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According to the universality hypothesis, the phase behavior of different block copolymer melt models having fixed composition depends solely on two parameters: the invariant chain length $\bar{N}$ and the effective interaction parameter $\chi N$. If models behave universally, they can be compared to each other and can predict experiment quantitatively. Here, we present a simple way to achieve this universality for coarse-grained models. Our method relies on the properties of the monomer interaction potential energy $z$ distribution. In particular, models having near-symmetric $z$-distributions exhibit universal phase behavior using the standard linear definition of the Flory-Huggins parameter $\chi\propto\alpha$, where $\alpha = \epsilon_{AB}-(\epsilon_{AA}+\epsilon_{BB})/2$, and $\epsilon_{xy}$ is the interaction energy between monomers of type $x$ and $y$. Previously, universality had been achieved using a nonlinear $\chi(\alpha)$ function which is difficult to obtain and interpret physically. The main parameter controlling the symmetry of the $z$-distribution is the monomer density $\rho$. Above certain $\rho$, models have symmetric $z$-distributions, and their order-disorder transition points follow the universal curve predicted by Fredrickson-Helfand theory in the experimentally relevant $\bar{N} > 10^2$ range. On the other hand, low-$\rho$ models exhibit skewed $z$-distributions, and the simple $\chi\propto\alpha$ formula is no longer universally applicable to them. Our results can be used for correct block copolymer model building leading to a simple and direct comparison of simulations to experiments, which will facilitate the screening of new block copolymer morphologies and support materials design.

In this paper, we consider the coupling of the metric-affine bumblebee gravity to the Abelian gauge field and obtain the effective model corresponding to the weak gravity limit of this theory. The effective bumblebee theory displays new unconventional couplings between the bumblebee field and its field strength, and the $U(1)$ gauge field along with its respective field strength, as a result of the non-metricity effects. Thus, being a new gauge-bumblebee theory, it represents an example of vector-vector couplings which are very rarely considered, if not entirely overlooked, in the Abelian case. For this theory we calculate the lower perturbative corrections. We close the paper with discussions of other possible vector-vector couplings., Comment: 12 pages

In this paper, we introduce a new category of mappings within metric spaces, specifically focusing on three-point analogs of the well-established Chatterjea type mappings. We demonstrate that Chatterjea type mappings and their three-point analogs are different classes of mappings. A fixed point theorem for generalized Chatterjea type mappings is established. It is shown that these mappings are continuous at fixed point. Connections between generalized Chatterjea type mappings, generalized Kannan type mappings, Chatterjea type mappings, and mappings contracting perimeters of triangles are found. Additionally, we derive two fixed point theorems for generalized Chatterjea type mappings in metric spaces, even when completeness is not mandatory., Comment: 16 pages, submitted to a journal on 11 January 2024. arXiv admin note: text overlap with arXiv:2308.05419

Accurate models of turbulent buoyant flows are essential for the design of nuclear reactors thermal hydraulics and passive safety systems. However, available models fail to fully capture the physics of turbulent mixing when buoyancy becomes predominant with respect to momentum. Therefore, high-fidelity experiments of well-controlled fundamental flows are needed to develop and validate more accurate models. We analyze experiments of positive and negative turbulent buoyant jets, both in uniform and stratified environments, with the aim of understanding the thermal hydraulics of turbulent mixing with variable density and providing high-fidelity data for the development and validation of turbulence models. Non-intrusive, simultaneous Particle Image Velocimetry and Laser Induced Fluorescence measurements were carried out to acquire instantaneous velocity and concentration fields on a vertical section parallel to the axis of a jet in the self-similar region. The Refractive Index Matching method was applied to measure high-resolution buoyant jets with up to 8.6% density difference. These data are free of the typical errors that characterize optical measurements of buoyancy driven flows (e.g., natural and mixed convection) where the refractive index of the fluid is inhomogeneous throughout the measurement domain. Turbulent statistics and entrainment of buoyant jets in uniform and stratified environments are presented. These data are compared with non-buoyant jets in uniform environment, as a reference to investigate the effects of buoyancy and stratification on turbulent mixing. The results will be used for the assessment of current turbulence models and as basis for the development of a new one that captures turbulent mixing.

We introduce GEM3D -- a new deep, topology-aware generative model of 3D shapes. The key ingredient of our method is a neural skeleton-based representation encoding information on both shape topology and geometry. Through a denoising diffusion probabilistic model, our method first generates skeleton-based representations following the Medial Axis Transform (MAT), then generates surfaces through a skeleton-driven neural implicit formulation. The neural implicit takes into account the topological and geometric information stored in the generated skeleton representations to yield surfaces that are more topologically and geometrically accurate compared to previous neural field formulations. We discuss applications of our method in shape synthesis and point cloud reconstruction tasks, and evaluate our method both qualitatively and quantitatively. We demonstrate significantly more faithful surface reconstruction and diverse shape generation results compared to the state-of-the-art, also involving challenging scenarios of reconstructing and synthesizing structurally complex, high-genus shape surfaces from Thingi10K and ShapeNet., Comment: Webpage: https://lodurality.github.io/GEM3D/ -- Cond. accept. to SIGGRAPH 2024 (conf. track) -- Changes (based on reviews): changed style to sigconf; rearranged figures for readability; added missing citations; fixed misaligned centers in Fig. 3; added failure cases (Fig. 10); rewrote discussion; added categories averages to Tab. 8; added Tab. 10 with model capacities

Despite the widespread adoption of prompting, prompt tuning and prefix-tuning of transformer models, our theoretical understanding of these fine-tuning methods remains limited. A key question is whether one can arbitrarily modify the behavior of pretrained model by prompting or prefix-tuning it. Formally, whether prompting and prefix-tuning a pretrained model can universally approximate sequence-to-sequence functions. This paper answers in the affirmative and demonstrates that much smaller pretrained models than previously thought can be universal approximators when prefixed. In fact, the attention mechanism is uniquely suited for universal approximation with prefix-tuning a single attention head being sufficient to approximate any continuous function. Moreover, any sequence-to-sequence function can be approximated by prefixing a transformer with depth linear in the sequence length. Beyond these density-type results, we also offer Jackson-type bounds on the length of the prefix needed to approximate a function to a desired precision.

Within the framework of the spontaneous Lorentz symmetry breaking, we consider a metric--affine generalization of the gravitational sector of the Standard--Model Extension (SME), including the Lorentz--violating (LV) coefficients $u$ and $s^{\mu\nu}$. In this model, we derive the modified Einstein field equations in order to obtain a new axisymmetric vacuum spinning solution for a particular bumblebee's profile. Such a solution has the remarkable property of incorporating the effects of Lorentz symmetry breaking (LSB) through the LV dimensionless parameter $X=\xi b^2$, as the LSB is turned off, $X=0$, we recover the well--established result, the Kerr solution, as expected. Afterwards, we calculate the geodesics, the radial acceleration and thermodynamic quantities for this new metric. We also estimate an upper bound for $X$ by using astrophysical data of the advance Mercury's perihelion., Comment: 36 pages, version accepted to JCAP

Natural Language Inference (NLI) remains an important benchmark task for LLMs. NLI datasets are a springboard for transfer learning to other semantic tasks, and NLI models are standard tools for identifying the faithfulness of model-generated text. There are several large scale NLI datasets today, and models have improved greatly by hill-climbing on these collections. Yet their realistic performance on out-of-distribution/domain data is less well-understood. We explore the opportunity for synthetic high-quality datasets to adapt NLI models for zero-shot use in downstream applications across new and unseen text domains. We demonstrate a new approach for generating NLI data in diverse domains and lengths, so far not covered by existing training sets. The resulting examples have meaningful premises, the hypotheses are formed in creative ways rather than simple edits to a few premise tokens, and the labels have high accuracy. We show that models trained on this data ($685$K synthetic examples) have the best generalization to completely new downstream test settings. On the TRUE benchmark, a T5-small model trained with our data improves around $7\%$ on average compared to training on the best alternative dataset. The improvements are more pronounced for smaller models, while still meaningful on a T5 XXL model. We also demonstrate gains on test sets when in-domain training data is augmented with our domain-general synthetic data.

X-ray Multi-Projection Imaging (XMPI) is an emerging technology that allows for the acquisition of millions of 3D images per second in samples opaque to visible light. This breakthrough capability enables volumetric observation of fast stochastic phenomena, which were inaccessible due to the lack of a volumetric X-ray imaging probe with kHz to MHz repetition rate. These include phenomena of industrial and societal relevance such as fractures in solids, propagation of shock waves, laser-based 3D printing, or even fast processes in the biological domain. Indeed, the speed of traditional tomography is limited by the shear forces caused by rotation, to a maximum of 1000 Hz in state-of-the-art tomography. Moreover, the shear forces can disturb the phenomena in observation, in particular with soft samples or sensitive phenomena such as fluid dynamics. XMPI is based on splitting an X-ray beam to generate multiple simultaneous views of the sample, therefore eliminating the need for rotation. The achievable performances depend on the characteristics of the X-ray source, the detection system, and the X-ray optics used to generate the multiple views. The increase in power density of the X-ray sources around the world now enables 3D imaging with sampling speeds in the kilohertz range at synchrotrons and megahertz range at X-ray Free-Electron Lasers (XFELs). Fast detection systems are already available, and 2D MHz imaging was already demonstrated at synchrotron and XFEL. In this work, we explore the properties of X-ray splitter optics and XMPI schemes that are compatible with synchrotron insertion devices and XFEL X-ray beams. We describe two possible schemes designed to permit large samples and complex sample environments. Then, we present experimental proof of the feasibility of MHz-rate XMPI at the European XFEL., Comment: 47 pages, 17 figures

This paper introduces a framework for depth and pitch control of underwater vehicles in near-surface wave conditions. By effectively managing tail, sail plane angles and hover tank operations utilizing a Linear Quadratic Regulator controller and L1 Adaptive Autopilot augmentation, the system ensures balanced control input distribution and significantly attenuates wave disturbances. This development in underwater vehicle control systems offers potential for improved functionality across a range of marine applications. The proposed framework is demonstrated to be robust in a variety of wave conditions, enabling more precise navigation and improved safety in operational scenarios. The effectiveness of this control strategy is validated through extensive simulations using the Joubert BB2 model., Comment: 8 pages. Submitted to IFAC conference (for September 15, 2024)

We consider a new type of mappings in metric spaces so-called mappings contracting total pairwise distance on $n$ points. It is shown that such mappings are continuous. A theorem on the existence of periodic points for such mappings is proved and the classical Banach fixed-point theorem is obtained like a simple corollary as well as the fixed-point theorem for mappings contracting perimeters of triangles. Examples of mappings contracting total pairwise distance on $n$ points and having different properties are constructed., Comment: 10 pages, 1 figure

Tight relationships exist in the local universe between the central stellar properties of galaxies and the mass of their supermassive black hole. These suggest galaxies and black holes co-evolve, with the main regulation mechanism being energetic feedback from accretion onto the black hole during its quasar phase. A crucial question is how the relationship between black holes and galaxies evolves with time; a key epoch to probe this relationship is at the peaks of star formation and black hole growth 8-12 billion years ago (redshifts 1-3). Here we report a dynamical measurement of the mass of the black hole in a luminous quasar at a redshift of 2, with a look back time of 11 billion years, by spatially resolving the broad line region. We detect a 40 micro-arcsecond (0.31 pc) spatial offset between the red and blue photocenters of the H$\alpha$ line that traces the velocity gradient of a rotating broad line region. The flux and differential phase spectra are well reproduced by a thick, moderately inclined disk of gas clouds within the sphere of influence of a central black hole with a mass of 3.2x10$^{8}$ solar masses. Molecular gas data reveal a dynamical mass for the host galaxy of 6x10$^{11}$ solar masses, which indicates an under-massive black hole accreting at a super-Eddington rate. This suggests a host galaxy that grew faster than the supermassive black hole, indicating a delay between galaxy and black hole formation for some systems., Comment: 5 pages Main text, 8 figures, 2 tables, to be published in Nature, under embargo until 29 January 2024 16:00 (London)

From Nov. 2019 to May 2020, the red supergiant star Betelgeuse experienced an unprecedented drop of brightness in the visible domain called the great dimming event. Large atmospheric dust clouds and large photospheric convective features are suspected to be responsible for it. To better understand the dimming event, we used mid-infrared long-baseline spectro-interferometric measurements of Betelgeuse taken with the VLTI/MATISSE instrument before (Dec. 2018), during (Feb. 2020), and after (Dec. 2020) the GDE. We present data in the 3.98 to 4.15\,$\mu$m range to cover SiO spectral features molecules as well as adjacent continuum. We have employed geometrical models, image reconstruction, as well as radiative transfer models to monitor the spatial distribution of SiO over the stellar surface. We find a strongly in-homogeneous spatial distribution of SiO that appears to be looking very different between our observing epochs, indicative of a vigorous activity in the stellar atmosphere. The contrast of our images is small in the pseudo-continuum for all epochs, implying that our MATISSE observations support both cold spot and dust cloud model.

Although defocus can be used to generate partial phase contrast in transmission electron microscope images, cryo-electron microscopy (cryo-EM) can be further improved by the development of phase plates which increase contrast by applying a phase shift to the unscattered part of the electron beam. Many approaches have been investigated, including the ponderomotive interaction between light and electrons. We review the recent successes achieved with this method in high-resolution, single-particle cryo-EM. We also review the status of using pulsed or near-field enhanced laser light as alternatives, along with approaches that use scanning transmission electron microscopy (STEM) with a segmented detector rather than a phase plate.

Current generation of ground based gamma-ray telescopes observed dozens of sources of photons above 100 TeV. Supernova remnants, pulsar wind nebulae, young stellar clusters and superbubbles are considered as possible sites of PeV-regime particles producing the radiation. Another possible source of PeV particles could be gamma-ray binary systems. In these systems, a strong relativistic outflow from a compact object (neutron star or black hole) collides with the dense wind from a massive companion early-type star. Gamma-ray binaries are observed from radio to high energy gamma-rays as luminous non-thermal sources. Apart from acceleration of very high energy leptons producing most of the non-thermal radiation, these systems may also efficiently accelerate protons. We present here the results of numerical simulation of the PeV-regime proton acceleration in gamma-ray binaries. The simulation is based on relativistic MHD modeling of local flows of magnetized plasma in the region of interaction of two colliding winds. We then inject 0.1 PeV protons into the system and directly follow their trajectories to demonstrate that they are accelerated to energies above PeV. High magnetization of the wind of the young massive star providing a Gauss range field in the winds interaction region is of paramount importance for the acceleration of protons above PeV. The maximum energies of protons accelerated by colliding winds in gamma ray binaries can significantly exceed the energy of the pulsar potential's drop, which limits from above the energy of particles accelerated by an isolated pulsar., Comment: 13 pages, 4 figures, Adv. Space Res., in print

We report here on a major improvement of the control and characterization capabilities of 14N nuclear spin of single NV centers in diamond, as well as on a new method that we have devised for characterizing quantum states, i.e. quantum state tomography using Rabi experiments. Depending on whether we use amplitude information or phase information from Rabi experiments, we define two sub-methods namely Rabi amplitude quantum state tomography (RAQST) and Rabi phase quantum state tomography (RPQST). The advantage of Rabi-based tomography methods is that they lift the requirement of unitary operations used in other methods in general and standard methods in particular. On one hand, this does not increase the complexity of the tomography experiments in large registers, and on the other hand, it decreases the error induced by MW irradiation. We used RAQST and RPQST to investigate the quality of various two-qubit pure states in our setup. As expected, test quantum states show very high fidelity with the theoretical counterpart., Comment: The reviewing process has revealed some inconsistencies in this version

High-rate satellite communications among hundreds and even thousands of satellites deployed at low-Earth orbits (LEO) will be an important element of the forthcoming sixth-generation (6G) of wireless systems beyond 2030. With millimeter wave communications (mmWave, ~30GHz-100GHz) completely integrated into 5G terrestrial networks, exploration of its potential, along with sub-terahertz (sub-THz, 100GHz-300GHz), and even THz (300GHz-3THz) frequencies, is underway for space-based networks. However, the interference problem between LEO mmWave/THz satellite cross-links in the same or different constellations is undeservedly forgotten. This article presents a comprehensive mathematical framework for modeling directional interference in all key possible scenario geometries. The framework description is followed by an in-depth numerical study on the impact of cross-link interference on various performance indicators, where the delivered analytical results are cross-verified via computer simulations. The study reveals that, while highly directional mmWave and, especially, THz beams minimize interference in many cases, there are numerous practical configurations where the impact of cross-link interference cannot be neglected and must be accounted for., Comment: 16 pages, 10 Figures, 2 Tables. The work has been accepted for publication in IEEE Journal on Selected Areas in Communications (JSAC), 2024

The Very Large Telescope Interferometer (VLTI) has been providing breakthrough images of the dust in the central parsecs of Active Galactic Nuclei (AGN), a key component of the AGN unification scheme and AGN host galaxy interaction. In single IR bands, the images can have multiple interpretations some of which could challenge the unification scheme. This is the case for the archetypal type 2 AGN of NGC1068. The ambiguity is reduced by multi-band temperature maps which are hindered by uncertainty in intra-band alignment. We create a chromatic model capable of simultaneously explaining the VLTI GRAVITY+MATISSE 2$\mu$m-13$\mu$m observations of the AGN in NGC1068. We use a simple disk and wind geometry populated with spherical black body emitters and dust obscuration to create a versatile multi-wavelength model for IR interferometric data of dusty objects. This simple geometry is capable of reproducing the K-N-band VLTI data, explains the complex single band images, and solves the alignment between bands. We find that the resulting geometry is consistent with previous studies. Compared to molecular gas emission, our model wind position angle (PA) of $22^3_2{\deg}$ is close to the mas scale outflowing CO(6-5) PA of ~33{\deg} seen with the ALMA. The equivalent 90{\deg} offset model disk PA is also consistent with the CO(6-5) disk axis of 112{\deg} as well as the mas scale disk axis from CO(2-1), CO(3-2), and HCO$^+$(4-3) of 115$\pm$5{\deg}. Furthermore, the resulting model visually resembles the equivalent achromatic image reconstructions. We conclude that the IR emitting structure surrounding the AGN can indeed be explained by the clumpy disk+wind iteration of the AGN unification scheme. Within the scheme, we find it is best explained as a type 2 and the obscuring dust chemistry is consistent with a mix of olivine silicates and 16$\pm$1% amorphous carbon., Comment: 15 pages, 19 appendix pages, 23 figures, and 2 tables. Accepted for publication in A&A

This report introduces a new family of multimodal models, Gemini, that exhibit remarkable capabilities across image, audio, video, and text understanding. The Gemini family consists of Ultra, Pro, and Nano sizes, suitable for applications ranging from complex reasoning tasks to on-device memory-constrained use-cases. Evaluation on a broad range of benchmarks shows that our most-capable Gemini Ultra model advances the state of the art in 30 of 32 of these benchmarks - notably being the first model to achieve human-expert performance on the well-studied exam benchmark MMLU, and improving the state of the art in every one of the 20 multimodal benchmarks we examined. We believe that the new capabilities of the Gemini family in cross-modal reasoning and language understanding will enable a wide variety of use cases. We discuss our approach toward post-training and deploying Gemini models responsibly to users through services including Gemini, Gemini Advanced, Google AI Studio, and Cloud Vertex AI.

We report the reconstruction of the mass component spectra of cosmic rays (protons, helium, carbon, silicon and iron) and their mean mass composition, at energies from 1.4 to 100 PeV. The results are derived from the archival data of the extensive air shower experiment KASCADE. We use a novel machine learning technique developed specifically for this reconstruction, and post-LHC hadronic interaction models: QGSJet-II.04, EPOS-LHC and Sibyll 2.3c. We have found an excess of the proton component and a deficit of intermediate and heavy nuclei components compared to the original KASCADE results. The spectra of protons and helium show a knee-like behavior at ~ 4.4 PeV and ~ 11 PeV, with significances 5.2${\sigma}$ and 3.9${\sigma}$, respectively. The spectrum of the iron component has a hint (2.4${\sigma}$) of a hardening at ~ 4.5 PeV, which can be interpreted as a counterpart of a hardening in the proton spectrum at 166 TeV, recently reported by the GRAPES-3 experiment. The systematic uncertainties of our analysis were found to be smaller than those of the original KASCADE, as well as those of IceTop and TALE experiments, over the most part of the energy range studied. We also estimated separately the uncertainty related to the difference between the three mentioned hadronic interaction models. We also compute a mean logarithm mass of cosmic ray flux as a function of energy. It is in agreement with the results of IceTop, TALE and LHAASO within the uncertainties., Comment: accepted to JCAP; significant content additions compared to the previous version

Efficient trapping of light in nanostructures is essential for the development of optical devices that are based on the interaction between light and matter. In this work, we show theoretically and experimentally that one-dimensional arrays of subwavelength dielectric Mie-resonant particles can support collective resonances with increased $Q$-factors. We demonstrate that the increase of the $Q$-factor can be explained by interaction between the collective electric and magnetic dipole modes of the chain resulting in appearance of the inflection point at the band edge. The considered effect is studied experimentally in the chain of high-index ceramic cylinders in the microwave spectral range., Comment: 11 pages, 8 figures

This paper explores the application of automated planning to automated theorem proving, which is a branch of automated reasoning concerned with the development of algorithms and computer programs to construct mathematical proofs. In particular, we investigate the use of planning to construct elementary proofs in abstract algebra, which provides a rigorous and axiomatic framework for studying algebraic structures such as groups, rings, fields, and modules. We implement basic implications, equalities, and rules in both deterministic and non-deterministic domains to model commutative rings and deduce elementary results about them. The success of this initial implementation suggests that the well-established techniques seen in automated planning are applicable to the relatively newer field of automated theorem proving. Likewise, automated theorem proving provides a new, challenging domain for automated planning., Comment: Automated Planning Techniques for Elementary Proofs in Abstract Algebra. Petrov, A. & Muise, C. In Scheduling and Planning Applications woRKshop. 2023

Sequential Recommendation is a popular recommendation task that uses the order of user-item interaction to model evolving users' interests and sequential patterns in their behaviour. Current state-of-the-art Transformer-based models for sequential recommendation, such as BERT4Rec and SASRec, generate sequence embeddings and compute scores for catalogue items, but the increasing catalogue size makes training these models costly. The Joint Product Quantisation (JPQ) method, originally proposed for passage retrieval, markedly reduces the size of the retrieval index with minimal effect on model effectiveness, by replacing passage embeddings with a limited number of shared sub-embeddings. This paper introduces RecJPQ, a novel adaptation of JPQ for sequential recommendations, which takes the place of item embeddings tensor and replaces item embeddings with a concatenation of a limited number of shared sub-embeddings and, therefore, limits the number of learnable model parameters. The main idea of RecJPQ is to split items into sub-item entities before training the main recommendation model, which is inspired by splitting words into tokens and training tokenisers in language models. We apply RecJPQ to SASRec, BERT4Rec, and GRU4rec models on three large-scale sequential datasets. Our results showed that RecJPQ could notably reduce the model size (e.g., 48% reduction for the Gowalla dataset with no effectiveness degradation). RecJPQ can also improve model performance through a regularisation effect (e.g. +0.96% NDCG@10 improvement on the Booking.com dataset). Overall, RecJPQ allows the training of state-of-the-art transformer recommenders in industrial applications, where datasets with millions of items are common., Comment: Accepted by ACM WSDM 2024

The discovery of ultracold dilute liquids has significantly elevated our interest in various phenomena which go under the name of beyond-mean-field (BMF) physics. In these lecture notes we give an elementary introduction to the quantum stabilization and liquefaction of a collapsing weakly interacting Bose-Bose mixture. A detailed derivation of the leading BMF correction, also known as the Lee-Huang-Yang (LHY) term, in this system is presented in a manner suitable for further generalizations and extensions. Although the LHY term is a nonanalytic function of the density $n$, under certain conditions the leading BMF correction becomes analytic and can be expanded in integer powers of $n$, effectively introducing three-body and higher-order interactions. We discuss why and how well the Bogoliubov approach can predict these few-body observables., Comment: 36 pages, Proceedings of the International School of Physics "Enrico Fermi", Course 211 - Quantum Mixtures with Ultra-cold Atoms, July 2022

The Coulomb drag is a many-body effect observed in proximized low-dimensional systems. It appears as emergence of voltage in one of them upon passage of bias current in another. The magnitude of drag voltage can be strongly affected by exchange of plasmonic excitations between the layers; however, the reverse effect of Coulomb drag on properties of plasmons has not been studied. Here, we study the plasmon spectra and damping in parallel two-dimensional systems in the presence of Coulomb drag. We find that Coulomb drag leads to selective damping of one of the two fundamental plasma modes of a coupled bilayer. For identical electron doping of both layers, the drag suppresses the acoustic plasma mode; while for symmetric electron-hole doping of the coupled pair, the drag suppresses the optical plasma mode. The selective damping can be observed both for propagating modes in extended bilayers and for localized plasmons in bilayers confined by source and drain contacts. The discussed effect may provide access to the strength of Coulomb interaction in 2d electron systems from various optical and microwave scattering experiments.