Gesture-driven music generation is an emerging human-computer interaction paradigm for touch-free and expressive musical interaction. However, many existing approaches treat the task as isolated gesture classification or map gestures to symbolic outputs such as MIDI followed by a separate rendering stage, which limits temporal continuity and real-time responsiveness. This work presents Gesture2Music, a low-latency streaming framework for continuous gesture-driven music generation from live webcam feed. The system processes sequences of body and hand landmarks and uses a causal temporal convolutional network (TCN) to predict note-level musical control events, including pitch, octave, onset, sustain, amplitude, and activity state. Because available gesture-note datasets typically contain only isolated single-note recordings rather than continuous performance sequences, a synthetic stream generation strategy is introduced to construct continuous gesture streams by concatenating single-note clips and deriving heuristic temporal event labels. Temporal consistency and spectral proxy losses are further used to reduce prediction jitter and encourage audio-consistent outputs. During inference, predicted musical events are rendered into continuous music using predefined note samples with rhythmic quantization and scale-constrained filtering for improved musical stability. Experiments on a custom gesture-to-music dataset with 21 gesture-note classes spanning seven tones across three pitch levels demonstrate stable real-time performance, low inference latency of 30\,ms, and improved temporal continuity.

Efficient energy management is essential for reliable and sustainable microgrid operation amid increasing renewable integration. In this paper, an imitation learning-based framework to approximate mixed-integer Economic Model Predictive Control (EMPC) is proposed for microgrid energy management, considering fuel generators, renewable energy resources, a unified energy storage unit, and curtailable loads. Within the proposed framework, a neural network is trained to imitate expert EMPC control actions from offline trajectories, thereby enabling fast real-time decision making without solving online mixed-integer optimization problems, which often exhibit highly variable solution times across instances and do not scale well to large problem sizes; in particular, worst-case solve times can be excessively large and therefore unsuitable for real-time deployment. In contrast, the learned policy provides predictable and consistently low computation times. To enhance robustness and generalization, the learning process incorporates noise injection during training to mitigate distribution shift and explicitly accounts for forecast uncertainty in renewable generation and demand. Furthermore, a constraint-tightening approach combined with a projection layer is proposed to ensure recursive feasibility and constraint satisfaction of the learned controller. Simulation results demonstrate that the learned policy achieves economic performance comparable to EMPC, while reducing computation time by approximately one order of magnitude relative to the optimization-based EMPC.

The Model Context Protocol (MCP) has emerged as a standard for connecting large language models (LLMs) with external tools. However, this MCP ecosystem introduces new security risks across hosts, servers, and registries. In this paper, we present the first cross-entity security study of MCP under a two-stage attack surface. At the registry-level, weak vetting and ownership checks allow adversarial or hijacked servers to enter hosts. After integration, attacker-controlled tool metadata can shape LLM reasoning and induce attacker-intended operations, which hosts execute without independent verification. Code-level vulnerabilities (e.g., code injection) are not required but can amplify attacker-controlled parameters into exploitation. We analyze 67,057 servers across six public registries and identify widespread conditions enabling server hijacking and invocation manipulation. We further implement MCPInspect, a pre-integration analysis tool that detects misleading tool metadata and exploitable code vulnerabilities, identifying 833 vulnerable servers and 18 with suspicious descriptions.

The adoption of large language models (LLMs) is transforming the peer review process, from assisting reviewers in writing detailed evaluations to generating entire reviews automatically. While these capabilities offer new opportunities, they also raise concerns about fairness and reliability. In this paper, we investigate bias in LLM-generated peer reviews through controlled interventions on author metadata, including affiliation, gender, seniority, and publication history. Our analysis consistently shows a strong affiliation bias favoring authors from highly ranked institutions. We also identify directional preferences associated with seniority and prior publication record, which can influence acceptance decisions for borderline papers. Gender effects are smaller but present in several models. Notably, implicit biases become more pronounced when examining token-level soft ratings, suggesting that alignment may mask but not fully eliminate underlying preferences

Large language models (LLMs) have demonstrated remarkable versatility across a wide range of natural language processing tasks and domains. One such task is Named Entity Recognition (NER), which involves identifying and classifying proper names in text, such as people, organizations, locations, dates, and other specific entities. NER plays a crucial role in extracting information from unstructured textual data, enabling downstream applications such as information retrieval from unstructured text. Traditionally, NER is addressed using supervised machine learning approaches, which require large amounts of annotated training data. However, historical texts present a unique challenge, as the annotated datasets are often scarce or nonexistent, due to the high cost and expertise required for manual labeling. In addition, the variability and noise inherent in historical language, such as inconsistent spelling and archaic vocabulary, further complicate the development of reliable NER systems for these sources. In this study, we explore the feasibility of applying LLMs to NER in historical documents using zero-shot and few-shot prompting strategies, which require little to no task-specific training data. Our experiments, conducted on the HIPE-2022 (Identifying Historical People, Places and other Entities) dataset, show that LLMs can achieve reasonably strong performance on NER tasks in this setting. While their performance falls short of fully supervised models trained on domain-specific annotations, the results are nevertheless promising. These findings suggest that LLMs offer a viable and efficient alternative for information extraction in low-resource or historically significant corpora, where traditional supervised methods are infeasible.

Quantum machine learning models that leverage quantum circuits as quantum feature maps (QFMs) are recognized for their enhanced expressive power in learning tasks. Such models have demonstrated rigorous end-to-end quantum speedups for specific families of classification problems. However, deploying deep QFMs on real quantum hardware remains challenging due to circuit noise and hardware constraints. Additionally, variational quantum algorithms often suffer from computational bottlenecks, particularly in accurate gradient estimation, which significantly increases quantum resource demands during training. We propose Iterative Quantum Feature Maps (IQFMs), a hybrid quantum-classical framework that constructs a deep architecture by iteratively connecting shallow QFMs with classically computed augmentation weights. By incorporating contrastive learning and a layer-wise training mechanism, the IQFMs framework effectively reduces quantum runtime and mitigates noise-induced degradation. In tasks involving noisy quantum data, numerical experiments show that the IQFMs framework outperforms quantum convolutional neural networks, without requiring the optimization of variational quantum parameters. Even for a typical classical image classification benchmark, a carefully designed IQFMs framework achieves performance comparable to that of classical neural networks. This framework presents a promising path to address current limitations and harness the full potential of quantum-enhanced machine learning.

Computing classical centrality measures such as betweenness and closeness is computationally expensive on large-scale graphs. In this work, we introduce an efficient force layout algorithm that embeds a graph into a low-dimensional space, where the radial distance from the origin serves as a proxy for various centrality measures. We evaluate our method on multiple graph families and demonstrate strong correlations with degree, PageRank, and paths-based centralities. As an application, it turns out that the proposed embedding allows one to find high-influence nodes in a network, and provides a fast and scalable alternative to the standard greedy algorithm.

Software Quality Assurance (SQA) is critical for delivering reliable, secure, and efficient software products. The Software Quality Assurance Process aims to provide assurance that work products and processes comply with predefined provisions and plans. Recent advancements in Large Language Models (LLMs) present new opportunities to enhance existing SQA processes by automating tasks like requirement analysis, code review, test generation, and compliance checks. Simultaneously, established standards such as ISO/IEC 12207, ISO/IEC 25010, ISO/IEC 5055, ISO 9001/ISO/IEC 90003, CMMI, and TMM provide structured frameworks for ensuring robust quality practices. This paper surveys the intersection of LLM-based SQA methods and these recognized standards, highlighting how AI-driven solutions can augment traditional approaches while maintaining compliance and process maturity. We first review the foundational software quality standards and the technical fundamentals of LLMs in software engineering. Next, we explore various LLM-based SQA applications, including requirement validation, defect detection, test generation, and documentation maintenance. We then map these applications to key software quality frameworks, illustrating how LLMs can address specific requirements and metrics within each standard. Empirical case studies and open-source initiatives demonstrate the practical viability of these methods. At the same time, discussions on challenges (e.g., data privacy, model bias, explainability) underscore the need for deliberate governance and auditing. Finally, we propose future directions encompassing adaptive learning, privacy-focused deployments, multimodal analysis, and evolving standards for AI-driven software quality.

Cardiovascular diseases (CVDs) are disorders impacting the heart and circulatory system. These disorders are the foremost and continuously escalating cause of mortality worldwide. One of the main tasks when working with CVDs is analyzing and identifying pathologies on a 12-lead electrocardiogram (ECG) with a standard 10-second duration. Using machine learning (ML) in automatic ECG analysis increases CVD diagnostics' availability, speed, and accuracy. However, the most significant difficulty in developing ML models is obtaining a sufficient training dataset. Due to the limitations of medical data usage, such as expensiveness, errors, the ambiguity of labels, imbalance of classes, and privacy issues, utilizing synthetic samples depending on specific pathologies bypasses these restrictions and improves algorithm quality. Existing solutions for the conditional generation of ECG signals are mainly built on Generative Adversarial Networks (GANs), and only a few papers consider the architectures based on Variational Autoencoders (VAEs), showing comparable results in recent works. This paper proposes the publicly available conditional Nouveau VAE model for ECG signal generation (cNVAE-ECG), which produces high-resolution ECGs with multiple pathologies. We provide an extensive comparison of the proposed model on various practical downstream tasks, including transfer learning scenarios showing an area under the receiver operating characteristic (AUROC) increase up to 2% surpassing GAN-like competitors.

Semantic communications aim to enhance transmission efficiency by jointly optimizing source coding, channel coding, and modulation. While prior research has demonstrated promising performance in simulations, real-world implementations often face significant challenges, including noise variability and nonlinear distortions, leading to performance gaps. This article investigates these challenges in a multiple-input multiple-output (MIMO) and orthogonal frequency division multiplexing (OFDM)-based semantic communication system, focusing on the practical impacts of power amplifier (PA) nonlinearity and peak-to-average power ratio (PAPR) variations. Our analysis identifies frequency selectivity of the actual channel as a critical factor in performance degradation and demonstrates that targeted mitigation strategies can enable semantic systems to approach theoretical performance. By addressing key limitations in existing designs, we provide actionable insights for advancing semantic communications in practical wireless environments. This work establishes a foundation for bridging the gap between theoretical models and real-world deployment, highlighting essential considerations for system design and optimization.

The HeartBert model is introduced with three primary objectives: reducing the need for labeled data, minimizing computational resources, and simultaneously improving performance in machine learning systems that analyze Electrocardiogram (ECG) signals. Inspired by Bidirectional Encoder Representations from Transformers (BERT) in natural language processing and enhanced with a self-supervised learning approach, the HeartBert model-built on the RoBERTa architecture-generates sophisticated embeddings tailored for ECG-based projects in the medical domain. To demonstrate the versatility, generalizability, and efficiency of the proposed model, two key downstream tasks have been selected: sleep stage detection and heartbeat classification. HeartBERT-based systems, utilizing bidirectional LSTM heads, are designed to address complex challenges. A series of practical experiments have been conducted to demonstrate the superiority and advancements of HeartBERT, particularly in terms of its ability to perform well with smaller training datasets, reduced learning parameters, and effective performance compared to rival models. The code and data are publicly available at https://github.com/ecgResearch/HeartBert.

Variational principles play a central role in classical mechanics, providing compact formulations of dynamics and direct access to conserved quantities. While holonomic systems admit well-known action formulations, non-holonomic systems -- subject to non-integrable velocity constraints or position inequality constraints -- have long resisted a general extremized action treatment. In this work, we construct an explicit and general action for non-holonomic motion, motivated by the classical limit of the quantum Schwinger-Keldysh action formalism, rediscovered by Galley. Our formulation recovers the correct dynamics of the Lagrange-d'Alembert equations via extremization of a scalar action. We validate the approach on canonical examples using direct numerical optimization of the novel action, bypassing equations of motion. Our framework extends the reach of variational mechanics and offers new analytical and computational tools for constrained systems.

Bilevel optimization reveals the inner structure of otherwise oblique optimization problems, such as hyperparameter tuning, neural architecture search, and meta-learning. A common goal in bilevel optimization is to minimize a hyper-objective that implicitly depends on the solution set of the lower-level function. Although this hyper-objective approach is widely used, its theoretical properties have not been thoroughly investigated in cases where the lower-level functions lack strong convexity. In this work, we first provide hardness results to show that the goal of finding stationary points of the hyper-objective for nonconvex-convex bilevel optimization can be intractable for zero-respecting algorithms. Then we study a class of tractable nonconvex-nonconvex bilevel problems when the lower-level function satisfies the Polyak-Łojasiewicz (PL) condition. We show a simple first-order algorithm can achieve better complexity bounds of $\tilde{\mathcal{O}}(ε^{-2})$, $\tilde{\mathcal{O}}(ε^{-4})$ and $\tilde{\mathcal{O}}(ε^{-6})$ in the deterministic, partially stochastic, and fully stochastic setting respectively. The complexities in the first two cases are optimal up to logarithmic factors.

Semantic communications are expected to enable the more effective delivery of meaning rather than a precise transfer of symbols. In this paper, we propose an end-to-end deep neural network-based architecture for image transmission and demonstrate its feasibility in a real-time wireless channel by implementing a prototype based on a field-programmable gate array (FPGA). We demonstrate that this system outperforms the traditional 256-quadrature amplitude modulation system in the low signal-to-noise ratio regime with the popular CIFAR-10 dataset. To the best of our knowledge, this is the first work that implements and investigates real-time semantic communications with a vision transformer.

This paper corroborates a statement that perturbative string theory does not admit a solution whose spacetime metric is de Sitter times a closed manifold, to all orders in the $α'$ and $g_s$ expansions, under the assumption that the logarithm of the sphere partition function of Euclidean quantum gravity receives a nonzero contribution proportional to $\frac{1}{G_N}$ in a saddle-point approximation. This assumption is related to the Gibbons-Hawking proposal that the entropy of the cosmological horizon of the static patch is $\frac{A}{4G_N}$. Evidence for the statement comes from independent approaches to the effective action of string theory, all of which agree that the tree-level action vanishes for closed Euclidean target-space solutions. One possible implication is that the state of the Universe will depart from an asymptotically de Sitter spacetime.

Using the worldline effective field theory formalism, we derive the nonlocal-in-time conservative contributions arising from tail effects in gravitational scattering to fifth Post-Minkowskian (5PM) and tenth self-force (10SF) orders. The result features multiple polylogarithms of up to weight three. This challenging computation relies on state-of-the-art integration techniques, including a novel integration-by-parts algorithm: the Sparse Integral Reducer (SpideR). We find perfect agreement in the overlap with all existing literature through sixth post-Newtonian order. The results presented here provide a key ingredient for isolating the local-in-time component of the conservative two-body dynamics of binary inspirals at 5PM order.

Nitrogen-bearing molecules are more difficult to observe than oxygen-bearing ones, mainly due to the lower abundance of nitrogen in the interstellar medium. Therefore, the formation pathways of many of these species is still under debate. Studies prior to the launch of the JWST did not have the sensitivity to observe ices toward the youngest and most deeply embedded Class 0 objects. Here we will focus on OCN$^-$, CH$_3$CN, C$_2$H$_5$CN, NO, and N$_2$O in ices to better understand their formation. We use the data from the JOYS+ program to study 8 Class 0 and 11 Class I objects with JWST. We firmly detect OCN$^-$ in ices for all these objects, tentatively detect CH$_3$CN, C$_2$H$_5$CN, and N$_2$O toward three sources, and find upper limits on the NO abundance in ices. The OCN$^-$/CO$_2$ ratios are found to be larger by a factor of ~2-3 for the objects that have a visible CO$_2$ double peak (a sign of ice thermal processing) pointing to the moderate effect of temperature on OCN$^-$ production. Relation of H$_2$O, CO$_2$, and OCN$^-$ with $A_{\rm V}$ indicates that OCN$^-$ may tentatively form at a later stage than H$_2$O and CO$_2$. We find that the ratios of CH$_3$CN, C$_2$H$_5$CN, and N$_2$O with respect to OCN$^-$ are relatively constant within one order of magnitude across our objects, likely suggesting that they have similar ice environments. The upper limit abundances of NO are ~1 order of magnitude lower than what was previously predicted in ices of a mature protoplanetary disk. This indicates that the detected gas-phase NO in that disk may be a product of another molecule (e.g. N$_2$O) in the ices. We conclude that OCN$^-$ can get enhanced at higher temperatures by only a factor of ~2-3 and thus OCN$^-$ detection alone does not imply ice heating. Large-sample studies of OCN$^-$ toward pre-stellar cores will be useful to further confirm the formation timeline of this molecule.

In decentralized non-custodial micropayments, the central challenge is not whether payments can be executed directly, but under what conditions such systems can offer credit limits without requiring full collateral backing. Existing approaches typically tie available credit to posted collateral, causing liquidity requirements to scale with transaction volume and settlement exposure and limiting the practical usefulness of credit-based micropayments. This paper characterizes the incentive conditions under which credit-based non-custodial micropayments can operate beyond full collateralization while remaining incentive compatible. We model repeated buyer--merchant interactions under public monitoring and identify the roles of bounded exposure, verifiable settlement outcomes, and continuation value in deterring strategic default under non-custodial execution. The resulting characterization clarifies the trade-off between capital efficiency and the enforcement conditions required to sustain under-collateralized credit expansion without custodial trust. As an illustrative application-layer instantiation, an Arbitrum Nitro prototype provides execution-level evidence that the settlement, commitment, and incentive-enforcement paths of a credit-limit-based design can be realized with low on-chain overhead.

A permutation $π$ strongly avoids the pattern $τ$ if both $π$ and $π^2$ avoid $τ$. In this paper, we enumerate permutations of size $n$ that strongly avoid the pattern 132. This enumeration allows us to prove a conjecture that the growth rate of such permutations is 2.

Multi-wavelength observations of molecular and ionized gas indicate that GMCs are short-lived, generally dispersing within one or two dynamical timescales. To investigate the physical origin of these short lifetimes and the role of star formation prescriptions, we conduct radiation-hydrodynamic simulations of an NGC 300-like disk galaxy with RAMSES-RT. We compare two distinct star formation models, one based on a local gravo-thermo-turbulent (GTT) condition and the other employing sink particles, to examine how star formation and feedback collectively regulate GMC evolution. The sink-particle-based model yields bursty yet self-regulated global star formation rates of $0.1$-$0.5$ $M_{\odot}\,yr^{-1}$ and produces GMC lifetimes of $\sim20$-$30$ Myr, with star formation efficiencies (SFEs) per free-fall time of a few percent, consistent with observations. In contrast, the GTT model generates a population of long-lived clouds with lifetimes $\gtrsim200$ Myr, owing to the extremely low SFEs per free-fall time $(\lesssim3\times10^{-3})$, which renders stellar feedback ineffective. With both models, cloud-cloud mergers extend the lifetimes of GMCs and increase their integrated SFEs by lengthening the star-forming duty cycle, while having only a minor impact on instantaneous efficiencies. On galactic scales, both models broadly reproduce the observed KS relation within its scatter, yielding gas depletion times of a few Gyr. In comparison, an extreme feedback model with the supernova energy boosted by a factor of five, combined with the GTT star formation model, excessively suppresses star formation and produces much longer depletion times ($6$-$20$ Gyr) for this isolated system. These results demonstrate that GMC lifecycles are strongly governed by the adopted star formation model, highlighting the need for improved prescriptions that realistically capture clump-scale star formation.

Generation of highly non-classical quantum states of light is essential for optical quantum information processing and quantum metrology. Given the lack of sufficiently strong nonlinear interactions between optical fields, the commonly employed optical quantum-state preparation schemes are conditional, based on nonlinearity induced by heralding photon number measurement on a part of a multimode squeezed Gaussian state. Development and optimization of such probabilistic quantum-state engineering schemes represents one of the central challenges in current quantum optics. As technology advances and experiments progress to detection of higher numbers of photons, the maximization of the heralding probability becomes essential to ensure sufficiently high state-preparation rates. Here, we show that for the conditional quantum state preparation schemes based on Gaussian states and photon number measurements the maximization of the heralding probability can be formulated as finding solution to a system of polynomial equations, which offers an efficient way to find the optimal configuration and allows us to apply techniques dedicated specifically to solving such systems of equations. Our approach can seamlessly incorporate bounds on the available single-mode quadrature squeezing, which is highly experimentally relevant. We mainly consider generation of finite superpositions of Fock states but show that the approach can be straightforwardly extended to generation of squeezed superpositions of Fock states. We focus on Gaussian states with vanishing coherent displacements, hence the conditionally generated states have well defined photon number parity. We illustrate our general methodology on examples of generation of single-mode and two-mode states with two heralding modes.

Boundary controllers have been recently proposed in the literature, via modal decomposition, to achieve $H^1$ stabilization of linear parabolic equations in two and three dimensions. In one dimension ($1$-D), $H^1$ exponential stability is known to imply boundedness and asymptotic convergence of the state to zero in the sense of the max norm. However, in two ($2$-D) and three dimensions ($3$-D), this implication does not systematically hold. In this paper, focusing on the full-state feedback case, our objective is to prove that the modal-decomposition based controller in \cite{Munteanu2017IJC} guarantees, not only $H^1$ exponential stability, but also $H^2$ exponential stability. This implies, in particular, boundedness and asymptotic convergence of the state to zero in the sense of the max norm. Our approach consists in rewriting the Laplacian of the state, required in the $H^2$ norm, as a linear combination of the state and its time derivative. The $L^2$ norm of the state being bounded by the $H^1$ norm, we only analyze the $L^2$ norm of the time derivative of the state.

The structural stability, electronic structure, and bonding characteristics of the silver-doped boron cluster B18Ag2 were investigated using density functional theory (DFT) combined with global optimization techniques. Basin-hopping searches identify a bent double-ring structure as the global minimum, consisting of two stacked B9 rings symmetrically stabilized by Ag atoms located above and below the boron framework. The UV-Vis absorption spectrum exhibits weak transitions in the near-infrared region and intense bands in the visible and near-ultraviolet regions, reflecting delocalized electronic excitations within the boron framework. Charge analysis indicates moderate electron redistribution from Ag atoms to the boron scaffold. Real-space bonding analyses based on the electron localization function (ELF), reduced density gradient (RDG), and molecular electrostatic potential (MEP) reveal that bonding is dominated by {$σ$}-delocalization over the boron skeleton, while Ag-B interactions are weak, non-directional, and primarily electrostatic. The continuous annular electron delocalization within the double-ring structure suggests an aromatic-like character. These findings establish B18Ag2 as a silver-stabilized boron double-ring cluster in which global electron delocalization governs structural stability, while Ag atoms act as axial stabilizing centers that modulate the electronic structure. This work provides new insight into the role of coinage-metal doping in stabilizing extended boron nanostructures.

One reason the Web is more useful than a simple collection of documents is that the structure created by hyperlinks enables flexible navigation from one web page to another. However, hyperlinks are typically created manually and cannot fully capture a corpus' implicit semantic structures. Is there a general way to make an arbitrary collection navigable? Recent work has formalized this problem generally as constructing a Hypergraph of Text (HoT), which provides a formal mathematical structure for supporting navigation and browsing. However, how to construct and evaluate a Hypergraph of Text remains a challenge. In this paper, we propose and study several methods for constructing a HoT. We also propose a novel quantitative metric, effort ratio, for evaluating the structural quality of a constructed HoT. Experimental results show that even simple TF-IDF baselines can match LLM-based methods on our proposed effort ratio metric.

We prove a sharp stable $2$-systolic inequality for complex projective space under the scalar curvature lower bound of the normalized Fubini-Study metric. If $M$ is diffeomorphic to $\mathbb{C}\mathrm{P}^n$ and $\mathrm{scal}_g\ge 4n(n+1)$, then $\mathrm{sys}_2^{\mathrm{st}}(M,g)\le π$. Moreover, equality holds only for the Fubini-Study metric, up to biholomorphism after choosing the corresponding complex structure. The proof uses Spin$^c$ Dirac operators, a comass estimate for the curvature term in the Lichnerowicz formula, and stable norm-comass duality.

The $H$--$T$ phase diagram of UTe$_2$ for magnetic field along the hard $b$ axis contains an unresolved internal boundary near $μ_0H \sim 14$--15~T, previously inferred from ac susceptibility and transport experiments but lacking thermodynamic evidence. We report ultrasound results for several elastic modes in an ultraclean UTe$_2$ single crystal with $T_c>2$~K for $H \parallel b$ down to 0.33~K and up to 18~T. A pronounced anomaly in the longitudinal $C_{33}$ mode, with a weaker response in $C_{44}$ and no resolvable anomaly in $C_{55}$, establishes this feature as a bulk thermodynamic phase boundary and reveals a symmetry-selective coupling to lattice strain. The phase line remains nearly constant in field near 14~T and terminates near 13.5~T and 1.25~K at a tetracritical point, providing the thermodynamic evidence for the fourth phase boundary in the $H$--$T$ phase diagram. The results constrain the order-parameter structure of the high-field phase and support field-induced multicomponent superconductivity in UTe$_2$.

In this paper we develop a consistent variable selection procedure for GARCH-X models that identifies the truly relevant exogenous covariates influencing volatility dynamics. The proposed method is based on a multiple hypothesis testing framework with Wald-type test statistics and the Benjamini-Yekutieli False Discovery Rate (FDR) procedure to control the proportion of false discoveries. We establish the consistency of the selection rule, showing that it asymptotically recovers the correct set of covariates as the sample size increases. Monte Carlo simulations across different distributions and dependence structures validate the method's accuracy and robustness. The procedure is applied to modeling the volatility of the SP 500 using macroeconomic and commodity indicators.

We prove a structural result for sets of integers with doubling at most $4 + δ$, with $δ>0$ sufficiently small. This generalises earlier work of Eberhard--Green--Manners which dealt with sets of integers with doubling strictly less than $4$, and makes progress towards a question of Green.

We study certain dynamical and metric aspects of Kiselman's semigroup $K_n$. The level function $\mathcal{L}$ is introduced and shown to admit a simple description in terms of right multiplication by generators. We show that every sequence of partial products in $K_n$ is eventually constant. Using $\mathcal{L}$, we further study sequences of random partial products in $K_n$ and show that, in the independent and identically distributed setting where every generator is chosen with positive probability, the hitting time of the eventual constant value is distributed as a sum of $n$ independent geometric random variables. Finally, we define a natural ultrametric on $K_n$ arising from the level function and obtain some basic results on the associated metric balls and spheres.

We present an observation-guided neural surrogate-learning framework for scientific simulation emulation, demonstrated on urban flood-inundation mapping. The framework combines LISFLOOD-FP hydrodynamic simulations with a real Gauge L stage record that is mapped to the simulation grid and converted to a datum-consistent local water-depth target before being used as single-site supervision. Focusing on a 256 x 256 crop around Gauge L in the Chicago metropolitan area, the method first constructs an ensemble-approximated Gaussian-process/local analogue surrogate (EnsCGP) to obtain a coarse flood-depth estimate and an uncertainty proxy. A U-Net-ASPP neural corrector then refines the coarse map using only simulation-derived and geospatial inputs: EnsCGP depth, the uncertainty proxy, rainfall, and spatial coordinates. The converted gauge-derived local depth is used only as a pointwise training target at the mapped gauge pixel; simulation-based losses are evaluated away from that pixel. Across temporally held-out events from 2013-2019, the emulator closely reproduces LISFLOOD-FP simulation targets outside the gauge-constrained pixel, with R^2 approximately 0.99 and mean absolute error below 0.01 m, and shows strong pointwise consistency with the converted Gauge L local depth target under the stated rolling-year protocol. We interpret these results as strong simulator-emulation agreement with pointwise observation-guided correction, not as independent validation of real-world inundation accuracy or as a complete operational flood-forecasting system.