Recent results from the DAMIC-M and PandaX collaborations have excluded the standard freeze-in production of dark matter for masses in the range $3~\mathrm{MeV} \lesssim m_χ\lesssim 1~\mathrm{GeV}$ in the context of extensions of the Standard Model featuring an additional ultra-light $U(1)_{\rm X}$ gauge boson. In this work, we analyze the constraints induced by DAMIC-M and PandaX results on the reheating temperature in freeze-in models at stronger coupling, or when a non-thermal source (such as inflaton decay) comes into play. We identify viable scenarios in which the DM relic abundance is correctly reproduced while evading current experimental bounds on the electron-scattering cross section, $\overlineσ_\mathrm{e}$. In particular, we show that for reheating temperatures below the electroweak scale, Boltzmann suppressed production can be compensated by stronger couplings, bringing freeze-in scenarios within present experimental reach. Finally, we study a hybrid scenario in which a small branching ratio of inflaton decay seeds a nonzero initial dark-matter abundance. We show that such contributions can significantly modify freeze-in predictions across broad regions of parameter space, offering an additional pathway for probing extremely feeble interactions.

Small-scale galaxy clustering is expected to contain substantial cosmological information, but the extent to which this information constrains halo-based cosmologies independent of an assumed galaxy--halo connection remains unclear. We quantify this dependence using LRG-like mock galaxy catalogs built from 81 cosmologies in the {\tt \textsc{AbacusSummit}} suite. We analyze two-point correlation function multipoles on scales ranging from $5$--$80$ Mpc/$h$ and compare two limiting treatments, the \enquote{floor} and \enquote{ceiling}, of the standard five-parameter HOD model. In the conservative floor case, we impose only broad initial HOD bounds and profile over HOD parameters to determine the minimum constraining power available; we accomplish this with {\tt HODmin}, a two-stage global optimization algorithm written for minimizing $χ^2$ in HOD space. In the optimistic ceiling case, we assume the HOD parameters are known exactly. We find a significant difference between the floor and ceiling when comparing against the same Planck $Λ$CDM mock data vector with identical modeling assumptions: for the floor, $25\%$ of the discrete {\tt \textsc{AbacusSummit}} cosmologies tested are excluded at $3σ$, whereas for the ceiling, $\sim81\%$ are excluded. Many cosmologies agree well with data in the floor, and yet in the ceiling are excluded by multiple orders of magnitude in $χ^2$. We therefore observe the strength of small-scale clustering constraints depends heavily on the amount of prior HOD information assumed. We compare the sensitivity of this effect to various choices like scale cut, angle cut, multipole inclusion, mock phase, and mock HOD model. Our wide floor--ceiling bracket indicates that informative galaxy--halo priors are necessary for extracting strong small-scale clustering constraints.

Neutrino evolution in dense astrophysical environments is typically described either within a quantum kinetic framework, which neglects the build-up of multi-body correlations, or through simplified many-body calculations that allow significant entanglement to develop. In this work, we compare these two approaches in a simple neutrino-gas configuration, with particular emphasis on the role of non-forward scattering processes. These effects are incorporated either through a collision term in the kinetic description, or by considering the full neutrino-neutrino many-body Hamiltonian. We highlight differences between the two descriptions in both their characteristic timescales and asymptotic behavior. Motivated by the natural suitability of quantum computing for many-body calculations, we further investigate the non-classicality of neutrino evolution, discussing Trotter error scaling, along with the associated costs of constructing quantum circuits in terms of entangling gates and non-Clifford gates. We find that the resources needed for neutrino many-body evolution are on the low end of typical high-energy physics problems and on the mid to high end with respect to quantum chemistry problems. For the full Hamiltonian, resource requirements increase relative to the truncated version. We emphasize the importance of efficient fermion-to-qubit encodings, which are essential for reducing the substantial computational resources required for such simulations.

Isotopic ratios trace the formation and evolution of planets and link their atmospheres to the chemistry of their natal protoplanetary discs. We measure $^{12}\mathrm{C}/^{13}\mathrm{C} = 58^{+18}_{-15}$ in the atmosphere of the young super-Jupiter $β$ Pic b from 11 nights of CRIRES+ K-band spectroscopy ($\mathcal{R} \approx 100{,}000$) at the Very Large Telescope (VLT). We detect both $^{12}\mathrm{CO}$ and $^{13}\mathrm{CO}$ and constrain $^{12}\mathrm{C}/^{13}\mathrm{C}$ with a Bayesian retrieval jointly fitted with near-infrared photometry. The inferred $^{12}\mathrm{C}/^{13}\mathrm{C}$ is consistent with the present-day interstellar medium (ISM), is below the solar value, and is comparable to measurements in other young super-Jupiters. We also retrieve $T_{\rm eff} = 1629^{+30}_{-28}\,\mathrm{K}$, near-solar to mildly super-solar metallicity ([M/H]$ = 0.20^{+0.16}_{-0.12}$), a solar-like carbon-to-oxygen ratio (C/O$ = 0.52 \pm 0.03$), and tentative evidence for thick clouds. We analyse each night independently and combine the results of the six epochs with the highest signal-to-noise ratio (S/N), propagating night-to-night scatter into the final uncertainties. This provides an isotopic benchmark for a directly imaged planet interior to the CO snow line.

This paper introduces peri urban dislocation as a structural condition that complements existing sprawl metrics by capturing hierarchical misalignments between inner city and peripheral areas. Whereas conventional measures emphasise density, land-use mix, or fragmentation, peri-urban dislocation reflects deeper divergences in the core periphery relational functional organisation of urban systems. We operationalise this concept using percolation analysis of street networks, revealing hierarchical patterns via clustering maps and dendrograms, providing a relational structure between urban elements. Two case studies, Valdivia, Chile, and Boston, USA, demonstrate contrasting manifestations: a structural reversal in Valdivia, where a homogeneous residential periphery dominates the hierarchical clustering process, and peri-urban voids in Boston, where isolated parcellations persist despite metropolitan consolidation. These findings position peri-urban dislocation as a structural dimension linked to sprawl yet distinct from metrics based on density or peripherality; one that may occur independently or represent a previously unidentified structural signature of sprawl. Methodologically, we apply established percolation techniques to expose this previously unarticulated structural phenomenon, enabling the detection of hierarchical misalignments within urban systems. Conceptually, we introduce peri urban dislocation as a new dimension of urban structure, helping articulate debates on sprawl and peri urbanisation through a complexity informed lens and enabling core periphery diagnostics across diverse urban contexts.

The efficiency of multi-photon emission is an important characteristic of quantum light sources. Bright multi-photon emission is desirable for high-power lighting and lasers, while its complete suppression is required for high-purity single-photon generation. In colloidal quantum emitters, multi-photon emission can vary significantly between individual particles. Resolving this heterogeneity remains challenging with conventional particle-by-particle approaches. Here, we introduce a crosstalk-suppressed SPAD-array photon-correlation approach for high-throughput quantification of multi-photon emission from more than 1000 colloidal quantum shells. By projecting two images of the same sample onto distant regions of the detector array, we avoid short-range crosstalk between detector pixels. Time gating suppresses dark-count coincidences and distinguishes individual emitters from clusters. Applying this method to quantum shells reveals a near-Gaussian distribution of biexciton emission efficiencies, with a mean of 0.55 and an estimated intrinsic standard deviation of 0.12. Intra-batch correlations between the biexciton efficiency and the particle brightness are consistent with the volume scaling of Auger quenching. These results establish SPAD-array photon correlation as a scalable route to resolve multi-photon heterogeneities in nanoparticle ensembles.

We consider the problem of purifying noisy qubit unitary channels. Given the ability to apply an unknown qubit unitary channel followed by depolarizing noise, we aim to construct a superchannel that purifies the noisy unitary back to the original unknown unitary. We first provide numerical evidence that sequential strategies can strictly outperform parallel strategies when the number of channel uses is finite, highlighting the fundamental distinction from state purification. We then provide a concrete $\mathrm{U}(2)$-covariant parallel protocol based on a novel entanglement-assisted quantum error-correcting code that suppresses the first-order noise strength as $O(1/n)$ with $n$ channel uses and show this scaling is asymptotically optimal in the low-noise regime, even when sequential strategies are allowed.

We critically examine the expectation that in a fundamental quantum field theory, dimensionless couplings in the Lagrangian density should all be of order unity. We propose a measure to quantify the adherence of a theory to this: the spread (the ratio of the largest to the smallest of the magnitudes) of such dimensionless couplings, obtaining various closed-form results. If we take independent identically distributed (IID) couplings to parameterise our uncertainty on the values of the order unity couplings, ratios of couplings can be much larger than one might naively expect. For a theory with 20 IID unit normal couplings, the probability that the magnitude of the ratio of two of them is greater than 100 is 0.29, for example. Even when the IID couplings have exponentially suppressed tails, the distribution of ratios of order one couplings has fat power-law tails which grow with the number of independent couplings.

Electromagnetic ion cyclotron (EMIC) waves are commonly observed in Earth's inner magnetosphere, particularly during geomagnetic storms driven by anisotropic ring-current protons. While their role in radiation belt scattering of hot ions is well established, their interaction with the cold (less than 100 eV) plasma remains less understood. This is partly due to limited magnetospheric cold ion observations, as spacecraft charging can prevent cold ions from reaching onboard instruments. It is well-known that the electric field of a parallel-propagating EMIC wave can drive inter-species perpendicular polarization drifts that excite lower-hybrid secondary instabilities. In multi-component plasmas, these include the modified two-stream and the ion-ion cross-field instabilities. In this paper, we study the impact of such secondary instabilities on the parallel-propagating EMIC wave and multi-component plasma via a fully kinetic particle-in-cell simulation and linear theory. We find that the secondary waves persist even at low EMIC amplitudes, provided the cold population remains sufficiently cold. The kinetic simulation demonstrates that these secondary modes produce anisotropic heating of cold protons and singly-charged oxygen ions, primarily in the direction perpendicular to the ambient magnetic field and of electrons in both parallel and perpendicular directions.

Overview: Wind-driven bubbles are dynamic systems that can accelerate cosmic rays, depending on their physical properties, up to very high energies. We investigate how a time-dependent description of the particle transport may impact the escaping cosmic-ray flux. Model: The wind bubble system is modeled as spherically symmetric. Cosmic rays are continuously injected at the position of the termination shock and propagate through advection and diffusion until the escape at the time-dependent position of the forward shock, which is treated as a free escape boundary. Methods: The one-dimensional spherical time-dependent transport equation is solved by transforming it into the corresponding set of stochastic differential equations, and integrated with a modified version of the open source cosmic-ray propagation framework CRPropa. Results: We find that, during the wind driven phase, the downstream escaping spectra from wind bubbles can be harder than $\sim E^{-2}$, the conventional expectation from diffusive shock acceleration. Depending on the turbulence model the initial energy spectrum can be significantly suppressed at lowest energies, which could be an observable feature to distinguish between different turbulence realizations. This effect could lead to an efficient confinement of low energy particles, potentially leading to observable implication in terms of multi-messenger radiation and cosmic-ray accumulated grammage within the bubble.

Weak lensing by large-scale structure is a powerful cosmological probe. While most analyses rely on second-order correlations, these are primarily sensitive to the parameter combination $S_8 = σ_8 (Ω_m/0.3)^{0.5}$, limiting their ability to constrain $Ω_m$ and other cosmological parameters independently. Higher-order statistics capture non-Gaussian features of the density field and can therefore break parameter degeneracies and extract more cosmological information from weak lensing surveys. We present a joint analysis of second- and third-order cosmic shear in the final data release of the Kilo-Degree Survey (KiDS-Legacy). We combine COSEBIs (Complete Orthogonal Sets of E-/B-mode Integrals) at scales between 2' and 300' with third-order aperture mass moments at scales between 4' and 32' to perform a joint analysis of second- and third-order statistics. Compared to previous KiDS analyses, we implement several methodological advances: an intrinsic alignment model with redshift and mass dependence, a baryon correction model validated on multiple hydrodynamical simulations, and corrections for reduced shear and source clustering. Combining COSEBIs with third-order aperture mass statistics in KiDS-Legacy yields $Ω_m = 0.297^{+0.056}_{-0.040}$ and $S_8 = 0.806^{+0.025}_{-0.023}$, significantly tightening the $Ω_m$ constraints and more than doubling the figure of merit in the $Ω_m$--$S_8$ plane compared to the two-point analysis alone. The third-order measurements pass stringent internal consistency tests, are fully compatible with the KiDS-Legacy 2-point constraints, other 2+3-point lensing results and with Planck CMB measurements within $1σ$, providing no evidence for an $S_8$ tension and demonstrating the maturity of 3-point cosmic shear as a key probe for forthcoming surveys.

We prove short-time well-posedness for the Muskat problem with surface tension in the full two-phase setting, allowing different viscosities, arbitrary density contrast, and rigid boundaries. In particular, no Rayleigh--Taylor sign condition on the density contrast is imposed. The interface is assumed to be a graph, uniformly separated from the fixed boundaries, and the initial data may be large in the log-critical class $\dot C^{1,\log^\varkappa}\cap H^1$, with $\varkappa>1$. Thus the result reaches the natural Lipschitz threshold up to a logarithmic correction. The main difficulty is that, in the presence of viscosity jump and boundaries, the interface equation is not given by a closed explicit contour dynamics law. Instead, the normal velocity is recovered through an elliptic transmission problem in moving domains, and the resulting evolution is a genuinely nonlocal quasilinear equation. We derive sharp Schauder-type estimates, adapted to the log-critical scale, for the transmission operators generated by the bulk Darcy flow. These estimates identify the third-order parabolic mechanism produced by surface tension and control the nonlinear coupling between the interface geometry and the elliptic transmission structure. The proof builds on the Schauder framework developed in Part~I of this series \cite{CHN1}, but requires a new analysis of the Muskat transmission problem in moving domains. Combining this elliptic theory with the contour formulation and time-weighted Hölder estimates, we obtain existence, uniqueness, smoothing, and stability for large interfaces in arbitrary dimension.

The stabilizer fragment of the ZX calculus is amongst the most important fragments of the theory. The closely related Clifford+T fragment is approximately universal (arXiv:1705.11151). Additionally, the stabilizer calculus can be described by a small collection of rewrites, most of which have been shown to be necessary (arXiv:1709.08903). However, two rules, describing the red/green compact-structure coincidence and the important bialgebra law, had not been shown to be necessary. We present a countermodel-style argument showing that both of these rules are individually necessary relative to the connectivity meta-rule of Backens--Perdrix--Wang (arXiv:1709.08903), and hence establish that the rule set presented in arXiv:1709.08903 has no redundant rewrite rule.

In this paper we prove the Markov property for the solution to stochastic partial differential equations driven by a cylindrical orthogonal martingale-valued measure. We assume our coefficients are time-dependent and satisfy some growth and Lipschitz conditions. We also prove that for time-independent coefficients and under mild assumptions on the cylindrical orthogonal martingale-valued measure, the solutions to our stochastic partial differential equations are Feller. Finally, in the case that the $C_{0}$-semigroup is quasi-contraction, we show that the solution to our stochastic partial differential equation possesses a càdlàg version.

A family of $m \times n$ matrices $\mathcal{F} \subseteq \mathbb{F}_q^{m \times n}$ is {$(t-1)$-intersection-free} if $\dim \ker(A-B) \neq t-1$ for all $A,B \in \mathcal{F}$. A \emph{forbidden $(t-1)$-intersection problem} for a collection of matrices asks for the size and structure of extremal $(t-1)$-intersection-free families within that collection. We solve this problem in $\mathrm{GL}(n,q)$ for all pairs $(n,t)$ such that $t<c\cdot n$ where $c$ is a universal constant. We show that the $t$-umvirates and their duals, are the only maximal $(t-1)$-intersection-free families $\mathcal{F} \subset \mathrm{GL}(n,q)$. Here, a $t$-umvirate is defined as the family of all matrices that agree on a fixed $t$-dimensional subspace, and its dual as those whose transposes agree on it. The best previously known result, due to Ellis, Kindler, and Lifshitz, established this bound under the assumption $n \geq e^{Ct\log t}$ for some constant $C>0$. We also give Frankl--Rödl-type constructions showing that this range of $t$ is almost the best possible: we show that for values of $t>n/2$ the extremal behavior changes and no clean analogue is expected. Our proof builds upon recent global hypercontractivity results for matrix spaces due to Evra, Kindler, and Lifshitz, and broadly applies to any sufficiently dense class of matrices.

We continue our local singularity analysis for Ricci flow initiated in ArXiv:2006.16227. Building on that framework, we study Type I singular points in general Ricci flows, without assuming any global Type I curvature bound, and prove that the scalar curvature must blow up at a Type I rate at each such point in all dimensions. As a consequence, Ricci flows with bounded scalar curvature cannot develop Type I singular points. This extends earlier results of the first author with Enders and Topping and with Mantegazza that relied on a global Type I assumption. We then adapt the same local perspective to ancient Ricci flows and analyse the curvature behaviour as time goes to negative infinity, showing in particular that every ancient Type I point exhibits scalar curvature behaviour of ancient Type I order.

We show that, under a division condition, the tangential Cauchy--Riemann cohomology of a compact Lie group with a left-invariant CR structure can be computed on a suitable maximal torus. As a consequence, we conclude that the tangential Cauchy--Riemann cohomology is finite-dimensional. We also show that, for a class of CR structures, this division condition is necessary for the total cohomology to be finite-dimensional. The proof combines Fourier analysis on compact Lie groups, highest-weight representations and Lie algebra cohomology. This not only generalizes but provides completely new proofs for the analogous result due to Pittie and for its extensions to Levi-flat CR structures, obtained by Jacobowitz and Jahnke.

In this note we give a lower bound for the second moment of a ratio of zeta functions summed over the non-trivial zeros of the Riemann zeta function that is half the size of the conjectured value. Our result is conditional on the assumption of the Riemann Hypothesis and that all the non-trivial zeros of the zeta function are simple.

This work presents a finite element formulation for coupled chemo-mechano-thermodynamical large deformation contact. The formulation is based on the contact theory of Sauer et al. (2022) that contains six coupled (but separate) fields: the deformation and temperature of the two contacting bodies, as well as an interfacial bonding field and interfacial temperature. The latter is governed by the chemical and mechanical energy dissipation at the interface. Here the focus is placed on the evolution of bonding and debonding, and how it is coupled to the mechanical and thermal contact state. Several elementary models are proposed for this based on a quadratic contact potential. The resulting contact formulation becomes very general and versatile, which is illustrated by several challenging examples. They include pressure- and gap- depended bonding, exothermic bonding reactions, thermal hardening and thermal expansion, as well as simultaneous bonding and debonding. They are based on a monolithic finite element implementation using classical and isogeometric shape functions together with implicit time integration. Its full linearization, required for the Newton-Raphson solution method, is also provided. If bonding sites are material points, the bonding variable can be condensed-out locally.

Large language models (LLMs) are increasingly used as decision-making components in social simulations. This introduces a methodological risk: the simulation may deviate from the explicit behavioral policy defined by the researcher. In online social network (OSN) simulations, action choices shape system dynamics, interaction patterns, and model interpretability. This paper evaluates whether LLM action selectors preserve an interpretable reference policy in an OSN simulation. The reference is a finite state machine implemented as a first-order Markov model, with transition probabilities depending on the user type. The evaluation uses a synthetic network with 1,000 agents and 10,000 action decisions. Three open-weight LLMs are tested: LLaMA 3.1, GPT-OSS, and Mistral 24B. Each model is evaluated under three prompting strategies: base, guided, and probabilistic. Alignment is measured using Jensen-Shannon Divergence with Laplace smoothing, and execution time is reported. Results show that LLMs can approximate the reference policy in some configurations, but do not preserve it reliably. Alignment varies across models and prompts, and additional guidance can introduce systematic action biases. Even the best-aligned LLM configurations are several hundred times slower than direct Markov chain sampling. These findings indicate that LLM-based action selection is not a direct replacement for explicit decision policies: it can alter the intended behavior while increasing computational cost.

Bell's theorem shows that entangled quantum particles can exhibit correlations that classical particles cannot reproduce without an additional nonlocal resource, such as communication. In this sense, quantum particles are fundamentally more nonlocal than classical ones, and entanglement becomes unavoidable in physics. Here we prove the analogous result within quantum theory itself: indistinguishable fermions transmitted through a quantum network can generate correlations that distinguishable particles or indistinguishable bosons cannot reproduce without additional communication. In the same sense, fermions are fundamentally more nonlocal than bosons or distinguishable particles, motivating fermionic anticommutation and indistinguishability as unavoidable operational resources. Our result further implies that fermions can strictly surpass all qubit-based protocols for certain distributed computing tasks, demonstrating that a complete understanding of information processing requires going beyond qubits to fermionic information carriers - febits.

Coronal mass ejections (CMEs) undergo significant geometric evolution as they propagate from the Sun to 1 AU, influencing their radial size, expansion, and space weather impact. We investigate the evolution of CME aspect ratio and expansion dynamics for four fast and four slow Earth-directed CMEs. Using multipoint coronagraphic observations with the Graduated Cylindrical Shell (GCS) model and corrected in situ measurements of associated magnetic clouds (MCs) at 1 AU, we track the evolution of aspect ratio from the low-middle corona to interplanetary space. We find that aspect ratio does not remain constant but exhibits a systematic three-phase evolution: a rise phase in the low-middle corona ($\lesssim10$-$15\,R_{\odot}$), a saturation phase at intermediate heights, and then a decline phase in the interplanetary space. The ratio of radial expansion speed to leading-edge speed ($V_{\rm exp}/V_{\rm LE}$) decreases substantially from the corona to 1 AU, indicating a reduction in radial expansion efficiency during interplanetary propagation. The consistent evolution of aspect ratio and $V_{\rm exp}/V_{\rm LE}$ suggests a transition from magnetically dominated expansion in the corona to a regime increasingly controlled by the heliospheric environment. We note that fast CMEs show stronger early expansion and evolve into larger, more radially extended structures, whereas slow CMEs exhibit a more gradual rise and a steeper decline. These results demonstrate that CME geometry evolves significantly during propagation and highlight the need to incorporate aspect ratio evolution in models to improve predictions of CME size, arrival time, and geoeffectiveness.

In a recent paper, the authors introduced an infinite hierarchy of $q$-hypergeometric identities, of which the first three orders, $0$, $1$, and $2$, relate to the partition theorems of Euler, Lebesgue, and Capparelli, and stated a partition theorem at order 4 which lies beyond Capparelli's theorem. Here, we first state certain partition theorems that hold at all even orders beyond Capparelli and provide bijective proofs for these theorems. In doing so, we show that there is a fourfold infinite hierarchy of partition theorems that emanates from Capparelli's theorem, which is the base case. It is also shown that the equality of two of the four generating functions holds for all orders, odd and even. Lastly, a very general framework for the remaining two functions is constructed via the method of weighted words, encompassing all possible orders and yielding several infinite hierarchies with different dilations and translations.

We give a higher-order higher-dimensional Eckmann-Hilton argument that is entirely algebraic. First we give an explicit argument showing that if we have two monoidal structures on a category with suitable interchange, we can derive a braiding on either of the monoidal structures. Then we show that given third monoidal structure, with suitable pairwise interchange on any pair of monoidal structures, each canonical braiding is forced to be a symmetry. As a motivating example, we show that for $n \geq 3$ any $n$-degenerate semi-strict $(n + 1)$-category has three suitably coherent monoidal structures on its single hom-category, thus the hom-category has the structure of a symmetric monoidal category.

Recent Very Long Baseline Interferometry (VLBI) and Gaia astrometry reveal systematic milliarcsecond-scale offsets between the radio and optical centroids of active galactic nuclei (AGN). These "radio-optical offsets" do not alter the standard opacity-driven interpretation of radio core shifts. Instead, they indicate that the optical emission centroid is frequently displaced downstream of the radio synchrotron optical depth $τ= 1$ surface, implying that additional dissipation and particle reacceleration occur beyond the opacity radio core within relativistic jets. We perform steady-state, axisymmetric relativistic magnetohydrodynamic (RMHD) simulations of AGN jets, including baryonic mass-load from stellar winds, varying jet kinetic power, and stellar core radius. Synthetic synchrotron emission maps in radio and optical bands are generated via a radiative transfer code, and centroid offsets are extracted for comparison with observations. Parsec-scale radio-optical offsets arise only for jet powers $L_{\rm j} \sim 10^{42.5} - 10^{44}\,\rm{erg}\,\rm{s}^{-1}$. In this regime, stellar winds trigger jet deceleration at intrinsic distances of a few $10^2-10^3\,\rm{pc}$, shifting the optical centroid downstream and producing offsets of $\sim 0.1 - 4\,\rm{mas}$ (a few tens of parsecs at $z=1$). Offsets depend on stellar distribution, viewing angle, and optical jet dominance, and vanish outside this power range. We reproduce the observed redshift evolution of offset incidence, linking it to the cosmic evolution of thermally pulsing asymptotic giant branch (TP-AGB) mass loss. Although stellar mass loading is unlikely to be the sole dissipation mechanism, its unavoidable presence in galactic nuclei makes it a natural baseline for energy dissipation. Radio-optical offsets therefore offer a constraint on AGN jet power and jet-host coupling, independent of traditional lobe-based methods.

Little Red Dots (LRDs) are a heterogeneous class of objects, with several proposed scenarios for their physical nature and evolution. While these theories have been tested on individual LRDs using limited spectral features, a systematic Bayesian analysis of the LRD population incorporating the different models across a broad wavelength range is still lacking. In this study, we conduct a consistent ultraviolet (UV)-to-optical continuum fitting analysis of 66 LRDs at 2<z<6 using JWST/NIRSpec PRISM spectroscopy. Employing a modified version of Bagpipes--including blackbody (BB) emission affected by Balmer absorption, stellar and nebular emission attenuated by dust, and an active galactic nucleus (AGN) component--we assess the performance of the black hole star (BH*) model in describing the LRD population. We adopt broad priors and therefore do not impose any specific physical scenario. Our results show that only ~6% of LRDs with statistically robust solutions (52 objects in total) are best-fit by a BH* in the optical and a host galaxy in the UV. ~8% of LRDs show BB-dominated optical continua but lack a stellar component or exhibit AGN UV leakage. Most LRDs are dominated by stellar and/or AGN emission in the optical, with minor BB contribution. When we adopt a prior that disfavors a strong AGN continuum to enforce BH*-like solutions, the percentage of BH$^*$ systems increases to ~40%, highlighting the strong degeneracy between a BH* solution and alternative scenarios. Even when BH*-like solutions are enforced, many LRDs still require a stellar-dominated optical continuum. This may reveal limitations of the BH* model or point to an evolutionary sequence in which the BB contribution decreases as the host grows, leading to lower BB temperatures and higher stellar masses at lower z. In this scenario, more pronounced ''V'' shapes would correspond to later stages in LRD evolution.

Operational organizations increasingly require Cyber Situational Awareness (CySA) capabilities that go beyond isolated technical alerts, providing mission-relevant artefacts that can be embedded into heterogeneous toolchains and cyber security or cyber defense processes. ECYSAP EYE addresses this need through an adoption-oriented System-of-Systems (SoS) architecture centered on seven groups of mission-focused artefacts: the Recognized Cyberspace Picture (RCyP), Cyber Situational Reports (CySRs), the What-If Analysis Report (WIAR), Option Recommendations (OPRE), an operator Dashboard/HMI (DSH), Action Enforcement (AE), and After-Action Reports (AAR). The ECYSAP EYE architecture structures the transition from perception (full-spectrum RCyP views), to decision-oriented reasoning (WIAR/CySRs/OPRE), and to operational execution and learning (DSH/AE/AAR), with explicit integration surfaces that support incremental deployment and validation. This paper presents this innovative project from a technology transfer perspective, summarizing the updated architecture, the functional role of seven groups of artefacts, and the expected impact of cyber situations on the decision-making process in the context of a mission planning and execution.

We theoretically investigate spin- and valley-resolved quantum transport in monolayer tungsten diselenide (WSe$_2$) described by an effective massive Dirac Hamiltonian. Particular attention is devoted to a finite barrier region characterized by simultaneously modulated Fermi velocity and scalar potential. The barrier velocity $v_2$ is related to the external velocity $v_1$ through a velocity ratio $ξ=v_2/v_1$, motivated by an optical analogy with the Snell-Descartes law. The exact refraction condition depends on the full spin- and valley-resolved dispersion, and the simple ratio $ξ=v_2/v_1$ is recovered only in the massless, symmetric limit. The interplay of intrinsic spin-orbit coupling in the conduction and valence bands, quantified by $λ_c$ and $λ_v$, with spin- and valley-dependent Zeeman fields, $M_s$ and $M_v$, gives rise to substantial changes in the quasiparticle dispersion, leading to pronounced modifications of the transport characteristics. By solving the Dirac equation and enforcing current-conserving matching conditions at the interfaces, we compute the spin- and valley-dependent transmission probability and conductance. Our results demonstrate that the barrier velocity, scalar potential, incidence angle, incident energy, and barrier width serve as effective control parameters for transport, giving rise to strong anisotropy and resonant tunneling features. Furthermore, we show that both the magnitude and orientation of spin- and valley-polarized currents can be continuously tuned via velocity and potential modulation. These findings establish combined velocity and potential engineering as a powerful theoretical framework for controlling spin-valley physics in two-dimensional transition-metal dichalcogenides.

We establish structure theorems for polarised flag type quotients arising in the study of the moduli space of supersingular abelian varieties. In particular, we prove a refined normal form for the top level of these flags and derive an explicit, computable descent criterion for quasi-polarisations. These results provide a complete classification of the first and last step of these flags. As an application, we compute polarised flag type quotients in dimensions $g\leq 5$, describing the fibers of the truncation morphisms as classification objects of supersingular abelian varieties.

This paper presents an improved physics-informed neural network for simulating the spatio-temporal solution profile of the multidimensional coupled Burgers' equations with high Reynolds numbers. As time evolves, the sharp shock fronts emerge in the solution, creating significant computational challenges for the conventional mesh-based numerical methods. In particular, numerical methods such as finite differences and finite elements suffer from poor stability and strong mesh dependency when resolving the steep solution gradients. To address these challenges, the proposed framework employs a layerwise self-adaptive weighting strategy that dynamically adjusts the penalty weights for the physics residual, initial conditions, and boundary conditions throughout training. Moreover, the framework uses a dual-phase optimization strategy to achieve more stable convergence. To check the effectiveness and accuracy of the proposed framework, a set of numerical experiments is conducted to compare it with the standard Physics-Informed Neural Network (PINN) with and without Limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) optimization. Numerical results exhibit that the proposed framework achieves higher accuracy in terms of relative $L_2-$ error norm than the standard PINN and is able to capture the development of sharp shock fronts as time evolves in the solution.