Symmetric Response Research Articles

Abstract This study examines the relationship between fertility and social policies across countries within the European Union. Using European Union Statistics on Income and Living Conditions (EU‐SILC) data from 2005 to 2020, the research investigates how increases and reductions in family allowances are connected to the likelihood of subsequent births in the short term. Based on the social investment hypothesis and a general expansion of family policies in the European Union since 2005, we investigate if and how increased family support contributes to birth events within families. The novel contribution of the analysis is to assess asymmetric fertility reactions to changes in family‐related social benefits. We present the first comparative study that not only analyses expansive policy changes but also retrenchments. Specifically, we look at changes in benefit generosity and universalism from one year to another. Findings indicate that enhancing the generosity of cash benefits is positively related to an increase in the likelihood of having a child. However, reductions in generosity are associated with larger declines in fertility responses, highlighting a negativity bias. In contrast, changes in universalism exhibit more symmetric behavioral responses, with expansions and retrenchments linked to comparable effect sizes regarding subsequent births. Similarly, the combined indicator of generosity and universalism reveals balanced associations in both directions.

Abstract The unique wave-manipulation capabilities of zero-index metamaterials (ZIMs) offer a new opportunity for realizing bound states in the continuum (BICs). However, the relationship between anomalous scattering and BICs remains underexplored when parity-time (PT) symmetry is introduced. In this work, we demonstrate that a BIC splits into a pair of lasing modes carrying opposite topological charges by introducing PT symmetry through gain-loss cylinders embedded in ZIM layers. Theoretical analysis and numerical simulations reveal that lasing and unidirectional transparency phenomena result from the singularities and exceptional points of the scattering matrix. Moreover, exceptional points can be tuned via propagation phase modulation in the air gap, and their coalescence produces quasi-BICs with symmetric responses. This work provides a framework for manipulating BICs and topological lasing modes in non-Hermitian systems, offering new insights for designing non-Hermitian photonic devices.

High-performance broadband photodetectors traditionally based on III-V and II-VI semiconductors, despite their commercial success in the near- and mid-infrared regions, suffer from high fabrication cost, poor CMOS compatibility, and the need for cryogenic cooling, thus limiting their large-scale integration. Here, we demonstrate a virtual graphene/PbTe/Si heterojunction photodetector fabricated by magnetron sputtering, offering a scalable and cost-effective route to high-performance optoelectronic devices. The device exhibits a bias-tunable photoresponse governed by quantum tunneling at the PbTe/Si interface. At ±3 V biases, the photocurrent differs by nearly 2 orders of magnitude under low light intensities, whereas a symmetric response with less than 5% variation is observed at high light intensities. Exploiting this nonlinear response, we establish a dual-mode optical communication scheme, where plaintext is transmitted at high intensities and encrypted inverse codes are generated under low intensities. This built-in encoding functionality enables a simple yet effective strategy for secure optical communication without complex external circuits. Moreover, the CMOS-compatible fabrication process ensures seamless integration with existing silicon photonic platforms, highlighting the potential of this approach for future large-scale on-chip optical communication technologies.

The present research deals with analyzing the role of oil rent in Russian economy and finance system as well as identifying systemic restrictions stipulated by today’s dependence of the country on hydrocarbon export. The basis of the work is formed by historic – economic and macro-analytical approaches, which allows us to trace transformation of economic growth mechanism in Russia from mobilization model of the Soviet Union to the current model of the Russian Federation, where power resources perform the function of capital source. Historically in conditions of insufficient amount of private savings and limited possibilities of finance institutions earnings from power resource export became the base of budget revenue of the budget system in the Russian Federation, the source of investment project implementation and safe backing of long-term social and economic stability. However, oil price drop in spring 2025 caused by foreign economic factors (trade war of the US with record high custom-tariff restrictions and symmetric response of countries-counteragents, a growth in oil supply on the part of OPEK+ countries and general decline in demand on traditional power carriers) exposes vulnerability of the current finance and in general macro-economic structure. Analysis of the federal budget of Russia fulfillment for the 1sr quarter 2025 shows a sharp rise in deficit, drop in oil and gas revenues and reduction in the liquidity part of the National Wealth Foundation. These factors can threaten sustainability of the finance system of Russia. Today’s compensatory steps, i.e. tax adjustment, foreign currency interventions, operative redistribution of expenses should be considered as short-term ones. Without structural transformation and cutting rent dependence Russian economy could run into risk of entering a long-term stagnation. In conclusion the research highlighted the necessity of institutional reforms, strengthening investment climate and passing to saving model based mainly on internal capital but not on export rent.

Anisotropic nonlinear optical effects, including second- and third-harmonic generation (SHG and THG), in two-dimensional (2D)-layered materials are critical for developing on-chip nonlinear photonic and polarization-sensitive devices. Here, we investigate the layer-dependent anisotropic SHG and THG in a few-layer palladium diselenide (PdSe2). Bilayer PdSe2 exhibits a 4-fold symmetric polar response, whereas four-layer PdSe2 displays a distinctive dumbbell-shaped polar pattern under parallel pump-SHG polarization configurations. By tuning the pump polarization direction, we reveal pronounced differences in SHG polarization orientation and ellipticity between the bilayer and four-layer samples. Notably, in four-layer PdSe2, the SHG polarization direction is strongly coupled with the excitation ellipticity, producing orthogonal SHG orientations under left- and right-circularly polarized excitation. We also observe pronounced layer-dependent THG anisotropy, with the THG amplitude in bilayer PdSe2 exceeding that of monolayer molybdenum disulfide by more than 60-fold. Harnessing this intrinsic anisotropy, we demonstrate a simple yet effective approach to control SHG polarization directly through pump pulses without additional optical components. This study enhances the fundamental understanding of nonlinear optical anisotropy in 2D materials with implications for the design of ultracompact nonlinear optical devices featuring specific polarization properties.

This study examines the asymmetric impact of macroeconomic volatility on gold price volatility in Vietnam, focusing on inflation, interest rates, exchange rates, and global gold prices. Unlike prior research centered on developed markets with assumptions of symmetric price responses, this paper addresses the unique dynamics of Vietnam’s gold market, where gold functions both as a commodity and quasi-financial asset, within a tightly regulated environment. A key institutional factor is Decree 24, introduced by the State Bank of Vietnam in 2012 to curb speculation, stabilize prices, and centralize gold trading. While initially effective, its long-term efficacy remains uncertain, particularly in the face of global disruptions such as the COVID-19 pandemic. Using an Exponential Generalized Autoregressive Conditional Heteroskedasticity (EGARCH) model, the study analyzes monthly data from January 2007 to May 2023 across three phases: pre-Decree 24, post-Decree 24, and during COVID-19. The model captures volatility persistence and asymmetric responses of gold prices to macroeconomic shocks. Findings show that global gold prices consistently influence Vietnam’s gold price volatility, though this linkage weakens post-Decree 24, reflecting partial market insulation. Inflation becomes a more prominent driver of volatility in the regulated period, underscoring gold’s inflation-hedging role. Interest and exchange rates exhibit limited effects, and the COVID-19 period reveals heightened vulnerability, raising concerns over the rigidity of the existing regulatory regime. These results suggest the need for a more adaptive policy framework to balance market stability with responsiveness. The study contributes to emerging market literature by integrating regulatory context with asymmetric macroeconomic analysis.

Two EEG-responses to periodical auditory 40-Hz stimulation – auditory steady-state response (ASSR) and sustained wave (SW) – are important neurophysiological correlates of temporal and spectral aspects of auditory perception, respectively. However, little is known about the sex difference of their development in children of 3–6 years, the period of extensive language acquisition. We registered a 32-channel electroencephalogram (EEG) while 500-ms 40-Hz click trains (n = 150) were presented to 57 typically developing children (27 females). We also assessed total language skill, expressive and receptive speech abilities, the perception of speech in noise and pseudowords repetition. 40-Hz ASSR was not very clearly expressed in our sample but showed developmental increase for both boys and girls. Topography of SW showed significant right-hemisphere predominance in boys, while girls had more symmetric response. On a subsample of boys (n = 14) we also found that the laterality index of SW correlated with speech in noise repetition score: the greater rightwarded the laterality was, the worse boys repeated words in noise. Our results are also consistent with the findings of greater lateralization of some components of EEG-activity in men.Supplementary InformationThe online version contains supplementary material available at 10.1038/s41598-025-08266-x.

Symmetrical response of plant diversity but asymmetrical response of biomass production to rainfall reduction and addition in global grasslands

Lateralization of neuronal functions plays a critical role in regulating behavioral flexibility, but the underlying molecular mechanisms are challenging to establish at a single-neuron level. We previously showed that attraction of C. elegans to a medium-chain alcohol switches to avoidance in a uniform background of a second attractive odorant. This context-dependent behavioral plasticity is mediated by symmetric inversion of the odor-evoked response sign in the bilateral AWC olfactory neurons. Here we show that this symmetric response plasticity is driven by asymmetric molecular mechanisms in the AWC neuron pair. Mutations in the gcy-12 receptor guanylyl cyclase abolish odor response plasticity only in AWCOFF; the opposing odor-evoked response signs in AWCOFF and AWCON in gcy-12 mutants results in these animals being behaviorally indifferent to this chemical. We find that gcy-12 is expressed, and required, in both AWC neurons to regulate odor response plasticity only in AWCOFF. We further show that disruption of AWC fate lateralization results in loss of asymmetry in the response plasticity in gcy-12 mutants. Our results indicate that symmetric neuronal response plasticity can arise from asymmetry in underlying molecular mechanisms, and suggest that lateralization of signaling pathways in defined conditions may enhance neuronal and behavioral flexibility.

Abstract Optical chiral metasurfaces provide distinct responses to circularly polarized light of different handedness, which hold great promise for practical applications in chiral lasers, biomedical sensors and drug development, etc. Recently, some fascinating Janus metasurfaces featuring asymmetric chiral transmission/reflection are demonstrated to boost the information capacity and enable efficient optical applications. However, the quality factor (Q‐factor) of the realized Janus chiral metasurfaces so far is relatively low due to substantial radiative loss under broken symmetry or the nonradiative loss inherent to the plasmonic structures. Apart from that, the realized asymmetric circular dichroism functionality is often limited. To address the issue, a multifunctional all‐dielectric chiral Janus metasurface supporting high‐Q multipolar resonances is proposed. By controlling both the in‐plane and out‐of‐plane symmetry of the metasurface, tunable high Q‐factor multipolar resonances with controllable far‐field polarization states can be achieved. This study showcases that for both top‐down and bottom‐up excitations, the high‐Q (Q > 3000) metasurface exhibits symmetric and maximum intrinsic chiroptical responses, and simultaneous high‐contrast asymmetric extrinsic chiroptical responses. Moreover, the near‐field unbalanced chiral responses of the metasurface also contribute to enhanced and unidirectional third‐harmonic generation. The study may offer a broadly applicable strategy for the design of high‐Q multifunctional spin‐selective optical devices.

VLSI design of symmetric two-dimensional finite impulse response filter architecture using approximate circuits and parallel Processing

Abstract The free-vibration response of the conservative planar elastic pendulum falls into one of several categories, depending on the system parameters and the initial conditions. It has been shown in many previous studies that the free-vibration response of the system can be chaotic, quasi-periodic, or periodic. In this work, we present a new category of response: a slow sequential, back-and-forth switching between a nearly periodic response and its mirror-image. This switching resembles the Dzhanibekov effect. We show that the frequency of switching is unrelated to the frequency of the pendulum swings but rather depends on initial conditions. Specifically, we demonstrate Dzhanibekov-like transitions of symmetric and asymmetric nearly periodic responses. For each of these responses, we present Fourier transforms that reveal frequency combs at two scales. One frequency comb is related to the nearly periodic response of the elastic pendulum, and the other frequency comb is related to the much slower Dzhanibekov transitions.

Biological studies on symmetry can be expanded to consider red (longer wavelengths) and blue (shorter wavelengths) shifts as antisymmetries (opposite-pattern symmetries), which may arise from similar underlying causes (invariant process symmetries). In this context, classic shift asymmetries of redder plumage in response to higher dietary carotenoids appear conceptually incomplete, as potential blue-shifted counterparts were not considered. A latent symmetric response is highlighted by recent evidence showing that the maximum absorbance bands of various colorful plumage pigments are red-shifted in birds with ultraviolet-sensitive (UVS) color vision but blue-shifted in those with violet-sensitive (VS) color vision. Blue-shifted responses to increased dietary carotenoid contents may also be underestimated, as relevant studies have focused on species-rich but uniformly UVS Passerida passerines. This study explored the relationship between pattern–process symmetries and diets of VS Piciformes–Coraciiformes by gauging the responses of their plumage reflectance to a modified diet index (Dietc), where the overall rank carotenoid contents of food items were weight-averaged by three levels of importance in a species’ diet. In the case of both sexes, the main long-wavelength reflectance band for the three carotenoid-based pigment classes defined the same graded series of blue shifts in response to higher Dietc. Yellow showed a strong absolute (negative slope) blue shift, orange showed a weaker absolute blue shift, and red exhibited only a blue shift (flat, non-significant slope) relative to absolute red shifts (positive slope). The secondary shorter-wavelength reflectance band was also unresponsive to Dietc in the VS Piciformes–Coraciiformes (relative blue shift) compared with earlier evidence for it decreasing (absolute red shift) at higher Dietc in UVS species. Results for the intervening minimum reflectance (maximum absorbance) band were intermediate between those for the other reflectance bands. No pigment class monopolized lower or higher Dietc, but red was less variable overall. Phylogenetic independence, sexually similar responses, and specimen preservation reinforced characterizations. A review of avian perceptual studies suggested that VS models discriminate yellows and oranges extremely well, consistent with the importance of the corresponding carotenoids as Dietc indicators. Both UVS and VS species appear to produce putatively more costly and possibly beneficial carotenoid metabolites and/or concentrations in response to higher Dietc, supporting underlying invariant processes in relation to carotenoid limitations and honest signaling despite opposite plumage shifts and their different chemical bases. In symmetry parlance, pigment classes (red) or wavebands (short) that lack responses to Dietc suggest broken pattern and process symmetry. The biology of VS Piciformes–Coraciiformes may favor such exceptions owing to selection for visual resemblance and tuning specializations, although universal constraints on physical and chemical properties of (particularly red) carotenoids may favor certain functional tendencies. Thus, symmetry principles organize carotenoid diversity into a simplified and predictive framework linked to color vision.

Demand response (DR) has high regulation potential, which can reduce the power supply–demand imbalance caused by extreme disasters. However, its actual effectiveness still needs to be improved because of low user willingness and incomplete compensation mechanisms. To address this issue, a symmetrical incentive mechanism for DR is proposed. Building upon this mechanism, a bi-level load restoration optimization model under extreme events is proposed. The upper-level model minimizes grid-side costs during load restoration, determining load restoration ratios and incentive coefficients transmitted to the lower level. The lower-level model maximizes user profits while considering comfort-level losses from DR participation, solving for actual response quantities that are fed back to the upper level. To efficiently solve the proposed load restoration model, an iterative mixed-integer load restoration solver is proposed. Case studies demonstrate that the proposed symmetrical mechanism achieved an 89.6% participation rate, showing a 2.46% improvement over fixed incentive schemes. Grid payment costs were reduced by CNY 365,400, achieving incentive compatibility that facilitates rapid load restoration post extreme disasters.

This study reports the implementation of a proof-of-concept, artificial intelligence (AI)-driven clinical decision support system for detecting nystagmus. The system collects and analyzes real-time clinical data to assist in diagnosing, demonstrating its potential for integration into telemedicine platforms. Patients may benefit from the system's convenience, reduced need for travel and associated costs, and increased flexibility and increased flexibility through both in-person and virtual applications. A bedside clinical test revealed vertigo during rightward body movement, and the patient was referred for videonystagmography (VNG). The VNG showed normal central ocular findings. During the right Dix-Hallpike maneuver, the patient demonstrated rotatory nystagmus accompanied by vertigo. Caloric tests revealed symmetric responses, with no evidence of unilateral or bilateral weakness. A cloud-based deep learning framework was developed and trained to track eye movements and detect 468 distinct facial landmarks in real time. Ten subjects participated in this study. The slow-phase velocity (SPV) value was verified for statistical significance using both VNG machine-generated graphs and clinician assessment. The average SPV was compared to the value generated by the VNG machine. The calculated statistical values were as follows: p < 0.05, a meansquared error of 0.00459, and a correction errorof±4.8%. This deep learning model demonstrates the potential to provide diagnostic consultation to individuals in remote locations. To some extent, it may supplement or partially replace traditional methods such as VNG.Ongoing advancements in machine learning within medicine will enhance the ability to diagnose patients, facilitate appropriate specialist referrals, and support physicians in post-treatment follow-up. As this was a proof-of-concept pilot study, further research with a larger sample size is warranted.

Exchange rate volatility has long been a central concern in international finance due to its implications for trade, investment, and monetary policy. This article presents a comprehensive theoretical review of modeling exchange rate volatility using ARCH (Autoregressive Conditional Heteroskedasticity) and GARCH (Generalized ARCH) frameworks, emphasizing recent advancements over the past decade (2015–2025). Beginning with the foundational concepts introduced by Engle (1982) and Bollerslev (1986), the paper outlines the mathematical structure and interpretative significance of ARCH and GARCH models in capturing volatility clustering, persistence, and time-varying variance in exchange rate returns. A detailed comparison is provided between standard models and their extensions, including GARCH-M, EGARCH, and TGARCH, which incorporate features like risk premia and asymmetric responses to shocks. Recent empirical applications are discussed to highlight how these models have been expanded to include macroeconomic variables (via GARCH-MIDAS), account for structural breaks, and better capture tail risk using alternative error distributions such as the Normal Tempered Stable. Furthermore, the article explores how GARCH-based models are applied beyond traditional currency pairs, including in cryptocurrency markets and during crisis periods, underscoring their adaptability. Despite certain limitations, such as sensitivity to structural changes and assumptions of symmetric responses, ARCH/GARCH models remain foundational in volatility forecasting due to their tractability, empirical robustness, and capacity to incorporate evolving market dynamics. The article concludes that while modern econometrics has introduced increasingly complex hybrid models, the core principles of ARCH and GARCH continue to offer a reliable and interpretable framework for understanding exchange rate volatility. Keywords: Exchange rate volatility, ARCH model, GARCH model, Risk premium, Asymmetric volatility, Financial econometrics

Exchange rate volatility has long been a central concern in international finance due to its implications for trade, investment, and monetary policy. This article presents a comprehensive theoretical review of modeling exchange rate volatility using ARCH (Autoregressive Conditional Heteroskedasticity) and GARCH (Generalized ARCH) frameworks, emphasizing recent advancements over the past decade (2015–2025). Beginning with the foundational concepts introduced by Engle (1982) and Bollerslev (1986), the paper outlines the mathematical structure and interpretative significance of ARCH and GARCH models in capturing volatility clustering, persistence, and time-varying variance in exchange rate returns. A detailed comparison is provided between standard models and their extensions, including GARCH-M, EGARCH, and TGARCH, which incorporate features like risk premia and asymmetric responses to shocks. Recent empirical applications are discussed to highlight how these models have been expanded to include macroeconomic variables (via GARCH-MIDAS), account for structural breaks, and better capture tail risk using alternative error distributions such as the Normal Tempered Stable. Furthermore, the article explores how GARCH-based models are applied beyond traditional currency pairs, including in cryptocurrency markets and during crisis periods, underscoring their adaptability. Despite certain limitations, such as sensitivity to structural changes and assumptions of symmetric responses, ARCH/GARCH models remain foundational in volatility forecasting due to their tractability, empirical robustness, and capacity to incorporate evolving market dynamics. The article concludes that while modern econometrics has introduced increasingly complex hybrid models, the core principles of ARCH and GARCH continue to offer a reliable and interpretable framework for understanding exchange rate volatility. Keywords: Exchange rate volatility, ARCH model, GARCH model, Risk premium, Asymmetric volatility, Financial econometrics

BackgroundEcological land evolution is pivotal in shaping regional landscapes and ecosystem functions. However, existing metrics are limited in quantifying patch-scale dynamics of connectivity and fragmentation during the processes of ecological land degradation and restoration. This study introduces the Ecological Land Evolution Index (ELEI), a novel framework integrating spatial proximity and connectivity to evaluate spatiotemporal complexities of ecological land changes at the patch level. By incorporating adjacency rules and continuous value systems, ELEI offers a granular analysis of connectivity-fragmentation tradeoffs, addressing limitations in traditional landscape metrics.ResultsUsing four temporal land use datasets (1990–2020) from the urban agglomeration in the middle reaches of the Yangtze River (UAMRYR) in China, we applied ELEI to characterize ecological land restoration (ELR) and degradation (ELD). Sensitivity analysis confirmed ELEI’s robustness, identifying connected patch area and spatial proximity as primary drivers. Monte Carlo simulations validated formula stability, highlighting symmetrical responses to connectivity changes but residual uncertainties in extreme scenarios (|ELEI|> 60). Additionally, the results demonstrate significant spatiotemporal heterogeneity in ecological land evolution. Degradation of ecological land initially intensified from 2000 to 2010, but then decelerated from 2010 to 2020, while the restoration process first weakened and subsequently strengthened. Notably, the area of degraded ecological land steadily expanded throughout the study period, reaching 17,684.20 km2 between 1990 and 2020, while the restored area totaled 12,025.56 km2. Fragmentation dominated degradation processes, while connection patterns drove restoration. Urban centers like Wuhan and Changsha experienced severe fragmentation aligned with rapid urbanization, whereas cities such as Yichang, Hengyang, and Jiujiang achieved significant restoration via infilling and connection.ConclusionsELEI provides a nuanced understanding of ecological land dynamics in rapidly urbanizing regions by identifying restoration successes and ongoing degradation hotspots. Additionally, the integration of ELEI variants (arithmetic mean ELEI (MELEI) and area-weighted mean ELEI (AWMELEI)) highlights their value in tracking long-term connectivity trends and degradation processes. This framework offers actionable insights for balancing urban development and conservation, underscoring its value in regional planning and sustainable landscape management.

This paper proposes a spatially adaptive feature fine fusion network consisting of a Fast Convolution Decomposition Sequence (FCDS) and a Spatial Selection Mechanism (SSM). Firstly, in FCDS, a large kernel convolution decomposition operation is used to break down dense convolution kernels into small convolutions with gradually increasing hole rates, forming a continuous kernel sequence to obtain finer scale features. This approach significantly reduces the number of parameters, improves network inference efficiency, and preserves the spatial feature expression ability of the network. Notably, the decomposed convolution kernel sequence adopts a symmetric dilation rate increment strategy, maintaining symmetry constraints in kernel weight distribution while expanding receptive fields. On this basis, the spatial selection mechanism is utilized to enhance the key features and background differences of the target location in the feature map, dynamically allocate weights to different fine scale feature maps, and improve the adaptive ability of multi-scale domains. This mechanism employs symmetric attention weight allocation (symmetric channel attention + spatial attention) to establish complementary symmetric response patterns across feature maps in both channel and spatial dimensions. Numerous experiments have shown that our method achieves higher performance with 81.64%, 91.34%, 91.20%mAP on three commonly used remote sensing target datasets (DOTA, UCAS AOD, HRSC2016) compared to existing advanced detection networks.

Symmetric responses of microbial carbon and nutrient limitations to warming and cooling in boreal forests: Insights from a transplant experiment