Standard Gaussian splatting methods rely on heuristic densification and pruning to adaptively allocate primitives during training, and the resulting Gaussian count strongly influences both reconstruction quality and runtime. This makes comparisons across methods fragile: improvements can stem from higher representational capacity rather than algorithmic design. A common and naive workaround for this is hard-stopping or budgeting densification/pruning once a target count is reached, which biases training because different methods hit the cap at different times, yielding non-uniform densify/prune exposure across views and uneven point distributions. We propose a target point control scheme that preserves the standard densification window and cadence, but adjusts only the existing densification and opacity-culling hyper-parameters to track a quadratic target count trajectory. This quota-governor reaches the desired count by 15k iterations without abrupt cutoffs, ensuring that all methods and views receive equal densification and pruning cycles, enabling fairer, capacity-matched evaluation.

This paper explores epistemic realizability, a form of realizability in which the property that a piece of data constitutes evidence for a logical proposition is semi-decidable. In this framework, each proposition A is assigned a verifier} program that checks whether a datum X is a realizer for A, and a dual generator program that behaves as a generic realizer for X. We propose epistemic realizability interpretations for minimal logic, second-order intuitionistic logic, and higher-order intuitionistic logic, proving that each system is sound and complete under the proposed semantics.

The possible interaction between the dark components of the Universe (dark matter and dark energy) stands as an attractive alternative to the standard $Λ$CDM cosmological model. In this work, we present a novel analysis of three sign-changeable interaction models whose coupling term $Q$ depends explicitly on the deceleration parameter $q$ and is proportional to different energy densities: dark matter, dark energy, and total energy density. To constrain these models, we combine strong gravitational lensing data on two complementary scales: a sample of early-type galaxies acting as lenses and the galaxy cluster Abell 1689. Our results show that the interaction strength $β$ depends on the choice of the coupling term $Q$, with all models yielding negative values of $β$, indicative of a dark interaction scenario. The $β$ values obtained in this work are significantly larger in magnitude than those previously reported using Type Ia supernovae, CMB, and BAO. The strong-lensing constraints indicate a transition to cosmic acceleration at earlier redshifts ($z_t \sim 1.8-2.1$) than that predicted by the $Λ$CDM model, while remaining consistent with cosmic chronometer measurements within the reconstructed confidence regions. Therefore, our study shows that strong gravitational lensing data provide an independent and competitive cosmological probe capable of testing interacting dark energy scenarios. The sensitivity of lensing observables to the expansion history enables access to complementary information about dark-sector dynamics beyond standard cosmological probes.

We prove measurable analogues of Whitney's classical theorems on weak isomorphisms of finite graphs. In the setting of locally finite graphings, we introduce a notion of weak isomorphism as an edge-measure-preserving Borel bijection that preserves cycles and hyperfinite subgraphs, modulo null sets. We first show a rigidity theorem, proving that for weakly 3-connected infinitely-ended graphings, every weak isomorphism is induced by an isomorphism of graphings. To our knowledge, this gives the first general sufficient condition in measurable combinatorics for the existence of an isomorphism between two given graphings. Next, we give a full measurable version of Whitney's theorem, showing that every weak isomorphism between graphings can be implemented by countably many measurable Whitney operations, which we introduce in this setting. The proofs require new measurable-combinatorial tools, including a careful analysis of infinitely-ended subforests. This work further develops the limit theory of matroids recently initiated by Lovász.

Quantum measurements can be incompatible, i.e., they can fail to be jointly measurable. Recently, a weaker notion of joint-measurability, called partial joint-measurability, was proposed by Masini et al. in [Quantum 8, 1574 (2024)]. In this work, we further generalize this notion to the setting where only a subset of the outcomes of each measurement is required to be jointly determined by classical variables. We provide two mathematical formulations of partial joint-measurability and show that, like full joint-measurability, it can be decided by solving a single semidefinite program. We prove that in the case of an untrusted measurement device, an adversary Eve, limited to classical side information, can perfectly guess the outcomes of the measurement device if and only if the set of measurements is partially jointly measurable. We derive analytical thresholds on the detection efficiency below which generic measurements become partially jointly measurable. Such bounds directly yield limits on the robustness of device-independent and semi-device-independent quantum cryptographic protocols against detection inefficiency. In particular, our results highlight the importance of a careful treatment of postselection in security analyses.

Space plasmas are generally characterized by non-Maxwellian distributions with suprathermal populations, as routinely revealed by in situ observations. Such departures from standard Maxwellian distributions can be understood as signatures of quasiequilibrium states, in which the distribution of the medium can be expressed as a continuous superposition of Maxwellian distributions, namely through superstatistics. Here, we construct macroscopic relations linking fluxes to their associated driving forces in such plasmas, where superstatistical effects enter the picture through the transport coefficients. After comparing the resulting superstatistical distributions with observed electron distributions in the solar wind, we turn to the kinetic response of quasiequilibrium plasmas and derive the corresponding transport coefficients, including the electric and thermal conductivities, the mobility, and the diffusion coefficient. We further extend the analysis to viscous plasmas and compute the shear and bulk viscosity coefficients. Overall, quasiequilibrium effects are found to systematically enhance the transport coefficients relative to their Maxwellian values. We quantify this enhancement for the three main universality classes of superstatistics, which are the most commonly encountered in experimental and observational situations, and interpret it as a consequence of the increased population of energetic particles in the non-Maxwellian tails.

Minimal Phenomenal Experiences (MPEs) are states of consciousness in which wakefulness is preserved but phenomenal content is low or absent. The Entropic Brain Hypothesis (EBH) is a model of conscious processes that regards the entropy of spontaneous brain activity as a marker of 'phenomenal richness', exemplified by high-content psychedelic experiences (HCPEs). Yet recent human neuroimaging studies of MPEs induced by meditation -- and possibly 5-MeO-DMT -- suggest that these states, defined by their phenomenological simplicity, also show signs of increased neurophysiological entropy. This presents a conundrum for the EBH: brain entropy is elevated with increased and decreased richness of the phenomenal experience. Here, we put forward the Complex Brain Hypothesis (CBH), which proposes that the richness of experience differentiating MPEs from HCPEs is better indexed by complexity than by entropy. We argue that brain complexity is modulated by the grain of inference through which the brain resolves uncertainty: some HCPEs exemplify a fine-grained regime, in which loosened constraints amplify fluctuations into proliferating content, whereas some MPEs exemplify a coarse-grained regime, in which a simpler model dissolves variety into an experience of 'contentless' awareness. Both regimes can be associated with elevated brain entropy, but they diverge in phenomenology and perturbational signatures. By resolving the entropy-content conundrum, the CBH refines the EBH and highlights MPEs as an important test case for computational theories of consciousness.

Wireless networks support multi-user (MU) communication with multiple-input multiple-output (MIMO) and orthogonal frequency-division multiple access (OFDMA) technologies. In the joint MU-MIMO-OFDMA-enabled transmission mode, network throughput can be significantly increased by effectively utilizing the multi-channel resources to schedule numerous wireless users/stations (STAs) simultaneously. In this paper, we study ways to optimize the user scheduling and resource allocation (SRA) for the UL scheduled access (UL-SA) of a joint MU-MIMO-OFDMA-enabled wireless local area network (WLAN). In particular, we propose a multi-agent (MA) framework that utilizes an openly available pretrained small/medium-sized Language Model (xLM) to perform SRA for the UL-SA. To facilitate autonomous SRA using our proposed technique, we introduce the AI-assisted Wireless Systems Engineering and Research (WiSER) platform. We evaluate the performance of MAxLM-optimized SRA for network scenarios with a varying number of STAs and antenna settings on the WLAN Access Point. Numerical results confirm that our proposed technique achieves higher UL-SA throughput than the benchmark techniques.

SiFo, a wireless foundation model-based framework, is proposed for low-overhead site-specific channel state information (CSI) feedback. In 3GPP NR, Type-II feedback provides an expressive codebook-based CSI representation, but it requires substantial reference-signal overhead, UE-side search, and feedback. Learning-based site-specific feedback can reduce these online costs while retaining high-quality subspace representation by exploiting deployment-dependent propagation structure. However, existing site-specific designs typically train a dedicated neural network for each new site, which limits scalability when the number of deployments is large. SiFo addresses this scalability issue by pretraining a CSI feedback model across source sites and adapting it to a target site through lightweight calibration. A small set of target-site users reports low-dimensional reference signal received power (RSRP) fingerprints, and their full-CSI-based subspace labels are stored as calibration memory. During online operation, a served user is matched to calibrated users through the same SSB probing and RSRP reporting procedure, so nearby calibration samples provide site-specific subspace guidance without updating model parameters. SiFo therefore transfers common propagation knowledge while retaining local adaptation. Numerical results across ten city scenarios demonstrate that SiFo (i) achieves higher CSI-capture efficiency than separately trained site-specific learning baselines under the same target-site labeled budget, (ii) approaches the high-overhead 3GPP NR Type-II feedback reference using only RSRP measurements collected during online SSB probing, and (iii) converts the high CSI-capture efficiency and low overhead into effective spectral efficiency improvement under limited target-site data.

We investigate the problem of covert quickest change detection in a Bayesian and infinite-horizon setting. A legitimate entity seeks to detect a change in the state of a discrete memoryless channel as quickly as possible by actively probing it. Simultaneously, the entity must ensure its probing remains covert from an adversary monitoring the channel for active sensing. We introduce the expected covertness budget (ECB) as an analytically tractable covertness metric that bounds from above the relative entropy between the observation sequences induced by active and passive sensing. Under constraints on both the probability of false alarm (PFA) and the ECB, we establish a second-order asymptotic converse bound on the average detection delay as the PFA constraint approaches zero, for any positive ECB constraint, explicitly quantifying the maximum square-root-order covert sensing gain possible. Furthermore, we propose an achievability scheme utilizing a constant-sensing-probability Shiryaev-type policy and show that it matches the second-order asymptotic converse. We illustrate our result with a numerical example.

We study finite systems of vectors whose frame operator matrices are unitarily equivalent, via explicit and computationally efficient unitary transformations, to block-diagonal matrices. We call such systems block-equivalent. We show that a Gabor system $\mathcal{G}=\mathcal{G}(g,L\times K)\subset \mathbb C^N$ is block-equivalent when either the modulation set $L$ or the translation set $K$ is a subgroup of $\mathbb Z_N$. We also characterize situations in which the frame operator matrix becomes diagonal. Finally, we show that geometric conditions on subsets of $\mathbb Z_N$ force certain diagonals of the frame operator matrix of $\mathcal{G}$ to vanish, yielding additional sparsity and block structures.

In this work, Lie symmetry analysis is performed on a coupled nonlinear cross-diffusion system with varying cross-section geometry. The system describes two interacting quantities whose material properties, namely the capacity functions and the diffusion coefficients, depend nonlinearly on the dependent variables. The classical Lie invariance criterion produces a set of sixteen determining equations for infinitesimal symmetry generators. The determining equations are solved by first establishing the universal geometric structure of the admitted generators and then classifying the constitutive functions according to their invariance properties in the state space. It is shown that the system always admits time translation and parabolic scaling as kernel symmetries, with an additional spatial translation admitted only in the Cartesian case. Further symmetries, such as translations, scalings, and rotations in the dependent-variable plane, are obtained by making precise structural assumptions about the constitutive functions. The analysis shows that the strong nonlinear coupling in the governing equations prohibits any new point symmetries from arising in the general case, and that larger symmetry algebras are only attainable in degenerate or linearizable special cases. The symmetries obtained in this work are geometrically consistent with parabolic and radial structure of governing equations.

Inter-core skew (ICS), the differential group delay between cores of a multicore fiber (MCF), is a critical parameter for both classical space-division multiplexed communications and quantum photonic networks. We present a high-precision measurement of ICS in a commercially available four-core fiber using two-photon Hong--Ou--Mandel (HOM) interference in a fiber-integrated $4\times4$ multiport beam splitter. By extracting the center position of HOM interference dips and peaks across all twelve core-pair combinations, we obtain individual ICS values with a demonstrated precision of $\pm0.11\,$ps, limited by the delay-stage positioning uncertainty. The root-mean-square ICS grows as $σ_τ(L) = κ\sqrt{L}+c$ with $κ= 48.7 \pm 2.5\,\mathrm{ps}/\!\sqrt{\mathrm{km}}$ and $c = 9.76 \pm 1.2\,$ps, over fiber lengths from $7.7\,$m to $1300\,$m. This first direct validation of the stochastic random-walk scaling across a length range spanning laboratory to field-deployed scales was made possible by HOM's immunity to first-order path fluctuations, which renders classical interferometric methods impractical for long installed fibers. The demonstrated $\pm0.11\,$ps precision represents a $\sim\!180$-fold improvement over correlation optical time-domain reflectometry (C-OTDR), the standard method for long-fiber ICS characterization. Fisher information analysis establishes a fundamental Cramér--Rao precision limit in the femtosecond range, indicating further improvement is achievable with better delay control. These results establish a practical platform for characterising timing uniformity in MCF-based networks for both quantum and classical space-division multiplexed applications.

Technical Debt (TD) refers to the long-term costs incurred when developers prioritize short-term delivery over quality-improving work. Architectural Technical Debt (ATD) arises when architectural decisions (e.g., technology choices, patterns, or decomposition) prioritize near-term progress over future maintainability and evolvability. Because ATD affects a system's core structure and propagates through architectural dependencies, it is often more expensive and disruptive to remediate than localized code-level debt. Although ATD has been widely studied, an important but underexplored aspect of repayment is who performs it. Prior work provides limited empirical evidence on repayment responsibility in ATD and its relationship to time-to-fix. We empirically study self-fixed ATD, where the introducer also repays the debt, and contrast it with non-self-fixed ATD in large Apache open-source projects. We reconstruct ATD lifecycles by tracing Jira artifacts to version-control history to identify introduction and repayment points and attribute developer roles. We address three research questions on the prevalence of self-fixed ATD, time-to-fix differences between self-fixed and non--self-fixed items, and how factors related to code change and collaboration metrics relate to repayment speed. Using descriptive statistics, non-parametric tests, and survival analysis, we show that self-fixed and non--self-fixed ATD exhibit distinct repayment dynamics and differences in how changes are shared on ATD-affected files. In particular, non--self-fixed ATD is more likely to remain unresolved longer when changes are spread across many developers. These results provide actionable guidance for maintainers to identify high-risk ATD items and to reduce handoff costs by increasing introducer involvement when possible and documenting the design rationale during repayment.

Neutron star mergers are today considered a major production site for rapid neutron capture elements. While the bulk of the matter escapes at fast, but non-relativistic velocities (${\sim} 0.2\,c$), a small amount of the dynamically ejected mass reaches mildly relativistic velocities (${\gtrsim}0.6\,c$). It has been suggested earlier, that in such ejecta parts neutrons may avoid being captured and that their decay could power an early blue precursor to the main kilonova event. Here we study in detail the nucleosynthesis in such fast ejecta with nuclear network calculations along both parametrized and numerical relativity trajectories. We find that the nucleosynthesis can be divided into three channels, in one of which a substantial amount of free neutrons survives when the main r-process has frozen out. We provide a (semi-)analytical model for surviving free neutrons which agrees very well with the network calculations. If the mass fraction of the free neutrons exceeds ${\sim} 0.05$, their $β^-$-decay dominates the nuclear heating rate between ${\sim} 100$ and ${\sim} 10^4$ seconds. This dominance leads to a pronounced kilonova precursor that should for plausible ejecta parameters be visible for ULTRASAT out to ${\sim}200\,\rm Mpc$. Since at low electron fractions free neutrons can survive even for moderate velocities, mergers with large tidal ejecta, such as asymmetric neutron star mergers or favorable neutron star black hole mergers, may produce particularly bright blue precursors to their subsequent kilonovae.

Dicke superradiance by an ensemble of quantum emitters produces a collective burst of radiation, but no entanglement in the mixed state of the emitters. We show that adding a local kinetic constraint between the emitters generates extensive mixed-state entanglement, while otherwise preserving all key features of Dicke superradiance. Specifically, for any local Boolean constraint, we analytically derive a lower bound for the emission rate which implies a peak intensity $\propto N^2$ and a peak time $\propto (\log N)/N$ with number of spins $N$. This effect enables the superradiantly accelerated preparation of entangled dark states. Hereby, Hilbert-space fragmentation of the Dicke ladder leads to an exponentially branching decay tree that generates a hierarchy of dark states. Importantly, these disconnected manifolds include exponentially many long-range entangled singlet dark states. The explored kinetic constraints and superradiant dynamics can be realized in neutral-atom arrays coupled to an optical cavity, and we suggest a simple and accessible witness to detect the predicted mixed-state entanglement in such experiments. Moreover, we show that entanglement generation is robust against atomic decay and collective dephasing, and should be observable under recently reported experimental conditions. Our results, thereby, offer a general framework and experimentally viable approach for the dissipative engineering of entangled dark states enhanced by superradiance.

Adaptive transport networks in biological and physical systems exhibit hierarchical organization, characteristic channel spacing, and robust scaling relations. Existing adaptive network models, formulated on a lattice, successfully reproduce many observed topologies and conduit scaling laws; however, the mechanism that selects network density and spatial spacing remains unclear. We address this in a continuum formulation where conductivity evolves as a tensor field coupled to pressure-driven flow. Linearizing about a homogeneous conducting state, we identify a finite-wavelength instability with a $-1/4$ preferred wavelength scaling in the control parameter. Simulations of the full equations confirm the analytical predictions and demonstrate the formation of anisotropic conducting structures above threshold. These results establish a scale-selection principle for adaptive transport network formation which arises from a pattern-forming instability rather than solely from relaxation within a nonconvex energy landscape. The instability mechanism places adaptive transport systems within a broader class of nonequilibrium pattern-forming media in which constitutive transport feedback generates spatial organization. Beyond reproducing hierarchical scaling laws, the theory additionally predicts the intrinsic density of transport networks and the spatial scale of resource delivery.

The future behavioural fate of a forced nonlinear system can depend sensitively on the forcing profile as well as natural fluctuations within the system. This is especially the case for rate-induced tipping, where the forcing pushes the system to a basin boundary of a future behaviour and small changes in the forcing can lead to drastically different eventual behaviours. This sensitivity may be present only for a limited period of time, for example when the forcing is most rapidly changing. Moreover, critical slowing down based methods fail to be informative in such cases. We investigate a geometric early warning to evaluate when a system is in such a sensitive state. This involves computing the R-tipping indicator, namely the signed distance to an approximate R-tipping threshold. The latter is a dynamic state that embeds knowledge of the system and future behaviour of the forcing. We contrast this with early warnings of bifurcation-induced tipping, where tipping is associated with passing a threshold on slow variation of forcing. As an example, we consider methods of early prediction of the future state for a 3-box model of the Atlantic Meridional Overturning Circulation (AMOC) with specified rapid forcing. We show that the skill of the geometric early warning compares favourably with simple thresholds.

One-dimensional alternating particle systems are widely used to study interconnections between the hydrodynamics of blast waves in a gas-like medium and the Newtonian dynamics of its corpuscular constituents. We study the model in which point particles with masses $m,μ, m,μ,\dots, (m\geqμ)$ are distributed on the positive half-line $\mathbb{R}_{+}$. Their dynamics are initiated by giving a positive velocity to the leftmost particle; in its course, the particles undergo elastic collisions. For this model with $m/μ=2$, it has previously been established that the dynamics that start from random initial positions are consistent with predictions based on Euler's hydrodynamic equation. In particular, they have the following properties: (i) the position of the rightmost particle (shock front) evolves as $t^δ$ with $δ<1$; (ii) recoiled particles behind the front enter the negative half-axis; (iii) particles with locations $x\leq0$ move ballistically and eventually take over the total energy of the system. In this paper, we present numerical and analytical results for the dynamics of this model with nonrandom (typically equidistant) initial positions and various values of $m/μ$. For $m/μ=2$ and equidistant initial positions, our results qualitatively agree with those just mentioned. At the same time, we found an infinite family of numbers $\{\mathcal{M}_k\}$ such that, for $m/μ=\mathcal{M}_k$, the hydrodynamic behavior mentioned changes drastically to the following. At each moment, only a single triplet $m,μ, m$ is in motion, whereas all other particles are at rest. As a result, the shock front moves ballistically with an average velocity equal to the initial one. Such a `staggering domino-like' picture is obtained as an exact solution, which yields, in particular, explicit formulas for $\mathcal{M}_k$ and the particle velocities and positions.

In this note we consider linear functionals on an unital commutative R-algebra. We give an integral representation of a nonnegative functional on an Archimedean cone where we do not assume that this cone is a semiring or a quadratic module. We also give a solution of the moment problem on a product of intervals and determine conditions for a functional to be a moment functional on a compact of characters.

Thermal conductivity is a fundamental material property that plays a crucial role in understanding the dynamics and evolution of planetary interiors. Despite its importance, the thermal conductivity of seifertite and pyrite-type SiO$_2$ remains unknown. Here, we calculate the lattice thermal conductivities of seifertite and pyrite-type SiO$_2$ using the Green-Kubo method based on molecular dynamics (MD) simulations driven by two machine learning potentials (MLPs) constructed from the SCAN and PBEsol exchange-correlation functionals, with $\textit{ab initio}$-level accuracy. To demonstrate our methodology, we also compute thermal conductivities using the phonon quasiparticle approach for comparison. Overall, the Green-Kubo method predicts up to 119 % higher thermal conductivity with a temperature dependence close to $T^{-1}$, as it fully captures diffusion-like phonons at high temperatures that are missed by the phonon quasiparticle approach. The 19 % reduction in thermal conductivity across the phase transition from seifertite to the pyrite-type phase suggests the potential formation of a thermally insulating layer in the mantle of super-Earths.

The growth of online video platforms drives the need for effective, semantically grounded event retrieval. We present MERVIN, a unified multimodal framework for Vietnamese news videos that integrates keyframes, transcripts, and video summaries. Transcript quality is enhanced via Gemini 1.5 Flash, reducing noise from accents, background sounds, and recognition errors. Visual features are extracted with Perception Encoder, while a Vietnamese language model produces textual embeddings; both are indexed in Milvus for efficient similarity-based retrieval. In addition, a React-based interface enables iterative query refinement across modalities, improving semantic alignment. Experimental results on Vietnamese news videos demonstrate the effectiveness of the proposed system, with MERVIN achieving 79 out of 88 points in AI Challenge HCMC 2025 qualification phase and successfully retrieved all results for every query in the final round.

We consider the bulk $ϕ^3$ deformation of the free boundary conformal field theory in the $ε$ expansion. We determine the leading corrections to the scaling dimensions of boundary fundamental operators and some boundary operator expansion coefficients. Our procedure combines the conformal multiplet recombination with the boundary crossing symmetry. The results cover both the single field case and the multi-field case with $S_{N+1}$ global symmetry, which are associated with the Yang-Lee model and the $(N+1)$-state Potts model respectively. These semi-infinite models describe branched polymers, percolation, and spanning forest at a surface. We generalize these results to some higher derivative theories. In addition, we study the $ϕ^{2n+1}$ theories with $n>1$, but only obtain some boundary operator expansion coefficients.

Grain-boundary (GB) local stress is central to the initiation and evolution of long-term creep damage in polycrystalline superalloys. Owing to the high-dimensional nonlinear relationships between the GB stress response and multiple crystallographic, microstructural, and micromechanical characteristics, it remains challenging to identify the key characteristics governing GB stress and to elucidate their mechanisms of influence. Dislocation-climb-affected crystal-plasticity finite-element simulations of minimal grain clusters are combined with an integrated causation-guided machine-learning framework, in which mechanics-informed descriptors are analyzed by causation entropy to identify governing mechanisms and then distilled into a reduced-order regression form for interpretable prediction of GB normal stress. Among 18 physically motivated characteristics, the GB inclination angle, the slip transmission, the climb-related Schmid-type indicator, and the elastic-modulus mismatch are found to be dominant, revealing the coupled roles of interfacial geometry, crystallographic compatibility, creep stress relaxation, and micromechanical contrast. The identified characteristics hierarchy and functional representation remain effective under multiaxial loading and can be extended to tricrystal systems through physically interpretable nonlocal augmentation when a purely local description becomes insufficient, demonstrating strong physical consistency and robust generalizability across physical conditions. The extracted candidate functions also improve surrogate-model performance across multiple machine-learning model classes, providing supporting evidence for the physical relevance and efficiency of the identified representation. The proposed methods demonstrate strong potential for the development of interpretable machine-learning models and for the study of microscale nonlocal damage.

High-entropy spinel oxides provide an excellent platform for investigating entropy-stabilized correlated systems with strong configurational disorder. In this work, we systematically study the temperature evolution of the structural and magnetic properties of Cr-based high-entropy spinels with compositions $(Mn_{0.2}Co_{0.2}Ni_{0.2}Cu_{0.2}Zn_{0.2})Cr_2O_4$ and $(Mg_{0.2}Co_{0.2}Ni_{0.2}Cu_{0.2}Zn_{0.2})Cr_2O_4$. Our results reveal that both systems crystallize in cubic structure with space group \textit{$Fd\overline{3}m$} at room temperature. Each system undergoes antiferromagnetic ordering below the Néel temperatures $ T_N$ = 49 K and 35 K, respectively. Neutron diffraction measurements confirm the emergence of long-range magnetic order with spiral spin arrangement. Both systems exhibit a structural phase transition from cubic \textit{$Fd\overline{3}m$} to orthorhombic \textit{Fddd} symmetry at approximately 55 K and 85 K, respectively. Notably, despite the significant chemical disorder at the A site, both systems undergo transitions analogous to those observed in low entropy spinel systems. This behavior suggests that high configurational entropy may promote global structural stabilization despite local chemical disorder, thereby preserving long-range orderings and the characteristic symmetry-breaking transitions of the pristine spinel systems.

The Milky Way hosts a flattened nuclear stellar disc (NSD) that dominates the gravitational potential in the inner few hundred parsecs. Whether the NSD is purely axisymmetric or contains a nuclear bar remains an open question. We test for the presence of a nuclear bar using kinematic diagnostics by combining line-of-sight velocities from the KMOS NSD survey with proper motions from VIRAC2 to construct the $ (v_\ell, v_\mathrm{los}) $ velocity ellipse. After applying strict quality cuts to minimise contamination from large-scale bar stars, we measure the vertex deviation $ l_v $ and anisotropy $ β$ for several subsamples. For our primary sample ($ |\ell| < 0.9^\circ $, $ -0.4^\circ < b < 0.25^\circ $, $ \mathrm{[Fe/H]} > -0.3 $), we find a significant negative vertex deviation $ l_v = -54.8^{+13.1}_{-14.8}\,^\circ $ with moderate anisotropy $ β= 0.16^{+0.08}_{-0.05} $. A subsample restricted to the innermost four fields yields an even stronger signal with $ l_v = -64.3^{+12.1}_{-12.2}\,^\circ $ and $ β= 0.38^{+0.12}_{-0.07} $. The direction of maximum velocity dispersion is oriented along Galactic longitude, opposite to that observed in large-scale bar-dominated samples. These signatures are robust against extinction-driven incompleteness, primary-bar contamination, and the choice of metallicity threshold. They are inconsistent with an axisymmetric NSD or one oriented orthogonally to the primary bar, but match expectations for a nuclear bar oriented at $ α\approx 60^\circ $-$75^\circ$ to the Sun-Galactic-Centre line with its near side pointing toward positive Galactic longitude. While definitive confirmation awaits larger and more precise samples from upcoming surveys, our results provide the first kinematic indication of a possible nuclear bar in the Milky Way.

Predicting drug-induced cellular state changes at single-cell resolution remains a central challenge in virtual cell modeling, particularly under out-of-distribution (OOD) conditions. Current approaches predominantly rely on RNA-based assays, which often fail to adequately capture the diverse cellular states underlying drug responses. Moreover, conditional distribution shifts and low signal-to-noise ratios frequently cause models to learn spurious correlations rather than genuine state transitions. To address these limitations, we introduce StateXDiff, a cell State-contextualized multimodal (X) Diffusion framework for predicting single-cell responses to drug perturbations. The framework operates sequentially: first, it learns a disentangled, multimodal representation of cellular state by integrating transcriptomic profiles with inferred protein features; second, it employs a conditional diffusion model to generate perturbation-specific changes. Our approach introduces a Virtual Multimodal Cell State, which augments RNA-based representations with protein-level context, and a Mechanism-aware Drug-Gene Template, which consolidates multi-source biological knowledge for accurate drug representation. Generation is driven by a latent-space diffusion Transformer, regularized through quality-aware triplet constraints, including positive drug-protein pairs or protein-drug mismatched pairs, and explicit protein-reliability weighting. Extensive evaluation demonstrates that StateXDiff consistently enhances generalization performance across three challenging settings: unseen cell lines, unseen drugs, and combinatorial perturbations.

Fractional boundary value problems are often used to model complex systems and processes characterized by memory effects and anomalous diffusion. In this paper, we consider fractional boundary value problems involving the Riesz-Caputo operator, which is particularly suited for modeling physical phenomena exhibiting symmetric diffusive effects. We provide an integral representation of the solution to prove existence and uniqueness of the fractional differential problem. We introduce a B-spline collocation method to approximate the solution of the problem and provide a convergence analysis, with both theoretical insights and numerical experiments.

Measurement is an important scientific activity. In most of science, including classical physics, is may be understood as a way of finding out about the physical world and representing the results numerically. No-go theorems show that measurement of quantum observables is not like that: the recorded outcome is typically created rather than revealed in a quantum measurement, in which case there is no objective fact about the observable's prior value. Other no-go theorems show that unitary quantum theory can generally neither explain nor even represent a unique recorded outcome, thereby threatening that outcome's objectivity. Methodological norms inherent in quantum physical practice nevertheless institute the objectivity, not only of unique recorded outcomes of quantum measurements, but also of non-quantum features of the world that physicists and other scientists take their models to represent.

We study the role of retardation in the energy shift of Rydberg states induced by thermal radiation, focusing on the case of temperatures higher than those for which the electric-dipole approximation is expected to apply. As anticipated by Farley and Wing [Phys. Rev. A {\bf 23}, 2397 (1981)], retardation needs to be taken into account in calculations of this energy shift at and above the temperature $α\, mc^2/(3k_{\rm B}\,n^2)$, where $n$ is the principal quantum number of the state considered, $m$ is the mass of the electron and $k_{\rm B}$ is Boltzmann constant.The corresponding non-dipole shift dominates the electric-dipole shift at about 2.5 times that characteristic temperature. We also show that the electric-quadrupole thermal shift is of the same order of magnitude as the diamagnetic thermal shift and would thus need to be taken into account in the circumstances where the latter is relevant.