Accelerator-based neutrino oscillation experiments have the potential to revolutionise our understanding of fundamental physics, offering an opportunity to characterise charge-parity violation in the lepton sector; to determine the neutrino mass ordering; and to explore the possibility of physics beyond three-flavour neutrino mixing. However, as more data is collected, the current and next-generation of experiments will require increasingly precise control over the systematic uncertainties within their analyses. It is well known that some of the most challenging uncertainties to overcome stem from our uncertain modelling of neutrino--nucleus interactions, which also affect the event rates used to infer the oscillation probability. The sources of these uncertainties are often related to subtle details of the pertinent nuclear physics which are extremely difficult to control with sufficient precision. Confronting such uncertainties requires both state-of-the-art theoretical modelling and precise measurements of neutrino interaction event rates at experiment's near detectors, before oscillations occur. In this work, we review the role of neutrino interaction systematic uncertainties in current and future measurements of neutrino oscillation as well as the experimental and theoretical prospects for reducing them to an acceptable level for the next generation of experiments.

In the present paper, we first describe the principal basis of non-integral geometry. Non-integral geometry is a new field of generalized function (distribution) theory where the effects breaking the symmetry of integration measure have been investigated. In turn, the non-symmetric integration measure (the non-invariant measure) leads to the complex form of the universal, dimension-independent inverse operator with the additional contributions compared to the methods of integral geometry. The additional term with the complex integration measure serves to the extension that improves the image reconstruction procedure. Then, we proof that this additional term $f_A$ in the universal inverse Radon transforms plays a role of the regularizing contribution. In particular, we show that owing to the presence of $f_A$ the corresponding complex singularities can be eliminated in the image reconstruction process.

Let $n\geq 3$ and let $Ω\subset \mathbb{R}^n$ be a $\mathcal{C}^1$ bounded domain which is diffeomorphic to a ball. We investigate here the problem of finding critical points of the $n$-energy in the space $\mathcal{I}=\{v\in W^{1,n}(Ω,\mathbb{R}^n) ; \ |\mathrm{tr}_{|\partial Ω}v|=1\}$. Maps in $\mathcal{I}$ have a well-defined topological degree on $\partial Ω$ but this degree is not continuous for the weak convergence in $W^{1,n}$. Hence finding critical points with prescribed degrees results in a problem of lack of compactness. We first prove that minimizers of the $n$-energy exist only when $Ω$ is a round ball and when the prescribed degree is $-1,0$ or $1$. We then develop a mountain pass approach for the $(n+α)$-energies and study the convergence, when $α$ goes to zero, of the resulting critical points via a bubbling analysis. We exclude the existence of bubbles in the case where $Ω$ is close to a ball by proving an energy gap result for free boundary $n$-harmonic maps from $\mathbb{B}^n$ to $\mathbb{B}^n$. We thus obtain the existence of critical points of the $n$-energy with prescribed degree $1$ when $Ω$ is close to a ball.

We discuss the production of a lepton pair in quark-antiquark annihilation in the electroweak Standard Model. We present the ultraviolet-renormalised and infrared-subtracted finite contribution of the complete set of second-order virtual corrections with a closed fermionic loop, to the cross section of the process $u\bar u\to μ^+μ^-$. The evaluation of these contributions is based on an automated methodology, whose validity is discussed with explicit tests. These corrections are one of the building blocks necessary for the simulation of the inclusive lepton-pair production cross section at next-to-next-to-leading order in the electroweak interaction.

Motivated by the prevalence of non-smooth, possibly non-periodic signals in real-world applications, the output regulation of linear systems subject to non-smooth non-periodic exogenous signals has emerged as a challenging problem. A fundamental prerequisite for solving this problem is the existence of solutions to the so-called ``quasi-regulator equations''. In this paper, we investigate the solvability of these equations. To this end, we reformulate the quasi-regulator equations as differential-algebraic equations and highlight the critical role played by the system's relative degree. We finally propose a ``non-smooth non-resonance condition'' that, under specific relative degree requirements, provides a necessary and sufficient characterization of the solvability of the quasi-regulator equations.

We present a systematic theoretical framework for investigating first-order electromagnetic (EM) perturbations induced by gravitational waves (GWs). Beginning with the covariant Maxwell equations, we derive the complete first-order perturbation equations in terms of both the EM field tensor and the four-potential, demonstrating their equivalence alongside the residual gauge invariance under the Lorenz gauge condition. Furthermore, explicit first-order expressions for the induced electric and magnetic fields, as well as the associated EM energy-momentum tensor, are obtained. As an explicit illustration, we analytically evaluate the interaction between a plane EM wave and a GW within the transverse-traceless gauge. By demonstrating that the maximum modulus of the coupling coefficient is on the order of $10^2$, we quantitatively establish that a typical astrophysical GW with a dimensionless strain of $h_0 \sim 10^{-21}$ generates a first-order EM response on the order of $10^{-19}$ relative to the incident field amplitude.

We employ the sample of 244 gamma-ray bursts (GRBs; i.e., C244) with the Combo correlation to test cosmic anisotropy. Meanwhile, the Pantheon sample is introduced to verify whether the GRB sample can suppress the fake anisotropic signals induced by inhomogeneous spatial distributions. In the dipole fitting (DF) method, under the dipole-modulated $Λ$CDM model, the C244 sample shifts the best-fitting longitude $l$ derived from the Pantheon sample by $54.09^\circ$ and reduces the uncertainty in $l$ by approximately $40\%$. Compared to the 118 GRBs (i.e., A118) with the $E_\mathrm{p}$-$E_\mathrm{iso}$ correlation, the shift in longitude $l$ increases by additional $21.35^\circ$. In the hemisphere comparison (HC) method, the preferred direction derived from the C244+Pantheon sample deviates from that of the Pantheon-only sample by more than $1σ$. In contrast, the preferred direction from the A118+Pantheon sample is consistent with the Pantheon-only result within the $1σ$ uncertainty. The preferred direction changes significantly as the number of GRBs increases from 118 to 244. Our results show that a larger GRB sample can reduce the fake anisotropic signals caused by inhomogeneous spatial distributions. Accordingly, we suggest that GRBs have the potential to provide a reliable probe of cosmic anisotropy.

We present spin phase continuous modulation (SPCM), a new method for characterization of neutron beam properties. By utilizing spin-precession modulation induced by two oscillating magnetic fields, the method enables precise determination of neutron velocity and monochromaticity. We derive a theoretical formulation of the SPCM signal and experimentally validate it using measurements with a monochromatized neutron beam, obtaining reasonable agreement between experiment and prediction. SPCM enables quantitative determination of neutron beam velocity and monochromaticity.

This paper studies cryptographic key exchange in satellite communications, which requires specific solutions because the satellite context presents unique challenges, particularly concerning onboard resource constraints and long transmission latency. We address these challenges by considering the Internet Key Exchange (IKE) protocol, which is widely used in terrestrial networks, and studying its applicability in the satellite context. This requires addressing two main issues: i) its efficiency in terms of the resources and bandwidth required to adapt to satellite terminals, and ii) its resistance even to attackers equipped with a quantum computer, in order to resist obsolescence and defend against harvest-now-decrypt-later attacks. We study these aspects from both a design and experimental point of view, defining and assessing some protocol variants characterized by low complexity and quantum resistance. To address the need to manage the transition from classic cryptographic primitives to post-quantum ones, we also consider the possibility of using hybrid cryptographic solutions that combine them both.

The measurement of the Hubble constant $H_0$ plays a central role in modern cosmology. In this work, we investigate the potential of strongly lensed gravitational-wave (SLGW) signals from massive binary black hole mergers to constrain $H_0$ using future space-based detector networks. We consider two observational scenarios: one in which the source redshift is unknown, and another in which it is independently determined through electromagnetic observations. We show that meaningful constraints on $H_0$ can still be achieved without source-redshift information, provided that the lens redshift is known. For individual SLGW events, the joint Taiji+LISA analysis improves the measurement precision of $H_0$ by approximately a factor of two compared with the Taiji-only configuration. Extending the analysis to the population level, we combine five simulated SLGW events and find that the uncertainty in $H_0$, quantified by the 95\% credible interval, reaches the $1.1\times10^{-1}$ level when the source redshift is treated as unknown, and further improves to $4.2\times10^{-2}$ when the source redshift is independently measured. Our results demonstrate that joint space-based gravitational-wave observations can substantially enhance the cosmological capability of SLGW events and provide a promising avenue for precision measurements of the Hubble constant.

Altermagnetism features momentum-dependent spin splitting without net magnetization, extending spintronics beyond conventional ferromagnetism and antiferromagnetism. However, the photonic realization of altermagnetism has remained a formidable challenge due to the fundamental differences between fermionic electrons and bosonic photons. Here, we report the first experimental realization of an orbital altermagnetic photonic crystal, based on an antiunitary $C_{4z}\mathcal{T}$ symmetry enforced correspondence between a local $p$-orbital $σ/π$ doublet and crystal momentum. We experimentally demonstrate that the resulting system exhibits momentum-dependent spin splitting with alternating pseudospin polarization and a $d_{xy}$-wave form factor, as confirmed by measured band structures and iso-frequency contours. Moreover, we show that the orbital altermagnetic photonic crystal supports unique pseudospin-selective transport of electromagnetic waves, including photonic pseudospin splitting and pseudospin filtering. Our results extend the field of alternagnetism to photonic systems, opening a new avenue for designing spinphotonic devices.

The e-value is gaining traction as a robust alternative to p-values and Bayes factors for quantifying statistical evidence. e-values are a promising method for adaptive clinical trials due to their anytime-validity: e-values ensure type I error rate control at any stopping time, facilitating repeated interim analyses, complex stopping rules, and valid inference under protocol deviations. The e-value literature focuses mostly on asymptotic optimality; however, sample sizes in clinical trials are often limited. To this end, we investigate e-value-based designs with finite-horizon optimality for single-arm multi-stage clinical trials with binary data. This setting is relevant in early-phase cancer trials, but it also facilitates an accessible introduction to the betting interpretation of e-values, which we use to construct e-values that either (1) maximize statistical power, or (2) minimize the expected sample size, with or without constraints on the minimum power. We construct these designs through (constrained) dynamic programming based on the currently observed e-value, the maximum sample size, and the pre-specified significance level. Using exact calculations, we show that, next to robustness, e-value-based designs can provide competitive operating characteristics to standard (non-)adaptive designs with and without futility stopping and outperform growth-rate-optimal e-values in finite samples. In addition, small e-values automatically indicate trial continuation is futile, e.g., an e-value of zero indicates the impossibility of an efficacy conclusion. Hence, e-value-based designs provide a viable alternative to the current state-of-the-art in single-arm binary trials, warranting extension to other adaptive clinical trial settings such as multi-arm multi-stage and response-adaptive designs.

From molecular, cellular, to ecological systems, the modeling of biological processes often stands on the assumption that fast components immediately reach the equilibrium at each moment (quasi-steady state) and only slow components govern the relevant system dynamics. This quasi-steady state approximation (QSSA) simplifies the modeling but discards the effects of the relaxation towards each quasi-steady state. Unclear is the QSSA's suitability around the transition point, a specific condition where the system changes to a qualitatively different state. In this regard, we here derived a theoretical framework for the near-transition dynamics of biological systems, explicitly considering the relaxation processes overlooked by the QSSA. Numerical simulations verify our predictions for cellular decision-making, metabolic oscillations, and ecological cycles. Despite the extreme slowdown near the transition point, the QSSA alone misestimates the duration of the transition from one state to another. Moreover, the QSSA erroneously predicts the transition point itself for the onset of oscillations, while the relaxation dynamics facilitates or suppresses the oscillation onset with a counterintuitive time-delay effect. Common feedback interactions between biological components are pivotal to those relaxation effects. Our study provides an analytical foundation to understand the rich transient or rhythmic dynamics of interacting biological components near the transitions.

Phase separation of various materials has been studied for one and a half centuries. In the last two decades, phase separation of proteins and nucleic acids has received enormous attention, due its relevance to cellular functions. However, many of the observations on the resulting biomolecular condensates lack a theoretical underpinning. The first goal of this Account is to put forward theoretical frameworks for the phase-separation propensities, material states, and material properties of biomolecular condensates. Using these frameworks, I rationalize mechanistic interpretations from our recent experimental and computational studies, and synthesize these studies with prior literature to draw new conclusions. For phase-separation propensities, I relate the threshold (or saturation) concentration to the excess chemical potential in the dense phase, which in turn depends on intermolecular interaction strength and valency. For material states, I posit that liquid droplets form via complete phase separation, whereas amorphous dense liquids, reversible aggregates, and gels arise from premature termination of spinodal decomposition, due to overly weak or overly strong interactions or directional interactions. In particular, gels and aggregates are different forms of dynamically arrested states, with gels driven by tip growth via directional interactions whereas aggregates driven by monomer addition at interior sites to maximize valency. For material properties, I highlight the crucial roles of the stress relaxation time, which is determined by the mean lifetime of intermolecular bonds in a condensate. This relaxation time dictates how the condensate manifests viscoelasticity, including shear thickening and shear thinning, and accounts for the wide variation in zero-shear viscosity among different condensates.

We develop a graphical calculus for monoidal categories equipped with twisted pivotal structures, which are a generalization of pivotal structures originating from the study of orientation structures in the context of the Cobordism Hypothesis. This graphical calculus depends on a possibly singular foliation, and we use it to construct twisted string net modules for surfaces equipped with a Morse function or a Morse foliation. We prove that, despite the apparent dependence on this Morse function, the twisted string net modules assemble in an oriented categorified 2-TQFT. We study when the twisted string net module of the 2-sphere vanishes, relate it to the distinguished invertible object for finite tensor categories and exhibit examples of non-unimodular finite tensor categories with non-vanishing twisted string net module on the 2-sphere. This vanishing is expected to be the main obstruction for extending our categorified 2-TQFT to a non-compact 3-TQFT.

Understanding the connection between galaxies and dark matter halos is a central challenge in modern cosmology. The Halo Occupation Distribution (HOD) framework provides a widely used statistical description of how galaxies populate dark matter halos, enabling precise modelling of galaxy clustering. A common assumption in standard HOD models is that the number of satellite galaxies follows a Poisson distribution at fixed halo mass. In this work, we revisit this assumption and introduce the Conway-Maxwell-Poisson (CMP) distribution as a minimal extension of of the Poisson model, which add a single parameter, $ν$, to explore sub- and super-Poisson behaviour. We derive analytical approximations for the CMP expectation parameter $λ$ and develop a numerical scheme that smoothly connects small- and large-$λ$ regimes, achieving $\sim5\%$ accuracy for $0.5 < ν< 2$. Using the \texttt{HODDIES} package, we study the impact of non-Poisson satellite occupations on mock galaxy catalogues and clustering statistics. Variations in the variance of the satellite occupation significantly affect small-scale clustering, producing deviations of up to $10\%$ in projected clustering and $5\%$ in the monopole and quadrupole. We further investigate higher-order statistics using counts-in-cylinders (CiC) and the tree-level galaxy bispectrum. CiC statistics are highly sensitive to changes in the variance, with variations up to $\sim30\%$, while the tree-level galaxy bispectrum (in the Sugiyama basis) is only weakly affected ($<2\%$ up to $k_\mathrm{max} = 0.3$). These results suggest that non-Poisson satellite statistics are important for small-scale analyses, but should have a limited impact on cosmological constraints from power spectrum and bispectrum measurements using large scales $k_\mathrm{max} < 0.3$.

The existence of positive, pointwise decaying at infinity, weak solutions to a fractional $p$-Laplacian problem in the whole space and with singular reaction is established. Truncation arguments, variational methods, as well as suitable a priori estimates are exploited.

The shapes and densities of mid-sized and large trans-Neptunian objects (TNOs) are pivotal for understanding a variety of important aspects of planet formation. In this work, we present a Bayesian shape modeling method which combines constraints from rotational light curves and satellite orbits to construct three-dimensional shape models of TNOs. We use it to reanalyze three stellar occultations of the TNOs (229762) G!kún||'hòmdímà (2007 UK$_{126}$), (136108) Haumea, and (174567) Varda. By assuming that their satellites (or ring) orbit in their respective equatorial planes, we are able to derive unique shape models for both G!kún||'hòmdímà and Haumea. Our derived shape for G!kún||'hòmdímà is spheroidal with $a = b = 329^{+4}_{-3}$ km and $c = 294^{+11}_{-10}$ km, with a system density $ρ= 1007^{+50}_{-49}$ kg m$^{-3}$. For Haumea, we find $a = 1061^{+87}_{-71}$ km, $b = 844^{+5}_{-7}$ km, and $c = 514^{+18}_{-19}$ km, providing $ρ= 2050^{+157}_{-152}$ kg m$^{-3}$. For Varda, after updating its mutual orbit with its satellite Ilmarë, we find that currently published data are unable to fully constrain its three-dimensional shape. Intriguingly, Varda's elongated limb appears to point towards its satellite at the time of the occultation. With a $\sim$2\% chance of such an alignment happening randomly, this may be suggestive of a frozen-in tidal and/or rotational bulge. Our work emphasizes the importance of how external constraints can improve occultation analyses. With continued observations of rotational light curves, stellar occultations, and satellite orbits, these and other TNOs can have their shapes and densities further refined.

For ground-based high-resolution spectroscopic exoplanet atmosphere studies, removing the contamination from telluric and stellar lines is a crucial step in the analysis process. Despite that, there is no consensus in the literature on the most appropriate way to carry this out. Typically, tellurics are either directly modelled to a percent-level precision, or blindly detrended via Principal Component Analysis (PCA) algorithms, the latter particularly common at infrared wavelengths. Here, we compare three different detrending methods, PCA, Molecfit and our own fitting algorithm Astroclimes, measuring their performance in the context of removing telluric and stellar lines to detect exoplanetary atmospheric signals. We specifically look for H2O detections, which are particularly affected by residual, time-correlated variability of the telluric spectrum. We use near-infrared CARMENES observations of the day-side of $τ$ Bootis b to carry out injection and recovery tests. We find that while PCA can sometimes achieve higher SNR, it comes at the expense of stronger signal degradation. All methods struggle more for injected signals with lower orbital velocities, not just affecting the signal's magnitude but its location in velocity space as well. This behaviour is more prominent for PCA than for Astroclimes and Molecfit. These results highlight the importance of understanding the effects of different detrending methods on exoplanetary signals, which can lead to biases when characterising real detections. Finally, we report that our attempts to detect a previously claimed water signal from $τ$ Bootis b all resulted in non-detections.

Predicting the alignment of non-spherical particles in dense granular flows under shear remains a central challenge in soft matter physics. We demonstrate that the first-order behavior of granular fabric,the anisotropic distribution of contacts, is a direct consequence of particle boundary geometry. By assuming uniform contact probability along a particle's perimeter, we derive a mapping between local curvature and the macroscopic distribution of contact normals. This minimal geometric framework accurately predicts the uniaxial nematic order parameter S2 observed in both three-dimensional discrete element simulations and laboratory experiments using various particle geometries (e.g., rice, fibers, and disks) across a wide range of aspect ratios. Our results show that particle shape dictates the available orientation statistics, providing a purely geometric baseline for the emergence of fabric in dense granular systems.

We investigate the fragmentation dynamics of methane dication (CH$_4^{2+}$) produced in collisions with 50-MeV C$^{6+}$ ions using the COLTRIMS technique. The method provides complete three-dimensional momentum vectors of the charged fragments, enabling full kinematic reconstruction of the fragmentation process. The dynamics are analyzed using Dalitz plots, Newton diagrams, and the native-frame method to distinguish between concerted and sequential dissociation mechanisms. The data indicate the presence of sequential fragmentation pathways for the CH$_4^{2+}$ $\rightarrow$ CH$_2^+$ + H$^+$ + H, CH$_4^{2+}$ $\rightarrow$ CH$^+$ + H$^+$ + 2H, and CH$_4^{2+}$ $\rightarrow$ C$^+$ + H$^+$ + 3H channels, consistent with dissociation via short-lived dicationic intermediates CH$_3^{2+}$, CH$_2^{2+}$, and CH$^{2+}$, respectively. From the Newton-diagram momentum distributions, we further estimate the half-rotational periods of the intermediate states, providing insight into their rotational dynamics and finite lifetimes prior to fragmentation. The experimental observations are further supported by comparisons with calculated potential-energy curves.

With the recent proliferation of heterogeneous, GPU-accelerated supercomputers, high-order computational fluid dynamics (CFD) simulations of complex, turbulent flows are more accessible than ever. To leverage the computing power of these machines, CFD software must adapt. However, complicating the situation is the emerging need to support hardware from multiple GPU vendors. Addressing this need is the GPU-accelerated, discontinuous Galerkin spectral element method (DGSEM) framework GALÆXI, a high-order, open source, architecture-agnostic toolchain for the study of complex, compressible, turbulent flows on unstructured, hexahedral grids. GPU-accelerated computations with GALÆXI are possible on GPU hardware by interfacing Fortran source code to the vendor models CUDA C++ for NVIDIA and HIP C++ for AMD. The DGSEM implementation in GALÆXI was verified using the method of manufactured solutions to rigorously confirm the expected order of convergence. Simulations of a compressible Taylor-Green-Vortex also demonstrated excellent agreement with reference solutions across all supported architectures. GALÆXI achieved near ideal strong and weak scaling on GPU hardware from both NVIDIA and AMD. In the largest case, GALÆXI performed a simulation with 67.1 billion degrees of freedom on 65,536 AMD MI250X graphics compute devices with a parallel efficiency of 82.6%. Comparing node-to-node performance, GPU simulations offered speedups between 7.75x and 8.08x over CPU computations in time-to-solution while consuming less than half the energy. To demonstrate GALÆXI's effectiveness for production-scale simulations, wall-resolved large eddy simulations of the transonic flow past a NACA 64A-110 airfoil and an ONERA OAT15A airfoil under shock buffet conditions were computed.

Let $X$ be a smooth proper variety over an algebraically closed field of characteristic zero, and let $\mathcal{A} \subset D^{b}_{\mathrm{coh}}(X)$ be an admissible subcategory. Let $Z \subset X$ be the union of set-theoretical supports of all objects in $\mathcal{A}$ and assume that $Z \neq X$. We show that for any morphism from $Z$ to an abelian variety each fiber has no isolated points; this implies, for example, that $Z$ cannot be isomorphic to an abelian variety. The key input is the fact that while not all line bundles on $Z$ lift to infinitesimal thickenings of $Z$, sufficiently many do: specifically, we show that for any infinitesimal thickening $Z \subset \widetilde{Z}$ the restriction morphism $\mathrm{Pic}^0(\widetilde{Z}) \to \mathrm{Pic}^0(Z)$ on the connected components of Picard schemes induces an isogeny between Albanese group schemes of those connected components.

Light and matter share fundamental statistical properties, yet the experimental probes of quantum optics and many-body physics have largely evolved along separate trajectories. While many-body physics explores emergent collective phenomena, quantum optics has refined the measurement of correlations between individual photons. Here, we introduce photon correlation microscopy (PCM) - which bridges the two domains by leveraging correlations of emitted light to probe the correlations in quantum matter at mesoscopic scales. We demonstrate this approach using a one-dimensional (1D) ensemble of dipolar excitons confined at a lateral monolayer MoSe$_2$-WSe$_2$ heterojunction. We use gate-defined potentials to confine the 1D excitons to a mesoscopic lengthscale to enhance the visibility of matter correlations in the emitted photon field. Power-dependent spectroscopy reveals a transition from a compressible to an incompressible phase, signaled by the simultaneous saturation of the emission intensity and energy blueshift, which is supported by numerical simulations. Through this crossover, photon correlation measurements show a striking evolution from bunching at low densities to antibunching at high densities. This constitutes a many-body blockade of photon emission emerging directly from a number-stabilized state, driven by collective dipolar repulsion. Our results establish PCM as a powerful probe of many-body physics through the lens of quantum optics, extensible to a broad class of correlated electronic phases, while pointing toward a route to generating non-classical light through many-body correlations.

Given a positive integer $p$, we consider $W^{1,p}$-maps from a Euclidean domain of dimension $p+1$ into a closed Riemannian manifold $\mathcal{N}$. The target manifold is required to satisfy suitable topological conditions; in particular, the action of $π_1(\mathcal{N})$ over the $π_p(\mathcal{N})$ must be trivial. However, we do not assume that $\mathcal{N}$ is $(p-1)$-connected. Using tools from geometric measure theory -- namely, flat chains with coefficients in~$π_p(\mathcal{N})$ -- we associate to each map $u$ in the weak sequential closure of smooth maps an object that captures its point singularities. The vanishing of this object characterizes local strong approximability by smooth maps.

LVMB manifolds are a class of non-Kähler compact complex manifolds with a remarkably rich geometry: in many cases they admit a holomorphic bundle structure over a compact toric manifold. In fact, such a bundle is determined by an algebro-combinatoric datum encapsulating a simplicial fan. This is reflected in a close relationship between the geometry of an LVMB manifold and that of its toric base space. Throughout this paper, we restrict to this subclass of LVMB manifolds. We provide a formula for the characteristic class of the bundle in terms of the original LVMB datum. Subsequently, this expression is employed to address the existence of Hermitian metrics satisfying ``special'' conditions. We consider balanced and SKT metrics, showing that the former are obstructed in most cases. Moreover, within the LVMB class, we construct a new example of a manifold admitting a balanced metric. Finally, restricting ourselves to the subclass of LVM manifolds, we characterize those admitting an SKT metric.

In this Part 2 of our article we give a detailed discussion of the compatibility between the analytic Gysin maps we have defined in Part 1 and the topological Gysin maps defined by the second author. A significant role is played by a bordism-like description of K-homology due to Jakob which is closely related to the geometric K-homology theory of Baum and Douglas. We give a self-contained proof of the equivalence of the former with the analytic K-homology theory of Kasparov. As an intermediate step towards proving our main result we use Thom's transversality theorem to describe Gysin maps compatibly with Jakob's definition of K-homology.

Recent advances in speech generation have enabled high-fidelity synthesis, yet systematic evaluation of models under long-context conditions remains largely underexplored. A comprehensive evaluation benchmark for long-form speech is indispensable for two reasons: 1) existing test scenarios are often confined to limited domains, creating a significant gap with the diverse downstream applications; 2) existing metrics overlook critical long-text factors such as consistency and coherence, failing to generalize reliably. To this end, we propose Swanbench-Speech, a comprehensive benchmark that decomposes long-form speech quality into specific, disentangled dimensions. SwanBench-Speech has three key properties. 1) Rich speech scenarios: Focusing on long-form speech generation and dialog generation, SwanBench-Speech covers acoustics, semantics, and expressiveness challenges, and consists of 1,101 samples spanning 17 common speech scenarios; 2) Comprehensive evaluation dimensions: Along the acoustics, semantics, and expressiveness axes, SwanBench-Speech defines an automated evaluation protocol with seven metrics to provide a comprehensive, accurate, and standardized assessment; 3) Valuable Insights: Through extensive experiments, we reveal that current models still struggle in highly expressive scenarios and exhibit a notable gap in consistency and hierarchy compared to real recordings.

In 1988, William Duke showed that CM points of fundamental discriminant $D$ are equidistributed in the complex upper half-plane $\mathcal H$ as $D \to -\infty$. He also showed a similar result for RM curves (a positive discriminant analog of CM points). In this paper, we investigate analogous problems concerning the distribution of CM points and RM curves along fixed geodesics in $\mathcal H$, and around fixed points in $\mathcal H$. Specifically, we show that CM points and RM curves are equidistributed along every fixed rational geodesic in $\mathcal H$, and around every fixed CM point in $\mathcal H$. To prove these results, we solve the aggregate Linnik problem for arbitrary binary quadratic forms.

Excitons are key quasiparticles determining the optical properties of solids. As such, they can be utilized to coherently control the electronic structure of materials using optical femtosecond pulses. Identifying the decoherence mechanism during the early non-equilibrium dynamics is crucial to achieve light-induced band-structure engineering in semiconductors. Here, we generate excitons in the direct band gap semiconductor black phosphorus with a resonant mid-infrared photoexcitation. Using time- and angle-resolved photoemission spectroscopy, we track their complex ultrafast dynamics on the few-picosecond time scale. We develop a quantum-kinetic theoretical framework to model the decoherence of excitons into dark excitons via phonon scattering. By combining simulation and experiment, we quantify key parameters describing the early dynamics of the excitons. Our work highlights phonon-mediated intravalley scattering as a fundamental limitation for coherent exciton phenomena in single-valley semiconductors.