The mass assembly and chemical enrichment of the first galaxies provide key insights into their star-formation histories and the earliest stellar populations at cosmic dawn. Here we compile and utilize new, high-quality spectroscopic JWST/NIRSpec Prism observations from the JWST archive. We extend the wavelength coverage beyond the standard pipeline cutoff up to 5.5$μ$m, enabling a detailed examination of the rest-frame optical emission-line properties for galaxies at $z\approx 10$. The improved calibration allows us to detect H$β$ and the [OIII]$λλ4959,5007$ doublet and resolve the auroral [OIII]$λ4363$ line for the 11 galaxies in our sample ($z=9.3-10.0$) to obtain direct $T_e$-based metallicity measurements. We find that all galaxies show high ionisation fields and electron temperatures, with derived metallicities in the range $12+\log {\rm (O/H)} = 7.1 - 8.3$, consistent with previous strong-line diagnostics at high-z. We derive an empirical relation for $M_{\rm UV}$ and 12+log(O/H) at $z\approx 10$, useful for future higher-z studies, and show that the sample galaxies are `typical' star-forming galaxies though with relatively high specific star-formation rates and with evidence for bursty star formation. Combining the rest-frame optical line analysis and detailed UV to optical SED modelling, we determine the mass-metallicity relation and the fundamental-metallicity relation of the sample, pushing the redshift frontier of these measurements to $z=10$. These results, together with literature measurements, point to a gradually decreasing MZR at higher redshifts, with a break in the FMR at $z\approx 3$, decreasing to metallicities $\approx 3\times$ lower at $z=10$ than observed during the majority of cosmic time at $z=0-3$, likely caused by massive pristine gas inflows diluting the observed metal abundances during early galaxy assembly at cosmic dawn.

Free-floating planetary mass objects--worlds that roam interstellar space untethered to a parent star--challenge conventional notions of planetary formation and migration, but also of star and brown dwarf formation. We focus on the multiplicity among free-floating planets. By virtue of their low binding energy (compared to other objects formed in these environments), these low-mass substellar binaries represent a most sensitive probe of the mechanisms at play during the star formation process. We use the HST and its WFC3 and the VLT and its ERIS AO facility to search for visual companions among a sample of 77 objects members of the USco and Taurus young nearby associations with estimated masses in the range between approximately 6-66 M$_{\rm Jup}$. We report the discovery of one companion candidate around a Taurus member with a separation of 111.9$\pm$0.4~mas, or $\sim$18~au assuming a distance of 160~pc, with an estimated primary mass in the range between 3--6~M$_{\rm Jup}$and a secondary mass between 2.6--5.2~M$_{\rm Jup}$ depending on the assumed age. This corresponds to an overall binary fraction of 1.8$^{+2.6}_{-1.3}$\% among low-mass brown dwarfs and free-floating planetary mass objects over the separation range $\ge$7~au. Despite the limitations of small-number statistics and variations in spatial resolution and sensitivity, our results, combined with previous high-spatial-resolution surveys, suggest a notable difference in the multiplicity properties of objects below $\sim$30--50~M$_{\rm Jup}$ between USco and Taurus. In Taurus, a binary fraction of $5.6^{+3.2}_{-2.3}$\% is found for objects with masses below 30M$_{\rm Jup}$, and of $7.8^{+3.0}_{-2.4}$\% for objects with masses below 50M$_{\rm Jup}$, whereas no binary were found among 80 objects over the matching luminosity range in USco, corresponding to an upper limit of $\le$1.2\%.

In this work, we show that extending the standard description of space-time symmetries from groups of isometries to the more flexible framework of kinematical groupoids allows for the extension of Wigner's program to curved space-times. We propose a new definition of elementary particles as irreducible projective representations of the kinematical groupoids supporting the theory. By choosing a natural kinematical groupoid associated with any space-time, called the \textit{Wigner groupoid}, we demonstrate that such irreducible projective representations are characterized by quantum numbers similar to those characterizing the irreducible projective representations of the Poincaré group. Describing the irreducible projective representations of groupoids poses its own difficulties. To address this, we develop a suitable extension of Mackey's theory of induced representations of groups, proving that projective representations of transitive Lie groupoids with connected isotropy groups are in one-to-one correspondence with the projective representations of their isotropy groups. The application of these results provides a classification of elementary particles valid for a large class of space-times. This classification largely reproduces Wigner's standard classification on Minkowski space-time, while a new family of representations emerges, corresponding to massless particles in the presence of a magnetic-like background field.

Subspace clustering becomes inherently difficult near intersections, where points from different subspaces are barely separated. Most existing theoretical results address this issue by imposing separation or sampling assumptions that limit the statistical effect of points near the intersection. We study a minimal setting of two intersecting lines in which the latent sampling law places polynomially large mass in small neighborhoods of the intersection. We derive information-theoretic lower bounds for exact and almost exact recovery under Gaussian noise. In particular, we show that the exact-recovery threshold is determined by the rate at which the latent law concentrates near the intersection. Since any two points are collinear, pairwise information alone does not reveal whether they are sampled from the same latent line. We therefore construct a hypergraph in which nearly collinear triples form hyperedges, and study the resulting hypergraph similarity matrix. Under a simple regularity condition on the latent distribution, we introduce a spectral algorithm that achieves the information-theoretic bounds up to polylogarithmic factors.

About 30\% of disk galaxies show lopsidedness in their stellar disk. Although such a large-scale asymmetry in the disk can be primarily looked upon as a long-lived mode ($m=1$), the physical origin of the lopsidedness in the disk continues to be a puzzle. In this work, we employ a transfer-learning approach for the automated identification of lopsided galaxies using SDSS DR18 imaging by fine-tuning a Zoobot model, a deep convolutional neural network package pre-trained on the Galaxy Zoo dataset. We obtain 7,042 well-resolved, nearly face-on spiral galaxies from SDSS DR18 over the redshift range 0.01 $\leq z \leq 0.1$, with extinction-corrected g-band model magnitude < 16 and Petrosian radius (enclosing 90 \% of the flux) $\geq$ 3 arcsec. Out of these, we visually identify 490 lopsided and 444 symmetric galaxy samples suitable for training. The trained model achieves a testing accuracy of $(87 \pm 0.02)$ \%, averaged over 10 independent trials. Using the best-performing model, we identify 3,679 lopsided and 2,429 symmetric galaxies from the remaining sample. Of these, 2,658 lopsided and 1,455 symmetric galaxies are predicted with are predicted with high prediction probability $P_{pred} \geq 0.85$. Lopsided galaxies in our predicted samples are relatively high star-forming, bluer, low-concentration (late-type), low-mass galaxies compared to the symmetric galaxies. Our study produces an usable catalogue of lopsided and symmetric galaxies, which will offer new insights into the formation of lopsidedness in disk galaxies. The dataset and the best-performing model are made publicly available through GitHub at https://github.com/bijusaha-astro/CNN_lopsided

Amortized Bayesian inference (ABI) with neural networks has emerged as a powerful simulation-based approach for estimating complex mechanistic models. However, extending ABI to hierarchical models, a cornerstone of modern Bayesian analysis, has been a major hurdle due to the need to simulate and process massive datasets. Our study tackles these challenges by extending compositional score matching (CSM), a divide-and-conquer strategy for Bayesian updating using diffusion models. We develop a new error-damping estimator to address previous stability issues of CSM when aggregating large numbers of data points. We first verified the numerical stability with up to 100,000 data points on a controlled benchmark. We then evaluated our method on a hierarchical AR model, achieving competitive performance to direct ABI baselines on smaller problem sizes while using less than one full model simulation for larger problem sizes. Finally, we address a large-scale inverse problem in advanced microscopy with over 750,000 parameters, demonstrating its relevance to real scientific applications.

In this short paper, we investigate the impact of selecting only a subset of bright galaxies to provide redshift information for a dark standard siren measurement of the Hubble constant $H_0$. Employing gravitational-wave observations from the Third Gravitational-Wave Transient Catalogue (GWTC-3) in conjunction with the GLADE+ galaxy catalogue, we show that restricting to bright galaxy subsets can enhance the precision of the $H_0$ estimate by up to $80\%$ in the most favorable scenario. A comprehensive assessment of systematic uncertainties is still required. This work lays the foundation for employing alternative tracers -- such as brightest cluster galaxies (BCGs) and luminous red galaxies (LRGs) -- in gravitational-wave cosmology, particularly at redshifts where conventional galaxy catalogues offer limited coverage.

We investigate a class of slow roll inflationary models in the light of the recent Cosmic Microwave Background constraints from Planck 2018, ACT DR6, DESI DR1, and BICEP/\textit{Keck} 2018. The combined dataset favors a higher value of the scalar spectral index $n_{_\mathrm{S}}=0.9743 \pm 0.0034$, which places increased pressure on several conventional inflationary scenarios. In this study, we analyze the observational viability of various well-motivated models, including the $α$-attractor E- and T-models, chaotic inflation, hilltop inflation, and natural inflation. We incorporate the effects of a post-inflationary phase of reheating and examine how the dynamics of reheating influence the predictions in the $n_{_\mathrm{S}}-r$ plane. We also impose a lower bound on the reheating temperature based on the constraint from the effective number of relativistic species ($Δ{N}_{\mathrm{eff}}$) arising from primordial gravitational waves. While reheating improves agreement with observations for some models, significant regions of parameter space remain disfavored. Finally, we explore the impact of a non Bunch-Davies initial state and demonstrate that it can substantially improve the fit to the $n_{_\mathrm{S}}-r$ data across a broader class of inflationary models, thereby offering a potentially viable mechanism for reconciling theory with the latest observations.

This paper grew out of the author's work on arXiv:2504.18460. Differential operators in the sense of Grothendieck acting between modules over a commutative ring can be interpreted as torsion elements in the bimodule of all operators with respect to the diagonal ideal in the tensor square of the ring. Various notions of torsion modules for an infinitely generated ideal in a commutative ring lead to various notions of differential operators. We discuss differential operators of transfinite orders and differential operators having no global order at all, but only local orders with respect to specific elements of the ring. Many examples are presented. In particular, we prove that every ordinal can be realized as the order of a differential operator acting on the algebra of polynomials in infinitely many variables over a field. We also discuss extension of differential operators to localizations of rings and modules, and to colocalizations of modules.

With the promise of greater decentralization and sustainability, Ethereum transitioned from a Proof-of-Work (PoW) to a Proof-of-Stake (PoS) consensus mechanism. The new consensus protocol introduces novel vulnerabilities that warrant further investigation. The goal of this paper is to investigate the security of Ethereum's PoS system from an Internet routing perspective. To this end, this paper makes two contributions: First, we devise a novel framework for inferring the distribution of validators on the Internet without disturbing the real network. Second, we introduce a class of network-level attacks on Ethereum's PoS system that jointly exploit Internet routing vulnerabilities with the protocol's reward and penalty mechanisms. We describe two representative attacks: StakeBleed, where the attacker triggers an inactivity leak, halting block finality and causing financial losses for all validators; and KnockBlock, where the attacker increases her expected MEV gains by preventing targeted blocks from being included in the chain. We find that both attacks are practical and effective. An attacker executing StakeBleed can inflict losses of almost 300 ETH in just 2 hours by hijacking as few as 30 IP prefixes. An attacker implementing KnockBlock could increase their MEV expected gains by 44.5% while hijacking a single prefix for less than 2 minutes. Our paper serves as a call to action for validators to reinforce their Internet routing infrastructure and for the Ethereum P2P protocol to implement stronger mechanisms to conceal validator locations.

We consider fully discrete numerical approximations for axisymmetric Willmore flow that are unconditionally stable and work reliably without remeshing. We restrict our attention to surfaces without boundary, but allow for spontaneous curvature effects. The axisymmetric setting allows us to formulate our schemes in terms of the generating curve of the considered surface. We propose a novel weak formulation, that combines an evolution equation for the surface's mean curvature and the curvature identity of the generating curve. The mean curvature is used to describe the gradient flow structure, which enables an unconditional stability result for the discrete solutions. The generating curve's curvature, on the other hand, describes the surface's in-plane principal curvature and plays the role of a Lagrange multiplier for an equidistribution property on the discrete level. We introduce two fully discrete schemes and prove their unconditional stability. Numerical results are provided to confirm the convergence, stability and equidistribution properties of the introduced schemes.

We examine the validity of a potential extension of the adiabatic theorem to quantum quenches, i.e., nonadiabatic changes. In particular, the transverse field Ising model (TFIM) and the axial next nearest neighbor Ising (ANNNI) model are studied. The proposed extension of the adiabatic theorem is stated as follows: Consider the overlap between the initial ground state and the postquench Hamiltonian eigenstates for quenches within the same phase. This overlap is largest for the postquench ground state. In the case of the TFIM, this conjecture is confirmed for both the paramagnetic and ferromagnetic phases numerically and analytically. In the ANNNI model, the conjecture could be analytically proven for a special case. Numerical methods were employed to investigate the conjecture's validity beyond this special case.

We study random dynamical systems composed of LSV maps with varying parameters, without any mixing assumptions on the base space of random dynamics. We establish a quenched central limit theorem and identify conditions under which the associated limit variance varies continuously and differentiably with respect to perturbations of the random dynamics. Our arguments rely on recent results on statistical stability and linear response for random intermittent maps established in Dragicevic et al. (J. Lond. Math. Soc. 111 (2025), e70150).

The mass range of observed black holes extends from stellar-mass to supermassive scales, yet the existence of objects in the intermediate-mass range of $10^{2} - 10^{5} \text{M}_{\odot}$ remains unconfirmed. Black holes are suspected to compress the surrounding dark matter distribution, forming a ``spike''. If dark matter is self-annihilating, the spike could produce gamma-ray emission sufficiently luminous to be detected. This work aims to estimate the number of expected unmerged intermediate-mass black holes in a Milky Way-like galaxy that could form such spikes. These intermediate-mass black holes are assumed to have formed from the collapse of high-mass Population III stars, such that the resulting merger rate is constrained by observations of gravitational wave emission. It is furthermore estimated to what extent the progenitor Population III stars contribute to the extragalactic background light. The Population III stars are simulated and tracked using the A-SLOTH semi-analytical simulation code and the resulting number of intermediate-mass black holes is constrained by applying the Population III binary black hole merger rate to an effective volume determined from the Population III star formation rate. In this framework, $\sim 130$ unmerged IMBHs from Population III stars are expected to reside in a Milky Way-like galaxy. The contribution of their progenitors to the extragalactic background light in the near-infrared is less than $10^{-3} \text{nW} \text{m}^{-2} \text{sr}^{-1}$, well below previous estimates.

We investigate the evolutionary histories of a population of high mass, high redshift, quiescent galaxies in the cosmohydrodynamical simulation Thesan, studying the characteristic properties of their haloes and environments over the epoch of reionisation. Thesan employs a modified version of the Arepo moving-mesh code utilised in IllustrisTNG, which incorporates on-the-fly radiative transfer to couple haloes and galaxies with the evolving radiation field. Thesan exhibits nine massive quiescent galaxies at $z=5.5$, in a $(95.5 \text{cMpc})^3$ volume, with no counterpart in IllustrisTNG. A numerical issue in the simulation reduces AGN feedback efficiency by a factor of 25 while enhancing accretion rates, creating a regime of suppressed feedback. We find their stellar mass assembles rapidly through smooth halo accretion in dense environments, particularly from massive neighbouring structures, while their early-forming haloes develop fast-growing potential wells hosting massive black holes. This suppressed feedback allows prolonged black hole growth before eventual kinetic-mode quenching, providing insight into galaxy evolution under weakened AGN regulation. We find that megaparsec-scale overdensities and halo masses continue growing after quenching, suggesting these galaxies will reside in some of the largest haloes and densest regions of space by $z=6$. With massive quiescent galaxies found in JWST data, the identification of such galaxies in Thesan enables isolation of halo and environmental conditions most conducive to their evolution under this suppressed feedback regime, guiding future deep surveys and N-body simulation studies of analogous systems.

Blockchains rely on economic incentives to ensure secure and decentralised operation, making incentive compatibility a core design concern. However, protocols are rarely deployed in isolation. Applications interact with the underlying consensus and network layers, and multiple protocols may run concurrently on the same chain. These interactions give rise to complex incentive dynamics that traditional, isolated analyses often fail to capture. We propose the first compositional game-theoretic framework for blockchain protocols. Our model represents blockchain protocols as interacting games across the application, network, and consensus layers. It enables formal reasoning about incentive compatibility under composition by introducing two key abstractions: the cross-layer game, which models how strategies in one layer influence others, and cross-application composition, which captures how application protocols interact concurrently through shared infrastructure. We illustrate our framework through case studies on Hashed Timelock Contracts (HTLCs), Layer-2 protocols, and Maximal Extractable Value (MEV) showing how compositional analysis reveals new subtle incentive vulnerabilities and supports modular security proofs. Also, by introduction of a novel rational miner model, we derive new conditions for the robustness of timelocks to bribing attacks.

A bootstrap program is presented for algebraically solving the $R$-matrix of a generic integrable quantum spin chain from its Hamiltonian. The Yang-Baxter equation contains an infinite number of seemingly independent constraints on the operator valued coefficients in the expansion of the $R$-matrices with respect to their spectral parameters, with the lowest order one being the Reshetikhin condition. These coefficients can be solved iteratively in a self consistent way using a lemma due to Kennedy, which reconstructs the $R$-matrix after an infinite number of steps. For a generic Hamiltonian, the procedure could fail at any step, making the conditions useful as an integrability test. However, at least for the most common examples, they always turn out to be satisfied whenever the lowest order condition is. It remains to be understood whether they are indeed implied by the Reshetikhin condition.

One proposal to compute parton distributions from first principles is the large momentum effective theory (LaMET), which requires the Fourier transform of matrix elements computed non-perturbatively. Lattice quantum chromodynamics (QCD) provides calculations of these matrix elements over a finite range of Fourier harmonics that are often noisy or unreliable in the largest computed harmonics. It has been suggested that enforcing an exponential decay of the missing harmonics helps alleviate this issue. Using non-perturbative data, we show that the uncertainty introduced by this inverse problem in a realistic setup remains significant without very restrictive assumptions, and that the importance of the exact asymptotic behavior is minimal for values of $x$ where the framework is currently applicable. We show that the crux of the inverse problem lies in harmonics of the order of $λ=zP_z \sim 5-15$, where the signal in the lattice data is often barely existent in current studies, and the asymptotic behavior is not firmly established. We stress the need for more sophisticated techniques to account for this inverse problem, whether in the LaMET or related frameworks like the short-distance factorization. We also address a misconception that, with available lattice methods, the LaMET framework allows a "direct" computation of the $x$-dependence, whereas the alternative short-distance factorization only gives access to moments or fits of the $x$-dependence.

We prove the correctness of the AKS algorithm \cite{AKS} within the bounded arithmetic theory $T^{count}_2$ or, equivalently, the first-order consequences of the theory $VTC^0$ expanded by the smash function, which we denote by $VTC^0_2$. Our approach initially demonstrates the correctness within the theory $S^1_2 + iWPHP$ augmented by two algebraic axioms and then show that they are provable in $VTC^0_2$. The two axioms are: a generalized version of Fermat's Little Theorem and an axiom adding a new function symbol which injectively maps roots of polynomials over a definable finite field to numbers bounded by the degree of the given polynomial. To obtain our main result, we also give new formalizations of parts of number theory and algebra: $\bullet$ In $PV_1$: We formalize Legendre's Formula on the prime factorization of $n!$, key properties of the Combinatorial Number System and the existence of cyclotomic polynomials over the finite fields $\mathbb{Z}/p$. $\bullet$ In $S^1_2$: We prove the inequality $lcm(1,\dots, 2n) \geq 2^n$. $\bullet$ In $VTC^0$: We verify the correctness of the Kung--Sieveking algorithm for polynomial division.

Gas within the influence sphere of accreting massive black holes is responsible for the emission of the broad lines observed in optical-UV spectra of unobscured active galactic nuclei. Since the region contributing the most to the broad emission lines (i.e. the broad line region) depends on the active galactic nucleus luminosity, the study of broad line reverberation to a varying continuum can map the morphology and kinematics of gas at sub-pc scales. In this study, we modify a preexisting model for disc-like broad line regions, including non-axisymmetric structures, by adopting an emissivity profile that mimics the observed luminosity-radius relation. This makes our implementation particularly well suited for the analysis of multi-epoch spectroscopic campaigns. After validating the model, we use it to check if strongly non-axisymmetric, single broad line regions could mimic the short time-scale evolution expected from massive black hole binaries. We explore different orientations and anisotropy degrees of the broad line region, as well as different light curve patterns of the continuum to which the broad line region responds. Our analysis confirms that recently proposed algorithms designed to search for massive black hole binaries in large multi-epoch spectroscopic data are not contaminated by false positives ascribed to anisotropic broad line regions around single MBHs.

We revisited the equivalence between the second- and first-order formulations of the Yang-Mills (YM) and gravity using the path integral formalism. We demonstrated that structural identities can be derived to relate Green's functions of auxiliary fields, computed in the first-order formulation, to Green's functions of composite fields in the second-order formulation. In YM theory, these identities can be verified at the integrand level of the loop integrals. For gravity, the path integral was obtained through the Faddeev-Senjanović procedure. The Senjanović determinant plays a key role in canceling tadpole-like contributions, which vanish in the dimensional regularization scheme but persist at finite temperature. Thus, the equivalence between the two formalisms is maintained at finite temperature. We also studied the coupling to matter. In YM theory, we investigated both minimal and non-minimal couplings. We derived first-order formulations, equivalent to the respective second-order formulations, by employing a procedure that introduces Lagrange multipliers (LM). This procedure can be easily generalized to gravity. We also considered an alternative gravity model, which is both renormalizable and unitary, that uses LM to restrict the loop expansion to one-loop order. However, this approach leads to a doubling of one-loop contributions due to the additional degrees of freedom associated with Ostrogradsky instabilities. To address this, we proposed a modified formalism that resolves these issues by requiring the path integral to be invariant under field redefinitions. This introduces ghost fields responsible for canceling the extra one-loop contributions arising from the LM fields, while also removing unphysical degrees of freedom. We also demonstrated that the modified formalism and the Faddeev-Popov procedure commute, indicating that the LM can be viewed as purely quantum fields.

Fermionic averaged circuit eigenvalue sampling (FACES) is a protocol to simultaneously learn the averaged error rates of many fermionic linear optical (FLO) gates simultaneously and self-consistently from a suitable collection of FLO circuits. It is highly flexible, allowing for the in situ characterization of FLO-averaged gate-dependent noise under natural assumptions on a family of continuously parameterized one- and two-qubit gates. We rigorously show that our protocol has an efficient sampling complexity, owing in-part to useful properties of the Kravchuk transformations that feature in our analysis. We support our conclusions with numerical results. As FLO circuits become universal with access to certain resource states, we expect our results to inform noise characterization and error mitigation techniques on universal quantum computing architectures which naturally admit a fermionic description.

This note is an addendum to the work initiated by Eberlein, Kabanov, and Schmidt and developed further by Kabanov and Promyslov on the asymptotics of the ruin probabilities in the Sparre Andersen model with investments in a risky asset. Using more advanced methods of the implicit renewal theory, we provide complements to some results of the mentioned works.

We address the challenge of product configuration in the context of increasing customer demand for diverse and complex products. We propose a solution through a curated selection of product model benchmarks formulated in the COOM language, divided into three fragments of increasing complexity. Each fragment is accompanied by a corresponding bike model example, and additional scalable product models are included in the COOM suite, along with relevant resources. We outline an ASP-based workflow for solving COOM-based configuration problems, highlighting its adaptability to different paradigms and alternative ASP solutions. The COOM Suite aims to provide a comprehensive, accessible, and representative set of examples that can serve as a common ground for stakeholders in the field of product configuration.

The feedback particle filter (FPF) is an innovative, control-oriented and resampling-free adaptation of the traditional particle filter (PF). In the FPF, individual particles are regulated via a feedback gain, and the corresponding gain function serves as the solution to the Poisson's equation equipped with a probability-weighted Laplacian. Owing to the fact that closed-form expressions can only be computed under specific circumstances, approximate solutions are typically indispensable. This paper is centered around the development of a novel algorithm for approximating the gain function in the FPF. The fundamental concept lies in decomposing the Poisson's equation into two equations that can be precisely solved, provided that the observation function is a polynomial. A free parameter is astutely incorporated to guarantee exact solvability. The computational complexity of the proposed decomposition method shows a linear correlation with the number of particles and the polynomial degree of the observation function. We perform comprehensive numerical comparisons between our method, the PF, and the FPF using the constant-gain approximation and the kernel-based approach. Our decomposition method outperforms the PF and the FPF with constant-gain approximation in terms of accuracy. Additionally, it has the shortest CPU time among all the compared methods with comparable performance.

Concepts on quantum physics are generally difficult for the general public to understand and grasp due to its counter-intuitive nature and requirement for higher level of mathematical literacy. With categorical quantum mechanics (CQM), quantum theory is re-formalized into a more intuitive diagrammatic approach, which we will refer to as the first level of transformation, to improve the accessibility and readability of quantum theory to a broader audience since the mathematical details are embedded into diagrammatic rules. Taking inspiration from this diagrammatic approach, we propose the second level of transformation by gamifying the diagrammatic rules of quantum teleportation into a quantum card game called Quantum Port. In this work, we discuss the gamification of quantum teleportation and provide a moderator guideline to use Quantum Port as a public engagement or learning module.

Given a unital algebra $\mathscr A$ of locally Lipschitz functions defined over a metric measure space $({\mathrm X},{\mathsf d},\mathfrak m)$, we study two associated notions of function of bounded variation and their relations: the space ${\mathrm BV}_{\mathrm H}({\mathrm X};\mathscr A)$, obtained by approximating in energy with elements of $\mathscr A$, and the space ${\mathrm BV}_{\mathrm W}({\mathrm X};\mathscr A)$, defined through an integration-by-parts formula that involves derivations acting in duality with $\mathscr A$. Our main result provides a sufficient condition on the algebra $\mathscr A$ under which ${\mathrm BV}_{\mathrm H}({\mathrm X};\mathscr A)$ coincides with the standard metric BV space ${\mathrm BV}_{\mathrm H}({\mathrm X})$, which corresponds to taking as $\mathscr A$ the collection of all locally Lipschitz functions. Our result applies to several cases of interest, for example to Euclidean spaces and Riemannian manifolds equipped with the algebra of smooth functions, or to Banach and Wasserstein spaces equipped with the algebra of cylinder functions. Analogous results for metric Sobolev spaces ${\mathrm H}^{1,p}$ of exponent $p\in(1,\infty)$ were previously obtained by several different authors.

Property-based testing (PBT) relies on generators for random test cases, often constructed using embedded domain specific languages, which provide expressive combinators for building and composing generators. The effectiveness of PBT depends critically on the speed of these generators. However, careful measurements show that the generator performance of widely used PBT libraries falls well short of what is possible, due principally to (1) the abstraction overhead of their combinator-heavy style and (2) suboptimal sources of randomness. We characterize, quantify, and address these bottlenecks. To eliminate abstraction overheads, we propose a technique based on multi-stage programming, dubbed Allegro. We apply this technique to leading generator libraries in OCaml and Scala 3, significantly improving performance. To quantify the performance impact of the randomness source, we carry out a controlled experiment, replacing the randomness in the OCaml PBT library with an optimized version. Both interventions exactly preserve the semantics of generators, enabling precise, pointwise comparisons. Together, these improvements find bugs up to $13\times$ faster.

Dark matter may accumulate in neutron stars given its gravitational interaction and abundance. We investigate the influence of strongly-interacting dark matter, described by a QCD-like one-flavor $G_2$ gauge theory, on neutron stars. This choice allows to test, for the first time, a first-principles-determined non-Abelian dark matter equation of state, which supports composite fermionic dark matter and thus a Fermi-pressure-stabilized dark matter component. The ordinary matter part of the mixed star is described by available model-agnostic equations of state that interpolate between the low-density regime and high-density regime. We find that strongly-interacting dark matter has a similar impact on neutron stars as other model equation of states and confirm that strongly-interacting dark matter can be accommodated by constraints from neutron star observations within our uncertainties.

Let $Γ$ be a torsion-free subgroup of $SL_3(R)$ commensurable with $SL_3(Z)$, and $Y=SO_3(R)\backslash SL_3(R)/Γ$ be endowed with the natural locally symmetric space structure. We prove that for any point y in Y, the set of directions in which the geodesic ray starting from y is bounded in Y, is hyperplane absolute winning.