We establish the existence of a single-parameter family of the concave kite central configurations in the 4-body problem with two pairs of equal masses. In such configurations, one pair of masses must lie on the base of an isosceles triangle, and the other pair on its symmetric axis with one mass positioned inside the triangle formed by the other three. Using a rigorous computer-assisted analytical approach, we prove that for any non-negative mass ratio, the number of such configurations is either zero, one, or two, thereby providing a complete classification of this family. Furthermore, we show that the unique configuration corresponding to a specific mass ratio is a fold-type bifurcation point within the reduced subspace. We also give a clear and complete bifurcation picture for both symmetric and asymmetric cases of this concave type across the entire planar 4-body configuration space.

This paper proposes a scalable decentralized safety filter for multi-agent systems based on high-order control barrier functions (HOCBFs) and auction-based responsibility allocation. While decentralized HOCBF formulations ensure pairwise safety under input bounds, they face feasibility and scalability challenges as the number of agents grows. Each agent must evaluate an increasing number of pairwise constraints, raising the risk of infeasibility and making it difficult to meet real-time requirements. To address this, we introduce an auction-based allocation scheme that distributes constraint enforcement asymmetrically among neighbors based on local control effort estimates. The resulting directed responsibility graph guarantees full safety coverage while reducing redundant constraints and per-agent computational load. Simulation results confirm safe and efficient coordination across a range of network sizes and interaction densities.

In this paper we develop an algebraic theory to study the problem of finding the minimum distance point from an algebraic variety with respect to the Hermitian distance function. The theory generalizes the Euclidean Distance degree introduced in arXiv:1309.0049, replacing a positive symmetric bilinear form by a Hermitian form. Various examples are presented to show the robustness of the machinery.

Human bone marrow stromal cells (BMSC) include skeletal stem cells with ground-breaking therapeutic potential. However, BMSC colonies have very heterogeneous in vivo behaviour, due to their different potency; this unpredictability is the greatest hurdle to the development of skeletal regeneration therapies. Colony-level heterogeneity urges a fundamental question: how is it possible that one colony as a collective unit behaves differently from another one? If cell-to-cell variability were just an uncorrelated random process, a million cells in a transplant-bound colony would be enough to yield statistical homogeneity, hence washing out any colony-level traits. A possible answer is that the differences between two originating cells are transmitted to their progenies and collectively persist through an hereditary mechanism. But non-genetic inheritance remains an elusive notion, both at the experimental and at the theoretical level. Here, we prove that heterogeneity in the lineage topology of BMSC clonal colonies is determined by heritable traits that regulate cell-cycle exit. The cornerstone of this result is the definition of a novel entropy of the colony, which measures the hereditary ramifications in the distribution of inactive cells across different branches of the proliferation tree. We measure the entropy in 32 clonal colonies, obtained from single-cell lineage tracing experiments, and show that in the greatest majority of clones this entropy is decisively smaller than that of the corresponding non-hereditary lineage. This result indicates that hereditary epigenetic factors play a major role in determining cycle exit of bone marrow stromal cells.

The repeating changing-look active galactic nuclei (RCL AGNs) exhibit multiple appearances and disappearances of broad emission lines (BELs), whose underlying mechanism remains a puzzle. Expanding the sample of RCL AGNs is valuable for constraining the transition timescale and probing the accretion physics driving CL behaviors. This study aims to identify RCL AGNs using the multi-epoch spectroscopic data of confirmed CL AGNs from the Sloan Digital Sky Survey, Large Sky Area Multi-Object Fiber Spectroscopic Telescope, and Dark Energy Spectroscopic Instrument, supplemented with mid-infrared (MIR) light curves. Through selection criteria and visual inspection, we identify 22 RCL AGNs among 299 CL AGNs, corresponding to an occurrence rate of about 7\%, indicating that repeated transitions are not extremely rare in CL AGNs. Among the 22 RCL AGNs, 16 are newly identified, which significantly expands the known RCL AGN sample. Based on the spectra and densely sampled MIR light curves, we derive MIR variability timescales for 18 RCL AGNs, and find no significant correlation between the timescale and the black hole mass.

We compute the two-loop renormalisation group equation for the effective Higgs to gluon coupling in Standard Model Effective Field Theory. Concretely, we present the contributions generated by the operators belonging to class 3 and 7 in the Warsaw basis, completing the two-loop renormalization program of the Higgs-gluon coupling proportional to the top Yukawa coupling for potentially tree-level generated operators. We investigate the phenomenological impact of the contributions in fits to Higgs data both in a bottom-up approach and a top-down approach in terms of UV models with vector-like quarks.

We show that the canonical actions of the Thompson group V and its generalizations on the Cantor set are not strongly ergodic. This implies that the associated crossed product von Neumann algebras are not full. This also yields a non-embedding result for the Thompson groups.

In this paper, we consider a contextual stochastic optimization problem in which unknown parameters follow distributions that depend on contextual covariates and decisions. The problem is motivated by transportation infrastructure decisions such as facility location or network design. In such high-stakes settings, decisions must often be communicated, justified, and reconsidered under alternative stakeholder requirements. To this end, we propose a framework for computing relative counterfactual explanations. These explanations identify the smallest changes in the covariates required for a solution to satisfy prescribed constraints while limiting the performance loss to a controlled level. Whereas relative explanations have been introduced in prior literature, to the best of our knowledge, this is the first work focusing on problems with binary decision variables and endogenous uncertainty. We propose a methodology that uses the Wasserstein distance as a regularization term in the objective. Beyond improving tractability, this regularization yields explanations with desirable structural properties: it produces sparser counterfactuals, induces smoother transitions in the underlying choice distributions, and keeps the counterfactual behavior close to realistic demand patterns. We illustrate the method using a choice-based competitive facility location problem and present numerical experiments that demonstrate its ability to efficiently compute sparse, plausible, and interpretable explanations. We further validate the framework on a real-world case study of electric vehicle charging station planning in Montreal, where the explanations reveal the minimal capacity investments and environmental conditions required to justify including a candidate location in the charging network.

We propose a fully mixed virtual element method for the numerical approximation of the coupling between linear poroelasticity equations with strong symmetry of total poroelastic stress (using the Hellinger--Reissner principle) and stress-altered solute diffusion (where diffusive flux depends on the poroelastic stress and nonlinearly on the concentration gradient). Because of the nonlinear coupling, the function spaces associated with the nonlinear diffusion sub-problem are of Banach type. To handle this structure, the solvability of both the continuous and discrete problems is established through a decoupled fixed-point strategy. The linear poroelasticity component is analysed using the theory for perturbed saddle-point problems, whereas the nonlinear diffusion problem, relies on the classical Minty--Browder theorem for monotone global operators. The existence of solutions for the fully coupled system is rigorously proven via Schauder's fixed-point theorem. Additionally, we establish rigorous a priori error estimates for the discrete scheme, successfully handling the strongly cross-coupled nonlinearities. These findings are supported by computational evidence, demonstrating that the formulation asymptotically recovers optimal convergence rates in practice. As a key contribution, both the numerical scheme and its underlying analysis prove to be robust with respect to the poromechanical parameters. Finally, several numerical examples are presented to illustrate the properties and applicability of the proposed scheme in the study of solute transport in the context of brain multiphysics.

In this article, we investigate the late-time growth of holographic complexity, defined via the complexity-volume (CV) and complexity-action (CA) prescriptions, for BTZ, Schwarzschild, Reissner-Nordström, and Kerr black holes. Extending previous analyses beyond asymptotically AdS spacetimes, we include asymptotically flat geometries and employ the CV and CA prescriptions as comparative geometric diagnostics of black hole interior dynamics. In all cases considered, the complexity growth rate is governed by horizon thermodynamic data and scales with $T_H S_H$. While the CV prescription exhibits geometry-dependent proportionality constants, the CA prescription yields a universal thermodynamic scaling across all black holes studied, including non-AdS cases. We further analyze variations in the complexity growth rate, $δ\dot{\mathcal{C}}$, under physical processes such as the Penrose process, superradiance, and particle accretion. We find that $δ\dot{\mathcal{C}}$ exhibits non-trivial behavior: it increases under the Penrose process and superradiance, while under particle accretion it can increase, remain unchanged, or decrease depending on the angular momentum of the infalling particle. In quasi-equilibrium regimes, the variation in complexity closely tracks the behavior of the horizon area and interior volume growth, whereas out-of-equilibrium processes render it sensitive to angular momentum transfer and may lead to negative values within an equilibrium approximation. This behavior highlights the limitations of equilibrium-based treatments and motivates a fully dynamical analysis incorporating horizon stresses and transient hair.

In this survey, we describe recent progress on asymptotic properties of various automorphic orbits in free groups. In particular, we address the problem of counting potentially positive elements of a given length. We also discuss complexity (worst-case, average-case, and generic-case) of Whitehead's automorphism problem and relevant properties of automorphic orbits, including orbit-blocking words.

A family of compact n-manifolds is locally combinatorially defined (LCD) if it can be specified by a finite number of local triangulations. We show that LCD is equivalent to the existence of a compact branched n-manifold W, such that the family is precisely those manifolds that immerse into W. In subsequent papers, the equivalence will be used to show that, for each of the eight Thurston geometries, the family of closed 3-manifolds admitting that geometry is LCD.

Quasiperiodic eruptions (QPEs) are intense, recurring outbursts of X-ray radiation originating from the nuclei of distant galaxies. One of the promising models of QPE explains these eruptions using extreme-mass-ratio inspirals (EMRIs), in which a stellar-mass object-such as a star or a stellar-mass black hole-orbits a central massive black hole (MBH) and periodically plows through its accretion disk. In this work, we compute the gravitational wave (GW) signals emitted by such EMRI systems. We find that the physical drag and perturbations due to shock caused by the orbiter-disk collisions leave a distinct imprint on the emitted waveforms. Rather than the smooth, monochromatic evolution observed in vacuum systems, these interactions excite non-discrete modes that manifest as subtle shifts in the orbital frequency and as high-frequency ``tails'' in the signal spectrum. We demonstrate as an example outcome of our model that a specific QPE source RX J1301.9+2747 could be detectable by future space-based GW detectors, provided the orbiter maintains a moderate eccentricity of approximately $0.25$ and a mass exceeding $35\;M_\odot$. Our analysis shows that the signal-to-noise ratio for these events would be high enough to clearly distinguish them from standard vacuum EMRIs. Consequently, GW observations offer a powerful tool to probe the dense environments surrounding MBHs and could give further insight into the elusive origins of QPEs.

The $T_{c\bar{s}}$ state observed in the decay $D_{s1}(2460)^+ \to D_s^+π^+π^-$ provides direct evidence for an isovector open-charm tetraquark state with strangeness--a discovery that demands a systematic framework connecting its origin to the nature of the parent $D_{s1}$. We successfully achieve this connection by two mechanisms, triangle loops and the coupled channel of $DK$-$D_sπ$ with pure off-diagonal potentials. We first point out the behavior of propagator of $D_sπ$ will influence the effective potential of $DK\to DK$, then we can successfully obtain the pole of $T_{c\bar{s}}$ on the second Reimann Sheet. By combing with the $ππ$-$KK$ rescattering, not only the two-peak structure in $D_{s1}(2460)$ decay is well reproduced, but also a single-peak structure is predicted in $D_{s1}(2536)$ decay. The marked difference, testable at LHCb and Belle II, is driven by the $S$-wave versus $D$-wave nature of their $D^*K$ couplings, revealing the underlying structural distinction between the two $D_{s1}$ states. By directly linking hadronic structure to decay patterns, this work provides a template for deciphering the nature of such exotic states. More broadly, by revealing how non-perturbative coupled-channel effects manifest in exotic hadrons, our analysis connects to a universal mechanism shared by systems ranging from halo nuclei to atomic Feshbach resonances, offering a unified perspective across these fields.

We present an investigation into the semileptonic and nonleptonic weak decays of bottom baryons $Ω^{*}_{b}$ and $Ω_{b}$ within the framework of three-point QCD sum rules. In the semileptonic sector, the $Ω^{*}_b\rightarrowΩ_c\ell\barν_{\ell}$ and $Ω_b\rightarrowΩ^*_c\ell\barν_{\ell}$ transitions are specifically considered. Utilizing the operator product expansion up to dimension six, the responsible form factors of these decays are obtained. The acquired form factors enable us to determine the decay widths in three leptonic channels. Branching ratios related to the $Ω_{b}$ baryon semileptonic decays are also presented. These invariant form factors are subsequently employed as inputs to determine the nonleptonic weak decay widths in various modes with emitting a pseudoscalar or vector meson. An extensive investigation into all possible decay channels of bottom baryons provides valuable information for future experiments to examine the SM predictions, explores the new physics effects in heavy baryonic decays, and advances the understanding of the internal structure of heavy baryons.

We update our previous extraction of transverse momentum distributions of unpolarized quarks in the pion by implementing a more comprehensive description of theoretical uncertainties and, for the first time, by exploring possible differences among quark flavors. We extract such distributions from all available data for unpolarized pion-nucleus Drell-Yan processes, where the cross section is differential in the transverse momentum of the final lepton pair. The cross section involves transverse momentum distributions in the nucleon, that we consistently take from our previous studies.

Given $m \ge 2$ discrete probability distributions over $n$ states each, the minimum-entropy coupling is the minimum-entropy joint distribution whose marginals are the same as the input distributions. Computing the minimum-entropy coupling is NP-hard, but there has been significant progress in designing approximation algorithms; prior to this work, the best known polynomial-time algorithms attain guarantees of the form $H(\operatorname{ALG}) \le H(\operatorname{OPT}) + c$, where $c \approx 0.53$ for $m=2$, and $c \approx 1.22$ for general $m$ [CKQGK '23]. A main open question is whether this task is APX-hard, or whether there exists a polynomial-time approximation scheme (PTAS). In this work, we design an algorithm that produces a coupling with entropy $H(\operatorname{ALG}) \le H(\operatorname{OPT}) + \varepsilon$ in running time $n^{O(\operatorname{poly}(1/\varepsilon) \cdot \operatorname{exp}(m) )}$: showing a PTAS exists for constant $m$.

This is an expository paper which discusses an approach to the linear quadratic Gaussian/loop transfer recovery (LQG/LTR) design problem for finite-dimensional single-variable (single-input/single-output, SISO) control systems. The approach is based on the utilisation of weighting augmentation for incorporating design specifications into the framework of the LTR technique for LQG compensator design. The LQG compensator is to simultaneously meet given analytical low- and high-frequency design specifications expressed in terms of desirable sensitivity and controller noise sensitivity functions. The paper is aimed at non-specialists and, in particular, practitioners in finite-dimensional LQG theory interested in the design of feedback compensators for closed-loop performance and robustness shaping of SISO control systems in realistic situations. The proposed approach is illustrated by a detailed design example: the torque control of a geared DC motor with an elastically mounted output shaft.

We analyse the classic two-level additive Schwarz domain-decomposition GMRES preconditioner for finite-element discretisations of the Helmholtz equation with large wavenumber $k$, where both the fine and coarse spaces consist of piecewise polynomials with polynomial degree increasing like $\log k$. We exhibit choices of these fine and coarse spaces such that -- up to factors of $\log k$ -- both are pollution free (with the ratio of the coarse-space dimension to the fine-space dimension arbitrarily small), the number of degrees of freedom per subdomain is constant, and the number of GMRES iterations is proved to be bounded independently of $k$. These are the first $k$-explicit convergence results about a two-level Schwarz preconditioner for high-frequency Helmholtz with a coarse space that is pollution free and does not consist of problem-adapted basis functions.

In this paper, we investigate the existence of nontrivial least-energy solutions for the super-Liouville equation with positive coefficient functions on the two-dimensional sphere. Firstly, we derive a global Pohozaev-type identity by analyzing the behavior of solutions under conformal transformations, which generalizes the classical Kazdan-Warner obstruction for the two-dimensional Nirenberg problem. Secondly, by exploiting conformal symmetry, we establish a pointwise estimate that bounds the norm of the spinor component by the scalar component, and show that the $H^1 \times H^{1/2}$ energy of the spinor part remains uniformly bounded. As a byproduct of our analysis, parallel techniques are applied to the Dirac-Einstein equations on the 3-sphere, demonstrating that nontrivial solutions are uniformly bounded away from the trivial solution in the $H^1 \times H^{1/2}$ norm. Moreover, the compactness of the solution space is also analyzed from two perspectives: in the low-energy regime, and modulo the action of the Möbius group. Finally, by introducing a new natural constraint $\mathcal{A}$ and employing variational methods, we obtain a supersymmetric generalization of the Moser-Trudinger-Onofri inequality and establish the existence of least-energy solutions for even coefficient functions. In particular, these solutions are shown to be nontrivial provided that a certain spectral parameter associated with the coefficients satisfies $λ_1(h_2, h_1) < 1$. Concurrently, we provide a complete classification of nontrivial least-energy solutions in the case of positive constant coefficients.

We derive converse Lyapunov theorems for input-to-state stability (ISS) of linear infinite-dimensional analytic systems. While we show that ISS in general does not imply the existence of a coercive quadratic ISS Lyapunov function, even if the input operator is bounded, we prove that indeed quadratic ISS Lyapunov functions always exist for $p$-admissible input operators with $p<2$, provided the semigroup is similar to a contraction on a Hilbert space. The constructions are semi-explicit and rely on classical results on analytic semigroups and similarity to contractive ones. In the case of self-adjoint generators, they coincide with the canonical Lyapunov function being the norm squared.

In this paper, we prove tilting equivalence for the finite almost derived algebraic cobordism spectrum $\mathrm{dMGL}^{a,\rm fin}$ of perfectoid algebras. More precisely, if $V$ is an integral perfectoid valuation ring and $A$ is an integral perfectoid $V$-algebra, then the tilting functor induces a weak equivalence \[ \mathrm{dMGL}^{a,\rm fin}(A) \simeq \mathrm{dMGL}^{a,\rm fin}(A^\flat). \] This invariant is a finite syntomic, derived, and non-$\mathbb{A}^1$-local version of algebraic cobordism, designed to retain infinitesimal deformation data over mixed characteristic bases. To prove the result, we first establish the corresponding finite non-unital statement and isolate a form of excisive approximation for pointed $\infty$-categories, including non-presentable ones. In the locally finitely presentable case, this agrees with the framework of Heuts. We also define approximation functors along natural transformations and apply them to the comparison between periodic algebraic cobordism and homotopy $K$-theory, obtaining Bott periodicity and Gabber rigidity.

We study the interaction between photons, dark photons, and axions at future lepton colliders, focusing on single-photon events with missing energy as the experimental signature. We find that future facilities such as the ILC, CEPC, and FCC-ee will be sensitive to the axion--photon--dark photon coupling down to the order of $10^{-4}\, \mathrm{GeV}^{-1}$ for dark photon masses around $O(10~\mathrm{GeV})$, assuming that the axion is extremely light and escapes detection. We further show that longitudinal beam polarization at the ILC can enhance the signal significance by a factor of four, providing the strongest projected reach in the model parameter space. Existing constraints from LEP II are analyzed for comparison. Furthermore, the mass of dark photon can be determined by measuring the sharp drop-off in the distribution of the recoil mass.

We introduce the Cycle Walk, a new Markov chain Monte Carlo method for sampling distributions on balanced graph partitions, motivated by applications in political redistricting. The method operates on spanning forests and combines two types of updates: local "cycle" moves within districts and global moves that exchange population between adjacent districts while preserving balance constraints. This construction enables efficient Metropolis--Hastings correction while allowing proposals at multiple spatial scales. We show that the Cycle Walk naturally interpolates between existing approaches based on local updates and a class of global update methods derived from recombination (RECOM). Through a range of numerical experiments on synthetic graphs and real-world precinct data, we demonstrate that the Cycle Walk exhibits improved empirical convergence diagnostics for distributions that place weaker weight on spanning-tree counts, a regime that is challenging for existing methods. In particular, the algorithm remains effective when incorporating alternative compactness measures that more closely reflect policy-relevant criteria. These results suggest that the Cycle Walk provides a flexible and computationally efficient framework for sampling from a broader class of redistricting distributions than previously accessible with MCMC techniques.

Living organisms rely on molecular networks, such as gene circuits and signaling pathways, for information processing and robust decision-making in crowded, noisy environments. Recent advances show that interacting biomolecules self-organize by phase transitions into coexisting spatial compartments called condensates, often on cellular surfaces such as chromatin and membranes. In this paper, we demonstrate that multicomponent fluids can be designed to recruit distinct condensates to surfaces with differing compositions, performing a form of surface classification by condensation. We draw an analogy to multidimensional classification in machine learning and explore how hidden species, analogous to hidden nodes, expand the expressivity and capacity of these interacting ensembles to facilitate complex decision boundaries. By simply changing levels of individual species, we find that the same molecular repertoire can be reprogrammed to solve new tasks. Together, our findings suggest that the physical processes underlying biomolecular condensates can encode and drive adaptive information processing beyond compartmentalization.

We introduce a purely Lie algebraic formalization of the Feigin--Tipunin's geometric construction of logarithmic CFTs/VOAs. After reformulating the geometric representation theory of FT construction under this new setting, within this framework, we uniformly construct the (multiplet) principal W-algebras at positive integer level associated with any simple Lie algebra $\mathfrak{g}$ and Lie superalgebra $\mathfrak{osp}(1|2r)$, thereby establishing Weyl-type character formulas and simplicity theorems that extend the first author's previous results.

This paper considers systems in which two or more ligands bind independently to a common scaffold. Such systems arise in a range of applications, including immunotherapy and synthetic biology. We show that each stoichiometric compatibility class contains a unique steady state, and that this steady state is asymptotically stable. The main result gives a rigorous proof that the steady-state concentration of the fully bound complex, viewed as a function of the total scaffold concentration, has a unique maximum. This biphasic dose response is a characteristic feature of scaffolding systems and, in the special case of two ligands, plays an important role in the design and analysis of bispecific antibody drugs.

Spatially resolved observations of the Sun and the astronomical sample size of stellar bodies are the respective key strengths of solar and stellar observations. However, the large difference in object brightness between the Sun and other stars has led to distinctly different instrumentation and methodologies between the two fields. We produce and analyze synthetic full-disk spectra derived from 19 small area field-of-view optical observations of solar flares acquired by the Swedish 1-m Solar Telescope (SST) between 2011 and 2024. These are used to investigate what can and cannot be inferred about physical processes on the Sun from Sun-as-a-star observations. The recently released Numerical Empirical Sun-as-a-Star Integrator (NESSI) code provides synthetic full-disk integrated spectral line emission based on smaller field-of-view input, accounting for center-to-limb variations and differential rotation. We use this code to generate pseudo-Sun-as-a-star spectra from the SST observations. ...

Hybrid Analog and Digital (HAD) architectures significantly reduce hardware overhead but introduce severe dimensionality compression, which strips the Spatial Covariance Matrix (SCM) of the degrees of freedom required for high-resolution Direction-of-Arrival (DoA) estimation. This challenge is further compounded by passive Butler-matrix implementations of Discrete Fourier Transform (DFT) analog beamforming, which avoid active phase shifters and amplifiers. In this paper, we propose a Generalized Least Squares (GLS) framework that exploits the Cauchy-like displacement structure that arises after DFT beamforming. By leveraging this structure, we develop a highly efficient numerical technique to recover the SCM for uniform linear arrays with a complexity of $\mathcal{O}(N_{\text{RF}}^2 N_x)$, where $N_x$ is the number of antennas and $N_{\text{RF}}$ the number of RF-chains. Simulations demonstrate that our estimator approaches the Cramér-Rao Bound (CRB) while outperforming state-of-the-art methods.

The bulk photovoltaic effect (BPVE), a manifestation of broken centrosymmetry, has attracted interest as a probe of the symmetry and quantum geometry of materials, and for use in photovoltaic and optoelectronic devices. However, so far the effect has not been captured directly in space and time. Here, we use contactless pump-probe microscopy to visualize the spatiotemporal evolution of photoexcited carriers in single-crystal, mono-domain $BiFeO_{3}$, a prototypical ferroelectric material. We observe asymmetric carrier transport along the polar axis, which confirms the intrinsic bulk- and symmetry-driven nature of the BPVE. Remarkably, this asymmetric transport persists for several nanoseconds after photoexcitation, which cannot be explained by conventional short-lived shift or phonon ballistic current BPVE mechanisms. Our Monte Carlo simulations show that asymmetric momentum scattering by defects, such as oxygen vacancies, leads to long-lived asymmetric carrier transport, as observed experimentally. Beyond fundamental insights, this paves the way towards controlling symmetry- and defect-driven photoresponses.