Papers

Fermilab has embarked on its next evolution for future neutrino experiments through the Proton Improvement Plan II (PIP-II). The injection system now requires an increase from a 15 Hz to a 20 Hz injection rate with approximately a 30% increase in the field strength from the original Orbital Bump (ORBUMP) dipole magnets in the Booster ring [1]. The four series connected dipoles will require 3 kV, 20 kA, 660 $\mu$s pulses at the aforementioned injection rate with a flatness of $\pm$0.12%. This is achieved through a dual-capacitor pulsed power supply (PPS) comprised of ten parallel cells and must last for 25 years. The supply utilizes high-voltage film caps for the rise and fall portion of the waveform; however, it switches over to a 6 F electrolytic capacitor bank for the flattop portion to meet flatness. The supply utilizes energy recovery to reduce high voltage charging supplies and required power to operate.

Additive Manufacturing (AM), consists of depositing material in successive layers to obtain the desired part. The parts produced by AM can thus adopt geometries inaccessible by conventional manufacturing means, for example hollow or lattice structures which considerably reduce their weight while keeping or even improving their mechanical properties. Among the many existing processes, Wire Arc Additive Manufacturing (WAAM) is particularly well suited to the manufacture of large metallic parts. It is characterized by a supply of heat in the form of an electric arc (produced by a welding generator) and a supply of material in the form of wire. This paper will discuss the impact of additive manufacturing to enhance the performances of high value components, based on naval application: the manufacturing of a hollow propeller blade demonstrator of 1.5 m high realized in the laboratory.

We construct a smooth projective family of rational surfaces over $\mathbb{G}_{m,\mathbb{Z}}$. The Mori dream property of a fiber is determined by the torsion of the normal bundle of an anticanonical cycle. Over $\mathbb{C}$, the locus of Mori dream fibers is Zariski dense. For every prime $p$, every geometric fiber over a closed point of the reduction modulo $p$ is a Mori dream surface, whereas the geometric generic fiber is not a Mori dream space. In either setting, no restriction to a nonempty open subset is a Mori dream morphism. We also prove that, over any algebraically closed field, a projective fibration becomes a Mori dream morphism after shrinking the base whenever the set of points with Mori dream fibers is not contained in a countable union of proper closed subsets.

Simulating nuclear magnetic resonance (NMR) spectra is a promising application of quantum simulation. Using Quantinuum's System Model H2, a trapped-ion quantum computer, we demonstrate an end-to-end, large-scale digital NMR simulation of a classically challenging benchmark molecule, 1,2-di-tert-butyl-diphosphane. We implement a hardware-efficient reduction of the nuclear-spin Hamiltonian, enabling Trotterized real-time evolution of an effective 21-spin model with tailored error suppression to reduce the effects of device noise. The reconstructed liquid-state proton NMR spectrum agrees with classical reference calculations and reproduces key spectroscopic features that previous quantum hardware demonstrations did not capture. Given the widespread use of NMR in chemical analysis and industrial research, these results advance digital quantum simulation of NMR spectra towards practical quantum utility.

The purpose of this paper is the identification of high-fidelity digital twin data models from numerical code outputs by non-intrusive techniques (i.e., not requiring Galerkin projection of the governing equations onto the reduced modes basis). In this paper the author defines the concept of the digital twin data model (DTM) as a model of reduced complexity that has the main feature of mirroring the original process behavior. The significant advantage of a DTM is to reproduce the dynamics with high accuracy and reduced costs in CPU time and hardware for settings difficult to explore because of the complexity of the dynamics over time. This paper introduces a new framework for creating efficient digital twin data models by combining two state-of-the-art tools: randomized dynamic mode decomposition and deep learning artificial intelligence. It is shown that the outputs are consistent with the original source data with the advantage of reduced complexity. The DTMs are investigated in the numerical simulation of three shock wave phenomena with increasing complexity. The author performs a thorough assessment of the performance of the new digital twin data models in terms of numerical accuracy and computational efficiency.

Liver cancer is a complex disease responsible for a high number of deaths across the globe each year, making automated solutions for liver cancer classification urgent. The most common form of liver cancer is hepatocellular carcinoma (HCC), accounting for over 90% of liver cancer cases. There is a distinct lack of publicly available HCC datasets utilizing genomic data, which is necessary for training artificial intelligence (AI) models for automated HCC classification. This study proposes constructing a multi-stage HCC dataset using XGBoost and Semi-Supervised learning on three separate datasets of genomic biomarkers, utilizing their existing labels in the Semi-Supervised learning process to label the proposed dataset. The proposed dataset consists of 770 patient samples in total, categorized into five classes that represent normal tissue alongside different stages of HCC. Each sample in the dataset consists of 11,150 different gene expression levels. The XGBoost model demonstrated a final classification accuracy of 96.5% during the Semi-Supervised learning process.

Human videos provide rich manipulation experience, but extracting action representations that preserve useful motion remains challenging. Visual reconstruction alone can entangle manipulation-related motion with appearance changes and camera movement. We present GeoLAM, a framework for learning geometry-grounded latent actions from action-free human videos. GeoLAM combines future-frame reconstruction through a frozen geometric feature hierarchy with motion supervision from a training-only 4D geometry teacher. The geometric representation provides a structural prior, while the teacher's predictions yield spatially pooled targets capturing 3D displacement, residual image-plane motion, and surface-orientation changes. Visibility and confidence weighting reduces the contribution of unreliable estimates, encouraging continuous latent actions to retain geometric motion without explicit hand-pose or hand-trajectory annotations. After video pretraining without action labels, the learned representation provides transition targets for a world-action model trained on action-labeled robot demonstrations. The model jointly denoises latent actions and executable action chunks, with future-video prediction used only as an auxiliary training task. Deployment therefore requires neither the geometry teacher nor future-video generation. Evaluations on a latent-action benchmark and robotic manipulation tasks demonstrate the strong performance of GeoLAM.

Stable ternary compounds lie below every competing phase on a conventional convex hull, but this does not reveal whether their stability is inherited from already favorable binaries or created by bringing three elements into one crystal. We define the emergent ternary stabilization energy, delta E3, as the energy by which a stable ternary lies below the complete unary-binary hull at the same composition. Applied to 19,209 Materials Project compounds calculated within the GGA framework, delta E3 has a median of 63.3 meV/atom and spans from nearly binary-degenerate phases to compounds stabilized by several hundred meV/atom. The distribution separates recognizable chemical limits: intermetallics have the smallest median stabilization, single-anion compounds occupy a broad intermediate regime, and polyanion compounds receive the largest gains. Within single anion families, large delta E3 is associated with cation electronegativity contrast, bandgap opening, and reconstruction of coordination, bond geometry, and local neighbour chemistry relative to the actual binary decomposition products. Experimentally linked compounds obtain a median 4.92% of their formation energy from ternary stabilization, compared with 3.53% for theoretical compounds, with the clearest separation in sulphides and selenides. delta E3 therefore provides a compact measure of the thermodynamic value of compositional complexity: low values identify phases whose stability is largely reproducible by binaries, while high values identify compounds that gain substantially from ternary specific electronic and structural organization.

This course on two-dimensional quantum gases, prepared for the São Paulo ICTP-SAIFR IVth School on Light and Cold Atoms, is organized into three lectures. The first introductory lecture addresses Bose-Einstein condensation in an ideal gas, the effect of interactions in the weakly interacting limit, Gross-Pitaevskii equation and its hydrodynamic formulation, as well as superfluidity. The second lecture is devoted to the main features of two-dimensional quantum gases: importance of the interactions, enhanced phase fluctuations and the emergence of a quasi long-range order, superfluidity through the Berezinskii-Kosterlitz-Thouless mechanism, scaling symmetry. The third lecture has taken the form of a seminar on fast rotating quasi two-dimensional Bose gases and thermal melting of the vortex lattice. The slides accompanying these notes can be found on the school website: https://www.ictp-saifr.org/slca2025/.

This paper develops an embedded-hybridized discontinuous Galerkin (E-HDG) method combined with a first-order implicit-explicit scalar auxiliary variable (IMEX-SAV) time discretization for variational initial-state data assimilation governed by the unsteady incompressible Navier-Stokes equations. We adopt an optimize-then-discretize strategy. The spatial discretization uses discontinuous piecewise polynomials of degrees $k$ and $k-1$ for the element velocity and pressure, respectively, a continuous degree-$k$ velocity trace, and a discontinuous degree-$k$ pressure trace. The resulting state and adjoint velocities, as well as the reconstructed initial velocity, are globally divergence-free. The forward IMEX-SAV state scheme is unconditionally energy stable. Under suitable regularity and local-trajectory assumptions whose bounds introduce no explicit negative powers of the viscosity, the mesh-dependent condition $\Delta t\lesssim h^2$, and a contractivity condition on the Tikhonov parameter, we establish local existence and uniqueness of the fully discrete OTD optimality system and Reynolds-semi-robust $L^2$ error estimates of order $O(h^k+\Delta t)$ for the state, adjoint and reconstructed initial velocities; the constants contain no explicit negative powers of the viscosity. Numerical experiments confirm convergence on smooth tests and demonstrate machine-precision discrete incompressibility, effective nonlinear-solver behavior, and stable performance in small-viscosity regimes.

In order to solve practical problems on a quantum computer, it is necessary to use fault-tolerant quantum error correction schemes to overcome noise: the errors arising from imperfections in physical components. The Gottesman-Kitaev-Preskill (GKP) code aims at achieving this in a hardware efficient manner by encoding finite-dimensional logical subspaces in the Hilbert space of one or more continuous variable modes. In near term implementations, however, it is not feasible to eliminate errors entirely, so it is natural to also employ alternative error mitigation techniques together with error correction. In this work, we study a quantum error mitigation method known as probabilistic error cancellation in the context of the GKP code. We compare Steane-type and teleportation-based GKP error correction, and calculate the sampling overheads associated with the technique for square and hexagonal GKP codes. We employ the stabilizer subsystem decomposition for GKP codes to obtain an effective logical channel for noisy operations that is used to express the ideal one of a target logical unitary. We consider noise from finite squeezing on the data and the two ancilla modes, needed for error correction, and examine the relationship between the sampling overhead and the noise for different decoding methods. Our results are calculated for single- and two-qubit GKP Clifford gates and one round of error correction, and show the nontrivial combination of error correction and mitigation in continuous variable codes.

Multimodal representation learning seeks shared representations for cross-modal retrieval and knowledge transfer. Hub-based binding reduces pairwise supervision costs, but separate hub connections cannot guarantee reliable alignment between modalities without direct joint training. We introduce Hub-Spectral Activation (HSA), a closed-form method for recovering and activating the hub-readable component of latent multimodal knowledge in frozen representations. We formalize this knowledge as source-induced cross-modal dependence and characterize the component determined by the second-order statistics of two trained hub edges. Under a second-order source model, we establish conditions for exact recovery of the complete source-induced relation and bound the dimension of its hub-readable component by the hub covariance rank. HSA composes and standardizes hub-edge statistics, extracts paired spectral directions, and combines reliability-weighted matching evidence with source-gated candidate resolution for bidirectional retrieval and prototype classification. HSA requires no target-pair supervision, gradient optimization, or backbone updates. Across 19 retrieval and 11 prototype-classification relations on ImageBind and LanguageBind, HSA raises mean bidirectional Recall@10 from 18.27% to 31.15% and mean macro Top-1 accuracy from 29.01% to 52.43%, respectively. Controlled analyses further identify valid hub-edge correspondence and leading spectral directions as key sources of retrieval gains, demonstrating the utility of latent multimodal knowledge beyond native similarity scores. Code and models are publicly available at https://github.com/Luo1Yan/HSA.

We prove the generalized Cartan-Hadamard conjecture, also known as the Aubin conjecture, in the small volume regime under a lower Ricci curvature bound, for any dimension $n\geq 2$. More precisely, we show that if $(M^n,g)$ is a Cartan-Hadamard manifold satisfying $\mathrm{Sec}_g\leq\bar k\leq 0$ and $\mathrm{Ric}_g\geq (n-1)\underline k$, then its isoperimetric profile is at least that of the model space of curvature $\bar k$ for small enough volumes. We also reduce the proof of the generalized Cartan-Hadamard conjecture to establishing rigidity in the equality case.

We address three-dimensional (3D) solitons maintained by spin-orbit coupling (SOC) in the binary self-interacting Bose-Einstein condensate (BEC) held in the 3D optical lattice (OL). The analysis reveals that the SOC-OL interplay results in the formation of stable full-vortex (FV) soli-tons, built as sets of four density peaks residing in neighboring wells of the lattice potential, with the superimposed global vortical phase, and site-centered semi-vortices (SV), in which the vorticity is present in only one component. The full-vortex solitons, with their specific phase textures, do not exist in a uniform BEC with SOC. Full-vortex and semi-vortex states in the binary self-attractive BEC are stable despite the possibility of the supercritical collapse in the 3D system. Such states also exist, as gap solitons, in the self-repulsive 3D system. In terms of the chemical potential and number of particles, the stability regions of the 3D full-vortex solitons and semi-vortices expand with the increase of the SOC strength and OL depth. The results open the route to the creation of 3D complexes of vorticity-carrying condensates that can be realized with existing experimental techniques.

Multi-target regression requires a model to simultaneously predict several related outputs. Conformal prediction provides distribution-free, finite-sample marginal coverage guarantees, but extending these to joint multi-dimensional regions in a model-agnostic, sample-efficient manner remains challenging: max-aggregation ignores scale differences, copula-based methods are only asymptotically valid, rectangular methods typically split the calibration set, and quantile or density-based methods require training a specialised model beyond a plain point predictor. We propose the scaling-score conformal method, which is model-agnostic (requires only component-wise absolute residuals), uses a single calibration set, and yields four nested output types: an outer rectangle (SCO) with valid joint coverage, the exact set R $\alpha$ , a staircase (SC 2 ) over approximation of R $\alpha$ , and an inner rectangle (SCI). A single hyperparameter $\gamma$ $\in$ (0, 1) controls the base-rectangle quantile level independently of $\alpha$. We prove downward-closedness and a rectangular sandwich bound and derive a closed-form outer rectangle. Experiments on 29 realworld datasets confirm valid joint coverage; SC 2 with $\gamma$ = 1-$\alpha$ consistently achieves competitive volume relative to baselines, with the advantage growing with output dimension d.

Three-dimensional (3D) reconstruction of histopathology tissue requires accurate pairwise registration of serial whole-slide images (WSIs). Cross-stain benchmarks have advanced registration of differently stained histology, including structural-to-immunohistochemistry (IHC) pairs, but serial renal biopsy stacks remain difficult: they interleave several structural stains with diverse IHC markers whose expression can be sparse or absent, leaving few shared features to match. We present StainBridge, a stain-aware framework for registering serial renal biopsy WSIs across structural and IHC stains. StainBridge couples three preprocessing components, stain deconvolution, intensity normalization, and tissue-mask injection, with XFeat-based affine initialization and four nonrigid backends (VoxelMorph, ConvexAdam, FireANTs, and DeeperHistReg). We evaluate it on 23 cases comprising 338 WSIs, four structural stains, and ten IHC markers, with functional tissue units annotated on consecutive sections to give 1,468 landmark correspondences across 272 image pairs, and report tissue-mask Dice, functional-unit centroid error in micrometers, and tissue-restricted structural similarity. Nonrigid refinement improves on the affine initialization for three of four backends, VoxelMorph being the exception. DeeperHistReg, which computes its own initialization rather than relying on XFeat, gives the best pooled landmark accuracy and registers the most pairs, including every attempted structural-IHC pair. Preprocessing improves landmark accuracy for ConvexAdam and FireANTs in every stain-pairing category, and FireANTs shows both the largest single preprocessing gain on structural-IHC pairs and the best pooled tissue overlap. These results offer practical guidance for cross-stain registration and a foundation for integrated 3D analysis of renal tissue architecture and molecular expression.

The choice of Riemannian metric can strongly influence the convergence of gradient-based optimization over covariance matrices. Euclidean, Bures-Wasserstein and affine-invariant metrics are common choices, but their relative effectiveness depends on the objective. We introduce a two-parameter family defined by $X^{p}LX^{q}+X^{q}LX^{p}=U$, solved for $L$ at each tangent vector $U$, that contains all three as exact members, at $(0,0)$, $(1,0)$ and $(1,1)$, and extends past them. We treat the choice of member as a particular way of preconditioning for a given problem. To this end, we analyze the conditioning of the Riemannian Hessian at the solution. We show that it obeys a lower bound that depends on $(p,q)$ only through the exponent $r=p+q$. When the Euclidean Hessian is a pure power that mixes no eigendirections, the member $p=q=r/2$ attains that bound, and a closed-form criterion identifies the other members that do. We discuss ways to tune $r$ for a given problem. Experiments on real covariance data confirm the predicted conditioning and the benefit of tuning $r$. A task covariance example shows a further gain from tuning the shape.

Recent advancements in large language models have significantly enhanced the capabilities of agents in modeling long-term conversations. Despite these successes, existing approaches typically adopt a static heuristic paradigm, where information is passively archived without adaptive memory valuation. Consequently, these methods fail to self-evolve or align their memory management with evolving user needs. To address this, we propose ICML (InteraCtive Memory Learning), a multi-agent framework that transforms the memory mechanism from a passive archive into a learnable, interactive memory policy. Specifically, we first employ a session synthesis pipeline to generate expert data, facilitating rapid test-time adaptation in unseen scenarios. Building on this, ICML utilizes an online reinforcement learning mechanism where a Planner agent selectively encodes high-value information and a Trigger agent dynamically retrieves it to optimize response quality, whereby the two agents co-evolve through continuous interaction feedback. Crucially, both agents are synchronized through a delayed reward mechanism that propagates future feedback back to earlier storage decisions, ensuring memory policies are precisely aligned with user expectations. Experimental results demonstrate that ICML significantly outperforms strong baselines, exhibiting the unique capability to continuously improve response quality as interactions accumulate.

If ZFC is consistent, then so is ZF+DC+BPI+there is no Vitali set.

The conformal boundary of asymptotically flat spacetime is null and therefore carries a Carrollian rather than Lorentzian geometry. This changes the relation between symmetry, variational principles and evolution equations in an essential way: unlike a Lorentzian Levi-Civita connection, a torsion-free Carrollian connection compatible with the conformal structure contains genuine independent data. We develop a metric-affine formulation of conformal dynamics that keeps track of these connection degrees of freedom through hypermomenta. Local Carroll boosts, rotations, Weyl transformations and diffeomorphisms then imply a set of covariant evolution equations. We apply this framework to Einstein gravity in four-dimensional asymptotically flat spacetimes. Penrose's conformal compactification identifies null infinity as a conformal Carrollian manifold; the undetermined transverse symmetric part of its compatible connection is the asymptotic Bondi shear. After fixing a Bondi-van der Burg-Metzner-Sachs (BMS) frame and identifying the Carrollian momenta and hypermomenta with the Bondi data, the general Carrollian evolution equations reproduce the standard evolution equations for the mass and angular-momentum aspects. The result provides a boundary-intrinsic derivation of the gravitational evolution equations and a geometric realization of radiative degrees of freedom in flat-space holography. This is a proceedings contribution to the "Athens Workshop in Theoretical Physics: 10th Anniversary", held at the National and Kapodistrian University of Athens on December 17-19 2025.

We continue to develop a theory of Besov and Triebel-Lizorkin spaces associated with weighted subcoercive operators on a real connected Lie group, specializing to the case of groups with polynomial volume growth. We consider the full scale of spaces and consider equivalent definitions, inclusions, discretization, and duality.

The Asset Administration Shell (AAS) is increasingly recognized as a fundamental model for the realization of and data exchange between digital twins in manufacturing. An AAS defines a hierarchical data structure to represent any type of asset throughout its entire lifecycle. In the context of AAS-based systems, comparing different AAS instances constitutes a practical challenge, as neither a widely accepted methodological framework nor a maturity model are available to systematically support such analyses. To address this gap, we propose a novel concept of AAS maturity that characterizes the extent to which established digital twin criteria are met and thus enabling comparability of AAS instances. The concepts are derived from the literature and applied through exemplification. These emerging results enable practitioners and researchers to systematically compare AAS instances and support the identification and assessment of further development steps in the digital twin engineering process.

In the present paper, we study the maximization problem of the $k$-Torsional rigidity under quermassintegral constraint, with particular emphasis on the role of the ball. Our main result shows a phenomenon which, as far as we know, has not previously been observed: the ball, rather than being an extremal shape, is a saddle point. More precisely, for suitable quermassintegral constraints, we show that the $k$-torsional rigidity admits both increasing and decreasing perturbations around the ball. The proof is based on a second-order analysis of the corresponding variational problem. To the best of our knowledge, this is the first use of a second-order shape derivative approach in the study of variational problems for $k$-Hessian operators. We also establish an analogous saddle-point behavior for a related curvature functional under a volume constraint, highlighting a structural distinction between the intermediate Hessian regime and the classical Laplace and Monge-Ampère cases.

Communication complexity studies how much information must be exchanged to solve a problem whose input is split among two or more parties. In this work, we study an algebraic variant, where the inputs are vectors over a field $\mathbb{F} \in \{\mathbb{R}, \mathbb{C}\}$. There are two players, Alice and Bob, with inputs $X\in \mathbb{F}^n$ and $Y\in \mathbb{F}^n$, respectively. In the polynomial evaluation problem, the goal is to compute the value of a polynomial $g\in \mathbb{F}[X,Y]$ on the given input. In the set-recognition problem, the goal is to decide whether $(X,Y)\in S$, for a given set $S\subseteq \mathbb{F}^{n} \times \mathbb{F}^n$. In both settings, Alice and Bob send evaluations of polynomials depending only on their own inputs. In the set-recognition problem, a referee receives the messages and may apply polynomial tests to the messages received so far; the outcomes of these tests determine acceptance or rejection. The protocols may be deterministic or probabilistic. We give non-trivial upper bounds for a range of natural polynomial evaluation and set-recognition problems. We also prove reductions between different problems. Our main technical contribution is a general framework for proving lower bounds for algebraic set-recognition problems. Using this framework, we prove several probabilistic lower bounds for natural problems. In a number of cases, these lower bounds match the corresponding upper bounds, giving tight or near-tight characterizations of their algebraic communication. Finally, we give two applications of our framework. First, we use the communication lower bounds to prove lower bounds for a class of left-to-right algebraic algorithms, which we call algebraic scanners. Second, we show that our lower bound arguments extend beyond polynomials to a more general algebraic computational setting inspired by the Blum–Shub–Smale model.

Grounded language-model systems are often evaluated by final answer accuracy, yet a correct answer can be unsupported, drawn from the wrong source, or produced when evidence is insufficient or contradictory. We introduce EviScope, a paired counterfactual benchmark that holds the question fixed while adding, removing, distracting, or contradicting its evidence. EviScope-v1.1 contains 40 four-condition quartets with repaired counterfactual claims and span-level support labels for automatic evaluation. Across 960 gold-blind generations from Qwen2.5-7B, Llama 3.1 8B, and Gemini 3.5 Flash, paired metrics expose model-dependent grounding behavior that answer accuracy hides. On two local open models, an explicit evidence-action gate underperforms vanilla RAG on QCS: 0.15 vs. 0.50 for Qwen and 0.10 vs. 0.375 for Llama. Gemini reaches 0.944 joint success under both prompts, yet still answers 5% of conflict cases after contradiction insertion. EviScope therefore distinguishes unsupported answering, conflict blindness, and wrong non-answer actions rather than scoring answers alone.

CeRh$_2$As$_2$ has been receiving considerable attention due to its unusual two-phase superconductivity. The superconducting (SC) phase appears at $T_{\mathrm{c}}$ = 0.35 K in an ordered state (phase I) of the Ce-4$f$ moments, which develops below $T_{\mathrm{0}}$ = 0.55 K. The microscopic nature of phase I has not been fully established yet. We report a single-crystal study of the effect of La substitution on these low-temperature phases in Ce$_{1-\textit{x}}$La$_\textit{x}$Rh$_2$As$_2$ up to $x$ = 0.1. The lattice parameters increase monotonically with $x$, corresponding to an effective negative pressure of approximately -0.3 GPa for $x$ = 0.1. While the Ce$^{3+}$ local valence state and the non-Fermi-liquid behavior are preserved, the resistivity coherence maximum $T^{*}_{\mathrm{max}}$ $\approx$ 45 K in the pristine sample shifts to lower temperatures with increasing $x$, indicating a suppression of the Kondo energy scale upon lattice expansion. On the other hand, both $T_{\mathrm{c}}$ and $T_{\mathrm{0}}$ are rapidly suppressed to below 0.1 K for $x$ $>$ 0.05. Notably, such a rapid decrease of $T_{\mathrm{c}}$ under moderate negative pressure is unexpected, but is rather consistent with substitution-induced disorder effect which leads to strong pair breaking in unconventional superconductors. The observed fragility of phase I under both pressure and disorder may imply its itinerant origin.

The purpose of this paper is to extend an article by Hilhorst, Mimura and Schätzle [18] about the limit as the latent heat coefficient tends to zero of a two-phase Stefan problem arising in biology. We introduce a rather general additive noise white in time and colored in space, and search for the limit of the solution of the corresponding stochastic Stefan problem as the latent heat coefficient vanishes. We first prove the existence and uniqueness of the weak solution of this problem, and then study the limit of the solution as the latent heat coefficient tends to zero. Unlike in [18], our method of proof is based upon an error estimate between the solution of the Stefan problem with positive latent heat and that of the Stefan problem with zero latent heat, which seems to be novel even in the deterministic case when no noise is added.

We study complete stable minimal hypersurfaces in Riemannian manifolds under various curvature assumptions. In an $(n+1)$-dimensional complete oriented manifold with nonnegative scalar curvature, we prove that no complete oriented noncompact stable minimal hypersurface can be conformally equivalent to a bounded domain in an $n$-dimensional manifold with nonpositive scalar curvature. As a consequence, there exists no complete stable minimal hypersurface in $\mathbb{R}^{n+1}$ that is conformally equivalent to a bounded domain in $\mathbb{R}^n$. We also show that compact stable minimal hypersurfaces in manifolds with nonnegative scalar curvature have nonnegative smooth Yamabe invariant and we characterize the equality case. Next, we consider complete two-sided stable minimal hypersurfaces in ambient manifolds with pinched sectional curvature. Under an additional curvature condition that makes the second fundamental form a Codazzi tensor, we obtain a rigidity result under an $L^2$-condition on the second fundamental form and derive an upper bound for the first eigenvalue of the Laplacian. Finally, we establish that any complete noncompact two-sided minimal hypersurface immersed in a warped product manifold is stable, provided that the angle function is positive and the second derivative of the warping function is nonnegative.

Pseudospectral analysis provides a powerful way to probe the spectral stability of non-self-adjoint operators and has been widely used in black hole physics, but its application to braneworld scenarios has not yet been explored. In this work, we apply this method to tensor gravitational perturbations in a representative scalar-field-generated thick brane background. To the best of our knowledge, we provide the first hyperboloidal formulation of braneworld perturbations and propose a height-function gauge adapted to the warped geometry. This construction converts the outgoing boundary conditions of quasinormal modes into regularity conditions at finite compactified boundaries and recasts the perturbation equation as a first-order system generated by a non-self-adjoint hyperboloidal evolution operator. With the corresponding energy norm, we compute the condition numbers and pseudospectra of the localized graviton zero mode and the quasinormal-mode spectrum. We find that the condition numbers grow rapidly along the overtone sequence and that the corresponding pseudospectral contours develop broad, connected structures in the high-overtone region. These results show a strongly mode-dependent spectral sensitivity: among the damped modes analyzed, the higher overtones are less robust than the fundamental mode. The zero mode also has a larger condition number than the fundamental mode, indicating stronger local first-order sensitivity. These diagnostics characterize sensitivity to generic norm-bounded operator perturbations. Relating that sensitivity to a specific braneworld deformation requires the corresponding self-consistent perturbation constraints.

Few-shot audio classifiers may rely on foreground-background co-occurrences and fail when those correlations shift. On SpurAudio, the resulting representation shift is concentrated and class dependent: for ResNet12, the top 10 percent of channels explain 82.80 percent of the null-corrected shift contribution. We propose SAMPLESELECT, which predicts a fixed-budget feature mask independently for each input while keeping the encoder and source classifier frozen. Training uses differentiable Gumbel Top-k selection with foreground classification and cross-background contrastive losses; inference uses deterministic Top-k masks and support-only linear adaptation. Across ResNet12 and Conv64 in 5-way 1-shot and 5-shot evaluation, SAMPLESELECT gives the best OOD accuracy among the compared methods and improves the matched full-representation control by 4.90-8.38 percentage points. Ablations and representation analyses further support the learned selection mechanism. Code is available at https://github.com/Cross-Innovation-Lab/SAMPLESELECT/