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Density of Brown measure of free circular Brownian motion
No full textWe consider the Brown measure of the free circular Brownian motion, a+t√x , with an arbitrary initial condition a , i.e. a is a general non-normal operator and x is a circular element ∗ -free from a . We prove that, under a mild assumption on a , the density of the Brown measure has one of the following two types of behavior around each point on the boundary of its support -- either (i) sharp cut, i.e. a jump discontinuity along the boundary, or (ii) quadratic decay at certain critical points on the boundary. Our result is in direct analogy with the previously known phenomenon for the spectral density of free semicircular Brownian motion, whose singularities are either a square-root edge or a cubic cusp. We also provide several examples and counterexamples, one of which shows that our assumption on a is necessary
RUBIES: JWST/NIRSpec confirmation of an infrared-luminous, broad-line Little Red Dot with an ionized outflow
No full textThe JWST discovery of "little red dots" (LRDs) is reshaping our picture of the early Universe, yet the physical mechanisms driving their compact size and UV-optical colors remain elusive. Here, we report an unusually bright LRD (zspec = 3.1) observed as part of the RUBIES program. This LRD exhibits broad emission lines (FWHM ∼ 4000 km s−1), a blue UV continuum, a clear Balmer break, and a red continuum sampled out to rest-frame 4 μm with MIRI. We develop a new joint galaxy and active galactic nucleus (AGN) model within the Prospector Bayesian inference framework and perform spectrophotometric modeling using NIRCam, MIRI, and NIRSpec/Prism observations. Our fiducial model reveals a M* ∼ 109 M⊙ galaxy alongside a dust-reddened AGN driving the optical emission. Explaining the rest-frame optical color as a reddened AGN requires AV ≳ 3, suggesting that a great majority of the accretion disk energy is reradiated as dust emission. Yet, despite clear AGN signatures, we find a surprising lack of hot torus emission, which implies that either the dust emission in this object must be cold, or the red continuum must instead be driven by a massive, evolved stellar population of the host galaxy—seemingly inconsistent with the high-EW broad lines (Hα rest-frame EW ∼ 800 Å). The widths and luminosities of Pa-β, Pa-δ, Pa-γ, and Hα imply a modest black hole mass of MBH ∼ 108 M⊙. Additionally, we identify a narrow blueshifted He i λ 1.083 μm absorption feature in NIRSpec/G395M spectra, signaling an ionized outflow with kinetic energy up to ∼1% the luminosity of the AGN. The low redshift of RUBIES-BLAGN-1, combined with the depth and richness of the JWST imaging and spectroscopic observations, provides a unique opportunity to build a physical model for these so-far mysterious LRDs, which may prove to be a crucial phase in the early formation of massive galaxies and their supermassive black holes
LNCS
No full textThe possibility of errors in human-engineered formal verification software, such as model checkers, poses a serious threat to the purpose of these tools. An established approach to mitigate this problem are certificates—lightweight, easy-to-check proofs of the verification results. In this paper, we develop novel certificates for model checking of Markov decision processes (MDPs) with quantitative reachability and expected reward properties. Our approach is conceptually simple and relies almost exclusively on elementary fixed point theory. Our certificates work for arbitrary finite MDPs and can be readily computed with little overhead using standard algorithms. We formalize the soundness of our certificates in Isabelle/HOL and provide a formally verified certificate checker. Moreover, we augment existing algorithms in the probabilistic model checker Storm with the ability to produce certificates and demonstrate practical applicability by conducting the first formal certification of the reference results in the Quantitative Verification Benchmark Set
Sound statistical model checking for probabilities and expected rewards (experimental reproduction package)
No full textArtifact to reproduce the experimental results presented in the article "Sound Statistical Model Checking for Probabilities and Expected Rewards" by Carlos E. Budde, Arnd Hartmanns, Tobias Meggendorfer, Maximilian Weininger, and Patrick Wienhöft (TACAS 2025).
The contents include all data and software (formal models, software tools, Python & bash scripts) used in the experimental evaluation presented in sections 3, 4, and 6 of the article. Detailed instructions on how to reproduce the results are bundled in the artifact
Token-driven totally asymmetric simple exclusion processes
No full textWe consider a family of totally asymmetric simple exclusion processes (TASEPs), consisting of particles on a lattice that require binding by a “token” in various physical configurations to advance over the lattice. Using a combination of theory and simulations, we address the following questions: (i) How does token binding kinetics affect the current-density relation on the lattice? (ii) How does this current-density relation depend on the scarcity of tokens? (iii) How do tokens propagate the effects of the locally imposed disorder (such as a slow site) over the entire lattice? (iv) How does a shared pool of tokens couple concurrent TASEPs running on multiple lattices? and (v) How do our results translate to TASEPs with open boundaries that exchange particles with the reservoir? Since real particle motion (including in biological systems that inspired the standard TASEP model, e.g., protein synthesis or movement of molecular motors) is often catalyzed, regulated, actuated, or otherwise mediated, the token-driven TASEP dynamics analyzed in this paper should allow for a better understanding of real systems and enable a closer match between TASEP theory and experimental observations
Probing the many-body localized spin-glass phase through quench dynamics
No full textEigenstates of quantum many-body systems are often used to define phases of matter in and out of equilibrium; however, experimentally accessing highly excited eigenstates is a challenging task, calling for alternative strategies to dynamically probe nonequilibrium phases. In this work, we characterize the dynamical properties of a disordered spin chain, focusing on the spin-glass regime. Using tensor-network simulations, we observe oscillatory behavior of local expectation values and bipartite entanglement entropy. We explain these oscillations deep in the many-body localized spin-glass regime via a simple theoretical model. From perturbation theory, we predict the timescales up to which our analytical description is valid and confirm it with numerical simulations. Finally, we study the correlation length dynamics, which, after a long-time plateau, resume growing in line with renormalization group (RG) expectations. Our work suggests that RG predictions can be quantitatively tested against numerical simulations and experiments, potentially enabling microscopic descriptions of dynamical phases in large systems
MIRI Deep Imaging Survey (MIDIS) of the Hubble Ultra Deep Field: Survey description and early results for the galaxy population detected at 5.6 µm
No full textContext. The recently launched James Webb Space Telescope (JWST) is opening new observing windows on the distant Universe. Among JWST’s instruments, the Mid Infrared Instrument (MIRI) offers the unique capability of imaging observations at wavelengths of λ > 5 μm. This enables unique access to the rest frame near-infrared (NIR, λ ≥ 1 μm) emission from galaxies at redshifts of z > 4 and the visual (λ ≳ 5000 Å) rest frame for z > 9. We report here on the guaranteed time observations (GTO), from the MIRI European Consortium, of the Hubble Ultra Deep Field (HUDF), forming the MIRI Deep Imaging Survey (MIDIS), consisting of an on source integration time of ∼41 hours in the MIRI/F560W (5.6 μm) filter. The F560W filter was selected since it would produce the deepest data in terms of AB magnitudes in a given time. To our knowledge, this constitutes the longest single filter exposure obtained with JWST of an extragalactic field as of yet.
Aims. The HUDF is one of the most observed extragalactic fields, with extensive multi-wavelength coverage, where (before JWST) galaxies up to z ∼ 7 have been confirmed, and at z > 10 suggested, from HST photometry. We aim to characterise the galaxy population in HUDF at 5.6 μm, enabling studies such as: the rest frame NIR morphologies for galaxies at z ≲ 4.6, probing mature stellar populations and emission lines in z > 6 sources, intrinsically red and dusty galaxies, and active galactic nuclei (AGNs) and their host galaxies at intermediate redshifts.
Methods. We reduced the MIRI data using the official JWST pipeline, augmented by in-house custom scripts. We measured the noise characteristics of the resulting image. Galaxy photometry was obtained, and photometric redshifts were estimated for sources with available multi-wavelength photometry (and compared to spectroscopic redshifts when available).
Results. Over the deepest part of our image, the 5σ point source limit is 28.65 mag AB (12.6 nJy), ∼0.35 mag better than predicted by the JWST exposure time calculator. We find ∼2500 sources, the overwhelming majority of which are distant galaxies, but we note that spurious sources likely remain at faint magnitudes due to imperfect cosmic ray rejection in the JWST pipeline. More than 500 galaxies with available spectroscopic redshifts, up to z ≈ 11, have been identified, the majority of which are at z 100 objects with very red NIRCam vs MIRI (3.6–5.6 μm > 1 mag) colours have been found, suggestive of dusty or old stellar populations at high redshifts.
Conclusions. We conclude that MIDIS surpasses preflight expectations and that deep MIRI imaging has great potential to characterise the galaxy population from cosmic noon to dawn
Pulsatile basal gene expression as a fitness determinant in bacteria
No full textActive regulation of gene expression, orchestrated by complex interactions of activators and repressors at promoters, controls the fate of organisms. In contrast, basal expression at uninduced promoters is considered to be a dynamically inert mode of nonfunctional “promoter leakiness,” merely a byproduct of transcriptional regulation. Here, we investigate the basal expression mode of the mar operon, the main regulator of intrinsic multiple antibiotic resistance in Escherichia coli, and link its dynamic properties to the noncanonical, yet highly conserved start codon of marR across Enterobacteriaceae. Real-time, single-cell measurements across tens of generations reveal that basal expression consists of rare stochastic gene expression pulses, which maximize variability in wildtype and, surprisingly, transiently accelerate cellular elongation rates. Competition experiments show that basal expression confers fitness advantages to wildtype across several transitions between exponential and stationary growth by shortening lag times. The dynamically rich basal expression of the mar operon has likely been evolutionarily maintained for its role in growth homeostasis of Enterobacteria within the gut environment, thereby allowing other ancillary gene regulatory roles to evolve, e.g., control of costly-to-induce multidrug efflux pumps. Understanding the complex selection forces governing genetic systems involved in intrinsic multidrug resistance is crucial for effective public health measures
Simplet-based signatures and approximation in simplicial complexes: Frequency, degree, and centrality
No full textSimplets are elementary units within simplicial complexes and are fundamental for analyzing the structure of simplicial complexes. Previous efforts have mainly focused on accurately counting or approximating the number of simplets rather than studying their frequencies. However, analyzing simplet frequencies is more practical for large-scale simplicial complexes. This paper introduces the Simplet Frequency Distribution (SFD) vector, which enables the analysis of simplet frequencies in simplicial complexes. Additionally, we provide a bound on the sample complexity required to approximate the SFD vector using any uniform sampling-based algorithm accurately. We extend the definition of simplet frequency distribution to encompass simplices, allowing for the analysis of simplet frequencies within simplices of simplicial complexes. This paper introduces the Simplet Degree Vector (SDV) and the Simplet Degree Centrality (SDC), facilitating this analysis for each simplex. Furthermore, we present a bound on the sample complexity required for accurately approximating the SDV and SDC for a set of simplices using any uniform sampling-based algorithm. We also introduce algorithms for approximating SFD, geometric SFD, SDV, and SDC. We also validate the theoretical bounds with experiments on random simplicial complexes and demonstrate the practical application through a case study