This article settles Problem 7.2 posed by [Banerjee, Special Matrices (2022)] for the induced subgraph $G_2$ of the comaximal graph $Γ(\mathbb Z_n)$ when $n$ is squarefree. Let $n=p_1p_2\cdots p_m$ with distinct primes $p_1<\cdots<p_m$, and let $G_2$ be the graph on the nonzero nonunit residue classes modulo $n$. We use Chinese remainder representation of $\mathbb Z_n$, and encodes each vertex by the set of vanishing coordinates. This converts $G_2$ into a weighted blow-up of a disjointness graph on nonempty proper subsets of $\{1,\dots,m\}$. Within this model, we derive exact class sizes, explicit degree formulas, the minimum-degree layer, and a short-path criterion. The main theorem proves the connectivity of $G_{2}$ as $κ(G_2)=\prod_{i=1}^{m-1}(p_i-1)=\tfrac{ϕ(n)}{p_m-1}$. Consequently, earlier upper bound is sharp, $G_2$ is maximally connected, and its edge connectivity agrees with its minimum degree. We also obtain distance formulas, diameter and radius information, and a linear-time algorithm once the prime factorization is known.

Despite unprecedented growth in biodiversity data, a persistent gap remains between what is known and what is acted upon. Existing frameworks such as the FAIR and CLEAR Principles have improved data accessibility and interpretability but do not provide the components required to translate knowledge into context-sensitive action. We argue that closing this knowledge-action gap requires a shift toward statement-centred and action-oriented knowledge infrastructures. We identify a fundamental distinction between actionability as the structural capacity of a representation to support operations and applicability as the epistemic validity of using that knowledge in a specific context. Building on the Semantic Units Framework, we introduce Action Units as structured extensions of plan specifications that make applicability conditions and contextual grounding explicit as first-class typed components. Three types are distinguished, epistemic, transformational, and intervention action units, corresponding to three operation classes that define a minimal operational architecture for actionable knowledge. Action units can also be granularly composed across operation classes, reflecting the cross-class character of real-world knowledge-driven processes. Conditional action units, operationalized as executable IF-THEN structures, enable knowledge graphs to function as graph-native decision-support systems, constituting a transition toward post-FAIR knowledge infrastructures. Applied to biodiversity science, the framework reinterprets documented intervention and epistemic failures as consequences of incomplete action unit structures and constructs worked examples across all three operation classes. We propose the TripleA Principle: Actionability, Applicability, and Auditability, as a guiding framework for next-generation knowledge infrastructure design extending the FAIR and CLEAR Principles.

Computational notebooks are notoriously prone to reproducibility failures. By permitting out-of-order cell execution, notebooks accumulate hidden state and implicit dependencies that cause interactive executions to silently diverge from clean top-to-bottom runs. Prior approaches either employ dependency analyses or enforce reactive dataflow models that face fundamental tradeoffs among expressiveness, precision, and performance. This paper exploits the insight that reproducibility can be enforced without precise dependency tracking: a notebook is reproducible if and only if executing its cells in top-to-bottom order from an empty store produces exactly the outputs currently recorded. We formalize this notion of reproducibility and present FlowBook, which implements a dynamic analysis that enforces reproducibility by tracking read and write sets at cell boundaries. FlowBook detects stale cells whose recorded outputs may no longer reflect the current notebook state and prevents operations that would violate reproducibility. FlowBook incurs near-imperceptible latency overhead (median: 70 ms).

Optimal intervention design is formulated as a hybrid optimal control problem for multiphase homogeneous epidemiological systems. The system extends a foundational compartmental model through intermediate phases that incorporate work-from-home (WFH) policies and a vaccination protocol, yielding a four-phase hybrid system that captures policy escalation and relaxation. Key characteristics of the resulting hybrid system include (i) phase-dependent continuous dynamics and running costs that respectively capture distinct disease transmission mechanisms and shifting public health socioeconomic trade-offs, (ii) a combination of autonomous and controlled switchings for intervention policies, whose times are co-optimized - whether indirectly via state thresholds or directly as decision variables alongside continuous inputs to minimize the overall cost, and (iii) nontrivial state jump maps that govern transitions between phases with differing state and control space dimensions. The Hybrid Minimum Principle (HMP) is invoked to obtain the optimal solutions. Numerical results demonstrate that coordinating WFH policies with vaccination efforts provides improved mitigation of disease spread compared to single-phase policy interventions.

This paper studies a non-trivial gradient Kähler-Ricci soliton, of complex dimension $n$, with an isometry group of dimension at least $n^2-1$. We show that the isometry group acts by cohomogeneity one and, consequently, admits a special ansatz involving a Sasakian model. In complex dimension two, we can actually say more: namely, that every such soliton has maximal symmetry; that is, the isometry group is exactly of dimension $2^2$. In addition, we prove that, if the isometry group acts by cohomogeneity one on a non-trivial gradient Ricci soliton (not necessarily Kähler), the potential function is invariant by the action.

This work develops a unified optimal control framework for a Quadrotor Biplane tailsitter UAV capable of operating seamlessly across hover, transition, and cruise flight regimes. Although the tailsitter configuration enables mechanically simple mode switching, the transition maneuver remains challenging due to strong nonlinearities and rapidly varying aerodynamics. To address this, a trajectory optimization scheme based on nonlinear programming with direct collocation is formulated, incorporating nonlinear dynamics, actuator limits, and angle-of-attack constraints. The resulting optimal trajectories are safe, reliable, and time-efficient. For the cruise-to-hover maneuver, optimal trajectories are generated over a range of initial cruise velocities and subsequently learned using feedforward multilayer neural networks. The learned model generalizes across operating conditions and enables real-time generation of constraint-satisfying transition trajectories. These trajectories provide both feedforward control inputs and reference state profiles, which are tracked using a Model Predictive Controller (MPC). The MPC eliminates the need for controller switching or gain scheduling across flight envelopes, enabling a single universal controller for hover, transition, and cruise. A nonlinear Dynamic Inversion (DI) controller is also designed for comparison. Two numerical schemes for MPC are implemented and evaluated. Simulation results across all flight modes demonstrate that MPC achieves superior robustness to parameter uncertainties compared to DI. A computational cost analysis further highlights the trade-off between execution time and performance for the different MPC solvers.

A fascinating approach to teaching Newton's Third Law using readily available technology is presented in this article. Magnetic forces are measured by using a smartphone's pressure sensor, two ring magnets, and common household items. Students can measure the magnitudes of forces, gain a more tangible understanding of the law, and see how 'action' and 'reaction' are quantitatively equal and opposite.

This paper presents a physics-consistent digital twin framework for end-to-end modeling and evaluation of Global Navigation Satellite Systems (GNSS) user receiver equipment. In contrast to conventional GNSS simulations that rely on predefined signal models, the proposed framework enforces dynamic consistency between satellite ephemerides, user motion, and received signal observables through trajectory-driven injection of code-phase and Doppler dynamics. The GPS L1 C/A signal is synthesized in accordance with the IS-GPS-200 Rev. N specification, with motion-induced effects derived directly from orbital and user kinematics, and augmented by ionospheric and tropospheric delay models. The resulting complex baseband signal is converted to radio frequency using a software-defined radio platform disciplined by an external reference clock, enabling seamless hardware-in-the-loop integration with commercial and software receivers. Validation across static, moderate-motion, and high-dynamics scenarios, including projectile-like trajectories, demonstrates close agreement between truth-model and receiver-estimated code phase, Doppler, and position, as well as strong correspondence between simulated and measured intermediate frequency spectra. The results establish the proposed digital twin as a high-fidelity, repeatable, and physically consistent platform for GNSS receiver evaluation, tracking-loop stress testing, and development of robust navigation algorithms.

Collective strong coupling of molecular ensembles to optical cavities opens a route to modifying matter through genuinely collective electronic correlations. Yet even in the absence of a cavity, Coulomb correlations are notoriously difficult to describe, and cavity coupling adds transverse correlation channels extending over the entire molecular ensemble. Here we show that this seemingly intractable problem admits a controlled description by mapping the collective intermolecular electronic correlations to the analytically solvable spherical Sherrington-Kirkpatrick model. The resulting theory predicts two collective correlation phases, a paracorrelated phase and a spin-glass correlation phase, beyond the conventional uncorrelated molecular regime. These phases reveal an entropy-driven localization-delocalization mechanism that transfers molecular electronic states into collectively correlated cavity-dressed states. Our work establishes cavity-mediated electron correlations as a microscopic mechanism for emergent phases in strongly coupled molecular ensembles.

The scaling-law era has transformed artificial intelligence from research into a global industry, but its rapid growth raises concerns over energy usage, carbon emissions, and environmental sustainability. Unlike traditional sectors, the AI industry still lacks systematic carbon accounting methods that support large-scale estimates without reproducing the original model. This leaves open questions about how large the problem is today and how large it might be in the near future. Given that the Hugging Face (HF) platform well represents the broader open-source community, we treat it as a large-scale, publicly accessible, and audit-ready corpus for carbon accounting. We propose a FLOPs-based framework to estimate aggregate training emissions of HF open-source models. Considering their uneven disclosure quality, we introduce a tiered approach to handle incomplete metadata, supported by empirical regressions that verify the statistical significance. Compute is also converted to AI training carbon intensity (ATCI, emissions per compute), a metric to assess the sustainability efficiency of model training. Our results show that training the most popular open-source models (with over 5,000 downloads) has resulted in approximately $5.8\times10^4$ metric tons of carbon emissions. This paper provides a scalable framework for emission estimations and a practical methodology to guide future standards and sustainability strategies in the AI industry.

A Pólya-Szegö inequality for the circular rearrangement is proven, under general assumptions. In addition, sufficient conditions are given, under which all the extremals of the inequality are symmetric.

Dental caries is one of the most common chronic diseases worldwide, caused by acid production from bacterial metabolism of fermentable carbohydrates and affecting people of all ages. To evaluate the cariogenic and erosive properties of widely consumed food products, such as energy drinks, intraoral pH changes are measured during consumption. The gold standard for such measurements is miniaturized silicon-lithium-barium glass membrane electrodes. These electrodes allow dental plaque to form on their surface, thereby enabling in situ monitoring of pH changes in a biologically relevant environment. Due to their high impedance and susceptibility to external interference, they can currently only be measured using a large analog amplification and recording unit, which is highly limiting for study design and participant comfort, as individual measurements can take upwards of an hour. This work presents the first battery-powered, low power wireless and wearable pH telemetry evaluation system designed for real time intraoral pH monitoring with glass electrodes. The system comprises a miniaturized pH telemetry frontend, a neck-worn Bluetooth Low Energy (BLE) node, and software tools for data acquisition, visualization, and reporting. The front end integrates with a custom dental prosthesis, directly digitizing the pH signal in the mouth and minimizing noise. The data is transmitted over BLE to a host computer, and analyzed using dedicated software that supports calibration, drift compensation, region marking, and PDF report generation. The system integrates an 8.6 by 3.3 mm, 0.2 g pH front-end and a 37.6 g neck-worn BLE node which consume 8.89 mW to transmit data at 10 Hz to a host computer during a measurement.

Imperfections in X-ray imaging systems can limit their performance, especially in High Energy Density (HED) or Inertial Fusion Energy (IFE)-relevant experiments that are typically single shot, by introducing structured, non-stationary features that overlap with the signal of interest. When the X-ray transmission is reconstructed by typical flat-field normalization, even small shot-to-shot drift of structured features imprints residual patterns onto transmission maps, degrading signal visibility and biasing measurements such as electron density, velocity and feature sizes. We investigate this limitation by modeling the artifacts as a separable feature layer and training a U-Net architecture to estimate and infer them directly from the experimental data. We compare our method against Fourier filtering and more advanced procedures like Dynamic Flat-Field Normalization (DFFN) to evaluate artifact suppression capability and signal preservation in the reconstructed transmission maps. In multiple synthetic injection tests, our Physics-Guided Deep Learning approach is able to obtain an improvement in mean Structural Similarity Index (SSIM) from 0.345 to 0.906 and from 0.0679 to 0.945, while better preserving filament profiles and reducing degradation of the filament signal during artifact suppression. Additionally, we utilize deep ensembles to obtain predictive epistemic uncertainty estimates for the U-Net based reconstruction, to ensure Out Of Distribution (OOD) robustness for this procedure.

We introduce Veronese-Avoiding hypersurfaces, inspired by the theory of associated forms of Alper--Isaev. In the smooth case, we reinterpret their criterion via Macaulay inverse systems: the Veronese-Avoiding condition is equivalent to the non-degeneracy of the associated form. In the singular case, our main theorem shows that a reduced hypersurface with exactly $n$ isolated singular points is Veronese-Avoiding if and only if these points are ordinary nodes in general linear position; we also classify singular plane cubics and treat fewer than $n$ nodes via a natural rational map. We then study the parameter space, proving local closedness and identifying a distinguished irreducible nodal locus. Finally, we prove a Lefschetz-type consequence for the Milnor algebra in degree $1$.

Wearable body-attached multi-sensor systems enable detailed analysis of human motion and physiological signals in sports, rehabilitation, and movement research. While wireless synchronization techniques can reliably align sensor data streams, interpreting and validating complex or unconstrained activities often requires an additional, objective visual reference. Existing laboratory-grade reference systems provide high accuracy but are impractical for outdoor or field deployments. In contrast, commercial video timecode solutions typically rely on local device-to-device synchronization, which increases the power required to maintain synchronization. This is not desirable in many application scenarios. This paper presents a lightweight Timecode Generator (TCG) that converts Global Navigation Satellite System (GNSS)-derived time directly into a Linear Timecode (LTC) signal that is injected into the recording via a camera audio channel. The approach eliminates continuous handshaking, allowing the system to be activated immediately before the action of interest, thus reducing power consumption and enabling smaller batteries and unobtrusive hardware designs of body-attached sensor nodes. The TCG supports common video frame rates of 24, 25, and 30 frames per second (fps). Experimental evaluation confirms that accurate time alignment is maintained for several minutes without GNSS updates. At 30 fps, the alignment duration is 543 s before a potential frame-level shift occurs. With an average power consumption of 35.37 mW, the system achieves an operating time of up to 75 h when powered by two standard AAA alkaline batteries.

We present an uncertainty-aware description of leading-power fragmentation for all-charm pentaquark states ($S$-wave $|cccc\bar{c}\rangle$) at hadron colliders. We construct a multimodal set of collinear fragmentation functions, PQ5Q1.1, incorporating both perturbative and nonperturbative uncertainties. Perturbative effects are estimated via missing higher-order variations (F-MHOUs), while the nonperturbative wave function is modeled through controlled modifications of its transverse-momentum structure (F-NPWF), consistently combined within a replica-like framework. The initial-scale input for constituent charm fragmentation is refined to describe both compact multiquark and diquark-driven production mechanisms. We employ the (sym)JETHAD interface to study NLL/NLO$^+$ semi-inclusive pentaquark-plus-jet production at the HL-LHC and future FCC. The bottom sector is left to future dedicated studies due to its enhanced sensitivity to nonperturbative modeling. Our results provide a flexible framework for uncertainty-controlled predictions, bridging exotic-hadron structure, heavy-flavor fragmentation, and high-energy QCD.

Generalized winding numbers provide a robust measure of point insidedness for 3D surfaces - whether open, self-intersecting, or non-manifold - and are central to numerous geometry processing tasks. However, existing methods trade off between accuracy and computational efficiency, limiting their use in interactive and large-scale applications. We introduce a new formulation and algorithm for computing generalized winding numbers that is both fast and accurate to arbitrary precision, applicable to meshes and parametric surfaces. Our approach expresses the winding number as the sum of two intuitive geometric quantities: the signed number of ray-surface intersections and a boundary integral over the surface's projection onto the unit sphere. This insight leads to an efficient discretization that avoids expensive surface integrals and spherical arrangements. For meshes, our method achieves average speedups of $22\times$ on a CPU compared to the fastest precise methods and $3\times$ compared to the fastest approximation method, while maintaining full precision. On a GPU, for moderately complex meshes we reach a throughput of $10^9$ queries per second, or $4K$ generalized winding number slices at 120 FPS ($13\times$ faster than a naive GPU method). For parametric surfaces, our method is on average $5.6\times$ faster than the state-of-the-art method, with the same precision. Our method naturally handles complex topologies and non-manifold inputs. We extensively validate its accuracy, robustness, and time performance. Our code is available at https://github.com/MartensCedric/antipodal.

We show that, in dimensions $n\geq 3$, continuity and boundedness do not restore the Sobolev regularity conjecture of Iwaniec and Martin for weakly quasiregular mappings below the critical exponent. For every bounded domain $Ω\subset\mathbb R^n$ and every $1\leq p<nK/(K+1)$, we construct a bounded continuous weakly $K$-quasiregular mapping $$ f\in W^{1,\,p}(Ω;\,\mathbb R^n)\cap C(Ω;\,\mathbb R^n) \cap L^\infty(Ω;\mathbb R^n) $$ which fails to be quasiregular. We further construct weakly quasiregular mappings whose singular sets have Hausdorff dimension arbitrarily close to the maximal size permitted by their Sobolev regularity. These examples show that, the almost-everywhere sign condition on the Jacobian is too weak to serve as an orientation-preserving hypothesis below $W^{1,n}$. In contrast, we show that, for $n-1<p<n$, quasiregularity follows once this condition is replaced by a one-sided condition on the distributional degree (together with boundedness).

A novel use of the LiDAR sensor of a smartphone in introductory physics experiments is discussed in this article. We have determined the spring constant for various combinations of springs using the LiDAR sensor of a smartphone through the phyphox application. An electrical heater coil is used as a spring, and the period of oscillation of a vertical spring-mass system is measured using a LiDAR sensor. The experimental values of spring constants agree with the theoretical values. A high school student can perform this simple experiment in a smart way at home.

Microservice architecture is widely adopted in modern systems, where auto-scaling is critical for satisfying service-level objectives (SLOs). However, determining optimal scaling for microservices is difficult, and reactive resource allocation often leads to costly over- or under-provisioning. We propose AutoSLO, a learning-based, self-adaptive scaling framework that dynamically adjusts microservice replicas to meet SLOs while minimizing resource usage. AutoSLO uses a continuous monitoring-adaptation feedback loop and leverages genetic programming to learn and evolve scaling logic, enabling the deployed microservice system to proactively prevent SLO violations rather than repeatedly searching for one-off scaling actions. We evaluate AutoSLO on two case-study systems -- an online shopping platform and a chatbot based on large language models -- and show that this framework substantially reduces resource usage while maintaining a low frequency of SLO violations, all of which are resolved within a short time window.

This paper presents a survey of the Fermat principle within the framework of general relativity, tracing its evolution from classical optics to its modern variational formulation in Lorentzian geometry. In particular, we provide its proof in the framework of smooth lightlike curves. We also analyze the mathematical difficulties inherent in the relativistic setting, specifically demonstrating that the space of lightlike curves in the Sobolev topology does not admit a smooth manifold structure due to the cone nature of the null condition. To address these variational obstacles, we discuss alternative frameworks highlighting the role of the quadratic arrival time functional in establishing multiplicity results for light rays. Furthermore, we explore significant extensions of the principle, such as its application to extended sources and receivers, arbitrary arrival curves, timelike geodesics with prescribed proper time, Finsler spacetimes, or settings with a non-continuous interface giving rise to a Snell law.

Programmable folding of elastic sheets typically relies on predefined flexible creases or active materials-enabled hinges, which lack intrinsic bistability and limit reprogrammability within a single structure. Here, we present a dimple-encoded origami platform that converts bistable dimple snapping into spatially addressable hinges with prescribed folding angles in a continuous sheet. This interaction-enabled mechanism enables the design of distributed hinge networks through the arrangement and selective inversion of dimples. We establish folding-angle design charts that can be directly used to select local dimple arrangements for target fold angle, forming a practical hinge library without altering the underlying unit geometry. Using this approach, a single dimpled sheet can be reprogrammed to realize multiple distinct configurations, such as triangle, square, and pentagon shapes. We further extend the method to flat-to-3D morphing of polyhedral origami and validate the results through experiments and finite element simulations. As demonstrations, we realize self-supporting cubic shells with enhanced impact resistance and partially deployable cube configurations that remain stable upon opening, highlighting their potential for protective enclosures and deployable architectural structures. The proposed strategy provides a fabrication-friendly route to reprogrammable shape-morphing and adaptive mechanical systems.

A novel method is proposed to determine the magnetic moment of a magnet by studying its free-falling motion inside a non-ferromagnetic and conducting pipe. The dynamics of a neodymium magnet falling inside a pipe is tracked by using sound waves of a fixed frequency generated by one smartphone and detecting acoustic resonance in the pipe simultaneously by the other. This tracking technique leads to the measurement of the terminal velocity of the falling magnet, as the interaction between the magnet and the conducting pipe creates viscosity artificially. The result obtained is verified by studying torsional oscillations of the suspended magnet and conforms to the reported value in such a low-cost setup. The experiment is designed with concepts integrating the domains of general physics, electromagnetic induction, and acoustics.

This short paper explores trends in extremist Facebook data from July 2023 to June 2024. We examined engagement, sentiment, and topics within Facebook groups categorized as anti-Israel/Semitic, anti-Palestine/Muslim, and anti-both, mapping these trends against five major events related to the recent Israel-Hamas conflict. Our findings support the hypothesis that shifts in trends correspond with these key events, showing varying patterns across different group categories. We observed decreased activity proportion in anti-both groups and increased activity proportion in the two one-sided hate groups at the conflict's onset. This pattern reversed after the Israeli troop withdrawal from Khan Yunis, Gaza. During the conflict, negative content proportion surged, and neutral content proportion fell in all the three group categories. Anti-Palestine/Muslim groups' discourses shifted from religious to social media activism and political/protest around the time the war began, while anti-Israel/Semitic groups moved from political/protest to religious topics a couple of weeks before the war.

Forward two-particle angular correlations in $pA$ collisions have long been recognized as a particularly sensitive observable for exploring gluon saturation effects. In the back-to-back regime, two-particle correlations receive substantial contributions from both soft-gluon radiation and saturation effects. In this work, we study heavy meson pair correlation in forward proton-nucleus collisions by incorporating a unified Sudakov resummation for heavy meson pair correlations in the Color Glass Condensate effect theory. Our results are in good agreement with the $Δϕ$ data measured by the LHCb Collaboration for $D^0 \bar D^0$ pairs in forward $pp$ and $pA$ collisions, as well as $J/ψ$ pairs from $b\bar b$ decays in forward $pp$ collisions. Furthermore, we present predictions for $D\bar D$ and $B\bar B$ correlations in the forward rapidity regions at the Large Hadron Collider. A pronounced mass-hierarchy is observed in the nuclear modification factor, $R_{pA}\big|_{m_b}<R_{pA}\big|_{m_c}$, indicating stronger sensitivity to saturation effects at small $x$. As the rapidity increases, the suppression becomes more pronounced while the mass hierarchy remains robust. This study will help us to search for the saturation signal via heavy-meson pair correlations in forward $pA$ collisions.

The paper provides an overview of core functionalities that digital democracy software needs to provide in order to support democratic deliberative processes at scale. Developing these functionalities poses novel computational challenges and requires algorithmic solutions to interesting mathematical problems. The aim of the paper is to break the first ground towards a structured inventory of such problems, and to position possible approaches to them within current academic research in computer science and artificial intelligence.

Provider exposure fairness is crucial for sustaining a healthy content ecosystem and preventing monopolization in recommender systems. Yet, most existing methods either incorporate fairness constraints during model training, requiring expensive retraining when fairness objectives change, or rely on post-hoc reranking with fixed criteria, which lacks adaptability to diverse fairness requirements. To overcome these limitations, we propose Post-hoc Fairness Adaptation (PFA), a lightweight framework that equips a frozen recommender with a fairness adapter, enabling flexible fairness control without retraining the backbone model. Specifically, the fairness adapter learns personalized additive score adjustments from user-item embeddings, which are injected into the original ranking scores to steer provider exposure toward fairness. To train the adapter, we minimize the KL divergence between the actual and the target fair exposure distributions. However, this global objective implicitly treats all providers equally, ignoring structural disparities such as imbalanced provider group sizes and heterogeneous exposure within groups. Consequently, fairness may appear satisfied at an aggregate level while severe inter-group and intra-group exposure imbalances persist, undermining practical fairness. To address this, we design Hierarchical Exposure Fairness Alignment (HEFA), which explicitly balances inter- and intra-group provider exposure disparities, enabling flexible adaptation to diverse fairness requirements. To mitigate potential accuracy degradation, PFA jointly optimizes HEFA with a differentiable NDCG loss, enabling end-to-end fairness optimization while preserving ranking quality. Extensive experiments on three public datasets demonstrate that PFA achieves substantial fairness gains with negligible accuracy loss, consistently outperforming strong baselines.

Virtually all practical settings where preemptive scheduling is employed are susceptible to preemption overhead, and accounting for these overheads is necessary to make informed scheduling design decisions. However, preemption overhead is almost never accounted for in queueing-theoretic analyses of preemptive scheduling policies. This is true even for simple preemptive policies in simple queueing models: even the stability region, let alone the response time distribution, is difficult to analyze under overhead. In this work, we give the first response time distribution analysis of an M/G/1 under a preemptive scheduling policy with preemption overhead. Specifically, we consider class-based preemptive priority, where a stochastic overhead is incurred when pausing or resuming a job. We derive a recursive formula for the Laplace transform of response time for jobs of any given class, from which all response time moments can be extracted. Beyond the specific policy and model we analyze, our broader aim is to provide a first step towards a general framework for analyzing queues with preemption overhead. To that end, we perform much of our analysis in a way that applies to a wide variety of overhead models by introducing a new theoretical tool called the job joint transform.

We revisit games in partition function form, i.e. cooperative games where the payoff of a coalition depends on the partition of the entire set of players. We assume that each coalition computes its worth having probabilistic beliefs over the coalitional behavior of the outsiders, i.e., it assigns various probability distributions over the set of partitions that the outsiders can form. These beliefs are not necessarily consistent with respect to the actual choices of the outsiders. We apply this framework to symmetric partition function form games characterized by either positive or negative externalities and we derive conditions on coalitional beliefs that guarantee the non-emptiness of the core of the induced games.

Principal Component Analysis (PCA) is widely used for dimensionality reduction in hyperspectral imaging, genomics, and neurosciences. However, it suffers from computational bottlenecks in matrix multiplication and singular value decomposition (SVD). Prior PCA hardware accelerators either target only one of these stages, rely on High Level Synthesis (HLS) that limits microarchitectural optimizations or use fixed point datapaths with limited dataset scalability. There is a need for a unified PCA accelerator that is suitable for datasets of any input dimension. Hence, the proposed work presents MANOJAVAM, a scalable PCA accelerator fabric, unifying matrix multiplication and SVD in a single architecture. MANOJAVAM(T,S) comprises an S number of TxT TPU-style systolic arrays employing block streaming for high-throughput matrix multiplication. It further integrates a highly parallel Jacobian unit implementing the Jacobi method for SVD with pipelined CORDIC based rotations. A two tier cache hierarchy and mode-aware memory policies adapts to the distinct memory access patterns of covariance matrix and rotation computation. For demonstration, MANOJAVAM(4,8) is realized on a Xilinx Artix-7 FPGA, achieving a frequency of 200 MHz at 1.271W. MANOJAVAM(16,32) is realized on Xilinx Virtex-Ultrascale+ FPGA, achieving a frequency of 434 MHz at 16.957W. Benchmarking on real-world datasets reveals that MANOJAVAM(16,32) achieves up to a 22.75x speedup in SVD latency and a 42.14x reduction in total energy consumption compared to a high-performance NVIDIA A6000 GPU. The architecture offers a unified, scalable, and energy-efficient platform for large-scale data analytics in both high-performance and edge-computing environments.