Modern mobile applications consume large amounts of data to function, raising significant privacy concerns and regulatory challenges. While prior work has primarily focused on detecting compliance gaps through policy analysis, there remains a lack of actionable guidance for developers to implement privacy principles at the code level. In this paper, we focus on data minimization as a developer-operationalizable principle and investigate its realization in Android applications. We conduct a formative study on 1,114 open-source Android apps to identify ten recurring data minimization scenarios across five data-handling stages. Building on this, we perform a large-scale analysis of 9,875 real-world APKs and distill 31 actionable coding guidelines to support privacy-compliant development. We further examine LLM-based code generation in Android development and find that state-of-the-art models consistently reproduce data minimization-risky practices, indicating that they inherit and amplify patterns from real-world code. Encouragingly, incorporating our guidelines eliminates these issues across all evaluated models. Our work advocates a shift toward responding to privacy regulatory requirements at their code-level root causes, enabling better compliance in both human and AI-assisted programming.

The application of AI in education has evolved from monolithic intelligent tutoring systems to a diverse ecosystem of pedagogical agents, including conversational assistants, virtual coaches, and adaptive tutors. This shift requires a unified and scalable data architecture to manage the complex information feedback loops between human instructors, learners, and the varied AI agents. The design, development, and deployment of the data architecture in turn raises a critical issue of validation. This paper addresses this critical need by describing a practical validation strategy for a high-volume data pipeline developed as part of a data architecture for AI-augmented adult learning at the National AI Institute for Adult Learning and Online Education. Our approach involves a two-stage testing methodology to ensure both functional diversity and real-world scalability. First, the QA environment uses a blend of synthetic and real-world data to validate functional correctness across various event types produced from learner and agent interactions. Following this, the production environment successfully processed a total of over 2.7 million production requests across 21 successful runs carrying authentic event data from a large-scale online program. This validation process surfaced crucial insights into data privacy, a key challenge when handling varied data from multiple AI agent data sources. By outlining a replicable testing strategy for a unified data backbone, this research offers a clear framework for institutions and developers aiming to build and support their own heterogeneous suites of AI-powered learning tools. Keywords: Pedagogical Agents, Learning Ecosystems, Data Architecture, Validation, Scalability, Learning Analytics.

Control barrier functions (CBFs) have become a standard tool in safety critical-control systems. CBFs convert state constraints into real time control conditions that certify forward invariance (meaning that once the system starts in a safe region, it remains there for all future times) and minimally modify a nominal controller only when safety is at risk. In power systems, CBF based methods have been proposed for frequency and voltage safety, but they largely remain disconnected from three key features that are central to power system operation: differential algebraic equation (DAE) models that capture network power flow constraints, safety specifications involving algebraic variables such as bus voltages, and formal verification of the resulting closed loop system. This paper closes this gap by developing a CBF framework for power system DAE models that supports safety constraints on both dynamic and algebraic variables. The framework provides real time safety filtering through an optimization layer that wraps around an existing controller and minimally modifies its command to enforce safety. In addition, it provides formal verification (i.e., a mathematical guarantee that all admissible trajectories satisfy the prescribed safety constraints) through an offline reachability based certificate of safe operation. The result is a unified filter and verify methodology for enforcing and certifying frequency and voltage safety in power systems while preserving the DAE structure of the underlying model.

Public scientific and metrology releases can leak the hidden settings that produced them. We formalize and quantify this risk as a profiled statistical side-channel audit: a release map exposes finite-band statistics of a power spectral density (PSD), a profiled observer trains labeled template spectra under an explicit budget, and a challenge release is drawn from one of two utility-equivalent recipes separated by a protected coordinate. Averaged PSD bins follow a gamma channel, replaced by a covariance-weighted log-spectrum channel when the bins are correlated; this yields exact Kullback-Leibler divergences, Chernoff exponents, protected-bit advantage bounds, and finite-training, finite-library, finite-compute, and model-mismatch corrections. Our headline result is a finite-band transport-leakage law: after amplitude and blur are eliminated, the protected acid-transport information obeys $I_{λ|α,β}(K) = (64/1225)\, w λ^{6} K^{9} + O(w λ^{8} K^{11})$ for $Kλ\ll 1$, a ninth-order exponent with a closed-form safe band. A step-by-step protocol turns a measured release into these numbers, and a fixed-seed reproducibility package regenerates every table and figure. We instantiate the audit on screened extreme-ultraviolet (EUV) roughness spectra as a model-conditioned case study, with deployment on measured releases the next step.

Generative AI (GenAI) is becoming a widely adopted learning support tool for both students and instructors, as it offers benefits such as personalized tutoring and scaffolded learning. However, recent research highlights potential drawbacks such as overreliance and metacognitive issues, especially in novice programmers. Most prior work focuses on introductory programming courses, and important questions remain about the underlying mechanisms behind the negative effects of GenAI and if findings can be generalized when students learn more advanced computer science concepts. To address this gap, we conducted a mixed-methods study comparing student interactions with GenAI to two traditional learning supports in a second-year algorithms course: algorithm visualization (AV) and human live tutoring (LT). Twelve students participated in three 90-minute study sessions focusing on sorting, tree, and graph algorithms. We recorded gaze and interaction data, and each session concluded with a test assessing their conceptual understanding of the topic. Our analysis classifies when during the problem-solving process participants sought help, and compares the interaction patterns across the three learning supports. Although GenAI produced a larger increase in self-efficacy compared to live tutoring, it was associated with noticeably lower results in learning outcomes. We found that participants did not use algorithm visualizations effectively, faced usage barriers when using GenAI to learn advanced topics, and that live tutoring yielded the highest learning outcomes.

Large-scale graph neural network (GNN) training often requires distributed clusters because graph structure and feature tensors no longer fit in a single node's memory. In sampling-based training, each mini-batch expands into a receptive field that spans partitions and triggers thousands of remote feature fetches per epoch. This wastes energy for two main reasons: each small RPC pays a fixed initiation and protocol cost, and GPUs continue drawing substantial baseline power while waiting for remote features. We present GreenGNN, an energy-aware distributed GNN training system that reduces communication energy by exploiting the bursty, short-lived temporal locality of neighbor sampling. GreenGNN groups training into windows of W consecutive mini-batches, stages each window's hot features in a local cache, and merges remote requests from each partition owner into a small number of bulk transfers. This amortizes RPC overhead across many features while preserving an on-demand path for cache misses. Because window size controls the trade-off between communication amortization and hot-set staleness, GreenGNN selects W offline using a discrete-event simulator that replays a deterministic one-epoch access trace with a hybrid energy model. We implement GreenGNN on DGL and evaluate it on a 4-node GPU cluster with benchmark datasets. Across datasets and batch sizes, GreenGNN reduces total system energy by 27--43% relative to baseline while improving end-to-end throughput by up to 3.9x. GPU energy drops by 36--71%, driven by fewer RPC initiations and lower GPU stall time.

Public broadcasts are at the center of civic discourse: Traditional television talk shows, alongside emerging podcast and web video formats, capture and guide the attention of our societies, shaping how citizens encounter politics, science, and societal issues. Yet, systematic or even simple analyses of these formats face similar challenges: guest and content metadata are scarce, fleeting, fragmented, and not standardized. Research conducted and questions answered are based on extensive, laborious, yet isolated data-curation efforts that capture only a fraction of the relevant landscape. This work seeks to address this issue using a scaling-oriented framework for FAIR data curation in public broadcasting. Evaluated on 15 broadcasting programs, the pipeline aggregates ZDF Archive PDFs, fernsehserien.de, and Wikidata into a unified knowledge graph. Of the 31,817 candidate guest mentions from these three sources, 17,729 could be automatically disambiguated, further 5,958 via 64 hours of manual reconciling using OpenRefine. Results are published at speakermining.wikibase.cloud and linked to Wikidata, enabling SPARQL-based question answering based on gender, age, occupation, or institutional affiliation across 8,436 canonical persons with 23,527 appearances in 6,469 aligned episodes. Our iterative experience reveals that correctly disambiguating and deduplicating speaker data from heterogeneous sources demands dedicated effort on sustainable infrastructure. For scalable and reliable question answering on public broadcasts to be accessible to everyone, we recommend fostering the potential of linked open data: Advancing alignment and utilization approaches like this work, particularly towards crowdsourced development and curation, but also more FAIR data interfaces from public broadcast service providers.

A novel power delivery framework, comprising a package-embedded inductor topology and an inductance-island methodology, is introduced to maximize both inductance and current densities in vertical power delivery (VPD). The framework leverages multiple multi-phase converters, a common strategy in high-performance computing systems, to enhance efficiency and scalability. The proposed topology employs an array of tightly coupled spiral square inductors sharing a common magnetic rod, serving multiple converters operating in the same conversion phase. The array is optimized to maximize coupling and minimize conversion losses, achieving superior inductance and current densities of 250 nH/mm^2 and 10 A/mm^2, respectively. At the system level, the inductance-island methodology partitions the power delivery network into multiple islands, each dedicated to a converter phase and supplying a portion of the load current, thereby enabling scalable and efficient distribution. To validate the framework, the inductor array is designed and simulated in ANSYS Maxwell 3D and Mechanical, exhibiting an average quality factor of 23.6 and efficiency of 97.4% at 2 A load current, 6 V input, and 10 MHz switching frequency. The inductor array netlist is extracted from ANSYS and co-designed in Cadence Virtuoso with a distributed dual-phase power conversion system, ensuring joint optimization of passive and active components. The co-designed converter achieves a significant efficiency gain of 5.65% on average and up to 11.04% at 40 A load over a similar converter with uncoupled inductors, demonstrating the practical benefits of the approach.

Circuit optimization is an indispensable step in analog/RF IC design. Classical fast gradient-based optimization methods are typically infeasible due to lack of access to simulator source code and the technical barriers to implementing adjoint methods. Therefore, surrogate-based black-box optimization is widely used in practice; however, it can be costly to build and sensitive to hyperparameters, whereas population heuristics often suffer from slow convergence and large evaluation counts under tight simulator-call budgets. To address these limitations, we propose the Zeroth-Order Analog/RF Framework (ZOAF), which recovers gradient-descent directions from a small number of black-box circuit simulations, combining the benefits of both gradient-based optimization and black-box optimization. We also employ several surrogate-free techniques to improve the efficiency and accuracy, including (1) a hybrid ZO scheduling method that switches between random-direction ZO for budget-efficient exploration and coordinate-wise ZO for accurate late-stage refinement, (2) one-shot quasi-random multi-start to focus evaluations, and (3) a sliding-window monitor that triggers early stops and box-projected updates to maintain feasibility. Evaluated on three distinct schematics, ZOAF consistently outperforms state-of-the-art baselines, achieving the best median final value on every reported figure of merit -- with up to an order-of-magnitude advantage in median peaking on the 22-parameter two-stage amplifier -- together with the most robust worst-case behavior across seeds, while reducing simulator calls to convergence by $1.3$--$3.8\times$. Code is publicly available at https://github.com/LiyanTan111/ZOAF.

Cybersecurity threats are increasing in all aspects of society due to the integration of digital systems into modern-day life and a volatile geo-political landscape. Technical factors are an ongoing arms race; however, the threat surface from human and social factors is still present, often providing malicious actors the means to bypass complex technical security controls. Understanding human factors in light of technical evolution is essential to ensure security controls remain effective. This study presents the results of a survey on cybersecurity challenges within public and private sector organisations, including critical infrastructure providers, in Iceland (N = 130). From the management perspective, human factors were strongly noted as challenges and barriers to their organisations' security. These challenges include a lack of adequate training or awareness, hiring issues, poor cybersecurity culture, and time and/or financial resource constraints. Based on these findings, recommendations for mitigating threats from human factors are derived. These include: prioritising targeted over generic training to reduce employee fatigue, external government support for financially constrained organisations, and building a strong cybersecurity culture through constructive communication around shared responsibilities.

Transformer models have set new performance standards for machine learning (ML) tasks. However, their resource-intensive deployment on resource-constrained edge devices for cloud-free, on-chip transformer inference remains challenging. The ARM Compute Library (ARM-CL) framework provides low-latency CNN inference on ARM-based edge devices but lacks support for transformer inference. In this work, we implement several new transformer kernels in ARM-CL to support native transformer execution. Our extended ARM-CL achieves up to three times faster transformer inference compared to state-of-the-art CPU/GPU implementations on an ARM-based embedded board. Furthermore, heterogeneous multi-processor system-on-chips (HMPSoCs) powering edge devices provide both embedded CPUs and GPUs. We introduce cooperative CPU-GPU transformer inference, which executes memory-intensive operations on the CPU while utilizing the GPU for highly parallelizable, compute-intensive operations. This cooperative execution, implemented with minimal overhead, further reduces transformer inference latency by up to 15.72% compared to the best single-processor inference on ARM-CL.

We show that incorporating fairness constraints into virtual power plant (VPP) operations can incentivize consumer participation and thus improve the aggregator's long-run profitability. VPPs rely on sustained participation from heterogeneous consumers to provide a variety of grid services whose timing and frequency are often uncertain. As a result, consumers' willingness and ability to provide flexibility evolve over time, creating a dynamic link between past participation and future resource availability. We develop a dynamic aggregation framework to study how fairness in service allocation affects future participation and long-run profitability. By linking current dispatch decisions to future resource availability, we show that fairer allocations can strengthen consumer engagement, expand aggregate availability, and create additional value during high-price and high-demand events. To balance fairness and operational efficiency, we introduce a slack-augmented allocation mechanism that preserves most of the participation benefits from fairness while avoiding unnecessary reductions in service procurement. We derive conditions under which the resulting availability gains outweigh the short-run cost of redistribution and validate the approach using real-world consumer behavior and electricity market data from Norway.

Laws and institutions shape individual outcomes through complex interactions with citizens' diverse circumstances, yet how different voting methods navigate this coupled landscape remains poorly understood. We model collective governance as optimization on NK fitness landscapes, where shared bits (laws) are updated by voting while individual bits (personal traits) remain fixed. A cross-dependency parameter $α$ controls how legislation's effects depend on individual circumstances. We compare eight standard voting methods and a generalized scoring family across landscape ruggedness $K \in \{1,\ldots,20\}$ and $α\in [0,1]$ with 1000 runs per configuration. Under direct democracy, the optimal voting method undergoes sharp phase transitions as a function of landscape complexity: cardinal score voting dominates on smooth landscapes, ordinal scoring with $p=0.35$ at low-to-moderate ruggedness, Borda count across a wide middle range, and STAR voting at the highest complexity. A two-parameter empirical formula reduces the $(K, α)$ plane to a single complexity axis for visualization. Borda count achieves the highest mean fitness and lowest variance across most of the parameter space. We further introduce a representative democracy model parameterized by identity weight $β$ and candidate self-interest $p_{\mathrm{self}}$. Representation reshapes the complexity-dependent structure even under favorable conditions: cardinal score voting dominates across most regimes, with plurality emerging as the top method at high $β$ and low-to-moderate $p_{\mathrm{self}}$.

The Workshop on Designing Accountable Software Systems (DASS) was convened in November 2024 with support from the U.S. National Science Foundation to engage a wide range of current and future stakeholders from government, academia, and industry on the cross-disciplinary topic of accountability in software systems. Over two days, attendees engaged in a series of panels, invited talks, and breakout sessions covering: (1) the dimensions of accountability, including legal compliance as well as business and societal aspects and drivers; (2) a conceptual model of the various structures needed to realize accountability; (3) the sources of legal requirements that affect software; (4) the operationalization of legal requirements in software; (5) the requirements to preserve evidence needed to conduct investigations; and (6) a range of challenges and contextual factors beyond software that affect why some accountability structures succeed, while others fail. The workshop was conducted as a collaborative systematization of knowledge that culminated in several research directions. The findings include the importance of clarifying definitions and responsibilities within accountable organizations, which can affect whether those researching accountability are making assumptions that limit the generalizability of findings. Further research was also identified as needed to study the ways to improve the translation of accountability structures into the software design process while improving engagement with stakeholders, such as legislators, regulators, business executives and system developers. Finally, a key finding was the high demands that DASS-like research projects place on interdisciplinary teams: both in terms of team formation and sustainment, as well as, the specific demands of cross-disciplinary learning that covers both research methods, research dissemination, and career development.

Approximate nearest neighbor search (ANNS) is a fundamental primitive in large-scale retrieval, recommendation, and AI systems. As vector datasets grow to billions or even trillions of items, disk-based ANNS systems have emerged to handle this scale by storing vector data and index structures on storage systems, but their query performance remains dominated by I/O latency. Existing disk-based ANNS systems primarily optimize I/O efficiency or overlap I/O with computation, but they treat CPU computation and I/O access as largely separate components. This separation misses a critical opportunity: selectively processing candidates already cached in memory before making I/O decisions can reduce unnecessary disk accesses and improve search quality. However, exploiting this opportunity is challenging because excessive computation can delay critical I/O operations, while poorly chosen computation provides little benefit, potentially increasing overall query latency. In this paper, we present LAANN, a disk-based ANNS system that makes graph search explicitly I/O-aware by co-optimizing CPU computation and I/O access. LAANN combines three techniques: look-ahead search, which adapts the search strategy across query stages to balance I/O reduction and timely I/O issuance; a priority I/O-CPU pipeline, which uses I/O waiting time to process candidates cached in memory according to their expected impact on upcoming I/O decisions; and a fast lightweight in-memory graph index, which provides high-quality initial candidates to accelerate convergence and reduce disk accesses. Experiments on million- and billion-scale datasets demonstrate that LAANN substantially outperforms state-of-the-art disk-based ANNS systems. At Recall@10 = 0.9, LAANN achieves 1.41x-4.66x higher throughput, 29%-79% lower latency, and 1.59x-6.34x fewer I/O operations.

AI chat tools are shifting problem-solving and brainstorming conversations away from colleagues and into private AI interactions, reducing the shared awareness that supports team coordination. We introduce InquiryBits, a system that shares minimal summaries of AI conversations within configurable trust boundaries, separating AI-only analysis from human-visible sharing. In a study with 80 professionals, we find that people are broadly willing to share these traces to support collaboration and avoid duplicating work - but only within bounded groups. Comfort drops sharply as audience expands beyond close teams; the level of detail shared matters less than who can see it, with a preference for more detail over less within trusted groups. These findings suggest that trust boundaries, more than information granularity, may be the most impactful design parameter.

Advanced Air Mobility (AAM) uses electric vertical take-off and landing (eVTOL) vehicles to address urban congestion and emissions. However, corridor design, operation management, and separation standards remain underexamined for safe high-density operations. This paper applies the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) guidelines to systematically review relevant literature from IEEE Xplore and Web of Science, focusing on publications from 2010 to 2024. A Context, Intervention, Mechanism, and Outcome (CIMO) framework guided the development of research questions. After screening 2,039 journal and conference papers, 62 articles met the inclusion criteria. The findings reveal a lack of integrated corridor design approaches, limited operational strategies, and reliance on standards originally designed for conventional aviation. A unified corridor design and separation definition frameworks and taxonomies are proposed to address these shortcomings, informing future investigations and operational frameworks for safe, efficient eVTOL operation deployment in urban settings.

The k-Nearest Neighbors (kNN) algorithm has long been widely used in Machine Learning (ML) applications. However, the main concern when using it is the computational cost required for neighborhood search, which can make it unfeasible for large-scale applications. Optimization algorithms, such as the K-d tree, become an option in such scenarios. Under data streams, it can be challenging to maintain the properties of the K-d tree, as it requires inserting and deleting nodes on the fly. These operations can make maintaining the tree's balance and invariants difficult. Additionally, traditional K-d trees were initially designed for Minkowski-based distance functions. In this work, we describe an Online K-d tree and its adaptation to the Canberra distance that supports dynamic updates over data streams while preserving the structural invariants required for efficient traversal. Experimental analysis demonstrates that the Online K-d tree algorithm achieves faster processing time under data streams, and that adapting to the Canberra distance enabled effective subtree pruning, as evidenced by a minor loss in average accuracy and a substantial gain in instances processed per second. Our implementation can be found in our GitHub repository

The rapid proliferation of multi-cloud and SaaS platforms has transformed Identity Security Posture Management (ISPM) into a fundamentally cross-vendor challenge: critical misconfigurations and privilege escalation paths increasingly span multiple identity providers, infrastructure layers, and authentication systems never designed to interoperate. Existing evaluations focus on isolated single-platform environments and provide no means to assess whether an AI agent can reason across these fragmented boundaries. To address this gap, we introduce the Cross-Vendor Sola ISPM Benchmark, a production-grade benchmark of 50 data-grounded tasks requiring multi-hop entity resolution and cross-system correlation across eight integrated enterprise platforms including AWS, Okta, Azure AD, and Google Workspace. We also contribute an evaluation framework measuring not only final answer correctness but also evidentiary grounding, structural join fidelity, retrieval quality, and SQL equivalence. We evaluate the Sola AI Agent across five context configurations - from no injected metadata to full schema, graph, and retrieval context - using three frontier LLMs. Results show that structured relational context improves answer correctness by approximately 34% relatively and reduces exploration queries by approximately 70% across all tested models, with the largest gains driven by cross-vendor graph topology. Our findings indicate that frontier LLMs possess substantial latent security reasoning capability, but reliable cross-vendor identity analysis is fundamentally constrained by the availability of explicit relational context for entity resolution and evidentiary grounding. Under full context, the best configuration achieves 78% answer correctness while reducing complete failure to 4%.

Coding agents gate consequential actions behind a human-in-the-loop approval dialog, but the dialog is narrated by the agent itself: the human approves a summary the agent writes. The Lies-in-the-Loop (LITL) attack shows that summary is forgeable, so a compromised agent can show a benign description while a different action runs. This paper names the missing property, Consent Integrity, by importing What You See Is What You Sign (WYSIWYS) and the trusted-path property into the agent approval channel: the action shown to the human must be rendered by a trusted mediator from the real action at the boundary, not the agent's narration, over a path the agent cannot spoof, and bound to the exact action that executes. Two twists distinguish it from classical WYSIWYS: the renderer is the adversary, and the boundary ground truth is a low-level event that must be decoded without trusting the agent. Since no decoder is complete, the realizable target is analyzer-relative: whatever the analyzer cannot classify is surfaced as uninspectable rather than silently approved. A prototype implements the analyzer, renderer, and bind-to-execution; total mediation and the trusted path are specified but assumed, not implemented. On GTFOBins, an independent corpus of 1330 trusted-tool abuses, the prototype silently passes 10.0% (every instance through a trusted tool); on tldr, 28,798 normal-usage commands, it marks 87.0% uninspectable. These two independent measurements bracket the design's central tension: the trust list that bounds silent passes is the same one that drives over-prompting, and a boundary-only mediator can move along that frontier but not escape it. The contribution is the property, the mechanism, and an honest position on that frontier, not a solved defense.

Enforcing invariants in safety-critical systems is increasingly urgent as AI-generated code becomes widespread. Unfortunately, the runtimes required to support high-level specification languages are too large for most embedded targets. In this article, we show how formally verified firmware is achievable today. We built Encore!, a bare-metal Continuation Passing Style (CPS) virtual machine (VM) that runs Rocq-extracted Scheme on microcontrollers. We also show how to structure firmware as a pure state-transition function, making its core fully provable in Rocq while keeping the unverified host layer constant regardless of firmware complexity. Large Language Model (LLM)-assisted tactic synthesis fits naturally into this workflow: formal theorem statements replace manual code review, allowing AI-generated firmware to prove itself.

We present Streami, an extensible GPU-accelerated library for the computation of field lines in fluid flows on high-performance computers. Streami acts as a thin layer used for both post-hoc or in-situ analysis and can interface with existing MPI applications. We discuss Streami's application programming interface, key design decisions that led to Streami's high performance and extensibility, as well as extensions to support different fluid flow field representations. We also present a sample application for rapid prototyping and interactive seed point placement. Streami is released under a permissive open-source software license.

World models are often evaluated by native frame cadence, but higher nominal frame rate can trade away long-horizon scene stability. This article reports an independent proof of concept implemented using Overworld's Waypoint-1.5 family and WorldEngine runtime on a Windows fallback stack with ONNX Runtime + DirectML and an FSR4 DX12 bridge. The tested coherence-first branch generates higher-context anchor frames at a 15 FPS presentation-timeline cadence and reconstructs presentation to 30 FPS using latent-delta motion guidance and synthesized depth. It is compared against a lower-context cadence-first baseline that generates about 30 FPS natively under the same seed, route, control script, target presentation duration, and local time-scaling regime. Across forest, sword, desert, and snow scenes, the coherence-first branch preserves path geometry, object identity, large silhouettes, and depth layering longer, while the baseline degrades earlier into brightness drift and geometric distortion. Lightweight temporal metrics and paired videos support the visual comparison, with LPIPS favoring the coherence-first branch across all tested scenes. Here compute-normalized means approximately matched same-GPU, same-timescale operating points, not exact FLOP parity or measured realtime throughput. A separate heavier sword-scene probe suggests local non-monotonicity: more context and denoising did not automatically improve quality. These results support coherence-first allocation as a practical proof-of-concept strategy under limited inference budget, not as a finished realtime renderer.

We propose a localized physics-informed kernel function neural network (LPIKFNN), which is an improved physics-informed neural network (PINN) based on physics-informed kernel function (PIKF). In the LPIKFNN framework, the localized collocation scheme discretizes the physical quantities within the local domain, where the physical field is represented as a linear combination of PIKFs. Based on this representation, the multilayer perceptron is trained to iteratively learn the physical quantities. To overcome the computational challenges of conventional PINN in higher-order derivative and high wavenumber problems, the LPIKFNN constructs the loss function using the PIKF and a localized collocation scheme rather than relying on automatic differentiation. As a result, the costly derivative evaluations required to enforce governing equations during iterative training are eliminated, leading to significantly improved computational efficiency and training performance. Moreover, incorporating PIKFs into the loss function enables the proposed LPIKFNN to significantly improve computational accuracy in high-wavenumber problems characterized by highly oscillatory physical fields. To overcome the computational bottleneck of the physics-informed kernel function neural network (PIKFNN) in heterogeneous problems, the LPIKFNN introduces a localized collocation scheme that removes reliance on global PIKFs, enabling accurate predictions where global PIKFs are unavailable. The feasibility and accuracy of the proposed LPIKFNN are demonstrated through a series of benchmark studies, including high wavenumber problems, higher-order derivative problems, nonlinear problems, heterogeneous problems, and potential-based inverse electromyography. The numerical predictions obtained by LPIKFNN show excellent agreement with available analytical solutions and experimental measurements.

We present a complete workflow for predicting stone degradation phenomena, such as marble sulfation, in works of art. The main challenge is to accurately acquire the geometry of the artwork and then use it to perform simulations based on a mathematical model of the degradation process, typically formulated as a system of partial differential equations (PDEs). To address this, we generate a point cloud of the object surface using photogrammetric techniques and subsequently post-process it to obtain a level-set description of the three-dimensional geometry. This representation is then incorporated into the numerical discretization of the PDE system. Combined with suitable time-stepping and preconditioning strategies, the resulting framework enables the prediction of degradation evolution, such as the growth of gypsum crust thickness on marble, under different scenarios.

In 1983, Kusner conjectured that the largest equilateral set in $\mathbb{R}^{n}$ with metric $\ell_{p}$ has cardinality $n+1$ when $1<p<\infty$ and $2n$ when $p=1.$ This conjecture was proved only in the isolated cases $p=2$ and $p=4$, and was disproved when $1<p<2$. The best general upper bound $O_p(n^{\frac{2p+2}{2p-1}})$ is due to the celebrated work of Alon and Pudlák~[GAFA, 2003]. Our main contributions include: (1) We prove Kusner's conjecture for every dimension $n\ge 1$ when $2\le p\le 4$. More generally, for every integer $k\ge 0$ and every $p\in[4k+2,4k+4]$, every equilateral set in \(\mathbb{R}^{n}\) with metric $\ell_p$ has cardinality at most $(2k+1)n+1$. On the complementary intervals $p\in(4k,4k+2)$ with $p\geq 1$, we obtain the almost linear bound $O_p(n\log n)$. (2) We also consider the analogous problem on the torus $\mathbb{T}^n$, recently initiated by Alon, where the cyclic distance makes the problem substantially more delicate than in $\mathbb R^n$. We prove the almost linear bound $O_p(n\log n)$ for $1\le p\le 2$ and $O_p(n^{\frac{3}{2}-\frac{1}{p}})$ for every fixed real $p>2$, improving Alon's bounds $O_p(n^{2+\frac{2}{\lfloor p\rfloor}})$ for all finite $p\ge 1$.

We construct an explicit two-parameter family of complete, non-compact, three-dimensional, smooth steady gradient generalized Ricci solitons with $\mathrm{SO}(2)\times\mathbb{R}$ symmetry, providing a cylindrical counterpart to the spherically symmetric solitons recently found by Podestà and Raffero. The family is parametrized by a flux constant $k>0$ and a conserved quantity $\mathcal{C}\ge 0$. For $\mathcal{C}=0$, the asymptotic geometry exhibits power-law decay; for $\mathcal{C}>0$, the metric converges exponentially fast to a flat cylinder of finite radius.

In this paper we confirm several conjectures on determinants and permanents. For example, we prove that for any prime $p\equiv3\pmod 4$ the number $2\det[a_{jk}]_{0\le j,k\le (p-1)/2}$ is congruent to a square modulo $p$, where $a_{jk}=(\frac{j+k}{p})+(\frac{j^2+k^2}{p})$ with $(\frac{\cdot}{p})$ the Legendre symbol. We also prove that ${\rm per}[j^{k-1}]_{1\leq j,k\leq n-1}\equiv0\pmod n$ for any integer $n>1$ with $n\not\equiv2\pmod 4$.

These lecture notes provide an introduction to first-order optimization methods with a particular emphasis on stochastic gradient methods. We begin with deterministic gradient based methods for unconstrained optimization and study their convergence under standard assumptions such as smoothness, convexity, strong convexity, and the Polyak-Lojasiewicz condition. We then turn to stochastic approximation and stochastic gradient descent, motivated by empirical and expected risk minimization in machine learning. The main focus is on convergence theory: we discuss almost sure convergence and convergence in expectation, derive classical convergence rates, and present selected advanced topics, including almost sure convergence rates and variance reduction methods.

The study on shift spaces in ergodic theory has been beyond the classical setting, but there is a room to discuss an extension of the Kolmogorov-Sinai entropy in the ergodic theoretical point of view. On the other hand, the rate distortion dimension recently attracted attention in mean dimension theory because it behaves like the Kolmogorov-Sinai entropy on dynamical systems in the ``large" spaces in which the usual entropies is in general infinite. According to these background, we investigate the connection between the Gibbs measure on the product spaces and the variational principle based on the rate distortion dimension: we concretely calculate the rate distortion dimension of the Gibbs measure on the concrete setting and it satisfies the simplest case of thermodynamical formalism based on the rate distortion dimension: the extension of the maximal measure of topological entropy. Remark that the result shows a new phenomenon which does not hold in the classical setting. We also discuss another variational principle under more concrete settings.