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Mixed-integer programming (MIP) is a well-established framework for computer-aided molecular design (CAMD). By precisely encoding the molecular space and score functions, e.g., a graph neural network, the molecular design problem is represented and solved as an optimization problem, the solution of which corresponds to a molecule with optimal score. However, both the extremely large search space and complicated scoring process limit the use of MIP-based CAMD to specific and tiny problems. Moreover, optimal molecule may not be meaningful in practice if scores are imperfect. Instead of pursuing optimality, this paper exploits the ability of MIP in molecular generation and proposes Limeade as an end-to-end tool from real-world needs to feasible molecules. Beyond the basic constraints for structural feasibility, Limeade supports inclusion and exclusion of SMARTS patterns, automating the process of interpreting and formulating chemical requirements to mathematical constraints., Comment: 32 pages, 2 figures

Random walks and related spatial stochastic models have been used in a range of application areas including animal and plant ecology, infectious disease epidemiology, developmental biology, wound healing, and oncology. Classical random walk models assume that all individuals in a population behave independently, ignoring local physical and biological interactions. This assumption simplifies the mathematical description of the population considerably, enabling continuum-limit descriptions to be derived and used in model analysis and fitting. However, interactions between individuals can have a crucial impact on population-level behaviour. In recent decades, research has increasingly been directed towards models that include interactions, including physical crowding effects and local biological processes such as adhesion, competition, dispersal, predation and adaptive directional bias. In this article, we review the progress that has been made with models of interacting individuals. We aim to provide an overview that is accessible to researchers in application areas, as well as to specialist modellers. We focus particularly on derivation of asymptotically exact or approximate continuum-limit descriptions and simplified deterministic models of mean-field behaviour and resulting spatial patterns. We provide worked examples and illustrative results of selected models. We conclude with a discussion of current areas of focus and future challenges.

Parameter inference is essential when interpreting observational data using mathematical models. Standard inference methods for differential equation models typically rely on obtaining repeated numerical solutions of the differential equation(s). Recent results have explored how numerical truncation error can have major, detrimental, and sometimes hidden impacts on likelihood-based inference by introducing false local maxima into the log-likelihood function. We present a straightforward approach for inference that eliminates the need for solving the underlying differential equations, thereby completely avoiding the impact of truncation error. Open-access Jupyter notebooks, available on GitHub, allow others to implement this method for a broad class of widely-used models to interpret biological data., Comment: 11 pages, 2 figures

We present complete results for the hadronic vacuum polarization (HVP) contribution to the muon anomalous magnetic moment $a_\mu$ in the short- and intermediate-distance window regions, which account for roughly 10% and 35% of the total HVP contribution to $a_\mu$, respectively. In particular, we perform lattice-QCD calculations for the isospin-symmetric connected and disconnected contributions, as well as corrections due to strong isospin-breaking. For the short-distance window observables, we investigate the so-called log-enhancement effects as well as the significant oscillations associated with staggered quarks in this region. For the dominant, isospin-symmetric light-quark connected contribution, we obtain $a^{ll,\,{\mathrm{SD}}}_{\mu}(\mathrm{conn.}) = 48.116(16)(94)[96] \times 10^{-10}$ and $a^{ll,\,{\mathrm{W}}}_{\mu}(\mathrm{conn.}) = 207.06(17)(63)[66] \times 10^{-10}$. We use Bayesian model averaging combined with a global bootstrap to fully estimate the covariance matrix between the individual contributions. Our determinations of the complete window contributions are $a^{{\mathrm{SD}}}_{\mu} = 69.01(2)(21)[21] \times 10^{-10}$ and $a^{{\mathrm{W}}}_{\mu} = 236.57(20)(94)[96] \times 10^{-10}$. This work is part of our ongoing effort to compute all contributions to HVP with an overall uncertainty at the few permille level.

We investigate ultra slow-roll inflation in a black hole background finding a correspondence between scalar solutions of ultra slow-roll inflation and quasi-normal modes of the cosmological black hole spacetime. Transitions from slow-roll to ultra slow-roll can enhance the peak of the primordial power spectrum increasing the likelihood of primordial black hole formation. By following such a transition in a black hole background, we observe a decay of the slow-roll attractor solution into the quasi-normal modes of the system. With a large black hole, the ringing modes dominate, which could have implications for the background of cosmological scalar perturbations and peak enhancement., Comment: 34 pages, 10 figures

When analyzing stellarator configurations, it is common to perform an asymptotic expansion about the magnetic axis. This so-called near-axis expansion is convenient for the same reason asymptotic expansions often are, namely, it reduces the dimension of the problem. This leads to convenient and quickly computed expressions of physical quantities, such as quasisymmetry and stability criteria, which can be used to gain further insight. However, it has been repeatedly found that the expansion diverges at high orders, limiting the physics the expansion can describe. In this paper, we show that the near-axis expansion diverges in vacuum due to ill-posedness and that it can be regularized to improve its convergence. Then, using realistic stellarator coil sets, we show that the near-axis expansion can converge to ninth order in the magnetic field, giving accurate high-order corrections to the computation of flux surfaces. We numerically find that the regularization improves the solutions of the near-axis expansion under perturbation, and we demonstrate that the radius of convergence of the vacuum near-axis expansion is correlated with the distance from the axis to the coils., Comment: 43 pages, 8 figures

In a supervised classification split conformal/inductive framework with $K$ classes, a calibration sample of $n$ labeled examples is observed for inference on the label of a new unlabeled example. In this work, we explore the case where a "batch" of $m$ independent such unlabeled examples is given, and a multivariate prediction set with $1-\alpha$ coverage should be provided for this batch. Hence, the batch prediction set takes the form of a collection of label vectors of size $m$, while the calibration sample only contains univariate labels. Using the Bonferroni correction consists in concatenating the individual prediction sets at level $1-\alpha/m$ (Vovk 2013). We propose a uniformly more powerful solution, based on specific combinations of conformal $p$-values that exploit the Simes inequality (Simes 1986). Intuitively, the pooled evidence of fairly "easy" examples of the batch can help provide narrower batch prediction sets. We also introduced adaptive versions of the novel procedure that are particularly effective when the batch prediction set is expected to be large. The theoretical guarantees are provided when all examples are iid, as well as more generally when iid is assumed only conditionally within each class. In particular, our results are also valid under a label distribution shift since the distribution of the labels need not be the same in the calibration sample and in the new `batch'. The usefulness of the method is illustrated on synthetic and real data examples., Comment: 27 pages, 6 figures, 6 tables

The rapid validation of newly predicted materials through autonomous synthesis requires real-time adaptive control methods that exploit physics knowledge, a capability that is lacking in most systems. Here, we demonstrate an approach to enable the real-time control of thin film synthesis by combining in situ optical diagnostics with a Bayesian state estimation method. We developed a physical model for film growth and applied the Direct Filter (DF) method for real-time estimation of nucleation and growth rates during pulsed laser deposition (PLD) of transition metal dichalcogenides. We validated the approach on simulated and previously acquired reflectivity data for WSe$_2$ growth and ultimately deployed the algorithm on an autonomous PLD system during growth of 1T$^\prime$-MoTe$_2$ under various synthesis conditions. We found that the DF robustly estimates growth parameters in real-time at early stages of growth, down to 15% percent monolayer area coverage. This approach opens new opportunities for adaptive film growth control based on a fusion of in situ diagnostics, modern data assimilation methods, and physical models which promises to enable control of synthesis trajectories towards desired material states.

A Berge cycle of length $\ell$ in a hypergraph is an alternating sequence of $\ell$ distinct vertices and $\ell$ distinct edges $v_1,e_1,v_2, \ldots, v_\ell, e_{\ell}$ such that $\{v_i, v_{i+1}\} \subseteq e_i$ for all $i$, with indices taken modulo $\ell$. We call an $n$-vertex hypergraph pancyclic if it contains Berge cycles of every length from $3$ to $n$. We prove a sharp Dirac-type result guaranteeing pancyclicity in uniform hypergraphs: for $n \geq 70$, $3 \leq r \leq \lfloor (n-1)/2\rfloor - 2$, if $\cH$ is an $n$-vertex, $r$-uniform hypergraph with minimum degree at least ${\lfloor (n-1)/2 \rfloor \choose r-1} + 1$, then $\cH$ is pancyclic.

We present a novel python-based 1D sub-Neptune evolution model that emphasizes the thermal evolution and potential solidification of the rock/iron core and the structure of the radiative atmosphere. This model explores planetary structure from the molten center to nbar pressure levels. Treating the radiative atmosphere is crucial for sub-Neptunes, due to the large scale height and low gravity, which contributes up to 40\% of their observed radius, especially for low-mass, highly irradiated planets. Consequently, we generically find that lower H/He mass fractions are needed to match a given planetary radius, compared to previous work. While the presence of metal-enrichment in the H/He layers (here modeled as 50$\times$ solar) does not substantially influence the size of the convective envelope, it notably reduces the transit radius by shrinking the radiative atmospheric scale height. Sub-Neptunes cool differently from terrestrial planets, with the rock/iron core's cooling rate limited by the envelope, leading to longer solidification timescales. Complete solidification of the silicate mantle by 10 Gyr is found only for planets with very low masses ($\leq 1M_\oplus$) and small H/He envelopes ($\leq$ 0.1\%). Dynamo action in sub-Neptune iron cores persists as long as the mantle surface remains molten, often exceeding 10 Gyr, and becomes sensitive to core thermal conductivity after solidification. We examine aspects of ''boil-off,'' which sets the maximum allowed H/He mass and planetary radius for subsequent evolution. The rock/iron's cooling energy moderately decreases the post-boil-off H/He mass fraction in planets with large atmospheric scale heights only., Comment: 32 pages, 17 figures, submitted to ApJ

Time domain simulations of electromagnetic problems are highly valuable in engineering applications, as they allow for the analysis of transient behavior and broadband responses. These simulations utilize time stepping schemes, where each solution is derived from the solutions of previous time steps. Although each time step involves relatively straightforward computations, the high dimensionality of the problem can significantly increase the overall computational time. This work introduces a reduced order model (ROM) for finite element method in time domain (FEMTD) simulations, specifically applied to microwave devices. The proposed methodology, called ROMTD, enables efficient analysis of time evolution in electromagnetic problems while substantially reducing computational demands. Its main advantage is the use of a much smaller number of degrees of freedom (DoFs) to capture the same electromagnetic dynamics, compared to the large number of DoFs typically required by traditional methods such as finite difference in time domain (FDTD) and FEMTD. To construct the ROM basis, a novel criterion for selecting FEMTD solutions is introduced, ensuring that only the most relevant snapshots are retained. The capabilities of the ROMTD approach are demonstrated through various examples, including a quad-mode dielectric resonator filter, a side-coupled four-pole filter in quarter-mode substrate integrated waveguide technology, and a microstrip dual-band bandpass planar filter. These examples illustrate the potential of the proposed ROMTD strategy to efficiently solve time evolution problems in electromagnetics, providing significant reduction in computation time without compromising accuracy., Comment: 14 pages

Large language models (LLMs) are employed to simulate human-like responses in social surveys, yet it remains unclear if they develop biases like social desirability response (SDR) bias. To investigate this, GPT-4 was assigned personas from four societies, using data from the 2022 Gallup World Poll. These synthetic samples were then prompted with or without a commitment statement intended to induce SDR. The results were mixed. While the commitment statement increased SDR index scores, suggesting SDR bias, it reduced civic engagement scores, indicating an opposite trend. Additional findings revealed demographic associations with SDR scores and showed that the commitment statement had limited impact on GPT-4's predictive performance. The study underscores potential avenues for using LLMs to investigate biases in both humans and LLMs themselves.

The gravitational physics landscape is evolving rapidly, driven by our ability to study strong-field regions, in particular black holes. Black Holes Inside and Out gathered world experts to discuss the status of the field and prospects ahead. We hope that the ideas and perspectives are a source of inspiration. Structure: Black Hole Evaporation - 50 Years by William Unruh The Stability Problem for Extremal Black Holes by Mihalis Dafermos The Entropy of Black Holes by Robert M. Wald The Non-linear Regime of Gravity by Luis Lehner Black Holes Galore in D > 4 by Roberto Emparan Same as Ever: Looking for (In)variants in the Black Holes Landscape by Carlos A. R. Herdeiro Black Holes, Cauchy Horizons, and Mass Inflation by Matt Visser The Backreaction Problem for Black Holes in Semiclassical Gravity by Adrian del Rio Black Holes Beyond General Relativity by Enrico Barausse and Jutta Kunz Black Holes as Laboratories: Searching for Ultralight Fields by Richard Brito Primordial Black Holes from Inflation by Misao Sasaki Tests of General Relativity with Future Detectors by Emanuele Berti Black Holes as Laboratories: Tests of General Relativity by Ruth Gregory and Samaya Nissanke Simulating Black Hole Imposters by Frans Pretorius Black Hole Spectroscopy: Status Report by Gregorio Carullo VLBI as a Precision Strong Gravity Instrument by Paul Tiede Testing the nature of compact objects and the black hole paradigm by Mariafelicia De Laurentis and Paolo Pani Some Thoughts about Black Holes in Asymptotic Safety by Alessia Platania Black Hole Evaporation in Loop Quantum Gravity by Abhay Ashtekar How the Black Hole Puzzles are Resolved in String Theory by Samir D. Mathur Quantum Black Holes: From Regularization to Information Paradoxes by Niayesh Afshordi and Stefano Liberati, Comment: 221 pages, 21 contributions

The dynamical properties of the bodies in the outer Solar System hold information regarding the planets' orbital histories. In early Solar System numerical simulations, where chaos is a primary driver, it is difficult to explore parameter space in a systematic way. In such simulations, stable configurations are hard to come by, and often require special fine-tuning. In addition, it is infeasible to run suites of well-resolved, realistic simulations with massive particles to drive planetary evolution where enough particles remain to represent the transneptunian populations to robustly statistically compare with observations. To complement state of the art full N-body simulations, we develop a method to artificially control each planet's orbital elements independently from each other, which when carefully applied, can be used to test a wider suite of models. We modify two widely used publicly available N-body integrators: (1) the C code, REBOUND and (2) the FORTRAN code, Mercury. We show how the application of specific fictitious forces within numerical integrators can be used to tightly control planetary evolution to more easily explore migration and orbital excitation and damping. This tool allows us to replicate the impact a massive planetesimal disk would have on the planets, without actually including the massive planetesimals, thus decreasing the chaos and simulation runtime. We highlight an appropriate application that shows the impact of Neptune's eccentricity damping and radial outward migration on Uranus' eccentricity, Comment: submitted to ApJ

Risk perception plays a key role in shaping the collective behavior of moving animal groups, yet the effects of variation in perceived risk within groups is unknown. Here, we merge two subgroups of fish with different levels of perceived risk, manipulated through habituation to the experimental arena, and quantitatively analyze their movement. Fish with heightened risk perception tend to occupy more central positions within the group, consistent with the selfish herd hypothesis. This behavior appears to be driven by adjusted local interactions with nearby individuals. Compared to more habituated fish, these individuals also exhibit greater coordination, shorter burst-and-coast dynamics, more efficient information transmission, and a stronger tendency to adopt follower roles. To validate the findings, we develop a machine learning tool that successfully classifies the subgroup identity of individual fish. Our study demonstrates how differences in local-scale inter-individual interactions can drive spatial assortment within groups, based on heterogeneity in the perception of risk., Comment: Main paper (12 pages) + Supplementary Information (14 pages)

We develop a python-based state-of-the-art sub-Neptune evolution model that incorporates both the post-formation boil-off at young ages $\leq$ 1 Myr and long-lived core-powered mass loss ($\sim$ Gyrs) from interior cooling. We investigate the roles of initial H/He entropy, core luminosity, energy advection, radiative atmospheric structure, and the transition to an XUV-driven mass-loss phase, with an eye on relevant timescales for planetary mass loss and thermal evolution. With particular attention to the re-equilibration process of the H/He envelope, including the energy sources that fuel the hydrodynamic wind, and energy transport timescales, we find boil-off and core-powered escape are primarily driven by stellar bolometric radiation. We further find that both boil-off and core-powered escape are decoupled from the thermal evolution. We show that, with a boil-off phase that accounts for the initial H/He mass fraction and initial entropy, post-boil-off core-powered escape has an insignificant influence on the demographics of small planets, as it is only able to remove at most 0.1% of the H/He mass fraction. Our numerical results are directly compared to previous work on analytical core-powered mass loss modeling for individual evolutionary trajectories and populations of small planets. We examine a number of assumptions made in previous studies that cause significant differences compared to our findings. We find that boil-off, though able to completely strip the gaseous envelope from a highly irradiated ($F \geq 100 F_\oplus$) planet that has a low-mass core ($M_c \leq 4M_\oplus$), cannot by itself form a pronounced radius gap as is seen in the observed population., Comment: 41 pages, 23 figures, accepted by ApJ

In organic semiconductors charge transport typically takes place via slow hopping processes. Molecular aggregation can lead to enhanced exciton and charge transport through coupling of the transition dipole moments. In this work, we investigate the optical, morphological, and electronic properties of thin films of a merocyanine dye, that aggregates due to its high ground-state dipole moment. The degree of aggregation of spin-coated thin films can be easily tuned by thermal annealing. We demonstrate the relationship between charge carrier mobility and the degree of aggregation. The mobility is increased by approximately three orders of magnitude due to aggregation. We combine variable angle spectroscopic ellipsometry and polarization-resolved absorption spectroscopy with density functional theory to demonstrate that the aggregated molecules are oriented in an upright, standing configuration relative to the substrate surface. This arrangement involves a co-facial orientation of the molecular pi-systems which is advantageous for lateral charge transport. By utilizing highly oriented pyrolytic graphite as an ordered substrate, we are able to template the growth of the merocyanine layer in vapor phase deposition, and to improve the in-plane morphological order drastically. By correlating atomic force microscopy and photoluminescence microspectroscopy we observe oriented domains of 100s of {\mu}m^2 in size, emitting linearly polarized light, whereby maintaining the edge-on molecular arrangement. This promises a further significant enhancement of lateral charge carrier mobility.

We have probed the capability of third-generation Gravitational Waves (GW) interferometers, such as the Einstein Telescope and Cosmic Explorer, to constrain a cosmological model with an interacting dark sector. We focused on GW events with a detected electromagnetic counterpart being the $\gamma$ or X emission of Gamma-Ray Burst, and a Kilonova emission. We assume the first one to be detected by the THESEUS satellite, while the second one to be detected by the Vera Rubin Observatory. We probed three different interaction kernels and found that the posterior estimation of the cosmological parameters is biased due to the existing degeneracies between the dark and matter sectors. We also found that introducing an external prior on the matter density parameter breaks the degeneracy, removes the bias results, and improves the accuracy on the dark sector parameters., Comment: 16 pages, 6 Table, and 3 Figures. Accepted for publication in Physical Review D

Tipping points (TP) are often described as low-dimensional bifurcations, and are associated with early-warning signals (EWS) due to critical slowing down (CSD). CSD is an increase in amplitude and correlation of noise-induced fluctuations away from a reference attractor as the TP is approached. But for high-dimensional systems it is not obvious which variables or observables would display the critical dynamics and carry CSD. Many variables may display no CSD, or show changes in variability not related to a TP. It is thus helpful to identify beforehand which observables are relevant for a given TP. Here we propose this may be achieved by knowledge of an unstable edge state that separates the reference from an alternative attractor that remains after the TP. This is because stochastic fluctuations away from the reference attractor are preferentially directed towards the edge state along a most likely path (the instanton). As the TP is approached the edge state and reference attractor typically become closer, and the fluctuations can evolve further along the instanton. This can be exploited to find observables with substantial CSD, which we demonstrate using conceptual dynamical systems models and climate model simulations of a collapse of the Atlantic Meridional Overturning Circulation (AMOC).

The existence of high-$\alpha$ stars with inferred ages < 6 Gyr has been confirmed recently with large spectroscopic and photometric surveys. However, stellar mergers or binary interactions can induce properties associated with young ages, such as high mass, rapid rotation, or high activity, even in old populations. Literature studies have confirmed that at least some of these apparently young stars are old merger products. However, none have ruled out the possibility of genuinely young high-$\alpha$ stars. Because cool GKM dwarfs spin down, rapid rotation can be used to indicate youth. In this paper, we provide strong evidence that truly young high-$\alpha$ stars exist by studying high-$\alpha$ rotators in the Kepler and K2 field with abundance measurements from GALAH and APOGEE. After excluding close binaries using radial velocity (RV) measurements from Gaia DR3 and multi-epoch RVs from APOGEE, we find a total of 70 high-$\alpha$ rapid rotators with periods ~10-30 days, 29 of which have lithium measurements from GALAH, indicating that they have not gone through past mass transfer or stellar merger events. We identify 10 young high-$\alpha$ candidates with no signs of merger-induced mixing or close companions. One clear example is a G dwarf with a measurable rotation and an age of 1.98$^{+0.12}_{-0.28}$ Gyr that is likely a single star with multiple RV measurements from APOGEE, has significant lithium detection from GALAH (A(Li) = 1.79), and has no signs of planet engulfment., Comment: 21 pages, 13 figures, submitted to AJ

A key initial step in mechanistic modelling of dynamical systems using first-order ordinary differential equations is to conduct a global structural identifiability analysis. This entails deducing which parameter combinations can be estimated from certain observed outputs. The standard differential algebra approach answers this question by re-writing the model as a system of ordinary differential equations solely depending on the observed outputs. Over the last decades, alternative approaches for analysing global structural identifiability based on so-called full symmetries, which are Lie symmetries acting on independent and dependent variables as well as parameters, have been proposed. However, the link between the standard differential algebra approach and that using full symmetries remains elusive. In this work, we establish this link by introducing the notion of parameter symmetries, which are a special type of full symmetry that alter parameters while preserving the observed outputs. Our main result states that a parameter combination is structurally identifiable if and only if it is a differential invariant of all parameter symmetries of a given model. We show that the standard differential algebra approach is consistent with the concept of considering structural identifiability in terms of parameter symmetries. We present an alternative symmetry-based approach, referred to as the CaLinInv-recipe, for analysing structural identifiability using parameter symmetries. Lastly, we demonstrate our approach on a glucose-insulin model and an epidemiological model of tuberculosis., Comment: 36 pages, 2 figures

Perturbative guiding center theory adequately describes the slow drift motion of charged particles in the strongly-magnetized regime characteristic of thermal particle populations in various magnetic fusion devices. However, it breaks down for particles with large enough energy. We report on a data-driven method for learning a non-perturbative guiding center model from full-orbit particle simulation data. We show the data-driven model significantly outperforms traditional asymptotic theory in magnetization regimes appropriate for fusion-born $\alpha$-particles in stellarators, thus opening the door to non-perturbative guiding center calculations., Comment: 23 pages, 4 figures, single column, double spaced

Hydrocarbon pyrolysis is a complex chemical reaction system at extreme temperature and pressure conditions involving large numbers of chemical reactions and chemical species. Only two kinds of atoms are involved: carbons and hydrogens. Its effective description and predictions for new settings are challenging due to the complexity of the system and the high computational cost of generating data by molecular dynamics simulations. On the other hand, the ensemble of molecules present at any moment and the carbon skeletons of these molecules can be viewed as random graphs. Therefore, an adequate random graph model can predict molecular composition at a low computational cost. We propose a random graph model featuring disjoint loops and assortativity correction and a method for learning input distributions from molecular dynamics data. The model uses works of Karrer and Newman (2010) and Newman (2002) as building blocks. We demonstrate that the proposed model accurately predicts the size distribution for small molecules as well as the size distribution of the largest molecule in reaction systems at the pressure of 40.5 GPa, temperature range of 3200K-5000K, and H/C ratio range from 2.25 as in octane through 4 as in methane., Comment: 58 pages, 23 figures, 3 tables