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The fall 2023 and spring 2024 undergraduate enrollment increases, marking the first growth since the COVID-19 pandemic, show signs of a post-pandemic turnaround for higher education. However, a significant share of current undergraduates will eventually disengage from college before earning a degree or other credential. They will join tens of millions of other adult Americans who are Some College, No Credential (SCNC). The SCNC population has been consistently rising over time. Re-engaging those who stop out remains a persistent challenge and a priority for the forty states that have set ambitious postsecondary attainment goals. This report aims to provide timely insights into the SCNC population, offering state leaders and policymakers accurate data on its current status, along with tracking progress and outcome measures for SCNC students. The first section of this report describes who makes up the SCNC population and how it has changed since the last report. In this section, the authors pay particular attention to Recent Stopouts, who joined the SCNC population after being stopped out between January 2021 and July 2022. In the second section, the authors report on SCNC re-enrollment in the 2022-23 academic year as well as first-year credential earning for re-enrollees. The authors also provide new updates on continued enrollment and second-year credential earning for SCNC re-enrollees in the 2021-22 academic year, whom were first reported on last year.

We perform fully relativistic simulations of the head-on collisions between intermediate-mass black holes and very massive stars. Such collisions are expected to occur in dense stellar clusters and may play an important role in growing the mass of the seed black hole. For the cases considered here, for which the masses of the black holes and stars are comparable, the vast majority of the stellar material is accreted onto the black hole within a stellar dynamical timescale, as expected from analytical estimates, and leads to a rapid growth of the black hole. A small amount of mass, which is shock-heated in the wake of the black hole, is ejected from the collision and will contribute to the interstellar material in the cluster., Comment: 17 pages, 7 figures

Generalizing the results in our previous paper, we consider pseudo-involutions in the Riordan group where the generating function $g$ for the first column of a Riordan array satisfies a functional equation of certain types involving a polynomial. For those types of equations, we find the pseudo-involutory companion of $g$. We also develop a general method for finding B-functions of Riordan pseudo-involutions in the cases we consider, and show that these B-functions involve Chebyshev polynomials. We apply our method for several families of Riordan arrays, obtaining new results and deriving known results more efficiently., Comment: 24 pages

Grassroots platforms aim to offer an egalitarian alternative to global platforms -- centralized/autocratic (Facebook etc.) and decentralized/plutocratic (Bitcoin etc.) alike. Key grassroots platforms include grassroots social networks, grassroots cryptocurrencies, and grassroots democratic federations. Previously, grassroots platforms were defined formally and proven grassroots using unary distributed transition systems, in which each transition is carried out by a single agent. However, grassroots platforms cater for a more abstract specification using transactions carried out atomically by multiple agents, something that cannot be expressed by unary transition systems. As a result, their original specifications and proofs were unnecessarily cumbersome and opaque. Here, we aim to provide a more suitable formal foundation for grassroots platforms. To do so, we enhance the notion of a distributed transition system to include atomic transactions and revisit the notion of grassroots platforms within this new foundation. We present crisp specifications of key grassroots platforms using atomic transactions: befriending and defriending for grassroots social networks, coin swaps for grassroots cryptocurrencies, and communities forming, joining, and leaving a federation for grassroots democratic federations. We prove a general theorem that a platform specified by atomic transactions that are so-called interactive is grassroots; show that the atomic transactions used to specify all three platforms are interactive; and conclude that the platforms thus specified are indeed grassroots. We thus provide a better mathematical foundation for grassroots platforms and a solid and clear starting point from which their implementation can commence.

This work presents a novel Bayesian framework for unsupervised domain adaptation (UDA) in medical image segmentation. While prior works have explored this clinically significant task using various strategies of domain alignment, they often lack an explicit and explainable mechanism to ensure that target image features capture meaningful structural information. Besides, these methods are prone to the curse of dimensionality, inevitably leading to challenges in interpretability and computational efficiency. To address these limitations, we propose RemInD, a framework inspired by human adaptation. RemInD learns a domain-agnostic latent manifold, characterized by several anchors, to memorize anatomical variations. By mapping images onto this manifold as weighted anchor averages, our approach ensures realistic and reliable predictions. This design mirrors how humans develop representative components to understand images and then retrieve component combinations from memory to guide segmentation. Notably, model prediction is determined by two explainable factors: a low-dimensional anchor weight vector, and a spatial deformation. This design facilitates computationally efficient and geometry-adherent adaptation by aligning weight vectors between domains on a probability simplex. Experiments on two public datasets, encompassing cardiac and abdominal imaging, demonstrate the superiority of RemInD, which achieves state-of-the-art performance using a single alignment approach, outperforming existing methods that often rely on multiple complex alignment strategies., Comment: Accepted by IPMI 2025 (Information Processing in Medical Imaging)

Diagnosing diseases through histopathology whole slide images (WSIs) is fundamental in modern pathology but is challenged by the gigapixel scale and complexity of WSIs. Trained histopathologists overcome this challenge by navigating the WSI, looking for relevant patches, taking notes, and compiling them to produce a final holistic diagnostic. Traditional AI approaches, such as multiple instance learning and transformer-based models, fail short of such a holistic, iterative, multi-scale diagnostic procedure, limiting their adoption in the real-world. We introduce PathFinder, a multi-modal, multi-agent framework that emulates the decision-making process of expert pathologists. PathFinder integrates four AI agents, the Triage Agent, Navigation Agent, Description Agent, and Diagnosis Agent, that collaboratively navigate WSIs, gather evidence, and provide comprehensive diagnoses with natural language explanations. The Triage Agent classifies the WSI as benign or risky; if risky, the Navigation and Description Agents iteratively focus on significant regions, generating importance maps and descriptive insights of sampled patches. Finally, the Diagnosis Agent synthesizes the findings to determine the patient's diagnostic classification. Our Experiments show that PathFinder outperforms state-of-the-art methods in skin melanoma diagnosis by 8% while offering inherent explainability through natural language descriptions of diagnostically relevant patches. Qualitative analysis by pathologists shows that the Description Agent's outputs are of high quality and comparable to GPT-4o. PathFinder is also the first AI-based system to surpass the average performance of pathologists in this challenging melanoma classification task by 9%, setting a new record for efficient, accurate, and interpretable AI-assisted diagnostics in pathology. Data, code and models available at https://pathfinder-dx.github.io/

Recent research in consensus has often focussed on protocols for State-Machine-Replication (SMR) that can handle high throughputs. Such state-of-the-art protocols (generally DAG-based) induce undue overhead when the needed throughput is low, or else exhibit unnecessarily-poor latency and communication complexity during periods of low throughput. Here we present Morpheus Consensus, which naturally morphs from a quiescent low-throughput leaderless blockchain protocol to a high-throughput leader-based DAG protocol and back, excelling in latency and complexity in both settings. During high-throughout, Morpheus pars with state-of-the-art DAG-based protocols, including Autobahn. During low-throughput, Morpheus exhibits competitive complexity and lower latency than standard protocols such as PBFT and Tendermint, which in turn do not perform well during high-throughput. The key idea of Morpheus is that as long as blocks do not conflict (due to Byzantine behaviour, network delays, or high-throughput simultaneous production) it produces a forkless blockchain, promptly finalizing each block upon arrival. It assigns a leader only if one is needed to resolve conflicts, in a manner and with performance not unlike Autobahn.

This paper describes a method for steering deformable linear objects using two robot hands in environments populated by sparsely spaced obstacles. The approach involves manipulating an elastic inextensible rod by varying the gripping endpoint positions and tangents. Closed form solutions that describe the flexible linear object shape in planar environments, Euler's elastica, are described. The paper uses these solutions to formulate criteria for non self-intersection, stability and obstacle avoidance. These criteria are formulated as constraints in the flexible object six-dimensional configuration space that represents the robot gripping endpoint positions and tangents. In particular, this paper introduces a novel criterion that ensures the flexible object stability during steering. All safety criteria are integrated into a scheme for steering flexible linear objects in planar environments, which is lifted into a steering scheme in three-dimensional environments populated by sparsely spaced obstacles. Experiments with a dual-arm robot demonstrate the method.

We prove limiting absorption resolvent bounds for the semiclassical Schr\"odinger operator with a repulsive potential in dimension $n\ge 3$, which may have a singularity at the origin. As an application, we obtain time decay for the weighted energy of the solution to the associated wave equation with a short range repulsive potential and compactly supported initial data., Comment: 21 pages

We extend the previous work about the cosmological solutions with bounce without modifications of gravity or introducing an extra scalar field. The main finding was that the bounce is possible in the initially contracting Universe filled with matter. After a strong contraction, matter gains the equation of state close to the one of radiation, such that the effect on matter on the evolution of the FLRW metric disappears at the classical level. However, this effect comes back owing to the quantum trace anomaly in the matter/radiation sector. In the present contribution, we explore the weak impact of massive fields on the anomaly-driven bounce solution and discuss the role of the vacuum terms. The masses are assumed small and regarded as small perturbations, which enables using trace anomaly even in this case. On the other hand, by adding the $R^2$ term to the action, we arrive at the model with the trans-Planckian bounce and subsequent Starobinsky inflation. In such a framework, using the numerical analysis, we consider three scenarios providing bounce solutions., Comment: Contribution to the A.A. Starobinsky Memorial Volume, Springer 2025. 18 pages, three figures, LaTeX

Directional couplers are a fundamental building block in integrated photonics, particularly in quantum applications and optimization-based design where precision is critical. Accurate functionality is crucial to ensure reliable operation within classical and quantum circuits. However, discrepancies between simulations and measurements are frequently observed. These inaccuracies can compromise the performance and scalability of integrated photonic systems, underscoring the critical need for advanced, precise simulation methods that bridge the gap between design and implementation. In this work, we show that this discrepancy can be mainly attributed to density changes in the oxide cladding. We conduct a systematic study involving experimental optical measurements, numerical simulations, and direct electron microscopy imaging to investigate this discrepancy in directional couplers. We find that the impact of cladding density variations on performance increases as feature gaps shrink. By incorporating these effects into our simulations using a novel and physically motivated Effective Trench Medium Model (ETMM), we achieve highly accurate reproduction of experimental measurements. We quantify the effects of cladding density variations on the SU(2) symmetry parameters that govern light propagation in directional couplers. This insight is crucial for advancing the precision of compact device fabrication, enabling reliable simulation of photonic integrated devices.

Enterprise social media platforms (ESMPs) are web-based platforms with standard social media functionality, e.g., communicating with others, posting links and files, liking content, etc., yet all users are part of the same company. The first contribution of this work is the use of a difference-in-differences analysis of $99$ companies to measure the causal impact of ESMPs on companies' communication networks across the full spectrum of communication technologies used within companies: email, instant messaging, and ESMPs. Adoption caused companies' communication networks to grow denser and more well-connected by adding new, novel ties that often, but not exclusively, involve communication from one to many employees. Importantly, some new ties also bridge otherwise separate parts of the corporate communication network. The second contribution of this work, utilizing data on Microsoft's own communication network, is understanding how these communication technologies connect people across the corporate hierarchy. Compared to email and instant messaging, ESMPs excel at connecting nodes distant in the corporate hierarchy both vertically (between leaders and employees) and horizontally (between employees in similar roles but different sectors). Also, influence in ESMPs is more `democratic' than elsewhere, with high-influence nodes well-distributed across the corporate hierarchy. Overall, our results suggest that ESMPs boost information flow within companies and increase employees' attention to what is happening outside their immediate working group, above and beyond email and instant messaging., Comment: Accepted to WebSci 2025; please cite accordingly!

Given a surface, the fine $k$-curve graph of the surface is a graph whose vertices are simple closed essential curves and whose edges connect curves that intersect in at most $k$ points. We note that the fine $k$-curve graph is hyperbolic for all $k$ and, for $k\geq 2,$ show that it contains as induced subgraphs all countable graphs. We also show that the direct limit of this family of graphs, which we call the finitary curve graph, has diameter 2, has a contractible flag complex, contains every countable graph as an induced subgraph, and has as its automorphism group the homeomorphism group of the surface. Finally, we explore some finite graphs that are not induced subgraphs of fine curve graphs., Comment: 22 pages, 15 figures

Numerical hydrodynamics simulations of gases dominated by ideal, nondegenerate matter pressure and thermal radiation pressure in equilibrium entail finding the temperature as part of the evolution. Since the temperature is not typically a variable that is evolved independently, it must be extracted from the the evolved variables (e.g. the rest-mass density and specific internal energy). This extraction requires solving a quartic equation, which, in many applications, is done numerically using an iterative root-finding method. Here we show instead how the equation can be solved analytically and provide explicit expressions for the solution. We also derive Taylor expansions in limiting regimes and discuss the respective advantages and disadvantages of the iterative versus analytic approaches to solving the quartic., Comment: 5 pages, 1 figure

Fermionic time-reversal-invariant insulators in two dimensions -- class AII in the Kitaev table -- come in two different topological phases. These are characterized by a $\mathbb{Z}_2$-index: the Fu-Kane-Mele index. We prove that if two such insulators with different indices occupy regions containing arbitrarily large balls, then the spectrum of the resulting operator fills the bulk spectral gap. Our argument follows a proof by contradiction developed in an earlier work by two of the authors for quantum Hall systems. It boils down to showing that the $\mathbb{Z}_2$-index can be computed only from bulk information in sufficiently large balls. This is achieved via a result of independent interest: a local trace formula for the $\mathbb{Z}_2$-index., Comment: 14 pages, 1 figure

Targeted alpha-particle therapy (TAT) employs alpha-emitting radionuclides conjugated to tumor-targeting molecules to deliver localized radiation to cancer cells, showing great promise in treating metastatic cancers. Among these radionuclides, Actinium-225 ($^{225}$Ac, t$_{1/2}$ = 9.9 days) has emerged as a clinically promising candidate. Its decay chain generates four successive alpha emissions, resulting in highly localized and effective cytotoxic damage to cancer cells when delivered to tumor sites. However, the assumption of complete retention of $^{225}$Ac and its radioactive daughters at these target sites is often inaccurate. The nuclear recoil effect can lead to off-target distribution and unintended toxicity. Our results revealed distinct spectral differences between radiolabeled cells and reference samples, demonstrating [$^{225}$Ac]Ac-crown-TATE uptake by AR42J cells. Detection of $^{213}$Po, one of the $^{225}$Ac decay daughters, highlighted partial retention and release of decay products from cells, providing information on intracellular retention and daughter redistribution. Geant4 simulations confirmed the alignment of experimental data with theoretical models, validating the method's accuracy. This study establishes a direct alpha spectroscopy approach for investigating $^{225}$Ac and its daughters' behavior in cells and offers a powerful tool for microdosimetry estimation.

Let $R$ be a unitary operator whose spectrum is the circle. We show that the set of unitaries $U$ which essentially commute with $R$ (i.e., $[U,R]\equiv UR-RU$ is compact) is path-connected. Moreover, we also calculate the set of path-connected components of the orthogonal projections which essentially commute with $R$ and obey a non-triviality condition, and prove it is bijective with $\mathbb{Z}$.

We propose MedicalNarratives, a dataset curated from medical pedagogical videos similar in nature to data collected in Think-Aloud studies and inspired by Localized Narratives, which collects grounded image-text data by curating instructors' speech and mouse cursor movements synchronized in time. MedicalNarratives enables pretraining of both semantic and dense objectives, alleviating the need to train medical semantic and dense tasks disparately due to the lack of reasonably sized datasets. Our dataset contains 4.7M image-text pairs from videos and articles, with 1M samples containing dense annotations in the form of traces and bounding boxes. To evaluate the utility of MedicalNarratives, we train GenMedClip based on the CLIP architecture using our dataset spanning 12 medical domains and demonstrate that it outperforms previous state-of-the-art models on a newly constructed medical imaging benchmark that comprehensively evaluates performance across all modalities. Data, demo, code and models available at https://medical-narratives.github.io

Solar irradiance and its variations in the ultraviolet (UV) control the photochemistry in Earth's atmosphere and influence Earth's climate. The variability of Mg II h and k core-to-wing ratio, also known as the Mg II index, is highly correlated with the solar UV irradiance variability. Because of this, Mg II index is routinely used as a proxy for solar UV irradiance variability, which can help to get insights into the influence of solar UV irradiance variability on Earth's climate. Measurements of the Mg II index, however, have only been carried out since 1978 and do not cover the climate relevant timescales longer than a few decades. Here we present a model to calculate the Mg II index and its variability based on the well-established SATIRE (Spectral And Total Irradiance REconstruction) model. We demonstrate that our model calculations yield an excellent agreement with the observed Mg II index variations, both on the solar activity cycle and on the solar rotation timescales. Using this model, we synthesize Mg II index timeseries on climate relevant timescales of decades and longer. Here we present the timeseries of the Mg II index spanning nearly three centuries., Comment: Accepted for publication in ApJ

The manipulation of flexible objects such as cables, wires and fresh food items by robot hands forms a special challenge in robot grasp mechanics. This paper considers the steering of flexible linear objects in planar environments by two robot hands. The flexible linear object, modeled as an elastic non-stretchable rod, is manipulated by varying the gripping endpoint positions while keeping equal endpoint tangents. The flexible linear object shape has a closed form solution in terms of the grasp endpoint positions and tangents, called Euler's elastica. This paper obtains the elastica solutions under the optimal control framework, then uses the elastica solutions to obtain closed-form criteria for non self-intersection, stability and obstacle avoidance of the flexible linear object. The new tools are incorporated into a planning scheme for steering flexible linear objects in planar environments populated by sparsely spaced obstacles. The scheme is fully implemented and demonstrated with detailed examples.

We present new results on quantum tunneling between deep potential wells, in the presence of a strong constant magnetic field. We construct a family of double well potentials containing examples for which the low-energy eigenvalue splitting vanishes, and hence quantum tunneling is eliminated. Further, by deforming within this family, the magnetic ground state can be made to transition from symmetric to anti-symmetric. However, for typical double wells in a certain regime, tunneling is not suppressed, and we provide a lower bound for the eigenvalue splitting., Comment: 6 pages, 2 figures

The Dicke-Ising model, one of the few paradigmatic models of matter-light interaction, exhibits a superradiant quantum phase transition above a critical coupling strength. However, in natural optical systems, its experimental validation is hindered by a "no-go theorem''. Here, we propose a digital-analog quantum simulator for this model based on an ensemble of interacting qubits coupled to a single-mode photonic resonator. We analyze the system's free energy landscape using field-theoretical methods and develop a digital-analog quantum algorithm that disentangles qubit and photon degrees of freedom through a parity-measurement protocol. This disentangling enables the emulation of a photonic Schr\"odinger cat state, which is a hallmark of the superradiant ground state in finite-size systems and can be unambiguously probed through the Wigner tomography of the resonator's field., Comment: 14 pages, 9 figures

Stellar superflares are energetic outbursts of electromagnetic radiation, similar to solar flares but releasing more energy, up to $10^{36}$ erg on main sequence stars. It is unknown whether the Sun can generate superflares, and if so, how often they might occur. We used photometry from the Kepler space observatory to investigate superflares on other stars with Sun-like fundamental parameters. We identified 2889 superflares on 2527 Sun-like stars, out of 56450 observed. This detection rate indicates that superflares with energies $>10^{34}$ erg occur roughly once per century on stars with Sun-like temperature and variability. The resulting stellar superflare frequency-energy distribution is consistent with an extrapolation of the Sun's flare distribution to higher energies, so we suggest that both are generated by the same physical mechanism., Comment: Accepted for publication in Science

Modern wearable devices can conveniently record various biosignals in the many different environments of daily living, enabling a rich view of individual health. However, not all biosignals are the same: high-fidelity biosignals, such as photoplethysmogram (PPG), contain more physiological information, but require optical sensors with a high power footprint. Alternatively, a lower-fidelity biosignal such as accelerometry has a significantly smaller power footprint and is available in almost any wearable device. While accelerometry is widely used for activity recognition and fitness, it is less explored for health biomarkers and diagnosis. Here, we show that an accelerometry foundation model can predict a wide variety of health targets. To achieve improved performance, we distill representational knowledge from PPG encoders to accelerometery encoders using 20 million minutes of unlabeled data, collected from ~172K participants in the Apple Heart and Movement Study under informed consent. We observe strong cross-modal alignment on unseen data, e.g., 99.2% top-1 accuracy for retrieving PPG embeddings from accelerometry embeddings. We show that distilled accelerometry encoders have significantly more informative representations compared to self-supervised or supervised encoders trained directly on accelerometry data, observed by at least 23%-49% improved performance for predicting heart rate and heart rate variability. We also show that distilled accelerometry encoders are readily predictive of a wide array of downstream health targets, i.e., they are generalist foundation models. We believe accelerometry foundation models for health may unlock new opportunities for developing digital biomarkers from any wearable device., Comment: updated format

Indexing is an important step towards strong performance in retrieval-augmented generation (RAG) systems. However, existing methods organize data based on either semantic similarity (similarity) or related information (relatedness), but do not cover both perspectives comprehensively. Our analysis reveals that modeling only one perspective results in insufficient knowledge synthesis, leading to suboptimal performance on complex tasks requiring multihop reasoning. In this paper, we propose SiReRAG, a novel RAG indexing approach that explicitly considers both similar and related information. On the similarity side, we follow existing work and explore some variances to construct a similarity tree based on recursive summarization. On the relatedness side, SiReRAG extracts propositions and entities from texts, groups propositions via shared entities, and generates recursive summaries to construct a relatedness tree. We index and flatten both similarity and relatedness trees into a unified retrieval pool. Our experiments demonstrate that SiReRAG consistently outperforms state-of-the-art indexing methods on three multihop datasets (MuSiQue, 2WikiMultiHopQA, and HotpotQA), with an average 1.9% improvement in F1 scores. As a reasonably efficient solution, SiReRAG enhances existing reranking methods significantly, with up to 7.8% improvement in average F1 scores.

Pulse profile stability is a central assumption of standard pulsar timing methods. Thus, it is important for pulsar timing array experiments such as the North American Nanohertz Observatory for Gravitational Waves (NANOGrav) to account for any pulse profile variability present in their data sets. We show that in the NANOGrav 15-yr data set, the integrated pulse profile of PSR J1022+1001 as seen by the Arecibo radio telescope at 430, 1380, and 2030 MHz varies considerably in its shape from observation to observation. We investigate the possibility that this is due to the "ideal feed assumption" (IFA), on which NANOGrav's routine polarization calibration procedure relies. PSR J1022+1001 is $\sim 90\%$ polarized in one pulse profile component, and also has significant levels of circular polarization. Time-dependent deviations in the feed's polarimetric response (PR) could cause mixing between the intensity I and the other Stokes parameters, leading to the observed variability. We calibrate the PR using a mixture of Measurement Equation Modeling and Measurement Equation Template Matching techniques. The resulting profiles are no less variable than those calibrated using the IFA method, nor do they provide an improvement in the timing quality of this pulsar. We observe the pulse shape in 25-MHz bandwidths to vary consistently across the band, which cannot be explained by interstellar scintillation in combination with profile evolution with frequency. Instead, we favor phenomena intrinsic to the pulsar as the cause., Comment: 18 pages, 16 figures, 4 tables. Submitted to ApJ

In 2011, Barot and Marsh provided an explicit construction of presentation of a finite Weyl group $W$ by any quiver mutation-equivalent to an orientation of a Dynkin diagram with Weyl group $W$. The construction was extended by the authors of the present paper to obtain presentations for all affine Coxeter groups, as well as to construct groups from triangulations of unpunctured surfaces and orbifolds, where the groups are invariant under change of triangulation and thus are presented as quotients of numerous distinct Coxeter groups. We extend the construction to include most punctured surfaces and orbifolds, providing a new invariant for almost all marked surfaces., Comment: 28 pages, many figures

The thermal Sunyaev-Zel'dovich (tSZ) effect arises from inverse Compton scattering of low energy photons onto thermal electrons, proportional to the integrated electron pressure, and is usually observed from galaxy clusters. However, we can expect that the Epoch of Reionization (EoR) also contributes to this signal, but that contribution has not been previously evaluated. In this work we analyse a suite of fully-coupled radiation-hydrodynamics simulations based on RAMSES-CUDATON to calculate and study the tSZ signal from the Reionization Epoch. We construct lightcones of the electron pressure in the intergalactic medium for $6

Multimodal language models (MLMs) still face challenges in fundamental visual perception tasks where specialized models excel. Tasks requiring reasoning about 3D structures benefit from depth estimation, and reasoning about 2D object instances benefits from object detection. Yet, MLMs can not produce intermediate depth or boxes to reason over. Finetuning MLMs on relevant data doesn't generalize well and outsourcing computation to specialized vision tools is too compute-intensive and memory-inefficient. To address this, we introduce Perception Tokens, intrinsic image representations designed to assist reasoning tasks where language is insufficient. Perception tokens act as auxiliary reasoning tokens, akin to chain-of-thought prompts in language models. For example, in a depth-related task, an MLM augmented with perception tokens can reason by generating a depth map as tokens, enabling it to solve the problem effectively. We propose AURORA, a training method that augments MLMs with perception tokens for improved reasoning over visual inputs. AURORA leverages a VQVAE to transform intermediate image representations, such as depth maps into a tokenized format and bounding box tokens, which is then used in a multi-task training framework. AURORA achieves notable improvements across counting benchmarks: +10.8% on BLINK, +11.3% on CVBench, and +8.3% on SEED-Bench, outperforming finetuning approaches in generalization across datasets. It also improves on relative depth: over +6% on BLINK. With perception tokens, AURORA expands the scope of MLMs beyond language-based reasoning, paving the way for more effective visual reasoning capabilities.

This paper, being the sequel of [An inverse problem in Polya-Schur theory. I. Non-genegerate and degenerate operators], studies a class of linear ordinary differential operators with polynomial coefficients called \emph{exactly solvable}; such an operator sends every polynomial of sufficiently large degree to a polynomial of the same degree. We focus on invariant subsets of the complex plane for such operators when their action is restricted to polynomials of a fixed degree and discover a connection between this topic and classical complex dynamics and its multi-valued counterpart. As a very special case of invariant sets we recover the Julia sets of rational functions., Comment: 23 pages, 5 figures

A pulsar's scintillation bandwidth is inversely proportional to the scattering delay, making accurate measurements of scintillation bandwidth critical to characterize unmitigated delays in efforts to measure low-frequency gravitational waves with pulsar timing arrays. In this pilot work, we searched for a subset of known pulsars within $\sim$97% of the data taken with the PUPPI instrument for the AO327 survey with the Arecibo telescope, attempting to measure the scintillation bandwidths in the dataset by fitting to the 2D autocorrelation function of their dynamic spectra. We successfully measured 38 bandwidths from 23 pulsars (six without prior literature values), finding that: almost all of the measurements are larger than the predictions from NE2001 and YMW16 (two popular galactic models); NE2001 is more consistent with our measurements than YMW16; Gaussian fits to the bandwidth are more consistent with both electron density models than Lorentzian ones; and for the 17 pulsars with prior literature values, the measurements between various sources often vary by factors of a few. The success of Gaussian fits may be due to the use of Gaussian fits to train models in previous work. The variance of literature values over time could relate to the scaling factor used to compare measurements, but also seems consistent with time-varying interstellar medium parameters. This work can be extended to the rest of AO327 to further investigate these trends, highlighting the continuing importance of large archival datasets for projects beyond their initial conception., Comment: 21 pages, 8 figures, 2 tables

Evidence has emerged for a stochastic signal correlated among 67 pulsars within the 15-year pulsar-timing data set compiled by the NANOGrav collaboration. Similar signals have been found in data from the European, Indian, Parkes, and Chinese PTAs. This signal has been interpreted as indicative of the presence of a nanohertz stochastic gravitational wave background. To explore the internal consistency of this result we investigate how the recovered signal strength changes as we remove the pulsars one by one from the data set. We calculate the signal strength using the (noise-marginalized) optimal statistic, a frequentist metric designed to measure correlated excess power in the residuals of the arrival times of the radio pulses. We identify several features emerging from this analysis that were initially unexpected. The significance of these features, however, can only be assessed by comparing the real data to synthetic data sets. After conducting identical analyses on simulated data sets, we do not find anything inconsistent with the presence of a stochastic gravitational wave background in the NANOGrav 15-year data. The methodologies developed here can offer additional tools for application to future, more sensitive data sets. While this analysis provides an internal consistency check of the NANOGrav results, it does not eliminate the necessity for additional investigations that could identify potential systematics or uncover unmodeled physical phenomena in the data., Comment: 21 pages, 11 figures, 2 tables

Accurate calculations of starspot spectra are essential for multiple applications in astronomy. The current standard is to represent starspot spectra by spectra of stars that are cooler than the quiet star regions. This implies approximating a starspot as a non-magnetic 1D structure in radiative-convective equilibrium, parametrizing convective energy transport by mixing length theory. It is the inhibition of convection by the starspot magnetic field that is emulated by using a lower spot temperature relative to the quiet stellar regions. Here, we take a different approach avoiding the approximate treatment of convection and instead self-consistently accounting for the interaction between matter, radiation, and the magnetic field. We simulate spots on G2V, K0V, M0V stars with the 3D radiative magnetohydrodynamics code MURaM and calculate spectra ($R \approx 500$ from 250~nm to 6000~nm) using ray-by-ray radiative transfer with the MPS-ATLAS code. We find that the 1D models fail to return accurate umbral and penumbral spectra on K0V and M0V stars where convective and radiative transfer of energy is simultaneously important over a broad range of atmospheric heights rendering mixing length theory inaccurate. However, 1D models work well for G2V stars, where both radiation and convection significantly contribute to energy transfer only in a narrow region near the stellar surface. Quantitatively, the 1D approximation leads to errors longward of 500 nm of about 50\% for both umbral and penumbral flux contrast relative to quiet star regions on M0V stars, and less than 2\% (for umbrae) and 10\% (for penumbrae) for G2V stars., Comment: Accepted for publication in the Astrophysical Journal Letters

In this work, we develop an analytical framework to understand quantum friction across distinct stability regimes, providing approximate expressions for frictional forces both in the deep stable regime and near the critical threshold of instability. Our primary finding is analytical proof that, near the instability threshold, the quantum friction force diverges logarithmically. This result, verified through numerical simulations, sheds light on the behavior of frictional instabilities as the system approaches criticality. Our findings offer new insights into the role of instabilities, critical divergence and temperature in frictional dynamics across quantum and classical regimes.

Dispersion measures (DM) of fast radio bursts (FRBs) probe the density of electrons in the intergalactic medium (IGM) along their lines-of-sight, including the average density versus distance to the source and its variations in direction. While previous study focused on low-redshift, FRBs are potentially detectable out to high redshift, where their DMs can, in principle, probe the epoch of reionization (EOR) and its patchiness. We present the first predictions from large-scale, radiation-hydrodynamical simulation of fully-coupled galaxy formation and reionization, using Cosmic Dawn (``CoDa")~II to model the density and ionization fields of the universe down to redshifts through the end of the EOR at $z_{re}\approx6.1$. Combining this with an N-body simulation CoDa~II--Dark Matter of the fully-ionized epoch from the EOR to the present, we calculate the mean and standard deviation of FRB DMs as functions of their source redshift. The mean and standard deviation of DM increase with redshift, reaching a plateau by $z(x_{HII}\lesssim0.25)\gtrsim8$, i.e. well above $z_{re}$. The mean-DM asymptote $\mathcal{DM}_{max} \approx 5900~\mathrm{pc\, cm^{-3}}$ reflects the end of the EOR and its duration. The standard deviation there is $\sigma_{DM, max}\approx497 ~\mathrm{pc\, cm^{-3}}$, reflecting inhomogeneities of both patchy reionization and density. Inhomogeneities in ionization during the EOR contribute $\mathcal{O}(1$ per cent) of this value of $\sigma_{DM,max}$ from FRBs at redshifts $z\gtrsim 8$. Current estimates of FRB rates suggest this may be detectable within a few years of observation., Comment: 14 pages, 10 figures, 2 tables, 2 appendices

The oscillation modes of neutron star (NS) merger remnants, as encoded by the kHz postmerger gravitational wave (GW) signal, hold great potential for constraining the as-yet undetermined equation of state (EOS) of dense nuclear matter. Previous works have used numerical relativity simulations to derive quasi-universal relations for the key oscillation frequencies, but most of them omit the effects of a magnetic field. We conduct full general-relativistic magnetohydrodynamics simulations of NSNS mergers with two different masses and two different EOSs (SLy and ALF2) with three different initial magnetic field topologies (poloidal and toroidal only, confined to the interior, and "pulsar-like": dipolar poloidal extending from the interior to the exterior), with four different initial magnetic field strengths. We find that the magnetic braking and magnetic effective turbulent viscosity drives the merger remnants towards uniform rotation and increases their overall angular momentum loss. This causes the remnant to contract and the angular velocity of the quadrupole density oscillation to increase in such a way that it rotates faster than the fluid itself, in stark contrast with nonmagnetized simulations. As a result, the $f_2$ frequency of the dominant postmerger GW mode shifts upwards over time. The overall shift is up to ~ 200Hz for the strongest magnetic field we consider and ~ 50Hz for the median case and is therefore detectable in principle by future GW observatories, which should include the magnetic field in their analyses., Comment: 33 pages, 22 figures

Recent nonmagnetized studies of binary neutron star mergers have indicated the possibility of identifying equation of state features, such as a phase transition or a quark-hadron crossover, based on the frequency shift of the main peak in the postmerger gravitational wave spectrum. By performing a series of general relativistic, magnetohydrodynamic simulations we show that similar frequency shifts can be obtained due to the effect of the magnetic field. The existing degeneracy can either mask or nullify a shift due to a specific equation of state feature, and therefore the interpretation of observational data is more complicated than previously thought, requiring a more complete treatment that would necessarily include the neutron star's magnetic field., Comment: 6 pages, 4 figures

We consider the symplectic groupoid of pairs $(B, A)$ with $A$ real unipotent upper-triangular matrix and $B\in GL_n$ being such that $\tilde A=BAB^T$ is also a unipotent upper-triangular matrix. Fock and Chekhov defined a Poisson map of Teichm\"uller space ${\mathcal T_{g,s}$ of genus $g$ surfaces with $s$ holes into the space of unipotent upper-triangular $n\times n$ matrices whose image forms the \emph{geometric locus}. The elements of geometric locus satisfy \emph{rank condition}. We describe the Hamiltonian reduction of the Poisson cluster variety of symplectic groupoid by the rank condition for $n=5$ and $6$. In both cases, we analyze the induced cluster structures on the results of Hamiltonian reduction and recover celebrated cluster structure on ${\mathcal T}_{2,1}$ for $n=5$ and ${\mathcal T}_{2,2}$ for $n=6$.

We investigate quantum phase transitions in a topological Josephson junction with an embedded ferromagnetic layer, revealing a rich landscape of critical phenomena. The low-energy excitations comprise Majorana fermions propagating along the junction, coupled to the magnons in the ferromagnet. Based on mean-field and renormalization group arguments, we predict Berezinskii-Kosterlitz-Thouless (BKT) transitions in this system, both in the case of a magnetic easy-plane and weak easy-axis anisotropy. In the latter case, this is based on an emergent effective easy-plane, spanned by the easy-axis and the component of the magnetization which couples to the Majoranas. We conclude by presenting a conjecture for the full phase diagram of the model. It covers BKT transitions as well as exotic multicritical and supersymmetric points known from related models of interacting real fermions and bosons., Comment: 11 pages, 8 figures

Stellar limb darkening must be properly accounted for to accurately determine the radii of exoplanets at various wavelengths. The standard approach to address limb darkening involves either using laws with coefficients from modelled stellar spectra or determining the coefficients empirically during light curve fitting of the data. Here, we test how accurately three common laws -- quadratic, power, and a three-parameter law -- can reproduce stellar limb darkening at different wavelengths and across a broad range of stars. We show that using a quadratic limb darkening law, which is most frequently employed by the community, leads to wavelength-dependent offsets in retrieved transmission spectra. For planets with high impact parameters ($b$ larger than about 0.5) the amplitude of these offsets can reach 1\% of the transit depth which is some cases is comparable to and can even exceed the expected signals from the planetary atmosphere. Furthermore, the quadratic law causes an offset in the value of the impact parameter when it is determined by fitting the broadband transit light curves. In contrast, using the Kipping--Sing three-parameter law leads to robust retrievals. We advocate the use of this law in retrievals, especially for transits with large impact parameters., Comment: submitted to ApJ

Besides a dense coverage of their high latitudes by starspots, rapidly rotating cool stars also display low-latitude spots in Doppler images, although generally with a lower coverage. In contrast, flux emergence models of fast-rotating stars predict strong poleward deflection of radially rising magnetic flux as the Coriolis effect dominates over buoyancy, leaving a spot-free band around the equator. To resolve this discrepancy, we consider a flux tube near the base of the convection zone in a solar-type star rotating eight times faster than the Sun, assuming field intensification by weak-tube explosions. For the intensification to continue into to the buoyancy-dominated regime, the upper convection zone must have a significantly steeper temperature gradient than in the Sun, by a factor that is comparable with that found in 3D simulations of rotating convection. Within the hypothesis that stellar active regions stem from the base of the convection zone, flux emergence between 1-20 degree latitudes requires highly supercritical field strengths of up to 500 kG in rapidly rotating stars. These field strengths require explosions of 100-kG tubes within the convection zone, compatible with reasonable values of the superadiabatic temperature gradient associated with the more rapid rotation., Comment: 12 pages, 9 figures, published in ApJ

Evidence of chirality was observed at the Fe metal center in Fe(III) spin crossover coordination salts [Fe(qsal)2][ Ni(dmit)2] and [Fe(qsal)2](TCNQ)2 from X-ray absorption spectroscopy at the Fe 2p3/2 core threshold. This indicates the formation of chiral domains that influence the octahedral coordination on the Fe core., Comment: 5 pages, 4 figures. Submitted for publication in JPCM

Recently, NIRSpec PRISM/CLEAR observations by JWST have begun providing rest-frame UV continuum measurements of galaxies at $z\gtrsim7$, revealing signatures of Ly$\alpha$ damping-wing (DW) absorption by the intergalactic medium (IGM). We develop a methodology to constrain the global ionization fraction of the IGM $(Q_{\rm HII})$ using low-resolution spectra, employing the random forest classification (RFC) method. We construct mock spectra using the simulated galaxies and the IGM from the Cosmic Dawn II simulation and train RFC models to estimate $Q_{\rm HII}$ at the redshift of the source and to detect the presence of a damped Ly$\alpha$ absorber (DLA). We find that individual galaxy spectra with spectral bins between 1220 and 1270 {\AA} and with signal-to-noise ratios greater than 20 can place tight constraints on $Q_{\rm HII}$, provided the UV continuum is accurately modeled. This method is particularly effective for the early phase of reionization ($Q_{\rm HII}<50\%$), when the IGM opacity is high in the DW. As a demonstration, we apply our model to existing NIRSpec PRISM/CLEAR spectra, placing upper bounds of $Q_{\rm HII}=59.6\%$, $5.6\%$, and $18.5\%$ at $z=7.7,~9.4,$ and $10.6$, respectively, with $68\%$ confidence, though several modeling uncertainties remain to be discussed. These constraints favor late-starting reionization models, where $\gtrsim 80\%$ of the IGM is ionized after $z=8$. We conclude that high SNR observations of carefully selected targets around $z\sim7-9$ can effectively constrain reionization models., Comment: 20 pages, 11 figures, submitted to ApJ