Radio Frequency Fingerprinting (RFF) has evolved from an early idea for radar emitter identification into a broad research field for wireless device identification and spectrum monitoring for security. Rather than presenting a conventional literature survey, this work provides a critical historical analysis of RFF organized around the field's major conceptual paradigm shifts from 1993 to 2026. We discuss the evolution of RFF across its fundamental methodological phases, beginning with early transient-based approaches, in which transmitter turn-on behavior, unintentional modulation, and hardware nonlinearities were treated as the primary fingerprint sources. We then examine the transition to digital communications, during which attention shifted to steady-state impairments and to engineered features extracted from signals. Next, we discuss the Machine Learning period, which standardized the RFF workflow around feature extraction, dimensionality reduction, and supervised classification, followed by the Deep Learning period, in which representation learning from raw IQ samples significantly improved performance and expanded the application space. Beyond a chronological list of methods and best practices, this paper critically examines the changing assumptions and persistent limitations that have driven these transitions. We highlight the central challenges that continue to shape the field, including channel dependence, receiver sensitivity, limited dataset realism, poor cross-domain generalization, open-set recognition, and adversarial robustness. By organizing more than three decades of work into a coherent narrative, this paper clarifies the evolution of RFF, identifies persistent limitations, and outlines the key research directions required to move the field toward dependable real-world adoption.

The high efficiency of domain-specific hardware has sparked substantial interest in adopting accelerators in data analytics systems. Among many choices, GPUs and FPGAs thrived as two popular solutions due to their prevalent deployments in cloud data centers. This paper investigates hardware acceleration solutions for aggregation, a critical data analytics operation. Specifically, we implement aggregation with a unified hardware acceleration framework, which trades efficiency for ease of programming and portability, and then further develop hardware-specific optimizations. We evaluate these solutions on three recent computing hardware platforms: a CPU, a GPU, and an FPGA, with metrics that cover both the performance and energy consumption of on-device and end-to-end processing.

Cyber-physical systems (CPSs) are increasingly employed in applications with various levels of mission criticality, making the reliability of digital system components essential for maintaining service quality. On the other hand, advancements in technology nodes have heightened reliability concerns in these systems. This paper presents a method for characterizing and enhancing the fault tolerance of combinational standard cells using 3D-TCAD simulations. Through detailed simulations, we identify fault-sensitive regions in widely used standard cells under diverse scenarios that include variations in fault energy, particle angle, and the adjacency effect of identical and non-identical neighboring cells. Following this high-precision characterization, a hardened version of a universal logic NAND cell is proposed that mitigates its vulnerabilities. Simulation results demonstrate substantial improvements in resilience to particle-induced faults.

Modular multiplication is a fundamental arithmetic primitive in Residue Number Systems (RNS) and is often the dominant source of delay, area, and energy consumption in RNS datapaths used in cryptography, signal processing, and machine-learning accelerators. Recent work introduced a twit-based residue representation for moduli of the form $2^n \pm δ$, with $0 \le δ\le 2^{n-1}-1$, and showed that it enables efficient generic modular addition and subtraction across the full admissible $δ$ range. However, an efficient modular multiplier compatible with the same representation has remained unavailable. This paper presents a generic twit-based modulo-$(2^n \pm δ)$ multiplier for RNS channels. The proposed architecture computes the product through operand splitting, modular partial-product generation, carry-save accumulation, overflow folding, and a twit-compatible final modular addition. By deferring carry propagation to the final stage, the resulting organization avoids the long critical paths characteristic of conventional multiply-then-reduce designs. To demonstrate the effectiveness of the proposed approach, we study a modulus set with 5-bit residue channels and show that, owing to the broad admissible range of $δ$, it can provide a sufficiently wide dynamic range. Moreover, additional 8-bit and 11-bit configurations are used to evaluate the proposed approach at larger channel widths. We implement and synthesize the proposed multiplier in a FreePDK 45\,nm flow, and the results show average reductions of 20.5\% in delay, 13.2\% in area, and 28.0\% in power relative to baseline designs. A system-level study further indicates that these circuit-level improvements translate into lower end-to-end latency over a broad range of modular multiplication and addition workloads.

Data prefetching is a critical technique for bridging the processor-memory performance gap by predicting future memory accesses and retrieving data into on-chip caches before demand. While traditional prefetchers based on next-line, stride, and correlation heuristics perform well for regular access patterns, they are fundamentally inadequate for the irregular, data-dependent patterns prevalent in modern workloads such as graph analytics, sparse matrix computations, and pointer-intensive applications. This survey presents a systematic review of papers using a PRISMA-guided selection methodology. We propose a structured taxonomy that organizes prefetching techniques across three dimensions: locality type, including spatial and temporal locality; implementation layer, including hardware, software, and hybrid approaches; and, for the increasingly important class of ML-based prefetchers, learning paradigm, including supervised, reinforcement, and unsupervised learning, paired with training mode, including online and offline training. Through a multi-dimensional comparative analysis of ML-based prefetchers evaluated across storage overhead, accuracy, inference latency, hardware feasibility, and generalization ability, we identify three key findings: an accuracy-overhead Pareto frontier defined by model class, a natural architectural mapping between model complexity and cache hierarchy level, and a fundamental tension between runtime adaptability and model capacity that motivates hierarchical ensemble architectures.

RowHammer vulnerability continues to intensify with DRAM scaling, reducing the activation threshold needed to induce bitflips and rendering existing defenses such as TRR, ECC, and refresh-based mechanisms vulnerable to sophisticated multi-bank hammering patterns. This work presents ARTA, a lightweight reinforcement-learning-based throttling mechanism that detects and suppresses RowHammer activity by monitoring fine-grained memory access behavior within the DRAM refresh window (t_REFW) and dynamically adjusting core throughput using a Q-learning frequency scaling governor. ARTA requires no DRAM-side hardware modification or offline training, using small SRAM structures in the memory controller -- a per-core, per-bank FIFO queue (CBF) and a compact Q-table -- for immediate deployment. Our evaluation shows that ARTA eliminates all bitflips at N_BO values down to 64, reduces bitflips up to 22K times at N_BO of 20, and improves performance up to 73.6% over state-of-the-art mitigation mechanisms by limiting preventive action overheads for improved memory bandwidth throughput. These results demonstrate that adaptive RL-based throttling provides robust, scalable, and high-performance RowHammer mitigation for emerging DRAM systems.

This volume contains the proceedings of GASCom 2026, held on June 8-12 2026, in Malosco (Italy). This series of conferences brings together researchers in combinatorics, algorithms, probabilities, and more generally mathematical computer science, around the theme of random and exhaustive generation of combinatorial structures, mostly considered from a theoretical point of view. In connection with this main theme, contributions in enumerative or analytic combinatorics, and interactions with other areas of mathematics, computer science, physics or biology are wellcome. The topics cover both the methods for random or exhaustive generation, and original results on combinatorial or algorithmic problems, whose solution has been made possible by an approach involving random or exhaustive generation. A (non exhaustive) list of topics of the conference is: random and exhaustive generation of combinatorial objects; tilings and polyominoes; bijective, enumerative, algebraic and analytic combinatorics; algorithmic aspects: analysis of algorithms, probabilistic algorithms; interactions: bio-informatics, combinatorics on words, number theory.

We present a QPU-first ML runtime stack for Raspberry Pi 5's VideoCore VII QPU, built on top of the py-videocore7 assembly library. The system comprises reusable tiled matrix-multiplication substrate, GEMM-backed convolution, a single-head attention-style core, persistent executors, and integer execution based on smul24 instructions. For dense integer kernels, packed INT16-input with INT32 accumulation achieves nearly two orders of magnitude higher throughput over NumPy. Across operations (min/max, pooling, convolution, attention), we report improved performance over both PyTorch and NumPy. Our preliminary results indicate that Raspberry QPUs can serve as a practical execution substrate towards accelerating AI model execution at the edge.

We present Safecloud, a distributed, encrypted, self-pricing storage and streaming network whose storage and routing nodes never see plaintext and never hold keys. Each file is split into chunks, encrypted on the owner's device, and distributed across Drops (browser tabs storing ciphertext in IndexedDB) and Jets (federated routing servers). Only the owner, or an authorised grantee, can decrypt. We make five contributions: (1) A one-root key hierarchy: every key derives deterministically from a single root via HKDF, and owner and range-scoped grantee derive identical chunk keys (derivation agreement); a subtree key derives its range and nothing else (delegation containment). (2) Convergent content addressing: identical content yields identical ciphertext and identifiers, enabling deduplication without plaintext exposure, with identifiers binding authenticated ciphertext so a keyless Drop verifies integrity (blind verifiability). (3) Three parallel trees over one navigation path (Merkle for integrity, key-derivation for confidentiality, access for authorisation), with sound Merkle-verified retrieval. (4) The key tree doubles as a streaming index: a player derives each segment key in O(1), seeking by derivation, while parallel tracks (video, audio, captions) are independent subtrees unlockable per-track and per-segment, a combination we believe no prior encrypted-storage network offers. (5) Jets and Drops earn Safebux verifiably, kept honest by a one-signature proof-of-storage challenge under chilling-effect Proof-of-Corruption, a zero-sum economy that is significantly cheaper than Filecoin's proof-of-replication sealing (which is slow and provides no confidentiality). We give the architecture, cryptographic construction, a threat model, and an open-source reference implementation, stating precisely what is implemented versus designed.

Authoring and refining presentation slides is a highly time-consuming core task in academic and business domains. While generative AI tools have lowered the barrier for creating initial drafts, their "black-box, one-way generation" paradigm severely deprives users of fine-grained control. Through a formative study (N=10), we identified "trial-and-error anxiety" and "inconsistent cross-page formatting" as primary bottlenecks in human-AI co-creation. Consequently, we present ECHO, an interactive system based on multimodal intent grounding and explainable operation plans. ECHO enables precise local edits via a "natural language + visual selection" paradigm, utilizing a decoupled "Plan-Confirm-Execute" loop and dynamic memory mechanisms to transform implicit AI intents into highly controllable layout co-creation. To systematically evaluate document refinement, we propose the CoEdit-Eval framework. Objective evaluations across multiple foundation models (e.g., GPT-5, GLM-4.7) demonstrate that while baselines uniformly fail in intent mapping (0% accuracy) and spatial grounding (0% Hit@1), the ECHO architecture boosts Target Hit@1 to 55%--85% depending on the base model. Furthermore, integrating Vision-Language Models (VLMs) effectively resolves spatial ambiguities -- achieving significant win rates in LLM blind evaluations -- and our Undo mechanism guarantees 100% physical file consistency (MD5 hash). Finally, a controlled study with 14 participants shows that ECHO significantly reduces cognitive workload (NASA-TLX scores dropped by 20.8%, from 82.6 to 65.4) and reveals the dynamic evolution of human control allocation across different cognitive tasks.

While feminist and critical data theories have long critiqued the use of data to uphold a positivist-informed view about science, few examples offer alternative methods to display scientific constructs. In response, we present Data and Me: an exhibit informed by feminist and critical data theories, which we designed and launched at a local science museum. Data and Me introduces museum visitors to data using a [AT]:hugging_face: vibe -- a vibe that signals that data can be [hashtag]slow, [hashtag]handmade, and [hashtag]personal. We designed this vibe to be noticeably different than the [AT]Science vibe in the rest of the museum. Throughout our design process, we adapted visualization vibes as an analytic and generative tool in the context of a science museum. We present four design choices that enable the design of a vibe: visual, topical, material, and crediting. We discuss how our exhibit aligns with ongoing discussions about alternative research outcomes and calls for plurality in HCI.

Generative AI tutors hold significant promise for higher education, yet designing systems that scaffold learning without undermining academic integrity remains an open design challenge. This paper presents PeteChat, a course-aligned AI tutor developed and deployed at Purdue University, documented through the lens of design-based research (DBR). Drawing on literature-informed design inputs, a pre-deployment baseline analysis of authentic student-system interactions, and formative expert evaluation with teaching assistants and UX/developer stakeholders, we report eight transferable design principles for assessment-aware AI tutors: from homework guardrails and debugging scaffolds to self-regulated learning support and instructor-facing customization tools. The system is built on a locally hosted Llama-3 model enhanced with retrieval-augmented generation (RAG) grounded in course-specific materials. Rather than reporting controlled experimental outcomes, this design case foregrounds the situated design reasoning, iterative refinement, and principled decision-making that shaped PeteChat across multiple development phases. The resulting principles and methodological approach offer actionable guidance for institutions seeking to deploy responsible, integrity-preserving AI tutors at scale.

Underground room-and-pillar coal mining requires shuttle car operators to make safety-critical routing decisions under conditions of low visibility, dynamic miner movement, congestion, and limited real-time information. This paper presents a human-centered AI decision-support system that recommends safe shuttle car routes using a Graph Neural Network (GNN) trained on expert-informed synthetic data and deployed through a browser-based interface backed by cloud inference services. Rather than making a purely model-centric contribution, the paper shows how interviews, participatory design, usability testing, interaction logs, and interpretability analysis shaped both the interface and the AI model. The resulting application evolved beyond route recommendation to include inline user feedback, blockage reporting, audio cues, and SHAP-based interpretability within a single interactive system. Evaluation across two usability sessions with six participants showed improved task completion, faster response times, fewer errors, higher usability scores, lower cognitive load, and stronger agreement with AI recommendations in the later version. The paper contributes a focused example of how human-centered design can transform an AI routing prototype into a more transparent, auditable, and safety-supportive decision-support system.

Sensemaking is central to knowledge work, where people search, evaluate, interpret, and use information over time to construct durable understanding. The rise of generative AI has begun to reshape this process: GenAI systems now perform interpretive functions such as summarization, synthesis, and thematic grouping that knowledge workers have traditionally carried out themselves. In collaborative settings, these shifts compound, complicating how teams divide interpretive labor, trust one another's contributions, and negotiate shared understanding. In this position paper, we examine how GenAI reshapes sensemaking in collaborative knowledge work and propose five design principles for multi-human, multi-agent collaborative sensemaking: dynamic multi-layer information representations, active identification and bridging of gaps in understanding, critical engagement with information, verifiability, and accountability. Building on these principles, we introduce a conceptual framework for a dynamic shared representational workspace in which knowledge workers and specialized AI agents jointly gather evidence, schematize, hypothesize, and pursue collaborative goals. Through a partner agent, a shared space agent, and an orchestrator agent, the framework preserves the provenance and authorship of contributions and traces the evolution of both individual and shared interpretations, supporting coherent, negotiated knowledge construction that current generative AI systems tend to obscure.

During severe weather events, people must interpret rapidly evolving information to make time-sensitive safety decisions. Broadcast meteorologists have traditionally served as credentialed intermediaries within established media organizations, while independent "weatherfluencers" on YouTube have emerged as prominent real-time interpreters for large and growing audiences. This mixed-methods study provides one of the first empirical comparisons of how viewers evaluate broadcast meteorologists against YouTube weatherfluencers across credibility, legitimacy, objectivity, and practical utility. Broadcast meteorologists were consistently rated higher on credibility, legitimacy, and safety utility, while weatherfluencers achieved parity on objectivity. Yet weatherfluencer audiences continue to grow, revealing a critical decoupling between audience attention and official or professional authorization that existing crisis communication models do not fully account for. Qualitative findings illuminate the mechanisms underlying these judgments and their implications for emergency communication in hybrid information ecosystems.

Visualization researchers utilize workshops both for applied research and to engage different populations with visualization-based activities. While there are many benefits to running visualization workshops, their utility and impact rely on the presence of a researcher who has deep knowledge about visualization theory and practice. In this work, we introduce workshop-in-a-box as a design concept intended to challenge the researcher-centric approach to data physicalization workshops. Through a design study with a socially innovative organization, we deployed several data physicalization workshops that our collaborator ran instead of us. Based on this experience, along with two accompanying case studies that validate the concept, we present material and procedural considerations for how to put data physicalization workshops into a box and the implications it has for extending visualization research outside the bounds of academia.

Digital twin technology creates bidirectional synchronization between physical and virtual environments, yet current implementations fail to provide authentic environmental experiences that enhance user presence in shared virtual spaces. While digital twin environments using commercial metaverse platforms for IoT sensor data visualization have been proposed, translating environmental information into meaningful sensory experiences remains largely unexplored, particularly lacking approaches for weather conditions that significantly influence spatial perception. We developed a weather synchronization system that integrates real-time environmental data from ``The GEAR'' smart building with the Cluster metaverse platform, enabling shared VR experiences with authentic atmospheric immersion. Our system processes temperature, humidity, precipitation, wind speed, and solar radiation measurements to generate corresponding virtual environmental effects including dynamic sky rendering, precipitation particles, and ambient audio modulation. Performance evaluation demonstrated practical response times of 0.8-1.0 seconds for weather data transmission and reflection in the virtual environment. This work establishes a foundation for seamless physical-digital space integration, potentially enhancing remote collaboration efficiency and facilitating more dynamic discussions in shared virtual workspaces.

The symmetric determinantal complexity sdc(f) of a polynomial f is the least m such that f = det(M) for an m x m symmetric matrix M of affine-linear forms. We prove, over the complex numbers, that sdc(sum_{i=1}^n x_i^n) >= (1/(2e) - o(1)) n^2. This is a symmetric companion to the author's non-symmetric polar-degree preprint (arXiv:7680505); the method parallels that work, but the proof here is self-contained and redoes the load-bearing local incidence analysis in the symmetric setting. The general theorem: if X = V(f) in P^{N-1} is a smooth degree-d hypersurface, N >= 3, and f = det(A_0 + sum x_i A_i) with all A_i symmetric of size m, then the top polar degree d(d-1)^{N-2} is at most 2^{N-2} C(m, N-1). The proof uses the symmetric rank-one kernel incidence M(z,x) u = 0. At a genuine polar point M has rank m-1, and a symmetric Schur-complement normal form eliminates the unique kernel line scheme-theoretically; on the resulting local graph the lifted conormal forms u^T A_i u are a common unit multiple of the partials d_i f, so the lifted polar equations cut the ordinary polar slice up to units and each genuine lifted polar point is a zero-dimensional isolated solution. Multihomogeneous Bezout on P^N x P^{m-1} then yields the bound 2^{N-2} C(m, N-1). For F_n = sum x_i^n this gives the constant 1/(2e). More generally, for F_{N,d} = sum_{i=1}^N x_i^d the same theorem gives sdc(F_{N,d}) >= (1/(2e) - o_N(1)) N(d-1) as N -> infinity. We give an explicit symmetric representation of F_{N,d} of size 2N(d+1)+1, so the diagonal bounds are non-vacuous and tight up to a constant. The result is for exact symmetric determinantal complexity in characteristic zero; it is not a border statement and not a uniform positive-characteristic theorem.

The bandwidth of a timed language characterizes the quantity of information per time unit (with a finite observation precision $\varepsilon$). The asymptotic behavior of the bandwidth as $\varepsilon \to 0$ classifies timed regular languages in three classes: meager, normal, and obese. Normal timed automata have a bounded frequency of events and some non-punctual transitions, and, up to now, were the only class of timed automata for which no algorithm was available for computing their bandwidth. In this article, we compute the bandwidth of any such automaton in the form $\approxα\log{1/\varepsilon}$. Our approach reduces this problem to computing the best reward-to-cost ratio in a weighted finite graph constructed from the given timed automaton.

Max-policy iteration is an approach to computing precise numeric program invariants by successive attempts at resolving maximum operators and reduction to mathematical optimization. Mathematical optimization, though, may be expensive. Here, we show, for max-policy iteration on systems of equations over integers as well as over floating point numbers, that mathematical optimization can be replaced by plain value iteration -- which is still guaranteed to terminate. As an application, a precise bound analysis for integer or floating point variables is obtained, avoiding widening operators altogether. We also consider max-policy iteration over the rational numbers, where the right-hand sides are maxima of minima of affine combinations of unknowns. We propose min-policy iteration as an alternative to linear programming for solving the optimization problems posed by max-policy iteration. We prove that max-min policy iteration is guaranteed to return the least solution for bounded systems. We also show how to extend this algorithm to unbounded systems, and how to construct certificates of soundness as well as of optimality of the computed results.

Tamed stochastic-gradient Langevin dynamics (SGLD) stabilizes large drifts by adding a denominator to the update. If this denominator uses the same stochastic-gradient sample as the update step, it can also change the conditional mean drift. We study deterministic denominators: the state-dependent envelope is fixed before the current oracle sample is drawn. The main question is how to design this envelope in practice. The design starts from an oracle score, builds a low-cost proxy score on pilot states, chooses activation thresholds by empirical quantiles, and then applies a small calibration layer. The analysis tracks three steps: proxy and threshold errors become envelope errors; envelope errors perturb one SGLD step; and the local residuals give stationary errors through a conditional perturbation bridge. Experiments show that the proxy-quantile denominators are close to oracle-score behavior, avoid the random-denominator mean-shift channel, and improve simple deterministic taming choices.

This paper addresses the backstepping boundary stabilization of coupled multidimensional first-order hyperbolic systems. We consider systems whose transport velocity fields are collinear, meaning that each velocity field is a scalar multiple of a common base velocity field. Building upon a recent framework developed for scalar multidimensional first-order hyperbolic equations, we introduce a change of variables, based on characteristic curves defined entirely in the spatial domain, that converts the original multidimensional system into a continuum of coupled one-dimensional first-order hyperbolic systems. By designing a backstepping controller for each system in the continuum representation, and assuming that the transit times of the characteristic curves are uniformly bounded, we achieve finite-time stabilization of the multidimensional system.

In the implicit version of a propositional proof system Q, we work with Q-proofs that are not written down directly, but are succinctly encoded by circuits. Thus implicit Q-proofs are potentially exponentially shorter than usual Q-proofs. We study narrow implicit proofs, a restricted version of this notion, in which lines in the encoded proof can only have polynomial size. We use a cut-elimination construction to show that G_{i+1} is equivalent to narrow implicit G_i, for i >= 1, where G_i is the extension of Frege allowing reasoning with Sigma^q_i quantified propositional formulas. We show that G_1 is equivalent to implicit resolution.

``Block what you can and randomize what you cannot'' is the core principle for treatment effect estimation in randomized controlled trials. Although a wealth of allocation strategies has been developed, an explicit trade-off between the covariate balance achieved by blocking and the robustness guaranteed by randomization is seldom quantified. Motivated by the second law of thermodynamics, this work posits a new criterion that lowers the covariate imbalance while maximizing the entropy that quantifies contrast and allocation diversity. The resulting optimal strategy, termed the minimum free energy randomized design, is then derived, thereby formally achieving such a trade-off. To facilitate practical implementation, we further develop a computationally efficient dynamic allocation algorithm with theoretical guarantees. Using a finite-sample variance decomposition, the proposed randomization strategy is shown to control covariate imbalance while preventing unobserved heterogeneity from dominating the mean squared error, thus retaining minimax efficiency under the prescribed design constraints. Extensive numerical simulations demonstrate that our method achieves superior statistical efficiency and greater robustness than existing approaches.

In this paper, we consider the data-driven discovery of Lyapunov functions for autonomous dynamical systems. We represent the Lyapunov function as an expression tree of fixed depth and formulate the Lyapunov discovery task as a constrained self-supervised symbolic regression problem. The constraints model the output of the Lyapunov function for a given input as well as the Lyapunov stability conditions. This modeling approach makes no a priori assumptions about the functional form of the Lyapunov function, is inherently interpretable since the function is obtained in a symbolic form, and, in principle, can be applied to any continuous dynamical system. We also develop a tailored branch-and-bound-and-check solution approach to efficiently solve the resulting learning task. Applications to several case studies show the ability of the proposed approach to discover Lyapunov functions.

We present a new proof that an integer rectifiable current with finite mass, and whose boundary has also finite mass, is integral. We deduce the result from De Giorgi's structure theorem for integer-valued $BV$ functions and a cylindrical projection argument. As a consequence, we also give a new proof of the compactness of integral currents that is ultimately based on the $BV$ theory.

We initiate the study of nonparametric empirical Bayes denoising methods in the setting where both the latent variables and their measurements lie on a compact Riemannian manifold, and where the likelihood is a Riemannian Gaussian distribution. Our starting point is a novel Tweedie-Eddington formula for Riemannian Gaussian mixture models which identifies a certain surrogate oracle denoiser in terms of the marginal distribution of the measurements; it avoids the explicit computation of the posterior Fréchet mean (as required by the Bayes denoiser) via a first-order approximation, hence we refer to it as the "tangential" Bayes denoiser. We show that this surrogate oracle achieves nearly the Bayes risk in a low-noise regime, we construct a fully data-driven approximation of it using the spectral theory of the Laplace-Beltrami operator, and we establish finite-sample rates of convergence for the distance between the the surrogate oracle and its approximation. Contrasting the nearly-parametric rates from the Euclidean setting, the rates in the Riemannian setting are slower due to the singularities of the Riemannian Gaussian density at the cut locus of its Fréchet mean; in the special case of the circle we establish matching lower bounds which show that our proposed denoiser is minimax-optimal, and that the denoising problem exhibits a genuinely nonparametric rate of convergence. Lastly, we implement our methodology in two scientific applications: in astronomy, the sphere-valued problem of denoising the locations of gamma ray bursts; in structural biology, the torus-valued problem of denoising pairs of torsion angles of adjacent amino acids in a protein (i.e., the Ramachandran plot).

Prior work has shown that shifted contact derived Artin stacks admit smooth Darboux atlases. However, establishing enumerative invariants and linearizing these categorical structures requires equivariant local models. We establish an equivariant Darboux theorem for $-1$-shifted contact derived Artin stacks. We prove that, in the smooth topology, these stacks admit smooth atlases by the derived contact Darboux scheme $Δ\mathrm{loc}(s)$ associated to the derived discriminant locus of a relative section $s$. In the presence of reductive stabilizers $G$, this refines to the equivariant geometric quotient stack $[Δ\mathrm{loc}(s)/G]$. By applying the BBDJS minimal model to the derived symplectification and descending algebraically along the structural free $\mathbb{G}_m$-action, we construct an $\ell$-adic perverse sheaf on any oriented $-1$-shifted contact stack. We utilize Verdier's specialization equivalence for monodromic sheaves to equip this perverse sheaf with a tame geometric monodromy automorphism $T$. This structure allows for the extraction of derived enumerative invariants via the $\ell$-adic Grothendieck-Lefschetz trace, thereby resolving the issue of generic topological acyclicity. The content of the other main results in this paper relies on a prior work, in which we have shown that derived intersections of $n$-shifted Legendrians yield $(n-1)$-shifted contact stacks and formulated the non-linear 2-categories of Legendrians $\mathcal{F}_c(X)$ and $Leg_n$. Using this geometric setup, we formulate in this paper a contact analogue of Joyce's conjecture to linearize these structures. We then construct the categorified Legendrian 2-categories $\mathfrak{L}\mathcal{F}c(X)$ and $LLeg_0$ via $\ell$-adic Fourier-Mukai pull-push functors, connecting the study of derived contact moduli spaces to microlocal sheaf theory.

A central open question in extremal design theory is Nash-Williams' Conjecture from 1970 that every triangle-divisible graph on $n$ vertices (for $n$ large enough) with minimum degree at least $0.75 n$ has a triangle decomposition. In this paper, we prove this conjecture in full. In 2016, Barber, Kühn, Lo, and Osthus proved that if the fractional relaxation of Nash-Williams' Conjecture holds for minimum degree $cn$ for some constant $c\ge 0.75$, then Nash-Williams' Conjecture holds for any constant $c' > c$. The previously best-known bound on the fractional relaxation was due to Delcourt and Postle from 2021 with $c= \frac{7+\sqrt{21}}{14} \approx 0.82733$. This bound on the fractional relaxation has grown in importance over the years as it has been directly tied to bounds for a number of other problems in extremal design theory. This paper consists of three parts. In Part I, our first main result is a proof of the Fractional Nash-Williams' Conjecture: if $G$ is a graph on $n$ vertices with minimum degree at least $\frac{3n}{4}$, then $G$ has a fractional triangle decomposition. In Part II, our second main result is a Fractional Stability Theorem for Nash-Williams' Conjecture: if a graph $G$ on $n$ vertices has minimum degree close to $\frac{3n}{4}$ but no fractional $K_3$-decomposition, then $G$ is close (in edit distance) to the join of two $\frac{n}{4}$-regular graphs each on $\frac{n}{2}$ vertices. We use this to prove that if a triangle-divisible graph $G$ on $n$ vertices has minimum degree close to $\frac{3n}{4}$ but no $K_3$-decomposition, then $G$ is close (in edit distance) to the join of two $\frac{n}{4}$-regular graphs each on $\frac{n}{2}$ vertices. In Part III, our final main result is a proof of Nash-Williams' Conjecture in full.

In this paper, we prove that for every $k$ and every graph $H$ with $m$ edges and no isolated vertices, the Ramsey number $R(C_k,H)$ is at most $(k-1)m+1\le km$. This settles a problem of Erdős, Faudree, Rousseau and Schelp, which is listed as problem 34 in the graph theory collection.