We investigate the strong decays of the recently observed hidden-charm pentaquarks \(P_ψ^N(4312)\), \(P_ψ^N(4440)\), and \(P_ψ^N(4457)\), as well as \(P_{ψs}^Λ(4338)\) and \(P_{ψs}^Λ(4459)\), within the molecular framework using the effective Lagrangian approach. We construct the effective Lagrangians describing the S-wave couplings between these pentaquarks and their constituent hadrons, namely \(Σ_c\bar{D}^{(*)}\) and \(Ξ_c\bar{D}^{(*)}\), and determine the coupling constants via the residues of the scattering \(T\)-matrix at the bound-state poles. Our results show that the decay widths are sensitive to the cutoff parameters in the form factors, whereas the branching fractions exhibit only weak dependence. Using \(P_ψ^N(4312)\) to calibrate the cutoff range, we further explore the spin assignments of \(P_ψ^N(4440)\) and \(P_ψ^N(4457)\). Our calculations favor the assignment where the lower-mass state \(P_ψ^N(4440)\) carries higher spin \(J = 3/2\) and the higher-mass state \(P_ψ^N(4457)\) carries lower spin \(J = 1/2\). In addition, the experimental widths of \(P_{ψs}^Λ(4338)\) and \(P_{ψs}^Λ(4459)\) can both be well reproduced under the molecular interpretation. We look forward to future experimental analyses with more accumulated data to clarify whether the lineshape of \(P_{ψs}^Λ(4459)\) contains contributions from both spin-\(1/2\) and spin-\(3/2\) states.

We investigate the problem of improving the greedy-type constant of a basis by means of an equivalent renorming of the ambient Banach space. Our main result shows that if a Banach space admits an unconditional and bidemocratic basis whose fundamental function satisfies certain regularity properties, then the space can be renormed so that the basis becomes isometrically greedy. The renorming simultaneously ensures lattice $1$-unconditionality, isometric bidemocracy, and allows prescribing the fundamental function up to a suitable regularization. As a principal application, we resolve a long-standing problem posed by Albiac--Wojtaszczyk in 2006 by proving that for each $1<p<\infty$ the $L_p$-normalized Haar system can be made $1$-greedy under an equivalent norm of $L_p$. Further applications include isometric greedy renormings for bases of Besov spaces, mixed-norm direct sums, and for a wide class of subsymmetric and conditional bases, including spreading models and the canonical basis of Schlumprecht space. These results show that isometric greedy renormings arise in far greater generality than previously known.

Quantum error correction (QEC) is critical for scalable fault-tolerant quantum computing. Topological codes, such as the toric code, offer hardware-efficient architectures but their Tanner graphs contain many girth-4 cycles that degrade the performance of belief-propagation (BP) decoding. For this reason, BP decoding is typically followed by a more complex second stage decoder such as minimum-weight perfect matching. These combined decoders achieve a remarkable performance, albeit at the cost of increased complexity. In this paper we propose two key improvements for the decoding of toric code. The first one is replacing the BP decoder by a neural BP decoder, giving rise to the neural belief-matching decoder which substantially decreases the average decoding complexity. The main drawback of this approach is the high cost associated with the training of the neural BP decoder. To address this issue, we impose a convolutional architecture on the neural BP decoder, enabling weight sharing across the spatially homogeneous structure of the code's factor graph. This design allows a model trained on a modest-size topological code to be directly transferred to much larger instances, preserving decoding quality while dramatically lowering the training burden. Our numerical experiments on toric-code lattices of various sizes demonstrate that this technique does not result in a noticeable loss in performance.

Stimulated Brillouin microlasers offer chip-scale light sources with high spectral purity and low phase noise--key attributes for applications spanning precision metrology, quantum technologies, and coherent information processing. However, simultaneously bringing both pump and scattered waves into resonance often compromises photon confinement or modal volume, resulting in limited conversion efficiency and elevated thresholds. In this work, a novel approach is proposed to generate Brillouin microlasers with high efficiency, low threshold, and narrow linewidth, by combining a cross-polarized stimulated Brillouin scattering scheme with intentional Stokes mode splitting to compensate for mode detuning. Triple-resonance and phase-matching conditions are simultaneously achieved in a 114-um-diameter thin-film lithium niobate (TFLN) microresonator, enabling precise alignment with both the ~10-GHz Brillouin shift and the ~100-MHz narrow gain bandwidth. The resulting Brillouin microlaser achieves a narrow intrinsic linewidth of 2.88 Hz, a short-term integral linewidth of 185 Hz, an on-chip conversion efficiency of 57.92%, and a pump threshold as low as 1.03 mW. Both the conversion efficiency and the lasing threshold represent record-high performance for the TFLN platform to date.

We report the presence of a highly ionized absorber in the transient, eclipsing low-mass X-ray binary AX J1745.6-2901, observed from Feb. 26 to 29, 2024 with XRISM's Resolve and Xtend instruments. During a soft/high state without dips, Resolve's high spectral resolution (E/dE ~ 1000, full width at half maximum) revealed narrow velocity widths (sigma ~ 110 km/s) for Fe XXVI and Ni XXVIII lines, even with low photon statistics. These widths are consistent with binary orbital motion. The observed modest blueshift velocity (~160 km/s) indicates that the absorber is located sufficiently far from the neutron star (> 10^9 cm), so that gravitational redshift effects are not dominant. On the other hand, broad-band spectral analysis using a photoionized plasma model applied to the Xtend data constrains the absorber to lie within a radius of < 10^9.5 cm, as inferred from the upper limits of the best-fit ionization parameter (log xi ~ 4.4) and the large column density (~ 1.6 x 10^24 cm^-2). At this distance, the observed outward velocity of the absorber is about an order of magnitude smaller than the escape velocity from the neutron star.

The development of Artificial Intelligence (AI) has enabled agentic robots an appealing paradigm for various applications, such as research and rescue in complex environment. In this context, the next wireless communication technology facilitates robot cooperation for efficient environment sensing and exploration. However, traditional AI solutions cannot always provide reasonable resource utilization decisions, which makes it challenging to achieve both accurate and low-latency research and rescue. To address this issue, we propose a, LSAI, a large small AI model codesign framework to achieve highly accurate and real-time robot cooperation with deep interaction between large AI model and small AI model. We first propose an attention-based model aggregation for LAI construction. It can assist agentic robots in accurately sensing physical environments. Next, we design an adaptive model splitting and update algorithm to enable the robots to perform accurate path planning for high-efficiency environment sensing with low energy consumption. Finally, we demonstrate the effectiveness of our proposed LSAI framework. The simulation results indicate that our solution achieves sensing accuracy of up to 20.4% while reducing sensing cooperation latency by an average of 17.9% compared to traditional AI solutions.

Belle and Belle II experiments have collected $e^+e^-$ collision data with center-of-mass energies at or near the $Υ(4S)$ resonance. Using total $1.4\,\mathrm{ab}^{-1}$ combined dataset, we present new measurements of branching fractions for $Ξ_c^{0/+}$ and $Λ_c^+$ baryons, including several first observations. Additionally, we report the initial search for $CP$ violation in singly Cabibbo-suppressed three-body decays of charmed baryons, providing a test of $U$-spin symmetry.

Reliable quantum memory is essential for scalable quantum networks and fault-tolerant photonic quantum computing. We present a quantitative analysis of an all-optical quantum memory architecture in which a Gottesman-Kitaev-Preskill (GKP) encoded qubit is stored in a fibre loop and periodically stabilized using teleportation-based error correction. By modelling fibre propagation as a pure-loss channel and representing each correction round as an effective logical map acting on the Bloch vector, we obtain a compact description of the full multi-round memory channel. We show that syndrome decoder optimization plays a crucial role in the experimentally relevant finite-squeezing regime. The optimal decoder deviates from standard square-grid GKP decoder in both tile-size and tile-shape, leading to significant improved logical performance. Using this optimized decoding strategy, we identify a squeezing-dependent optimal spacing between correction nodes that maximizes the memory lifetime. Remarkably, this optimal segment length is largely independent of the desired storage time, providing a simple and practical design rule for fibre-loop quantum memory. We further find a squeezing threshold of approximately 6.7 dB below which intermediate error correction becomes counterproductive, while above threshold the achievable storage time increases approximately exponentially with squeezing. For example, at 17 dB squeezing, storage times exceeding 400 ms can be achieved with logical infidelity below 1%. These results establish clear performance benchmarks and reveal the fundamental trade-off between photon loss, squeezing, and correction frequency in continuous-variable architectures. Our findings provide actionable design principles for near-term photonic quantum memory and clarify the path toward scalable all-optical fault-tolerant quantum storage.

The transition to Electric Vehicles (EVs) demands intelligent, congestion-aware infrastructure planning to balance user convenience, economic viability, and traffic efficiency. We present a joint optimisation framework for EV Charging Station (CS) placement and pricing, explicitly capturing strategic driver behaviour through coupled non-atomic congestion games over road networks and charging facilities. From a Public Authority (PA) perspective, the model minimises social cost, travel times, queuing delays and charging expenses, while ensuring infrastructure profitability. To solve the resulting Mixed-Integer Nonlinear Programme, we propose a scalable two-level approximation method, Joint Placement and Pricing Optimisation under Driver Equilibrium (JPPO-DE), combining driver behaviour decomposition with integer relaxation. Experiments on the benchmark Sioux Falls Transportation Network (TN) demonstrate that our method consistently outperforms single-parameter baselines, effectively adapting to varying budgets, EV penetration levels, and station capacities. It achieves performance improvements of at least 16% over state-of-the-art approaches. A generalisation procedure further extends scalability to larger networks. By accurately modelling traffic equilibria and enabling adaptive, efficient infrastructure design, our framework advances key intelligent transportation system goals for sustainable urban mobility.

To investigate the rest-frame optical emission of "Little Red Dots", we model the formation of and evolution of quasi-stars, i.e. stellar envelopes supported by the accretion luminosity onto a central black hole, originating from rapidly accreting proto-stars reaching the supermassive star regime ($>10^4$ M$_{\odot}$) and undergoing general relativistic instability. We compute stellar evolution models with net mass gain rates $=0.01$, 0.1, and 1 M$_{\odot}$/yr and metallicities $Z=0$-0.01. For the mass gain rates $\ge 0.1$ M$_{\odot}$/yr, stars remain nearly fully convective with $T_\mathrm{eff}\sim4000$-9000~K. The general relativistic instability leading to central BH formation occurs at $M_\star\sim3.5\times10^4$ M$_{\odot}$ ($6.6\times10^4$ M$_{\odot}$) for $\dot{M}_{\rm acc}=0.1$ M$_{\odot}$/yr (1 M$_{\odot}$/yr), at luminosities $L \sim 10^9$ L$_{\odot}$. The lifetime of quasi-stars is estimated to be $10^7$-$10^8$~yr, $\sim$100-1000 times longer than their progenitors. In an environment allowing for rapid accretion the formation, evolution, and properties of quasi-stars are found be essentially independent of metallicity. Comparing the luminosities of our models with those of Little Red Dots at $z<4.5$ ($L_\mathrm{bol}\sim10^{9.5}$-$10^{11.5}$ L$_{\odot}$) yields quasi-star masses $10^{4.5}$-$10^{6.5}$ M$_{\odot}$. The observed minimum luminosity of $\sim10^{9.5}$~\Lsun\ implies accretion rates $\gtrsim0.1$ M$_{\odot}$/yr for Little Red Dots progenitors. Our models offer a metallicity-independent framework supporting quasi-stars as the source of Little Red Dot optical emission, and provide insights into their lifetimes, composition, and progenitor environment.

We give a differential geometric construction of the holomorphic family of Higgs bundle moduli spaces over a curve C as a fibration over Teichmüller space. The method uses a function f defined on the character variety, essentially the energy of a harmonic map, which is dependent on the complex structure of C. Using f we define a natural family of flat Ehresmann connections parametrized by the circle which reveal various aspects of these moduli spaces and their hyperkähler metrics.

In this paper, we introduce the notion of a characteristic operator for closable linear operators and explore their connected spectral properties via equivalence. Additionally, we develop an explicit scheme for constructing characteristic operators for a broad class of closable linear operators which are commonly encountered in periodic evolution equations. Our findings are illustrated through examples involving classical delay differential equations, delay differential equations with infinite delay and mixed functional differential equations. Notably, we resolve an open problem concerning the discrete spectral structure of the Floquet exponents for this latter class of differential equations. This work can be regarded as a natural and significant extension of the powerful framework developed by Kaashoek and Verduyn Lunel [40] on characteristic matrices and spectral properties induced by autonomous evolution equations.

As the state-of-the-art methods for high-dimensional data retrieval, Approximate Nearest Neighbor Search (ANNS) approaches with graph-based indexes have attracted increasing attention and play a crucial role in many real-world applications, e.g., retrieval-augmented generation (RAG) and recommendation systems. Unlike the extensive works focused on designing efficient graph-based ANNS methods, this paper delves into merging multiple existing graph-based indexes into a single one, which is also crucial in many real-world scenarios (e.g., cluster consolidation in distributed systems and read-write contention in real-time vector databases). We propose a Fast Graph-based Indexes Merging (FGIM) framework with three core techniques: (1) Proximity Graphs (PGs) to $k$ Nearest Neighbor Graph ($k$-NNG) transformation used to extract potential candidate neighbors from input graph-based indexes through cross-querying, (2) $k$-NNG refinement designed to identify overlooked high-quality neighbors and maintain graph connectivity, and (3) $k$-NNG to PG transformation aimed at improving graph navigability and enhancing search performance. Then, we integrate our FGIM framework with the state-of-the-art ANNS method, HNSW, and other existing mainstream graph-based methods to demonstrate its generality and merging efficiency. Extensive experiments on six real-world datasets show that our FGIM framework is applicable to various mainstream graph-based ANNS methods, achieves up to 3.5$\times$ speedup over HNSW's incremental construction and an average of 7.9$\times$ speedup for methods without incremental support, while maintaining comparable or superior search performance.

This paper studies wideband channel estimation for OFDM systems assisted by extremely large RIS (XL-RIS). Due to the large aperture of XL-RISs, the user equipment may operate in the near-field region, while the base station-XL-RIS link remains in the far field, leading to a cascaded channel with hybrid near-field and far-field characteristics. Moreover, wideband effects further complicate channel estimation in mmWave/THz systems. To address these challenges, we propose a frequency-independent orthogonal dictionary by augmenting the discrete Fourier transform (DFT) matrix with additional parameters, which enables an efficient representation of the wideband cascaded channel using a two-dimensional block-sparse structure. Based on this property, the considered channel estimation problem is effectively solved within a tailored compressed sensing framework. Simulation results demonstrate that the proposed method significantly outperforms conventional polar-domain channel estimation approaches in terms of estimation accuracy.

We construct a vertex coproduct on the Kontsevich--Soibelman cohomological Hall algebra (CoHA) of a quiver with potential, following Joyce (2018). We show it forms a vertex bialgebra. By applying a vertex algebraic analogue of Majid--Radford bosonisation, we form an extension of the CoHA of quivers with potential which incorporates a Cartan part. In the case of ADE quivers our vertex coproduct recovers Drinfeld's deformed coproduct on the Yangian. We compare the vertex coproduct with a localised coproduct defined by Davison and with the construction of Dotsenko--Mozgovoy when the potential is trivial. Our construction gives a new proof of the cohomological integrality theorem for symmetric quivers with trivial potential.

This study presents the development and validation of an independent software tool based on the Varian Eclipse Scripting API (ESAPI) for multi-modal brachytherapy Quality Assurance (QA). The tool addresses GEC-ESTRO HDR protocols and LDR positional uncertainty analysis. Engineered in C#, the application interfaces with BrachyVision, Vitesse, and Variseed, enabling independent TG-43 dose calculations -- comparing point and line source models -- integrated with EQD2-based radiobiological summation. In HDR cervical cancer, the tool successfully automated EMBRACE II protocol reporting, streamlining clinical workflows by combining dosimetric QA with predictive and prospective planning. For LDR prostate treatments, a stochastic simulation module quantified the impact of systematic (rigid-body) versus random seed displacements on target coverage ($D_{90\%}$) and Organs at Risk (OAR) safety ($D_{0.1cc}$). Sensitivity analysis in LDR prostate implants was benchmarked using two clinical cases (prostate volumes 31 cc and 71.3 cc). LDR simulations revealed that systematic displacements ($\pm$ 2 mm) yielded significantly higher dosimetric deviations than stochastic movements. In the 31 cc case, systematic shifts resulted in a rectal ($D_{0.1cc}$) standard deviation (SD) of 24.3 Gy, whereas random displacements reduced this to 12.4 Gy. In the 71.3 cc case, random displacements resulted in a rectal $D_{0.1cc}$ SD of 7.6 Gy, confirming that smaller volumes exhibit heightened sensitivity to errors. Technical analysis demonstrated that the point source model overestimated bladder $D_{10\%}$ by 8% relative to the line source model. Our findings confirm that systematic rigid-body shifts represent a greater clinical risk for OAR toxicity than stochastic migration. Integrating predictive sensitivity analysis into the clinical workflow significantly enhances patient safety through robust plan verification.

Self-driving laboratories (SDLs), by combining automation with machine learning-guided experiment selection, have the potential to transform experimental materials science. To date, most SDLs have been optimisation-driven, designed to rapidly converge on performance metrics, by embedding multiple mechanistic layers within platform-specific surrogate models. Such approaches excel at process tuning yet offer limited insight into the underlying physics governing synthesis-property relationships. Here we articulate a complementary paradigm: the exploration-driven, or scientific, SDL, whose primary purpose is the generation of data for data-driven science. We exemplify this concept for the case of inorganic optoelectronic materials, arguing that defect physics, which forms the central mechanistic link between synthesis conditions and functional properties, provides the foundation for designing a suitable SDL. Because defect populations and their spatial organisation cannot generally be resolved directly - nor fully predicted from first principles - the task of the SDL is to generate datasets in which thermodynamic and kinetic synthesis variables are systematically perturbed and defect-sensitive observables measured in parallel. From this basis, we propose a set of design principles for scientific SDLs that will enable them to operate close to the physics of optoelectronic materials, thereby generating transferrable and reusable datasets offering radical insight. We use Cu2ZnSn(S,Se)4 as a case study, both to show the scale of the task of defect-aware materials exploration as well to highlight as the deficiencies in the current paradigm. We propose that properly designed SDLs can generate the structured datasets necessary to enable mechanistic inference and advance synthesis-aware materials design.

Smart homes are increasingly targeted by cyberattacks, yet residents often lack guidance when incidents occur. Since affected residents are likely to seek help from trustworthy sources, this paper asks: What actionable cybersecurity guidance do governments provide to smart home users whose systems have been compromised? To answer this question, we conduct an exploratory, user-centered review of governmental cybersecurity guidance for smart homes across eleven countries to identify and characterize the types of guidance governments provide and to systematize their content. Using a standardized search and screening process, we derive three emergent clusters: incident reporting, general security recommendations, and incident response. Our findings show that governments provide abundant general security advice and accessible reporting channels, but structured incident response guidance tailored to smart homes is rare. Only two sources offer step-by-step recovery guidance for non-expert users, highlighting a gap between preventive advice and post-incident support.

We introduce the notion of a neutral representation of a finite group, or finite group scheme, $G$; a representation $V$ with the property that if a gerbe $\mathcal{G}$ over a field $k$ that is a form of the classifying stack $\mathcal{B} G$ admits a vector bundle that is a form of $V$, then it is neutral, that is, $\mathcal{G}(k)$ is not empty. We give some criteria for a representation of a finite diagonalizable group scheme to be neutral. We apply this notion to give wide classes of examples of smooth curves, or varieties with a marked point, with cyclic automorphism groups, which are defined over their field of moduli, greatly generalizing some previous results.

Recommendation systems (RSs) are increasingly used to guide job seekers on online platforms, yet the algorithms currently deployed are typically optimized for predictive objectives such as clicks, applications, or hires, rather than job seekers' welfare. We develop a job-search model with an application stage in which the value of a vacancy depends on two dimensions: the utility it delivers to the worker and the probability that an application succeeds. The model implies that welfare-optimal RSs rank vacancies by an expected-surplus index combining both, and shows why rankings based solely on utility, hiring probabilities, or observed application behavior are generically suboptimal, an instance of the inversion problem between behavior and welfare. We test these predictions and quantify their practical importance through two randomized field experiments conducted with the French public employment service. The first experiment, comparing existing algorithms and their combinations, provides behavioral evidence that both dimensions shape application decisions. Guided by the model and these results, the second experiment extends the comparison to an RS designed to approximate the welfare-optimal ranking. The experiments generate exogenous variation in the vacancies shown to job seekers, allowing us to estimate the model, validate its behavioral predictions, and construct a welfare metric. Algorithms informed by the model-implied optimal ranking substantially outperform existing approaches and perform close to the welfare-optimal benchmark. Our results show that embedding predictive tools within a simple job-search framework and combining it with experimental evidence yields recommendation rules with substantial welfare gains in practice.

The present work investigates a type of morphisms between encryption schemes, called bridges. By associating an encryption scheme to every such bridge, we define and examine their security. Inspired by the bootstrapping procedure used by Gentry to produce fully homomorphic encryption schemes, we exhibit a general recipe for the construction of bridges. Our main theorem asserts that the security of a bridge reduces to the security of the first encryption scheme together with a technical additional assumption.

Real-world infrastructure planning increasingly involves strategic interactions among autonomous agents competing over congestible, limited resources. Applications such as Electric Vehicle (EV) charging, emergency response, and intelligent transportation require coordinated resource placement and pricing decisions, while anticipating the adaptive behaviour of decentralised, self-interested agents. We propose a novel multi-agent framework for joint placement and pricing under such interactions, formalised as a bi-level optimisation model. The upper level represents a central planner, while the lower level captures agent responses via coupled non-atomic congestion games. Motivated by the EV charging domain, we study a setting where a central planner provisions chargers and road capacity under budget and profitability constraints. The agent population includes both EV drivers and non-charging drivers (NCDs), who respond to congestion, delays, and costs. To solve the resulting NP-hard problem, we introduce ABO-MPN, a double-layer approximation framework that decouples agent types, applies integer adjustment and rounding, and targets high-impact placement and pricing decisions. Experiments on benchmark networks show that our model reduces social cost by up to 40% compared to placement- or pricing-only baselines, and generalises to other MAS-relevant domains.

Approaches to calculate SU(N) colored knot invariants (HOMFLY-PT polynomials) are well and widely developed. However, SO(N) case is mostly forgotten. With this paper we want to start the discusion of how to generalize Reshetikhin-Turaev approach to the SO(2n+1) case and which difficutlies arise in this discussion. We provide R and Racah matrices for the symmetric representation of the SO(5) group and show how to find the corresponding Kauffmann polynomials.

Neutrino telescopes provide a unique observational gateway to the high-energy universe, enabling the study of cosmic accelerators and extreme environments that remain inaccessible to the other high-energy messengers. Although they share core detection principles with neutrino experiments in particle physics, such as the observation of Cherenkov radiation, their scientific objectives and operational constraints diverge markedly. This paper reviews the motivations behind astrophysical neutrino detection, outlines key design strategies across various media and deployment environments, and highlights the critical role of neutrino telescopes in the context of multimessenger astronomy. In particular, we emphasize their potential to illuminate the origins of cosmic rays and to probe the mechanisms driving the most energetic phenomena in the universe.

We study the approximation of operators acting on probability measures on a product space with prescribed marginal. Let $I$ be a label space endowed with a reference measure $λ$, and define $\cal M_λ$ as the set of probability measures on $I\times \mathbb{R}^d$ with first marginal $λ$. By disintegration, elements of $\cal M_λ$ correspond to families of labeled conditional distributions. Operators defined on this constrained measure space arise naturally in mean-field control problems with heterogeneous, non-exchangeable agents. Our main theoretical result establishes a universal approximation theorem for continuous operators on $\cal M_λ$. The proof combines cylindrical approximations of probability measures with DeepONet-type branch-trunk neural architecture, yielding finite-dimensional representations of such operators. We further introduce a sampling strategy for generating training measures in $\cal M_λ$, enabling practical learning of such conditional mean-field operators. We apply the method to the numerical resolution of mean-field control problems with heterogeneous interactions, thereby extending previous neural approaches developed for homogeneous (exchangeable) systems. Numerical experiments illustrate the accuracy and computational effectiveness of the proposed framework.

Let $S$ be a Banach algebra over $\mathbb{Q}_p$ whose residue fields are finite extensions of $\mathbb{Q}_p$. Given an arithmetic family $V$ of Galois representations, i.e., a finite free $S$-module $V$ with a continuous action of the absolute Galois group of a $p$-adic number field, we construct a complex associated to $V$ over false-Tate extensions and construct explicit isomorphisms between its cohomology and the Galois cohomology. This recovers earlier results by Tavares Ribeiro when $S$ is a finite extension of $\mathbb{Q}_p$.

In this work, we aim to study a strong version of Ito's lemma for convex function. By considering the corresponding sub-martingale on a Brownian motion, we gain more insights about the convex function through a probabilistic viewpoint. The Doob-Meyer decomposition of this sub-martingale subsequently helps us deduce the Ito's lemma for convex function, and enables us to study a convex function via stochastic calculus. In particular, we use this version of Ito's lemma together probabilistic inequalities to recover an important analytic property of the convex function, which is its second-order differentiability.

Novel thermographic measurement and heat-flux compensation methods combined for evaluating aerodynamic heating in hypersonic flight were developed using high-speed thermography. A hypersonic spherical projectile with a diameter of 8 mm was launched at approximately Mach 5 in the test section of a ballistic range. Shadowgraph imaging was conducted to visualize the flight trajectory and the shock layer. Thermographic measurement was performed using a high-speed infrared (IR) camera to obtain the surface temperature distribution of the projectile. The temperature distribution on the spherical surface was reconstructed from the thermographic data, by considering the photoresponse time of the photodetector of the IR camera and the geometric characteristics of the projectile trajectory. Furthermore, to validate the shock-layer geometry and aerodynamic heating characteristics, a computational fluid dynamics (CFD) simulation was also performed. The shadowgraph results showed that a detached shock wave and a shock layer were formed in front of the projectile, consistent with the CFD result. From the thermographic result, it was found that the maximum surface temperature rise during the flight was 24.4 K above the ambient temperature and it decreased with increasing distance from the stagnation point. The Stanton number distribution was estimated from the reconstructed surface temperature by assuming a one-dimensional transient heat conduction caused during the flight. The stagnation Stanton number was calculated to be 0.00366, which was also consistent with both the CFD result and a previously reported empirical correlation.

We investigate isospin-breaking effects in double-charm molecular pentaquarks with the $D^{(*)}Σ_c^{(*)}$ configuration, using the one-boson-exchange potential framework. In these systems, the isospin-breaking effects arise from two sources: the strong interaction, which manifests as the threshold difference of the $D^{(*)}Σ_c^{(*)}$ components in the same isospin multiplet and the mass splittings of the exchanged isovector mesons ($π$ and $ρ$); and the electromagnetic interaction between charged $D^{(*)}$ and $Σ_c^{(*)}$ components. We calculate the binding properties and the isospin mixing angle between the $I=1/2$ and $I=3/2$ states of the $D^{(*)}Σ_c^{(*)}$ system. Our results show that the isospin-breaking effect contributes a significant correction of roughly $10\%-30\%$ to the binding energy. This effect is particularly pronounced in loosely bound molecular candidates, which are characterized by small binding energies and large root-mean-square radii. We therefore conclude that the explicit inclusion of isospin-breaking effects is essential for achieving the precision in theoretical calculations necessary to match rapidly advancing experimental programs. Our results are expected to provide valuable guidance for future high-precision experimental studies of deuteron-like molecular states.

Physical reservoir computing exploits the intrinsic dynamics of physical systems for information processing, while keeping the internal dynamics fixed and training only linear readouts; yet the role of input encoding remains poorly understood. We show that optimal input encoding is a geometric problem governed by the system's fluctuation-response structure. By measuring steady-state fluctuations and linear response, we derive an analytical criterion for the input direction that maximizes task-specific linear memory under a fixed power constraint, termed Response-based Optimal Memory Encoding (ROME). Backpropagation-based encoder optimization is shown to be equivalent to ROME, revealing a trade-off between task-dependent feature mixing and intrinsic noise. We apply ROME to various reservoir platforms, including spin-wave waveguides and spiking neural networks, demonstrating effective encoder design across physical and neuromorphic reservoirs, even in non-differentiable systems.