Search

In order to formally verify robotic controllers, we must tackle the inherent uncertainty of sensing and actuation in a physical environment. We can model uncertainty using stochastic hybrid systems, which combine discrete jumps with continuous, stochastic behaviour. The verification of these systems is intractable for state-exploration based approaches, so we instead propose a deductive verification approach. As a first step towards a deductive verification tool, we present a mechanisation of Brownian motion within Isabelle/HOL. For this, we mechanise stochastic kernels and Markov semigroups, which allow us to specify a range of processes with stationary, independent increments. Further, we prove the Kolmogorov-Chentsov theorem, which allows us to construct H\"older continuous modifications of processes that satisfy certain bounds on their expectation. This paves the way for modelling and verifying stochastic hybrid systems in Isabelle/HOL.

Galaxy clusters are the most massive, gravitationally-bound structures in the Universe, emerging through hierarchical structure formation of large-scale dark matter and baryon overdensities. Early galaxy ``proto-clusters'' are believed to be important physical drivers of the overall cosmic star-formation rate density and serve as ``hotspots'' for the reionization of the intergalactic medium. Our understanding of the formation of these structures at the earliest cosmic epochs is, however, limited to sparse observations of their galaxy members, or based on phenomenological models and cosmological simulations. Here we report the detection of a massive neutral, atomic hydrogen (HI) gas reservoir permeating a galaxy proto-cluster at redshift $z=5.4$, observed one billion years after the Big Bang. The presence of this cold gas is revealed by strong damped Lyman-$\alpha$ absorption features observed in several background galaxy spectra taken with JWST/NIRSpec in close on-sky projection. While overall the sightlines probe a large range in HI column densities, $N_{\rm HI} = 10^{21.7}-10^{23.5}$ cm$^{-2}$, they are similar across nearby sightlines, demonstrating that they probe the same dense, neutral gas. This observation of a massive, large-scale overdensity of cold neutral gas challenges current large-scale cosmological simulations and has strong implications for the reionization topology of the Universe., Comment: Submitted

We give conditions on sequences of positive algebraic numbers $\{a_{n,j}\}_{n=1}^\infty$, $j=1,\dots ,M$ and number field $\mathbb K$ to ensure that the numbers defined by the continued fractions $[0;a_{1,j},a_{2,j},\dots ]$, $j=1,\dots ,M$ and $1$ are linearly independent over $\mathbb K$.

Insect production for food and feed presents a promising supplement to ensure food safety and address the adverse impacts of agriculture on climate and environment in the future. However, optimisation is required for insect production to realise its full potential. This can be by targeted improvement of traits of interest through selective breeding, an approach which has so far been underexplored and underutilised in insect farming. Here we present a comprehensive review of the selective breeding framework in the context of insect production. We systematically evaluate adjustments of selective breeding techniques to the realm of insects and highlight the essential components integral to the breeding process. The discussion covers every step of a conventional breeding scheme, such as formulation of breeding objectives, phenotyping, estimation of genetic parameters and breeding values, selection of appropriate breeding strategies, and mitigation of issues associated with genetic diversity depletion and inbreeding. This review combines knowledge from diverse disciplines, bridging the gap between animal breeding, quantitative genetics, evolutionary biology, and entomology, offering an integrated view of the insect breeding research area and uniting knowledge which has previously remained scattered across diverse fields of expertise.

Gas kinematics affect the radiative transfer and escape of hydrogen Lyman-$\alpha$ (Ly$\alpha$) emission from galaxies. We investigate this interplay empirically by relating the ionised gas kinematics of 42 galaxies in the extended Ly$\alpha$ Reference Sample with their Ly$\alpha$ escape fractions, $f_\rm{esc}$, Ly$\alpha$ equivalent widths, $\rm{EW}_\rm{Ly\alpha}$, and Ly$\alpha$ luminosities, $L_\rm{Ly\alpha}$. To this aim we use PMAS integral-field spectroscopic observations of the Balmer-$\alpha$ line. We calculate shearing velocities, $v_\rm{shear}$, and intrinsic velocity dispersions, $\sigma_0^\rm{obs}$ (empirically corrected for beam-smearing effects), as global kinematical measures for each galaxy. The sample is characterised by highly turbulent motions and more than half of the sample shows dispersion dominated kinematics. We uncover clear trends between Ly$\alpha$ observables and global kinematical statistics. We discuss statistically the importance of $v_\rm{shear}$, $\sigma_0^\rm{obs}$, and $v_\rm{shear}/\sigma_0^\rm{obs}$ for regulating the Ly$\alpha$ observables in comparison to other galaxy parameters. It emerges that $\sigma_0^\rm{obs}$ is the dominating parameter for $\rm{EW}_\rm{Ly\alpha}$ and that is as important as nebular extinction, gas covering fraction, and ionising photon production efficiency in regulating $f_\rm{esc}$. A simple scenario where the starburst age is simultaneously regulating turbulence, $\rm{EW}_\rm{Ly\alpha}$, and $f_\rm{esc}$ does not find support by our observations. However, we show that the small scale distribution of dust appears to be influenced by turbulence in some galaxies. In support of our observational result we discuss how turbulence is theoretically expected to play a significant role in modulating $f_\rm{esc}$. (abridged), Comment: Accepted version for publication in A&A

One of the surprising early findings with JWST has been the discovery of a strong "roll-over" or a softening of the absorption edge of Ly$\alpha$ in a large number of galaxies at ($z\gtrsim 6$), in addition to systematic offsets from photometric redshift estimates and fundamental galaxy scaling relations. This has been interpreted as damped Ly$\alpha$ absorption (DLA) wings from high column densities of neutral atomic hydrogen (HI), signifying major gas accretion events in the formation of these galaxies. To explore this new phenomenon systematically, we assemble the JWST/NIRSpec PRImordial gas Mass AssembLy (PRIMAL) legacy survey of 494 galaxies at $z=5.5-13.4$. We characterize this benchmark sample in full and spectroscopically derive the galaxy redshifts, metallicities, star-formation rates, and ultraviolet slopes. We define a new diagnostic, the Ly$\alpha$ damping parameter $D_{\rm Ly\alpha}$ to measure and quantify the Ly$\alpha$ emission strength, HI fraction in the IGM, or local HI column density for each source. The JWST-PRIMAL survey is based on the spectroscopic DAWN JWST Archive (DJA-Spec). All the software, reduced spectra, and spectroscopically derived quantities and catalogs are made publicly available in dedicated repositories. The fraction of strong galaxy DLAs are found to be in the range $65-95\%$ at $z>5.5$. The fraction of strong Ly$\alpha$ emitters (LAEs) is found to increase with decreasing redshift, in qualitative agreement with previous observational results, and are predominantly associated with low-metallicity and UV faint galaxies. By contrast, strong DLAs are observed in galaxies with a variety of intrinsic physical properties. Our results indicate that strong DLAs likely reflect a particular early assembly phase of reionization-era galaxies, at which point they are largely dominated by pristine HI gas accretion. [abridged], Comment: 20 pages, 18 figures, 3 tables. Submitted to A&A. Comments welcome! All data and catalogs are available through the DAWN JWST Archive (DJA): https://dawn-cph.github.io/dja/ and https://github.com/keheintz/jwst-primal

As the nearest confirmed Lyman continuum (LyC) emitter, Haro 11 is an exceptional laboratory for studying LyC escape processes crucial to cosmic reionization. Our new HST/COS G130M/1055 observations of its three star-forming knots now reveal that the observed LyC originates in Knots B and C, with $903 - 912~\r{A}$ luminosities of $1.9\pm1.5 \times 10^{40}~\rm erg~s^{-1}$ and $0.9\pm0.7 \times 10^{40}~\rm erg~s^{-1}$, respectively. We derive local escape fractions $f_{\rm{esc, 912}} = 3.4\pm2.9\%$ and $5.1\pm4.3\%$ for Knots B and C, respectively. Our Starburst99 modeling shows dominant populations on the order of $\sim1-4$ Myr and $1-2\times10^7 \rm~M_\odot$ in each knot, with the youngest population in Knot B. Thus, the knot with the strongest LyC detection has the highest LyC production. However, LyC escape is likely less efficient in Knot B than in Knot C due to higher neutral gas covering. Our results therefore stress the importance of the intrinsic ionizing luminosity, and not just the escape fraction, for LyC detection. Similarly, the Ly$\alpha$ escape fraction does not consistently correlate with LyC flux, nor do narrow Ly$\alpha$ red peaks. High observed Ly$\alpha$ luminosity and low Ly$\alpha$ peak velocity separation, however, do correlate with higher LyC escape. Another insight comes from the undetected Knot A, which drives the Green Pea properties of Haro 11. Its density-bounded conditions suggest highly anisotropic LyC escape. Finally, both of the LyC-leaking Knots, B and C, host ultra-luminous X-ray sources (ULXs). While stars strongly dominate over the ULXs in LyC emission, this intriguing coincidence underscores the importance of unveiling the role of accretors in LyC escape and reionization., Comment: 22 pages, 5 figures. Accepted for publication in The Astrophysical Journal

Realizing lattices of exciton polariton condensates has been of much interest owing to the potential of such systems to realize analog Hamiltonian simulators and physical computing architectures. Prior work on polariton condensate lattices has primarily been on GaAs-based systems, with the recent advent of organic molecules and perovskite systems allowing room-temperature operation. However, in most of these room temperature systems, the lattices are defined using a bottom-up approach by patterning the bottom mirrors, significantly limiting the types of lattices and refractive index contrast that can be realized. Here, we report a direct write approach that uses a Focused Ion Beam (FIB) to etch 2D lattice into a planar microcavity. Such etching of the cavity allows for realizing high refractive index contrast lattices. We realize the polariton condensate lattice using the highly photostable host-guest Frenkel excitons of an organic dye small molecular ionic lattice (SMILES).1,2 The lattice structures are defined on a planar microcavity embedded with SMILES using FIB, allowing the realization of lattices with different geometries, including defect sites on demand. The band structure of the lattice and the emergence of condensation are imaged using momentum-resolved spectroscopy. The present approach allows us to study periodic, quasi-periodic, and disordered polariton condensate lattices at room temperature using a top-down approach without compromising on the quantum yield of the organic excitonic material embedded in the cavity.

We formally introduce IsaVODEs (Isabelle verification with Ordinary Differential Equations), a framework for the verification of cyber-physical systems. We describe the semantic foundations of the framework's formalisation in the Isabelle/HOL proof assistant. A user-friendly language specification based on a robust state model makes our framework flexible and adaptable to various engineering workflows. New additions to the framework increase both its expressivity and proof automation. Specifically, formalisations related to forward diamond correctness specifications, certification of unique solutions to ordinary differential equations (ODEs) as flows, and invariant reasoning for systems of ODEs contribute to the framework's scalability and usability. Various examples and an evaluation validate the effectiveness of our framework., Comment: Submitted to the Journal of Automated Reasoning

In this paper, harkening back to ideas of Hardy and Ramanujan, Mahler and de Bruijn, with the addition of more recent results on the Fibonacci Dirichlet series, we determine the asymptotic number of ways $p_F(n)$ to write an integer as the sum of non-distinct Fibonacci numbers. This appears to be the first such asymptotic result concerning non-distinct partitions over Fibonacci numbers. As well, under weak conditions, we prove analogous results for a general linear recurrences., Comment: 17 Pages. V2 does not address distinct partitions--there was a nuanced (fatal) flaw in that part of the paper

Timescales in astronomy comprise the largest range of any scientific discipline. In the construction of physical models, this circumstance may both be a blessing and a curse. For example, galaxy evolution occurs on typical timescales of hundreds of millions of years, but is affected by atomic processes on sub-second timescales, posing a challenge in analytical and, in particular, in numerical models. On the other hand, the vast dynamic range implies that we can often make meaningful predictions by simply comparing characteristic timescales of the physical processes involved. This review, aimed primarily at non-astronomer scientists, attempts to highlight some occasions in the context of galaxy formation and evolution in which comparing timescales can shed light on astrophysical phenomena, as well as some of the challenges that may be encountered. In particular we will explore the differences and similarities between theoretical predictions of dark matter halos, and the observed distribution of galaxies. The review concludes with an account of the most recent observations with the James Webb Space Telescope, and how they purportedly seem to defy the timescales of the currently accepted concordance model of the structure and evolution of the Universe, the {\Lambda}CDM model., Comment: A review-like tale of the physics leading to the formation of galaxies, aimed at non-astronomer scientists, but also of interest to students of astronomy, with several illustrative figures. Published on Springer Mathematics Online First Collections. To appear in the multidisciplinary anthology "Multiplicity of Time Scales in Complex Systems" (ed.: Dr. Bernhelm Booss-Bavnbek, Roskilde University)

Using Schmidt's Subspace Theorem, this paper improves and extends an existing transcendence result for sequences of algebraic numbers. The theorems thus produced correspond to a central theorem on the irrationality of sequences due to Erd\H{o}s., Comment: 28 pages

The onset of galaxy formation is thought to be initiated by the infall of neutral, pristine gas onto the first protogalactic halos. However, direct constraints on the abundance of neutral atomic hydrogen (HI) in galaxies have been difficult to obtain at early cosmic times. Here we present spectroscopic observations with JWST of three galaxies at redshifts $z=8.8 - 11.4$, about $400-600$ Myr after the Big Bang, that show strong damped Lyman-$\alpha$ absorption ($N_{\rm HI} > 10^{22}$ cm$^{-2}$) from HI in their local surroundings, an order of magnitude in excess of the Lyman-$\alpha$ absorption caused by the neutral intergalactic medium at these redshifts. Consequently, these early galaxies cannot be contributing significantly to reionization, at least at their current evolutionary stages. Simulations of galaxy formation show that such massive gas reservoirs surrounding young galaxies so early in the history of the universe is a signature of galaxy formation in progress., Comment: Submitted

Exciton-polaritons (EP), half-light half-matter quasiparticles that form in optical cavities, are attractive platforms for creating macroscopic coherent states like BECs. EPs based on organic molecules are of particular interest for realizing such states at room temperature while offering the promise of synthetic tunability. However, the demonstrations of such condensates have been limited to a few specific molecular systems1. Here we report a universal platform for realizing molecular polariton condensates using commercial dyes that solves long standing material challenges. This solution is made possible using a new and programable molecular material called small-molecule, ionic isolation lattices (SMILES) with the potential to incorporate a wide array of molecular fluorophores2. We show EP condensation in rhodamine by incorporating it into SMILES lattice placed in a planar microcavity. The SMILES approach overcomes the major drawbacks of organic molecular photophysical systems such as self-quenching, which sets the foundation for realizing practical polaritonic devices operating at ambient temperatures covering wide spectral range.

We present Ly $\alpha$ imaging of 45 low redshift star-forming galaxies observed with the Hubble Space Telescope. The galaxies have been selected to have moderate to high star formation rates using far-ultraviolet (FUV) luminosity and \ha equivalent width criteria, but no constraints on Ly $\alpha$ luminosity. We employ a pixel stellar continuum fitting code to obtain accurate continuum subtracted Ly $\alpha$, H $\alpha$ and H $\beta$ maps. We find that Ly $\alpha$ is less concentrated than FUV and optical line emission in almost all galaxies with significant Ly $\alpha$ emission. We present global measurements of Ly $\alpha$ and other quantities measured in apertures designed to capture all of the Ly $\alpha$ emission. We then show how the escape fraction of Ly $\alpha$ relates to a number of other measured quantities (mass, metallicity, star formation, ionisation parameter, and extinction). We find that the escape fraction is strongly anti-correlated with nebular and stellar extinction, weakly anti-correlated with stellar mass, but no conclusive evidence for correlations with other quantities. We show that Ly $\alpha$ escape fractions are inconsistent with common dust extinction laws, and discuss how a combination of radiative transfer effects and clumpy dust models can help resolve the discrepancies. We present a star formation rate calibration based on Ly $\alpha$ luminosity, where the equivalent width of Ly $\alpha$ is used to correct for non-unity escape fraction, and show that this relation provides a reasonably accurate SFR estimate. We also show stacked growth curves of Ly $\alpha$ for the galaxies that can be used to find aperture loss fractions at a given physical radius., Comment: 48 pages, 21 figures, accepted for publication in The Astrophysical Journal Supplement Series. Multipanel figures for all 45 galaxies will be available in the online version of the published paper (and here: https://stockholmuniversity.box.com/s/ghvnvjyhxts64hpbqh90uwcj5dlczlhm ). Data products will be available as a MAST HLSP soon (placeholder DOI: 10.17909/pbe1-m743)

This paper settles recent conjectures concerning the $p$-adic Haar measure applied to a family of sets defined in terms of Diophantine approximation. This is done by determining the spectrum of measure values for each family and seeing that this contradicts the corresponding conjectures., Comment: 28 pages