Survival analysis provides a well-established framework for modeling time-to-event data, with hazard and survival functions formally defined as population-level quantities. In applied work, however, these quantities are often interpreted as representing individual-level risk, despite the absence of a clear generative account linking individual risk mechanisms to observed survival data. This paper develops a latent hazard framework that makes this relationship explicit by modeling event times as arising from unobserved, individual-specific hazard mechanisms and viewing population-level survival quantities as aggregates over heterogeneous mechanisms. Within this framework, we show that individual hazard trajectories are not identifiable from survival data under partial information. More generally, the conditional distribution of latent hazard mechanisms given covariates is structurally non-identifiable, even when population-level survival functions are fully known. This non-identifiability arises from the aggregation inherent in survival data and persists independently of model flexibility or estimation strategy. Finally, we show that classical survival models can be systematically reinterpreted according to how they handle this unresolved conditional mechanism distribution. This paper provides a unified framework for understanding heterogeneity, identifiability, and interpretation in survival analysis, and clarifies how population-level survival models should be interpreted when individual risk mechanisms are only partially observed, thereby establishing explicit information constraints for principled modeling and inference.

A classical proposal to derive weights from a pairwise comparison matrix is the right eigenvector. The literature has identified some potential weaknesses of this method in previous decades. This chapter discusses five of these issues. First, right-left asymmetry emerges because of the difference between the right and inverse left eigenvectors. Second, group incoherence for choice means that, in group decision-making problems, the ranking given by the aggregated individual weight vectors is not guaranteed to coincide with the ranking derived from the aggregated pairwise comparison matrix. Third, the ranking based on the right eigenvector may depend on the intensity of the preferences, represented by taking a positive power of all comparisons. Fourth, both the ranking position and the normalised weight of an object might change counter-intuitively after modifying a particular comparison. Fifth, the right eigenvector is not necessarily Pareto efficient: a dominating weight vector that approximates each pairwise comparison at least as well, with an improvement in at least one position, could exist. All violations of the theoretical properties are highlighted by illustrative examples. We also present several open questions in order to inspire future research.

We investigate the dynamical generation of charmonium-like ($I=0$) with spin-parity $J^{PC}=0^{++}, 1^{++}, 2^{++}$, and $3^{--}$ in the mass range of $3.6$ to $4.3$ GeV. We employ the off-shell coupled-channel formalism, constructing kernel amplitudes from effective Lagrangians that respect heavy-quark spin-flavor and chiral symmetries. To focus solely on dynamically generated states, we explicitly exclude $s$-channel pole diagrams and include only $t$- and $u$-channel meson exchanges. Solving the integral equations, we identify six poles in the complex energy plane. In the scalar ($0^{++}$) sector, we find a bound state below the $D\bar{D}$ threshold and a resonance at $\sqrt{s_R}=(3861-i\,23)\,\mathrm{MeV}$. For the axial-vector ($1^{++}$) sector, the experimentally observed $χ_{c1}(3872)$ is reproduced as a bound state near the $D\bar{D}^*$ threshold, alongside a broader resonance at $(3961-i\,32)\,\mathrm{MeV}$, which is a plausible candidate for the $X(3940)$. Furthermore, we find a narrow tensor ($2^{++}$) state at $4005\,\mathrm{MeV}$ and a vector ($3^{--}$) state at $4030\,\mathrm{MeV}$. The present results demonstrate that coupled-channel dynamics, particularly involving the $D^*\bar{D}^*$ channel, play a crucial role in the formation of these charmonium-like exotic states.

We provide a set of general tools to study the problem of stellar equilibrium in any gravitational theory in which spherically symmetric spacetimes satisfy master field equations taking the form of an equality between an identically conserved tensor, with derivatives of up to second order in the metric, and an identically conserved matter tensor. We derive the most general expression for the Tolman--Oppenheimer--Volkoff equation of stellar equilibrium that is compatible with these minimal requirements. A general discussion of the conditions that guarantee geodesic completeness at the center of symmetry is also presented. The equations of stellar equilibrium are integrated in a subset of the space of allowed deformations of general relativity proposed by Ziprick and Kunstatter, allowing us to illustrate universal aspects associated with the weakening of the strength of gravity, such as the mitigation of the Buchdahl limit obtained in general relativity or the existence of static solutions describing regular black holes with perfect fluid cores.

The proliferation of civilian and commercial unmanned aerial vehicles (UAVs) has heightened the demand for reliable radio frequency (RF)-based drone identification systems that can operate under dynamic and uncertain airspace conditions. Most existing RF-based recognition methods adopt a closed-set assumption, where all UAV types are known during training. Such an assumption becomes unrealistic in practical deployments, as new or unknown UAVs frequently emerge, leading to overconfident misclassifications and inefficient retraining cycles. To address these challenges, this paper proposes a unified incremental open-set learning framework for RF-based UAV recognition that enables both novel class discovery and incremental adaptation. The framework first performs open-set recognition to separate unknown signals from known classes in the semantic feature space, followed by an unsupervised clustering module that discovers new UAV categories by selecting between K-Means and Gaussian Mixture Models (GMM) based on composite validity scores. Subsequently, a lightweight incremental learning module integrates the newly discovered classes through a memory-bounded replay mechanism that mitigates catastrophic forgetting. Experiments on a real-world UAV RF dataset comprising 24 classes (18 known and 6 unknown) show effective open-set detection, promising clustering performance under the evaluated noise settings, and stable incremental adaptation with minimal storage cost, supporting the potential of the proposed framework for open-world UAV recognition.

We demonstrate that a vector-like fourth family of quarks induces a genuine chiral enhancement in $b\to sγ$, which is absent in the Standard Model (SM). The coexistence of doublet and singlet states allows the chirality flip to occur inside the loop, leading to contributions proportional to the heavy vector-like mass. The resulting amplitude is enhanced by a factor $\overlineλ_d v_H/m_b$, which can be as large as $\mathcal{O}(40)$ for moderate Yukawa couplings. This leads to sizable deviation from the SM prediction even for $\mathcal{O}(\mathrm{TeV})$ vector-like quark masses and small mixing angles. We find that $\mathrm{Br}(\overline{B}\to X_sγ)$ provides the most stringent constraint on this scenario among a wide range of precision observables.

The additional information carried by an enlarged filtration and its measurement was studied by several authors. Already Meyer (Sur un theoreme de J. Jacod, 1978) and Yor (Entropie d'une partition, et grossissement initial d'une filtration, 1985), investigated stability of martingale spaces with respect to initial enlargement with atomic sigma-field. We extend these considerations to the case where information is disclosed progressively in time. We define the entropy of such information and we prove that its finiteness is enough for stability of some martingale spaces in progressive setting. Finally we calculate additional logarithmic utility of a discrete information disclosed progressively in time.

Low dimensional materials are critical for enabling next generation applications that are central to addressing critical global challenges. Titanium dioxide nanostructures stand out due to their structural versatility and relevance to catalysis, energy conversion, and environmental remediation. Here, we employ a combination of advanced electron microscopy, spectroscopy, and first principles theoretical calculations to investigate the structural and chemical properties of one and two dimensional lepidocrocite type titania. Special emphasis is placed on the one dimensional material, which exhibits anisotropic growth, extending exclusively along a single crystallographic direction. Our analysis suggests that this unusual growth behavior can be attributed to light element impurities, such as carbon, that are incorporated during the bottom up synthesis. The results extend the understanding for these unexplored low dimensional titania materials and offer fundamental insights into their structure and chemistry.

In this paper, we introduce a novel model for the meta-analysis of proportions that integrates the standard random-effects model (REM) with an extreme value theory (EVT)-based component. The proposed model, named XT-REM (Extreme-Tail Random Effects Model), extends the classical REM framework by explicitly accounting for extreme proportions through a partial segmentation of the study set based on a predefined threshold. While the majority of proportions are modeled using REM, proportions exceeding the threshold are analyzed using the Generalized Pareto Distribution (GPD). This formulation enables a dual interpretation of meta-analytic results, providing both an aggregate estimate for the central bulk of studies and a separate characterization of tail behavior. The XT-REM framework accommodates heteroskedastic variance structures inherent to proportion data, while preserving identifiability and consistency. Using real-world data on immunotherapy-related adverse events, together with simulation studies calibrated to empirical settings, we demonstrate that XT-REM yields a comparable central estimate while enabling a more explicit assessment of tail behavior, including high-percentile extreme proportions. Compared with the classical REM, XT-REM achieves higher log-likelihood values and lower AIC, in the considered scenarios, indicating a better fit within this modeling framework. In summary, XT-REM offers a theoretically grounded and practically useful extension of random-effects meta-analysis, with potential relevance to clinical contexts in which extreme event rates carry important implications for risk assessment.

To predict smooth physical phenomena from observations, spline interpolation provides an interpretable framework by minimizing an energy functional associated with the Laplacian operator. This work proposes a methodology to construct a spline predictor on a compact Riemannian manifold, while quantifying the uncertainty inherent in the classical deterministic solution. Our approach leverages the equivalence between spline interpolation and universal kriging with a specific covariance kernel. By adopting a Gaussian random field framework, we generate stochastic simulations that reflect prediction uncertainty. However, on compact manifolds, the covariance kernel depends on the generally unknown spectrum of the Laplace-Beltrami operator. To address this, we introduce a finite element approximation based on a triangulation of the manifold. This leads to the use of intrinsic Gaussian Markov Random Fields (GMRF) and allows for the incorporation of anisotropies through local modifications of the Riemannian metric. The method is validated using a temperature study on a sphere, where the operator's spectrum is known, and is further extended to a test case on a cylindrical surface.

We conjecture the existence of almost integer invariants governing the all-genus equivariant Gromov-Witten theory of Calabi-Yau fivefolds with a torus action. We prove the conjecture for skeletal, locally anti-diagonal torus actions by establishing a vertex formalism evaluating the Gromov-Witten invariants via the topological vertex of Aganagic, Klemm, Marino and Vafa. We apply the formalism in several examples.

The design of numerical integrators for solving stochastic dynamics with high weak order relies on tedious calculations and is subject to a high number of order conditions. The original approaches from the literature consider strong approximations and adapt them for the weak approximation by replacing the iterated stochastic integrals by appropriate random variables. The methods obtained this way are sub-optimal in their number of function evaluations and the analysis of order conditions is unnecessarily complicated. We provide in this paper a novel approach, relying on well-chosen sets of random Runge-Kutta coefficients, that greatly reduce the number of order conditions. The approach is successfully applied to the creation of a collection of new stochastic Runge-Kutta methods of second weak order with an optimal number of function evaluations and a smaller number of random variables. The efficiency of the new methods is confirmed with numerical experiments and a modern algebraic approach using Hopf algebras is provided for the derivation and the study of the order conditions.

Low-altitude wireless platforms increasingly require lightweight, conformal, and densely sampled antenna array apertures with high array gain and spatial selectivity. However, when deployed on nonplanar surfaces, curvature alters the array manifold, local visibility, and propagation support, potentially invalidating spatial-stationarity assumptions. In this paper, we investigate a holographic curvature-reconfigurable aperture (HoloCuRA), modeled as a curvature-controllable holographic surface, and develop a visibility-aware spatial characterization framework for its low-altitude applications. Specifically, the framework jointly quantifies array-domain spatial non-stationarity (SnS), and spatial degrees of freedom (DoF) in line-of-sight, 3GPP non-line-of-sight, and isotropic-scattering propagation environments. For SnS, a novel Power-balanced, Visibility-aware Correlation-Matrix Distance (PoVi-CMD) and a two-stage subarray-screening procedure are introduced. For DoF, the Rényi-2 effective rank is adopted, and tractable spatial-correlation expressions under isotropic scattering are developed for efficient DoF analysis. Furthermore, a realizable antenna port mode is introduced to connect SnS with DoF. Numerical results reveal that curvature and propagation support are the primary determinants of both SnS and DoF in HoloCuRA: array domain SnS determines whether subarray statistics can be treated as locally consistent, whereas DoF limits the global spatial modes. The findings provide useful guidance for low-altitude antenna-system design.

Centralized identity management systems continuously experience security and privacy challenges, motivating the exploration of Decentralized Identity (DI) and Self-Sovereign Identity (SSI) as alternatives. Despite privacy and security benefits to users, the adoption of DI/SSI systems remains limited. One contributing reason is the lack of reproducible approaches to evaluate system compliance with its promised qualities. Derivation of functional requirements (FR) is the first and necessary step to develop such an evaluation approach. Previous literature on DI/SSI significantly lacks the systematic operationalization of existing non-functional requirements (NFR) or SSI principles. This work addresses this research gap by deriving FR for a generalized DI/SSI use case, which encompasses the fundamental operations of the system. The paper details operationalization methodology, introduces a formalized functional model, and presents a comprehensive set of FR, that can be used for future development and evaluation of DI/SSI systems. As a result, establishing the fundamental step toward a reproducible evaluation framework, rooted in established requirements engineering methods.

We present homogeneous, near-infrared ($JHK_s$ bands) time-series observations of the classical Carina dwarf Spheroidal (dSph) galaxy to determine accurate and precise distances using the pulsating stars as standard candles. These observations cover two Carina dSph fields ($\sim10.8'\times10.8'$) obtained with the FourStar infrared camera mounted on the 6.5-m Magellan Telescope. We collected precise photometric measurements of 43 RR Lyrae, 11 anomalous Cepheids (ACep), and 102 dwarf Cepheids (DCep) in Carina dSph. Using RR Lyrae, we obtained a distance modulus of $20.079\pm0.028\mathrm{(statistical)}\pm0.045\mathrm{(systematic)}$~mag, or a distance to Carina of $103.7\pm1.3\mathrm{(statistical)}\pm2.2\mathrm{(systematic)}$~kpc. The literature calibrations based on SX Phoenicis or delta-Scuti stars were used to anchor the $JHK_s$ period-luminosity relations for DCep. This resulted in a distance modulus that is in excellent agreement with RR Lyrae based determination. Finally, the distance moduli estimates using the ACep were found to be systematically smaller than the RR Lyrae-based distance modulus, suggesting a metallicity dependence on the ACep period-luminosity relation.

We propose \geogap{}, a geometric method for detecting missing requirement types in software specifications. The method represents each requirement as a unit vector via a pretrained sentence encoder, then measures coverage deficits through $k$-nearest-neighbour distances z-scored against per-project baselines. Three complementary scoring components -- per-point geometric coverage, type-restricted distributional coverage, and annotation-free population counting -- fuse into a unified gap score controlled by two hyperparameters. On the PROMISE NFR benchmark, \geogap{} achieves 0.935 AUROC for detecting completely absent requirement types in projects with $N \geq 50$ requirements, matching a ground-truth count oracle that requires human annotation. Six baselines confirm that each pipeline component -- per-project normalisation, neural embeddings, and geometric scoring -- contributes measurable value.

Applications for ultra-stable lasers outside controlled laboratory environments require compact and robust optical resonators with reduced sensitivity to temperature fluctuations. The low thermal expansion coefficient (CTE) and the high stiffness make cordierite-based ceramics, such as NEXCERA, attractive for vibration insensitive room-temperature resonators. We revisit the effective CTE of resonators with spacers and mirrors made of different materials and use finite element simulations to analyze the impact of a CTE mismatch in a cordierite-based resonator with mirrors made of ultra-low expansion (ULE) glass or fused silica (FS). This enabled us to determine the CTE of a cordierite spacer from the measured effective CTE of a resonator. We confirm a six-fold larger CTE slope of cordierite around the zero-crossing temperature than in ULE glass. The steep CTE slope, in combination with the large stiffness, makes cordierite-based resonators far less sensitive to CTE mismatch with FS mirrors, thereby eliminating the need for additional compensation rings. We further consider the so far neglected case, where the CTE of the spacer is larger than that of the mirror, and propose resonator designs in which the thermal length change of the spacer is fully or partially compensated by the deflection of the mirrors. This results in a cordierite-based resonator with ULE mirrors whose effective CTE can be close to zero over a temperature range of several tens of Kelvin. We are extending our concept to resonators based on crystalline materials with high stiffness and low isothermal length change, such as silicon, enabling compact and robust room-temperature resonators for terrestrial and space-born applications.

Heatwaves are intensifying as a major climate extreme and have emerged as a growing public health threat in rapidly urbanizing regions such as India. In this study, we integrate long-term heat-related mortality records (1970-2023) with bias-corrected CMIP6 climate projections to quantify future heatwave-related mortality across 67 Indian cities under intermediate (SSP2-4.5) and high-emission (SSP5-8.5) scenarios. A time-series forecasting framework was applied using summer mean temperature as the primary climate driver to project mortality trajectories through the end of the 21st century. Results indicate a strong and sustained increase in heat-related mortality under both scenarios, with multi-fold amplification under SSP5-8.5 relative to SSP2-4.5, reflecting the high sensitivity of health outcomes to emission pathways. Spatial analysis reveals increasing regional divergence under high-emission conditions, with urban regions in the Deccan Plateau, western India, and parts of eastern and northeastern India exhibiting disproportionately higher mortality growth. Multidimensional scaling further highlights emerging clustering of state-level mortality behavior under extreme warming, indicating structurally different regional responses to future heat stress. In contrast, the intermediate mitigation pathway produces more moderate and spatially uniform mortality trends. These findings demonstrate that climate mitigation can substantially reduce both the magnitude and inequality of future urban heat-health burdens. By linking updated climate projections with long-term mortality data at national and sub-national scales, this study provides policy-relevant evidence to support heat adaptation planning and climate-resilient urban development in one of the world's most heat-vulnerable regions.

The detection of gravitational waves from a core-collapse supernova in the Milky Way or its vicinity represents a unique opportunity to probe the inner workings of these explosions. In this review, I briefly summarize our current understanding of the supernova explosion mechanism and then outline the physical processes that shape the supernova gravitational wave signal. The review highlights how the various components of the signal have the potential to constrain the progenitor rotation, the proto-neutron star structure, the nuclear equation of state, the nature of hydrodynamic instabilities, and the violence of turbulent motions in the supernova core. I also highlight some open questions and uncertainties in the theory of supernova gravitational wave astronomy as well as challenges for further progress. Specifically, there is a need to develop large model databases, systematic uncertainty quantification and methods for evidence assessment to prepare for multi-messenger observations from a Galactic supernova.

Stock trend prediction has attracted considerable attention for its potential to generate tangible investment returns. With the advent of deep learning in quantitative finance, researchers have increasingly recognized the importance of synergies between stocks, such as sector membership or upstream-downstream relationships, in accurately capturing market dynamics. However, previous work often relies on static industry graphs or constructs graphs at each time step via similarity measures, overlooking the fluid evolution of stock relationships. We observe that as companies interact competitively and cooperatively, their interdependencies change in a fine-grained, time-varying manner that cannot be fully captured by coarse, static connections or simple similarity-based snapshots. To address these challenges, we introduce the Stock State Space Graph (S$^{3}$G) framework for enhanced stock trend prediction. First, we apply wavelet transforms to denoise the inherently low signal-to-noise financial series and extract salient patterns. After that, we construct data-dependent graphs at each time point and employ state space models to characterize the evolutionary dynamics of these graphs. Finally, we perform a graph aggregation operation to obtain the predicted return. Extensive experiments on historical CSI 500 data demonstrate the state-of-the-art performance of S$^{3}$G, with superior annualized returns and Sharpe ratios compared to other baselines.

We study the consistency of several early-Universe scenarios within a framework of non-minimal effective sca\-lar--ten\-sor gravity. We show that bounce, inflation, and genesis stages are supported within the aforementioned theory. Consequently, this framework can serve as a viable model of the early Universe, where accelerated expansion is driven by the theory's own intrinsic degrees of freedom. Notably, the theory also provides two different values of the Hubble parameter, potentially explaining the different values of the Hubble constant measured from galaxy clusters and relic radiation, respectively.

Let $s\in(\frac{n}{n+1},1)$, $Ω\subset\mathbb{R}^n$ be an open set and let $f\in W^{s,n/s}(Ω,\mathbb{R}^n)$ be mapping with positive distributional Jacobian $\mathcal{J}_f>0$ which models some deformation in fractional Nonlinear Elasticity. We show change of variables formula in this class and as a consequence we show that the analogue of Ciarlet-Nečas condition $\mathcal{J}_f(Ω)=|f(Ω)|$ implies that our mapping is one-to-one a.e.

Italy and the surrounding seas are recognised as one of the European hotspots for tornadoes and waterspouts. In recent years, the town of Rosignano Solvay (on the Northern Tyrrhenian coast) experienced repeated waterspouts affecting the same areas, raising local concern about the possible influence of heated wastewater discharged into the sea by a nearby industrial site. We reconstruct the mesoscale meteorological conditions of four intense waterspouts near Rosignano Solvay using a limited-area weather model at high-to-very-high resolution (inner domain grid spacing 500 m; sensitivity tests at 100 m). At the reported event times, the intensity of key mesoscale precursors (low-level wind shear, 1 km storm-relative helicity, maximum updraft intensity, and lifting condensation level) is consistent with the values typically associated with EF1 (or stronger) tornadoes and waterspouts. The model systematically predicts the peak of instability indices 2-3 hours earlier than the reported event times. For one case study, we conduct two sea surface temperature sensitivity experiments to assess the potential atmospheric impact of heated wastewater discharge (temperature increases of +1.5 K and +5 K over a 10 km$^2$ area). The resulting changes in instability indices are marginal, with differences of at most 3\% relative to the control run. A simple mass-balance estimate for the modified sea patch suggests that, given the reported discharge rates, a plausible impact of the warm water released from the industrial site could lead to an increase in the local sea surface temperature of approximately +0.7 °C over two months. We conclude that synoptic and mesoscale conditions primarily govern waterspout initiation in this region, while the direct effect of the small, warm coastal plume from the industrial discharge appears to be minor.

Vacancy-mediated diffusion in multi-principal element alloys (MPEAs) remains poorly understood. Existing computational methods face challenges in connecting electronic structure to macroscopic transport coefficients due to the large number of chemical elements. To address this, we introduce the embedded local cluster expansion (eLCE), which bridges first-principles calculations with kinetic Monte Carlo simulations to compute the matrix of multicomponent diffusion coefficients. Applying this approach to refractory MPEAs in the V-Cr-Nb-Mo-Ta-W system, we evaluate the complete mobility and diffusion tensors of a six-component alloy at finite temperatures. We find that local kinetic barriers, rather than thermodynamics or vacancy correlation factors, primarily control diffusion in these materials. Whether diffusion is sluggish or anti-sluggish depends on the mean vacancy migration barrier relative to the rule-of-mixtures estimate and on the availability of percolating pathways of fast-diffusing species. We use this insight to screen the senary composition space and identify compositions with anti-sluggish diffusion. This study presents a predictive, first-principles approach for computing non-dilute transport coefficients and designing MPEAs with targeted transport properties.

Coexistence of different dynamical phases is a hallmark of glassy dynamics. This is well-studied in classical systems where the underlying theoretical framework is that of large deviation theory. The presence of a similar phase coexistence has been suggested in monitored quantum many-body systems, but the lack of suitable methods has yet prevented a systematic large deviation analysis. Here we present a tensor network framework that allows the application of large deviation theory to large quantum systems. Building on this, we locate a series of first-order dynamical phase transitions in a monitored discrete-time many-body quantum dynamics, at the level of the trajectory space. Crucially, our approach provides access not only to large-deviation statistics but also to conditioned quantum many-body states, enabling a microscopic characterization of the dynamical phases and their coexistence.

We investigate how Restricted Boltzmann Machines (RBMs) encode antiferromagnetic order when trained as variational ansätze for one-dimensional Heisenberg spin rings with periodic boundary conditions. Through systematic hidden unit analysis and ablation studies on $N=4$ and $N=8$ spin systems, we show that individual hidden units spontaneously specialize to capture staggered magnetization patterns characteristic of antiferromagnetic ground states. Hidden units naturally segregate into two classes: those essential for ground-state energy and correlation structure, and supplementary units providing smaller corrections. Removing important units induces clear energy penalties and disrupts the staggered correlation pattern in $C_{zz}(r)$, whereas removing supplementary units has modest effects. Single-unit analysis confirms that no individual hidden unit reproduces the full antiferromagnetic correlations, indicating that quantum order emerges through collective encoding across the hidden layer. Extending this analysis to $N=8$ through $20$ with hidden unit densities $α= 2$ to $5$ and ten independent seeds per configuration, we find that the fraction of important hidden units decreases with system size, consistent with sublinear growth $m' \sim N^k$ ($k \approx 0.4$). The energy-correlation impact relationship persists for small to moderate system sizes, though it weakens for the largest systems studied. These results provide a quantitative framework for RBM interpretability in quantum many-body systems.

We present topological insulator (TI)-based single-electron transistors (SETs) as magnetic-field-compatible charge sensing devices that are easily integrable with TI-superconductor hybrid platforms. We observe well-resolved Coulomb diamonds in the charge-stability diagrams of our devices confirming the charge quantization and single-electron transport. In some devices, the Coulomb resonances show persistent shifts corresponding up to $\sim$ e/2 charge. An axial magnetic field further displaces these shifts to higher or lower gate voltages. We find that the axial magnetic-field dependence of the shifts is consistent with the Zeeman shift of a trap state coupled to the SET, and we reproduce the observations using numerical simulations. The resonance shifts are therefore identified as a consequence of the sensitivity of our TI-SET devices to charges in proximity. Establishing this charge sensing capability is a first step toward integrating TI-SETs as charge sensors in more complex TI-based hybrid devices, with the overarching goal of detecting and braiding Majorana zero modes.

We examine the existence of thick bubble rings within the framework of the free-boundary capillary Euler equations, focusing on the regime of low Weber numbers. Although spheroidal bubbles are known to approach a spherical shape in this limit, the possibility of thick bubble rings persisting at low Weber numbers has remained uncertain. In contrast to the ordinary Euler equations, which admit thick vortex ring solutions, our analysis reveals that the free-boundary capillary Euler equations do not support thick bubble rings at low Weber numbers. This distinction highlights the significant impact of surface tension on the behavior of vortex rings in the capillary regime.

This study provides an analytic and numerical characterization of a class of regular, asymptotically flat black holes described by a deformed static spherical metric. The model is grounded in a four-dimensional non-polynomial quasi-topological framework in which higher-curvature corrections remain dynamically nontrivial while the static spherical sector retains a reduced-order structure, enabling tractable black-hole solutions with regular cores. Starting from the existence conditions of horizons and regularity, the allowed parameter domain and the extremal bound are derived. Hawking temperature, shadow radius, photon-ring Lyapunov exponent, and ISCO binding efficiency are then analyzed across the physically allowed parameter space. We further extend the analysis to Novikov--Thorne thin-disk accretion by deriving the flux kernel, effective-temperature profile, and bolometric luminosity scaling, and by providing representative numerical datasets for these quantities. A coherent trend emerges: increasing the deformation parameter drives the solution away from Schwarzschild behavior, reducing temperature, shadow size, and photon-orbit instability rate while enhancing orbital binding efficiency and accretion luminosity; increasing the exponent $ν$ suppresses deformation effects and restores Schwarzschild-like observables. These results provide a compact phenomenological map linking horizon structure, thermodynamics, optical signatures, dynamical instability, and thin-disk accretion diagnostics in this regular black-hole family.

The exciton insulator (EI) is a unique many-body ground state of condensed, spontaneously formed excitons (electron-hole pairs) in equilibrium, distinct from conventional band or Mott insulators. Originally proposed over half a century ago, the concept has recently gained renewed experimental traction thanks to advances in spectroscopic resolution, ultrafast probes, and materials synthesis. In this Review, we outline the essential theoretical ingredients underpinning excitonic order and discuss how dimensionality, disorder and screening affect stability. We then examine the diverse experimental fingerprints of the excitonic state, with central focus on strategies to disentangle excitonic order from competing phases such as charge density waves, Mott insulating states, and hybridization-driven insulators, particularly in systems where non-trivial band topology plays a role. We survey the rapidly expanding family of candidate materials, from layered chalcogenides and correlated rare-earth compounds to artificial excitonic platforms and optically driven non-equilibrium condensates. Finally, we discuss the key challenges and emerging opportunities in the field, identifying the theoretical and experimental frontiers that promise to shape the next decade of research.