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Brown dwarfs lack nuclear fusion and cool with time; the coldest known have an effective temperature below 500 K, and are known as Y dwarfs. We present a James Webb Space Telescope (JWST) photometric dataset of Y dwarfs: twenty-three were imaged in wide-field mode, 20 using NIRCam with the F150W and F480M filters, and 3 using NIRISS with the F480M filter. We present an F480M vs. F150W $-$ F480M color-magnitude diagram for our sample, and other brown dwarfs with F150W and F480M colors synthesized from JWST spectra by Beiler et al. (2024). For one target, WISEA J083011.95$+$283716.0, its detection in the near-infrared confirms it as one of the reddest Y dwarfs known, with F150W $-$ F480M $= 9.62$ mag. We provide its updated parallax and proper motion. One of the Beiler et al. Y dwarfs, CWISEP J104756.81+545741.6, is unusually blue, consistent with strong CO absorption seen in its spectrum which the F480M filter is particularly sensitive to. The strong CO and the kinematics of the object suggest it may be very low-mass and young. We update the resolved photometry for the close binary system WISE J033605.05$-$014350.4 AB, and find that the secondary is almost as cold as WISE 085510.83$-$071442.5, with $T_{\rm eff} \lesssim 300$ K, however the F150W $-$ F480M color is significantly bluer, possibly suggesting the presence of water clouds. Astrometry is measured at the JWST epoch for the sample which is consistent with parallax and proper motion values reported by Kirkpatrick et al. (2021) and Marocco et al. (in prep)., Comment: Accepted by AJ Jan 23 2025

We present a neural network verification toolbox to 1) assess the probability of satisfaction of a constraint, and 2) synthesize a set expansion factor to achieve the probability of satisfaction. Specifically, the tool box establishes with a user-specified level of confidence whether the output of the neural network for a given input distribution is likely to be contained within a given set. Should the tool determine that the given set cannot satisfy the likelihood constraint, the tool also implements an approach outlined in this paper to alter the constraint set to ensure that the user-defined satisfaction probability is achieved. The toolbox is comprised of sampling-based approaches which exploit the properties of signed distance function to define set containment., Comment: 7 pages, 8 figures, submitted to the 28th ACM International Conference on Hybrid Systems: Computation and Control

It is well known that descents and excedances are equidistributed in the symmetric group. We show that the descent and excedance enumerators, summed over permutations with a fixed first letter are identical when we perform a simple change of the first letter. We generalize this to type B and other colored permutation groups. We are led to defining descents and excedances through linear orders. With respect to a particular order, when the number of colors is even, we get a result that generalizes the type B results. Lastly, we get a type B counterpart of Conger's result which refines the well known Carlitz identity., Comment: 14 pages

We propose Diffusion Model Predictive Control (D-MPC), a novel MPC approach that learns a multi-step action proposal and a multi-step dynamics model, both using diffusion models, and combines them for use in online MPC. On the popular D4RL benchmark, we show performance that is significantly better than existing model-based offline planning methods using MPC and competitive with state-of-the-art (SOTA) model-based and model-free reinforcement learning methods. We additionally illustrate D-MPC's ability to optimize novel reward functions at run time and adapt to novel dynamics, and highlight its advantages compared to existing diffusion-based planning baselines., Comment: Preprint

Learning from previously collected data via behavioral cloning or offline reinforcement learning (RL) is a powerful recipe for scaling generalist agents by avoiding the need for expensive online learning. Despite strong generalization in some respects, agents are often remarkably brittle to minor visual variations in control-irrelevant factors such as the background or camera viewpoint. In this paper, we present theDeepMind Control Visual Benchmark (DMC-VB), a dataset collected in the DeepMind Control Suite to evaluate the robustness of offline RL agents for solving continuous control tasks from visual input in the presence of visual distractors. In contrast to prior works, our dataset (a) combines locomotion and navigation tasks of varying difficulties, (b) includes static and dynamic visual variations, (c) considers data generated by policies with different skill levels, (d) systematically returns pairs of state and pixel observation, (e) is an order of magnitude larger, and (f) includes tasks with hidden goals. Accompanying our dataset, we propose three benchmarks to evaluate representation learning methods for pretraining, and carry out experiments on several recently proposed methods. First, we find that pretrained representations do not help policy learning on DMC-VB, and we highlight a large representation gap between policies learned on pixel observations and on states. Second, we demonstrate when expert data is limited, policy learning can benefit from representations pretrained on (a) suboptimal data, and (b) tasks with stochastic hidden goals. Our dataset and benchmark code to train and evaluate agents are available at: https://github.com/google-deepmind/dmc_vision_benchmark., Comment: NeurIPS 2024 Datasets and Benchmarks Track. Dataset available at: https://github.com/google-deepmind/dmc_vision_benchmark

We present recent laboratory results demonstrating high-contrast coronagraphy for the future space-based large IR/Optical/Ultraviolet telescope recommended by the Decadal Survey. The High-contrast Imager for Complex Aperture Telescopes (HiCAT) testbed aims to implement a system-level hardware demonstration for segmented aperture coronagraphs with wavefront control. The telescope hardware simulator employs a segmented deformable mirror with 37 hexagonal segments that can be controlled in piston, tip, and tilt. In addition, two continuous deformable mirrors are used for high-order wavefront sensing and control. The low-order sensing subsystem includes a dedicated tip-tilt stage, a coronagraphic target acquisition camera, and a Zernike wavefront sensor that is used to measure and correct low-order aberration drifts. We explore the performance of a segmented aperture coronagraph both in static operations (limited by natural drifts and instabilities) and in dynamic operations (in the presence of artificial wavefront drifts added to the deformable mirrors), and discuss the estimation and control strategies used to reach and maintain the dark-zone contrast using our low-order wavefront sensing and control. We summarize experimental results that quantify the performance of the testbed in terms of contrast, inner/outer working angle and bandpass, and analyze limiting factors., Comment: 17 pages, 14 figures, SPIE Astronomical Telescopes + Instrumentation, 2022, Montr\'eal, Qu\'ebec, Canada

We present the final results of the Apodized Pupil Lyot Coronagraph (APLC) on the High-contrast imager for Complex Aperture Telescopes (HiCAT) testbed, under NASA's Strategic Astrophysics Technology program. The HiCAT testbed was developed over the past decade to enable a system-level demonstration of coronagraphy for exoplanet direct imaging with the future Habitable Wolds Observatory. HiCAT includes an active, segmented telescope simulator, a coronagraph, and metrology systems (Low-order and Mid-Order Zernike Wavefront Sensors, and Phase Retrieval camera). These results correspond to an off-axis (un-obscured) configuration, as was envisioned in the 2020 Decadal Survey Recommendations. Narrowband and broadband dark holes are generated using two continuous deformable mirrors (DM) to control high order wavefront aberrations, and low-order drifts can be further stabilized using the LOWFS loop. The APLC apodizers, manufactured using carbon nanotubes, were optimized for broadband performance and include the calibrated geometric aperture. HiCAT is, to this date, the only testbed facility able to demonstrate high-contrast coronagraphy with a truly segmented aperture, as is required for the Habitable World Observatory, albeit limited to ambient conditions. Results presented here include $6\times 10^{-8}$ (90% CI) contrast in 9% bandpass in a 360 deg dark hole with inner and outer working angles of $4.4 \lambda/D_{pupil}$ and $11 \lambda/D_{pupil}$ . Narrowband contrast (3% bandpass) reaches $2.4\times 10^{-8}$ (90% confidence interval)., Comment: 17 pages, 16 figures, SPIE Astronomical Telescopes + Instrumentation, 2024, Yokohama, Japan

This paper aims to increase the safety and reliability of executing trajectories planned for robots with non-trivial dynamics given a light-weight, approximate dynamics model. Scenarios include mobile robots navigating through workspaces with imperfectly modeled surfaces and unknown friction. The proposed approach, Kinodynamic Replanning over Approximate Models with Feedback Tracking (KRAFT), integrates: (i) replanning via an asymptotically optimal sampling-based kinodynamic tree planner, with (ii) trajectory following via feedback control, and (iii) a safety mechanism to reduce collision due to second-order dynamics. The planning and control components use a rough dynamics model expressed analytically via differential equations, which is tuned via system identification (SysId) in a training environment but not the deployed one. This allows the process to be fast and achieve long-horizon reasoning during each replanning cycle. At the same time, the model still includes gaps with reality, even after SysID, in new environments. Experiments demonstrate the limitations of kinematic path planning and path tracking approaches, highlighting the importance of: (a) closing the feedback-loop also at the planning level; and (b) long-horizon reasoning, for safe and efficient trajectory execution given inaccurate models.

It has recently been suggested that exotic quantum gravity effects could lead to large vacuum fluctuations, potentially observable with realistic detectors. Experiments are currently being built to search for these signals. Here we analyze the minimal model of quantum gravity at low energies -- the usual effective quantum field theory of gravitons -- and show that it unambiguously predicts an unobservably small variation in the measured interferometer length $\Delta L \sim \ell_{\rm pl} \sim 10^{-35}~{\rm m}$. Thus, detection of a large, gravitationally-induced length variation would signal a severe breakdown of effective quantum field theory in low energy quantum gravity., Comment: 4+2 pages, 3 figures

We present a method to overapproximate forward stochastic reach sets of discrete-time, stochastic nonlinear systems with interval geometry. This is made possible by extending the theory of mixed-monotone systems to incorporate stochastic orders, and a concentration inequality result that lower-bounds the probability the state resides within an interval through a monotone mapping. Then, we present an algorithm to compute the overapproximations of forward reachable set and the probability the state resides within it. We present our approach on two aerospace examples to show its efficacy., Comment: 8 pages, 3 figures, in the proceedings of the 63rd IEEE Conference on Decision and Control

Unimodality of the normalized coefficients of the characteristic polynomial of distance matrices of trees are known and bounds on the location of its peak (the largest coefficient) are also known. Recently, an extension of these results to distance matrices of block graphs was given. In this work, we extend these results to two additional distance-type matrices associated with trees: the Min-4PC matrix and the 2-Steiner distance matrix. We show that the sequences of coefficients of the characteristic polynomials of these matrices are both unimodal and log-concave. Moreover, we find the peak location for the coefficients of the characteristic polynomials of the Min-4PC matrix of any tree on $n$ vertices. Further, we show that the Min-4PC matrix of any tree on $n$ vertices is isometrically embeddable in $\mathbb{R}^{n-1}$ equipped with the $\ell_1$ norm.

Ice systems are prototypes of locally constrained dynamics. This is exemplified in Coulomb-liquid phases where a large space of configurations is sampled, each satisfying local ice rules. Dynamics proceeds through `flipping' rings, i.e., through reversing arrows running along the edges of a polygon. We examine the role of defect rings in such phases, with square-ice as a testing ground. When placed on a curved surface, the underlying square lattice will form defects such as triangles or pentagons. We show that triangular defects are statistically more `flippable' than the background. In contrast, pentagons and larger polygons are less flippable. In fact, flippability decreases monotonically with ring size, as seen from a Pauling-like argument. As an explicit demonstration, we wrap the square ice model on a sphere. We start from an octahedron and perform repeated rectifications, producing a series of clusters with sphere-like geometry. They contain a fixed number of defect triangles in an otherwise square lattice. We numerically enumerate all ice-rule-satisfying configurations. Indeed, triangles are flippable in a larger fraction of configurations than quadrilaterals. The obtained flippabilities are in broad agreement with the Pauling-like estimates. As a minimal model for dynamics, we construct a Hamiltonian with quantum tunnelling terms that flip rings. The resulting ground state is a superposition of all ice configurations. The dominant contribution to its energy comes from localized resonance within triangles. Our results suggest local dynamics as a promising observable for experiments in spin ice and artificial ice systems. They also point to hierarchical dynamics in materials such as ice V that contain rings of multiple sizes., Comment: 8 pages, 5 figures

A classical observer can measure elapsed proper time along their worldline. When observers are coupled to a system with internal correlations, measurements of elapsed time may inherit these correlations. We show that derivatives of the on-shell action with respect to worldline mass compute correlation functions of worldline proper length at tree level. We study worldlines coupled to a scalar field. We calculate the length-length two-point function and find it arises from correlated path fluctuations. As an application, we propose that the logarithm of local correlators serves as a generating function of length correlators, which generalizes the on-shell action prescription. Using this proposal, we extract AdS worldline observables from local CFT correlators as computed by Witten diagrams. We briefly discuss extensions to gravity, interferometers, and the holographic encoding of observer time., Comment: 45 pages, 1 figure

This paper compares two actuator line methodologies for modelling wind turbines employing high-order h/p solvers and large-eddy simulations. The methods combine the accuracy of high-order solvers (in this work the maximum order is 6) with the computational efficiency of actuator lines to capture the aerodynamic effects of wind turbine blades. Comparisons with experiments validate the actuator line methodologies. We explore the effects of the polynomial order and the smoothing parameter associated with the Gaussian regularization function, and use them to blend the actuator line forcing in the high-order computational mesh, to show that both parameters influence the distribution of forces along the blades and the turbine wake. The greatest impact is obtained when the polynomial order is increased, allowing one to better capture the physics without requiring new meshes. When comparing the actuator line methodologies, we show the advantages of performing weighted sums, over element averages, to compute the blade velocities and forces in high-order solvers. For low-order simulations (low polynomial orders), both methods provide similar results, but as the polynomial order is increased, the weighted sum method shows smoother thrust/torque distributions and better wake resolution. Furthermore, cell averaging introduces nonphysical oscillations when increasing the polynomial order beyond 3 (4th order accuracy).

Monolithic large language models (LLMs) like GPT-4 have paved the way for modern generative AI applications. Training, serving, and maintaining monolithic LLMs at scale, however, remains prohibitively expensive and challenging. The disproportionate increase in compute-to-memory ratio of modern AI accelerators have created a memory wall, necessitating new methods to deploy AI. Composition of Experts (CoE) is an alternative modular approach that lowers the cost and complexity of training and serving. However, this approach presents two key challenges when using conventional hardware: (1) without fused operations, smaller models have lower operational intensity, which makes high utilization more challenging to achieve; and (2) hosting a large number of models can be either prohibitively expensive or slow when dynamically switching between them. In this paper, we describe how combining CoE, streaming dataflow, and a three-tier memory system scales the AI memory wall. We describe Samba-CoE, a CoE system with 150 experts and a trillion total parameters. We deploy Samba-CoE on the SambaNova SN40L Reconfigurable Dataflow Unit (RDU) - a commercial dataflow accelerator architecture that has been co-designed for enterprise inference and training applications. The chip introduces a new three-tier memory system with on-chip distributed SRAM, on-package HBM, and off-package DDR DRAM. A dedicated inter-RDU network enables scaling up and out over multiple sockets. We demonstrate speedups ranging from 2$\times$ to 13$\times$ on various benchmarks running on eight RDU sockets compared with an unfused baseline. We show that for CoE inference deployments, the 8-socket RDU Node reduces machine footprint by up to 19$\times$, speeds up model switching time by 15$\times$ to 31$\times$, and achieves an overall speedup of 3.7$\times$ over a DGX H100 and 6.6$\times$ over a DGX A100., Comment: 2024 57th IEEE/ACM International Symposium on Microarchitecture (MICRO)

We observed the planet-hosting system PDS 70 with the James Webb Interferometer, JWST's Aperture Masking Interferometric (AMI) mode within NIRISS. Observing with the F480M filter centered at 4.8 $\mu$m, we simultaneously fit geometrical models to the outer disk and the two known planetary companions. We re-detect the protoplanets PDS 70 b and c at an SNR of 14.7 and 7.0, respectively. Our photometry of both PDS 70 b and c provides tentative evidence of mid-IR circumplanetary disk emission through fitting SED models to these new measurements and those found in the literature. We also newly detect emission within the disk gap at an SNR of $\sim$4, at a position angle of $220^{+10}_{-15}$ degrees, and an unconstrained separation within $\sim$200 mas. Follow-up observations will be needed to determine the nature of this emission. We place a 5$\sigma$ upper limit of 208 $\pm$ 10 $\mu$Jy on the flux of the candidate PDS 70 d at 4.8 $\mu$m, which indicates that if the previously observed emission at shorter wavelengths is due to a planet, this putative planet has a different atmospheric composition than PDS 70 b or c. Finally, we place upper limits on emission from any additional planets in the disk gap. We find an azimuthally averaged 5$\sigma$ contrast upper limit $>$7 magnitudes at separations greater than 110 mas. These are the deepest limits to date within $\sim$250 mas at 4.8 $\mu$m and the first space-based interferometric observations of this system., Comment: Accepted for publication in AJ

We derive the soft effective action in $(d+2)$-dimensional abelian gauge theories from the on-shell action obeying Neumann boundary conditions at timelike and null infinity and Dirichlet boundary conditions at spatial infinity. This allows us to identify the on-shell degrees of freedom on the boundary with the soft modes living on the celestial sphere. Following the work of Donnelly and Wall, this suggests that we can interpret soft modes as entanglement edge modes on the celestial sphere and study entanglement properties of soft modes in abelian gauge theories., Comment: 25 pages

Young, low-mass Brown Dwarfs orbiting early-type stars, with low mass ratios ($q\lesssim0.01$), appear intrinsically rare and present a formation dilemma: could a handful of these objects be the highest mass outcomes of ``planetary" formation channels (bottom up within a protoplanetary disk), or are they more representative of the lowest mass ``failed binaries" (formed via disk fragmentation, or core fragmentation)? Additionally, their orbits can yield model-independent dynamical masses, and when paired with wide wavelength coverage and accurate system age estimates, can constrain evolutionary models in a regime where the models have a wide dispersion depending on initial conditions. We present new interferometric observations of the $16\,\mathrm{Myr}$ substellar companion HD~136164~Ab (HIP~75056~Ab) with VLTI/GRAVITY and an updated orbit fit including proper motion measurements from the Hipparcos-Gaia Catalogue of Accelerations. We estimate a dynamical mass of $35\pm10\,\mathrm{M_J}$ ($q\sim0.02$), making HD~136164~Ab the youngest substellar companion with a dynamical mass estimate. The new mass and newly constrained orbital eccentricity ($e=0.44\pm0.03$) and separation ($22.5\pm1\,\mathrm{au}$) could indicate that the companion formed via the low-mass tail of the Initial Mass Function. Our atmospheric fit to the \texttt{SPHINX} M-dwarf model grid suggests a sub-solar C/O ratio of $0.45$, and $3\times$ solar metallicity, which could indicate formation in the circumstellar disk via disk fragmentation. Either way, the revised mass estimate likely excludes ``bottom-up" formation via core accretion in the circumstellar disk. HD~136164~Ab joins a select group of young substellar objects with dynamical mass estimates; epoch astrometry from future \textit{Gaia} data releases will constrain the dynamical mass of this crucial object further., Comment: Accepted for publication in The Astronomical Journal. 9 figures, 3 tables

We present infrared aperture masking interferometry (AMI) observations of newly formed dust from the colliding winds of the massive binary system Wolf-Rayet (WR) 137 with JWST using the Near Infrared Imager and Slitless Spectrograph (NIRISS). NIRISS AMI observations of WR 137 and a point-spread-function calibrator star, HD~228337, were taken using the F380M and F480M filters in 2022 July and August as part of the Director's Discretionary Early Release Science (DD-ERS) program 1349. Interferometric observables (squared visibilities and closure phases) from the WR 137 "interferogram" were extracted and calibrated using three independent software tools: ImPlaneIA, AMICAL, and SAMpip. The analysis of the calibrated observables yielded consistent values except for slightly discrepant closure phases measured by ImPlaneIA. Based on all three sets of calibrated observables, images were reconstructed using three independent software tools: BSMEM, IRBis, and SQUEEZE. All reconstructed image combinations generated consistent images in both F380M and F480M filters. The reconstructed images of WR 137 reveal a bright central core with a $\sim300$ mas linear filament extending to the northwest. A geometric colliding-wind model with dust production constrained to the orbital plane of the binary system and enhanced as the system approaches periapsis provided a general agreement with the interferometric observables and reconstructed images. Based on a colliding-wind dust condensation analysis, we suggest that dust formation within the orbital plane of WR 137 is induced by enhanced equatorial mass-loss from the rapidly rotating O9 companion star, whose axis of rotation is aligned with that of the orbit., Comment: 18 pages, 8 figures, Accepted for publication in ApJ. Updated plotting error in Fig. 2

We present a performance analysis for the aperture masking interferometry (AMI) mode on board the James Webb Space Telescope Near Infrared Imager and Slitless Spectrograph (JWST/NIRISS). Thanks to self-calibrating observables, AMI accesses inner working angles down to and even within the classical diffraction limit. The scientific potential of this mode has recently been demonstrated by the Early Release Science (ERS) 1386 program with a deep search for close-in companions in the HIP 65426 exoplanetary system. As part of ERS 1386, we use the same data set to explore the random, static, and calibration errors of NIRISS AMI observables. We compare the observed noise properties and achievable contrast to theoretical predictions. We explore possible sources of calibration errors and show that differences in charge migration between the observations of HIP 65426 and point-spread function calibration stars can account for the achieved contrast curves. Lastly, we use self-calibration tests to demonstrate that with adequate calibration NIRISS F380M AMI can reach contrast levels of $\sim9-10$ mag at $\gtrsim \lambda/D$. These tests lead us to observation planning recommendations and strongly motivate future studies aimed at producing sophisticated calibration strategies taking these systematic effects into account. This will unlock the unprecedented capabilities of JWST/NIRISS AMI, with sensitivity to significantly colder, lower-mass exoplanets than lower-contrast ground-based AMI setups, at orbital separations inaccessible to JWST coronagraphy., Comment: 20 pages, 12 figures, accepted to Astrophysical Journal Letters

Estimating the region of attraction (${\tt RoA}$) for a robot controller is essential for safe application and controller composition. Many existing methods require a closed-form expression that limit applicability to data-driven controllers. Methods that operate only over trajectory rollouts tend to be data-hungry. In prior work, we have demonstrated that topological tools based on ${\it Morse Graphs}$ (directed acyclic graphs that combinatorially represent the underlying nonlinear dynamics) offer data-efficient ${\tt RoA}$ estimation without needing an analytical model. They struggle, however, with high-dimensional systems as they operate over a state-space discretization. This paper presents ${\it Mo}$rse Graph-aided discovery of ${\it R}$egions of ${\it A}$ttraction in a learned ${\it L}$atent ${\it S}$pace (${\tt MORALS}$). The approach combines auto-encoding neural networks with Morse Graphs. ${\tt MORALS}$ shows promising predictive capabilities in estimating attractors and their ${\tt RoA}$s for data-driven controllers operating over high-dimensional systems, including a 67-dim humanoid robot and a 96-dim 3-fingered manipulator. It first projects the dynamics of the controlled system into a learned latent space. Then, it constructs a reduced form of Morse Graphs representing the bistability of the underlying dynamics, i.e., detecting when the controller results in a desired versus an undesired behavior. The evaluation on high-dimensional robotic datasets indicates data efficiency in ${\tt RoA}$ estimation., Comment: The first two authors contributed equally to this paper

This paper aims to improve the computational efficiency of motion planning for mobile robots with non-trivial dynamics through the use of learned controllers. Offline, a system-specific controller is first trained in an empty environment. Then, for the target environment, the approach constructs a data structure, a "Roadmap with Gaps," to approximately learn how to solve planning queries using the learned controller. The roadmap nodes correspond to local regions. Edges correspond to applications of the learned controller that approximately connect these regions. Gaps arise as the controller does not perfectly connect pairs of individual states along edges. Online, given a query, a tree sampling-based motion planner uses the roadmap so that the tree's expansion is informed towards the goal region. The tree expansion selects local subgoals given a wavefront on the roadmap that guides towards the goal. When the controller cannot reach a subgoal region, the planner resorts to random exploration to maintain probabilistic completeness and asymptotic optimality. The accompanying experimental evaluation shows that the approach significantly improves the computational efficiency of motion planning on various benchmarks, including physics-based vehicular models on uneven and varying friction terrains as well as a quadrotor under air pressure effects., Comment: To be presented at the IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), 2024. Website: https://prx-kinodynamic.github.io/projects/rogue

Model initialization techniques are vital for improving the performance and reliability of deep learning models in medical computer vision applications. While much literature exists on non-medical images, the impacts on medical images, particularly chest X-rays (CXRs) are less understood. Addressing this gap, our study explores three deep model initialization techniques: Cold-start, Warm-start, and Shrink and Perturb start, focusing on adult and pediatric populations. We specifically focus on scenarios with periodically arriving data for training, thereby embracing the real-world scenarios of ongoing data influx and the need for model updates. We evaluate these models for generalizability against external adult and pediatric CXR datasets. We also propose novel ensemble methods: F-score-weighted Sequential Least-Squares Quadratic Programming (F-SLSQP) and Attention-Guided Ensembles with Learnable Fuzzy Softmax to aggregate weight parameters from multiple models to capitalize on their collective knowledge and complementary representations. We perform statistical significance tests with 95% confidence intervals and p-values to analyze model performance. Our evaluations indicate models initialized with ImageNet-pre-trained weights demonstrate superior generalizability over randomly initialized counterparts, contradicting some findings for non-medical images. Notably, ImageNet-pretrained models exhibit consistent performance during internal and external testing across different training scenarios. Weight-level ensembles of these models show significantly higher recall (p<0.05) during testing compared to individual models. Thus, our study accentuates the benefits of ImageNet-pretrained weight initialization, especially when used with weight-level ensembles, for creating robust and generalizable deep learning solutions., Comment: 40 pages, 8 tables, 7 figures, 3 supplementary figures and 4 supplementary tables

Deep learning (DL) has demonstrated its innate capacity to independently learn hierarchical features from complex and multi-dimensional data. A common understanding is that its performance scales up with the amount of training data. Another data attribute is the inherent variety. It follows, therefore, that semantic redundancy, which is the presence of similar or repetitive information, would tend to lower performance and limit generalizability to unseen data. In medical imaging data, semantic redundancy can occur due to the presence of multiple images that have highly similar presentations for the disease of interest. Further, the common use of augmentation methods to generate variety in DL training may be limiting performance when applied to semantically redundant data. We propose an entropy-based sample scoring approach to identify and remove semantically redundant training data. We demonstrate using the publicly available NIH chest X-ray dataset that the model trained on the resulting informative subset of training data significantly outperforms the model trained on the full training set, during both internal (recall: 0.7164 vs 0.6597, p<0.05) and external testing (recall: 0.3185 vs 0.2589, p<0.05). Our findings emphasize the importance of information-oriented training sample selection as opposed to the conventional practice of using all available training data., Comment: 3 Tables, 11 Figures, 20 pages

This paper poses a theoretical characterization of the stochastic reachability problem in terms of probability measures, capturing the probability measure of the state of the system that satisfies the reachability specification for all probabilities over a finite horizon. We achieve this by constructing the level sets of the probability measure for all probability values and, since our approach is only for autonomous systems, we can determine the level sets via forward simulations of the system from a point in the state space at some time step in the finite horizon to estimate the reach probability. We devise a training procedure which exploits this forward simulation and employ it to design a deep neural network (DNN) to predict the reach probability provided the current state and time step. We validate the effectiveness of our approach through three examples., Comment: 8 pages, 4 figures, 1 table, Accepted to the Conference on Decision and Control 2024

WebAssembly (Wasm) is a low-level portable code format offering near native performance. It is intended as a compilation target for a wide variety of source languages. However, Wasm provides no direct support for non-local control flow features such as async/await, generators/iterators, lightweight threads, first-class continuations, etc. This means that compilers for source languages with such features must ceremoniously transform whole source programs in order to target Wasm. We present WasmFX, an extension to Wasm which provides a universal target for non-local control features via effect handlers, enabling compilers to translate such features directly into Wasm. Our extension is minimal and only adds three main instructions for creating, suspending, and resuming continuations. Moreover, our primitive instructions are type-safe providing typed continuations which are well-aligned with the design principles of Wasm whose stacks are typed. We present a formal specification of WasmFX and show that the extension is sound. We have implemented WasmFX as an extension to the Wasm reference interpreter and also built a prototype WasmFX extension for Wasmtime, a production-grade Wasm engine, piggybacking on Wasmtime's existing fibers API. The preliminary performance results for our prototype are encouraging, and we outline future plans to realise a native implementation

$\newcommand{\Max}{\mathrm{Max4PC}}$ The Four point condition (4PC henceforth) is a well known condition characterising distances in trees $T$. Let $w,x,y,z$ be four vertices in $T$ and let $d_{x,y}$ denote the distance between vertices $x,y$ in $T$. The 4PC condition says that among the three terms $d_{w,x} + d_{y,z}$, $d_{w,y} + d_{x,z}$ and $d_{w,z} + d_{x,y}$ the maximum value equals the second maximum value. We define an $\binom{n}{2} \times \binom{n}{2}$ sized matrix $\Max_T$ from a tree $T$ where the rows and columns are indexed by size-2 subsets. The entry of $\Max_T$ corresponding to the row indexed by $\{w,x\}$ and column $\{y,z\}$ is the maximum value among the three terms $d_{w,x} + d_{y,z}$, $d_{w,y} + d_{x,z}$ and $d_{w,z} + d_{x,y}$. In this work, we determine basic properties of this matrix like rank, give an algorithm that outputs a family of bases, and find the determinant of $\Max_T$ when restricted to our basis. We further determine the inertia and the Smith Normal Form (SNF) of $\Max_T$.

Let $T$ be a tree on $n$ vertices and let $L_q^T$ be the $q$-analogue of its Laplacian. For a partition $\lambda \vdash n$, let the normalized immanant of $L_q^T$ indexed by $\lambda$ be denoted as $d_{\lambda}(L_q^T)$. A string of inequalities among $d_{\lambda}(L_q^T)$ is known when $\lambda$ varies over hook partitions of $n$ as the size of the first part of $\lambda$ decreases. In this work, we show a similar sequence of inequalities when $\lambda$ varies over two row partitions of $n$ as the size of the first part of $\lambda$ decreases. Our main lemma is an identity involving binomial coefficients and irreducible character values of $S_n$ indexed by two row partitions. Our proof can be interpreted using the combinatorics of Riordan paths and our main lemma admits a nice probabilisitic interpretation involving peaks at odd heights in generalized Dyck paths or equivalently involving special descents in Standard Young Tableaux with two rows. As a corollary, we also get inequalities between $d_{\lambda_1}(L_q^{T_1})$ and $d_{\lambda_2}(L_q^{T_2})$ when $T_1$ and $T_2$ are comparable trees in the $GTS_n$ poset and when $\lambda_1$ and $\lambda_2$ are both two rowed partitions of $n$, with $\lambda_1$ having a larger first part than $\lambda_2$.