Max-Cut is a fundamental combinatorial optimization problem that has been studied in various computational settings. We initiate the study of its streaming complexity in \emph{general metric spaces} with access to distance oracles. We give a $(1 + ε)$-approximate algorithm for estimating the Max-Cut value in \emph{sliding-window} streams using only poly-logarithmic space. This is the first sliding-window algorithm for Max-Cut even in Euclidean spaces, and it matches a known insertion-only space bound in the special case of Euclidean spaces [Chen, Jiang, Krauthgamer, STOC'23]. In sharp contrast, we give a $\poly(n)$-space lower bound in the \emph{dynamic} streaming setting. This yields a separation from the Euclidean case, where the polylogarithmic-space $(1+ε)$-approximation extends to dynamic streams. On the technical side, our sliding-window algorithm builds on the smooth histogram framework of [Braverman and Ostrovsky, SICOMP'10]. To make this framework applicable, we establish the first smoothness bound for metric Max-Cut. Moreover, we develop a streaming algorithm for metric Max-Cut in insertion-only streams, whose key ingredient is a new metric reservoir sampling technique.

This work analyzes the inverse optimal transport (IOT) problem under Bregman regularization. We establish well-posedness results, including existence, uniqueness (up to equivalence classes of solutions), and stability, under several structural assumptions on the cost matrix. On the computational side, we investigate the existence of solutions to the optimization problem with general constraints on the cost matrix and provide a sufficient condition guaranteeing existence. In addition, we propose an inexact block coordinate descent (BCD) method for the problem with a strongly convex penalty term. In particular, when the penalty is quadratic, the subproblems admit a diagonal Hessian structure, which enables highly efficient element-wise Newton updates. We establish a linear convergence rate for the algorithm and demonstrate its practical performance through numerical experiments, including the validation of stability bounds, the investigation of regularization effects, and the application to a marriage matching dataset.

Initial states of dense matter with nonzero electron chiral imbalance could potentially give rise to strong magnetic fields through chiral plasma instability. Previous work indicated that unless chiral chemical potential is as large as the electron vector chemical potential, the growth of magnetic fields due to the instability is washed out by chirality flipping rate enabled by electron mass. We re-examine this claim in a broader range of parameters and find that at higher temperatures the hierarchy is reversed supporting a growing magnetic field for an initial electron chiral chemical potential much smaller than the electron vector chemical potential. Further, we identify a qualitatively new effect relevant for magnetized hot and dense medium where chiral magnetic effect (CME) sourced by density fluctuation acts as a powerful source of Joule heating. Remarkably, even modest chiral chemical potentials (keV) in such environment can deposit energy densities set by the QCD scale in a relatively short time of the order of a few milliseconds or seconds. We speculate how this mechanism makes CME-driven Joule heating a potentially critical ingredient in the dynamics of turbulent density fluctuation of supernovae and neutron star mergers.

The subject of viscoelastic flow phenomena is crucial to many areas of engineering and the physical sciences. Although much of our understanding of viscoelastic flow features stems from carefully designed experiments, preparation of model viscoelastic fluids remains a challenge; for example, fabricating a series of fluids with different fluid shear moduli $G_0$, but with an identical relaxation time $τ$, is nontrivial. In this work, we harness the non-ideality of nearly constant-viscosity elastic fluids, commonly known as `Boger fluids', made with polyisobutylene, to develop an experimental methodology that produces a set of fluids with desired viscoelastic properties, specifically, $G_0$, $τ$, and the first normal stress difference coefficient $ψ_1$. Through a linear algebraic relation between the rheological properties of interest ($G_0$, $τ$, $ψ_1$) and the fluid compositions in terms of polymer concentration $c$, molecular weight $M_w$, and solvent viscosity $η_s$, we developed a `design equation' that takes $G_0$, $τ$, $ψ_1$ as inputs and calculates values for $c$, $M_w$, $η_s$ as outputs. Using this method, fabrication of dilute viscoelastic fluids whose rheological properties are \textit{a priori} known can be achieved.

In this article, we present a parallel discretization and solution method for parabolic problems with a higher number of space dimensions. It consists of a parallel-in-time approach using the multigrid reduction-in-time algorithm MGRIT with its implementation in the library XBraid, the sparse grid combination method for discretizing the resulting elliptic problems in space, and a domain decomposition method for each of the subproblems in the combination method based on the space-filling curve approach. As a result, we obtain an extremely fast and embarrassingly parallel solver with excellent speedup and scale-up qualities, which is perfectly suited for parabolic problems with up to six space dimensions. We describe our new parallel approach and show its superior parallelization properties for the heat equation, the chemical master equation and some exemplary stochastic differential equations.

We present ARCH (Adaptive Reconstruction of Cluster Halos), a new gravitational lensing pipeline for cluster mass reconstruction that applies a joint shear-flexion analysis to JWST imaging. Previous approaches have explored joint shear+flexion reconstructions through forward modeling and Bayesian inference frameworks; in contrast, ARCH adopts a staged optimization strategy that incrementally filters and selects candidate halos rather than requiring a global likelihood model or strong priors. This design makes reconstruction computationally tractable and flexible, enabling systematic tests of multiple signal combinations within a unified framework. ARCH employs staged candidate generation, local optimization, filtering, forward selection, and global strength refinement, with a combined fit metric weighted by per-signal uncertainties. Applies to Abell 2744 and El Gordo, the pipeline recovers convergence maps and subcluster masses consistent with published weak+strong lensing results. In Abell 2744 the central core mass within 300$h^{-1}$ kpc is $2.1\times 10^{14} M_\odot h^{-1}$, while in El Gordo the northwestern and southeastern clumps are recovered at $2.6\times 10^{14} M_\odot h^{-1}$ and $2.3\times 10^{14} M_\odot h^{-1}$. Jackknife resampling indicates typical 1$σ$ uncertainties of $10^{12}-10^{13} M_\odot h^{-1}$, with the all signal and shear+$\mathcal{F}$ reconstructions providing the most stable results. These results demonstrate that flexion, when anchored by shear, enhances sensitivity to cluster substructure while maintaining stable cluster-scale mass recovery.

We show that the spatial increments of the KPZ fixed point starting from arbitrary initial data, exhibit strong quantitative comparison against rate two Brownian motion on compacts. The above estimates are uniform in the initial data supported in some compact set. As applications, we obtain a one-sided large deviation inequality for spatial increments of the KPZ fixed point and show that the Wiener density of the centred KPZ fixed point started from arbitrary initial data has finite entropy.

Volatility is the canonical measure of financial risk, a role largely inherited from Modern Portfolio Theory. Yet, its universality rests on restrictive efficiency assumptions that render volatility, at best, an incomplete proxy for true risk. This paper identifies three fundamental inconsistencies: (i) volatility is path-independent and blind to temporal dependence and non-stationarity; (ii) its relevance collapses in derivative-intensive strategies, where volatility often represents opportunity rather than risk; and (iii) it lacks an absolute benchmark, providing no guidance on what level of volatility is economically ``fair'' in efficient markets. To address these limitations, we propose a new paradigm that reconceptualizes risk in terms of predictability rather than variability. Building on a general class of stochastic processes, we derive an analytical link between volatility and the Hurst-Holder exponent within the Multifractional Process with Random Exponent (MPRE) framework. This relationship yields a formal definition of ``fair volatility'', namely the volatility implied under market efficiency, where prices follow semi-martingale dynamics. Extensive empirical analysis on global equity indices supports this framework, showing that deviations from fair volatility provide a tractable measure of market inefficiency, distinguishing between momentum-driven and mean-reverting regimes. Our results advance both the theoretical foundations and empirical assessment of financial risk, offering a definition of volatility that is efficiency-consistent and economically interpretable.

Recent studies suggest that dark matter could take the form of a Bose-Einstein condensate (BEC), a possibility motivated by anomalies in galactic rotation curves and the missing mass problem in galaxy clusters. We investigate the astrophysical properties of BEC dark matter halos and their potential observational signatures distinguishing them from alternative models. In this framework, dark matter behaves as a self-gravitating Newtonian fluid with a polytropic equation of state of index $n=1$. We derive analytic expressions for the mass distribution, gravitational potential, and dynamical profiles such as the density slope and tangential velocity. The lensing behavior of BEC halos is analyzed, yielding a general series representation of the projected surface density that enables precise predictions for deflection angles, lensing potentials, and magnifications. Finally, halo equilibrium and stability are examined via the scalar and tensor virial theorems, leading to perturbation equations that describe their response to small disturbances. Together, these results provide a unified framework linking the microscopic physics of condensate dark matter to macroscopic halo observables.

We introduce KRED (Korea Research Economic Database), a FRED-MD-compatible monthly macroeconomic database for Korea designed for data-rich policy analysis and cross-country comparison. KRED contains 125 monthly series from ECOS, KOSIS, and administrative labor-market sources, with coverage back to 1960. Using a balanced panel of 104 series over 2009:06--2025:12, principal-components analysis extracts four factors that explain about 30% of total variation. These factors correspond to financial conditions, real activity, housing and real-estate credit, and labor-market and price pressures, and their diffusion indices summarize major Korean macroeconomic episodes. We then use KRED in two empirical applications. First, factor-augmented VARs show that U.S. monetary tightening transmits strongly to Korea and that factor augmentation yields a more coherent inflation response than a low-dimensional VAR. Second, a grouped U.S.--Korea tensor autoregression shows that cross-country dependence is concentrated in financially oriented blocks, with stronger transmission from the U.S. financial block to Korea than in the reverse direction, while spillovers in real activity and housing are much weaker. KRED thus provides a transparent public database for Korean macroeconomic research and a useful building block for comparative work on macro-financial dependence in Asia.

We introduce a simple and flexible concept for a heralded -- spectrally pure -- single photon source. The scheme uses a probabilistic photon pair source pumped with a CW laser, whereby a rapid gating InGaAs/InP single photon avalanche diode provides a synchronous clock and temporally resolves, and hence spectrally filters, the heralded photons. We demonstrate the concept by combining this with a narrow-band integrated silicon nitride photon-pair source. This simple architecture is capable of heralding photons with high spectral purity in the telecom band, but could be adapted to other wavelengths and bandwidth regimes.

It is well-known that a $d$-dimensional polynomial Bézier curve of degree $n$ can be subdivided into two segments using the famous de Casteljau algorithm in $O(dn^2)$ time. Can this problem be solved more efficiently? In this paper, we show that it is possible to do this in $O(dn\log{n})$ time using the fast Fourier transform and its inverse. Experiments show that the direct application of the new method performs well only for small values of $n$, as the algorithm is numerically unstable. However, a slightly modified version -- which still has $O(dn\log{n})$ computational complexity -- offers good numerical quality, which is confirmed by numerical experiments conducted in \textsf{Python}. Moreover, the new method has a nice property: if a Bézier curve is extended by an additional control point, the subdivision can be updated in $O(d)$ time. A similar idea can be applied to speed up the subdivision of rational Bézier curves and rectangular Bézier surfaces, as well as to compute the derivatives of Bézier curves more efficiently.

Diffusive motion is a fundamental transport mechanism in physical and biological systems, governing dynamics across a wide range of scales -- from molecular transport to animal foraging. In many complex systems, however, diffusion deviates from classical Brownian behaviour, exhibiting striking phenomena such as Brownian yet non-Gaussian diffusion (BYNGD) and anomalous diffusion. BYNGD describes a frequently observed statistical feature characterised by the coexistence of linear mean-square displacement (MSD) and non-Gaussian displacement distributions. Anomalous diffusion, in contrast, involves a nonlinear time dependence of the MSD and often reflects mechanisms such as trapping, viscoelasticity, heterogeneity, or active processes. Both phenomena challenge the conventional framework based on constant diffusivity and Gaussian statistics. This review focuses the theoretical modelling of such behaviour via the Langevin equation with fluctuating diffusivity (LEFD) -- a flexible stochastic framework that captures essential features of diffusion in heterogeneous media. LEFD not only accounts for BYNGD but also naturally encompasses a wide range of anomalous transport phenomena, including subdiffusion, ageing, and weak ergodicity breaking. Ergodicity is discussed in terms of the correspondence between time and ensemble averages, as well as the trajectory-to-trajectory variability of time-averaged observables. The review further highlights the empirical relevance of LEFD and related models in explaining diverse experimental observations and underscores their value to uncovering the physical mechanisms governing transport in complex systems.

Topology optimization is a valuable tool in engineering, facilitating the design of optimized structures. However, topological changes often require a remeshing step, which can become challenging. In this work, we propose an isogeometric approach to topology optimization driven by topological derivatives. The combination of a level-set method together with an immersed isogeometric framework allows seamless geometry updates without the necessity of remeshing. At the same time, topological derivatives provide topological modifications without the need to define initial holes [7]. We investigate the influence of higher-degree basis functions in both the level-set representation and the approximation of the solution. Two numerical examples demonstrate the proposed approach, showing that employing higher-degree basis functions for approximating the solution improves accuracy, while linear basis functions remain sufficient for the level-set function representation.

The sources of turbulence in our Galaxy may be diverse, but core-collapse supernovae (SNe) alone provide enough energy to sustain a steady-state galactic turbulence cascade at the observed velocity dispersion. By localizing and analyzing supernova remnants (SNRs) in high-resolution SN-driven galactic disk cut-out simulations from Beattie et al. 2025, I show that isolated SNRs source incompressible turbulence through baroclinic vorticity generation localized at the unstable contact discontinuity. Through the spherical harmonic power spectrum of the corrugations, I provide evidence that this process is seeded by surface instabilities and 2D turbulence on the shell, which corrugates and folds the interface, becoming the strongest source of baroclinicity in the simulations. I present an analytical relation for a baroclinicity-fed incompressible mode (co)spectrum, which matches that observed in the simulated SNRs, and reveals a $\propto k^{3/4}$ spectrum that drives the turbulence. I show that vortex stretching allows for modes to be shed from the contact discontinuity into the surrounding medium and derive a timescale criterion for this process, revealing that young SNRs with radii close to the cooling radius are efficient at radiating turbulence. The unstable layer produces a spectrum of incompressible modes $\propto k^{-3/2}$ locally within the SNRs. Through the inverse cascade mechanism revealed in Beattie et al. 2025, this opens the possibility that the $k^{-3/2}$ spectrum, arising from corrugated folds in the unstable layer, imprints itself on kiloparsec scales, thereby connecting small-scale structure in the layer to the large-scale incompressible turbulence cascade.

Supernovae that interact with hydrogen-poor, helium-rich circumstellar material (CSM), known as Type Ibn supernovae (SNe Ibn), present a unique opportunity to probe mass-loss processes in massive stars. In this work, we report the first radio detection of a SN Ibn, SN 2023fyq, and characterize the mass-loss history of its stellar progenitor using the radio and X-ray observations obtained over 18 months post-explosion. We find that the radio emission from 58--185 days is best modeled by synchrotron radiation attenuated by free-free absorption from a CSM of density $\sim$ $10^{-18}$ g/$\rm{cm^{3}}$ ($\sim 10^{6} \mathrm{ρ_{ISM}}$) at a radius of $10^{16}$ cm, corresponding to a mass-loss rate of $\sim$ $4 \times 10^{-3} \ \mathrm{M_{\odot} \ yr^{-1}}$ (for a wind velocity of 1700 km/s from optical spectroscopy) from 0.7 to 3 years before the explosion. This timescale is consistent with the time frame over which pre-explosion optical outbursts were observed. However, our late-time observations at 525 days post-explosion yield non-detections, and the 3$σ$ upper limits (along with an X-ray non-detection) allow us to infer lower-density CSM at $2\times 10^{16}$ cm with $\rm{\dot{M}}$ $< 2.5\times 10^{-3} \ \mathrm{M_{\odot} \ yr^{-1}}$. These results suggest a shell-like CSM from at most $4 \times 10^{15}$ to $2 \times 10^{16}$ cm ($\sim 10^{5} R_{\rm{\odot}}$) with an elevated CSM density (0.004 $\mathrm{M_{\odot} \ yr^{-1}}$) that is roughly consistent with predictions from a merger model for this object. Future radio observations of a larger sample of SNe Ibn will provide key details on the extent and density of their helium-rich CSM.

Time synchronization is essential for industrial IoT and Industry 4.0/5.0 applications, but achieving high synchronization accuracy in Time-Sensitive Networking (TSN)-5G networks is challenging due to jitter and asymmetric delays. 3GPP TS 23.501 defines three 5G synchronization modes: time-aware system, boundary clock (BC), and transparent clock (TC), where TC offers a promising solution. However, to the best of our knowledge, there is no empirical evaluation of TC in a TSN-5G network. This paper empirically evaluates an 5G end-to-end TC in a TSN-5G network, implemented on commercial TSN switches with a single clock. For TC development, we compute the residence time in 5G and recover the clock domain at the slave node. We deploy a TSN-5G testbed with commercial equipment for synchronization evaluation by modifying the Precision Timing Protocol (PTP) message transmission rates. Experimental results show a peak-to-peak synchronization of 500 ns, meeting the industrial requirement of < 1 us, with minimal synchronization offsets for specific PTP message transmission rates.

As networks evolve towards 6G, Mobile Network Operators (MNOs) must accommodate diverse requirements and at the same time manage rising energy consumption. Integrated Access and Backhaul (IAB) networks facilitate dense cellular deployments with reduced infrastructure complexity. However, the multi-hop wireless backhauling in IAB networks necessitates proper routing and resource allocation decisions to meet the performance requirements. At the same time, cell densification makes energy optimization crucial. This paper addresses the joint optimization of routing and resource allocation in IAB networks through two distinct objectives: energy minimization and throughput maximization. We develop a novel capacity model that links power levels to achievable data rates. We propose two practical large-scale approaches to solve the optimization problems and leverage the closed-loop control framework introduced by the Open Radio Access Network (O-RAN) architecture to integrate the solutions. The approaches are evaluated on diverse scenarios built upon open data of two months of traffic collected by network operators in the city of Milan, Italy. Results show that the proposed approaches effectively reduces number of activated nodes to save energy and achieves approximately 100 Mbps of minimum data rate per User Equipment (UE) during peak hours of the day using spectrum within the Frequency Range (FR) 3, or upper midband. The results validate the practical applicability of our framework for next-generation IAB network deployment and optimization.

This paper presents the first measurements of the azimuthal anisotropy coefficients $v_{n}$, which quantify the $n^{\mathrm{th}}$-order Fourier modulation of charged-particle azimuthal distributions, for $n=2$-4 in $\sqrt{s_{\mathrm{NN}}}=5.36$ TeV $\mathrm{^{16}O}+\mathrm{^{16}O}$ and $\mathrm{^{20}Ne}+\mathrm{^{20}Ne}$ collisions recorded with the ATLAS detector at the Large Hadron Collider in 2025. The $v_{n}$ coefficients are measured as a function of transverse momentum ($p_{\mathrm{T}}$), collision centrality, and event multiplicity. They are extracted using two complementary methods: two-particle correlations with a template-fit subtraction of short-range non-flow contributions, and four-particle subevent cumulants, which intrinsically suppress non-flow effects and provide sensitivity to flow fluctuations. The results show a clear hierarchy $v_{2} > v_{3} > v_{4}$ and a non-monotonic dependence on $p_{\mathrm{T}}$, reaching a maximum around 2 GeV, consistent with trends observed in heavy-ion collisions. Detailed comparisons between the two collision systems reveal an enhanced $v_{2}$ in central $\mathrm{^{20}Ne}+\mathrm{^{20}Ne}$ collisions, consistent with theory expectations based on the predicted prolate deformation of neon nuclei, in contrast to the slightly tetrahedral structure predicted for oxygen. The four-particle cumulant results highlight strong event-by-event fluctuations and provide the greatest sensitivity to nuclear shape effects. These measurements can place new constraints on the initial geometry and the hydrodynamic response in light-ion collisions, offering valuable input for models of nuclear structure.

Charts are oriented labeled graphs in a disk. Any simple surface braid (2-dimensional braid) can be described by using a chart. Also, a chart represents an oriented closed surface embedded in 4-space. In this paper, we investigate embedded surfaces in 4-space by using charts. Let $Γ$ be a chart, and we denote by $Cross(Γ)$ the set of all the crossings of $Γ$, and we denote by $Γ_m$ the union of all the edges of label $m$. For a 4-chart $Γ$, if each connected component of the set $(Γ_1\cup Γ_3)-Cross(Γ)$ is acyclic, then $Γ$ is said to be {\it linear}. In this paper, we shall show that any linear minimal $4$-chart with three crossings is lor-equivalent (Label-Orientation-Reflection equivalent) to the chart describing a $2$-twist spun trefoil knot by omitting free edges and hoops.

We review a theoretical framework for the cuprate superconductors, rooted in a fractionalized Fermi liquid (FL*) description of the intermediate-temperature pseudogap phase at low doping. The FL* theory predicted hole pockets each of fractional area $p/8$ at hole doping $p$, in contrast to the area $p/4$ in spin density wave theory. Magnetotransport measurements, including observation of the Yamaji angle, show clear evidence of hole pocket quasiparticles which can tunnel coherently between square lattice layers, and are consistent with the FL* description. The FL* phase of a single-band model is described using a layer construction with a pair of ancilla qubits on each site: the Ancilla Layer Model (ALM). Fluctuations are described by the SU(2) gauge theory of a background spin liquid with critical Dirac spinons. A Monte Carlo study of the thermal SU(2) gauge theory transforms the hole pockets into Fermi arcs in photoemission. One route to confinement of FL* upon lowering temperature yields a $d$-wave superconductor via a Kosterlitz-Thouless transition of $h/(2e)$ vortices, with nodal Bogoliubov quasiparticles featuring anisotropic velocities and vortices surrounded by charge order halos. Increasing doping from the FL* phase in the ALM drives a transition to a conventional Fermi liquid (FL) at large doping, passing through an intermediate strange metal regime. We formulate a theory of the FL*-FL metal-metal transition without a symmetry-breaking order parameter, using a critical quantum `charge' liquid of mobile electrons in the presence of disorder, developed via an extension of the Sachdev-Ye-Kitaev model to two spatial dimensions. At low temperatures, and across optimal and over doping, we address the regimes of extended non-Fermi liquid behavior by Griffiths effects near quantum phase transitions in disordered metals.

We show short-time well-posedness of a diffuse interface model describing the flow of a fluid through a deformable porous medium consisting of two phases. The system non-linearly couples Biot's equations for poroelasticity, including phase-field dependent material properties, with the Cahn-Hilliard equation to model the evolution of the solid, where we further distinguish between the absence and presence of a visco-elastic term of Kelvin-Voigt type. While both problems will be reduced to a fixed-point equation that can be solved using maximal regularity theory along with a contraction argument, the first case relies on a semigroup approach over suitable Hilbert spaces, whereas treating the second case under minimal assumptions with respect to spatial regularity necessitates the application of Banach scales.

Implementations of quantum key distribution (QKD) need vulnerability assessment against loopholes in their optical scheme. Most of the optical attacks involve injecting or receiving extraneous light via the communication channel. An eavesdropper can choose her attack wavelengths arbitrarily within the quantum channel passband to maximise the attack performance, exploiting spectral transparency windows of system components. Here we propose a wide-spectrum security evaluation methodology to achieve full optical spectrum safety for QKD systems. This technique requires transmittance characterisation in a wide spectral band with a high sensitivity. We report a testbench that characterises insertion loss of fiber-optic components in a wide spectral range of 400 to 2300 nm and up to 70 dB dynamic range. To illustrate practical application of the proposed methodology, we give a full Trojan-horse attack analysis for some typical QKD system configurations and discuss briefly induced-photorefraction and detector-backflash attacks. Our methodology can be used for certification of QKD systems.

The anticipated widespread adoption of electric vehicles (EVs) necessitates a critical evaluation of existing power distribution infrastructures, as EV integration imposes additional stress on distribution networks that can lead to component overloading and power quality degradation. Implementing smart charging mechanisms can mitigate these adverse effects and defer or even avoid upgrades. This study assesses the performance of two smart charging strategies - Time of Use (TOU) pricing and Load Balancing (LB) on seven representative real-world feeders identified using k-means clustering. A time series-based steady-state load flow analysis was conducted on these feeders to simulate the impact of EV charging under both strategies across four different EV enrollment scenarios and three representative days to capture seasonal load characteristics. A grid upgrade strategy has been proposed to strengthen the power grid to support EV integration with minimal cost. Results demonstrate that both TOU and LB strategies effectively manage the additional EV load with reduced upgrade requirement and cost to existing infrastructure compared to the case without smart charging strategies and LB outperforms TOU when the customer enrollment levels are high. These findings support the viability of smart charging in facilitating EV integration while maintaining distribution network reliability and reducing investment cost.

We propose a symmetrization relation between BPS quivers encoding 4d $\mathcal{N}=2$ theories and symmetric quivers associated to 3d $\mathcal{N}=2$ theories. We analyse in detail the symmetrization of BPS quivers for a series of $A_m$ Argyres-Douglas theories by engineering 3d-4d systems in geometric backgrounds involving appropriate 3-manifolds and Riemann surfaces. We discuss properties of these geometric backgrounds and derive the corresponding quiver partition functions from the perspective of skein modules, which forms the foundation of the symmetrization map for the minimal chamber. We also prove that the structure of wall-crossing in 4d $A_m$ Argyres-Douglas theories is isomorphic to the structure of unlinking of symmetric quivers encoding their partner 3d theories, which allows for a proper definition of the symmetrization map outside the minimal chamber. Finally, we show that the Schur indices of 4d theories are captured by symmetric quivers that include symmetrization of 4d BPS quivers.

We investigate the physics reach and potential for the study of $B$-meson decays to invisible final states at the Future Circular Collider running electron-positron collisions at the $Z$ pole (FCC-ee). Signal and background candidates are simulated for a proposed multipurpose detector, including inclusive contributions from $Z$ decays to leptons or quarks. Signal candidates are selected by a mixture of rectangular cuts and a multiclass boosted decision tree classifier. We determine that branching fractions above $7.6\times10^{-9}$ ($9.7\times10^{-9}$) would be excluded at 90% (95%) confidence level, and branching fractions above $3.0\times10^{-8}$ would be within discovery reach at FCC-ee if $6\times 10^{12}$ $Z$ bosons are produced.

We classify finite subgroups of automorphism groups of non-trivial Severi--Brauer varieties of dimension $q-1$, where $q \geqslant 3$ is a prime number, over an arbitrary field. We also construct families of examples, namely, for every consistent set of finite groups, we construct a field together with a non-trivial Severi--Brauer variety over that field such that every group in the set acts on the constructed variety. Additionally, we show that non-trivial Severi--Brauer varieties of dimension $q-1$, where $q \geqslant 3$ is a prime number, over a field of characteristic not equal to $q$ are not $G$-birationally rigid.

Topological states, known for their robustness against disorder, offer promising avenues for disorder-resistant devices. However, their intrinsic spatial confinement at interfaces imposes geometric constraints that limit the scalability of topological functionalities. Here, we propose a strategy to overcome this limitation by using double-zero-index media to expand topological interfaces. Although occupying finite space, these media are optically equivalent to infinitesimal points, effectively altering the geometry of topological interfaces and breaking conventional bulk-edge correspondence. This strategy enables the spatial expansion of uniform topological states beyond their native interface, offering new possibilities for topological photonic devices. We have verified this behavior through numerical simulations and microwave experiments in a two-dimensional photonic Su-Schrieffer-Heeger lattice. Our findings offer a universal framework to overcome the inherent dimensional limitations of topological states, with implications extending to general wave systems such as acoustic metamaterials.

We extend an earlier lattice QCD analysis of heavy-quark current-current correlators to obtain new values for the $\overline{\mathrm{MS}}$ masses of the $b$, $c$, and $s$~quarks. The analysis uses gluon configurations from the MILC collaboration with vacuum polarization contributions from $u$, $d$, $s$, and~$c$ quarks ($n_f=4$), and lattice spacings down to~0.032~fm. We find that $\overline{m}_b(\overline{m}_b, n_f=5)=4.1923(63)$~GeV, $\overline{m}_c(3~\mathrm{GeV}, n_f=4)=0.9813(34)$~GeV, and $\overline{m}_s(3~\mathrm{GeV}, n_f=4)=83.39(26)$~MeV. These results are corrected for QED by including (quenched) QED in the simulations. They are among the most accurate values by any method to date. We give a detailed analysis of finite lattice-spacing errors that shows why the HISQ discretization of the quark action is particularly useful for $b$-quark simulations even for lattices where~$am_b\approx1$. We also calculate QED and isospin corrections to the (fictitious) $η_s$-meson mass, which is used to tune $s$-quark masses in lattice simulations.

This paper presents an exact and explicit tensor-network equation for the search of nontrivial divisors of a composite integer, together with an algorithm for its computation. The proposed method is based on the MeLoCoToN approach, which addresses combinatorial optimization problems through classical tensor networks. The presented tensor network tensorizes a binary multiplication circuit and projects its output onto the target integer to be factorized. Additionally, in order to make the algorithm more efficient, the number and dimension of the tensors and their contraction scheme are optimized, including a reduced auxiliary register that still preserves at least one valid factorization orientation. Finally, a series of tests on the algorithm are conducted, contracting the tensor network both exactly and approximately using tensor train compression, and evaluating its performance.