Search Results (160)

In this paper, we study the geometric structure induced by the canonical reciprocal cost function and its natural n-dimensional extension. In logarithmic coordinates, the potential depends only on the linear combination $S=\alpha ·t$, and the associated Hessian metric has rank one at every point. The geometry is intrinsically degenerate and effectively one-dimensional, with an $(n-1)$-dimensional null distribution. On the other hand, when the same function is expressed in the original x-coordinates, the corresponding Hessian is generically nondegenerate and defines a pseudo-Riemannian metric away from explicit singular hypersurfaces. We further analyze affine and Levi-Civita geodesics and compare their behavior. In particular, affine geodesics in logarithmic coordinates are globally defined, while in x-coordinates their behavior is restricted by the domain and the singular set. Finally, we relate the construction to symmetrized Itakura–Saito and Bregman divergences, and give a Fisher–Rao realization of the logarithmic Hessian metric. Full article

This paper revisits assimilation theory—developed to explain immigrant incorporation into U.S. society—and advances a reformulation centered on reciprocal assimilation. Classical models describe a linear convergence toward dominant Anglo-American norms, while segmented assimilation highlights multiple pathways shaped by context, race, and class. Both, however, tend to frame incorporation as a directional process in which minority groups adapt to dominant institutions. Drawing on contemporary autism scholarship, this paper brings assimilation theory into dialogue with neurodiversity to examine how its core assumptions extend beyond immigrant contexts. Using autism as a critical case, we show that social adaptation often occurs through camouflaging (masking, compensation, and behavioral adjustment), producing outward conformity without changing underlying neurological differences and often carrying psychological costs. These dynamics suggest that inclusion is frequently conditional on sustained performance of normative behavior rather than true structural incorporation. We identify an underlying assumption of universal assimilability within assimilation research and show how engaging with disability calls for a broader conception of incorporation. In response, we propose reciprocal assimilation as a framework in which adaptation emerges through dynamic interaction among individuals, institutions, and social structures. Integrating life-course concepts—turning points, cumulative (dis)advantage, agency, and social bonds—we illustrate how participation trajectories are shaped by accessibility, accommodations, stigma, and support over time. We conclude that a reciprocal model shifts emphasis from cultural convergence to meaningful participation, offering a more flexible framework for understanding incorporation across diverse populations, with implications for research, measurement, and policy. Full article

We develop an information-theoretic, cost-first framework for discrete dynamics in which the primitive operation is ratio-based comparison. Given two quantities compared via their ratio $x=a/b$, we assign a cost $F\left(x\right)$ measuring deviation from equilibrium ($x=1$). Adopting a reciprocal d’Alembert composition law motivated by coherent chaining, together with quadratic calibration at unity, uniquely determines a reciprocal comparison cost $J\left(x\right)=\frac{1}{2}\left(x+x^{-1}\right)-1$. Taking J as input, we model recognition events as deterministic updates on directed graphs recorded in a minimal ledger. Minimality (no intra-tick ordering metadata) together with non-commutativity of events implies atomic ticks: at most one event per tick. With conservation, pairwise locality, and quantization in $\delta \mathbb{Z}$, each event is recorded as a balanced double-entry posting. For graphs with cycles, assuming time-aggregated cycle closure over a finite clearing horizon, we show that cleared cycle closure is equivalent to path-independence and that the cumulative flow admits a scalar potential on each connected component (unique up to additive constant) via a discrete Poincaré lemma. On hypercube graphs $Q_d$, atomic single-edge updates impose a $2^d$-tick minimal period for timestamp-unique coverage, realized by cyclic Gray codes (explicitly for $d=3$). The framework links ratio-based cost functions, conservative graph flows, and discrete potential theory through explicitly stated axioms and structural assumptions. Full article

The rapid proliferation of artificial intelligence (AI) has pushed hyperscale data center rack densities beyond 100 kW, driving facility power requirements to the gigawatt scale. As developers attempt to deploy these massive Zettascale compute loads across US wholesale electricity markets, they encounter severe transmission planning bottlenecks, multi-year interconnection delays, and escalating grid transient stability risks. This paper presents a generalizable techno-economic framework for evaluating grid-tied, behind-the-meter (BTM) energy architectures as a means of bypassing these constraints. The framework is demonstrated through a detailed case study in the Electric Reliability Council of Texas (ERCOT), selected for its rapid data center growth and evolving large-load regulatory environment. Using a scenario-based comparative approach, this study models the feasibility of transitioning from pure-grid reliance to hybrid, on-site generation across a three-phase deployment pathway scaling from 25 MW to 250 MW. Six distinct microgrid configurations are evaluated, integrating baseload technologies—including Enhanced Geothermal Systems (EGSs), Small Modular Reactors (SMRs), and Reciprocating Internal Combustion Engines (RICEs)—with a tiered-performance Battery Energy Storage System (BESS) combining high C-rate lithium-ion units and repurposed electric vehicle batteries. System viability is assessed through two primary metrics: the Levelized Cost of Energy (LCOE) and the Avoided Loss of Load Probability (ALOLP). The results indicate that the blended LCOE scenario ranges from $64.50/MWh (Geothermal + Solar PPA) to $94.20/MWh (SMR-anchored), compared to a $75.00/MWh pure-grid baseline. The 100% Geothermal configuration achieves a scenario-dependent ALOLP exceeding 99.9%, while gas-dependent configurations range from 58.0% to 91.2%. These findings suggest that geographic siting co-optimized with localized generation offers a viable pathway for balancing regulatory compliance, capital cost, and Uptime Tier IV operational resilience in early-stage data center development across constrained grid environments. Full article

The weak-field, quasi-static regime of gravity is commonly described by the Newton–Poisson equation as an effective response law. We construct this response within a cost-first discrete variational framework. The Recognition Composition Law (RCL) uniquely selects a reciprocal closure cost within the restricted quadratic symmetric composition class; together with the discrete ledger axioms AX1–AX5 (including conservation) and standard DEC refinement, the Newton–Poisson baseline is then recovered in the instantaneous-closure limit. Conditional on Assumption AS1 (scale-free latency) and Assumption AS2 (causal frequency–wavenumber ansatz), allowing finite equilibration introduces fractional memory into the response, yielding a scale-free modification of the source–potential relation characterized by a power-law kernel $w_{\ker }\left(k\right)=1+C{(k_0/k)}^{\alpha }$ in Fourier space. The kernel exponent $\alpha =\frac{1}{2}(1-{\phi }^{-1})\approx 0.191$, where $\phi =(1+\sqrt{5})/2$, is derived from self-similarity of the discrete ledger closure; the amplitude $C={\phi }^{-2}\approx 0.382$ is identified as a hypothesis from a three-channel factorization argument. We evaluate this quasi-static kernel-motivated response against SPARC galaxy rotation curves under a strict global-only protocol (fixed $M/L=1$, no per-galaxy tuning, conservative ${\sigma }_{\mathrm{tot}}$), using a controlled multiplicative surrogate for the full nonlocal disk operator implied by the kernel. In this deliberately over-constrained setting, the surrogate interface achieves $\mathrm{median}({\chi }^2/N)=3.06$ over 147 galaxies (2933 points), outperforming a strict global-only NFW benchmark and remaining less efficient than MOND under identical constraints. The analysis is restricted to the non-relativistic, quasi-static sector and should be read as a falsifier-oriented galactic-regime consistency check of the scaling window, not as a relativistic completion or a claim of Solar System viability without additional UV regularization/screening. Full article

We study functions satisfying the composition law $F\left(xy\right)+F(x/y)=P\left(F\right(x),F(y\left)\right)$ with a symmetric polynomial combiner P. We prove that symmetry together with a quadratic degree bound on P forces a composition law of d’Alembert type. We establish a degree mismatch exclusion criterion showing that symmetric polynomial combiners with $degP(u,v)\ge 3$ do not admit nonconstant continuous solutions, provided the leading term does not cancel (Theorem 1). For continuous nonconstant functions $F:{\mathbb{R}}_{>0}\to \mathbb{R}$ with $F\left(1\right)=0$ satisfying the composition law with a symmetric polynomial P of degree at most two, the combiner is necessarily of the form $P(u,v)=2u+2v+cuv$, $c\in \mathbb{R}$ (Theorem 3). The equation reduces in logarithmic coordinates to the classical d’Alembert functional equation. For $c\ne 0$, one obtains hyperbolic or trigonometric branches, while $c=0$ yields the squared-logarithm family. Under the cost-function assumptions $F\ge 0$ and convexity, only the hyperbolic branch with $c>0$ remains. A unit log-curvature calibration selects the canonical value $c=2$, which yields the canonical reciprocal cost $F\left(x\right)=\frac{1}{2}(x+x^{-1})-1$. For $c\ne 0$, the result extends to ${\mathbb{R}}_{>0}^n$: every solution depends only on a single linear combination of coordinate logarithms; for $c=0$, the solution is a general quadratic form ${\sum }_{i,j}{a}_{ij}ln{x}_{i}ln{x}_j$. In either case, nontrivial coordinate-wise separable costs are excluded. Full article

This study presents a combined computational fluid dynamics (CFD) and experimental evaluation of an adjustable direct-injection reciprocating (IDR) metallurgical furnace fueled by a multicomponent residual oil–solvent mixture. An axisymmetric CFD model, incorporating k–ω SST turbulence modeling, Eddy Dissipation Concept (EDC) combustion, and Discrete Ordinates radiation, was validated against infrared thermography and Process Analytical Technology (PAT) measurements obtained under actual operational conditions. The residual mixture operated in a turbulence-controlled regime (Da < 1), reaching maximum internal temperatures of 1199 °C and achieving a thermal efficiency of 84.6% (based on LHV). Numerical predictions agreed with thermographic data to within 5% across the stabilized operational window. Under comparable process parameters, the alternative fuel reduced cycle time and operational costs compared with diesel and natural gas whilst maintaining stable combustion. Methodological clarifications encompass a consolidated, dimensionally consistent set of equations, a QoI-based mesh-independence study, and a concise summary of the experimental configuration to enhance reproducibility. Full article

Surface cracking is a key visible indicator of deterioration in concrete infrastructure and is routinely captured by vision sensors during field inspections. To translate inspection imagery into actionable maintenance information, crack delineation must be accurate at the pixel level and robust to challenging conditions where cracks are slender, discontinuous, low-contrast, and easily confused with joints, stains, texture patterns, and illumination artifacts. This study proposes a lightweight CNN–Mamba hybrid segmentation framework built upon Vm-unet for reliable crack mapping under heterogeneous inspection scenarios and resource-constrained deployment. The framework couples boundary-sensitive convolutional features with long-range state-space representations via a spatially modulated convolution design, refines skip-connection features using reciprocal co-modulation attention to suppress background interference, and enhances cross-scale interactions through a decoder interaction fusion scheme to preserve fine-crack continuity and sharp boundaries. Experiments on a multi-source composite dataset and public benchmarks show consistent improvements over representative CNN-, Transformer-, and Mamba-based baselines. The proposed method achieves 80.11% mIoU and 82.05% Dice on the composite dataset, while maintaining an efficient accuracy–cost trade-off (36.049 GFLOPs, 25.991 M parameters). The resulting crack masks provide a dependable basis for inspection-driven quantitative assessment and maintenance decision support. Full article

We study a rigidity problem for functions $F:{\mathbb{R}}_{>0}\to {\mathbb{R}}_{\ge 0}$ that penalize deviation of a positive ratio from equilibrium $x=1$. Assuming (i) a d’Alembert-type composition law on ${\mathbb{R}}_{>0}$, and (ii) a single quadratic calibration at the identity (in logarithmic coordinates), we prove that F is uniquely determined. The composition law implies the normalization $F\left(1\right)=0.$ The unique solution is called the canonical reciprocal cost, namely the difference between the arithmetic and geometric means of x and its reciprocal. Our proof uses the logarithmic coordinates $H\left(t\right)=F\left(e^t\right)+1$, where the composition law becomes d’Alembert’s functional equation on $\mathbb{R}$. The calibration provides the minimal regularity needed to invoke the classical classification of continuous solutions and fixes the remaining scaling freedom, selecting the hyperbolic-cosine branch. We also establish the necessity of each assumption: without calibration the composition law admits a continuous one-parameter family; without the composition law the calibration does not determine the global form; and without regularity the composition law admits pathological non-measurable solutions. Finally, we establish a stability estimate for approximate solutions under bounded defect and characterize some properties of the canonical cost. Full article

Anthropogenic pressures and climate change are accelerating the degradation of seagrass ecosystems and the ecological services they provide. In temperate systems, the decline of eelgrass (Zostera marina) has raised noticeable concern, particularly as restoration actions (e.g., transplantation) require accurate, nondestructive estimates of leaf biomass. Allometric power-law models can provide such proxies, but their applied value depends on whether fitted parameters remain transferable across sites and sampling periods. Here, using two extensive and independently collected datasets from San Quintín Bay (SQ) and Punta Banda estuary (PB), we evaluate three formulations: M1 (biomass–length), M2 (biomass–length–width), and M3 (biomass–area surrogate). All three models produced consistent fits in both datasets, and parameter-comparison tests detected no significant between-site differences. Reciprocal cross-projections of monthly mean leaf biomass showed high concordance, supporting practical parameter stability within the SQ–PB domain. A model-selection analysis based on goodness of fit and parsimony further identified the bivariate model M2 as the best-performing proxy across sites. Taken together, these results support a practical interpretation in which eelgrass may express phenotypic plasticity through shifts in trait distributions (length and width), while the scaling relation linking morphology to biomass remains effectively stable. For applied restoration-comparison purposes, we therefore recommend using M2—preferably with site-fitted parameters, or pooled/mean parameters when supported by reproducibility tests—to estimate aerial production non-destructively and cost-effectively. Full article

Rumor source detection aims to identify the initial origin of misinformation diffusion in social networks. Accurate source localization is essential for effective rumor intervention and early mitigation in large-scale social media platforms. Existing rumor source detection methods often struggle to model complex propagation structures. However, applying mathematical models uniformly to all samples introduces unnecessary computational overhead and limits scalability. By leveraging GNN-based candidate ranking, our approach effectively narrows the source search space and provides a reliable structural foundation for subsequent reasoning. Prior studies typically perform end-to-end inference without considering prediction confidence, leading to inefficient processing of low-uncertainty samples. To address this issue, we introduce an entropy-based uncertainty filtering mechanism that selectively identifies high-uncertainty cases requiring further reasoning, significantly reducing redundant computation. Meanwhile, existing methods lack semantic interpretability when handling ambiguous propagation patterns, motivating the incorporation of large language model (LLM) reasoning. We employ LLM-based reasoning only on filtered samples to enhance semantic understanding while controlling inference cost. Based on these designs, we propose TSR-RSD, a tri-stage selective reasoning framework that integrates GNN-based structural modeling, uncertainty-driven sample selection, and LLM-based semantic reasoning. Experimental results on GossipCop, PolitiFact, and PHEME demonstrate that TSR-RSD consistently outperforms GNN-based baselines in terms of Hit@1, Hit@3, Hit@5, and Mean Reciprocal Rank (MRR), reflecting improved accuracy and stability in rumor source ranking. Furthermore, the entropy-based uncertainty filtering mechanism significantly reduces the LLM invocation ratio by approximately 40–60%, while maintaining comparable or improved ranking performance. As a result, TSR-RSD achieves an overall inference time reduction of 35–50%, effectively balancing localization accuracy, computational efficiency, and interpretability. Full article

We study ratio-induced mismatch cost functions of the form $c(s,o)=J\left({\iota }_S\left(s\right)/{\iota }_O\left(o\right)\right)$ built from positive scale maps ${\iota }_S:S\to {\mathbb{R}}_{>0}$ and ${\iota }_O:O\to {\mathbb{R}}_{>0}$ and a penalty $J:(0,\infty )\to [0,\infty )$. Assuming inversion symmetry, strict convexity, coercivity, normalization at 1, and a multiplicative d’Alembert identity, we show that $f\left(u\right):=1+J\left(e^u\right)$ is continuous and satisfies the additive d’Alembert equation; hence, by a classical classification theorem, there exists $a>0$ such that $J\left(x\right)=cosh(alogx)-1={\displaystyle \frac{1}{2}}\left(x^a+x^{-a}\right)-1, x>0$. We then analyze the associated argmin mapping over feasible scale sets: existence under explicit subspace-closedness assumptions, an explicit geometric-mean decision geometry for finite dictionaries with stability away from boundaries, exact compositionality for product models, and an optimal sequential mediation principle described by a geometric mean (or its log-space projection when infeasible). The paper is purely mathematical; any semantic interpretation is optional and external to theorems proved here. Full article

Background: Although burnout among respiratory therapists (RTs) is well documented, qualitative insights into their lived experiences in Saudi Arabia remain limited. This study explored RTs’ experiences of burnout, systemic and organisational drivers of professional strain, and strategies for resilience and retention within Saudi hospitals. Methods: A qualitative descriptive design was employed. Purposive sampling was used to recruit 11 RTs from diverse regions across Saudi Arabia. Semi-structured interviews were conducted in Arabic between September and November 2025, audio-recorded, and transcribed verbatim. Data management and analysis followed a hybrid approach using NVivo 12 software alongside manual coding to support deep immersion in the data. Analysis was guided by Braun and Clarke’s reflexive thematic analysis. Methodological rigour was enhanced through reflexive memoing, peer debriefing, and adherence to a 15-point trustworthiness checklist. Results: Analysis generated one overarching theme, “Caught Between Care and Collapse: The Human Cost of Institutional Burnout,” alongside three interrelated themes. Participants described (1) “Living within a system that drains the self,” highlighting sustained physical and emotional exhaustion driven by understaffing and extended shifts; (2) “Losing meaning and recognition,” illustrating how organisational neglect eroded professional passion and replaced it with obligation and frustration; and (3) “Coping strategies and informal support,” reflecting quiet resilience through self-regulation, peer solidarity, and humane leadership. Many participants framed their endurance as an act of moral defiance rather than passive resignation. Conclusions: These findings suggest that RT burnout reflects not individual failure but a structural outcome of sustained strain and deficits in reciprocity. Burnout emerges as an institutional crisis in which therapists remain deeply committed to patient care while being pushed toward professional collapse by systemic neglect. Culturally informed, system-level interventions are urgently needed to preserve this essential workforce. Full article

Background/Objectives: Exercise calorimetry provides a means to quantify the relative contributions of lipid and carbohydrate (CHO) oxidation across a range of exercise intensities. Although lipid oxidation capacity has been widely studied—particularly in relation to exercise prescription for individuals with obesity—the factors governing CHO oxidation during exercise are less clearly defined. This study therefore aimed to investigate, within a large single-center cohort, not only the established determinants of maximal lipid oxidation (LIPOXmax) but also those influencing CHO oxidation. Methods: Exercise calorimetry was performed in a cohort of 6465 individuals (4561 women and 1904 men; mean age 46.5 years; mean BMI 33.6 kg/m²). Two principal physiological indices were derived: LIPOXmax, defined as the exercise intensity eliciting maximal rates of fat oxidation, and the carbohydrate cost of the watt (CCW), defined as the slope characterizing the relationship between CHO oxidation and power output. Results: LIPOXmax showed positive associations with lean and muscle mass, and negative associations with fat mass and age, supporting the notion that greater muscle mass enhances the capacity for fat oxidation. Although men demonstrated higher absolute maximal fat oxidation rates, adjustment for body composition revealed that women exhibited relatively higher lipid oxidation (+30%, p < 0.001), occurring at a greater percentage of $\dot{\mathrm{V}}$O_2max (+9.2%, p < 0.001). Furthermore, the carbohydrate cost of the watt was significantly elevated in women (+17.8% compared with men). CCW was positively correlated with BMI, fat mass, and age, and negatively correlated with muscle mass, LIPOXmax, and the crossover point—that is, the exercise intensity at which CHO becomes the predominant substrate. Discussion and Conclusions: Individuals with higher adiposity exhibited a greater reliance on carbohydrate oxidation, whereas leaner individuals preferentially oxidized lipids at comparable exercise intensities. These observations reinforce the reciprocal interplay between lipid and carbohydrate metabolism during exercise and highlight the substantial influence of body composition, age, and sex. Notably, this study provides the first comprehensive characterization of the determinants of CHO oxidation during exercise, identifying sex, age, and adiposity as major contributing factors. This underexplored facet of metabolic flexibility may hold practical relevance in clinical contexts such as obesity or susceptibility to exercise-induced hypoglycemia. Full article

With the rapid growth in the scale and complexity of software systems, automated vulnerability detection has become increasingly important. Although Large Language Models (LLMs) demonstrate strong code comprehension capabilities, their abilities in vulnerability detection are still limited by issues such as hallucinations, high fine-tuning costs, and difficulties in effectively leveraging fine-grained historical vulnerability patterns and domain knowledge. To address these challenges, we propose Retrieval-Augmented Semantic Mapping for Vulnerability Detection (RASM-Vul), a retrieval-augmented framework that enhances LLM detection capability through multi-perspective semantic mapping. The core of our approach is the construction of a comprehensive knowledge base composed of vulnerability–fix pairs and structured knowledge. We leverage multi-view (e.g., code, AST, knowledge) similarity retrieval to accurately match the most relevant vulnerability patterns with repair examples for the code under analysis. Our designed Weighted Reciprocal Ranking Fusion (WRRF) algorithm adaptively integrates contributions from different retrieval channels according to the problem type, significantly improving the relevance and accuracy of retrieval. Experiments show that RASM-Vul achieves an F1-score of 66.79%, outperforming existing baselines on the PrimeVul paired dataset. Our study demonstrates that knowledge-enhanced semantic mapping and retrieval can improve the robustness and reliability of automated vulnerability detection. Full article