Reciprocity Symmetry Research Articles

Energy-information trade-off induces continuous and discontinuous phase transitions in lateral predictive coding

Lateral predictive coding is a recurrent neural network that creates energy-efficient internal representations by exploiting statistical regularity in sensory inputs. Here, we analytically investigate the trade-off between information robustness and energy in a linear model of lateral predictive coding and numerically minimize a free energy quantity. We observed several phase transitions in the synaptic weight matrix, particularly a continuous transition that breaks reciprocity and permutation symmetry and builds cyclic dominance and a discontinuous transition with the associated sudden emergence of tight balance between excitatory and inhibitory interactions. The optimal network follows an ideal gas law over an extended temperature range and saturates the efficiency upper bound of energy use. These results provide theoretical insights into the emergence and evolution of complex internal models in predictive processing systems.

Magneto-chiral backscatterings by rotationally symmetric nonreciprocal structures

It was proved that the joint operation of electromagnetic reciprocity and n-fold (n ≥ 3) rotational symmetry would secure arbitrary polarization-independent backscattering efficiency [Phys. Rev. B 103(4), 045422 (2021)10.1103/PhysRevB.103.045422]. Here we remove the restriction of reciprocity and study the backscatterings of plane waves by rotationally symmetric magneto-optical structures, with collinear incident wavevector, rotational axis and externally applied magnetic field. It is revealed that though nonreciprocity removes the degeneracy of backscattering efficiencies for circularly-polarized incident waves of opposite handedness, the remaining rotational symmetry is sufficient to guarantee that the efficiency is related to the polarization ellipticity only, having nothing to do with the orientations of the polarization ellipses. Moreover, the backscattering efficiency reaches its extremes (maximum or minimum values) always for circularly-polarized incident waves, and for other polarizations the efficiency is their ellipticity-weighted arithmetic average. The principles we have revealed are dictated by rotational symmetries only, which are irrelevant to specific geometric or optical parameters and are intrinsically robust against any rotational-symmetry preserving perturbations. The correlations we have discovered could be further exploited for fundamental explorations in nonreciprocal photonics and practical applications including polarimetry and ellipsometry.

Analysis of the Influence of Polarization Measurement Errors on the Parameter and Characteristics Measurement of the Fully Polarized Entomological Radar

Measuring the orientation, mass and body length of migratory insects through entomological radar is crucial for early warnings of migratory pests. The fully polarized entomological radar is an efficient device for observing migratory insects by calculating insect parameters through the scattering matrix obtained from the target. However, the measured target scattering matrix will be affected by system polarization measurement errors, leading to errors in insect parameter calculation, while the related analysis is currently relatively limited. Therefore, the scattering matrix measurement process is modeled, followed by an analysis of the effects of different errors on orientation, mass and body length estimation. The influence of polarization measurement errors on insect scattering characteristics is also analyzed. The results present that for fixed polarization measurement errors, the measurement errors of insect orientation, mass and body length will vary with insect orientation in specific patterns, and the distribution of measured insect parameters will be drastically distorted compared to the true parameter distribution. In addition, polarization measurement errors could seriously disrupt the reciprocity and bilateral symmetry of the measured insect scattering matrix. These analyses and conclusions provide a good basis for eliminating the effects of polarization measurement errors and improving the accuracy of insect parameter measurement.

Jakutijos medžiotojų bei elnių augintojų ir plėšrūnų keršto santykiai taigoje

This article considers the notion of revenge as an agency of wolves, bears and the master-spirits in the animistic worldview of indigenous Eveny and Sakha hunters and the reindeer herders of the Eveno-Bytantaiskii and Tomponskii ulusy (districts) of North Yakutia. Predators are perceived by hunters and herders as conscious non-human beings that can enter into relations with humans on a reciprocal basis. The possibility that predators may carry out revenge on people can be perceived as showing that there are similarities between humans and non-human predators. This article shows how the notions of reciprocity, similarity and relational symmetry between people and predators are reflected in the narratives and hunting rituals of indigenous hunters and herders. As comparative examples, the blood feud customs that earlier existed among the Tungus, Sakha people and Chukchee clans are also considered here. Although these customs no longer exist in the contemporary societies of the indigenous people of Yakutia, the notions underlying them very much reflect the human-predator relations on the taiga today.

Universal embedding of a non-Hermitian reciprocal scattering optical system into a Hermitian time-reversal-invariant system

For Hermitian optical systems, reciprocity and time-reversal symmetry are equivalent. In non-Hermitian systems that have gain and/or loss, however, they are not equivalent. Here, we point out a connection between reciprocity and time-reversal symmetry in general. For a non-Hermitian system, we show that reciprocity can be viewed as a manifestation of the time-reversal symmetry of an enclosing Hermitian system. Our work deepens the understanding of the general constraints on the scattering matrix of non-Hermitian optical systems.

A Channel Imbalance Calibration Scheme with Distributed Targets for Circular Quad-Polarization SAR with Reciprocal Crosstalk

As polarimetric antennas can be isolated through excellent electronic frameworks in circular quad-polarization (CQP) synthetic aperture radar (SAR) systems, cross-polarization (x-pol) and co-polarization (co-pol) channel imbalances are more challenging and essential to calibrate than crosstalk in polarimetric calibration (PolCAL). In uncalibrated CQP SAR images without corner reflectors (CRs), the reciprocity and reflection symmetry assumptions of the distributed targets are commonly used to estimate the x-pol and co-pol channel imbalances, respectively. To suppress the influence of additive noise on determining channel imbalances through distributed targets, high signal-to-noise ratio (SNR) distributed targets should be obtained from the x-pol and co-pol channels of the CQP SAR images: namely, surface-dominated and volume-dominated targets. However, some reflection symmetry assumptions used in the existing calibration literature have poor applicability with volume-dominated targets, resulting in unsatisfactory estimation results for the co-pol channel imbalance phase. In this paper, we assess the priority of the reflection symmetry properties of volume-dominated targets used to calibrate the co-pol channel imbalance phase in CQP SAR data synthesized from linear quad-polarization data of ALOS, GF-3, and RADARSAT-2. In the theoretical part, high-priority reflection symmetry (termed semireflection symmetry) assumptions are confirmed as the most suitable for estimating the co-pol channel imbalance phase, and were selected to develop an algorithm for estimating the co-pol channel imbalance phase. Furthermore, based on the novel method for estimating the co-pol channel imbalance phase, a channel imbalance calibration scheme is proposed for CQP SAR systems with reciprocal crosstalk, including extracting surface-dominated and volume-dominated targets, and estimating and filtering channel imbalances. We demonstrate the effectiveness of our proposed scheme with CRs in simulated CQP SAR images. The experimental results show that the calibration scheme is an effective workflow for estimating channel imbalances in CQP SAR systems with reciprocal crosstalk.

Flip-component metasurfaces for camouflaged meta-domes.

Allowing microwaves to transmit through without changing the wavefront is one of the essential requirements of the dome structures of antenna arrays like radars. Here, we demonstrate a microwave metasurface as an array of two types of meta-atoms, which are the flip counterparts to each other. Due to the reciprocity and space-inversion symmetry, the wavefront in the transmission is unchanged by the metasurface in a broad spectrum; while at the same time, the wavefront in reflection can be manipulated independently by changing the arrangement of the meta-atoms. Specifically, a random-flip metasurface that produces diffuse reflection is realized, enabling a camouflaged meta-dome. The broadband, wide-angle, and polarization-independent diffuse reflection and undistorted transmission are numerically and experimentally verified. Our finding enables a unique meta-dome structure that has camouflage functionality.

Internal transformations and internal symmetries in linear photonic systems

Lorentz reciprocity, energy conservation, and time-reversal symmetry are three important global constraints of Maxwell's equations. Unlike time-reversal symmetry, Lorentz reciprocity and energy conservation usually are not considered as symmetries, i.e., they are not associated with operators. In this paper, we provide a unified treatment of these three global constraints from a perspective of internal symmetry. We define operators of transformations associated with each of these constraints, referred to as internal transformations. When Maxwell's equations are written as a linear system of equations, these internal transformations correspond to the operations of transpose, conjugate transpose, and conjugate of the system matrix, respectively. We show the three global constraints naturally follow from three fundamental identities of linear systems under the three matrix operations. We discuss the properties of electromagnetic fields and scattering matrices associated with these internal transformations. These internal transformations form the Klein four-group ${V}_{4}={\mathbb{Z}}_{2}\ifmmode\times\else\texttimes\fi{}{\mathbb{Z}}_{2}$, and the internal symmetry group of any photonic structure corresponds to one of the five subgroups of ${V}_{4}$. Our paper provides a theoretical foundation for further exploration of symmetries in photonic systems.

Universal Behavior of the Scattering Matrix Near Thresholds in Photonics.

Scattering thresholds and their associated spectral square root branch points are ubiquitous in photonics. In this Letter, we show that the scattering matrix has a simple universal behavior near scattering thresholds. We use unitarity, reciprocity, and time-reversal symmetry to construct a two-parameter model for a two-port scattering matrix near a threshold. We demonstrate this universal behavior in three different optical systems, namely, a photonic crystal slab, a planar dielectric interface, and a junction between metallic waveguides of different widths.

Symmetry constraints for vector scattering and transfer matrices containing evanescent components: Energy conservation, reciprocity, and time reversal

In this work we study the scattering and transfer matrices for electric fields defined with respect to an angular spectrum of plane waves. For these matrices, we derive the constraints that are enforced by conservation of energy, reciprocity and time reversal symmetry. Notably, we examine the general case of vector fields in three dimensions and allow for evanescent field components. Moreover, we consider fields described by both continuous and discrete angular spectra, the latter being more relevant to practical applications, such as optical scattering experiments. We compare our results to better-known constraints, such as the unitarity of the scattering matrix for far-field modes, and show that previous results follow from our framework as special cases. Finally, we demonstrate our results numerically with a simple example of wave propagation at a planar glass-air interface, including the effects of total internal reflection. Our formalism makes minimal assumptions about the nature of the scattering medium and is thus applicable to a wide range of scattering problems.

Dynamic Nonreciprocity in Loss-Compensated Piezophononic Media

In controlling sound, it is not trivial to engineer a device that can strongly break the reciprocity (symmetry under time reversal) of acoustic wave propagation. Despite significant progress, it is still difficult to obtain a large contrast ratio between the allowed (passing) and forbidden propagation directions, over a broad frequency range, without distortion or attenuation of the signal in the passing direction. The authors propose an approach, based on the acousto-electric effect in piezoelectric semiconductors, that could achieve all of these goals for acoustic waves in elastic solids, to the benefit of noise control, energy harvesting, and transducer technology in general.

A Study of Wind Direction Effects on Sea Surface Specular Scattering for GNSS-R Applications

A modeling study investigating the influence of wind direction on spaceborne global navigation satellite system reflectometry (GNSS-R) near-specular observations of the sea surface is reported. The study first focuses on a purely specular geometry under plane wave incidence, for which it is shown using the theorem of reciprocity and reflection symmetry that up-down wind variations are identically zero. It is also shown that “single-scattering” approximations of rough surface scattering predict no variations with wind direction of any kind for a purely specular geometry, while higher order approximations (such as the second-order small-slope approximation) can predict up/cross wind differences. Examples of these variations are reported and found to be small. Because the delay doppler maps (DDMs) measured in GNSS-R include some nonspecular contributions even for “specular” portions of the DDM, the second part of the study performs an examination of near-specular DDM variations with wind direction using the widely used geometrical optics approximation of surface scattering for a surface described with the non-Gaussian Cox–Munk slope probability density function. Variations with wind direction of the normalized radar cross section (NRCS) mapped onto the surface are examined, and again, it is shown that these variations are small for surface portions contributing to the near-specular portion of the DDM. In addition, it is shown that the dependencies of the bistatic NRCS on wind direction are such that differing portions of the surface “glistening zone” have differing phase shifts in their dependence on wind direction, causing the wind dependencies of the final near-specular DDM to be negligible. The final results of the study suggest that any wind direction dependence in spaceborne GNSS-R should be sought only in portions of the DDM away from the specular region. These results provide information to guide analyses of the wind direction information available in current GNSS-R missions such as TDS-1 and Cyclone Global Navigation Satellite System.

Gospodarka jako zinstytucjonalizowany proces. Instytucjonalizm Karla Polanyiego i jego etyczne konsekwencje

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Economic process as institutionalization of values. Karl Polanyi’s institutional theory and its ethical consequences

This article is devoted to a critical reconstruction of Karl Polanyi’s institutional theory and its ethical consequences. Starting with the distinction between the formal (neoclassical) and the substantive (institutional) understanding of the economy, the article proceeds to discuss the main forms of institutional integration of economic life described by Polanyi: reciprocity (symmetry), redistribution (centricity), and exchange (market). In this context, the author examines the connection between the work of Karl Polanyi and the economic anthropology represented by the works of Richard Thurnwald and Bronisław Malinowski. The author argues that three main forms of institutional integration of economic life introduced by Karl Polanyi can be interpreted both as analytical tools to describe institutions and as a grand scheme for the classification of different economic systems. The next section of the article is devoted to a comparison between the institutional theories of Douglass North and Karl Polanyi. For North, the main explanatory category is the idea of transaction costs, whereas for Polanyi the key idea is that of the social embeddedness of the economy. When speaking about the social embeddedness of the economy, Polanyi draws our attention to the inseparable bonds which exist between economic institutions on the one hand, and culture, social structure and politics on the other. This theoretical difference between North and Polanyi, the author argues, has important ethical consequences. If Polanyi is right, then institutions are not only alternative solutions to a certain economic problem (i.e. the efficient allocation of resources, the reduction of transaction costs) but above all they are the embodiment of different conceptions of a good life. In conclusion, the author emphasizes the political dimension of Karl Polanyi’s institutional theory, along with its intriguing promise of liberating our social and political life from the economistic fallacy, that is, from the unfortunate tendency to think about society in market terms.

Forward scattering of polarized light from a turbid slab: theory and Monte Carlo simulations.

It is proved that if reciprocity and mirror symmetry hold for single scattering by a particle, they also hold for multiple scattering in turbid slab media. Monte Carlo simulations generate a reduced effective Mueller matrix for forward scattering, which satisfies reciprocity and mirror symmetry, but satisfies only reciprocity if the medium contains chiral components. The scattering matrix was factorized by using the Lu-Chipman polar decomposition, which affords the polarization parameters as a function of the radial distance from the center. The depolarization coefficients decrease with increasing distance, whereas the scattering-induced linear diattenuation and retardance become larger in the middle-distance range. The optical rotation for a chiral medium increases with increasing distance.

Symmetry and structure of reflection matrices of celestial bodies with particulate surfaces

The polarization of electromagnetic radiation reflected by a particulate surface is determined by a four by four reflection matrix. Symmetry relations are quite common for such reflection matrices. The reciprocity and mirror symmetry relations are combined to derive a third symmetry relation. These three relations are used to simplify reflection matrices for a variety of special directions of incident and reflected radiation. We show that some elements of the reflection matrix can vanish or equal other elements that have the same or opposite sign. Several applications of the results for studies of particulate surfaces and atmospheres above them are pointed out.

Breaking temporal symmetries for emission and absorption.

Time-reversal symmetries impose stringent constraints on emission and absorption. Antennas, from radiofrequencies to optics, are bound to transmit and receive signals equally well from the same direction, making a directive antenna prone to receive echoes and reflections. Similarly, in thermodynamics Kirchhoff's law dictates that the absorptivity and emissivity are bound to be equal in reciprocal systems at equilibrium, e(ω, θ)=a(ω, θ), with important consequences for thermal management and energy applications. This bound requires that a good absorber emits a portion of the absorbed energy back to the source, limiting its overall efficiency. Recent works have shown that weak time modulation or mechanical motion in suitably designed structures may largely break reciprocity and time-reversal symmetry. Here we show theoretically and experimentally that a spatiotemporally modulated device can be designed to have drastically different emission and absorption properties. The proposed concept may provide significant advances for compact and efficient radiofrequency communication systems, as well as for energy harvesting and thermal management when translated to infrared frequencies.

Symmetry relationships for multiple scattering of polarized light in turbid spherical samples: theory and a Monte Carlo simulation.

This paper presents a theory describing totally incoherent multiple scattering of turbid spherical samples. It is proved that if reciprocity and mirror symmetry hold for single scattering by a particle, they also hold for multiple scattering in spherical samples. Monte Carlo simulations generate a reduced effective scattering Mueller matrix, which virtually satisfies reciprocity and mirror symmetry. The scattering matrix was factorized by using the symmetric decomposition in a predefined form, as well as the Lu-Chipman polar decomposition, approximately into a product of a pure depolarizer and vertically oriented linear retarding diattenuators. The parameters of these components were calculated as a function of the polar angle. While the turbid spherical sample is a pure depolarizer at low polar angles, it obtains more functions of the retarding diattenuator with increasing polar angle.

Constraints on the reciprocal propagation of a quantum particle through a one-dimensional localized complex potential

In the propagation of an electron through a one-dimensional asymmetric complex potential, it is known that while the conventional Green function reciprocity symmetry will ensure transmission to be symmetric between a “left-incident” and a “right-incident” beam, no such symmetry exists for the case of reflection. Here we derive generalized reciprocity relations for both the amplitude and phase of the reflected waves as constraints on the left- and right-incident beams, in complete analogy to what was established in optics. We further provide illustrations of these relations via direct analytical calculations in the case of a real potential, and via numerical studies in the case of a complex potential.

The newtonian limit of hermitian gravity

We construct the gauge invariant potentials of Hermitian Gravity and derive the linearized equations of motion they obey. A comparison reveals a striking similarity to the Bardeen potentials of general relativity. We then consider the response to a point particle source, and discuss in what sense the solutions of Hermitian Gravity reduce to the Newtonian potentials. In a rather intriguing way, the Hermitian Gravity solutions exhibit a generalized reciprocity symmetry originally proposed by Born in the 1930s. Finally, we consider the trajectories of massive and massless particles under the influence of a potential. The theory correctly reproduces the Newtonian limit in three dimensions and the nonrelativistic acceleration equation. However, it differs from the light deflection calculated in linearized generalrelativity by 25%. While the specific complexification of general relativity by extension to Hermitian spaces performed here does not agree with experiment, it does possess useful properties for quantization and is well-behaved around singularities. Another form of complex general relativity may very well agree with experimental data.