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Metasurfaces offer a powerful platform for effective light manipulation, which is crucial for advanced optical technologies. While designs of polarization-independent structures have reduced the need for polarized illumination, they are often limited by either low Q factors or low resonance modulation. Here, we design and experimentally demonstrate a metasurface with polarization-independent quasi-bound state in the continuum (quasi-BIC), where the unit cell consists of four silicon squares arranged in a two-dimensional array and the resonance properties can be controlled by adjusting the edge length difference between different squares. Our metasurface experimentally achieves a Q factor of approximately 100 and a resonance modulation of around 50%. This work addresses a common limitation in previous designs, which either achieved high Q factors exceeding 200 with a resonance modulation of less than 10%, leading to challenging signal-to-noise ratio requirements, or achieved strong resonance modulation with Q factors of only around 10, limiting light confinement and fine-tuning capabilities. In contrast, our metasurface ensures that the polarization-independent signal is sharp and distinct within the system, reducing the demands on signal-to-noise ratio and improving robustness. Experiments show the consistent performance across different polarization angles. This work contributes to the development of versatile optical devices, enhancing the potential for the practical application of BIC-based designs in areas such as optical filtering and sensing.

We review $H^{1}$-well-posedness for initial value problems of ordinary differential equations with state-dependent right-hand side. We streamline known approaches to infer existence and uniqueness of solutions for small times given a Lipschitz-continuous prehistory. The paramount feature is a reduction of the differential equation to a fixed point problem that admits a unique solution appealing to the contraction mapping principle. The use of exponentially weighted Sobolev spaces in this endeavor proves to be as powerful as for ordinary differential equations without delay. Our result includes a blow-up criterium for global existence of solutions. The discussion of well-posedness is concluded by new results covering continuous dependence on initial prehistories and on the right-hand sides.

We present an application of recent well-posedness results in the theory of delay differential equations for ordinary differential equations arXiv:2308.04730 to a generalized population model for stem cell maturation. The weak approach using Sobolev-spaces we take allows for a larger class of initial prehistories and makes checking the requirements for well-posedness of such a model considerably easier compared to previous approaches. In fact the present approach is a possible means to guarantee that the solution manifold is not empty, which is a necessary requirement for a $C^{1}$-approach to work.

Photonic metasurfaces offer exceptional control over light at the nanoscale, facilitating applications spanning from biosensing, and nonlinear optics to photocatalysis. Many metasurfaces, especially resonant ones, rely on periodicity for the collective mode to form, which makes them subject to the influences of finite size effects, defects, and edge effects, all of which have considerable negative impact at the application level. These aspects are especially important for quasi-bound state in the continuum (BIC) metasurfaces, for which the collective mode is highly sensitive to perturbations due to high quality factors and strong near-field enhancement. Here, we quantitatively investigate the mode formation in quasi-BIC metasurfaces on the individual resonator level using scattering scanning near-field optical microscopy (s-SNOM) in combination with a new image processing technique. We find that the quasi-BIC mode is formed at a minimum size of 10 x 10-unit cells much smaller than expected from far-field measurements. Furthermore, we show that the coupling direction of the resonators, defects and edge states have pronounced influence on the quasi-BIC mode. This study serves as a link between the far-field and near-field responses of metasurfaces, offering crucial insights for optimizing spatial footprint and active area, holding promise for augmenting applications such as catalysis and biospectroscopy., Comment: 30 pages, 6 figures, 8 supplementary figures

The (dual) Cauchy identity has an easy algebraic proof utilising a commutation relation between the up and (dual) down operators. By using Fomin's growth diagrams, a bijective proof of the commutation relation can be "bijectivised" to obtain RSK like correspondences. In this paper we give a concise overview of this machinery and extend it to Littlewood type identities by introducing a new family of relations between these operators, called projection identities. Thereby we obtain infinite families of bijections for the Littlewood identities generalising the classical ones. We believe that this approach will be useful for finding bijective proofs for Littlewood type identities in other settings such as for Macdonald polynomials and their specialisations, alternating sign matrices or vertex models., Comment: 29 pages

We introduce a probabilistic generalization of the dual Robinson--Schensted--Knuth correspondence, called $qt$RSK${}^*$, depending on two parameters $q$ and $t$. This correspondence extends the $q$RS$t$ correspondence, recently introduced by the authors, and allows the first tableaux-theoretic proof of the dual Cauchy identity for Macdonald polynomials. By specializing $q$ and $t$, one recovers the row and column insertion version of the classical dual RSK correspondence as well as of $q$- and $t$-deformations thereof which are connected to $q$-Whittaker and Hall--Littlewood polynomials. When restricting to Jack polynomials and $\{0,1\}$-matrices corresponding to words, we prove that the insertion tableaux obtained by $qt$RSK${}^*$ are invariant under swapping letters in the input word. Our approach is based on Fomin's growth diagrams and the notion of probabilistic bijections., Comment: 65 pages

The research communities studying visualization and sonification for data display and analysis share exceptionally similar goals, essentially making data of any kind interpretable to humans. One community does so by using visual representations of data, and the other community employs auditory (non-speech) representations of data. While the two communities have a lot in common, they developed mostly in parallel over the course of the last few decades. With this STAR, we discuss a collection of work that bridges the borders of the two communities, hence a collection of work that aims to integrate the two techniques into one form of audiovisual display, which we argue to be "more than the sum of the two." We introduce and motivate a classification system applicable to such audiovisual displays and categorize a corpus of 57 academic publications that appeared between 2011 and 2023 in categories such as reading level, dataset type, or evaluation system, to mention a few. The corpus also enables a meta-analysis of the field, including regularly occurring design patterns such as type of visualization and sonification techniques, or the use of visual and auditory channels, showing an overall diverse field with different designs. An analysis of a co-author network of the field shows individual teams without many interconnections. The body of work covered in this STAR also relates to three adjacent topics: audiovisual monitoring, accessibility, and audiovisual data art. These three topics are discussed individually in addition to the systematically conducted part of this research. The findings of this report may be used by researchers from both fields to understand the potentials and challenges of such integrated designs while hopefully inspiring them to collaborate with experts from the respective other field., Comment: 30 pages, 9 figures, accepted for EuroVis 2024 conference

We study the statistical resilience of the anti-concentration properties of Rademacher polynomials in face of adversarial deterministic noise taking the form of sign-flips. Given a multilinear polynomial $f:\mathbb{R}^n \to \mathbb{R}$ and a Rademacher vector $\boldsymbol{\xi} \in \{\pm 1\}^n$ (with independent entries), our results provide probabilistic lower bound estimations on the number of sign-flips that $\boldsymbol{\xi}$ can sustain without ``inflating" the atom probability $\sup_{x \in \mathbb{R} } \mathbb{P}\{f(\boldsymbol{\xi}) = x\}$ otherwise resulting in an adversarially biased distribution. Special emphasis is put on bilinear and quadratic forms, for which strengthened estimates are attained. From a computational perspective, our results in this venue are instance-bound in such a way that allows for an efficient computation of the statistical resilience guarantees from the quadratic polynomial itself directly. All of our probabilistic lower bound resilience guarantees are asymptotically tight. On route, we provide a short proof for a new small-ball probability estimate fitting Rademacher multilinear polynomials $f: \mathbb{R}^n \to \mathbb{R}$ removeing a polylog-factor from the classical Meka-Nguyen-Vu bound provided the coefficients are independent of $n$ (dimension-free, hereafter). This removal was conjectured to be possible by Meka-Nguyen-Vu regardless of our assumption. Bilinear Rademacher forms with dimension-free coefficients arise naturally in Combinatorics and specifically in the dense case of the edge-statistics conjecture posed by Alon, Hefetz, Krivelevich, and Tyomkyn. This case of the conjecture was resolved by Kwan and Sauermann. Replacing the appeal to the Meka-Nguyen-Vu classical bound in the work of Kwan, Sudakov, and Tran with our shortly proved result attains an additional proof of the dense case of the edge-statistics conjecture., Comment: Numerous changes from the last version: 1. An oversight in the proof fixed. 2. Added treatment of high degree polynomials 3. New results added

Enhancing and controlling light-matter interactions is crucial in nanotechnology and material science, propelling research on green energy, laser technology, and quantum cryptography. Central to enhanced light-matter coupling are two parameters: the spectral overlap between an optical cavity mode and the material's spectral features (e.g., excitonic or molecular absorption lines), and the quality factor of the cavity. Controlling both parameters simultaneously is vital, especially in complex systems requiring extensive data to uncover the numerous effects at play. However, so far, photonic approaches have focused solely on sampling a limited set of data points within this 2D parameter space. Here we introduce a nanophotonic approach that can simultaneously and continuously encode the spectral and quality factor parameter space of light-matter interactions within a compact spatial area. Our novel dual-gradient metasurface design is composed of a 2D array of smoothly varying subwavelength nanoresonators, each supporting a unique mode. This results in 27,500 distinct modes within one array and a resonance density approaching the theoretical upper limit for metasurfaces. By applying our dual-gradient to surface-enhanced molecular sensing, we demonstrate the importance of coupling tailoring and unveil an additional coupling-based dimension of spectroscopic data. Our metasurface design paves the way for generalized light-matter coupling metasurfaces, leading to advancements in the field of photocatalysis, chemical sensing, and entangled photon generation., Comment: 5 figures, 5 supplementary notes, 14 supplementary figures

Metasurfaces have unlocked significant advancements across photonics, yet their efficient active control remains challenging. The active materials required often lack continuous tunability, exhibit inadequate refractive index (RI) changes, or suffer from high losses. These aspects pose an inherent limitation for resonance-shifting based switching: when RI changes are small, the resulting shift is also minor. Conversely, high RI changes typically come with high intrinsic losses necessitating broad modes because narrow ones cannot tolerate such losses. Therefore, larger spectral shifts are required to effectively detune the modes. This paper introduces a novel active metasurface approach that converts the constraint of high intrinsic losses into a beneficial feature. This is achieved by controlling the losses in a hybrid vanadium dioxide (VO$_{2}$) - silicon metasurface, supporting symmetry-protected bound states in the continuum (BICs) within the infrared spectrum. By leveraging the temperature-controlled losses in VO$_{2}$ and combining them with the inherent far-field-coupling tunability of BICs, we gain unprecedented precision in independently controlling both the radiative and nonradiative losses of the resonant system. Our dual-control mechanism allows us to optimize our metasurfaces and we experimentally demonstrate quality factors above 200, a maximum reflectance amplitude of 90%, a relative switching contrast of 78%, and continuous tuning from under- to over-coupling within the infrared spectral range. This study provides a foundation for experimentally and technologically simple, fine-tunable, active metasurfaces for applications ranging from molecular sensors to filters and optical modulators., Comment: 25 pages, 4 figures, 4 supplementary figures

Let $\tilde K_t$ denote the $3$-uniform linear clique of order $t$. Given an even integer $t \geq 4$, let $M$ denote the asymmetric maximal density of $\tilde K_t$ and $\tilde K_{t/2}$. We prove that there exists a constant $C>0$ such that, if $(H_n)_{n \in \mathbb{N}}$ is any sequence of dense $3$-uniform hypergraphs and $p := p(n) \geq Cn^{-1/M}$, then $$ \lim_{n \to \infty} \Pr[H_n \cup R_n \to (\tilde K_t)_2] =1 $$ holds, whenever $R_n \sim \mathbb{H}(n,p)$, where the latter denotes the binomial $3$-uniform random hypergraph distribution. We conjecture that this result uncovers the threshold for the property in question for $t \geq 6$. The key tools of our proof are a new variant of the Strong Hypergraph Regularity Lemma along with a new Tuple Lemma accompanying it. Our variant incorporates both the strong and the weak hypergraph regularity lemmas into a single lemma; allowing for graph-like applications of the strong lemma to be carried out in $3$-uniform hypergraphs., Comment: 44 pages, 1 figure

Solid-state quantum emitters embedded in circular Bragg resonators are attractive due to their ability to emit quantum states of light with high brightness and low multi-photon probability. As for any emitter-microcavity system, fabrication imperfections limit the spatial and spectral overlap of the emitter with the cavity mode, thus limiting their coupling strength. Here, we show that an initial spectral mismatch can be corrected after device fabrication by repeated wet chemical etching steps. We demonstrate ~16 nm wavelength tuning for optical modes in AlGaAs resonators on oxide, leading to a 4-fold Purcell enhancement of the emission of single embedded GaAs quantum dots. Numerical calculations reproduce the observations and suggest that the achievable performance of the resonator is only marginally affected in the explored tuning range. We expect the method to be applicable also to circular Bragg resonators based on other material platforms, thus increasing the device yield of cavity-enhanced solid-state quantum emitters.

Visualization onboarding supports users in reading, interpreting, and extracting information from visual data representations. General-purpose onboarding tools and libraries are applicable for explaining a wide range of graphical user interfaces but cannot handle specific visualization requirements. This paper describes a first step towards developing an onboarding library called VisAhoi, which is easy to integrate, extend, semi-automate, reuse, and customize. VisAhoi supports the creation of onboarding elements for different visualization types and datasets. We demonstrate how to extract and describe onboarding instructions using three well-known high-level descriptive visualization grammars - Vega-Lite, Plotly.js, and ECharts. We show the applicability of our library by performing two usage scenarios that describe the integration of VisAhoi into a VA tool for the analysis of high-throughput screening (HTS) data and, second, into a Flourish template to provide an authoring tool for data journalists for a treemap visualization. We provide a supplementary website that demonstrates the applicability of VisAhoi to various visualizations, including a bar chart, a horizon graph, a change matrix or heatmap, a scatterplot, and a treemap visualization.

Advancements in mathematical programming have made it possible to efficiently tackle large-scale real-world problems that were deemed intractable just a few decades ago. However, provably optimal solutions may not be accepted due to the perception of optimization software as a black box. Although well understood by scientists, this lacks easy accessibility for practitioners. Hence, we advocate for introducing the explainability of a solution as another evaluation criterion, next to its objective value, which enables us to find trade-off solutions between these two criteria. Explainability is attained by comparing against (not necessarily optimal) solutions that were implemented in similar situations in the past. Thus, solutions are preferred that exhibit similar features. Although we prove that already in simple cases the explainable model is NP-hard, we characterize relevant polynomially solvable cases such as the explainable shortest path problem. Our numerical experiments on both artificial as well as real-world road networks show the resulting Pareto front. It turns out that the cost of enforcing explainability can be very small.

This paper is a call to action for research and discussion on data visualization education. As visualization evolves and spreads through our professional and personal lives, we need to understand how to support and empower a broad and diverse community of learners in visualization. Data Visualization is a diverse and dynamic discipline that combines knowledge from different fields, is tailored to suit diverse audiences and contexts, and frequently incorporates tacit knowledge. This complex nature leads to a series of interrelated challenges for data visualization education. Driven by a lack of consolidated knowledge, overview, and orientation for visualization education, the 21 authors of this paper-educators and researchers in data visualization-identify and describe 19 challenges informed by our collective practical experience. We organize these challenges around seven themes People, Goals & Assessment, Environment, Motivation, Methods, Materials, and Change. Across these themes, we formulate 43 research questions to address these challenges. As part of our call to action, we then conclude with 5 cross-cutting opportunities and respective action items: embrace DIVERSITY+INCLUSION, build COMMUNITIES, conduct RESEARCH, act AGILE, and relish RESPONSIBILITY. We aim to inspire researchers, educators and learners to drive visualization education forward and discuss why, how, who and where we educate, as we learn to use visualization to address challenges across many scales and many domains in a rapidly changing world: viseducationchallenges.github.io., Comment: Accepted for publication at VIS 2023 Conference, Melbourne, VIC

The {\em discrepancy} of a matrix $M \in \mathbb{R}^{d \times n}$ is given by $\mathrm{DISC}(M) := \min_{\boldsymbol{x} \in \{-1,1\}^n} \|M\boldsymbol{x}\|_\infty$. An outstanding conjecture, attributed to Koml\'os, stipulates that $\mathrm{DISC}(M) = O(1)$, whenever $M$ is a Koml\'os matrix, that is, whenever every column of $M$ lies within the unit sphere. Our main result asserts that $\mathrm{DISC}(M + R/\sqrt{d}) = O(d^{-1/2})$ holds asymptotically almost surely, whenever $M \in \mathbb{R}^{d \times n}$ is Koml\'os, $R \in \mathbb{R}^{d \times n}$ is a Rademacher random matrix, $d = \omega(1)$, and $n = \omega(d \log d)$. The factor $d^{-1/2}$ normalising $R$ is essentially best possible and the dependency between $n$ and $d$ is asymptotically best possible. Our main source of inspiration is a result by Bansal, Jiang, Meka, Singla, and Sinha (ICALP 2022). They obtained an assertion similar to the one above in the case that the smoothing matrix is Gaussian. They asked whether their result can be attained with the optimal dependency $n = \omega(d \log d)$ in the case of Bernoulli random noise or any other types of discretely distributed noise; the latter types being more conducive for Smoothed Analysis in other discrepancy settings such as the Beck-Fiala problem. For Bernoulli noise, their method works if $n = \omega(d^2)$. In the case of Rademacher noise, we answer the question posed by Bansal, Jiang, Meka, Singla, and Sinha. Our proof builds upon their approach in a strong way and provides a discrete version of the latter. Breaking the $n = \omega(d^2)$ barrier and reaching the optimal dependency $n = \omega(d \log d)$ for Rademacher noise requires additional ideas expressed through a rather meticulous counting argument, incurred by the need to maintain a high level of precision all throughout the discretisation process.

Knitted sensors frequently suffer from inconsistencies due to innate effects such as offset, relaxation, and drift. These properties, in combination, make it challenging to reliably map from sensor data to physical actuation. In this paper, we demonstrate a method for counteracting this by applying processing using a minimal artificial neural network (ANN) in combination with straightforward pre-processing. We apply a number of exponential smoothing filters on a re-sampled sensor signal, to produce features that preserve different levels of historical sensor data and, in combination, represent an adequate state of previous sensor actuation. By training a three-layer ANN with a total of 8 neurons, we manage to significantly improve the mapping between sensor reading and actuation force. Our findings also show that our technique translates to sensors of reasonably different composition in terms of material and structure, and it can furthermore be applied to related physical features such as strain.

We present multi-component knitted resistive sensors for tracking tensile force. The knits were fabricated using a Twill structure, which is a simple pattern featuring anisotropic elastic behavior, providing high stability along course-direction. Our sensors are made of two commercially available conductive yarn types, with highly different linear resistance. We present a variety of integration methods using the proposed Twill structure, all of which can be easily replicated on a two-bed weft-knitting machine. We evaluate the performance of the resulting sensor variations, with respect to consistency, hysteresis, short-term and long-term relaxation and drift, among other metrics. We found that particulars of the knit's loop composition have a crucial effect on the consistency of the sensor readings. Furthermore, we show that knitting resistive yarn more tightly than the substrate material gives superior results and that improving elastic recoil by adding Lycra to the supporting substrate can considerably improve performance.