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In this article, we derive Stein's method for approximating a spatial random graph by a generalised random geometric graph, which has vertices given by a finite Gibbs point process and edges based on a general connection function. Our main theorems provide explicit upper bounds for integral probability metrics and, at improved rates, a recently introduced Wasserstein metric for random graph distributions. The bounds are in terms of a vertex error term based on the Papangelou kernels of the vertex point processes and two edge error terms based on conditional edge probabilities. In addition to providing new tools for spatial random graphs along the way, such as a graph-based Georgii--Nguyen--Zessin formula, we also give applications of our bounds to the percolation graph of large balls in a Boolean model and to discretising a generalised random geometric graph., Comment: 40 pages

Artificial neural networks (ANNs) have fundamentally transformed the field of computer vision, providing unprecedented performance. However, these ANNs for image processing demand substantial computational resources, often hindering real-time operation. In this paper, we demonstrate an optical encoder that can perform convolution simultaneously in three color channels during the image capture, effectively implementing several initial convolutional layers of a ANN. Such an optical encoding results in ~24,000 times reduction in computational operations, with a state-of-the art classification accuracy (~73.2%) in free-space optical system. In addition, our analog optical encoder, trained for CIFAR-10 data, can be transferred to the ImageNet subset, High-10, without any modifications, and still exhibits moderate accuracy. Our results evidence the potential of hybrid optical/digital computer vision system in which the optical frontend can pre-process an ambient scene to reduce the energy and latency of the whole computer vision system., Comment: 21 pages, 4 figures, 2 tables

Utilizing the complementary strengths of wavelength-specific range or depth sensors is crucial for robust computer-assisted tasks such as autonomous driving. Despite this, there is still little research done at the intersection of optical depth sensors and radars operating close range, where the target is decimeters away from the sensors. Together with a growing interest in high-resolution imaging radars operating in the near field, the question arises how these sensors behave in comparison to their traditional optical counterparts. In this work, we take on the unique challenge of jointly characterizing depth imagers from both, the optical and radio-frequency domain using a multimodal spatial calibration. We collect data from four depth imagers, with three optical sensors of varying operation principle and an imaging radar. We provide a comprehensive evaluation of their depth measurements with respect to distinct object materials, geometries, and object-to-sensor distances. Specifically, we reveal scattering effects of partially transmissive materials and investigate the response of radio-frequency signals. All object measurements will be made public in form of a multimodal dataset, called MAROON.

While SmB$_6$ attracts attention as a possible topological Kondo insulator, EuB$_6$ is known to host magnetic polarons that give rise to large magnetoresistive effects above its ferromagnetic order transition. Here we investigate single crystals of Sm$_{1-x}$Eu$_x$B$_6$ by magnetic and magnetotransport measurements to explore a possible interplay of these two intriguing phenomena, with focus on the Eu-rich substitutions. Sm$_{0.01}$Eu$_{0.99}$B$_6$ exhibits generally similar behavior as EuB$_6$. Interestingly, Sm$_{0.05}$Eu$_{0.95}$B$_6$ combines global antiferromagnetic order with local polaron formation. A pronounced hysteresis is found in the magnetoresistance of Sm$_{0.1}$Eu$_{0.9}$B$_6$ at low temperature ($T=$ 1.9 K) and applied magnetic fields between 2.3 $-$ 3.6 T. The latter is in agreement with a phenomenological model that predicts the stabilization of ferromagnetic polarons with increasing magnetic field within materials with global antiferromagnetic order., Comment: 9 pages, 10 figures

When comparing multiple groups in clinical trials, we are not only interested in whether there is a difference between any groups but rather the location. Such research questions lead to testing multiple individual hypotheses. To control the familywise error rate (FWER), we must apply some corrections or introduce tests that control the FWER by design. In the case of time-to-event data, a Bonferroni-corrected log-rank test is commonly used. This approach has two significant drawbacks: (i) it loses power when the proportional hazards assumption is violated [1] and (ii) the correction generally leads to a lower power, especially when the test statistics are not independent [2]. We propose two new tests based on combined weighted log-rank tests. One as a simple multiple contrast test of weighted log-rank tests and one as an extension of the so-called CASANOVA test [3]. The latter was introduced for factorial designs. We propose a new multiple contrast test based on the CASANOVA approach. Our test promises to be more powerful under crossing hazards and eliminates the need for additional p-value correction. We assess the performance of our tests through extensive Monte Carlo simulation studies covering both proportional and non-proportional hazard scenarios. Finally, we apply the new and reference methods to a real-world data example. The new approaches control the FWER and show reasonable power in all scenarios. They outperform the adjusted approaches in some non-proportional settings in terms of power.

Materials exhibiting electronic inhomogeneities at the nanometer scale have enormous potential for applications. Magnetic polarons are one such type of inhomogeneity which link the electronic, magnetic and lattice degrees of freedom in correlated matter and often give rise to colossal magnetoresistance. Here, we investigate single crystals of Eu$_5$In$_2$Sb$_6$ by thermal expansion and magnetostriction along different crystallographic directions. These data provide compelling evidence for the formation of magnetic polarons in Eu$_5$In$_2$Sb$_6$ well above the magnetic ordering temperature. More specifically, our results are consistent with anisotropic polarons with varying extent along the different crystallographic directions and successfully explain the strongly temperature- and magnetic field-dependent resistivities in Eu$_5$In$_2$Sb$_6$. Within the magnetically ordered phase, the dilatometry measurements are highly sensitive to the material's magnetic structure and reveal a crossover not observed in magnetic and transport properties. This crossover can be associated with a surprising stabilization of ferromagnetic polarons within the global antiferromagnetic order upon decreasing temperature. These findings make Eu$_5$In$_2$Sb$_6$ a rare example of such coexisting and competing magnetic orders and, importantly, sheds new light on colossal magnetoresistive behavior beyond manganites., Comment: 9pages, 7 figures, additional supplement

As the signatories of this manifesto, we denounce the attention economy as inhumane and a threat to our sociopolitical and ecological well-being. We endorse policymakers' efforts to address the negative consequences of the attention economy's technology, but add that these approaches are often limited in their criticism of the systemic context of human attention. Starting from Buddhist philosophy, we advocate a broader approach: an ecology of attending, that centers on conceptualizing, designing, and using attention (1) in an embedded way and (2) focused on the alleviating of suffering. With 'embedded' we mean that attention is not a neutral, isolated mechanism but a meaning-engendering part of an 'ecology' of bodily, sociotechnical and moral frameworks. With 'focused on the alleviation of suffering' we explicitly move away from the (often implicit) conception of attention as a tool for gratifying desires., Comment: 21 pages, 1 figure

Long-range imaging in the thermal infrared band is critical for applications such as environmental monitoring, industrial inspections, and surveillance. To achieve high quality imaging, these systems typically require large apertures and many elements with complex shapes to correct aberrations, adding significant weight and cost. Large-area metasurface optics offer a promising solution for weight reduction; however, their substantial chromatic aberrations limit their effectiveness in the long-wave infrared (LWIR) band where broadband imaging is typically desired. In this work, we introduce a hybrid system comprising four refractive lenses and two all-silicon metasurface correctors (meta-correctors) to achieve high-quality, broadband thermal imaging at long range. Compared to a refractive-only assembly, our system demonstrates a three-fold contrast enhancement at the detector's half-Nyquist frequency. Testing outside the laboratory reveals noticeably sharper images, with human features clearly recognizable at distances of 250 meters. The assembly utilizes off-the-shelf refractive elements and avoids the use of germanium, which poses a supply chain risk. Our findings highlight the potential of hybrid meta-corrector systems to enable long-range, lightweight, and cost-effective LWIR imaging solutions.

Context. The duration of star formation (SF) in globular clusters (GCs) is an essential aspect for understanding their formation. Contrary to previous presumptions that all stars above 8 M explode as core-collapse supernovae (CCSNe), recent evidence suggests a more complex scenario. Aims. We analyse iron spread observations from 55 GCs to estimate the number of CCSNe explosions before SF termination, thereby determining the SF duration. This work for the first time takes the possibility of failed CCSNe into account, when estimating the SF duration. Methods. Two scenarios are considered: one where all stars explode as CCSNe and another where only stars below 20 M lead to CCSNe, as most CCSN models predict that no failed CCSNe happen below 20 M . Results. This establishes a lower ($\approx$ 3.5 Myr) and an upper ($\approx$ 10.5 Myr) limit for the duration of SF. Extending the findings of our previous paper, this study indicates a significant difference in SF duration based on CCSN outcomes, with failed CCSNe extending SF by up to a factor of three. Additionally, a new code is introduced to compute the SF duration for a given CCSN model. Conclusions. The extended SF has important implications on GC formation, including enhanced pollution from stellar winds and increased binary star encounters. These results underscore the need for a refined understanding of CCSNe in estimating SF durations and the formation of multiple stellar populations in GCs., Comment: 9 pages, 9 figures, accepted by A&A

Unresolved binaries have a strong influence on the observed parameters of stellar clusters (SCs). We quantify this influence and compute the resulting mass underestimates and stellar mass function (MF). N-body simulations of realistic SCs were used to investigate the evolution of the binary population in a SC and its tidal tails. Together with an empirically gauged stellar mass-luminosity relation, the results were then used to determine how the presence of binaries changes the photometric mass and MF of the SC and its tails as deduced from observations. Tail 1 (T1), which is the tidal tail caused by gas expulsion, contains a larger fraction of binaries than both the SC and tail 2 (T2), which forms after gas expulsion. Additionally, T1 has a larger velocity dispersion. Using the luminosity of an unresolved binary, an observer would underestimate its mass. This bias sensitively depends on the companion masses due to the structure of the stellar mass-luminosity relation. Combining the effect of all binaries in the simulation, the total photometric mass of the SC is underestimated by 15%. Dark objects (black holes/neutron stars) increase the difference between the real and observed mass of the SC further. For both the SC and the tails, the observed power-law index of the MF between a stellar mass of 0.3 and 0.7 $M_\odot$ is smaller by up to 0.2 than the real one, the real initial mass function (IMF) being steeper by this amount. This difference is larger for stars with a larger velocity dispersion or binary fraction. Since the stars formed in SCs are the progenitors of the Galactic field stars, this work suggests that the binary fractions of different populations of stars in the Galactic disc will differ as a function of the velocity dispersion. The direction of this correlation is currently unclear and a complete population synthesis will be needed to investigate this effect., Comment: 15 pages, 18 figures, accepted by A&A

The field of meta-optics has grown to include metalenses spanning the ultraviolet to terahertz regimes. Imaging is a key application of meta-optics, with recent works demonstrating meta-optical imaging with advanced functionalities including wide field of view, broadband operation, and polarization sensitivity. In this review, we focus on meta-optical imaging for thermal wavelengths. Thermal meta-optics are less well-studied than those in the visible range but have vast potential applications spanning defense, health, and geological sensing. We first introduce these applications and their specific challenges. With compact form-factor and multi-functional capabilities, we suggest that meta-optics are particularly well-suited to meet the needs of imaging in the mid- and long-wave infrared. Then, we review published experimental demonstrations of thermal imaging via meta-optics. These meta-optics vary in complexity from simple hyperboloid metalenses to complex systems composed of engineered meta-atoms and multiple layers of optics. Finally, we suggest some areas where thermal meta-optics may be useful, and we identify some emerging approaches to solve lingering challenges of meta-optical imaging.

The Fundamental Theorem of Statistical Learning states that a hypothesis space is PAC learnable if and only if its VC dimension is finite. For the agnostic model of PAC learning, the literature so far presents proofs of this theorem that often tacitly impose several measurability assumptions on the involved sets and functions. We scrutinize these proofs from a measure-theoretic perspective in order to extract the assumptions needed for a rigorous argument. This leads to a sound statement as well as a detailed and self-contained proof of the Fundamental Theorem of Statistical Learning in the agnostic setting, showcasing the minimal measurability requirements needed. We then discuss applications in Model Theory, considering NIP and o-minimal structures. Our main theorem presents sufficient conditions for the PAC learnability of hypothesis spaces defined over o-minimal expansions of the reals., Comment: 41 pages plus appendix

The Large Deformation Diffeomorphic Metric Mapping (LDDMM) or flow of diffeomorphism is a classical framework in the field of shape spaces and is widely applied in mathematical imaging and computational anatomy. Essentially, it equips a group of diffeomorphisms with a right-invariant Riemannian metric, which allows to compute (Riemannian) distances or interpolations between different deformations. The associated Euler--Lagrange equation of shortest interpolation paths is one of the standard examples of a partial differential equation that can be approached with Lie group theory (by interpreting it as a geodesic ordinary differential equation on the Lie group of diffeomorphisms). The particular group $\mathcal D^m$ of Sobolev diffeomorphisms is by now sufficiently understood to allow the analysis of geodesics and their numerical approximation. We prove convergence of a widely used Fourier-type space discretization of the geodesic equation. It is based on a new regularity estimate: We prove that geodesics in $\mathcal D^m$ preserve any higher order Sobolev regularity of their initial velocity.

RuO$_2$ was considered for a long time to be a paramagnetic metal with an ideal rutile-type structure down to low temperatures, but recent studies on single-crystals claimed evidence for antiferromagnetic order and some symmetry breaking in the crystal structure. We have grown single-crystals of RuO2 by vapor transport using either O$_2$ or TeCl$_4$ as transport medium. These crystals exhibit metallic behavior following a $T^2$ low-temperature relation and a small paramagnetic susceptibility that can be attributed to Pauli paramagnetism. Neither the conductance nor the susceptibility measurements yield any evidence for a magnetic or a structural transition between 300K and $\sim$4 K. Comprehensive single-crystal diffraction studies with neutron and X-ray radiation reveal the rutile structure to persist until 2K in our crystals, and show nearly perfect stoichiometry. Previous observations of symmetry forbidden reflections can be attributed to multiple diffraction. Polarized single-crystal neutron diffraction experiments at 1.6K exclude the proposed antiferromagnetic structures with ordered moments larger than 0.01 Bohr magnetons.

In this paper, we study the Dynamic Parameterized Subset Sampling (DPSS) problem in the Word RAM model. In DPSS, the input is a set,~$S$, of~$n$ items, where each item,~$x$, has a non-negative integer weight,~$w(x)$. Given a pair of query parameters, $(\alpha, \beta)$, each of which is a non-negative rational number, a parameterized subset sampling query on~$S$ seeks to return a subset $T \subseteq S$ such that each item $x \in S$ is selected in~$T$, independently, with probability $p_x(\alpha, \beta) = \min \left\{\frac{w(x)}{\alpha \sum_{x\in S} w(x)+\beta}, 1 \right\}$. More specifically, the DPSS problem is defined in a dynamic setting, where the item set,~$S$, can be updated with insertions of new items or deletions of existing items. Our first main result is an optimal algorithm for solving the DPSS problem, which achieves~$O(n)$ pre-processing time, $O(1+\mu_S(\alpha,\beta))$ expected time for each query parameterized by $(\alpha, \beta)$, given on-the-fly, and $O(1)$ time for each update; here, $\mu_S(\alpha,\beta)$ is the expected size of the query result. At all times, the worst-case space consumption of our algorithm is linear in the current number of items in~$S$. Our second main contribution is a hardness result for the DPSS problem when the item weights are~$O(1)$-word float numbers, rather than integers. Specifically, we reduce Integer Sorting to the deletion-only DPSS problem with float item weights. Our reduction implies that an optimal algorithm for deletion-only DPSS with float item weights (achieving all the same bounds as aforementioned) implies an optimal algorithm for Integer Sorting. The latter remains an important open problem. Last but not least, a key technical ingredient for our first main result is an efficient algorithm for generating Truncated Geometric random variates in $O(1)$ expected time in the Word RAM model., Comment: 29 pages, 10 figures, to be published in PODS25

We present a study combining experimental measurements, theoretical analysis, and simulations to investigate core-shell microcapsules interacting with a solid boundary, with a particular focus on understanding the short-range potential energy well arising from the tethered force. The microcapsules, fabricated using a Pickering emulsion template with a cinnamon oil core and calcium alginate shell, were characterized for size (5-6 microns in diameter) and surface charge (-20 mV). We employed total internal reflection microscopy and particle tracking to measure the microcapsule-boundary interactions and diffusion, from which potential energy and diffusivity profiles were derived. The potential energy profile was analyzed and simulated by considering electrostatic, gravitational, and tethered forces, while the diffusivity was compared to that of a solid particle-boundary interaction, inclusive of hydrodynamic forces. The diffusivity was represented as a normalized diffusion coefficient to eliminate the impact of fluid viscosity. The normalized diffusion coefficient of polymer-shell microcapsules (0.02) was found to be an order of magnitude smaller than that of solid polystyrene particles (0.2). The microcapsule sampled a potential well consisting of two distinct minima, as observed experimentally and supported by analytical expressions and Brownian dynamics simulations. A critical tethered height (49.8 nm) and the alginate radius of (35.2 nm) were obtained from fitting our model to experimental data. This work concludes that these benign core shell microcapsules interact with a nearby boundary via a transient tethering interaction, overall producing a mild sticky interaction that would likely be beneficial for applications in consumer products., Comment: 43 pages, 13 figures

Given a graph $G=(V,E)$ and a set $T=\{ (s_i, t_i) : 1\leq i\leq k \}\subseteq V\times V$ of $k$ pairs, the $k$-vertex-disjoint-paths (resp. $k$-edge-disjoint-paths) problem asks to determine whether there exist~$k$ pairwise vertex-disjoint (resp. edge-disjoint) paths $P_1, P_2, ..., P_k$ in $G$ such that, for each $1\leq i\leq k$, $P_i$ connects $s_i$ to $t_i$. Both the edge-disjoint and vertex-disjoint versions in undirected graphs are famously known to be FPT (parameterized by $k$) due to the Graph Minor Theory of Robertson and Seymour. Eilam-Tzoreff [DAM `98] introduced a variant, known as the $k$-disjoint-shortest-paths problem, where each individual path is further required to be a shortest path connecting its pair. They showed that the $k$-disjoint-shortest-paths problem is NP-complete on both directed and undirected graphs; this holds even if the graphs are planar and have unit edge lengths. We focus on four versions of the problem, corresponding to considering edge/vertex disjointness, and to considering directed/undirected graphs. Building on the reduction of Chitnis [SIDMA `23] for $k$-edge-disjoint-paths on planar DAGs, we obtain the following inapproximability lower bound for each of the four versions of $k$-disjoint-shortest-paths on $n$-vertex graphs: - Under Gap-ETH, there exists a constant $\delta>0$ such that for any constant $0<\epsilon\leq \frac{1}{2}$ and any computable function $f$, there is no $(\frac{1}{2}+\epsilon)$-approx in $f(k)\cdot n^{\delta\cdot k}$ time. We further strengthen our results as follows: Directed: Inapprox lower bound for edge-disjoint (resp. vertex-disjoint) paths holds even if the input graph is a planar (resp. 1-planar) DAG with max in-degree and max out-degree at most $2$. Undirected: Inapprox lower bound for edge-disjoint (resp. vertex-disjoint) paths hold even if the input graph is planar (resp. 1-planar) and has max degree $4$.

The net frequency (NF) of a string, of length $m$, in a text, of length $n$, is the number of occurrences of the string in the text with unique left and right extensions. Recently, Guo et al. [CPM 2024] showed that NF is combinatorially interesting and how two key questions can be computed efficiently in the offline setting. First, SINGLE-NF: reporting the NF of a query string in an input text. Second, ALL-NF: reporting an occurrence and the NF of each string of positive NF in an input text. For many applications, however, facilitating these computations in an online manner is highly desirable. We are the first to solve the above two problems in the online setting, and we do so in optimal time, assuming, as is common, a constant-size alphabet: SINGLE-NF in $O(m)$ time and ALL-NF in $O(n)$ time. Our results are achieved by first designing new and simpler offline algorithms using suffix trees, proving additional properties of NF, and exploiting Ukkonen's online suffix tree construction algorithm and results on implicit node maintenance in an implicit suffix tree by Breslauer and Italiano., Comment: Accepted at SPIRE 2024

In this work, we introduce Gemma 2, a new addition to the Gemma family of lightweight, state-of-the-art open models, ranging in scale from 2 billion to 27 billion parameters. In this new version, we apply several known technical modifications to the Transformer architecture, such as interleaving local-global attentions (Beltagy et al., 2020a) and group-query attention (Ainslie et al., 2023). We also train the 2B and 9B models with knowledge distillation (Hinton et al., 2015) instead of next token prediction. The resulting models deliver the best performance for their size, and even offer competitive alternatives to models that are 2-3 times bigger. We release all our models to the community.

Poisson distributed measurements in inverse problems often stem from Poisson point processes that are observed through discretized or finite-resolution detectors, one of the most prominent examples being positron emission tomography (PET). These inverse problems are typically reconstructed via Bayesian methods. A natural question then is whether and how the reconstruction converges as the signal-to-noise ratio tends to infinity and how this convergence interacts with other parameters such as the detector size. In this article we carry out a corresponding variational analysis for the exemplary Bayesian reconstruction functional from [arXiv:2311.17784,arXiv:1902.07521], which considers dynamic PET imaging (i.e.\ the object to be reconstructed changes over time) and uses an optimal transport regularization.

We propose the pivoting meta algorithm (PM) to enhance optimization algorithms that generate iterates as convex combinations of vertices of a feasible region $C\subseteq \mathbb{R}^n$, including Frank-Wolfe (FW) variants. PM guarantees that the active set (the set of vertices in the convex combination) of the modified algorithm remains as small as $\mathrm{dim}(C)+1$ as stipulated by Carath\'eodory's theorem. PM achieves this by reformulating the active set expansion task into an equivalent linear program, which can be efficiently solved using a single pivot step akin to the primal simplex algorithm; the convergence rate of the original algorithms are maintained. Furthermore, we establish the connection between PM and active set identification, in particular showing under mild assumptions that PM applied to the away-step Frank-Wolfe algorithm or the blended pairwise Frank-Wolfe algorithm bounds the active set size by the dimension of the optimal face plus $1$. We provide numerical experiments to illustrate practicality and efficacy on active set size reduction.

Lenses with dynamic focal length, also called zoom functionality, enable a variety of applications related to imaging and sensing. The traditional approach of stacking refractive lenses to achieve this functionality results in an expensive, heavy optical system. Especially for applications in the mid-infrared, light weight and compact form factor are required. In this work, we use a meta-optic triplet to demonstrate zoom imaging at mid-wave infrared wavelengths. By varying the axial distances between the optics, the meta-optic triplet achieves high quality imaging over a zoom range of 5x, with 50$^\circ$ full field of view in the widest configuration and an aperture of 8 mm. This triplet system demonstrates the potential for meta-optics to reduce conventional components in complex and multi-functional imaging systems to dramatically thinner and lighter components.

We consider the minimization of the $h$-mass over normal $1$-currents in $\mathbb{R}^n$ with coefficients in $\mathbb{R}^m$ and prescribed boundary. This optimization is known as multi-material transport problem and used in the context of logistics of multiple commodities, but also as a relaxation of nonconvex optimal transport tasks such as so-called branched transport problems. The $h$-mass with norm $h$ can be defined in different ways, resulting in three functionals $\mathcal{M}_h,|\cdot|_H$, and $\mathbb{M}_h$, whose equality is the main result of this article: $\mathcal{M}_h$ is a functional on $1$-currents in the spirit of Federer and Fleming, norm $|\cdot|_H$ denotes the total variation of a Radon measure with respect to $H$ induced by $h$, and $\mathbb{M}_h$ is a mass on flat $1$-chains in the sense of Whitney. On top we introduce a new and improved notion of calibrations for the multi-material transport problem: we identify calibrations with (weak) Jacobians of optimizers of the associated convex dual problem, which yields their existence and natural regularity.

We consider the Max Unique Coverage problem, including applications to the data stream model. The input is a universe of $n$ elements, a collection of $m$ subsets of this universe, and a cardinality constraint, $k$. The goal is to select a subcollection of at most $k$ sets that maximizes unique coverage, i.e, the number of elements contained in exactly one of the selected sets. The Max Unique Coverage problem has applications in wireless networks, radio broadcast, and envy-free pricing. Our first main result is a fixed-parameter tractable approximation scheme (FPT-AS) for Max Unique Coverage, parameterized by $k$ and the maximum element frequency, $r$, which can be implemented on a data stream. Our FPT-AS finds a $(1-\epsilon)$-approximation while maintaining a kernel of size $\tilde{O}(k r/\epsilon)$, which can be combined with subsampling to use $\tilde{O}(k^2 r / \epsilon^3)$ space overall. This significantly improves on the previous-best FPT-AS with the same approximation, but a kernel of size $\tilde{O}(k^2 r / \epsilon^2)$. In order to achieve our result, we show upper bounds on the ratio of a collection's coverage to the unique coverage of a maximizing subcollection; this is by constructing explicit algorithms that find a subcollection with unique coverage at least a logarithmic ratio of the collection's coverage. We complement our algorithms with our second main result, showing that $\Omega(m / k^2)$ space is necessary to achieve a $(1.5 + o(1))/(\ln k - 1)$-approximation in the data stream. This dramatically improves the previous-best lower bound showing that $\Omega(m / k^2)$ is necessary to achieve better than a $e^{-1+1/k}$-approximation., Comment: 26 pages. Accepted into APPROX 2024

Cell tracking is a subject of active research gathering great interest in medicine and biology. Positron emission tomography (PET) is well suited for tracking radio-labeled cells in vivo due to its exceptional sensitivity and whole-body capability. For validation, ground-truth data is desirable that realistically mimics the flow of cells in a clinical situation. This study develops a workflow (CeFloPS) for simulating moving radio-labeled cells in a human phantom. From the XCAT phantom, the blood vessels are reduced to nodal networks along which cells can move and distribute to organs and tissues. The movement is directed by the blood flow which is calculated in each node using the Hagen-Poiseuille equation and Kirchhoffs laws assuming laminar flow. Organs are voxelized and movement of cells from artery entry to vein exit is generated via a biased 3D random walk. The probabilities of whether cells move or stay in tissues are derived from rate constants of physiologically based compartment modeling. PET listmode data is generated using the Monte-Carlo simulation framework GATE based on the definition of a large-body PET scanner with cell paths as moving radioactive sources and the XCAT phantom providing attenuation data. From the flow simulation of 10000 cells, 100 sample cells were further processed by GATE and listmode data was reconstructed into images for comparison. As demonstrated by comparisons of simulated and reconstructed cell distributions, CeFloPS can realistically simulate the cell behavior of whole-body PET providing valuable data for development and validation of cell tracking algorithms., Comment: 8 pages, 6 figures

Encapsulating few-layer graphene (FLG) in hexagonal boron nitride (hBN) can cause nanoscale inhomogeneities in the FLG, including changes in stacking domains and topographic defects. Due to the diffraction limit, characterizing these inhomogeneities is challenging. Recently, the visualization of stacking domains in encapsulated four-layer graphene (4LG) has been demonstrated with phonon polariton (PhP)-assisted near-field imaging. However, the underlying coupling mechanism and ability to image subdiffractional-sized inhomogeneities remain unknown. Here, we retrieve direct replicas and magnified images of subdiffractional-sized inhomogeneities in hBN-covered trilayer graphene (TLG) and encapsulated 4LG, enabled by the hyperlensing effect. This hyperlensing effect is mediated by hBN's hyperbolic PhP that couple to the FLG's plasmon polaritons. Using near-field microscopy, we identify the coupling by determining the polariton dispersion in hBN-covered TLG to be stacking-dependent. Our work demonstrates super-resolution and magnified imaging of inhomogeneities, paving the way for the realization of homogeneous encapsulated FLG transport samples to study correlated physics.

In this paper, we introduce the Dynamic Modularity-Spectral Algorithm (DynMSA), a novel approach to identify clusters of stocks with high intra-cluster correlations and low inter-cluster correlations by combining Random Matrix Theory with modularity optimisation and spectral clustering. The primary objective is to uncover hidden market structures and find diversifiers based on return correlations, thereby achieving a more effective risk-reducing portfolio allocation. We applied DynMSA to constituents of the S&P 500 and compared the results to sector- and market-based benchmarks. Besides the conception of this algorithm, our contributions further include implementing a sector-based calibration for modularity optimisation and a correlation-based distance function for spectral clustering. Testing revealed that DynMSA outperforms baseline models in intra- and inter-cluster correlation differences, particularly over medium-term correlation look-backs. It also identifies stable clusters and detects regime changes due to exogenous shocks, such as the COVID-19 pandemic. Portfolios constructed using our clusters showed higher Sortino and Sharpe ratios, lower downside volatility, reduced maximum drawdown and higher annualised returns compared to an equally weighted market benchmark.

We provide a template to derive convergence rates for the following popular versions of the Frank-Wolfe algorithm on polytopes: vanilla Frank-Wolfe, Frank-Wolfe with away steps, Frank-Wolfe with blended pairwise steps, and Frank-Wolfe with in-face directions. Our template shows how the convergence rates follow from two affine-invariant properties of the problem, namely, error bound and extended curvature. These properties depend solely on the polytope and objective function but not on any affine-dependent object like norms. For each one of the above algorithms, we derive rates of convergence ranging from sublinear to linear depending on the degree of the error bound., Comment: 28 pages

Passive acoustic monitoring (PAM) in avian bioacoustics enables cost-effective and extensive data collection with minimal disruption to natural habitats. Despite advancements in computational avian bioacoustics, deep learning models continue to encounter challenges in adapting to diverse environments in practical PAM scenarios. This is primarily due to the scarcity of annotations, which requires labor-intensive efforts from human experts. Active learning (AL) reduces annotation cost and speed ups adaption to diverse scenarios by querying the most informative instances for labeling. This paper outlines a deep AL approach, introduces key challenges, and conducts a small-scale pilot study., Comment: accepted at IAL@ECML-PKDD24

Wide field of view and light weight optics are critical for advanced eyewear, with applications in augmented/virtual reality and night vision. Conventional refractive lenses are often stacked to correct aberrations at wide field of view, leading to limited performance and increased size and weight. In particular, simultaneously achieving wide field of view and large aperture for light collection is desirable but challenging to realize in a compact form-factor. Here, we demonstrate a wide field of view (greater than 60$^\circ$) meta-optic doublet eyepiece with an entrance aperture of 2.1 cm. At the design wavelength of 633 nm, the meta-optic doublet achieves comparable performance to a refractive lens-based eyepiece system. This meta-doublet eyepiece illustrates the potential for meta-optics to play an important role in the development of high-quality monochrome near-eye display and night vision systems.

Contactless hand pose estimation requires sensors that provide precise spatial information and low computational complexity for real-time processing. Unlike vision-based systems, radar offers lighting independence and direct motion assessments. Yet, there is limited research balancing real-time constraints, suitable frame rates for motion evaluations, and the need for precise 3D data. To address this, we extend the ultra-efficient two-tone hand imaging method from our prior work to a three-tone approach. Maintaining high frame rates and real-time constraints, this approach significantly enhances reconstruction accuracy and precision. We assess these measures by evaluating reconstruction results for different hand poses obtained by an imaging radar. Accuracy is assessed against ground truth from a spatially calibrated photogrammetry setup, while precision is measured using 3D-printed hand poses. The results emphasize the method's great potential for future radar-based hand sensing., Comment: 4 pages, 4 figures, accepted at European Microwave Week (EuMW 2024) to the topic "R28 Human Activity Monitoring, including Gesture Recognition" (EuRAD)

This paper introduces CodeGemma, a collection of specialized open code models built on top of Gemma, capable of a variety of code and natural language generation tasks. We release three model variants. CodeGemma 7B pretrained (PT) and instruction-tuned (IT) variants have remarkably resilient natural language understanding, excel in mathematical reasoning, and match code capabilities of other open models. CodeGemma 2B is a state-of-the-art code completion model designed for fast code infilling and open-ended generation in latency-sensitive settings., Comment: v1: 11 pages, 4 figures, 5 tables. v2: Update metadata

We introduce operator-valued twisted Araki-Woods algebras. These are operator-valued versions of a class of second quantization algebras that includes $q$-Gaussian and $q$-Araki-Woods algebras and also generalize Shlyakhtenko's von Neumann algebras generated by operator-valued semicircular variables. We develop a disintegration theory that reduces the isomorphism type of operator-valued twisted Araki-Woods algebras over type I factors to the scalar-valued case. Moreover, these algebras come with a natural weight, and we characterize its modular theory. We also give sufficient criteria that guarantee that factoriality of these algebras.

Divalent atoms provide excellent means for advancing control in Rydberg atom-based quantum simulation and computing, due to the second optically active valence electron available. Particularly promising in this context are circular Rydberg atoms, for which long-lived ionic core excitations can be exploited without suffering from detrimental autoionization. Here, we report the implementation of electric quadrupole coupling between the metastable 4D$_{3/2}$ level and a very high-$n$ ($n=79$) circular Rydberg qubit, realized in doubly excited $^{88}$Sr atoms prepared from an optical tweezer array. We measure the kHz-scale differential level shift on the circular Rydberg qubit via beat-node Ramsey interferometry comprising spin echo. Observing this coupling requires coherent interrogation of the Rydberg states for more than one hundred microseconds, which is assisted by tweezer trapping and circular state lifetime enhancement in a black-body radiation suppressing capacitor. Further, we find no noticeable loss of qubit coherence under continuous photon scattering on the ion core, paving the way for laser cooling and imaging of Rydberg atoms. Our results demonstrate access to weak electron-electron interactions in Rydberg atoms and expand the quantum simulation toolbox for optical control of highly excited circular state qubits via ionic core manipulation., Comment: 8 pages, 5 figures

Using controlled injection and recovery experiments, we devised an analysis prescription to assess the quality of dynamical measurements of protoplanetary disk gas masses based on resolved (CO) spectral line data, given observational limitations (resolution, sampling, noise), measurement bias, and ambiguities in the geometry and physical conditions. With sufficient data quality, this approach performed well for massive disks ($M_{\rm d}/M_\ast=0.1$): we inferred $M_{\rm d}$ posteriors that recovered the true values with little bias ($\lesssim$ 20%) and uncertainties within a factor of two (2$\sigma$). The gas surface density profiles for such cases are recovered with remarkable fidelity. Some experimentation indicates that this approach becomes insensitive when $M_{\rm d}/M_\ast\lesssim5$%, due primarily to degeneracies in the surface density profile parameters. Including multiple lines that probe different vertical layers, along with some improvements in the associated tools, might push that practical boundary down by another factor of $\sim$two in ideal scenarios. We also demonstrated this analysis approach using archival ALMA observations of the MWC 480 disk (\"Oberg et al. 2021): we measured $M_{\rm d}=0.13^{\: +0.04}_{\: -0.01} \: M_\odot$ (corresponding to $M_{\rm d}/M_\ast=7\pm1$%) and identified kinematic substructures consistent with surface density gaps around 65 and 135 au. Overall, this (and similar work) suggests that these dynamical measurements offer powerful new constraints with sufficient accuracy and precision to quantify gas masses and surface densities at the high end of the $M_{\rm d}/M_\ast$ distribution, and therefore can serve as key benchmarks for detailed thermo-chemical modeling. We address some prospects for improvements, and discuss various caveats and limitations to guide future work., Comment: ApJ, in press; 32 pages, 29 figures

We explore the bound neutrons decay into invisible particles (e.g., $n\rightarrow 3 \nu$ or $nn \rightarrow 2 \nu$) in the JUNO liquid scintillator detector. The invisible decay includes two decay modes: $ n \rightarrow { inv} $ and $ nn \rightarrow { inv} $. The invisible decays of $s$-shell neutrons in $^{12}{\rm C}$ will leave a highly excited residual nucleus. Subsequently, some de-excitation modes of the excited residual nuclei can produce a time- and space-correlated triple coincidence signal in the JUNO detector. Based on a full Monte Carlo simulation informed with the latest available data, we estimate all backgrounds, including inverse beta decay events of the reactor antineutrino $\bar{\nu}_e$, natural radioactivity, cosmogenic isotopes and neutral current interactions of atmospheric neutrinos. Pulse shape discrimination and multivariate analysis techniques are employed to further suppress backgrounds. With two years of exposure, JUNO is expected to give an order of magnitude improvement compared to the current best limits. After 10 years of data taking, the JUNO expected sensitivities at a 90% confidence level are $\tau/B( n \rightarrow { inv} ) > 5.0 \times 10^{31} \, {\rm yr}$ and $\tau/B( nn \rightarrow { inv} ) > 1.4 \times 10^{32} \, {\rm yr}$., Comment: 28 pages, 7 figures, 4 tables

Semantic Image Segmentation facilitates a multitude of real-world applications ranging from autonomous driving over industrial process supervision to vision aids for human beings. These models are usually trained in a supervised fashion using example inputs. Distribution Shifts between these examples and the inputs in operation may cause erroneous segmentations. The robustness of semantic segmentation models against distribution shifts caused by differing camera or lighting setups, lens distortions, adversarial inputs and image corruptions has been topic of recent research. However, robustness against spatially varying radial distortion effects that can be caused by uneven glass structures (e.g. windows) or the chaotic refraction in heated air has not been addressed by the research community yet. We propose a method to synthetically augment existing datasets with spatially varying distortions. Our experiments show, that these distortion effects degrade the performance of state-of-the-art segmentation models. Pretraining and enlarged model capacities proof to be suitable strategies for mitigating performance degradation to some degree, while fine-tuning on distorted images only leads to marginal performance improvements.

Computer vision techniques are on the rise for industrial applications, like process supervision and autonomous agents, e.g., in the healthcare domain and dangerous environments. While the general usability of these techniques is high, there are still challenging real-world use-cases. Especially transparent structures, which can appear in the form of glass doors, protective casings or everyday objects like glasses, pose a challenge for computer vision methods. This paper evaluates the combination of transparent objects in conjunction with (naturally occurring) contamination through environmental effects like hazing. We introduce a novel publicly available dataset containing 489 images incorporating three grades of water droplet contamination on transparent structures and examine the resulting influence on transparency handling. Our findings show, that contaminated transparent objects are easier to segment and that we are able to distinguish between different severity levels of contamination with a current state-of-the art machine-learning model. This in turn opens up the possibility to enhance computer vision systems regarding resilience against, e.g., datashifts through contaminated protection casings or implement an automated cleaning alert.

Laser powder bed fusion (LPBF) has shown promise for wide range of applications due to its ability to fabricate freeform geometries and generate a controlled microstructure. However, components generated by LPBF still possess sub-optimal mechanical properties due to the defects that are created during laser-material interactions. In this work, we investigate mechanism of spatter formation, using a high-fidelity modelling tool that was built to simulate the multi-physics phenomena in LPBF. The modelling tool have the capability to capture the 3D resolution of the meltpool and the spatter behavior. To understand spatter behavior and formation, we reveal its properties at ejection and evaluate its variation from the meltpool, the source where it is formed. The dataset of the spatter and the meltpool collected consist of 50 % spatter and 50 % melt pool samples, with features that include position components, velocity components, velocity magnitude, temperature, density and pressure. The relationship between the spatter and the meltpool were evaluated via correlation analysis and machine learning (ML) algorithms for classification tasks. Upon screening different ML algorithms on the dataset, a high accuracy was observed for all the ML models, with ExtraTrees having the highest at 96 % and KNN having the lowest at 94 %.

Object detectors in real-world applications often fail to detect objects due to varying factors such as weather conditions and noisy input. Therefore, a process that mitigates false detections is crucial for both safety and accuracy. While uncertainty-based thresholding shows promise, previous works demonstrate an imperfect correlation between uncertainty and detection errors. This hinders ideal thresholding, prompting us to further investigate the correlation and associated cost with different types of uncertainty. We therefore propose a cost-sensitive framework for object detection tailored to user-defined budgets on the two types of errors, missing and false detections. We derive minimum thresholding requirements to prevent performance degradation and define metrics to assess the applicability of uncertainty for failure recognition. Furthermore, we automate and optimize the thresholding process to maximize the failure recognition rate w.r.t. the specified budget. Evaluation on three autonomous driving datasets demonstrates that our approach significantly enhances safety, particularly in challenging scenarios. Leveraging localization aleatoric uncertainty and softmax-based entropy only, our method boosts the failure recognition rate by 36-60\% compared to conventional approaches. Code is available at https://mos-ks.github.io/publications., Comment: Accepted with an oral presentation at UAI 2024

Optical and hybrid convolutional neural networks (CNNs) recently have become of increasing interest to achieve low-latency, low-power image classification and computer vision tasks. However, implementing optical nonlinearity is challenging, and omitting the nonlinear layers in a standard CNN comes at a significant reduction in accuracy. In this work, we use knowledge distillation to compress modified AlexNet to a single linear convolutional layer and an electronic backend (two fully connected layers). We obtain comparable performance to a purely electronic CNN with five convolutional layers and three fully connected layers. We implement the convolution optically via engineering the point spread function of an inverse-designed meta-optic. Using this hybrid approach, we estimate a reduction in multiply-accumulate operations from 17M in a conventional electronic modified AlexNet to only 86K in the hybrid compressed network enabled by the optical frontend. This constitutes over two orders of magnitude reduction in latency and power consumption. Furthermore, we experimentally demonstrate that the classification accuracy of the system exceeds 93% on the MNIST dataset.

Knowing which strings in a massive text are significant -- that is, which strings are common and distinct from other strings -- is valuable for several applications, including text compression and tokenization. Frequency in itself is not helpful for significance, because the commonest strings are the shortest strings. A compelling alternative is net frequency, which has the property that strings with positive net frequency are of maximal length. However, net frequency remains relatively unexplored, and there is no prior art showing how to compute it efficiently. We first introduce a characteristic of net frequency that simplifies the original definition. With this, we study strings with positive net frequency in Fibonacci words. We then use our characteristic and solve two key problems related to net frequency. First, \textsc{single-nf}, how to compute the net frequency of a given string of length $m$, in an input text of length $n$ over an alphabet size $\sigma$. Second, \textsc{all-nf}, given length-$n$ input text, how to report every string of positive net frequency. Our methods leverage suffix arrays, components of the Burrows-Wheeler transform, and solution to the coloured range listing problem. We show that, for both problems, our data structure has $O(n)$ construction cost: with this structure, we solve \textsc{single-nf} in $O(m + \sigma)$ time and \textsc{all-nf} in $O(n)$ time. Experimentally, we find our method to be around 100 times faster than reasonable baselines for \textsc{single-nf}. For \textsc{all-nf}, our results show that, even with prior knowledge of the set of strings with positive net frequency, simply confirming that their net frequency is positive takes longer than with our purpose-designed method., Comment: Full version of a paper to be published at the 35th Annual Symposium on Combinatorial Pattern Matching (CPM 2024)

The work herein investigates the impact of resin molecular weight and solvent choice on drying kinetics and sag velocity in polymer films. These films, ranging in thickness from ~60 micrometer to ~120 micrometer were formulated with 45% by weight polymer resin in one of two solvent packages with different relative evaporation rates (RER). Gravimetry was initially used to track drying kinetics and a one-dimensional diffusion model was utilized to compute the apparent solvent diffusivity. In addition, the film thickness was tracked with optical profilometry. Results from these measurements showed that for fixed molecular weight the drying kinetics increased by approximately two-fold for the high RER solvent, whereas the apparent diffusivity tended to increase with increasing polymer molecular weight. Films formulated from higher molecular weight resins had greater initial viscosities and thicknesses for identical draw down blade clearance. By extension, the higher apparent diffusivities at greater molecular weights were attributed to effects of prolonged evaporation times for the thicker films. The sag velocity was measured through the thickness of the film for these systems at a 5 degree incline using the Variable Angle Inspection Microscope (VAIM). Measurements showed an increase in sag velocity for thinner and less viscous films, which was somewhat surprising both because a thinner film will experience lower gravitational stress and quicker drying times as compared to a thicker film. From these data we conclude that formulating a coating with higher molecular weight resin, although likely to increase drying time, will tend to deter sag because of the large impact of viscosity on these phenomena., Comment: 46 pages, 16 figures

The maximum coverage problem is to select $k$ sets from a collection of sets such that the cardinality of the union of the selected sets is maximized. We consider $(1-1/e-\epsilon)$-approximation algorithms for this NP-hard problem in three standard data stream models. 1. {\em Dynamic Model.} The stream consists of a sequence of sets being inserted and deleted. Our multi-pass algorithm uses $\epsilon^{-2} k \cdot \text{polylog}(n,m)$ space. The best previous result (Assadi and Khanna, SODA 2018) used $(n +\epsilon^{-4} k) \text{polylog}(n,m)$ space. While both algorithms use $O(\epsilon^{-1} \log n)$ passes, our analysis shows that when $\epsilon$ is a constant, it is possible to reduce the number of passes by a $1/\log \log n$ factor without incurring additional space. 2. {\em Random Order Model.} In this model, there are no deletions and the sets forming the instance are uniformly randomly permuted to form the input stream. We show that a single pass and $k \text{polylog}(n,m)$ space suffices for arbitrary small constant $\epsilon$. The best previous result, by Warneke et al.~(ESA 2023), used $k^2 \text{polylog}(n,m)$ space. 3. {\em Insert-Only Model.} Lastly, our results, along with numerous previous results, use a sub-sampling technique introduced by McGregor and Vu (ICDT 2017) to sparsify the input instance. We explain how this technique and others used in the paper can be implemented such that the amortized update time of our algorithm is polylogarithmic. This also implies an improvement of the state-of-the-art insert only algorithms in terms of the update time: $\text{polylog}(m,n)$ update time suffices whereas the best previous result by Jaud et al.~(SEA 2023) required update time that was linear in $k$.

Slurry electrodes are an effective means to improve flow battery performance by reducing electrode fouling and increasing the active surface area necessary for electrochemical reactions. It is critical to understand how the slurry formulation impacts its rheological profile and ultimately battery performance. We study the linear and nonlinear rheology of activated carbon (AC) based slurry electrode used in an all-iron flow battery in the presence of a nonionic surfactant (Triton X-100). Our results show the slurry mimics a colloidal gel with elasticity remaining constant despite increasing surfactant concentration until $\alpha$(=C$_{surf.}$/C$_{AC}$) < 0.65. However, at $\alpha \ge$ 0.65, the slurry abruptly transitions to a fluid with no measurable yield stress. This critical surfactant concentration at which the rheological profile undergoes a dynamic change matches the concentration found previously for gel collapse of this system. Moreover, this transition is accompanied by a complete loss of electrical conductivity. These data show that site specific adsorption of surfactant molecules often used in slurry formulation have a significant and dramatic impact on flow behavior, which should be considered when formulating a slurry electrode., Comment: 16 pages, 12 figures