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The famous Dirac's Theorem states that for each $n\geq 3$ every $n$-vertex graph $G$ with minimum degree $\delta(G)\geq n/2$ has a hamiltonian cycle. When $\delta(G)< n/2$, this cannot be guaranteed, but the existence of some other specific subgraphs can be provided. Gargano, Hell, Stacho and Vaccaro proved that every connected $n$-vertex graph $G$ with $\delta(G)\geq (n-1)/3$ contains a spanning {\em spider}, i.e., a spanning tree with at most one vertex of degree at least $3$. Later, Chen, Ferrara, Hu, Jacobson and Liu proved the stronger (and exact) result that for $n\geq 56$ every connected $n$-vertex graph $G$ with $\delta(G)\geq (n-2)/3$ contains a spanning {\em broom}, i.e., a spanning spider obtained by joining the center of a star to an endpoint of a path. They also showed that a $2$-connected graph $G$ with $\delta(G)\geq (n-2)/3$ and some additional properties contains a spanning {\em jellyfish} which is a graph obtained by gluing the center of a star to a vertex in a cycle disjoint from that star. Note that every spanning jellyfish contains a spanning broom. The goal of this paper is to prove an exact Ore-type bound which guarantees the existence of a spanning jellyfish: We prove that if $G$ is a $2$-connected graph on $n$ vertices such that every non-adjacent pair of vertices $(u,v)$ satisfies $d(u) + d(v) \geq \frac{2n-3}{3}$, then $G$ has a spanning jellyfish. As corollaries, we obtain strengthenings of two results by Chen et al.: a minimum degree condition guaranteeing the existence of a spanning jellyfish, and an Ore-type sufficient condition for the existence of a spanning broom. The corollaries are sharp for infinitely many $n$. One of the main ingredients of our proof is a modification of the Hopping Lemma due to Woodall.

Confidence intervals (CIs) are instrumental in statistical analysis, providing a range estimate of the parameters. In modern statistics, selective inference is common, where only certain parameters are highlighted. However, this selective approach can bias the inference, leading some to advocate for the use of CIs over p-values. To increase the flexibility of confidence intervals, we introduce direction-preferring CIs, enabling analysts to focus on parameters trending in a particular direction. We present these types of CIs in two settings: First, when there is no selection of parameters; and second, for situations involving parameter selection, where we offer a conditional version of the direction-preferring CIs. Both of these methods build upon the foundations of Modified Pratt CIs, which rely on non-equivariant acceptance regions to achieve longer intervals in exchange for improved sign exclusions. We show that for selected parameters out of m > 1 initial parameters of interest, CIs aimed at controlling the false coverage rate, have higher power to determine the sign compared to conditional CIs. We also show that conditional confidence intervals control the marginal false coverage rate (mFCR) under any dependency., Comment: 11 figures, 45 pages

In the seven years that the starship Voyager spent in the Delta Quadrant, it used many questionable techniques to engage with alien civilizations and ultimately find its way home. From detailed studies of their logs and opening credits, we simulate Voyager's practice of orbiting a planet, to examine the effect on planetary rings. We outline a feasible planetary system and simulate the extent to which its rings would be disrupted. We find that Voyager's orbit could inflate the height of the rings in the vicinity of the spacecraft by a factor of 2, as well as increase the relative speeds of neighboring planetesimals within the rings. This increase in ring thickness has the potential to alter shadows on any moons of this planet, impacting ring-shadow based religions. Additionally, the acceleration of these planetesimals could rival their gravity, bucking any alien inhabitants and their tiny civilizations off of their planetesimal homeworlds. Finally, we posit that due to increased collisions amongst the planetesimals (which may harbor tiny intelligent life) the trajectory of these civilizations may be forever altered, violating the prime directive.

In many applications, one is interested in classifying trajectories of Hamiltonian systems as invariant tori, islands, or chaos. The convergence rate of ergodic Birkhoff averages can be used to categorize these regions, but many iterations of the return map are needed to implement this directly. Recently, it has been shown that a weighted Birkhoff average can be used to accelerate the convergence, resulting in a useful method for categorizing trajectories. In this paper, we show how a modified version the reduced rank extrapolation method (named Birkhoff RRE) can also be used to find optimal weights for the weighted average with a single linear least-squares solve.Using these, we classify trajectories with fewer iterations of the map than the standard weighted Birkhoff average. Furthermore, for the islands and invariant circles, a subsequent eigenvalue problem gives the number of islands and the rotation number. Using these numbers, we find Fourier parameterizations of invariant circles and islands. We show examples of Birkhoff RRE on the standard map and on magnetic field line dynamics.

In previous work we have shown that the dipole in the low redshift supernovae of the Pantheon+SH0ES data does not agree with the one inferred from the velocity of the solar system as obtained from CMB data. We interpreted this as the presence of significant bulk velocities. In this paper we study the monopole, dipole and quadrupole in the Pantheon+SH0ES data. We find that in addition to the dipole also both, the monopole and the quadrupole are detected with high significance. They are of similar amplitudes as the bulk flow. While the monopole is only significant at very low redshift, the quadrupole even increases with redshift., Comment: 30 pages, 17 figures

In this contribution we present a novel, model-independent description of semileptonic $B\rightarrow D \pi \ell \nu$ decays. In addition, we discuss recent developments in the understanding of coupled-channel $D \pi$-$D \eta$-$D_s K$ S-wave scattering and, for the first time, apply them to semileptonic decays. We not only obtain model-independent predictions for kinematic distributions in $B\rightarrow D \pi \ell \nu$ decays, but also rule out the hypothesis that the gap between the inclusive $B\rightarrow X\ell\nu$ branching fraction and the sum over exclusive channels is made up predominantly by $B\rightarrow D^{(\ast)} \eta \ell \nu$ decays., Comment: Presented at the 12th Workshop on the CKM Unitarity Triangle, 18-22 September 2023, Santiago de Compostela

Coupled climate model simulations designed to isolate the effects of Arctic sea-ice loss often apply artificial heating, either directly to the ice or through modification of the surface albedo, to constrain sea-ice in the absence of other forcings. Recent work has shown that this approach may lead to an overestimation of the climate response to sea-ice loss. In this study, we assess the spurious impacts of ice-constraining methods on the climate of an idealised aquaplanet general circulation model (GCM) with thermodynamic sea-ice. The true effect of sea-ice loss in this model is isolated by inducing ice loss through reduction of the freezing point of water, which does not require additional energy input. We compare results from freezing point modification experiments with experiments where sea-ice loss is induced using traditional ice-constraining methods, and confirm the result of previous work that traditional methods induce spurious additional warming. Furthermore, additional warming leads to an overestimation of the circulation response to sea-ice loss, which involves a weakening of the zonal wind and storm track activity in midlatitudes. Our results suggest that coupled model simulations with constrained sea-ice should be treated with caution, especially in boreal summer, where the true effect of sea-ice loss is weakest but we find the largest spurious response. Given that our results may be sensitive to the simplicity of the model we use, we suggest that devising methods to quantify the spurious effects of ice-constraining methods in more sophisticated models should be an urgent priority for future work., Comment: Submitted to Journal of Climate

In supervised learning, including regression and classification, conformal methods provide prediction sets for the outcome/label with finite sample coverage for any machine learning predictor. We consider here the case where such prediction sets come after a selection process. The selection process requires that the selected prediction sets be `informative' in a well defined sense. We consider both the classification and regression settings where the analyst may consider as informative only the sample with prediction sets small enough, excluding null values, or obeying other appropriate `monotone' constraints. We develop a unified framework for building such informative conformal prediction sets while controlling the false coverage rate (FCR) on the selected sample. While conformal prediction sets after selection have been the focus of much recent literature in the field, the new introduced procedures, called InfoSP and InfoSCOP, are to our knowledge the first ones providing FCR control for informative prediction sets. We show the usefulness of our resulting procedures on real and simulated data., Comment: 50 pages, 15 figures, 1 table

Stellar age measurements are fundamental to understanding a wide range of astronomical processes, including galactic dynamics, stellar evolution, and planetary system formation. However, extracting age information from Main Sequence stars is complicated, with techniques often relying on age proxies in the absence of direct measurements. The Gaia data releases have enabled detailed studies of the dynamical properties of stars within the Milky Way, offering new opportunities to understand the relationship between stellar age and dynamics. In this study, we leverage high-precision astrometric data from Gaia DR3 to construct a stellar age prediction model based only on stellar dynamical properties; namely, the vertical action. We calibrate two distinct, hierarchical stellar age--vertical action relations, first employing asteroseismic ages for red giant branch stars, then isochrone ages for main-sequence turn-off stars. We describe a framework called "zoomies" based on this calibration, by which we can infer ages for any star given its vertical action. This tool is open-source and intended for community use. We compare dynamical age estimates from "zoomies" with ages derived from other techniques for a sample of open clusters and main-sequence stars with asteroseismic age measurements. We also compare dynamical age estimates for stellar samples from the Kepler, K2, and TESS exoplanet transit surveys. While dynamical age relations are associated with large uncertainty, they are generally mass-independent and depend on homogeneously measured astrometric data. These age predictions are uniquely useful for large-scale demographic investigations, especially in disentangling the relationship between planet occurrence, metallicity, and age for low-mass stars., Comment: 23 pages, 12 figures, 2 tables. Submitted to AAS Journals

We review different notions of cuts appearing throughout the literature on scattering amplitudes. Despite similar names, such as unitarity cuts or generalized cuts, they often represent distinct computations and distinct physics. We consolidate this knowledge, summarize how cuts are used in various computational strategies, and explain their relations to other quantities including imaginary parts, discontinuities, and monodromies. Differences and nuances are illustrated on explicit examples., Comment: 23 pages, invited contribution to the Encyclopedia of Mathematical Physics

To date, the most precise measurement of the observer's peculiar velocity comes from the dipole in the Cosmic Microwave Background (CMB). This velocity also generates a dipole in the source number counts, whose amplitude is governed not only by the observer velocity, but also by specific properties of the sources, that are difficult to determine precisely. Quantitative studies of the source number counts currently give dipoles which are reasonably well aligned with the CMB dipole, but with a significantly larger amplitude than that of the CMB dipole. In this work, we explore an alternative way of measuring the observer velocity from the source number counts, using correlations between neighboring spherical harmonic coefficients, induced by the velocity. We show that these correlations contain both a term sensitive to the source properties and another one directly given by the observer velocity. We explore the potential of a Euclid-like survey to directly measure this second contribution, independently of the characteristics of the population of sources. We find that the method can reach a precision of 4%, corresponding to a detection significance of 24 sigma, on the observer velocity. This will settle with precision the present "dipole tension"., Comment: 20 pages main, 12 pages appendix, 6 figures

Prediction models are increasingly proposed for guiding treatment decisions, but most fail to address the special role of treatments, leading to inappropriate use. This paper highlights the limitations of using standard prediction models for treatment decision support. We identify `causal blind spots' in three common approaches to handling treatments in prediction modelling: including treatment as a predictor, restricting data based on treatment status and ignoring treatments. When predictions are used to inform treatment decisions, confounders, colliders and mediators, as well as changes in treatment protocols over time may lead to misinformed decision-making. We illustrate potential harmful consequences in several medical applications. We advocate for an extension of guidelines for development, reporting and evaluation of prediction models to ensure that the intended use of the model is matched to an appropriate risk estimand. When prediction models are intended to inform treatment decisions, prediction models should specify upfront the treatment decisions they aim to support and target a prediction estimand in line with that goal. This requires a shift towards developing predictions under the specific treatment options under consideration (`predictions under interventions'). Predictions under interventions need causal reasoning and inference techniques during development and validation. We argue that this will improve the efficacy of prediction models in guiding treatment decisions and prevent potential negative effects on patient outcomes.

With the rise in engineered biomolecular devices, there is an increased need for tailor-made biological sequences. Often, many similar biological sequences need to be made for a specific application meaning numerous, sometimes prohibitively expensive, lab experiments are necessary for their optimization. This paper presents a transfer learning design of experiments workflow to make this development feasible. By combining a transfer learning surrogate model with Bayesian optimization, we show how the total number of experiments can be reduced by sharing information between optimization tasks. We demonstrate the reduction in the number of experiments using data from the development of DNA competitors for use in an amplification-based diagnostic assay. We use cross-validation to compare the predictive accuracy of different transfer learning models, and then compare the performance of the models for both single objective and penalized optimization tasks.

Zirconium alloys are widely used in nuclear reactors as fuel cladding materials. Fuel cladding is used to contain the nuclear fuel and cladding tubes are typically sealed using welds. Welding of zirconium alloys can result in changes in the local microstructure, with the potential to grow so called 'blocky {\alpha}' grains in the welded region during subsequent thermal processing and these blocky {\alpha} grains have the potential to be detrimental to the integrity of the component. In this work, complimentary heating experiments with ex situ and in situ electron backscatter diffraction (EBSD) analysis are used to aid understanding of the blocky {\alpha} grain growth within the weld region. These experiments reveal that blocky {\alpha} grain growth is related to the parent \b{eta} (high temperature) microstructure, as grains grow adjacent to a prior \b{eta} grain boundary and the orientation of the growing {\alpha} grain can be explained using neighbourhood orientations from this prior \b{eta} grain. This growth mechanism is explained via a simple mechanism which is related to the {\alpha} grain orientations, grain boundary structures and local stored energy. Ultimately, our findings indicate that the likely grain growth (size and morphology) across the weld region can now be predicted from the initial as-welded microstructure., Comment: as submitted

Precision medicine aims to create biomedical solutions tailored to specific factors that affect disease risk and treatment responses within the population. The success of the genomics era and recent widespread availability of electronic health records (EHR) has ushered in a new wave of genomic biobanks connected to EHR databases (EHR-linked biobanks). This perspective aims to discuss how race, ethnicity, and genetic ancestry are currently utilized to study common disease variation through genetic association studies. Although genetic ancestry plays a significant role in shaping the genetic landscape underlying disease risk in humans, the overall risk of a disease is caused by a complex combination of environmental, sociocultural, and genetic factors. When using EHR-linked biobanks to interrogate underlying disease etiology, it is also important to be aware of how the biases associated with commonly used descent-associated concepts such as race and ethnicity can propagate to downstream analyses. We intend for this resource to support researchers who perform or analyze genetic association studies in the EHR-linked biobank setting such as those involved in consortium-wide biobanking efforts. We provide background on how race, ethnicity, and genetic ancestry play a role in current association studies, highlight considerations where there is no consensus about best practices, and provide transparency about the current shortcomings.

Hidden Markov Models with an underlying Mixture of Gaussian structure have proven effective in learning Human-Robot Interactions from demonstrations for various interactive tasks via Gaussian Mixture Regression. However, a mismatch occurs when segmenting the interaction using only the observed state of the human compared to the joint state of the human and the robot. To enhance this underlying segmentation and subsequently the predictive abilities of such Gaussian Mixture-based approaches, we take a hierarchical approach by learning an additional mixture distribution on the states at the transition boundary. This helps prevent misclassifications that usually occur in such states. We find that our framework improves the performance of the underlying Gaussian Mixture-based approach, which we evaluate on various interactive tasks such as handshaking and fistbumps., Comment: Accepted as a Late Breaking Report in The ACM/IEEE International Conference on Human Robot Interaction (HRI) 2024

For ongoing studies of the role of rotation in stellar evolution, we require large catalogs of rotation periods for testing and refining gyrochronology. While there is a wealth of data from the Kepler and K2 missions, TESS presents both an opportunity and a challenge: despite its all-sky coverage, rotation periods remain hard to detect. We analyzed individual TESS sectors to detect short-period stellar rotation, using only parameters measured from light curves for a robust and unbiased method of evaluating detections. We used random forest classifiers for vetting, trained on a large corpus of period measurements in KELT data from the Oelkers et al. (2018) catalog and using TESS full-frame image light curves generated by eleanor (Feinstein et al. 2019). Finally, using data from the first 26 sectors of TESS, we analyzed 432,704 2-minute cadence single-sector light curves for FGKM dwarfs. We detected 16,800 periods in individual sector light curves, covering 10,909 distinct targets, and we present a catalog of the median period for each target as measured by a Lomb-Scargle periodogram., Comment: 23 pages, 15 figures, accepted for publication in The Astronomical Journal

Since graph neural networks (GNNs) are often vulnerable to attack, we need to know when we can trust them. We develop a computationally effective approach towards providing robust certificates for message-passing neural networks (MPNNs) using a Rectified Linear Unit (ReLU) activation function. Because our work builds on mixed-integer optimization, it encodes a wide variety of subproblems, for example it admits (i) both adding and removing edges, (ii) both global and local budgets, and (iii) both topological perturbations and feature modifications. Our key technology, topology-based bounds tightening, uses graph structure to tighten bounds. We also experiment with aggressive bounds tightening to dynamically change the optimization constraints by tightening variable bounds. To demonstrate the effectiveness of these strategies, we implement an extension to the open-source branch-and-cut solver SCIP. We test on both node and graph classification problems and consider topological attacks that both add and remove edges.