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Spontaneous symmetry breaking can persist at all temperatures in certain biconical $\mathrm{O}(N)\times \mathbb{Z}_2$ vector models when the underlying field theories are ultraviolet complete. So far, the existence of such theories has been established in fractional dimensions for local but nonunitary models or in 2+1 dimensions but for nonlocal models. Here, we study local models at zero and finite temperature directly in 2+1 dimensions employing functional methods. At zero temperature, we establish that our approach describes the quantum critical behaviour with high accuracy for all $N\geq 2$. We then exhibit the mechanism of discrete symmetry breaking from $\mathrm{O}(N)\times \mathbb{Z}_2\to \mathrm{O}(N)$ for increasing temperature near the biconical critical point when $N$ is finite but large. We calculate the corresponding finite-temperature phase diagram and further show that the Hohenberg-Mermin-Wagner theorem is fully respected within this approach, i.e., symmetry breaking only occurs in the $\mathbb{Z}_2$ sector. Finally, we determine the critical $N$ above which this phenomenon can be observed to be $N_c \approx 15$., Comment: 6 + 5 pages, 3 + 2 figures, comments welcome

The mechanism of X-ray outbursts in Be X-ray binaries remains a mystery, and understanding their circumstellar disks is crucial for a solution of the mass-transfer problem. In particular, it is important to identify the Be star activities (e.g., pulsations) that cause mass ejection and, hence, disk formation. Therefore, we investigated the relationship between optical flux oscillations and the infrared (IR) excess in a sample of five Be X-ray binaries. Applying the Lomb-Scargle technique to high-cadence optical light curves from the Transiting Exoplanet Survey Satellite (TESS), we detected several significant oscillation modes in the 3 to 24 hour period range for each source. We also measured the IR excess (a proxy for disk growth) of those five sources, using J-band light curves from Palomar Gattini-IR. In four of the five sources, we found anti-correlations between the IR excess and the amplitude of the main flux oscillation modes. This result is inconsistent with the conventional idea that non-radial pulsations drive mass ejections. We propose an alternative scenario where internal temperature variations in the Be star cause transitions between pulsation-active and mass-ejection-active states., Comment: 17 pages, 27 figures, 6 tables, accepted for publication in MNRAS

Objective: Head impact information including impact directions, speeds and force are important to study traumatic brain injury, design and evaluate protective gears. This study presents a deep learning model developed to accurately predict head impact information, including location, speed, orientation, and force, based on head kinematics during helmeted impacts. Methods: Leveraging a dataset of 16,000 simulated helmeted head impacts using the Riddell helmet finite element model, we implemented a Long Short-Term Memory (LSTM) network to process the head kinematics: tri-axial linear accelerations and angular velocities. Results: The models accurately predict the impact parameters describing impact location, direction, speed, and the impact force profile with R2 exceeding 70% for all tasks. Further validation was conducted using an on-field dataset recorded by instrumented mouthguards and videos, consisting of 79 head impacts in which the impact location can be clearly identified. The deep learning model significantly outperformed existing methods, achieving a 79.7% accuracy in identifying impact locations, compared to lower accuracies with traditional methods (the highest accuracy of existing methods is 49.4%). Conclusion: The precision underscores the model's potential in enhancing helmet design and safety in sports by providing more accurate impact data. Future studies should test the models across various helmets and sports on large in vivo datasets to validate the accuracy of the models, employing techniques like transfer learning to broaden its effectiveness.

Brain deformation caused by a head impact leads to traumatic brain injury (TBI). The maximum principal strain (MPS) was used to measure the extent of brain deformation and predict injury, and the recent evidence has indicated that incorporating the maximum principal strain rate (MPSR) and the product of MPS and MPSR, denoted as MPSxSR, enhances the accuracy of TBI prediction. However, ambiguities have arisen about the calculation of MPSR. Two schemes have been utilized: one (MPSR1) is to use the time derivative of MPS, and another (MPSR2) is to use the first eigenvalue of the strain rate tensor. Both MPSR1 and MPSR2 have been applied in previous studies to predict TBI. To quantify the discrepancies between these two methodologies, we conducted a comparison of these two MPSR methodologies across nine in-vivo and in-silico head impact datasets and found that 95MPSR1 was 5.87% larger than 95MPSR2, and 95MPSxSR1 was 2.55% larger than 95MPSxSR2. Across every element in all head impacts, MPSR1 was 8.28% smaller than MPSR2, and MPSxSR1 was 8.11% smaller than MPSxSR2. Furthermore, logistic regression models were trained to predict TBI based on the MPSR (or MPSxSR), and no significant difference was observed in the predictability across different variables. The consequence of misuse of MPSR and MPSxSR thresholds (i.e. compare threshold of 95MPSR1 with value from 95MPSR2 to determine if the impact is injurious) was investigated, and the resulting false rates were found to be around 1%. The evidence suggested that these two methodologies were not significantly different in detecting TBI.

Living things enact control of non-equilibrium, dynamical structures through complex biochemical networks, accomplishing spatiotemporally-orchestrated physiological tasks such as cell division, motility, and embryogenesis. While the exact minimal mechanisms needed to replicate these behaviors using synthetic active materials are unknown, controlling the complex, often chaotic, dynamics of active materials is essential to their implementation as engineered life-like materials. Here, we demonstrate the use of external feedback control to regulate and control the spatially-averaged speed of a model active material with time-varying actuation through applied light. We systematically vary the controller parameters to analyze the steady-state flow speed and temporal fluctuations, finding the experimental results in excellent agreement with predictions from both a minimal coarse-grained model and full nematohydrodynamic simulations. Our findings demonstrate that proportional-integral control can effectively regulate the dynamics of active nematics in light of challenges posed by the constituents, such as sample aging, protein aggregation, and sample-to-sample variability. As in living things, deviations of active materials from their steady-state behavior can arise from internal processes and we quantify the important consequences of this coupling on the controlled behavior of the active nematic. Finally, the interaction between the controller and the intrinsic timescales of the active material can induce oscillatory behaviors in a regime of parameter space that qualitatively matches predictions from our model. This work underscores the potential of feedback control in manipulating the complex dynamics of active matter, paving the way for more sophisticated control strategies in the design of responsive, life-like materials.

We use 1-4" (300-1200 au) resolution 12CO(2-1) data from the MASSES (Mass Assembly of Stellar Systems and their Evolution with the SMA) project to measure the projected opening angles of 46 protostellar outflows in the Perseus Molecular Cloud, 37 of which are measured with sufficiently high confidence to use in further analysis. We find that there is a statistically significant difference in the distributions of outflow opening angles for Class 0 and Class I outflows, with a distinct lack of both wide-angle Class 0 outflows and highly collimated Class I outflows. Synthesizing our results with several previous studies, we find that outflows widen with age through the Class 0 stage but do not continue to widen in the Class I stage. The maximum projected opening angle reached is approximately 90 degrees +/- 20 degrees, with the transition between widening and remaining constant occurring near the boundary between the Class 0 and Class I phases of evolution. While the volume fractions occupied by these outflows are no more than a few tens of percent of the total core volume, at most, recent theoretical work suggests outflows may still be capable of playing a central role in setting the low star formation efficiencies of 25%-50% observed on core scales., Comment: 35 pages, accepted by MNRAS

Transposable elements (TEs) constitute a significant portion of eukaryotic genomes, yet their role in chromatin organization remains poorly understood. This study investigates the distribution patterns of TEs around chromatin ligation points (LPs) identified through Micro-C experiments in human cells. We analyzed the density of various TE families within a 100kb window centered on LPs, focusing on major families such as Alu and LINE-1 (L1) elements. Our findings reveal distinct, non-random distribution patterns that differ between TE families and exhibit consistent strand-specific biases. These patterns were reproducible across two independent datasets and showed marked differences from random genomic distributions. Notably, we observed family-specific variations in TE density near LPs, with some families showing depletion at LPs followed by periodic fluctuations in density. The consistency of these patterns across TE families and their orientation relative to chromosome arms suggest a fundamental relationship between TEs and higher-order chromatin structure. Our results provide new insights into the potential role of TEs in genome organization and challenge the notion of TEs as passive genomic components. This study lays the groundwork for future investigations into the functional implications of TE distribution in chromatin architecture and gene regulation.

RX Pup is a symbiotic binary which experienced a nova outburst in the 1970's. Here we report a discovery of a ~1300 year old nova shell around the system and a possible detection of a ~7000 year old nova shell. Together with the nova shell ejected in the 1970's this makes RX Pup the first system with three nova shells observed. This triad of eruptions suggests a change in the nova recurrence time. The most likely explanation is an alteration in the mass transfer rate attributed to evolutionary changes of the mass-donor in the system. Notably, comparative analyses with theoretical models indicate an increase in the average mass transfer rate by a factor of three over the past 10,000 years. This makes RX Pup a unique system, which allows us to probe millenium-scale evolution of mass transfer rates in binary systems., Comment: 14 pages, 5 figures, 2 tables, Accepted for publication in ApJL

We derive an optimal power-weighted Hardy-type inequality in integral form on finite intervals and subsequently prove the analogous inequality in differential form. We note that the optimal constant of the latter inequality differs from the former. Moreover, by iterating these inequalities we derive the sequence of power-weighted Birman-Hardy-Rellich-type inequalities in integral form on finite intervals and then also prove the analogous sequence of inequalities in differential form. We use the one-dimensional Hardy-type result in differential form to derive an optimal multi-dimensional version of the power-weighted Hardy inequality in differential form on annuli (i.e., spherical shell domains), and once more employ an iteration procedure to derive the Birman-Hardy-Rellich-type sequence of power-weighted higher-order Hardy-type inequalities for annuli. In the limit as the annulus approaches $\mathbb{R}^n$, we recover well-known prior results on Rellich-type inequalities on $\mathbb{R}^n$., Comment: 19 pages

We revisit and extend a variety of inequalities related to power weighted Rellich and Hardy--Rellich inequalities, including an inequality due to Schmincke., Comment: 37 pages, corrections made and slight reorganization of appendix

This work proposes a methodology for determining the maximum dependency length of a recurrent neural network (RNN), and then studies the effects of architectural changes, including the number and neuron count of layers, on the maximum dependency lengths of traditional RNN, gated recurrent unit (GRU), and long-short term memory (LSTM) models., Comment: 13 pages, 12 figures

In the pursuit of understanding the population of stellar remnants within the Milky Way, we analyze the sample of $\sim 950$ microlensing events observed by the Spitzer Space Telescope between 2014 and 2019. In this study we focus on a sub-sample of nine microlensing events, selected based on their long timescales, small microlensing parallaxes and joint observations by the Gaia mission, to increase the probability that the chosen lenses are massive and the mass is measurable. Among the selected events we identify lensing black holes and neutron star candidates, with potential confirmation through forthcoming release of the Gaia time-series astrometry in 2026. Utilizing Bayesian analysis and Galactic models, along with the Gaia Data Release 3 proper motion data, four good candidates for dark remnants were identified: OGLE-2016-BLG-0293, OGLE-2018-BLG-0483, OGLE-2018-BLG-0662, and OGLE-2015-BLG-0149, with lens masses of $2.98^{+1.75}_{-1.28}~M_{\odot}$, $4.65^{+3.12}_{-2.08}~M_{\odot}$, $3.15^{+0.66}_{-0.64}~M_{\odot}$ and $1.4^{+0.75}_{-0.55}~M_{\odot}$, respectively. Notably, the first two candidates are expected to exhibit astrometric microlensing signals detectable by Gaia, offering the prospect of validating the lens masses. The methodologies developed in this work will be applied to the full Spitzer microlensing sample, populating and analyzing the time-scale ($t_{\rm E}$) vs. parallax ($\pi_{\rm E}$) diagram to derive constraints on the population of lenses in general and massive remnants in particular., Comment: submitted to ApJ

Interaction-induced charge orders with electronic origin occur as states of spontaneously broken symmetry in several materials platforms. An electronic mechanism for charge order requires an attractive component in the effective charge vertex. We put forward such a mechanism for the formation of unconventional charge density waves in a metal. These states result from the condensation of particle-hole pairs with finite wave vector and non-zero angular momentum and correspond to bond or loop current order on a lattice. The mechanism we describe can be viewed as Kohn Luttinger analysis in the particle-hole channel with finite transferred momentum. It incorporates one-loop spin and pairing correctionsn, which are then used as an input for a summation in the charge channel triggering an instability. We extend our analysis to a spin-fluctuation approach, where the effective charge interaction is dressed by the particle-hole ladder with exchanged momentum. We argue that this mechanism works for weakly-interacting metals with nested Fermi surface and a large number of fermion flavors. We apply the Kohn-Luttinger-like approach to square- and triangular-lattice Hubbard models with SU($N_f$) flavour symmetry and show that it leads to different types of $p$-wave charge density waves. We also study effects beyond weak coupling at and away from Van Hove filling in terms of a phenomenological model with additional exchange interaction. In the vicinity of Van Hove filling, we obtain $d$-wave charge density waves with wave vectors determined by nesting as leading instabilities. In addition, we find another charge density wave with wave vector $K/4$ on the triangular lattice on both sides of Van Hove filling. We demonstrate that this $K/4$ instability can win the competition against pairing for $N_f=4$ via an unbiased functional renormalisation group calculation., Comment: 12+5 pages, 8+1 figures

The principal purpose of this note is to prove a logarithmic refinement of the power weighted Hardy--Rellich inequality on $n$-dimensional balls, valid for the largest variety of underlying parameters and for all dimensions $n \in \mathbb{N}$, $n\geq 2$., Comment: 9 pages

We present a method for determining the unknown location of a sensor placed in a known 2D environment in the presence of unknown dynamic obstacles, using only few distance measurements. We present guarantees on the quality of the localization, which are robust under mild assumptions on the density of the unknown/dynamic obstacles in the known environment. We demonstrate the effectiveness of our method in simulated experiments for different environments and varying dynamic-obstacle density. Our open source software is available at https://github.com/TAU-CGL/vb-fdml2-public.

Vision-based imitation learning has shown promising capabilities of endowing robots with various motion skills given visual observation. However, current visuomotor policies fail to adapt to drastic changes in their visual observations. We present Perception Stitching that enables strong zero-shot adaptation to large visual changes by directly stitching novel combinations of visual encoders. Our key idea is to enforce modularity of visual encoders by aligning the latent visual features among different visuomotor policies. Our method disentangles the perceptual knowledge with the downstream motion skills and allows the reuse of the visual encoders by directly stitching them to a policy network trained with partially different visual conditions. We evaluate our method in various simulated and real-world manipulation tasks. While baseline methods failed at all attempts, our method could achieve zero-shot success in real-world visuomotor tasks. Our quantitative and qualitative analysis of the learned features of the policy network provides more insights into the high performance of our proposed method.

Bounding and predicting the generalization gap of overparameterized neural networks remains a central open problem in theoretical machine learning. Neural network optimization trajectories have been proposed to possess fractal structure, leading to bounds and generalization measures based on notions of fractal dimension on these trajectories. Prominently, both the Hausdorff dimension and the persistent homology dimension have been proposed to correlate with generalization gap, thus serving as a measure of generalization. This work performs an extended evaluation of these topological generalization measures. We demonstrate that fractal dimension fails to predict generalization of models trained from poor initializations. We further identify that the $\ell^2$ norm of the final parameter iterate, one of the simplest complexity measures in learning theory, correlates more strongly with the generalization gap than these notions of fractal dimension. Finally, our study reveals the intriguing manifestation of model-wise double descent in persistent homology-based generalization measures. This work lays the ground for a deeper investigation of the causal relationships between fractal geometry, topological data analysis, and neural network optimization., Comment: 17 pages, 6 figures

Deep-sea archives that include intermediate-lived radioactive $^{60}\mathrm{Fe}$ particles suggest the occurrence of several recent supernovae inside the present-day volume of the Local Bubble during the last $\sim 10$ Myr. The isotope $^{60}\mathrm{Fe}$ is mainly produced in massive stars and ejected in supernova explosions, which should always result in a sizeable yield of $^{26}\mathrm{Al}$ from the same objects. $^{60}\mathrm{Fe}$ and $^{26}\mathrm{Al}$ decay with lifetimes of 3.82 and 1.05 Myr, and emit $\gamma$-rays at 1332 and 1809 keV, respectively. These $\gamma$-rays have been measured as diffuse glow of the Milky Way, and would also be expected from inside the Local Bubble as foreground emission. Based on two scenarios, one employing a geometrical model and the other state-of-the-art hydrodynamics simulations, we estimate the expected fluxes of the 1332 and 1809 keV $\gamma$-ray lines, as well as the resulting 511 keV line from positron annihilation due to the $^{26}\mathrm{Al}$ $\beta^+$-decay. We find fluxes in the range of $10^{-6}$-$10^{-5}\,\mathrm{ph\,cm^{-2}\,s^{-1}}$ for all three lines with isotropic contributions of 10-50%. We show that these fluxes are within reach for the upcoming COSI-SMEX $\gamma$-ray telescope over its nominal satellite mission duration of 2 yr. Given the Local Bubble models considered, we conclude that in the case of 10-20 Myr-old superbubbles, the distributions of $^{60}\mathrm{Fe}$ and $^{26}\mathrm{Al}$ are not co-spatial - an assumption usually made in $\gamma$-ray data analyses. In fact, this should be taken into account however when analysing individual nearby targets for their $^{60}\mathrm{Fe}$ to $^{26}\mathrm{Al}$ flux ratio as this gauges the stellar evolution models and the age of the superbubbles. A flux ratio measured for the Local Bubble could further constrain models of $^{60}\mathrm{Fe}$ deposition on Earth and its moon., Comment: accepted in A&A, 18 pages, 13 figures, 2 tables

Discrepancy is a well-known measure for the irregularity of the distribution of a point set. Point sets with small discrepancy are called low-discrepancy and are known to efficiently fill the space in a uniform manner. Low-discrepancy points play a central role in many problems in science and engineering, including numerical integration, computer vision, machine perception, computer graphics, machine learning, and simulation. In this work, we present the first machine learning approach to generate a new class of low-discrepancy point sets named Message-Passing Monte Carlo (MPMC) points. Motivated by the geometric nature of generating low-discrepancy point sets, we leverage tools from Geometric Deep Learning and base our model on Graph Neural Networks. We further provide an extension of our framework to higher dimensions, which flexibly allows the generation of custom-made points that emphasize the uniformity in specific dimensions that are primarily important for the particular problem at hand. Finally, we demonstrate that our proposed model achieves state-of-the-art performance superior to previous methods by a significant margin. In fact, MPMC points are empirically shown to be either optimal or near-optimal with respect to the discrepancy for low dimension and small number of points, i.e., for which the optimal discrepancy can be determined. Code for generating MPMC points can be found at https://github.com/tk-rusch/MPMC., Comment: Published in Proceedings of the National Academy of Sciences (PNAS): https://www.pnas.org/doi/10.1073/pnas.2409913121

Planetary rovers can use onboard data analysis to adapt their measurement plan on the fly, improving the science value of data collected between commands from Earth. This paper describes the implementation of an adaptive sampling algorithm used by PIXL, the X-ray fluorescence spectrometer of the Mars 2020 Perseverance rover. PIXL is deployed using the rover arm to measure X-ray spectra of rocks with a scan density of several thousand points over an area of typically 5 x 7 mm. The adaptive sampling algorithm is programmed to recognize points of interest and to increase the signal-to-noise ratio at those locations by performing longer integrations. Two approaches are used to formulate the sampling rules based on past quantification data: 1) Expressions that isolate particular regions within a ternary compositional diagram, and 2) Machine learning rules that threshold for a high weight percent of particular compounds. The design of the rulesets are outlined and the performance of the algorithm is quantified using measurements from the surface of Mars. To our knowledge, PIXL's adaptive sampling represents the first autonomous decision-making based on real-time compositional analysis by a spacecraft on the surface of another planet., Comment: 24 pages including 11 figures and 7 tables. Submitted for publication to the journal Icarus

Spectral graph convolution, an important tool of data filtering on graphs, relies on two essential decisions; selecting spectral bases for signal transformation and parameterizing the kernel for frequency analysis. While recent techniques mainly focus on standard Fourier transform and vector-valued spectral functions, they fall short in flexibility to describe specific signal distribution for each node, and expressivity of spectral function. In this paper, we present a novel wavelet-based graph convolution network, namely WaveGC, which integrates multi-resolution spectral bases and a matrix-valued filter kernel. Theoretically, we establish that WaveGC can effectively capture and decouple short-range and long-range information, providing superior filtering flexibility, surpassing existing graph convolutional networks and graph Transformers (GTs). To instantiate WaveGC, we introduce a novel technique for learning general graph wavelets by separately combining odd and even terms of Chebyshev polynomials. This approach strictly satisfies wavelet admissibility criteria. Our numerical experiments showcase the capabilities of the new network. By replacing the Transformer part in existing architectures with WaveGC, we consistently observe improvements in both short-range and long-range tasks. This underscores the effectiveness of the proposed model in handling different scenarios. Our code is available at https://github.com/liun-online/WaveGC.

We report a proof-of-principle experimental demonstration of a turbulence-resistant quantum Lidar system. As a key technology for sensing and ranging, Lidar has drawn considerable attention for a study from quantum perspective, in search of proven advantages complementary to the capabilities of conventional Lidar technologies. Environmental factors such as strong atmospheric turbulence can have detrimental effects on the performance of these systems. We demonstrate the possibility of turbulence-resistant operation of a quantum Lidar system via two-photon interference of entangled photon pairs. Additionally, the reported quantum Lidar also demonstrates the expected noise resistance. This study suggests a potential high precision timing-positioning technology operable under turbulence and noise.

The Electron-Ion Collider (EIC) will use swap-out injection scheme for the Electron Storage Ring (ESR) to overcome limitations in polarization lifetime. However, the pursuit of highest luminosity with the required 28 nC electron bunches encounters stability challenges in the Rapid Cycling Synchrotron (RCS). One method is to inject multiple RCS bunches into a same ESR bucket. In this paper we perform simulation studies investigating proton emittance growth and electron emittance blowup in this injection scheme. Mitigation strategies are explored. These findings promise enhanced EIC stability and performance, shaping potential future operational improvements.

The first wave of observations with JWST has revealed a striking overabundance of luminous galaxies at early times ($z>10$) compared to models of galaxies calibrated to pre-JWST data. Early observations have also uncovered a large population of supermassive black holes (SMBHs) at $z>6$. Because many of the high-$z$ objects appear extended, the contribution of active galactic nuclei (AGNs) to the total luminosity has been assumed to be negligible. In this work, we use a semi-empirical model for assigning AGNs to galaxies to show that active galaxies can boost the stellar luminosity function (LF) enough to solve the overabundance problem while simultaneously remaining consistent with the observed morphologies of high-$z$ sources. We construct a model for the composite AGN+galaxy LF by connecting dark matter halo masses to galaxy and SMBH masses and luminosities, accounting for dispersion in the mapping between host galaxy and SMBH mass and luminosity. By calibrating the model parameters -- which characterize the $M_\bullet-M_\star$ relation -- to a compilation of $z>10$ JWST UVLF data, we show that AGN emission can account for the excess luminosity under a variety of scenarios, including one where 10\% of galaxies host BHs of comparable luminosities to their stellar components. Using a sample of simulated objects and real observations, we demonstrate that such low-luminosity AGNs can be `hidden' in their host galaxies and be missed in common morphological analyses. We find that for this explanation to be viable, our model requires a population of BHs that are overmassive ($M_\bullet/M_\star\sim10^{-2}$) with respect to their host galaxies compared to the local relation and are more consistent with the observed relation at $z=4-8$. We explore the implications of this model for BH seed properties and comment on observational diagnostics necessary to further investigate this explanation., Comment: 34 pages, 12 figures; accepted by JCAP

Considering non-stationary environments in online optimization enables decision-maker to effectively adapt to changes and improve its performance over time. In such cases, it is favorable to adopt a strategy that minimizes the negative impact of change to avoid potentially risky situations. In this paper, we investigate risk-averse online optimization where the distribution of the random cost changes over time. We minimize risk-averse objective function using the Conditional Value at Risk (CVaR) as risk measure. Due to the difficulty in obtaining the exact CVaR gradient, we employ a zeroth-order optimization approach that queries the cost function values multiple times at each iteration and estimates the CVaR gradient using the sampled values. To facilitate the regret analysis, we use a variation metric based on Wasserstein distance to capture time-varying distributions. Given that the distribution variation is sub-linear in the total number of episodes, we show that our designed learning algorithm achieves sub-linear dynamic regret with high probability for both convex and strongly convex functions. Moreover, theoretical results suggest that increasing the number of samples leads to a reduction in the dynamic regret bounds until the sampling number reaches a specific limit. Finally, we provide numerical experiments of dynamic pricing in a parking lot to illustrate the efficacy of the designed algorithm.

We surveyed nearly all the embedded protostars in seven nearby clouds (Corona Australis, Aquila, Chamaeleon I & II, Ophiuchus North, Ophiuchus, Serpens) with the Atacama Large Millimeter/submillimeter Array at 1.3mm observations with a resolution of 0.1$"$. This survey detected 184 protostellar disks, 90 of which were observed at a resolution of 14-18 au, making it one of the most comprehensive high-resolution disk samples across various protostellar evolutionary stages to date. Our key findings include the detection of new annular substructures in two Class I and two flat-spectrum sources, while 21 embedded protostars exhibit distinct asymmetries or substructures in their disks. We find that protostellar disks have a substantially large variability in their radii across all evolutionary classes. In particular, the fraction of large disks with sizes above 60\,au decreases as the protostar evolves from Class 0 to Class I. Compiling the literature data, we discovered an increasing trend of the gas disk radii to dust disk radii ratio ($R_{\rm gas,Kep}/R_{\rm mm}$) with increasing bolometric temperature (${\rm T}_{\rm bol}$). Our results indicate that the dust and gas disk radii decouple during the early Class I stage. However, in the Class 0 stage, the dust and gas disk sizes are similar, which allows a direct comparison between models and observational data at the earliest stages of protostellar evolution. We show that the distribution of radii in the 52 Class 0 disks in our sample is in high tension with various disk formation models, indicating that protostellar disk formation remains an unsolved question., Comment: Accepted by ApJ 2024.7.8, 70 pages, 30 figures

This paper considers risk-averse learning in convex games involving multiple agents that aim to minimize their individual risk of incurring significantly high costs. Specifically, the agents adopt the conditional value at risk (CVaR) as a risk measure with possibly different risk levels. To solve this problem, we propose a first-order risk-averse leaning algorithm, in which the CVaR gradient estimate depends on an estimate of the Value at Risk (VaR) value combined with the gradient of the stochastic cost function. Although estimation of the CVaR gradients using finitely many samples is generally biased, we show that the accumulated error of the CVaR gradient estimates is bounded with high probability. Moreover, assuming that the risk-averse game is strongly monotone, we show that the proposed algorithm converges to the risk-averse Nash equilibrium. We present numerical experiments on a Cournot game example to illustrate the performance of the proposed method.

We achieve, at room temperature, conductance enhancements over two orders of magnitude in single molecule circuits formed with polycyclic benzoquinoidal (BQn) diradicals upon increasing molecular length by ~0.5 nm. We find that this extreme and atypical anti-ohmic conductance enhancement at longer molecular lengths is due to the diradical character of the molecules, which can be described as a topologically non-trivial electronic state. We adapt the 1D-SSH model originally developed to examine electronic topological order in linear carbon chains to the polycyclic systems studied here and find that it captures the anti-ohmic trends in this molecular series. The mechanism of conductance enhancement with length is revealed to be constructive quantum interference (CQI) between the frontier orbitals with non-trivial topology, which is present in acene-like, but not in linear, molecular systems. Importantly, we predict computationally and measure experimentally that anti-ohmic trends can be engineered through synthetic adjustments of the diradical character of the acene-like molecules. Overall, we achieve an experimentally unprecedented anti-ohmic enhancement and mechanistic insight into electronic transport in a class of materials that we identify here as promising candidates for creating highly conductive and tunable nanoscale wires., Comment: 21 pages, 6 figures, submitted

This study addresses the limitations of the traditional analysis of message-passing, central to graph learning, by defining {\em \textbf{generalized propagation}} with directed and weighted graphs. The significance manifest in two ways. \textbf{Firstly}, we propose {\em Generalized Propagation Neural Networks} (\textbf{GPNNs}), a framework that unifies most propagation-based graph neural networks. By generating directed-weighted propagation graphs with adjacency function and connectivity function, GPNNs offer enhanced insights into attention mechanisms across various graph models. We delve into the trade-offs within the design space with empirical experiments and emphasize the crucial role of the adjacency function for model expressivity via theoretical analysis. \textbf{Secondly}, we propose the {\em Continuous Unified Ricci Curvature} (\textbf{CURC}), an extension of celebrated {\em Ollivier-Ricci Curvature} for directed and weighted graphs. Theoretically, we demonstrate that CURC possesses continuity, scale invariance, and a lower bound connection with the Dirichlet isoperimetric constant validating bottleneck analysis for GPNNs. We include a preliminary exploration of learned propagation patterns in datasets, a first in the field. We observe an intriguing ``{\em \textbf{decurve flow}}'' - a curvature reduction during training for models with learnable propagation, revealing the evolution of propagation over time and a deeper connection to over-smoothing and bottleneck trade-off., Comment: 15 pages, 4 figures

While neural network approaches have made significant strides in resolving classical signal processing problems, it is often the case that hybrid approaches that draw insight from both signal processing and neural networks produce more complete solutions. In this paper, we present a hybrid classical digital signal processing/deep neural network (DSP/DNN) approach to source separation (SS) highlighting the theoretical link between variational autoencoder and classical approaches to SS. We propose a system that transforms the single channel under-determined SS task to an equivalent multichannel over-determined SS problem in a properly designed latent space. The separation task in the latent space is treated as finding a variational block-wise disentangled representation of the mixture. We show empirically, that the design choices and the variational formulation of the task at hand motivated by the classical signal processing theoretical results lead to robustness to unseen out-of-distribution data and reduction of the overfitting risk. To address the resulting permutation issue we explicitly incorporate a novel differentiable permutation loss function and augment the model with a memory mechanism to keep track of the statistics of the individual sources.

Link prediction with knowledge graphs has been thoroughly studied in graph machine learning, leading to a rich landscape of graph neural network architectures with successful applications. Nonetheless, it remains challenging to transfer the success of these architectures to relational hypergraphs, where the task of link prediction is over $k$-ary relations, which is substantially harder than link prediction with knowledge graphs. In this paper, we propose a framework for link prediction with relational hypergraphs, unlocking applications of graph neural networks to fully relational structures. Theoretically, we conduct a thorough analysis of the expressive power of the resulting model architectures via corresponding relational Weisfeiler-Leman algorithms and also via logical expressiveness. Empirically, we validate the power of the proposed model architectures on various relational hypergraph benchmarks. The resulting model architectures substantially outperform every baseline for inductive link prediction, and lead to state-of-the-art results for transductive link prediction.

The path signature, having enjoyed recent success in the machine learning community, is a theoretically-driven method for engineering features from irregular paths. On the other hand, graph neural networks (GNN), neural architectures for processing data on graphs, excel on tasks with irregular domains, such as sensor networks. In this paper, we introduce a novel approach, Path Signature Graph Convolutional Neural Networks (PS-GCNN), integrating path signatures into graph convolutional neural networks (GCNN), and leveraging the strengths of both path signatures, for feature extraction, and GCNNs, for handling spatial interactions. We apply our method to analyze slow earthquake sequences, also called slow slip events (SSE), utilizing data from GPS timeseries, with a case study on a GPS sensor network on the east coast of New Zealand's north island. We also establish benchmarks for our method on simulated stochastic differential equations, which model similar reaction-diffusion phenomenon. Our methodology shows promise for future advancement in earthquake prediction and sensor network analysis.

We introduce a real-time, multichannel speech enhancement algorithm which maintains the spatial cues of stereo recordings including two speech sources. Recognizing that each source has unique spatial information, our method utilizes a dual-path structure, ensuring the spatial cues remain unaffected during enhancement by applying source-specific common-band gain. This method also seamlessly integrates pretrained monaural speech enhancement, eliminating the need for retraining on stereo inputs. Source separation from stereo mixtures is achieved via spatial beamforming, with the steering vector for each source being adaptively updated using post-enhancement output signal. This ensures accurate tracking of the spatial information. The final stereo output is derived by merging the spatial images of the enhanced sources, with its efficacy not heavily reliant on the separation performance of the beamforming. The algorithm runs in real-time on 10-ms frames with a 40 ms of look-ahead. Evaluations reveal its effectiveness in enhancing speech and preserving spatial cues in both fully and sparsely overlapped mixtures., Comment: Accepted for ICASSP 2024, 5 pages

Transformer-based models have recently become wildly successful across a diverse set of domains. At the same time, recent work has shown empirically and theoretically that Transformers are inherently limited. Specifically, they argue that as model depth increases, Transformers oversmooth, i.e., inputs become more and more similar. A natural question is: How can Transformers achieve these successes given this shortcoming? In this work we test these observations empirically and theoretically and uncover a number of surprising findings. We find that there are cases where feature similarity increases but, contrary to prior results, this is not inevitable, even for existing pre-trained models. Theoretically, we show that smoothing behavior depends on the eigenspectrum of the value and projection weights. We verify this empirically and observe that the sign of layer normalization weights can influence this effect. Our analysis reveals a simple way to parameterize the weights of the Transformer update equations to influence smoothing behavior. We hope that our findings give ML researchers and practitioners additional insight into how to develop future Transformer-based models.

External fragmentation of physical memory occurs when adjacent differently sized regions of allocated physical memory are freed at different times, causing free memory to be physically discontiguous. It can significantly degrade system performance and efficiency, such as reducing the ability to use huge pages, a critical optimization on modern large-memory system. For decades system developers have sought to avoid and mitigate fragmentation, but few prior studies quantify and characterize it in production settings. Moreover, prior work often artificially fragments physical memory to create more realistic performance evaluations, but their fragmentation methodologies are ad hoc and unvalidated. Out of 13 papers, we found 11 different methodologies, some of which were subsequently found inadequate. The importance of addressing fragmentation necessitates a validated and principled methodology. Our work fills these gaps in knowledge and methodology. We conduct a study of memory fragmentation in production by observing 248 machines in the Computer Sciences Department at University of Wisconsin - Madison for a week. We identify six key memory usage patterns, and find that Linux's file cache and page reclamation systems are major contributors to fragmentation because they often obliviously break up contiguous memory. Finally, we create and\'uril, a tool to artificially fragment memory during experimental research evaluations. While and\'uril ultimately fails as a scientific tool, we discuss its design ideas, merits, and failings in hope that they may inspire future research., Comment: 23 pages, 9 figures

The physics of driven collective modes in quantum materials underpin a number of striking non-equilibrium functional responses, which include enhanced magnetism, ferroelectricity and superconductivity. However, the coherent coupling between multiple modes at once are difficult to capture by single-pump probe (one-dimensional) spectroscopy, and often remain poorly understood. One example is phonon-mediated amplification of Josephson plasmons in YBa$_2$Cu$_3$O$_{6+x}$, in which at least three normal modes of the solid are coherently mixed as a source of enhanced superconductivity. Here, we go beyond previous pump-probe experiments in this system and acquire two-dimensional frequency maps using pairs of mutually delayed, carrier envelope phase stable mid-infrared pump pulses, combined with measurements of the time-modulated second-order nonlinear optical susceptibility. We find that the driven zone-center phonons amplify coherent pairs of opposite-momentum Josephson plasma polaritons, generating a squeezed state of interlayer phase fluctuations. The squeezed state is a potentially important ingredient in the microscopic physics of photo-induced superconductivity in this and other materials., Comment: 20 pages, 7 figures