreciprocal scattering phenomenon opens opportunities for nonlinear nanophotonics, asymmetric imaging and visibility, all-optical signal processing and directional sensing.

Polarimetric Helmholtz Stereopsis.

Helmholtz stereopsis (HS) exploits the reciprocity principle of light propagation (i.e., the Helmholtz reciprocity) for 3D reconstruction of surfaces with arbitrary reflectance. In this paper, we present the polarimetric Helmholtz stereopsis (polar-HS), which extends the classical HS by considering the polarization state of light in the reciprocal paths. With the additional phase information from polarization, polar-HS requires only one reciprocal image pair. We derive the reciprocity relationship of Mueller matrix and formulate new reciprocity constraint that takes polarization state into account. We also utilize polarimetric constraints and extend them to the case of perspective projection. For the recovery of surface depths and normals, we incorporate reciprocity constraint with diffuse/specular polarimetric constraints in a unified optimization framework. For depth estimation, we further propose to utilize the consistency of diffuse angle of polarization. For normal estimation, we develop a normal refinement strategy based on degree of linear polarization. Using a hardware prototype, we show that our approach produces high-quality 3D reconstruction for different types of surfaces, ranging from diffuse to highly specular.

Sustainable Data Rivers? Rebalancing the Data Ecosystem That Underlies Generative AI

Abstract The salient concern, today, is not whether copyright law will “allow robots to learn.” The pressing question is whether the exploitation of the data ecosystem that has made generative AI possible can be made socially sustainable. Just as the human right to water is only possible if reasonable use and reciprocity constraints are imposed on the economic exploitation of rivers, so is the fundamental right to access culture, learn, and build upon it. To restore this right to its proper place within the balancing act IP law is supposed to enable demands fundamental legal reform. This article explores the merits of reconstructing copyright as a permitted privilege (rather than property right). It also highlights the extent to which, for such reform to bear fruit and contribute to a socially sustainable data ecosystem, it needs to be supported by bottom-up participatory infrastructure.

A cross-carrier multilateral trading model for integrated electricity and natural gas systems

Multi-carrier systems have become an important research topic in view of electricity and gas systems synergies. We present a new model for the cross-carrier multilateral economic dispatch (MED) problem to account for transmission losses and network constraints in the integrated electricity and gas systems. To associate multilateral trades more effectively with the losses occurring in the network, the loss allocation ratio between suppliers and consumers involved in multilateral trades is introduced in the loss allocation policy. Two sets of reciprocity constraints are presented to ensure the equilibrium between production and consumption, both physically and economically. The price decomposition involved in multilateral trades is developed based on cross-carrier MED with product differentiation (PD). Combined with characteristics of price decomposition, an effective payment to keep less trading information access by the network operator in the decentralized market is presented. Numerical results show that when all losses are allocated to consumers, the MED model without PD performs similarly to a pool-based market model. It is also demonstrated that the inclusion of agents' preferences in the MED model can improve total social welfare.

Multi-band tunable strongly nonreciprocal thermal radiation in topological edge state coupled mode

Violating Kirchhoff's law of thermal radiation can break the reciprocity constraints on spectral emissivity and absorptivity, which provides new capabilities for managing photonic heat flow and fundamentally improves energy harvesting systems' efficiency. Currently, most micro-nano structures that violate Kirchhoff's law are mainly confined to single- or dual-band models, significantly limiting applications such as photonic energy conversion and thermal management. Here, a scheme is proposed for a topological one-dimensional photonic crystal heterostructure consisting of multiple photonic crystals and Weyl semimetals, and its absorptivity and emissivity are theoretically calculated by the transfer matrix method. The results show that the multi-band nonreciprocity that completely violates Kirchhoff's law can persist over broad angular and frequency ranges without requiring any external magnetic field via tuning the relevant parameters. Furthermore, the electric field distribution reveals that the formation of such multiple bands originates from the coupling between topological edge states, and the significant enhancement of the local field near the interface of the heterostructure provides favorable conditions for the realization of strong nonreciprocity. Our work may contribute to the design and development of multiband nonreciprocal devices for energy conversion and thermal management and may also provide design ideas for multiband reciprocal absorbers, filters, optical switching, etc.

The Devil Is in the Frequency: Geminated Gestalt Autoencoder for Self-Supervised Visual Pre-training

The self-supervised Masked Image Modeling (MIM) schema, following "mask-and-reconstruct" pipeline of recovering contents from masked image, has recently captured the increasing interest in the community, owing to the excellent ability of learning visual representation from unlabeled data. Aiming at learning representations with high semantics abstracted, a group of works attempts to reconstruct non-semantic pixels with large-ratio masking strategy, which may suffer from "over-smoothing" problem, while others directly infuse semantics into targets in off-line way requiring extra data. Different from them, we shift the perspective to the Fourier domain which naturally has global perspective and present a new Masked Image Modeling (MIM), termed Geminated Gestalt Autoencoder (Ge^2-AE) for visual pre-training. Specifically, we equip our model with geminated decoders in charge of reconstructing image contents from both pixel and frequency space, where each other serves as not only the complementation but also the reciprocal constraints. Through this way, more robust representations can be learned in the pre-trained encoders, of which the effectiveness is confirmed by the juxtaposing experimental results on downstream recognition tasks. We also conduct several quantitative and qualitative experiments to investigate the learning behavior of our method. To our best knowledge, this is the first MIM work to solve the visual pre-training through the lens of frequency domain.

Fermat’s Last Theorem over and

AbstractWe prove Fermat’s Last Theorem over $\mathbb {Q}(\sqrt {5})$ and $\mathbb {Q}(\sqrt {17})$ for prime exponents $p \ge 5$ in certain congruence classes modulo $48$ by using a combination of the modular method and Brauer–Manin obstructions explicitly given by quadratic reciprocity constraints. The reciprocity constraint used to treat the case of $\mathbb {Q}(\sqrt {5})$ is a generalization to a real quadratic base field of the one used by Chen and Siksek. For the case of $\mathbb {Q}(\sqrt {17})$ , this is insufficient, and we generalize a reciprocity constraint of Bennett, Chen, Dahmen, and Yazdani using Hilbert symbols from the rational field to certain real quadratic fields.

Reciprocity Constraints on Reflection.

Reciprocity is a fundamental symmetry of Maxwell's equations. It is known that reciprocity imposes constraints on transmission, absorption, and emission. Here, we reveal reciprocity constraints on reflection. We determine the sets of all attainable reflection coefficients of n-port scattering matrices with prescribed singular values, both with and without assuming reciprocity. Their difference establishes reciprocity constraints and nonreciprocal behaviors. As an application, we examine the conditions for all-zero reflections. Our results deepen the understanding of reciprocity in optics.

A self-consistent homogenization framework for dynamic mechanical behavior of fiber reinforced composites

This paper proposes a self-consistent homogenization framework for developing finite strain, elastic constitutive models of carbon fiber–epoxy composites for high strain-rate loading. The framework incorporates a concurrent multiscale model, in which an RVE is embedded in a homogenized exterior domain, is developed with self-consistent displacement compatibility and traction reciprocity constraints at the RVE-exterior domain interface. It overcomes limitations of periodic boundary conditions on the RVE for dynamic problems under high strain-rate conditions and allows for the evaluation of material constitutive relations accounting for micro-scale inertia. The proposed self-consistent formulation incorporates the effect of stress waves propagation in the microstructure, along with their interaction with heterogeneities resulting in reflection and transmission at the interfaces. The concurrent model is used to study dynamic composite behavior at strain-rates in the range of 102-105 s−1 for two RVEs, one containing a single fiber and another with 70 randomly distributed fibers. For strain-rates above 104 s−1, the dynamic part of the stress becomes significant and dominates over the static part of the stress. Results of the analysis show that for high strain-rate dynamic loading, constitutive models for the composites must account for micro-inertia, in addition to strain-rates and microstructural morphology.

The interaction among gut microbes, the intestinal barrier and short chain fatty acids.

The mammalian gut is inhabited by a massive and complicated microbial community, in which the host achieves a stable symbiotic environment through the interdependence, coordination, reciprocal constraints and participation in an immune response. The interaction between the host gut and the microbiota is essential for maintaining and achieving the homeostasis of the organism. Consequently, gut homeostasis is pivotal in safeguarding the growth and development and potential productive performance of the host. As metabolites of microorganisms, short chain fatty acids are not only the preferred energy metabolic feedstock for host intestinal epithelial cells, but also exert vital effects on antioxidants and the regulation of intestinal community homeostasis. Herein, we summarize the effects of intestinal microorganisms on the host gut and the mechanisms of action of short chain fatty acids on the four intestinal barriers of the organism, which will shed light on the manipulation of the intestinal community to achieve precise nutrition for specific individuals and provide a novel perspective for the prevention and treatment of diseases.

Reciprocal Twin Networks for Pedestrian Motion Learning and Future Path Prediction

Modeling the moving behaviors and predicting the future paths of pedestrians, especially for those in complex scenes, remain a challenging problem in machine learning. We recognize that human motion trajectories, governed by social norms and constrained by physical structures of the surrounding environment, are both forward predictable and backward predictable. Motivated by this observation, we develop a new approach, called reciprocal twin networks, for human trajectory learning and prediction. We design two networks, a forward prediction network to predict future trajectory from past observations and a backward prediction that performs the trajectory prediction backward in time. The backward prediction network serves as the inverse operation of the forward prediction network, forming a reciprocal constraint. During the training stage, this reciprocal constraint allows them to be jointly learned for accurate and robust human trajectory prediction. During the inference stage, we borrow the concept of adversarial attack of deep neural networks, which iteratively modifies the input of the network to match the given or forced network output, and develop a new method, called reciprocal attack for matched prediction, to achieve accurate human trajectory prediction. Our experimental results on benchmark datasets demonstrate that our new method outperforms the state-of-the-art methods for human trajectory prediction.

Polarimetric Calibration of L-Band UAVSAR Data

The polarimetric distortion in the PolSAR datasets causes the polarimetric decomposition and classification techniques to produce wrong outputs, which result in misinterpreting the scattering phenomenon and the ground targets. The most important polarimetric distortions in airborne PolSAR datasets are the channel imbalance and crosstalk. The minimization of these polarimetric distortions using polarimetric calibration techniques is very important to carry out the quantitative analysis using PolSAR data and time-series analysis and to compare the results between different sensors. The objective of this study was to implement the external polarimetric calibration of the L-band UAVSAR system using trihedral corner reflectors. The polarimetric distortion matrix (PDM) was formulated after considering the crosstalk and channel imbalance polarimetric distortions to derive the scattering matrix free from all kinds of polarimetric distortions from the observed scattering matrix. The channel imbalance between different polarization channels was estimated with the help of trihedral corner reflectors and homogeneously distributed targets. The crosstalk parameters were estimated by assuming the scattering reciprocity constraint, which is valid in the case of monostatic radars. The scattering matrix free from polarimetric distortions was derived from the PDM after estimating the polarimetric distortions. The polarimetric signatures and the coherency matrix behaviour of the trihedral corner reflectors were used to analyse the ground target characterization improvement after polarimetric calibration.

Identification of physically realistic state-space models for accurate component synthesis

For components that are difficult to model with conventional analytical or numerical tools, experimentally derived state-space models can instead be used in system synthesis. For successful state-space synthesis, a physically realistic model must be identified. For this purpose, a hybrid first- and second-order system description is used here as the basis for identification. In the identification procedure, a physically motivated rigid body rank constraint is imposed together with a reciprocity constraint. The two constraints are enforced during a re-estimation phase of the state-space matrices following after a traditional state-space subspace identification phase. In this paper, two complex and modally dense industrial components are combined into a dynamical system. An experimental model of a car body-in-white structure is identified. The identified subsystem model is coupled with a finite element model of a rear subframe in a system synthesis. The two subsystems are attached through four rubber bushings modelled by finite element procedures. It is shown that the experimental-analytical assembly successfully predicts the reference measured system, with higher accuracy than what could be achieved with a model based solely on finite elements. It is also shown that synthesis with individually calibrated rear subframe models can capture the variability in the coupled system.

Aid‐supported governance reforms in Solomon Islands: Piecemeal progress or persistent stalemate?

AbstractMotivationDespite seeming donor–recipient consensus on the importance of effective governance, aid‐linked reforms often fall short of the expected outcomes. Solomon Islands provides a highly relevant case to explore the dynamics of institutional reform processes, and understand why, even in a relatively favourable operating environment, structural reforms are difficult to implement.PurposeThis article aims to provide empirically grounded analysis of key factors that hinder institutional change in fragile aid‐receiving countries by addressing the reciprocal (rather than unilateral) constraints and trade‐offs faced by both recipients and donors, and examining their implications for the emerging institutional trajectories in host states.Approach and MethodsThis study is based on the use of a single case study that involves in‐depth review of related academic and policy literature, and media reports through the lens of “mutual dependencies.”FindingsSolomon Islands’ recent experience with the regulation of Constituency Development Funds and tertiary scholarships makes it clear that by continuously postponing the implementation of relevant policies, domestic authorities try to avoid the potential costs institutional reforms are likely to create. Similarly, donors concerned about their own strategic interests and power relationships with other actors remain unable to enforce full implementation of such reforms. The process in Solomon Islands further confirms that political trade‐offs facing all actors in different forms have a constraining effect on the achievement of desired policy objectives.Policy ImplicationsPolicy reforms require domestic authorities to develop specific mechanisms that have the potential to secure popular support in favour of proposed structural changes. Donors need new and more evidence‐based approaches that may help balance between their strategic concerns and the achievement of institutional outcomes.

A network approach to brain form, cortical topology and human evolution.

Network analysis provides a quantitative tool to investigate the topological properties of a system. In anatomy, it can be employed to investigate the spatial organization of body parts according to their contiguity and patterns of physical contact. In this study, we build a model representing the spatial adjacency of the major regions of the human brain often considered in evolutionary neuroanatomy, to analyse its topological features. Results suggest that the frontal lobe is topologically independent of the posterior regions of the brain, which in turn are more integrated and influenced by reciprocal constraints. The precentral gyrus represents a hinge between the anterior and posterior blocks. The lateral temporal cortex is particularly influenced by the neighbouring regions, while the parietal cortex is minimally constrained by the overall brain organization. Beyond the reciprocal spatial influences among cortical areas, brain form is further constrained by spatial and mechanical influence of the braincase, including bone and connective elements. The anterior fossa and the parietal bones are the elements more sensitive to the brain-braincase spatial organization. These topological properties must be properly considered when making inferences on evolutionary variations and macroscopic differences of the human brain morphology.

Electrically tunable harmonics in time-modulated metasurfaces for wavefront engineering

Modulation of metasurfaces in time gives rise to several exotic space–time scattering phenomena by breaking the reciprocity constraint and generation of higher-order frequency harmonics. We introduce a new design paradigm for time-modulated metasurfaces, enabling tunable engineering of the generated frequency harmonics and their emerging wavefronts by electrically controlling the phase delay in modulation. It is demonstrated that the light acquires a dispersionless phase shift regardless of incident angle and polarization, upon undergoing frequency conversion in a time-modulated metasurface which is linearly proportional to the modulation phase delay and the order of generated frequency harmonic. The conversion efficiency to the frequency harmonics is independent of modulation phase delay and only depends on the modulation depth and resonant characteristics of the metasurface, with the highest efficiency occurring in the vicinity of resonance, and decreasing away from the resonant regime. The modulation-induced phase shift allows for creating tunable spatially varying phase discontinuities with 2π span in the wavefronts of generated frequency harmonics for a wide range of frequencies and incident angles. Specifically, we apply this approach to a time-modulated metasurface in the Teraherz regime consisted of graphene-wrapped silicon microwires. For this purpose, we use an accurate and efficient semi-analytical framework based on multipole scattering. We demonstrate the utility of the design rule for tunable beam steering and focusing of generated frequency harmonics giving rise to several intriguing effects such as spatial decomposition of harmonics, anomalous bending with full coverage of angles and dual-polarity lensing. Furthermore, we investigate the angular and spectral performance of the time-modulated metasurface in manipulation of generated frequency harmonics to verify its constant phase response versus incident wavelength and angle. The nonreciprocal response of the metasurface in wavefront engineering is also studied by establishing nonreciprocal links with large isolations via modulation-induced phase shift. The proposed design approach enables a new class of high-efficiency tunable metasurfaces with wide angular and frequency bandwidth, wavefront engineering capabilities, nonreciprocal response and multi-functionality.

Neurophenomenology revisited: second-person methods for the study of human consciousness.

In the study of consciousness, neurophenomenology was originally established as a novel research program attempting to reconcile two apparently irreconcilable methodologies in psychology: qualitative and quantitative methods. Its potential relies on Francisco Varela’s idea of reciprocal constraints, in which first-person accounts and neurophysiological data mutually inform each other. However, since its first conceptualization, neurophenomenology has encountered methodological problems. These problems have emerged mainly because of the difficulty of obtaining and analyzing subjective reports in a systematic manner. However, more recently, several interview techniques for describing subjective accounts have been developed, collectively known as “second-person methods.” Second-person methods refer to interview techniques that solicit both verbal and non-verbal information from participants in order to obtain systematic and detailed subjective reports. Here, we examine the potential for employing second-person methodologies in the neurophenomenological study of consciousness and we propose three practical ideas for developing a second-person neurophenomenological method. Thus, we first describe second-person methodologies available in the literature for analyzing subjective reports, identifying specific constraints on the status of the first-, second- and third- person methods. Second, we analyze two experimental studies that explicitly incorporate second-person methods for traversing the “gap” between phenomenology and neuroscience. Third, we analyze the challenges that second-person accounts face in establishing an objective methodology for comparing results across different participants and interviewers: this is the “validation” problem. Finally, we synthesize the common aspects of the interview methods described above. In conclusion, our arguments emphasize that second-person methods represent a powerful approach for closing the gap between the experiential and the neurobiological levels of description in the study of human consciousness.

Nash Equilibrium and International Law

A new wave of realists argues that international law loses its normative force because states that ‘follow’ international law are merely participants in a Prisoner’s Dilemma seeking to achieve self-interested outcomes. Such claims are not just vastly exaggerated; they misunderstand the significance of game theory. Properly conceived, international law is a Nash Equilibrium – a focal point for states as they make rational decisions regarding strategy. In domains where international law has the greatest purchase, the preferred strategy is reciprocal compliance with international norms. This strategy is consistent with the normativity of law and morality, both of which are characterized by self-interested actors who accept reciprocal constraints to generate Nash Equilibria and, ultimately, a stable social contract. These agents – ‘constrained maximizers’, as the philosopher David Gauthier calls them – accept constraints in order to achieve cooperative benefits. This article concludes that it is also rational for states to comply with these constraints: agents evaluate competing plans and strategies, select the best course of action, and then stick to their decision, rather than obsessively re-evaluating their chosen strategy. A state that defects when the opportunity arises may reduce its overall payoff as compared to a state that selects and adheres to a strategy of constrained maximization.

Off‐Shoring Clinical Research: Exploitation and the Reciprocity Constraint

The last 20 years have seen a staggering growth in the practice of off-shoring clinical research to low-and middle-income countries (LICs and MICs), a growth that has been matched by the neoliberal policies adopted by host countries towards attracting trials to their shores. A recurring concern in this context is the charge of exploitation, linked to various aspects of off-shoring. In this paper, I examine Alan Wertheimer's approach and offer an alternative view of understanding exploitation in this context. I will suggest that the justification for the enterprise of research is largely dependent on its integration within a health system from which participants regularly benefit and I argue that an attention to a principle of reciprocity will enable us to better recognize and address exploitation in international research.

Trajectory planning for multiple unmanned vehicles under reciprocal constraints

In this article, a special class of trajectory optimization problems is formalized and solved. It involves the optimization of different unmanned vehicle (UMV) trajectories that are coupled through reciprocal constraints. It is shown in the article that searching for a solution to the problem at hand may stipulate not just planning a longer than the shortest possible path for each UMV, but also choosing slower travel speeds in order to co-ordinate between the UMVs. Although it seems that solving the problem possesses merits, it has been only partially treated before. Here it is solved by utilizing an evolutionary approach which involves a new algorithmic feature that allows striving towards the desired optimality. The approach is demonstrated and studied through solving and simulating several trajectory planning problems. It is shown that a wide range of problems might be related to that class of problems.