Carrollian $\mathbb{R}^\times$-bundles ($\mathbb{R}^\times := \mathbb{R}\setminus \{0\}$) offer a novel perspective on intrinsic Carrollian geometry using the powerful tools of principal bundles. Given a choice of principal connection, a canonical Lorentzian metric exists on the total space. This metric enables the development of Hodge theory on a Carrollian $\mathbb{R}^\times$-bundle; specifically, the Hodge star operator and Hodge--de Rham Laplacian are constructed. These constructions are obstructed on a Carrollian manifold due to the degenerate metric. The framework of Carrollian $\mathbb{R}^\times$-bundles bridges the gap between Carrollian geometry and (pseudo)-Riemannian geometry. As an example, the question of the Hodge--de Rham Laplacian on the event horizon of a Schwarzschild black hole is addressed. A Carrollian version of electromagnetism is also proposed.

Determinantal point processes (DPPs for short) are a class of repulsive point processes. They have found some statistical applications to model spatial point pattern datasets with repulsion between close points. In the case of DPPs on finite sets, they are defined by a matrix called the DPP kernel which is usually assumed to be symmetric. While there are a few known examples of DPPs with nonsymmetric kernels, not much is known on how this affects their usual properties. In this paper, we demonstrate how to adapt the results on $P_0$ matrices to the DPP setting in order to get necessary and sufficient conditions for the well-definedness of DPPs with nonsymmetric kernels. We also generalize various common results on DPPs. We then show how to use these results to construct attractive couplings of regular DPPs with symmetric kernels in order to model spatial marked point patterns with repulsion between points of the same mark and attraction between points of different marks.

The development of a digital twin (DT) framework for fast online adaptive proton therapy planning in prostate stereotactic body radiation therapy (SBRT) with dominant intraprostatic lesion (DIL) boost represents a significant advancement in personalized radiotherapy. This framework integrates deep learning-based multi-atlas deformable image registration, daily patient anatomy updates via cone-beam CT (CBCT), and knowledge-based plan quality evaluation using the ProKnow scoring system to achieve clinical-equivalent plan quality with substantially reduced reoptimization times compared to traditional clinical workflows. Drawing on a database of 43 prior prostate SBRT cases, the DT framework predicts interfractional anatomical variations for new patients and pre-generates multiple probabilistic treatment plans. Upon acquiring daily CBCT, it enables rapid plan reoptimization, achieving an average reoptimization time of 5.5 [2.8, 8.2] minutes, compared to 19.8 [7.9, 31.7] minutes for clinical plans. The DT-based plans yielded a plan quality score of 157.2 [151.6, 162.8], surpassing or matching clinical plans, with superior dose coverage for the DIL (V100: 99.5%) and clinical target volume (CTV V100: 99.8%). Additionally, the framework minimized doses to organs at risk (OARs), achieving bladder V20.8Gy of 11.4 [7.2, 15.6] cc, rectum V23Gy of 0.7 [0.3, 1.1] cc, and urethra D10 of 90.9% [88.6%, 93.2%], aligning with clinical standards. By addressing interfractional variations efficiently, the DT framework enhances treatment precision, reduces OAR toxicity, and supports real-time adaptive radiotherapy. This transformative approach not only streamlines the planning process but also improves clinical outcomes, offering a scalable solution for prostate SBRT with DIL boost and paving the way for broader applications in adaptive proton therapy.

The search for singularity-free cosmological solutions has become a highly active topic in the physics community in recent years, yet existing results are largely numerical or based on asymptotic analysis. To place these developments on a firm mathematical footing, we rigorously establish the global existence and estimates of a class of singularity-free cosmological solutions to the fully nonlinear Einstein--scalar system in Einstein-scalar-Gauss-Bonnet gravity with quadratic coupling, providing proofs of previous numerical results in mathematical perspective. We further prove nonlinear scalarization triggered by a Gauss-Bonnet-induced tachyonic instability. Our analysis relies on a novel structural identity, the power identity, which yields decoupled differential inequalities for the Hubble parameter. This framework provides a new method for converting numerical evidence into a mathmatical proof for nonlinear systems.

The fundamental goal of information theory is to characterize complex operational tasks using efficiently computable information quantities, Shannon's capacity formula being the prime example of this. However, many tasks in quantum information can only be characterized by regularized entropic measures that are often not known to be computable and for which efficient approximations are scarce. It is thus of fundamental importance to understand when regularization is not needed, opening the door to an efficiently computable characterization based on additive quantities. Here, we demonstrate that for a large class of problems, the question of whether regularization is needed or not can be determined at the single-copy level. Specifically, we demonstrate that regularization of the Umegaki relative entropy, along with related quantities such as the Petz and sandwiched relative entropies, is not needed if and only if a single-copy optimizer satisfies a certain property. These problems include hypothesis testing with arbitrarily varying hypotheses as well as quantum resource theories used to derive fundamental bounds for entanglement and magic state distillation. We derive the Stein, Chernoff, and Hoeffding exponents for these problems and establish necessary and sufficient conditions for their additivity, while also presenting partial results for the strong converse exponent.

Carrollian field theories are usually understood as limits of relativistic theories. In this note, we use Carrollian $\mathbb{R}^\times$-bundles equipped with a principal connection to construct Carrollian sigma models intrinsically. The resulting theories are neither ``electric'' nor ``magnetic'' in the usual sense. As a physically suggestive example, we derive a Carrollian wave equation governing the dynamics of a scalar field on the event horizon of a Schwarzschild black hole.

Motivated by recent developments in the study of quasi-one-dimensional iron systems with Fe$^{2+}$, we comprehensively study the Fe$^{3+}$ chalcogenide chain system. Based on first-principles calculations, the Fe$^{3+}$ chain has a similar electronic structure as discussed before in the iron 2+ chain, due to similar Fe$X_4$ ($X$ = S or Se) tetrahedron chain geometry. Furthermore, a three-orbital electronic Hubbard model for this chain was constructed by using the density matrix renormalization group method. A robust antiferromagnetic coupling was unveiled in the chain direction. In addition, in the intermediate electronic correlation $U/W$ region, we found an interesting orbital-selective Mott phase with the coexistence of localized and itinerant electrons ($U$ is the on-site Hubbard repulsion, while $W$ is the electronic bandwidth) {\color{blue}based on the orbital-selective behavior observed in the charge fluctuations}. Furthermore, we do not observe any obvious pairing tendency in the Fe$^{3+}$ chain in the electronic correlation $U/W$ region, where superconducting pairing tendencies were reported before in iron ladders. This suggests that superconductivity is unlikely to emerge in the Fe$^{3+}$ systems. Our results establish with clarity the similarities and differences between Fe$^{2+}$and Fe$^{3+}$ iron chains, as well as iron ladders.

In recent work, Amdeberhan and Merca considered the integer partition function $a(n)$ which counts the number of integer partitions of weight $n$ wherein even parts come in only one color (i.e., they are monochromatic), while the odd parts may appear in one of three colors. One of the results that they proved was that, for all $n\geq 0$, $a(7n+2) \equiv 0 \pmod{7}$. In this work, we generalize this function $a(n)$ by naturally placing it within an infinite family of related partition functions. Using elementary generating function manipulations and classical $q$--series identities, we then prove infinitely many congruences modulo 7 which are satisfied by members of this family of functions.

Let $(Ω, ¶)$ be a standard probability space and let $\vartheta:Ω\to Ω$ be a measure preserving ergodic homeomorphism. Let $\mathcal{A}$ be a $C^*$-algebra with a unit and let $\mathcal{A}_{\mathbb{Z}}$ be the quasi-local algebra associated to the spin chain with one-site algebra $\mathcal{A}$. Equip $\mathcal{A}_{\mathbb{Z}}$ with the group action of translation by $k$-units, $τ_k\in Aut(\mathcal{A}_{\mathbb{Z}})$ for $k\in \mathbb{Z}$. We study the problem of finding a disordered matrix product state decomposition for disordered states $ψ(ω)$ on $\mathcal{A}_{\mathbb{Z}}$ with the covariance symmetry condition $ψ(ω) \circ τ_k = ψ(\vartheta^k ω)$. This can be seen as an ergodic generalization of the results of Fannes, Nachtergaele, and Werner [31]. To reify our structure theory, we present a disordered state $ν_ω$ obtained by sampling the AKLT model [2] in parameter space. We go on to show that $ν_ω$ has a nearest-neighbor parent Hamiltonian, its bulk spectral gap closes, but it has almost surely exponentially decaying correlations, and finally, that $ν_ω$ is time-reversal invariant with a Tasaki index of $-1$ almost surely.

This paper is devoted to filtering, smoothing, and prediction of polynomial processes that are partially observed. These problems are known to allow for an explicit solution in the simpler case of linear Gaussian state space models. The key insight underlying the present piece of research is that in linear filtering applications polynomial processes and their discrete-time counterpart are indistinguishable from Gaussian processes sharing their first two moments. We describe the construction of these Gaussian equivalents of polynomial processes and explicitly compute optimal linear filters, predictors and smoothers for polynomial processes in discrete and continuous time. The consideration of Gaussian equivalents also opens the door to parameter estimation and linear-quadratic optimal control in the context of polynomial processes.

The work dissipated in pulling a polymer chain with internal friction is numerically calculated by considering a sequence of $N$ spring-dashpots tethered at one end and being pulled at the other using a harmonic trap via linear and symmetric protocols. The variation of the dissipation with the chain length, pulling trap stiffness, and the internal friction parameter are examined in detail for both the protocols. {While the dissipation increases with $N$ for chains without internal friction, the relationship between the dissipation and $N$ for chains with internal friction depends on the pulling trap stiffness. For chains with internal friction, the dissipation \textit{decreases} (increases) with $N$ as the the pulling trap stiffness is \textit{increased} (decreased), keeping all other parameters constant. Therefore, unlike in the case of a single-mode spring-dashpot ($N=1$) for which a simple relationship exists between the damping coefficient of the dashpot and the dissipated work [as shown in Phys. Rev. Res. \textbf{2}, 013331 (2020)], the same is not true for the general case of $N>1$ due to the stiffness-dependent dissipative response of bead-spring-dashpot chains.

We introduce a biharmonic Steklov problem with Neumann-type boundary conditions on differential forms and show that it is well-posed. We prove the existence of a discrete spectrum for this problem and provide associated variational characterizations of its eigenvalues. We establish eigenvalue estimates known as Kuttler-Sigillito inequalities, relating the eigenvalues of this problem to those of the Steklov, Dirichlet and Neumann problems, as well as the biharmonic Steklov problem with Dirichlet boundary conditions on differential forms.

We propose a homotopy method for solving mathematical programs with complementarity constraints (CCs). The indicator function of the CCs is relaxed by the Lasry--Lions double envelope, an extension of the Moreau envelope that enjoys an additional smoothness property, making it amenable to fast optimization algorithms. The proposed algorithm mimics the behavior of homotopy methods for systems of nonlinear equations or penalty methods for constrained optimization: it solves a sequence of smooth subproblems that progressively approximate the original problem, using the solution of each subproblem as the starting point for the next one. In the limiting setting, we establish the convergence to Mordukhovich and Clarke stationary points. We also provide a worst-case complexity analysis for computing an approximate stationary point. Preliminary numerical results on a suite of benchmark problems demonstrate the effectiveness of the proposed approach.

Ultrafast optical control of solids has uncovered new phenomena and advanced non-equilibrium condensed matter physics, where photon dressed electronic states - Floquet Bloch states (FBSs) - emerge under a strong oscillating laser field, also known as Floquet engineering. Although FBSs have been extensively investigated using time and angle resolved photoemission spectroscopy, direct evidence of their role in high-harmonic generation spectroscopy (HHGS) has remained elusive. Here, we present combined experimental and theoretical evidence that FBSs can be probed by HHG emission in the wide-bandgap solid magnesium oxide (MgO) driven by few cycle near infrared pulses. Experimentally, we observe clear evidence of FBSs in the HHG yield dependence on the crystal orientation. This specific feature is attributed to nonadiabatic coupling between FBSs and conduction bands near the Brillouin zone edge, where the strong laser field transiently breaks time reversal symmetry. We have confronted the experimental findings with numerical solutions of the time dependent Schrödinger equation, which reproduce the new feature and confirm its Floquet origin. The theoretical results show a coupling inducing a local band structure renormalization and Floquet like hybridization under strong field excitation. It also shows that FBS nonadiabatic dynamics persist in the strong field regime, establishing HHGS as a powerful probe of ultrafast light induced band hybridization in solids.

The next generation of circular electron-positron colliders, such as the Circular Electron Positron Collider and the Future Circular Collider, will provide an unprecedented level of precision in probing the properties of the Higgs boson. In this study, we examine the flavor-changing neutral Higgs decay $h\to bs$ produced via the Higgs-strahlung process within the framework of the Two-Higgs-Doublet Model Type III. We identify regions of the parameter space that remain viable after applying stringent constraints from current experimental data. By employing a multivariate analysis based on Boosted Decision Trees, we project that a signal significance of $5σ$ can be achieved, even after accounting for irreducible backgrounds and systematic uncertainties. Our findings show that these future colliders could offer a unique avenue for discovering signatures of physics beyond the standard model.

We study invariant pseudo-Kähler structures on a solvmanifold $G$ such that the Lie algebra $\mathfrak{g}$ is almost abelian, that is $\mathfrak{g}=\mathfrak{h}\rtimes\mathbb{R}$, with $\mathfrak{h}$ abelian; comparing with the positive-definite case, an additional situation occurs, corresponding to the ideal $\mathfrak{h}$ being degenerate. We obtain a classification up to unitary isomorphism in all dimensions. We deduce that every nilpotent almost abelian Lie algebra endowed with a complex structure also admits a compatible pseudo-Kähler structure, and prove that this is no longer true for general almost abelian Lie algebras; indeed, we classify all the almost abelian Lie algebras that admit a complex structure and a symplectic structure but no compatible pseudo-Kähler metric. We study the curvature of the metrics we have obtained, and use some of them to construct Einstein pseudo-Kähler metrics in two dimensions higher.

A non-Abelian gauge model with a complex isovector scalar field and a sixth-order self-interaction potential is considered. It is shown that it has a nontopological soliton solution. The features of this soliton include a monopole-like core surrounded by a Q-ball-like shell, the existence of radially excited states, and a long-range dipole chromomagnetic field. The properties of the soliton are studied using analytical and numerical methods. In particular, the asymptotic dependencies of the energy and the Noether charge on a phase frequency are obtained for two extreme regimes. It is also found that in these two extreme regimes, the chromomagnetic dipole moment of the soliton is proportional to its linear size.

We study the phenomena of neutrino oscillations and flavour mixing by incorporating the gravitational effects through the Dirac equation in curved spacetime inside a spherically symmetric star. We show that the flavour transition probabilities of the neutrinos depend on the interior spacetime metric as they propagate out of the star. As a consequence, we show that one could distinguish between different possible equation of states of nuclear matter even for an isolated neutron star if one could determine the flavour composition of emitted neutrinos near the stellar surface.

We have analysed a sample of 2MIG isolated galaxies hosting AGNs (isolated AGNs) to assess whether their nuclear activity differs from that in denser environments. The isolation criteria rule out interactions with other galaxies of similar evolutionary stage at least $\sim 3$~Gyr. We systematised the available \textit{Swift}, \textit{NuSTAR}, \textit{XMM-Newton}, \textit{Chandra}, and \textit{INTEGRAL} X-ray data for isolated AGNs at $z<0.05$, determining their general X-ray properties and peculiarities, spectral models, and supermassive black hole (SMBH) masses. We investigated the best spectral models for 20 isolated AGNs, including 9 sources fitted for the first time in this work. Our results indicate that an isolation of galaxies in the nearby Universe does not significantly affect nuclear activity. This conclusion is supported by the diversity of accretion types and the absence of any preference for a particular basic or composite spectral model. We note an interesting case for ESO~499$-$041, where the data-to-model ratio shows significant changes above 5~keV. These deviations from the continuum may tentatively indicate the presence of a relativistic iron line in the \textit{Chandra} spectrum of ESO~499$-$041 compared to the \textit{Swift} spectrum. We derived SMBH masses for 24/32 isolated AGNs applying the $M_{\rm BH}$--$σ_\star$ relation and used available estimates for 8/32. A general distribution is that 27/32 isolated AGNs host SMBHs with $M_{\mathrm{SMBH}} \lesssim 10^{8}\,M_\odot$. For the first time, we found evidence of the linear correlation between L$_{2-10, keV}$ and $\log M_{\mathrm{SMBH}}$ that is not observed in other AGNs samples. This trend may be affected by the limited sample size and requires further confirmation with larger datasets.

Traffic classification has a significant impact on maintaining the Quality of Service (QoS) of the network. Since traditional methods heavily rely on feature extraction and large scale labeled data, some recent pre-trained models manage to reduce the dependency by utilizing different pre-training tasks to train generic representations for network packets. However, existing pre-trained models typically adopt pre-training tasks developed for image or text data, which are not tailored to traffic data. As a result, the obtained traffic representations fail to fully reflect the information contained in the traffic, and may even disrupt the protocol information. To address this, we propose TraGe, a novel generic packet representation model for traffic classification. Based on the differences between the header and payload-the two fundamental components of a network packet-we perform differentiated pre-training according to the byte sequence variations (continuous in the header vs. discontinuous in the payload). A dynamic masking strategy is further introduced to prevent overfitting to fixed byte positions. Once the generic packet representation is obtained, TraGe can be finetuned for diverse traffic classification tasks using limited labeled data. Experimental results demonstrate that TraGe significantly outperforms state-of-the-art methods on two traffic classification tasks, with up to a 6.97% performance improvement. Moreover, TraGe exhibits superior robustness under parameter fluctuations and variations in sampling configurations.

This manuscript presents and advocates for a new form of scientific communication: free and open nowcasting of public opinion via web dashboard. I present an open-source automated system that gathers new human responses to survey items daily, anonymizes and publicly distributes microdata, and presents analyses through a publicly viewable Web dashboard. A demonstration implementation tracked support for further development of artificial intelligence among American adults. As of 2026-05-31, the system had autonomously produced 766 daily estimates of support from N=8551 respondents. The findings underscore the need for continuous, high-frequency surveys to accurately track shifts in public opinion on transformative technologies like AI. I argue that more scientists should adopt the method of open nowcasting, because it encourages transparency in research design and eases replication.

We report the results of a study to identify and quantify drivers of inventory record inaccuracy (IRI) in a grocery retailing environment, a context where products are often subject to promotion activity and a substantial share of items are perishable. The analysis covers ~24,000 stock keeping units (SKUs) sold in 11 stores. We find that IRI is positively associated with average inventory level, restocking frequency, and whether the item is perishable, and negatively associated with promotional activity. We also conduct a field quasi-experiment to assess the marginal effect of stockcounts on sales. While performing an inventory audit is found to lead to an 11% store-wide sales lift, the audit has heterogeneous effects with all the sales lift concentrated on items exhibiting negative IRI (i.e., where system inventory is greater than actual inventory). The benefits of inventory audits are also found to be more pronounced on perishable items, that are associated with higher IRI levels. Our findings inform retailers on the appropriate allocation of effort to improve IRI and reframes stock counting as a sales-increasing strategy rather than a cost-intensive necessity.

A long-standing conjecture by Albertson and Berman in 1979 states that every planar graph of order $n$ has an induced forest with at least $\lceil \frac{n}{2} \rceil$ vertices. As a variant of this conjecture, Chappell conjectured that every planar graph of order $n$ has an induced linear forest with at least $\lceil \frac{4n}{9} \rceil$ vertices. As a partial solution to the conjecture, Pelsmajer in 2004 proved that every outerplanar graph of order $n$ has an induced linear forest with at least $\lceil \frac{4n+2}{7}\rceil$ vertices and this bound is sharp. In this paper, we investigate the order of induced subgraphs with a given pathwidth in outerplanar graphs. The above result of Pelsmajer implies that every outerplanar graph of order $n$ has an induced subgraph with pathwidth at most 1 and at least $\lceil \frac{4n+2}{7}\rceil$ vertices. We extend this to obtain a result on the maximum order of induced subgraphs with a given pathwidth in an outerplanar graph. We also give its upper bound, which generalizes Pelsmajer's construction.

Bayesian model mixing (BMM) is a statistical technique that can combine constraints from different regions of an input space in a principled way. Here we extend our BMM framework for the equation of state (EOS) of strongly interacting matter from symmetric nuclear matter to asymmetric matter, specifically focusing on zero-temperature, charge-neutral, $β$-equilibrated matter. We use Gaussian processes (GPs) to infer constraints on the neutron star matter EOS at intermediate densities from two different microscopic theories: chiral effective field theory ($χ$EFT) at baryon densities around nuclear saturation, $n_B \sim n_0$, and perturbative QCD at asymptotically high baryon densities, $n_B \geqslant 20 n_0$. The uncertainties of the $χ$EFT and pQCD EOSs are obtained using the BUQEYE truncation error model. We demonstrate the flexibility of our framework through the use of two categories of GP kernels: conventional stationary kernels and a non-stationary changepoint kernel. We use the latter to explore potential constraints on the dense matter EOS by including exogenous data representing theory predictions and heavy-ion collision measurements at densities $\geqslant 2n_0$. We also use our EOSs to obtain neutron star mass-radius relations and their uncertainties. Our framework, whose implementation will be available through a GitHub repository, provides a prior distribution for the EOS that can be used in large-scale neutron-star inference frameworks.

Clustered randomized controlled trials are often stratified or pair-matched to improve covariate balance and efficiency. Sample average treatment effects (SATEs) are commonly estimated by averaging stratum-level treatment-control mean contrasts -- an approach that is natural and widely used. We show that, in stratified clustered trials with heterogeneous cluster sizes, such estimators need not be consistent for the SATE. They can converge to the wrong limit even under correct randomization and without model misspecification. The source is a covariance between cluster sizes and treatment effects: stratumwise averaging mis-weights clusters in a way that produces bias of constant order, regardless of sample size. We study the Hájek (ratio) estimator as a robust alternative. By aggregating outcomes within treatment groups before taking their difference, it remains consistent in clustered trials that grow by increasing strata sizes or the number of strata. Despite that, its use in design-based analyses of clustered trials has been limited by the lack of variance estimators. We develop a design-based variance estimator that applies to any number of strata of any size, and show that it is asymptotically conservative, a property that holds even when some strata contain only a single treated or control unit. We also present tests improving the coverage of Wald tests when the number of clusters is moderate. The framework extends naturally to covariate-adjusted estimators via a variance orthogonality property.

Motivated by the study of the dimension of random posets, it was conjectured by Bollobás and Brightwell in 1997 that if $P$ is a finite poset whose cover graph contains at most one cycle then its order dimension is at most $3$. In this paper we prove this conjecture by giving a constructive proof with explicit triplets of linear extensions realizing such posets.

In this paper, we show that any $\infty$-operad is equivalent to the localization of a discrete $Σ$-free operad; this result extends Joyal's delocalization theorem for categories to the operadic setting. Along the way, we pursue a systematic study of $\infty$-operadic localization in the dendroidal context and its compatibility with un/straightening equivalences, deducing another description of algebras over $\infty$-operads.

We confirm the conjecture posed by Guédon, Hinrichs, Litvak, and Prochno in 2017 that $\mathbb{E}\|(a_{ij}g_{ij})_{i\le m, j\le n}\colon \ell_p^n \to \ell_q^m\|$ is comparable, up to constants depending only on $p$ and $q$, to \[ \max_i \|(a_{ij})_j\|_{p^*} +\max_j \|(a_{ij})_i\|_{q} +\mathbb{E} \max_{i,j} |a_{ij}g_{ij}| \] provided that $1\le p \le 2\le q \le \infty$. This was known before only in the case $p=1$ or $q=\infty$, and in the spectral case $p=2=q$. We also reprove the conjecture in the case $p=2=q$ without using spectral theory (which was employed in the previously known proof).

We obtain the Phragmèn-Lindelöf principle on combinatorial infinite weighted graphs for the Cauchy problem associated to a certain class of parabolic equations with a variable density. We show that the hypothesis made on the density is optimal.

This paper presents a novel theoretical model motivate a new experimental scheme to simulate the Unruh temperature by relating it to the critical temperature of multiple Bose-Einstein thermal baths. These thermal baths are conceptualized as snapshots of a Bose-Firework originating from an evolving driven Bose-Einstein condensate (BEC). The critical temperature of each snapshot is determined from the heat capacity, which is numerically estimated by calculating the partition function derived from the system's Hamiltonian. By analyzing the relationship between the average number of the phononic excitations at the critical temperature, acceleration, and the critical temperature itself, our model demonstrates a significant agreement with the Unruh temperature formula, thereby validating our hypothesis. This theoretical approach offers a cost-effective alternative experimental setup compared to other resources-intensive experimental simulations. Furthermore, it provides a unique perspective on quantum simulation by utilizing the critical phenomena of condensed matter systems to probe fundamental quantum relativistic effects.