Search

In the literature, it has been shown that the evolution of the known explicit 3D surface to the target one can be learned from 2D images using the instantaneous flow field, where the known and target 3D surfaces may largely differ in topology. We are interested in capturing 4D shapes whose topology changes largely over time. We encounter that the straightforward extension of the existing 3D-based method to the desired 4D case performs poorly. In this work, we address the challenges in extending 3D neural evolution to 4D under large topological changes by proposing two novel modifications. More precisely, we introduce (i) a new architecture to discretize and encode the deformation and learn the SDF and (ii) a technique to impose the temporal consistency. (iii) Also, we propose a rendering scheme for color prediction based on Gaussian splatting. Furthermore, to facilitate learning directly from 2D images, we propose a learning framework that can disentangle the geometry and appearance from RGB images. This method of disentanglement, while also useful for the 4D evolution problem that we are concentrating on, is also novel and valid for static scenes. Our extensive experiments on various data provide awesome results and, most importantly, open a new approach toward reconstructing challenging scenes with significant topological changes and deformations. Our source code and the dataset are publicly available at https://github.com/insait-institute/N4DE., Comment: 15 pages, 21 figures

Waveguide tapers are critical components for leveraging the benefits of both single-mode and wide waveguides. Adiabatic tapers are typically hundreds of microns in length, dramatically limiting density and scalability. We reenvision the taper design process in an inverse-design paradigm, introducing the novel L-taper. We present a novel approach to inverse-designed tapers where the input and output waveguides are rotated 90 degrees with respect to each other. The resultant design has an order-of-magnitude smaller footprint, and the design process is compatible with a variety of fabrication processes. We demonstrate an L-taper designed on 220 nm silicon-on-insulator that converts a 0.5 micron waveguide to a 12 micron waveguide with -0.38 dB transmission and 40 nm 1-dB bandwidth. The footprint is 16 micron by 6 micron, representing a 12x smaller footprint than a linear taper with the same transmission., Comment: 4 pages, 3 figures

We present the results of a nearly decade-long photometric reverberation mapping (PRM) survey of the H$\alpha$ emission line in nearby ($0.01\lesssim z \lesssim0.05$) Seyfert-Galaxies using small ($15\,\mathrm{cm}-40\,\mathrm{cm}$) telescopes. Broad-band filters were used to trace the continuum emission, while narrow-band filters tracked the H$\alpha$-line signal. We introduce a new PRM formalism to determine the time delay between continuum and line emission using combinations of auto- and cross-correlation functions. We obtain robust delays for 33/80 objects, allowing us to estimate the broad-line region (BLR) size. Additionally, we measure multi-epoch delays for 6 objects whose scatter per source is smaller than the scatter in the BLR size-luminosity relation. Our study enhances the existing H$\alpha$ size-luminosity relation by adding high-quality results for 31 objects, whose nuclear luminosities were estimated using the flux-variation gradient method, resulting in a scatter of 0.26dex within our sample. The scatter reduces to 0.17dex when the 6 lowest luminosity sources are discarded, which is comparable to that found for the H$\beta$ line. Single-epoch spectra enable us to estimate black hole masses using the H$\alpha$ line and derive mass accretion rates from the iron-blend feature adjacent to H$\beta$. A similar trend, as previously reported for the H$\beta$ line, is implied whereby highly accreting objects tend to lie below the size-luminosity relation of the general population. Our work demonstrates the effectiveness of small telescopes in conducting high-fidelity PRM campaigns of prominent emission lines in bright active galactic nuclei.

Expander decompositions have become one of the central frameworks in the design of fast algorithms. For an undirected graph $G=(V,E)$, a near-optimal $\phi$-expander decomposition is a partition $V_1, V_2, \ldots, V_k$ of the vertex set $V$ where each subgraph $G[V_i]$ is a $\phi$-expander, and only an $\widetilde{O}(\phi)$-fraction of the edges cross between partition sets. In this article, we give the first near-optimal parallel algorithm to compute $\phi$-expander decompositions in near-linear work $\widetilde{O}(m/\phi^2)$ and near-constant span $\widetilde{O}(1/\phi^4)$. Our algorithm is very simple and likely practical. Our algorithm can also be implemented in the distributed Congest model in $\tilde{O}(1/\phi^4)$ rounds. Our results surpass the theoretical guarantees of the current state-of-the-art parallel algorithms [Chang-Saranurak PODC'19, Chang-Saranurak FOCS'20], while being the first to ensure that only an $\tilde{O}(\phi)$ fraction of edges cross between partition sets. In contrast, previous algorithms [Chang-Saranurak PODC'19, Chang-Saranurak FOCS'20] admit at least an $O(\phi^{1/3})$ fraction of crossing edges, a polynomial loss in quality inherent to their random-walk-based techniques. Our algorithm, instead, leverages flow-based techniques and extends the popular sequential algorithm presented in [Saranurak-Wang SODA'19]., Comment: To appear at SODA'25. Fixed a typo in Claim 3.9

Evaluating the output of generative large language models (LLMs) is challenging and difficult to scale. Most evaluations of LLMs focus on tasks such as single-choice question-answering or text classification. These tasks are not suitable for assessing open-ended question-answering capabilities, which are critical in domains where expertise is required, such as health, and where misleading or incorrect answers can have a significant impact on a user's health. Using human experts to evaluate the quality of LLM answers is generally considered the gold standard, but expert annotation is costly and slow. We present a method for evaluating LLM answers that uses ranking signals as a substitute for explicit relevance judgements. Our scoring method correlates with the preferences of human experts. We validate it by investigating the well-known fact that the quality of generated answers improves with the size of the model as well as with more sophisticated prompting strategies.

We give the first almost-linear total time algorithm for deciding if a flow of cost at most $F$ still exists in a directed graph, with edge costs and capacities, undergoing decremental updates, i.e., edge deletions, capacity decreases, and cost increases. This implies almost-linear time algorithms for approximating the minimum-cost flow value and $s$-$t$ distance on such decremental graphs. Our framework additionally allows us to maintain decremental strongly connected components in almost-linear time deterministically. These algorithms also improve over the current best known runtimes for statically computing minimum-cost flow, in both the randomized and deterministic settings. We obtain our algorithms by taking the dual perspective, which yields cut-based algorithms. More precisely, our algorithm computes the flow via a sequence of $m^{1+o(1)}$ dynamic min-ratio cut problems, the dual analog of the dynamic min-ratio cycle problem that underlies recent fast algorithms for minimum-cost flow. Our main technical contribution is a new data structure that returns an approximately optimal min-ratio cut in amortized $m^{o(1)}$ time by maintaining a tree-cut sparsifier. This is achieved by devising a new algorithm to maintain the dynamic expander hierarchy of [Goranci-R\"{a}cke-Saranurak-Tan, SODA 2021] that also works in capacitated graphs. All our algorithms are deterministc, though they can be sped up further using randomized techniques while still working against an adaptive adversary., Comment: 61 pages, Accepted to FOCS 2024

In this paper, we investigate the question of whether the electrical flow routing is a good oblivious routing scheme on an $m$-edge graph $G = (V, E)$ that is a $\Phi$-expander, i.e. where $\lvert \partial S \rvert \geq \Phi \cdot \mathrm{vol}(S)$ for every $S \subseteq V, \mathrm{vol}(S) \leq \mathrm{vol}(V)/2$. Beyond its simplicity and structural importance, this question is well-motivated by the current state-of-the-art of fast algorithms for $\ell_{\infty}$ oblivious routings that reduce to the expander-case which is in turn solved by electrical flow routing. Our main result proves that the electrical routing is an $O(\Phi^{-1} \log m)$-competitive oblivious routing in the $\ell_1$- and $\ell_\infty$-norms. We further observe that the oblivious routing is $O(\log^2 m)$-competitive in the $\ell_2$-norm and, in fact, $O(\log m)$-competitive if $\ell_2$-localization is $O(\log m)$ which is widely believed. Using these three upper bounds, we can smoothly interpolate to obtain upper bounds for every $p \in [2, \infty]$ and $q$ given by $1/p + 1/q = 1$. Assuming $\ell_2$-localization in $O(\log m)$, we obtain that in $\ell_p$ and $\ell_q$, the electrical oblivious routing is $O(\Phi^{-(1-2/p)}\log m)$ competitive. Using the currently known result for $\ell_2$-localization, this ratio deteriorates by at most a sublogarithmic factor for every $p, q \neq 2$. We complement our upper bounds with lower bounds that show that the electrical routing for any such $p$ and $q$ is $\Omega(\Phi^{-(1-2/p)}\log m)$-competitive. This renders our results in $\ell_1$ and $\ell_{\infty}$ unconditionally tight up to constants, and the result in any $\ell_p$- and $\ell_q$-norm to be tight in case of $\ell_2$-localization in $O(\log m)$., Comment: To appear in ICALP 2024

Optimal multi-layer device design requires consideration of fabrication uncertainties associated with inter-layer alignment and conformal layering. We present layer-restricted topology optimization (TO), a novel technique which mitigates the effects of unwanted conformal layering for multi-layer structures and enables TO in multi-etch material platforms. We explore several approaches to achieve this result compatible with density-based TO projection techniques and geometric constraints. Then, we present a robust TO formulation to design devices resilient to inter-layer misalignment. The novel constraint and robust formulation are demonstrated in 2D grating couplers and a 3D polarization rotator., Comment: 14 pages, 5 figures, 17 equations

Quantifying the semantic similarity between database queries is a critical challenge with broad applications, ranging from query log analysis to automated educational assessment of SQL skills. Traditional methods often rely solely on syntactic comparisons or are limited to checking for semantic equivalence. This paper introduces a novel graph-based approach to measure the semantic dissimilarity between SQL queries. Queries are represented as nodes in an implicit graph, while the transitions between nodes are called edits, which are weighted by semantic dissimilarity. We employ shortest path algorithms to identify the lowest-cost edit sequence between two given queries, thereby defining a quantifiable measure of semantic distance. A prototype implementation of this technique has been evaluated through an empirical study, which strongly suggests that our method provides more accurate and comprehensible grading compared to existing techniques. Moreover, the results indicate that our approach comes close to the quality of manual grading, making it a robust tool for diverse database query comparison tasks., Comment: 12 pages

In this work, we present the first algorithm to compute expander decompositions in an $m$-edge directed graph with near-optimal time $\tilde{O}(m)$. Further, our algorithm can maintain such a decomposition in a dynamic graph and again obtains near-optimal update times. Our result improves over previous algorithms of Bernstein-Probst Gutenberg-Saranurak (FOCS 2020), Hua-Kyng-Probst Gutenberg-Wu (SODA 2023) that only obtained algorithms optimal up to subpolynomial factors. At the same time, our algorithm is much simpler and more accessible than previous work. In order to obtain our new algorithm, we present a new push-pull-relabel flow framework that generalizes the classic push-relabel flow algorithm of Goldberg-Tarjan (JACM 1988), which was later dynamized for computing expander decompositions in undirected graphs by Henzinger-Rao-Wang (SIAM J. Comput. 2020), Saranurak-Wang (SODA 2019). We then show that the flow problems formulated in recent work of Hua-Kyng-Probst Gutenberg-Wu (SODA 2023) to decompose directed graphs can be solved much more efficiently in the push-pull-relabel flow framework.

NGC 1566 is known for exhibiting recurrent outbursts, which are accompanied by changes in spectral type. The most recent transient event occurred from 2017 to 2019 and was reported to be accompanied by a change in Seyfert classification from Seyfert 1.8 to Seyfert 1.2. We analyze data from an optical spectroscopic variability campaign of NGC 1566 taken with the 9.2m SALT between July 2018 and October 2019 and supplement our data set with optical to near-infrared spectroscopic archival data taken by VLT/MUSE in September 2015 and October 2017. We observe the emergence and fading of a strong power-law-like blue continuum as well as strong variations in the Balmer, HeI, HeII lines and the coronal lines [FeVII], [FeX] and [FeXI]. Moreover, we detect broad double-peaked emission line profiles of OI 8446 and the CaII 8498,8542,8662 triplet. This is the first time that genuine double-peaked OI 8446 and CaII 8498,8542,8662 emission in AGN is reported in the literature. All broad lines show a clear redward asymmetry with respect to their central wavelength and we find indications for a significant blueward drift of the total line profiles during the transient event. We show that the double-peaked emission line profiles are well approximated by emission from a low-inclination, relativistic eccentric accretion disk, and that single-peaked profiles can be obtained by broadening due to scale-height dependent turbulence. Small-scale features in the OI and CaII lines suggest the presence of inhomogeneities in the broad-line region. We conclude that the broad-line region in NGC 1566 is dominated by the kinematics of a relativistic eccentric accretion disk. The broad-line region can be modeled to be vertically stratified with respect to scale-height turbulence. The observed blueward drift might be attributed to a low-optical-depth wind launched during the transient event., Comment: 22 pages, 17 figures. Published in Astronomy & Astrophysics (A&A 686, A17 (2024))

A wealth of literature shows positive outcomes and experiences from arts learning, yet youth access to arts education has become significantly more inequitable over the past 30 years. Alongside the growing discourse around arts learning and equity issues, there is a recognized and persistent need for more research. We conducted a critical, qualitative study of out-of-school time (OST) arts organizations across the United States. Our primary research questions were: (1) How do community youth arts organizational leaders, teaching artists, and participants describe the leading ideas and practices in OST youth arts programming? (2) How can OST youth arts work center the cultural, historical, and geographic resources that artists and arts organizations bring to arts programming? We first developed a theoretical framework for understanding arts practices in education and summarize key learning outcomes associated with youth participation in the arts. We then talked with OST arts education experts across the United States to understand how their programs support and center youth in arts learning, particularly Black youth, Indigenous youth, and youth of color (BIPOC youth), youth from low-income backgrounds, and LGBTQIA+ youth. This report offers the concept of "cultural-regional scenes" to describe the critical, qualitative case studies we developed of OST youth arts practice. We describe four unique cultural-regional scenes--the Urban Midwest, the Bay Area, Texas-Mexico Border Towns, and the Indigenous Southwest--and provide examples of youth arts practice in each scene. We conclude with ideas that stretch across scenes and suggest that researchers and practitioners can take up this approach in the study of OST youth arts programs. [Written in collaboration with community artists and artist-leaders across the United States and Indigenous Nations.]

We present a general toolbox, based on new vertex sparsifiers, for designing data structures to maintain shortest paths in dynamic graphs. In an $m$-edge graph undergoing edge insertions and deletions, our data structures give the first algorithms for maintaining (a) $m^{o(1)}$-approximate all-pairs shortest paths (APSP) with \emph{worst-case} update time $m^{o(1)}$ and query time $\tilde{O}(1)$, and (b) a tree $T$ that has diameter no larger than a subpolynomial factor times the diameter of the underlying graph, where each update is handled in amortized subpolynomial time. In graphs undergoing only edge deletions, we develop a simpler and more efficient data structure to maintain a $(1+\epsilon)$-approximate single-source shortest paths (SSSP) tree $T$ in a graph undergoing edge deletions in amortized time $m^{o(1)}$ per update. Our data structures are deterministic. The trees we can maintain are not subgraphs of $G$, but embed with small edge congestion into $G$. This is in stark contrast to previous approaches and is useful for algorithms that internally use trees to route flow. To illustrate the power of our new toolbox, we show that our SSSP data structure gives simple deterministic implementations of flow-routing MWU methods in several contexts, where previously only randomized methods had been known. To obtain our toolbox, we give the first algorithm that, given a graph $G$ undergoing edge insertions and deletions and a dynamic terminal set $A$, maintains a vertex sparsifier $H$ that approximately preserves distances between terminals in $A$, consists of at most $|A|m^{o(1)}$ vertices and edges, and can be updated in worst-case time $m^{o(1)}$. Crucially, our vertex sparsifier construction allows us to maintain a low edge-congestion embedding of $H$ into $G$, which is needed for our applications.

We provide an algorithm which, with high probability, maintains a $(1-\epsilon)$-approximate maximum flow on an undirected graph undergoing $m$-edge additions in amortized $m^{o(1)} \epsilon^{-3}$ time per update. To obtain this result, we provide a more general algorithm that solves what we call the incremental, thresholded $p$-norm flow problem that asks to determine the first edge-insertion in an undirected graph that causes the minimum $\ell_p$-norm flow to decrease below a given threshold in value. Since we solve this thresholded problem, our data structure succeeds against an adaptive adversary that can only see the data structure's output. Furthermore, since our algorithm holds for $p = 2$, we obtain improved algorithms for dynamically maintaining the effective resistance between a pair of vertices in an undirected graph undergoing edge insertions. Our algorithm builds upon previous dynamic algorithms for approximately solving the minimum-ratio cycle problem that underlie previous advances on the maximum flow problem [Chen-Kyng-Liu-Peng-Probst Gutenberg-Sachdeva, FOCS '22] as well as recent dynamic maximum flow algorithms [v.d.Brand-Liu-Sidford, STOC '23]. Instead of using interior point methods, which were a key component of these recent advances, our algorithm uses an optimization method based on $\ell_p$-norm iterative refinement and the multiplicative weight update method. This ensures a monotonicity property in the minimum-ratio cycle subproblems that allows us to apply known data structures and bypass issues arising from adaptive queries., Comment: 25 pages, SODA 2024