We investigate the relation between neutral atomic hydrogen (HI) and dark matter halo mass (HIHM) using observations from the Deep Investigation of Neutral Gas Origins (DINGO) pilot survey 100h data, combined with spectroscopic data from the Galaxy and Mass Assembly (GAMA) survey and photometric data from the Wide Area VISTA Extragalactic Survey (WAVES) photometric catalog. We employ a combination of direct detections and spectral stacking to probe the HI content of halos across a wide mass range ($10^{10.5} \lesssim M_\mathrm{h}/M_\odot \lesssim 10^{14.5}$). By incorporating WAVES photometric members on top of the existing GAMA group catalog, we present a novel approach of extending stacking analyses beyond spectroscopic completeness limits, enabling recovery of satellite HI content otherwise missed. We find that the HIHM relation exhibits a double power-law form, with a turnover near $M_\mathrm{h} \sim 10^{11.2} \text{ M}_\odot$. Central galaxies dominate the halo HI budget below $M_\mathrm{h} \sim 6 \times 10^{12} \text{ M}_\odot$, while satellites dominate at higher halo masses. Including photometric members increases the measured HI content in halos above $10^{13} \text{ M}_\odot$ by a factor of 1.5-3, highlighting the importance of gas-rich satellites in the group and cluster regime. Comparison with previous group-stacking studies shows that low-surface brightness galaxies, and intra-group HI structures contribute only a minor fraction to the total HI mass in group and cluster halos, as the summed galaxy HI masses are consistent with the total halo HI content.

Quantum Bayesian networks provide a mathematical formalism to describe causal relations, to analyse correlations, and to predict the probabilities of measurement outcomes, in systems involving both classical and quantum data. They generalize Pearl's Bayesian networks -- prominent graphical models for classical probabilistic reasoning and inference. The goal of this paper is to bring compositional principles and a typing discipline into this setting. A key feature of our compositional semantics is that when all causes are classical, it coincides with the standard factor-based semantics of Bayesian networks, while in the purely quantum case it reduces to tensor networks. We then propose a typed formalism based on linear logic proof-nets, where types ensure well-behaved composition of systems, and which we prove sound and complete with respect to quantum Bayesian networks.

The bifurcated age-metallicity relation of globular clusters (GCs) in the Milky Way (MW) shows that GCs are either originated in situ or accreted into the Galaxy from former satellites of the MW. The effects of the Galactic tidal field can leave signatures on the dynamical evolution and structural properties of GCs. We present a homogeneous census of dynamical ages for a sample of 93 GCs in the MW, coupled with the knowledge of their common progenitors from the chemo-dynamical parameters from the Gaia mission, unavailable some years ago. We found that the majority of accreted GCs (61%) is dynamically young. This percentage drops to 38% for in situ GCs. Excluding the enigmatic low-energy (LE) GCs, with ambiguous origin, the fraction of dynamically young ex situ GCs raises to 70%. A two tail Kolmogorov-Smirnov test shows that the distribution of dynamical ages of LE GCs cannot be distinguished from the distribution of in situ bulge and disc GCs. Yet, the LE GCs are firmly located on the satellite branch of the age-metallicity relation. An explanation may be that the progenitor of LE GCs plunged very early into the MW, so that the gravitational field of the MW had time enough to act on the associated GCs. The dynamical ages offer a statistically robust evidence corroborating the scenario of an early accretion proposed by several recent studies on the origin of LE GCs.

We improve upon an Omega result due to Soundararajan with respect to general trigonometric polynomials having positive Fourier coefficients. Instead of Dirichlet's approximation theorem we employ the resonance method and this leads to better extreme results in lattice point problems such as Dirichlet's divisor problem and Gauss' circle problem. Moreover, the present approach shows that the resonance method can also be viewed as an additive device, which has been used in multiplicative problems so far. Its extension to trigonometric polynomials with complex coefficients is also discussed and its connection to Bohr and Jessen's proof of Kronecker's theorem is highlighted.

This paper presents a high-order bound-preserving oscillation-eliminating discontinuous Galerkin (BP-OEDG) scheme for simulating gas-gas and gas-liquid two-phase flows governed by the Kapila five-equation model with the Tammann equation of state (EOS). The primary computational bottleneck arises from the severe CFL restriction imposed by the stiff $κ$-source term in the volume fraction equation. To circumvent this, we propose a novel operator-splitting strategy that decouples the system into a transport model and a stiff $κ$-source term. The former is discretized via a quasi-conservative DG method \cite{cheng2020quasi}, while the latter is resolved by an adaptive implicit strategy hybridizing the backward Euler and SDIRK2 methods. We rigorously prove that this implicit treatment is unconditionally BP, effectively removing the stiffness-induced stability constraints inherent in traditional explicit schemes. To further enhance precision, a velocity divergence reconstruction inspired by the Local Discontinuous Galerkin (LDG) method is integrated into the implicit solver. Furthermore, an OE limiter is employed to suppress spurious oscillations without characteristic decomposition, complemented by a BP limiter to ensure the BP property of partial densities, pressure, and volume fraction. Crucially, we prove that the proposed BP-OEDG scheme, integrated with the splitting strategy, strictly satisfies the Abgrall condition. Extensive numerical experiments, including challenging water-air shock-bubble interactions, demonstrate the superior robustness and efficiency of the method.

We theoretically study ambient pressure superconductivity in thin films of La$_3$Ni$_2$O$_7$. We construct model Hamiltonians adopting the crystal structure theoretically determined by fixing the in-plane lattice constant to those substrates examined in the experiment. We also construct a model based on the experimentally determined lattice structure. To the models obtained, we apply the fluctuation exchange approximation, which takes into account the full momentum and frequency dependencies of the Green function and the pairing interaction. We find that the electronic structure, including the presence/absence of the so-called $γ$-pocket (the Fermi surface originating from the top of the $d_{3z^2-r^2}$ bonding band) depends on the crystal structure adopted and/or the presence/absence of $+U$ correction in the band structure calculation. Nonetheless, $s\pm$-wave pairing symmetry remains robust regardless of these details in the band structure. The robustness of the $s\pm$-wave pairing mainly owes to the fact that it is mediated by finite energy spin fluctuations, which are insensitive to the details of the Fermi surface topology and give rise to a nearly-momentum-independent gap function for the interlayer $d_{3z^2-r^2}$ pairing in the orbital representation. On the other hand, $T_c$ being halved from that of the pressurized bulk can only be understood by adopting the model with small $|t_{\perp}|$ derived from the experimentally determined crystal structure, at least within the present FLEX approach, although there may remain some other possibilities beyond this approach for the origin of the reduced $T_c$.

We study the phenomenology of heavy neutral leptons (HNLs) in $B$-meson decays as probes of physics beyond the Standard Model. Focusing on the leptonic channels $B \to μN$ and $B \to τN$, we constrain the allowed regions in the $M_N$--$|U_{\ell N}|^2$ plane using current experimental data. Using these constraints, we investigate lepton-number violating ($ΔL=2$) processes mediated by on-shell HNLs, including $B_{(c)}^- \to π^+ μ^- μ^-$ and $B_c^- \to J/ψ\, π^+ μ^- μ^-$. For benchmark values $|U_{μN}|^2 = 10^{-6}$ and $M_N = 2$-- $3\,\mathrm{GeV}$, the predicted branching ratios lie in the range $\mathcal{O}(10^{-13})$--$\mathcal{O}(10^{-8})$. Among the channels, $B_c^- \to π^+ μ^- μ^-$ shows the largest enhancement, while $B_c^- \to J/ψ\, π^+ μ^- μ^-$ is strongly suppressed. These results indicate a clear channel dependence, with $B_c$ modes providing enhanced sensitivity to HNL effects and offering promising avenues for future searches of lepton number violation.

We introduce a new regularization scheme for divergent integrals in quantum field theory. The framework is based on the structural decomposition of the integrand asymptotic expansion, which distinguishes between contributions that drive UV singularities and those that remain finite. This asymptotic regularization method isolates the genuinely singular sector and enables a consistent subtraction of divergences while maintaining covariance and gauge symmetry. In single-scale theories, we show that the renormalized quantities exhibit a non-local logarithmic dependence uniquely determined by the UV asymptotics, offering a derivation of logarithmic terms that is independent of standard renormalization-group flows. Because it relies only on asymptotic structure rather than on standard relativistic power counting, the method is naturally applicable to theories with modified dispersion relations and non-standard UV scaling. Although formulated here for ultraviolet divergences, the underlying strategy extends straightforwardly to infrared singularities.

We consider a recursive record-filtering procedure, which we informally call Disappear-Sort. Let $D_n$ denote the random variable giving the required number of passes in Disappear-Sort to eliminate a sequence of length $n$ sampled as i.i.d. copies of a continuous random variable $X$, where each pass retains the left-to-right records and discards all remaining entries. We show that this procedure admits two natural probabilistic interpretations. For the resampling variant we prove that $d_n=\mathbb{E}[D_n]$ satisfies an exact recurrence involving the unsigned Stirling numbers of the first kind. For the non-resampling variant, we associate to a permutation $p_n\in S_n$ a natural poset and prove that the recursive Disappear-Sort layers form an antichain decomposition of this poset. We deduce that the total number of passes equals $L(p_n)$, where $L(p_n)$ is the length of the longest decreasing subsequence of $p_n$. We then show that for a uniform random permutation of size $n$, the expectation $\mathbb{E}[D_n]$ of this second variant coincides with the expected first-column length of a Plancherel-random Young diagram. Using the Robinson--Schensted correspondence, we obtain an exact formula for this expectation in terms of partitions and standard Young tableaux, and classical Plancherel asymptotics then yield $\mathbb{E}[D_n]\sim 2\sqrt{n}$, with fluctuations on the $n^{1/6}$ scale governed by the Tracy--Widom law derived by Baik, Deift and Johansson. We conclude with an $O(n\log n)$ implementation.

This paper presents a symmetric unified transport (UT) compact model for metal-oxide-semiconductor field-effect transistors (MOSFETs) that bridges drift-diffusion (DD) and ballistic transport (BT) regimes. The proposed model self consistently accounts for both current and charge across the DD-BT transition. Quantum capacitance and carrier transport are incorporated into the charge density formulation. Drain side velocity saturation and the source side thermal velocity limit are unified within a single framework using a physically motivated high field scattering length, enabling accurate modeling from DD square law behavior to the ballistic limit. In addition, a physical channel charge and capacitance model is developed to capture capacitance reduction in the quasi-ballistic regime, which is not considered in standard compact models. The model is verified using theoretical analysis and experimental data from MOSFETs with multiple channel lengths, achieving accurate fitting using only physically motivated model parameters. The formulation is continuous and symmetric, and it passes both DC and AC symmetry tests.

Mercury telluride is a canonical material for realizing topological phases, yet a full understanding of its electronic structure remains challenging due to subtle competing effects. Using first-principles calculations and $\mathbf{k}\cdot\mathbf{p}$ modelling, we study its topological phase diagram under strain. We show that linearly $k$-dependent higher-order $C_4$ strain terms are important for capturing the correct low-energy behaviour. These terms lead to a nontrivial $k$-dependence of the sub-band splitting arising from the interplay of strain and bulk inversion asymmetry. This explains the camel-back feature in the tensile regime and supports the emergence of a Weyl semimetal phase under compressive strain.

Combining spin-orbit (SOT) and spin-transfer torques (STT) provides a practical approach for field-free switching in spin-orbit torque magnetic random-access memory (SOT-MRAM), a prerequisite for industrial deployment, but can compromise reliability through phenomena such as backhopping, especially in top-pinned stacks commonly used for SOT-MRAM. We investigate the write error rate (WER) of combined SOT + STT switching in top-pinned devices that are not optimized for STT switching. Experiments reveal clear indications of STT-induced backhopping and a pronounced field-free SOT switching asymmetry between AP-to-P and P-to-AP transitions. Our macrospin model, using two coupled Landau Lifshitz Gilbert equations for the free and the reference layers, qualitatively reproduces this asymmetry and reveals an intermediate loss-of-determinism regime in addition to the well-known backhopping region. Based on these simulations, we propose mitigation strategies and experimentally demonstrate that STT pulse shaping reduces WER and improves switching robustness in the presence of device imperfections.

In this paper, we propose an interpretable denoising method for graph signals using regularization by denoising (RED). RED is a technique developed for image restoration that uses an efficient (and sometimes black-box) denoiser in the regularization term of the optimization problem. By using RED, optimization problems can be designed with the explicit use of the denoiser, and the gradient of the regularization term can be easily computed under mild conditions. We adapt RED for denoising of graph signals beyond image processing. We show that many graph signal denoisers, including graph neural networks, theoretically or practically satisfy the conditions for RED. We also study the effectiveness of RED from a graph filter perspective. Furthermore, we propose supervised and unsupervised parameter estimation methods based on deep algorithm unrolling. These methods aim to enhance the algorithm applicability, particularly in the unsupervised setting. Denoising experiments for synthetic and real-world datasets show that our proposed method improves signal denoising accuracy in mean squared error compared to existing graph signal denoising methods.

In this paper we introduce and study a new kind of generalized Hilbert matrix operators, induced by a positive finite Borel measure on (0,1), acting on weighted sequence spaces. We establish a sufficient and necessary condition for the boundedness of these operators. These results extend some related ones obtained recently in [Bull. London Math. Soc., 55 (2023), no. 6, 2598-2610].

We probe the stellar mass growth in a sample of 568 Sunyaev-Zel'dovich (SZ) selected galaxy clusters with masses greater than $2.9 \times 10^{14} \mathrm{M_{\odot}}$ and redshifts in the range $0.2 < z < 0.8$, drawn from the fifth data release of the Atacama Cosmology Telescope (ACT DR5). By utilising deep photometry from the tenth data release of the Dark Energy Camera Legacy Survey (DECaLS DR10), we construct redshift- and cluster mass-binned composite cluster stellar mass functions (SMFs), down to $M_* = 10^{9.5} \mathrm{M_{\odot}}$. This work presents the first analysis of the cluster SMF for this cluster sample at this epoch. We find that the characteristic stellar mass ($M^*$) of the cluster SMF evolves marginally from $0.55 \leq z < 0.8$, with most of the measurable growth occurring at $ 0.2 < z < 0.55$. This suggests that most of the massive galaxy population in clusters ($M_* \gtrsim 10^{10.75} \mathrm{M_{\odot}}$) is largely established by $z \sim 0.8$, with subsequent evolution driven by late-time assembly processes. The low-mass slope ($α$) of the composite cluster SMF is flat at high-$z$ ($z \sim 0.8$) but steepens at $z < 0.55$, suggesting an abundance of massive galaxies in high-$z$ clusters compared to low-$z$ clusters. We measure the evolution of cluster stellar mass fractions contained within galaxies with $M_* > 10^{9.5} \mathrm{M_{\odot}}$ between $ 0.2 < z < 0.8$, and find evidence of significant growth, by a factor of $2.5$, after accounting for the growth in cluster halo mass over this epoch.

Standard quantum mechanics employs complex Hilbert spaces, but whether complex numbers are fundamental or merely convenient has long been debated. For decades, real-valued equivalents were considered mathematically possible but cumbersome. However, a highly cited 2021 result claimed that any quantum theory based on real numbers is experimentally falsifiable via network Bell experiments. Yet, it remains an open question whether this falsification applies to all real-valued theories. Here we show that this conclusion rests on an incomplete real formulation, and we present a rigorous real-valued framework that perfectly reproduces all predictions of standard quantum mechanics. We demonstrate that the standard real tensor product ($\otimes_{\mathbb{R}}$) used in previous no-go theorems is algebraically incompatible with the rich structure of conventional quantum mechanics. We present a real framework based on Kähler space and prove that it is exactly isomorphic to established quantum mechanics via an explicit bijection $γ$. The isomorphism extends to composite systems through a symplectic composition rule $\otimes^{\ks}$ that replaces the Kronecker product. Consequently, our formulation achieves the maximal $\mathrm{CHSH}_{3}$ violation of $6\sqrt{2}$ using purely real variables, directly contradicting previous falsification claims. These results demonstrate that complex numbers are not fundamentally required by nature; rather, they encode a deeper real geometric structure that governs quantum interference and entanglement, settling this long debate.

Globular clusters encode the hierarchical assembly history of the Milky Way and the physics of multiple stellar populations. Using homogeneous stellar parameters for 69 Galactic globular clusters derived while modelling multiple populations, we reconstruct progenitor-specific age--metallicity relations (AMRs) and test whether helium-related multiple-population (MP) properties depend on progenitor origin once cluster mass and metallicity are controlled for. Ages, helium spreads ($δY$), mean helium abundances ($\bar{Y}$), and first-population fractions ($f_{\rm P1}$) are drawn from hierarchical Bayesian CMD modelling. Progenitor families are identified via chemo-dynamical clustering, AMRs reconstructed within a hierarchical Bayesian framework, and MP indicators tested for environmental dependence. Enrichment timescales are consistent with $τ\lesssim 2$\,Gyr, though individual progenitors prefer shorter values when fitted independently. The primary distinction is the extent of chemical evolution: most systems reach $Δ[\mathrm{Fe/H}] \sim 1.1$--$1.3$\,dex while Sagittarius achieves ${\sim}1.6$\,dex and higher terminal metallicities. Gaia--Sausage--Enceladus and low-energy/Kraken are the dominant accretion events. Neither $δY$ nor $\bar{Y}$ depends on progenitor origin; the mass--MP scaling is indistinguishable across in-situ and accreted systems. Sequoia clusters alone show higher $f_{\rm P1}$ at fixed mass and metallicity. AMRs carry fossil signatures of progenitor chemical evolution and mass hierarchy. Helium enrichment amplitude is regulated by cluster mass and blind to environment, pointing to universal cluster-scale formation physics, with the sole exception of a residual dependence in $f_{\rm P1}$, suggesting the enriched-star fraction retains a secondary environmental imprint.

Following the 2022 alert of a TESS object of interest transiting TOI-5624 (a G7 V star $\sim$100 pc away), a CHEOPS campaign in 2023 detected four planetary signals at $P_b\approx3.4$, $P_c\approx7.9$, $P_d\approx13.7$, and $P_e\approx21.5$ days, later confirmed by additional TESS and CHEOPS photometry in 2024-2025. After analysing the TESS & CHEOPS photometric data, we extracted and modelled the HARPS-N & SOPHIE RV time series using two independent methodologies both within an MCMC framework. We further integrated the N-body equations of motion, while simultaneously fitting the transit times and the detrended RVs, to dynamically characterise the system. We present the discovery of four transiting sub-Neptunes with radii of $R_b=2.314\pm0.035 R_{\oplus}$, $R_c=2.474\pm0.042 R_{\oplus}$, $R_d=3.584_{-0.050}^{+0.051} R_{\oplus}$, and $R_e=3.247_{-0.043}^{+0.042} R_{\oplus}$ and masses of $M_b=9.4\pm1.4 M_{\oplus}$, $M_c=4.8\pm1.9 M_{\oplus}$, $M_d=4.9\pm2.2 M_{\oplus}$, and $M_e=8.9_{-3.0}^{+2.9} M_{\oplus}$. Our photometric analysis reveals that the outermost transiting planet TOI-5624 e shows significant TTVs. We find a robust Keplerian signal in the RV time series close to the 2:1 period commensurability with TOI-5624 e, which explains the TTV pattern exhibited by TOI-5624 e according to our dynamical analysis. We label this non-transiting planet as TOI-5624 f and find its minimum mass to be $M_f\sin{i_f}=13.0\pm3.7 M_{\oplus}$. Among the known systems hosting more than four planets, the remarkable precision with which the radii have been measured (<1.7%) and the firm assessment (>3$σ$) of the mass for at least three planets has been previously reached only for TRAPPIST-1. Additional photometric observations will enable a better sample of the TTV modulation and a more robust dynamical determination of the masses.

The atmospheres of hot rocky exoplanets are among the first primary targets of the JWST. Interpreting their atmospheric spectra requires understanding the link between silicate lava compositions and overlying atmospheres. We investigate the sensitivity of simulated emission spectra of dry lava planets to variations in oxide abundances in silicate melt. Our goal is to determine which molten surface features could be distinguishable with future observations. We combine our vaporisation code with gas chemical equilibrium and radiative transfer codes to self-consistently compute atmospheric chemistry and thermal structure. Alongside varying lava compositions, we assess the impact of host star spectral type on emission spectra. TiO2 melt abundance dictates atmospheric TiO, which strongly influences surface temperature and emission spectra due to its short-wave opacity. This creates a degeneracy with heat redistribution efficiency, potentially broken by observing the optical TiO emission feature. Atmospheric SiO and SiO2 abundances depend on melt SiO2 content, with stronger SiO and SiO2 emission features at higher melt abundances. For the currently best observable HREs, changes in TiO2 and SiO2 abundance of about an order of magnitude with respect to BSE, could potentially be observable with 12 JWST eclipse observations.

We prove that the Brin-Thompson group $nV$ is torsion locally finite for $ n \geq 1$ which is known only when $n = 1$, and $nV$ contains continuum many copies of the additive group of the rationals $\mathbb{Q}$ for $n \geq 2$ which is known to be false for the $n = 1$ case.

A galaxy-independent radial scaling of the SPARC rotation-curve data reveals a common structure of dark-matter halos across galaxies. Using all 2693 rotation-curve measurements from the 153 SPARC galaxies, we analyze the data within a unified radial framework rather than fitting parametric halo models to individual systems. An empirical relation between the observed centripetal acceleration $g_{obs}$ and the baryonic acceleration $g_{bar}$. The residual scatter of this relation is consistent with the observational uncertainties, indicating no detectable intrinsic galaxy-dependent bias. Motivated by the baryonic acceleration, a scaled radial coordinate $r_{sc}$ is introduced through $r = r_0 r_{sc}$, where $r_0$ is defined by $g_{bar} =2\times 10^{-12} m/s^2$. This transformation removes galaxy-to-galaxy scaling and allows all SPARC measurements to be analyzed within a single radial domain. In this representation empirical radial distributions are obtained for acceleration, dark-matter mass, density, and circular velocity. The combined data indicate the onset of dark-matter effects at $r_{sc} \approx 0.1$, dark-matter dominance for $r_{sc} \gtrsim 0.2$, a linear growth of dark-matter mass with radius $m_{DM}/M_{bar}$ = $(6.9 \pm 0.2)r_{sc} - (0.23 \pm 0.03)$, and a density profile $ρ\propto r_{sc}^{-2}$, and a nearly constant unified rotation velocity for $r_{sc} > 0.2$. The results suggest that the empirical acceleration relation reflects a common radial dark-matter structure shared by the SPARC galaxies.

We analyse the aggregate Loewner evolution (ALE), introduced in 2018 by Sola, Turner and Viklund to generalise versions of diffusion limited aggregation (DLA) in the plane using complex analysis. They showed convergence of the ALE for certain parameters to a single growing slit. Started from a non-trivial initial configuration of $k$ needles and the same parameters, we show that the small-particle scaling limit of ALE is the Laplacian path model, introduced by Carleson and Makarov in 2002, in which the tips grow along geodesics towards $\infty$. Our proof involves analysis of Loewner's equation near its singular points, and we extend martingale methods to the backward equation, where what we have to control is non-adapted. Most conformal growth models introduce an extra regularisation factor to deal with the singularities in Loewner's equation at the sharp tips and right-angle bases of slit particles. As an intermediate step we prove a limit result for a model with no such regularisation factor, developing methods which should prove useful in analysing other weakly-regularised models with non-trivial limits.

Tilting bundles provide a fundamental bridge between algebraic geometry and representation theory. For a tilting bundle on a smooth proper $d$-dimensional variety, the global dimension of its endomorphism algebra is at least $d$, and the most meaningful case is when this lower bound is attained. Such a tilting bundle, called a $d$-tilting bundle, fits into the framework of the derived McKay correspondence and higher Auslander--Reiten theory. The first main result of this paper shows that the existence of such a bundle forces the variety to be weak Fano: more precisely, if a smooth proper $d$-dimensional variety admits a $d$-tilting bundle, then its anti-canonical bundle is semiample and big. As a consequence, the endomorphism algebra of a $d$-tilting bundle is $d$-representation tame, so the geometry naturally produces higher-dimensional analogues of extended Dynkin quivers. Second, we prove a converse in dimension two: every weak del Pezzo surface over an algebraically closed field admits a $2$-tilting bundle. Together, these results give an affirmative answer to a conjecture posed by Daniel Chan for the variety case: a smooth projective surface admits a $2$-tilting bundle if and only if it is a weak del Pezzo surface. As an application, we construct non-commutative crepant resolutions (NCCRs) of anti-canonical cones over Du Val del Pezzo surfaces. Such an NCCR is obtained as the $3$-Calabi--Yau completion of the endomorphism algebra of a $2$-tilting bundle on the corresponding weak del Pezzo surface. This extends the known construction for smooth del Pezzo surfaces to the Du Val case and places Du Val del Pezzo cones within the framework of the derived McKay correspondence via higher Auslander--Reiten theory.

Recent advances in quantum Gibbs sampling leave open the central question of rapid mixing near and below phase transitions. This challenge is especially relevant for code Hamiltonians whose Gibbs states capture phenomena such as the thermal stability of quantum topological order. In this work, we formulate a new Markov chain, Code Swendsen-Wang dynamics, which uses global updates to prepare the Gibbs states of arbitrary code Hamiltonians. We establish Code Swendsen-Wang dynamics as the right generalization of Swendsen-Wang dynamics for the Ising model to quantum and classical code Hamiltonians: it mixes rapidly for all previously known code Hamiltonians with efficient Gibbs samplers, resolves the central open case of the 4D toric code, and meets fundamental barriers exactly at first-order phase transitions.

We propose an algorithm based on modulable hidden variables and adaptive step lengths, inspired by heuristic statistical physics and the replica method, to study the effect of mutual correlations and the emergent Wigner-Dyson distribution in a driven many-body system. Specifically, we apply this method to the driven Bose-Hubbard chain to illustrate the competition between coherent driving, hopping, and on-site interactions. Unlike the asymptotic high-dimensional statistics regime in random systems, here the randomness emerges dynamically from the interplay between the driving field $F$ and the nonlinearity $U$. We reveal the relation between the UV cutoff of the effective momentum space (related to the particle number truncation) and the system's chaotic behavior (SYK-like features). The inverse of the effective Hilbert space cutoff, acting as an essential degree-of-freedom (DOF) other than the bosonic modes, relates to the distribution and statistical variance of the interaction-induced coupling. By mapping the 1D chain to a high-dimensional feature space via a Gaussian-based self-attention mechanism, we replace the direct diagonalization of the full Hamiltonian with a predictive algorithm where the flavor number $O(M)$ is determined by the local potential difference generated by the Kerr non-linearity $\frac{1}{2}U$. Our algorithm allows for the automatic optimization and prediction of the resulting many-body spectrum to arbitrary accuracy, revealing non-Fermi liquid-like behavior in the strongly interacting bosonic phase.

Altermagnets provide a promising platform for a wide spectrum of applications integrating advantages of conventional ferromagnets and antiferromagnets. In this work, we implement a medium-throughput first-principles workflow and evaluate topological transport properties driven by quantum geometry for 135 altermagnets in the MAGNDATA database. Based on automated Wannier construction, both linear and nonlinear responses, including the anomalous Hall effect, magneto-optical Kerr effect, and bulk photovoltaic effect, are evaluated with further symmetry verifications. Detailed analysis is done on representative cases like metallic VNb3S6 with enhanced anomalous Hall conductivity, CaIrO3 with giant MOKE, and CuFeS2 with large shift current in non-centrosymmetric. These results establish a symmetry-guided computational route for identifying experimentally accessible fingerprints and functional transport properties in altermagnets.

Time-bin encoded quantum states of light are crucial for quantum technology applications. The integration of manipulation functionalities into chip-scale devices is essential for deploying scalable, high-performance, and cost-effective quantum networks. Here we develop a fully integrated, high-throughput quantum receiver based on the thin-film lithium niobate (TFLN) platform, capable of high-speed electro-optic manipulation of time-bin encoded quantum states. The device's novel architecture enables active switching of time-bin quantum states with an electro-optic bandwidth exceeding 30 Ghz, while supporting real-time arbitrary projective measurements with a bandwidth of over 1 GHz. We showcase its versatility and performance through several applications, including the certification of entanglement with Bell's inequality violation by 38 standard deviations and with >95% visibility. We then apply it to a fiber-based quantum communication scenario, where we experimentally demonstrate an entanglement-based quantum key distribution (QKD) protocol, achieving stable finite-size secure key rates exceeding 25 kbit/s over 12 hours of continuous operation. By leveraging a high-speed active switching scheme, the system overcomes the need for temporal post-selection, eliminating a fundamental loophole that compromises the security of time-bin entanglement-based QKD protocols and relaxes the temporal resolution requirements of single-photon detectors. Moreover, it enables active selection of the projection basis, increasing the flexibility for communication parties. This approach establishes a versatile and scalable architecture for time-bin encoded quantum communication, enabling practical protocols on industry-grade photonic technology.

We present a comprehensive analysis of the cosmological implications of the Dark Energy Spectroscopic Instrument (DESI) Data Release 2 (DR2) Lyman-$α$ forest baryon acoustic oscillation (BAO) measurements, combined with DESI DR2 galaxy BAO, Type Ia supernova samples (Pantheon$^+$, DES-Dovekie, and Union3), and the cosmic microwave background CamSpec likelihood. We consider several dark-energy parameterizations, including Chevallier-Polarski-Linder, logarithmic, exponential, Jassal-Bagla-Padmanabhan, Barboza-Alcaniz, and generalized emergent dark energy, as well as the $w$CDM model and non-flat extensions of $Λ$CDM and $w$CDM. Using the Metropolis-Hastings MCMC algorithm, we constrain cosmological parameters and compute Bayesian evidence with \texttt{MCEvidence}. We find that non-flat extensions remain consistent with spatial flatness, with $Ω_k \approx 0$. All parameterizations favor a dynamical dark-energy scenario with $w_0 > -1$, $w_a < 0$, and $w_0 + w_a < -1$, consistent with a Quintom-B behavior. A moderate preference for dynamical dark-energy models is found relative to $Λ$CDM, reaching up to $\sim3.10σ$ for Ly$α$ + CMB + galaxy BAO. When combined with SNe~Ia datasets, the deviations decrease to $\lesssim2σ$, corresponding to inconclusive preference. The Bayes factor ($\ln B_{ij}$) shows that model preference depends strongly on the dataset combination: $w$CDM and o$w$CDM exhibit moderate evidence for Ly$α$ + CMB + galaxy BAO, while most other models show weak or inconclusive evidence. With Pantheon$^{+}$ or DES-Dovekie, o$w$CDM shows strong evidence, whereas other models remain moderately favored.

Let $X$ be a compact Riemann surface. Let $f$ be a holomorphic self-correspondence of $X$ with dynamical degrees $d_1$ and $d_2$. Assume that $d_1\neq d_2$ or $f$ is non-weakly modular. We show that the graphs of the iterates $f^n$ of $f$ are equidistributed exponentially fast with respect to a positive closed current in $X\times X$.

This paper is the first one of two papers whose goal is to give a converse to the main result of my previous paper [6], so to prove the existence of multiple poles for the distribution |f|2$λ$ with an hypothesis on a Higher Bernstein Polynomial of the (a,b)-module generated by the germ $ω$$\in$$Ω$n+1 0 of a given holomorphic volum form. Note that, even for the existence of a simple pole this converse is already new. One difficulty to prove such a result comes from the use of the formal completion in f of the Brieskorn module of the holomorphic germ f\,: (Cn+1 ,0) $\rightarrow$(C,0) which does not give access to the cohomology of the Milnor's fiber of f, which by definition, is outside {f = 0}. This leads to introduce generalized Brieskorn modules (convergent geometric (a,b)-modules) which allow this passage. The first aim of this part I is to give a solid basis of the theory of convergent (a,b)-modules. In order to take in account Jordan blocs of the monodromy in our results we introduce the semi-simple filtration of a generalized Brieskorn module (convergent (a,b)-module) and we shall use it to define in part II the higher order Bernstein polynomials in this context. They correspond to a decomposition of the ``standard'' Bernstein polynomial of a generalized Brieskorn module, taking in account the nilpotent order of the monodromy. In this part I we obtain also a full description of generalized Brieskorn-modules in terms of (convergent) asymptotics expansions of Nilsson class which will be used as a starting point in part II. We conclude this part I by making explicite the relationship between the semi-simple filtration of a generalized Brieskorn module E and the nilpotent filtration of the monodromy on its saturation E___ .