Let $A=A(α, β)$ be a graded down-up algebra with weights $(\mathrm{deg}\, x, \mathrm{deg}\, y)=(n,m)$ and $β\neq 0$, and $\nabla A$ its Beilinson algebra. Such an algebra $A$ is a 3-dimensional cubic AS-regular algebra by Kirkman--Musson--Passman. Assuming $\mathrm{gcd}\,(n, m)=1$ and $m \geq n$, we extend the previous results on the Hochschild cohomology of $\nabla A$. Known cases include $(n,m) = (1,1)$ (Belmans) and $(n = 1,\,m \geq 2)$ (Itaba--Ueyama). In this paper, we determine the dimensions of the Hochschild cohomology groups of $\nabla A$ in the remaining case $n\geq 2$ and $m\geq 2$ by explicitly constructing the projective resolution and computing the ranks of the arising representation matrices. As a byproduct, for $m>n>1$, we show that the derived category of the noncommutative projective scheme associated to $A$ is not equivalent to the derived category of any smooth projective surface. Moreover, for all $m \geq n \geq 1$, we describe the ring structure of the Hochschild cohomology group $\nabla A$ with respect to the Yoneda product.

Let $G$ be a finite group and let $p$ be a prime. In this paper, we prove a strengthened version of Brauer's height zero conjecture for the principal $p$-block of $G$ that takes the action of a certain group of Galois automorphisms into account. This answers a conjecture recently proposed by Malle, Moretó, Rizo and Schaeffer Fry. We then use this to obtain a structural result which can be seen as a Galois version of the Itô-Michler theorem.

This paper studies the estimation of outage probability in GSC/MRC SIMO systems under Rician fading in the rare-event regime. The difficulty arises from the evaluation of the CDF of a partial sum of ordered non-central chi-square random variables, motivating the use of enhanced Monte-Carlo methods. For independent fading, we propose partition importance sampling (PIS), a theory-driven estimator tailored to this structure, and prove that it achieves bounded relative error (BRE). We further adapt exponential twisting, proving its BRE property, and cross-entropy to this setting. We then extend ET and CE to correlated Rician fading, where the joint distribution of the power gains is no longer tractable, yielding the ETC and CEC estimators; ETC enjoys the bounded-relative-error guarantee under arbitrary mean and arbitrary covariance. Numerical experiments compare these methods with universal importance sampling and multilevel splitting for independent fading, and an asymptotic approximation in the correlated case. Empirically, CE shows the most robust performance in the independent case; PIS and ET are competitive but degrade for larger means, with ET further degrading when the selected subset is much smaller than the antenna array. ETC yields a better estimate than the asymptotic approximation for moderately rare events.

The dynamic slowdown in glass-forming liquids remains a central topic in condensed matter science. Here, we report a theoretical investigation of the microscopic origin of the slowdown in amorphous silica, a prototypical strong glass former with a tetrahedral network structure. Using molecular dynamics simulations, we analyze atomic jump dynamics, the elementary structural change processes underlying relaxation. We find that the jump statistics deviate from Poisson behavior with decreasing temperature, reflecting the emergence of dynamic disorder in which slowly evolving variables modulate the jump motion. The slowdown is species-dependent: for silicon, the primary constraint arises from the fourth-nearest oxygen neighbor, while at lower temperatures, the fourth-nearest silicon also becomes relevant; for oxygen, the dominant influence comes from the second-nearest silicon neighbors. As the system is cooled, the jump dynamics become increasingly slow and intermittent, proceeding in a higher-dimensional space of multiple slow variables that reflect cooperative rearrangements of the network. Species-resolved point-to-set correlations further reveal that the spatial extent of cooperative relaxation grows differently for silicon and oxygen, directly linking their relaxation asymmetry to the extent of collective motion. Together, these results provide a microscopic framework linking dynamic disorder, species-dependent constraints, and cooperative correlations, offering deeper insight into the slowdown of strong glass-forming networks.

The band structure of elementary excitations of skyrmion crystal in thin ferromagnetic film with Dzyaloshinskii-Moriya interaction and uniaxial magnetic anisotropy under external magnetic field is studied. In the absence of anisotropy there is a topological transition in the spectrum of skyrmion crystal: the gap between breathing and counter-clock-wise modes closes, which is accompanied by changes of Berry curvature sign of these bands. In this work we demonstrate that such topological transition exists in some range of the uniaxial anisotropy values. We present a phase diagram showing that the value of the field of topological transition is higher in the easy-plane domain and lower in the easy-axis domain of anisotropy.

In this work, we investigate the emergence and control of genuine tripartite entanglement in a hybrid cavity quantum electrodynamics architecture consisting of two linearly coupled single mode resonators, one of which interacts coherently with a two level atom. An analytical framework is developed in a weak driving regime, where the system dynamically supports a delocalized hybrid excitation shared by the two photonic modes and the atomic degree of freedom. Tripartite concurrence fill has been used to characterize and identify parameter regimes of maximal multipartite quantum correlation that can be generated in this model. Additionally, we demonstrate how dissipative rates and detuning asymmetries govern the conversion of bipartite entanglement into a genuinely tripartite state, establishing a controllable transition from localized Jaynes Cummings correlations to delocalized photonic atomic entanglement networks. These findings outline a clear route to engineering steady state multipartite quantum resources in coupled cavity QED platforms, with direct relevance to quantum networking, distributed quantum information processing, and photonic state routing in scalable quantum architectures.

The $21\,$cm signal originating from Cosmic Dawn to the Epoch of Reionisation is highly sensitive to the processes governing star formation in the early universe as well as new physics. In this work, we focus on the imprint of non-cold dark matter (DM), which impacts the formation of the smallest halos. Our goal in particular is to clarify whether near-future radio telescopes such as the Hydrogen Epoch of Reionisation Array (HERA), will be able to distinguish between free-streaming dark matter, specifically in the form of thermal warm DM (WDM), and collisional damping due to neutrino-DM ($ν$DM) interactions giving rise to larger overdensities on small scales. For that purpose we first implement a mapping between the two models in terms of a cutoff scale and determine detection thresholds for the two DM models. Using Fisher matrix forecasts, we show that $ν$DM interaction strengths down to $σ_{ν{\rm DM}}\sim 3\times10^{-35}$ cm$^2$ could be probed by $21\,$cm cosmology when considering two populations of galaxies for a GeV mass DM. This would allow to either confirm or rule out a recent claimed preference for a non-zero $ν$DM interaction in Lyman-$α$ data. Furthermore, we find that HERA will not be able to distinguish between $ν$DM and WDM. In the latter context, the threshold for detection of $ν$DM interactions translates into WDM with mass up to $m_{\rm WDM}\sim 9$ keV that could be detected by HERA.

Recent detections of very-high-energy (VHE; $\gtrsim 100~{\rm GeV}$) emission from GRB afterglows, most notably the unprecedented brightness of GRB~221009A observed by LHAASO, reveal components beyond the standard electron synchrotron model. The multi-TeV photons motivate synchrotron self-Compton and possible hadronic contributions, while the non-detection of coincident neutrinos by IceCube/KM3NeT/GRAND200k constrains the microphysical parameters, jet kinetic energy, and ambient-medium density. We model the VHE afterglow of GRB~221009A with an external forward shock from a Gaussian structured jet in a uniform-density medium. This angular structure reproduces the extreme TeV output at an off-axis angle but without demanding large energies as in a top-hat jet. We compute the corresponding $pγ$ neutrino flux in the PeV-EeV range and derive a time-integrated upper limit using the effective areas of IceCube-Gen2 and GRAND200k. This provides insight into the contribution of individual GRBs to neutrino events. The predicted neutrino flux for GRB~221009A, using parameters inferred from the multi-wavelength spectral energy distribution, lies below the sensitivities of these detectors. Even our correlation analysis, optimized for neutrino searches with the upcoming GRAND200k, indicates that the expected number of events from this GRB is of order $\sim 0.1$ under a highly optimistic microphysical parameter regime. We also compare neutrino-flux variations from on-axis and off-axis viewing geometries and find an approximately order of magnitude difference in the signal. Thus, our study concludes that a brighter burst closer than GRB~221009A would be crucial for neutrino detection by upcoming telescopes. Future GRB detections by the Cherenkov Telescope Array will provide important constraints on their geometry, radiation mechanisms, and possible associated neutrino signals.

We present BIOMERO 2.0, a major evolution of the BIOMERO framework that transforms OMERO into a FAIR-compliant (findable, accessible, interoperable, and reusable), provenance-aware bioimaging platform. BIOMERO 2.0 integrates data import, preprocessing, analysis, and workflow monitoring through an OMERO.web plugin and containerized components. The importer subsystem facilitates in-place import using containerized preprocessing and metadata enrichment via forms, while the analyzer subsystem coordinates and tracks containerized analyses on high-performance computing systems via the BIOMERO Python library. All imports and analyses are recorded with parameters, versions, and results, ensuring real-time provenance accessible through integrated dashboards. This dual approach places OMERO at the heart of the bioimaging analysis process: the importer ensures provenance from image acquisition through preprocessing and import into OMERO, while the analyzer records it for downstream processing. These integrated layers enhance OMEROs FAIRification, supporting traceable, reusable workflows for image analysis that bridge the gap between data import, analysis, and sharing.

The astrophysical site(s) of the r-process are uncertain, with candidates such as neutron star mergers and magneto-rotational supernovae predicting different event rates, delay times, and heavy-element yields. Galactic chemical evolution models constrain these properties by comparing model predictions with observed abundances. We explore, in a systematic and data-driven way, the astrophysical conditions under which r-process enrichment can reproduce the observed trends of multiple neutron-capture elements in the Milky Way. Rather than assuming a fixed site, we adopt a flexible, parametric approach to test whether a common set of r-process parameters can explain the chemical evolution of several heavy elements. We compute a grid of one-infall, homogeneous models varying: Eu yield per event, r-process event rate, enrichment delay time, and progenitor mass range. For each of the $\sim 1.5 \times 10^5$ models, we predict [X/Fe] vs. [Fe/H] trends by scaling Eu yields with the solar r-process pattern. A multi-objective optimisation based on Pareto fronts identifies models that best reproduce the abundance trends. Best-fitting models favour short delay times ($\leq 30\ \rm Myr$), low-mass progenitors ($\sim 20-25\ \rm M_\odot$), and an effective Eu injection of $\sim 2 \times 10^{-7}\ \rm M_\odot$ per event. Stars more massive than $\sim 80\ \rm M_\odot$ are too rare to dominate the enrichment. While heavy elements can be reproduced, lighter ones show stronger conflicts with Eu, reflecting that the solar r-process scaling relation becomes less valid toward lighter elements. No single class of r-process events, under solar-scaled yields, can explain light and heavy neutron-capture elements; at least two components are required: a main r-process consistent with solar and r-rich stars, and a weaker component producing enhanced light r-process elements, similar to that observed in r-poor stars.

Cavity magnonics, owing to its strong magnon-photon coupling and excellent tunability, has attracted significant interest in quantum information science. However, achieving strong and robust macroscopic entanglement remains a long-standing challenge due to the inherently linear nature of the beam-splitter interaction. Here, we propose an experimentally feasible scheme to generate and enhance macroscopic entanglement between two remote magnon modes by injecting squeezed vacuum fields (SVFs) into coupled microwave cavities. We demonstrate that even a single SVF applied to one cavity can induce steady magnon-magnon entanglement, while applying two SVFs (the double-squeezed configuration) enables selective activation of two independent entanglement channels associated with the cavity supermodes. Remarkably, quantum interference between the two SVFs allows for phase-controlled enhancement of entanglement, resulting in significantly improved robustness against cavity dissipation and thermal noise. Under realistic parameters, the survival temperature of quantum entanglement increases from approximately $260$ mK to $450$ mK. Our results establish a versatile and controllable approach to generating and enhancing quantum entanglement through quantum interference between squeezed vacuum fields.

The 21-cm signal from neutral hydrogen is anticipated to reveal critical insights into the formation of early cosmic structures during the Cosmic Dawn and the subsequent Epoch of Reionization. However, the intrinsic faintness of the signal, as opposed to astrophysical foregrounds, poses a formidable challenge for its detection. Motivated by the recent success of machine learning based Gaussian Process Regression (GPR) methods in LOFAR and NenuFAR observations, we perform a Bayesian comparison among five GPR models to account for the simulated 4-hour tracking observations with the SKA-Low telescope. The simulated sky is convolved with the instrumental beam response and includes realistic radio sources and thermal noise from 122 to 134 MHz. A Bayesian model evaluation framework is applied to five GPR models to discern the most effective modelling strategy and determine the optimal model parameters. The GPR model with wedge parametrization ($\textit{Wedge}$) and its extension ($α\textit{Noise}$) with noise scaling achieve the highest Bayesian evidence of the observed data and the least biased 21-cm power spectrum recovery. The $α\textit{Noise}$ and $\textit{Wedge}$ models also forecast the best local power-spectrum recovery, demonstrating fractional differences of $-0.14\%$ and $0.47\%$ respectively, compared to the injected 21-cm power at $k = 0.32\ \mathrm{h\ cMpc}^{-1}$. We additionally perform Bayesian null tests to validate the five models, finding that the two optimal models also pass with the remaining three models yielding spurious detections in data containing no 21-cm signal.

We define the notion of loop torsors under certain group schemes defined over the localization of a regular henselian ring A at a strict normal crossing divisor D. We provide a Galois cohomological criterion for classifying those torsors. We revisit also the related theory of loop torsors on Laurent polynomial rings.

Motivated by recent experimental studies, we investigate the spectrum of the nearest-neighbour triangular XXZ model within the $1/S$ expansion, in the limit in which the exchange couplings present a strong easy-axis anisotropy $J_{xy}/J_{zz} \ll 1$. We show that in the limit in which $1/S \to 0$ and $J_{xy} \to 0$ at fixed $V = J_{zz}/(S J_{xy})$, the triangular spin model can be reduced to an effective boson model with quartic interactions on the honeycomb lattice. This effective model interpolates between a spin-wave ($V \to 0$) and a strong-coupling limit ($V \to \infty$) and encodes in a simple framework the regimes discussed by Kleine~\emph{et al.}~[Z. Phys. B Condens. Matter~{\bf 86}, 405 (1992);~{\bf 87}, 103 (1992)]. For zero field, the classical ground state of the model presents an accidental degeneracy, which can be traced to a simple symmetry of the classical energy. The model thus offers a transparent realization of a theory with quantum order-by-disorder and a pseudo-Goldstone mode. We analyze the spectrum at zero magnetic field by calculating the self-energy at one-loop order. In the calculation, we introduce a self-consistent renormalization of the energy scale and of the pseudo-Goldstone energy gap; the latter renormalization is essential to remove infrared divergences in the on-shell corrections to the energy dispersion. Finally, we discuss qualitatively the structure of the one-loop corrections in comparison with the spectrum observed experimentally in K$_{2}$Co(SeO$_{3}$)$_{2}$.

Considering turbulence is crucial to understanding clouds. However, covering all scales involved in the turbulent mixing of clouds with their environment is computationally challenging, urging the development of simpler models to represent some of the processes involved. By using full direct numerical simulations as a reference, this study compares several statistical approaches for representing small-scale turbulent mixing. All models use a comparable Lagrangian representation of cloud microphysics, and simulate the same cases of cloud-edge mixing, covering different ambient humidities and turbulence intensities. It is demonstrated that all statistical models represent the evolution of thermodynamics successfully, but not all models capture the changes in cloud microphysics (cloud droplet number concentration, droplet mean radius, and spectral width). Implications of these results for using the presented models as subgrid-scale schemes are discussed.

The advent of high-precision cosmological observations has challenged many traditional inflationary models. Data from $Planck$ 2018 along with the BICEP/$Keck$ 2018 result have already ruled out most of the established models by placing tight constraints on the tensor-to-scalar ratio $r$. Upcoming missions like LiteBIRD & CMB-S4 are expected to impose an even more stringent bound on $r$, potentially excluding further models from the viable landscape. In this evolving observational context, modified gravity theories offer a promising way to reconcile inflationary models with data. In this work, we explore several inflationary models, namely mutated hilltop inflation, D-brane inflation, and Woods-Saxon inflation, within the framework of $f(R,T)$ gravity. A minimally coupled and linear combination of Ricci scalar and trace of EM tensor is considered as $f(R,T)=R+16πG λT$ and the cosmological observable parameters, viz. scalar spectral tilt $n_s$, tensor-to-scalar ratio $r$, and running of scalar spectral index $n_{sk}$ are estimated for the three models, and their trajectories are plotted in the $n_s-r$ plane. The model results are evaluated in light of the $Planck$, BICEP/$Keck$, DESI DR2, and ACT DR6 data. We observe that for a certain model parameter space, these potentials are viable within the current observational bounds.

Optical systems are a main platform for quantum information processing. A main challenge is information loss due to scattering in unmonitored modes. These losses are modeled as state-independent beam-splitter interactions, with a thermal state (for all practical purposes, the vacuum) in the second input port. The perfect correction of these Gaussian lossy channels with Gaussian operations alone is known to be impossible. In this work, we investigate the Petz recovery map as an approximate recovery. For single mode losses and Gaussian reference states, the Petz map is found to use either a beam-splitter or a state-independent amplifier, depending on the parameters. Then we study the recovery performance on several examples, showing that it is near-optimal among the considered class of protocols. We also obtain more specific comparisons: Petz is always better than just re-preparing the reference state; but it is worse than doing nothing if the reference state is far from the true state. Finally, we extend our study to losses on two modes, and compare the global Petz map to the local implementation on each mode separately.

The study of bodies of constant width is a classical subject in convex geometry, with the 3-dimensional Meissner bodies being canonical examples. This paper presents a novel geometric construction of a body of constant width in $\mathbb R^4$, addressing the challenge of constructing such bodies in higher dimensions. Our method produces a natural analogue of the second Meissner body, by modifying a 4-dimensional Reuleaux simplex. The resulting body possesses tetrahedral symmetry and has a boundary composed of both smooth surfaces and a non-smooth subset of the Reuleaux 4-simplex. Furthermore, we analyze the orthogonal projection of this body onto the 3-dimensional hyperplane of its base. This "shadow" is a 3-dimensional body of constant width with tetrahedral symmetry. It has six elliptical edges and its volume is only slightly larger than that of the Meissner bodies. This body was recently constructed as a projection of a different 4-dimensional body, however the construction presented here is new and gives additional properties.

We analyse the nematic Helmholtz-Korteweg equation, a variant of the classical Helmholtz equation that describes time-harmonic wave propagation in calamitic fluids in the presence of nematic order. A prominent example is given by nematic liquid crystals, which can be modeled as nematic Korteweg fluids - that is, fluids whose stress tensor depends on density gradients and on a nematic director describing the orientation of the anisotropic molecules. These materials exhibit anisotropic acoustic properties that can be tuned by external electromagnetic fields, making them attractive for potential applications such as tunable acoustic resonators. We prove the existence and uniqueness of solutions to this equation in two and three dimensions for suitable (nonresonant) wave numbers and propose a convergent discretisation for its numerical solution. The discretisation of this problem is nontrivial as it demands high regularity and involves unfamiliar boundary conditions. We address these challenges by using high-order conforming finite elements and enforcing the boundary conditions with Nitsche's method. We illustrate our analysis with numerical simulations in two dimensions.

Computer generated holography requires high-speed spatial light modulators (SLMs) for dynamically patterning light in 3D. Piston-motion micromirror-based SLMs support high-speed ($\geq$ 10 kHz) phase modulation; however, fabricating micromirror arrays with sufficient fill factor necessary for high diffraction efficiency is challenging. In particular, the larger mirrors of high fill factor designs are susceptible to stress-induced curvature that significantly degrades optical performance. In this work, we introduce an optical compensation method using a pitch-matched microlens array (MLA) to focus light onto just the center of each mirror. Our approach thus avoids curvature-induced artifacts and improves optical fill factor to nearly 100$\%$, independent of the original mechanical fill factor. Through simulations and experiments on a fabricated micromirror array with bowed mirrors, we show that the Pearson correlation coefficient of the imparted phase profile is improved from 0.11 to 0.85 and the brightness of a holographically-generated single spot is enhanced by 8$\times$ with our microlens array in place. Our hybrid optical-electromechanical strategy thus provides a scalable path toward high-speed, high-fidelity wavefront control for applications such as adaptive optics, holographic displays, and optogenetics.

The travelling salesman problem is a well-known example of computationally-hard combinatorial problem for classical machines. Here, we propose a novel variational quantum algorithm to solve it. The method is based on the preparation of two maximally entangled quantum registers whose correlations are assigned to different paths between pairs of cities. For $N$ cities, this encoding requires $2 \lceil\log_2 N\rceil$ qubits and the solution to the problem is directly found in the correlation matrix of the two registers composing the overall trial state. As a proof-of-concept experiment, we implement this algorithm for generic problems with four cities on a reconfigurable room-temperature silicon photonic circuit with integrated photon-pair sources, used to initialize maximally entangled path-encoded single-photon states.

Neutrino-pair exchange induces a neutrino force that can drive dark matter (DM) self-interactions and impact small-scale structure formation. In the presence of the cosmic neutrino background (C$ν$B), this force can be modified, with important consequences for DM phenomenology. We study the effect of the C$ν$B on neutrino forces, generated by the scalar and pseudoscalar interactions. We explore the significance of the background neutrino force on the scalar DM-neutrino portal model, including DM self-scattering and annihilation. Our results show that the interplay between attractive vacuum potential and repulsive background potential leads to a screening effect that varies across DM mass ($m_χ$) regimes, strongly affecting DM self-scattering in the DM mass $m_ν\lesssim m_χ\lesssim T_{C νB}$. Meanwhile, for DM annihilation, the screening completely vanishes the Sommerfeld Enhancement induced by the neutrino force. Overall, the C$ν$B substantially reshapes the viable coupling range for DM self-interactions while remaining compatible with current constraints, offering a pathway to small-scale structure problems.

One way to approximate a quantum annealing schedule is to use multiple quantum walks chained together, without intermediate measurements, to produce a multi-stage quantum walk (MSQW). Previous work has shown that a MSQW is better than QAOA (quantum alternating operator ansatz) for solving optimization tasks using multiple stages [Gerblich et al, arXiv:2407.06663]. In this work, we develop an efficient heuristic for choosing the free parameters in MSQW, and use it to obtain improved scaling compared to single stage quantum walks. We show numerically that the heuristic works well for problems with a large minimum energy gap, giving a polynomial scaling in the number of stages, and leading to an overall algorithm that scales polynomially in time. For problems with a small minimum gap, the scaling breaks down such that adding more stages decreases the success probability, leading to an overall scaling that is exponential in time as expected. Our methods are general and can be applied to any optimization problem to obtain good annealing schedules.

Markov games with coupling constraints model constrained dynamical decision-making involving self-interested agents, where the feasibility of an individual agent's strategy depends on the joint strategies of the others. Such games arise in numerous real-world applications involving safety requirements and budget caps, for example, in environmental management, electricity markets, and transportation systems. In unconstrained dynamical decision-making, the correlated equilibrium has emerged as a desired solution concept due to its computational tractability and amenability to learning algorithms. Understanding how coupling constraints shape correlated equilibria is a crucial step towards computing solutions in constrained Markov games. In this paper, we formalize and characterize the notion of constrained correlated equilibria for Markov games, defined as feasible joint policies where any unilateral deviation is either unprofitable or infeasible. Building on this characterization, we further study existence conditions for constrained correlated equilibria. In particular, we provide a novel existence proof of such equilibria in Markov games with coupling constraints.

Motivated by the renewed attention from the recent BESIII experiment on the semileptonic decay $D\to V \ellν_{\ell}$, we investigate semileptonic decay $D^+\to ω\ell^+ν_{\ell}$ within the framework of QCD light-cone sum rule in this work. By constructing correlation function with right-handed chiral current, the transverse twist-2 light-cone distribution amplitudes (LCDA) $ϕ^{\perp}_{2;ω}(x,μ)$ dominates the contribution in TFFs. We study the properties of twist-2 LCDA $ϕ^{\perp}_{2;ω}(x,μ)$ through light-cone harmonic oscillator model. Applying it to the TFFs, we obtained $A_1(0)$, $A_2(0)$, $V(0)$, and $A_0(0)$ at large recoil point. Two TFF ratios are $r_V=1.40^{+0.21}_{-0.19}$ and $r_2=1.01^{+0.17}_{-0.16}$. After extrapolating those TFFs to the whole physical $q^2$ region by using the simplified $z(q^2,t)$ series expansion, the ratio of longitudinal and transverse decay widths is $Γ_{\rm{L}}/Γ_{\rm{T}}=0.987^{+0.107}_{-0.121}$. Then, we get branching fraction $\mathcal{B}(D^+\to ωe^+ν_e)=(1.848^{+0.365}_{-0.330})\times 10^{-3}$ and $\mathcal{B}(D^+\to ωμ^+ν_μ)=(1.782^{+0.334}_{-0.303})\times 10^{-3}$, which is in good agreement with BESIII and CLEO Collaborations. Taking into account the secondary decay $ω\to π^+π^-π^0$, we predict branching fraction of five body decay as $\mathcal{B}(D^+\to ω(\to π^+π^-π^0)e^+ν_{e})=(1.648^{+0.341}_{-0.305})\times 10^{-3}$ and $\mathcal{B}(D^+\to ω(\to π^+π^-π^0)μ^+ν_μ)=(1.589^{+0.313}_{-0.281})\times 10^{-3}$. Finally, we predict the forward-backward asymmetry $A_{\rm{FB}}^{\ell}$, lepton-side convexity parameter $C^{\ell}_{\rm{F}}$, longitudinal (transverse) polarization $P_{\rm{L}(\rm{T})}^{\ell}$, as well as longitudinal polarization fraction $F_{\rm{L}}^{\ell}$.

We propose a mathematically principled PDE gradient flow framework for distributionally robust optimization (DRO). Exploiting the recent advances in the intersection of Markov Chain Monte Carlo sampling and gradient flow theory, we show that our theoretical framework can be implemented as practical algorithms for sampling from worst-case distributions and, consequently, DRO. While numerous previous works have proposed various reformulation techniques and iterative algorithms, we contribute a sound gradient flow view of the distributional optimization that can be used to construct new algorithms. As an example of applications, we solve a class of Wasserstein and Sinkhorn DRO problems using the recently-discovered Wasserstein Fisher-Rao and Stein variational gradient flows. Notably, we also show some simple reductions of our framework recover exactly previously proposed popular DRO methods, and provide new insights into their theoretical limit and optimization dynamics. Numerical studies based on stochastic gradient descent provide empirical backing for our theoretical findings.

Computing Gröbner bases is known to have a very high upper bound on computation time with respect to input length. Due to the connection between polyhedral geometry and Gröbner bases through the Gröbner fan, one can attempt an incremental approach to compute Gröbner bases. First computing a Gröbner basis with respect to an `easy' term order and transforming that result to a Gröbner basis with respect to the desired term order by using information about this polyhedral fan is done by a family of algorithms termed as Gröbner walk. We implemented two variants of the Gröbner walk in the computer algebra system OSCAR and compared their performance with classical Gröbner basis methods already found in OSCAR.

We introduce and study a new class of generalized convex functions termed star quasiconvex functions. This class includes convex, star-convex, quasiconvex, quasar-convex, and positively homogeneous functions of any degree $p>0$ as special cases. Furthermore, we provide several characterizations of this class covering both nonsmooth and differentiable cases. In particular, in the general nonsmooth case, star quasiconvex functions are characterized by functions for which all its sublevel sets are star-shaped at a minimizer, while in the differentiable case strongly star quasiconvex functions coincides with those satisfying the restricted secant inequality property, and star quasiconvex functions are related with variationally coherent functions, thereby providing a rich framework for differentiable first-order methods. Additionally, we develop standard properties of the proximity operator and prove that the proximal point algorithm converges linearly to the unique solution when applied to strongly star quasiconvex functions defined over closed star-shaped sets that are not necessarily convex.

We investigate the sensitivity of present and future direct detection experiments to generalized neutrino interactions (GNI) through elastic neutrino electron scattering. Using data from LUX-ZEPLIN, PandaX-4T, and XENONnT, we derive constraints on vector, axial-vector, scalar, and tensor effective couplings, and compare them with existing limits. Our results show that current xenon-based detectors already provide competitive bounds, with XENONnT offering the most stringent constraints due to its larger exposure and reduced backgrounds. Among the GNI couplings, the scalar contributions remain more weakly constrained, while tensor interactions yield the strongest limits. We also present projected sensitivities for the DARWIN experiment, showing potential improvements. These results demonstrate the capability of direct detection experiments, originally designed for dark matter searches, to provide complementary and competitive constraints on generalized neutrino interactions.

Despite extensive research, the mechanisms through which online platforms shape extremism and polarization remain poorly understood. We identify and test a mechanism, grounded in empirical evidence, that explains how ranking algorithms can amplify both phenomena. This mechanism is based on well-documented assumptions: (i) users exhibit position bias and tend to prefer items displayed higher in the ranking, (ii) users prefer like-minded content, (iii) users with more extreme views are more likely to engage actively, and (iv) ranking algorithms are popularity-based, assigning higher positions to items that attract more clicks. Under these conditions, when platforms additionally reward \emph{active} engagement and implement \emph{personalized} rankings, users are inevitably driven toward more extremist and polarized news consumption. We formalize this mechanism in a dynamical model, which we evaluate by means of simulations and interactive experiments with hundreds of human participants, where the rankings are updated dynamically in response to user activity.