Abstract: This study examines the relationship between Vedic ritual practice and liberation (mokṣa) within an Āstika philosophical framework using the Bhagavad-Gītā as its principal interpretive source; it investigates how Agnihotra can be understood in relation to non-attached action (niṣkāma karma), sustained spiritual discipline, and the later Vedāntic classification of accumulated karma (sañcita karma). Through a qualitative textual and philosophical analysis of selected passages from the Bhagavad-Gītā, Śrauta literature, and relevant Vedāntic commentaries; the study compares Agnihotra with selected saṁskāras and yajñas in terms of ritual continuity, prescribed context, and philosophical relevance. It argues that Agnihotra's prescribed regularity makes it a useful case for examining the relationship between repeated ritual action and the Bhagavad-Gītā's teachings on disciplined, non-attached action; however, ritual continuity alone does not establish the destruction of accumulated karma or guarantee liberation. Within the Vedānta framework examined here, liberating knowledge is central to the understanding of liberation from karmic bondage while disciplined action can contribute to spiritual preparation. The study therefore proposes Agnihotra as a significant subject for hermeneutical inquiry rather than as an independently established or universally superior means of liberation.

Abstract: Background: The use of biodegradable polymeric implants for localised drug delivery is a strategy for improving cancer treatment, as it maintains high local drug concentrations while minimising systemic toxicity. Erufosine, a third-generation alkylphosphocholine, is active against a wide range of malignant cells, but its clinical application is limited due to the lack of suitable sustained-release formulations. Methods: Biodegradable polymer blends based on poly(ε-caprolactone) (PCL)/polyethylene glycol (PEG) and poly(D,L-lactide-co-glycolide) (PLGL)/PEG were developed as local drug delivery systems for erufosine. The polymer composition was optimised using doxorubicin as a model compound. Erufosine release was quantified by HPLC–MS/MS over 14 days. The therapeutic efficacy of the implants was evaluated in Graffi myeloid tumor bearing hamsters using two implantation strategies: primary implantation at the time of tumor inoculation and postoperative implantation following tumor resection (using primary and postoperative implantation). Histopathological examination was performed to assess tissue response and tumor morphology. Results: Incorporation of PEG significantly enhanced drug release from the biodegradable matrices, with the PCL/PEG (2:1, w/w) and PLGL/PEG (2:1, w/w) formulations showing the most favourable release profile. HPLC-MS/MS analysis showed an initial burst release followed by sustained erufosine release for up to 14 days. Local implantation of erufosine-loaded carriers significantly prolonged survival and decreased mortality of Graffi tumour-bearing hamsters with postoperatively drug-loaded implants. Histopathological analysis revealed extensive tumor cell degeneration and necrosis, confirming the biological activity of locally released erufosine. In PLGL/PEG-treated animals, the formation of a fibrovascular capsule around the implant suggested that host tissue response might partially restrict drug diffusion despite favourable in vitro release kinetics. Conclusions: Biodegradable PCL/PEG and PLGL/PEG implants provide sustained local erufosine delivery and moderate antitumor activity in vivo. The findings demonstrate that therapeutic efficacy depends not only on polymer-controlled drug release but also on the response of host tissues to the implanted biomaterial

Abstract: This paper presents a comprehensive philosophical and historical critique of mathematical Platonism, arguing instead for an instrumentalist framework where mathematics evolves as an open-ended, highly adaptive sequence of pragmatic conventions driven by utility and the empirical demands of physical reality. By deconstructing foundational transitions across geometry, analysis, logic, and mathematical physics, we illustrate how mathematical rigour routinely relies on conceptual accommodations rather than a priori absolute truths. We begin by exposing a material paradox in Euclidean geometry: the physical act of constructing a circle via a compass violates Euclid’s Elements (c. 300 BC) definitions of dimensionless points and two-dimensional surfaces by piercing a three-dimensional substrate. Moving to projective geometry, we explore the visual and structural conventions of the vanishing point as an engineered fiction designed to satisfy the pragmatic utility of sight. In mathematical analysis, we examine how numerical approximations of transcendental constants—from Archimedes’ bounding of π to the modern proofs of transcendence for e (1873) and π (1882)—reveal a qualitative mutation where discrete rational sequences transform into irrational realities upon touching infinity, necessitating artificial axioms of completeness. Furthermore, we unpack the conceptual paradoxes of complex analysis, highlighting Euler’s arbitrary branch cuts designed to domesticate the multi-valued nature of the logarithm of negative numbers. We contextualize these foundational constraints through Gödel’s Incompleteness Theorems (1931) and Turing’s Halting Problem (1936), demonstrating that formal systems cannot achieve closed autonomy and must look outward for new conventions when encountering unprovable truths. This dependency is mirrored in continuum mechanics, where Cauchy’s stress tensor (1827) introduced a nine-component algebraic entity born purely out of the physical necessity to couple force vectors with oriented surfaces, fracturing classical vector spaces to satisfy empirical constraints. Crucially, we extend this critique to computational fluid dynamics and field simulations, demonstrating how contemporary mesh-based solvers violently subvert the Eulerian assumption of mutually independent spatial and temporal variables, shackling them through the pragmatic constraints of the Courant-Friedrichs-Lewy (CFL) stability criterion. Finally, we deconstruct the relativism of numerical truth through modular arithmetic, tracing its formalization from Gauss’s Disquisitiones Arithmeticae (1801) to its contemporary manifestation in asymmetric cryptography (RSA, 1978). By demonstrating how the structural modulus shifts the output of basic operations, we illustrate that numbers are pliable symbols conforming to the spaces we construct for them. Ultimately, this essay conceptualizes mathematics as a fluid, dynamic conceptual technology whose validation and internal cohesion are dictated not by a transcendental realm, but by its instrumental utility in decoding and manipulating the physical universe.

Abstract: Introduction: Concurrent parliamentary and judicial inquiries are intended to strengthen accountability, yet overlapping investigative arrangements may also fragment responsibility, divert resources and weaken implementation. The supplied literature provides relevant evidence on South African commissions of inquiry, public-sector governance and municipal accountability, but offers limited direct evidence on simultaneous parliamentary and judicial investigations. Methods: The researcher-selected databases and information sources were Google Scholar, ERIC, OpenAlex and Crossref. The eligibility protocol restricted publication years to 2015–2026. COSTAQDA recorded source-level retrieval through OpenAlex (150 retrieved; 319 available), Crossref (150 retrieved; 691 available). Where researcher-selected sources did not expose a suitable direct bulk-search connector, COSTAQDA used its OpenAlex/Crossref discovery bridge while preserving the researcher-selected source names in the PRISMA record. The identification run recorded 300 records before cross-source deduplication and 298 unique records after deduplication. Results: Six codes, three categories and three analytical themes were developed. Institutional overlap expanded investigative capacity and public documentation but could reproduce fragmentation when existing enforcement systems remained unreformed. Repeated inquiries could displace prosecution and divert resources. Effective democratic oversight depended on institutional independence, professional capacity and implementation pathways. Direct South African evidence was sparse, and systematic comparative evidence on resource efficiency was absent. Discussion/Conclusion: Institutional overlap is neither intrinsically beneficial nor harmful. Its effects depend on whether overlapping mandates are coordinated with independent enforcement, clear responsibility and mechanisms that convert findings into sanctions or administrative change.

Abstract: The current definitions, explanations, and clinical classification of angina pectoris, particularly the traditional definitions of "typical" and “atypical” angina or chest pain and the stable versus unstable dichotomy, contains conceptual inconsistencies that impair understanding concepts, diagnostic clarity and clinical decision-making. This article challenges several long-standing assumptions about angina, especially regarding the "typical angina" construct and unstable angina definition. We argue for a redefinition grounded in pathophysiology of ischemia and clinical logic rather than rigid historical formulas. These criticisms carry important implications for both education and practice.

Abstract: A universal spatiotemporal coupling optimal low-dimensional dynamical system algorithm for compressible turbulence which unifies RANS, LES and DNS in the sense of Box filtering/spatial grid averaging and large-scale grids: the LMS method is outlined first. Then the equation error coursed by finite truncation in computational fluid dynamics(CFD) is reported first time. The use of the LMS method can reduce this error, leading to a unified new paradigm in CFD that combines numerical simulation of turbulence with computational fluid dynamics. Finally, a major surprising discovery: The essences of turbulence modelling theory is nothing, but just a part of the equation error coursed by finite truncation in CFD.

Abstract: The banking sector serves as a critical transmission belt for capital allocation toward renewable energy (RE) projects, yet traditional equity valuation models fail to capture banks' exposure to energy transition risks. To bridge this gap, this paper develops a novel fundamental-environmental indicator—the "Green F-Score"—tested on 10 major commercial banks listed on the Warsaw Stock Exchange (WSE) between 2023 and 2025. By synthesizing classical financial efficiency criteria with EU Taxonomy disclosures (Green Asset Ratio), the portfolio sorting methodology reveals how capital markets price sustainable energy financing in Central and Eastern Europe. The empirical results demonstrate that portfolios with high environmental-fundamental readiness ("Green Leaders") generate a superior mean annual return of 60.43% and a substantial price-to-book (P/B) premium. Conversely, banks lagging in RE financing suffer significant carbon risk discounts. Correlation analysis confirms a paradigm shift: the market premium is primarily driven by the ESG sub-score, rendering traditional financial metrics a mere operational hygiene factor. Consequently, the Green F-Score emerges as a robust tool for institutional investors, proving that accelerated lending to the energy transition effectively lowers the cost of equity capital for commercial banks.

Abstract: Using fish-processing residues in poultry diets requires assessment of performance alongside the nutrient changes caused by ingredient substitution. We evaluated six practical diets in 150 Hisex Brown laying hens (30 cages; five independent cages per diet) over 60 days: a basal control, four diets containing 0.5–2.0% fermented Pangasius by-product extract formulated with sugar palm starch, and a canthaxanthin reference. Cage-level responses were analyzed with one-way analysis of variance, and nutrient-density descriptors were calculated from formulation records. Hen-day production differed among diets (p = 0.0053), with means of 61.91% in the basal control and 80.36% at 2.0% inclusion; the overall feed conversion ratio did not differ significantly (p = 0.294). Across the graded series, calculated energy-to-crude-protein density rose from 16.22 to 16.86 kcal/g protein and the dietary omega-6:omega-3 ratio from 12.84 to 14.41, whereas the measured yolk omega-6:omega-3 class ratio fell from 11.57 to 9.69. Yolk cholesterol means declined from 1384.1 to 995.6 mg/100 g dry matter. These findings support multi-criterion screening of practical alternative-feed formulations but cannot establish a nutrient optimum or an isolated effect of the fermented preparation.

Abstract: As large language model (LLM) services expand toward distributed environments characterized by latency sensitivity, heterogeneous resources, and stringent privacy constraints, neither end-only nor cloud-only deployment can simultaneously balance generation quality, response latency, resource cost, and energy consumption. This survey systematically reviews optimization techniques for end-edge-cloud collaborative LLM inference services and establishes a four-layer taxonomy encompassing the algorithm, model, system, and chip levels. This taxonomy captures the end-to-end execution chain from collaborative decision-making to physical execution. The algorithm layer determines inference paths and task partitioning; the model layer provides deployable and collaborative model forms; the system layer manages resource mapping and pipeline execution; and the chip layer supplies the underlying computing, storage, and interconnect capabilities. These four layers are mutually dependent and collectively determine the end-to-end benefits of a collaborative solution. Furthermore, this survey defines representative collaboration paradigms and evaluation metrics, compares the performance gains, resource overheads, and applicability boundaries of different methods, and summarizes promising future directions, including cross-layer collaboration, dynamic adaptation, state-centric runtimes, and service-aware hardware.

Abstract: Forecasting solar radiation is crucial for the deployment of photovoltaic systems and for supporting renewable energy and agricultural planning in Sub-Saharan Africa. This manuscript compares the performance of two machine learning algorithms for this purpose: a classical Recurrent Neural Network (RNN) and a hybrid Quantum Neural Network (QNN), applied to monthly SWGDN prediction across 20 cities in Mali using MERRA-2 data from 1980 to 2025. The QNN architecture, comprising an LSTM feature extractor followed by an 8-qubit, 3-layer variational quantum circuit with Pauli-Z readout, outperforms the RNN in 9 of 20 Malian cities (45%). Notably, the quantum advantage is most easily noticeable in cities characterized by strong seasonal variability, whereas the RNN remains competitive in more arid, stable regions. These findings underline the potential of quantum machine learning for regional climate forecasting.

Abstract: Autonomous multi-agent systems are increasingly being designed to perform complex tasks with limited human intervention. However, increasing autonomy introduces challenges related to trust, transparency, accountability, controllability, and safe decision-making. This paper presents a web-based control-room prototype for a Trustworthy Multi-Agent System designed to monitor and govern autonomous agents while maintaining human oversight. The proposed framework integrates trust monitoring, evidence-based decision-making, adaptive self-correction, auditability, explainability, runtime monitoring, and Safe Mode controls. The system provides a Trust Posture dashboard for monitoring overall system trust, agent activity, self-corrections, human interventions, and trust trajectories. An Agent Roster provides information about individual agents, including their roles, trust scores, operational status, run counts, and available operator controls. Recent audit events maintain a human-readable record of approvals, reviews, corrections, and evidence updates. A Safe Mode mechanism provides controlled autonomy by requiring human confirmation before new autonomous actions can proceed. The evaluation framework considers Trust Score, Confidence Level, Agent Activity, Self-Correction Count, Human Intervention Count, Agent Status, Audit Events, and Decision/Action Status as measurable variables. Purposive sampling is used to identify meaningful system activities for evaluation. The proto-type demonstrates how monitoring, human oversight, evidence-based decisions, and adaptive correction can be integrated into a unified governance framework for trustworthy autonomous multi-agent systems.

Abstract: Non-specific cytotoxic cells (NCCs) are critical first-line defenses against bacterial pathogens in teleosts, yet the molecular mechanisms governing their activity remain poorly understood. This study characterized LOC109197777, a novel long non-coding RNA (lncRNA) from Nile tilapia (Oreochromis niloticus), as a positive regulator of NCC-mediated immunity against Streptococcus agalactiae. Bioinformatic and experimental analyses confirmed its non-coding potential and predominant cytoplasmic localization. In vitro, overexpression of LOC109197777 in tilapia head kidney cells upregulated NCC activation receptors while downregulating effector molecules and pro-inflammatory cytokines, indicating a "primed but restrained" activation state; conversely, siRNA-mediated knockdown reduced NCC cytotoxicity. In vivo, intraperitoneal delivery of LOC109197777 significantly enhanced survival following S. agalactiae challenge and reduced bacterial burdens in the head kidney and spleen. Furthermore, tissue-specific expression profiling revealed that LOC109197777 orchestrates spatially distinct regulatory programs: rapid activation in the head kidney, sustained responses in the spleen, early responses in the liver, and prolonged mucosal immunity in the intestine. Notably, the lncRNA differentially regulated perforin-1 and granzyme B in a tissue and time-dependent manner, balancing effective pathogen clearance with immune homeostasis. These findings establish LOC109197777 as the first characterized lncRNA regulator of NCC activity in teleosts, operating through a tissue-specific, temporally coordinated mechanism. This study provides a novel molecular target for genetic enhancement of disease resistance in tilapia aquaculture and offers a theoretical foundation for developing lncRNA-based immunomodulatory strategies.

Abstract: Several studies suggest that, in small cell lung cancer (SCLC), increasing age is associated with a lower incidence of brain metastases. This is conventionally explained by younger patients living long enough to develop them, an interpretation that fits poorly with the rapid course and short survival of SCLC. We propose a biological alternative grounded in the mechanics of brain-metastatic colonization. Because early colonization depends on the arrest of circulating tumour cells at microvessels, their perivascular survival, and outgrowth by co-option of the existing vasculature within a supportive perivascular niche, we hypothesize that the aging brain becomes a relatively resistant soil: microvascular rarefaction, endothelial senescence, chronic hypoperfusion and senescence of the perivascular niche reduce the competence of the brain to host metastatic colonization. We further propose that macroscopic cerebral atrophy is a radiologic surrogate of this reduced competence and should therefore be inversely associated with brain-metastatic incidence. The hypothesis is falsifiable, testable in matched radiologic cohorts and age-controlled experimental models, and clinically consequential for the selection of patients for prophylactic cranial irradiation.

Abstract: Family cultural capital includes household educational resources, parental qualifications, and everyday family practices that may be relevant to students’ science learning. Using PISA 2025 data, we examined how these dimensions predicted science achievement among 12,258 students in China (B-S-J-Z: Beijing, Shanghai, Jiangsu, and Zhejiang) and 2,291 U.S. questionnaire respondents. We used the same twelve family cultural-capital and science-participation indicators in both samples and evaluated two predictive models—ridge regression and XGBoost—through school-grouped cross-validation and ten science plausible values. The full XGBoost models achieved held-out R2 values of .361 in China (B-S-J-Z) and .327 in the U.S. sample. Perceived parental educational expectations and books at home ranked first and second among the focal indicators in both settings. The additional predictive information associated with perceived expectations was greater in the China (B-S-J-Z) model, whereas family conversations and science-related participation added relatively more information to the U.S. model. Parental qualifications were also more prominent in the China (B-S-J-Z) results. Together, the findings identify both shared cultural-capital patterns and different profiles of family educational resources and practices across the two educational settings.

Abstract: Strongly chirped dissipative solitons are coherent laser pulses sustained by a balance of gain and loss. They sit between two paradigms of statistical physics: their normal-dispersion spectra take the Rayleigh–Jeans form of thermalized waves, while their energy concentrates near zero frequency, as in wave condensation. Information measures quantify this dual character for the cubic–quintic complex Ginzburg–Landau equation. In normal dispersion, a Mellin–Gamma construction yields a Fermi–Dirac-like logistic spectral edge whose width, a dissipative linewidth, fixes the leading entropy correction. In anomalous dispersion, a scale-free spectral range carries logarithmic energy growth, and Rényi entropies of order above one third separate wing spreading from core weighting without truncating the spectrum. Resolved interference fringes lower the spectral entropy of coherent pulse complexes by a deficit that distinguishes in-phase, random, and flat-spectrum phase patterns. Linear fluctuation theory separates the coherent mean from fluctuations and reveals a soft energy mode near dissipative soliton resonance. At fixed net gain, its fluctuations track the static response to loss, with an effective noise strength exceeding the applied one by a factor proportional to the reactive-to-dissipative nonlinearity ratio; no cavity mode holds more than a small energy fraction. These results offer testable diagnostics for photonics and nonequilibrium physics.

Abstract: Plants seem simple, immobile and imperturbable organisms, passively undergoing the passage of time, the change of seasons and biotic and abiotic stress. In reality, it is not as it seems; in fact, plants are particularly complex organisms that have developed highly so-phisticated mechanisms to perform all the functions necessary for life: plants move, per-ceive stimuli, interact with the environment, and employ defensive strategies to counter external attacks. Being rooted to the ground, they do not use speed, like animal organisms, but obtain the same results using different mechanisms. Plants have evolved sophisticated survival strategies and are well suited to their environ-ments, demonstrating a strong ability to react to environmental changes and needs. Plants adopt several defensive strategies to defend themselves from predators, and their possible toxicity is also a defensive mechanism. Plant defences are not just tools of individual sur-vival, but actual social weapons used to communicate, form alliances, manipulate animal behaviour, and defend the entire plant community. Plant defence strategies create ex-tremely complex networks of social interaction. The aim of this manuscript is to describe the defensive strategies developed by plant or-ganisms, highlighting the mechanisms of action and the main characteristics reported in the scientific literature dealing with this topic. In particular, the evolutionary role of the listed strategies will be explored in depth. The following toxic plants will be described in detail: Ricinus communis, Atropa belladonna, Taxus baccata, and Ferula communis. Furthermore, this manuscript helps to interpret plant defensive strategies as the construction of plant-plant and plant-animal social relationships. In conclusion, plant defensive strategies help ensure the survival of global flora, protect ecosystem balances and develop modern and sustainable agriculture.

Abstract: Management of prehospital hemorrhagic shock and traumatic cardiac arrest remains a critical capability gap in trauma resuscitation. Hybrid endovascular and extracorporeal technologies and techniques are evolving to meet the challenges of noncompressible hemorrhage, tissue perfusion, gas exchange, and metabolic derangement correction in the setting of complex traumatic injuries and aim to improve patient outcomes by augmenting the capabilities of interdisciplinary trauma/critical care resuscitation teams. The clinical value of these emerging technological advancements depends upon matching the intervention(s) to the dominant physiological failure modes while assisting in damage control surgery and definitive surgical repair. This narrative review discusses advancements in resuscitative endovascular balloon occlusion of the aorta (REBOA) and inferior vena cava (REBOVC), selective regional perfusion, and extracorporeal membrane oxygenation (ECMO), and the technical and logistical barriers facing their clinical implementation. An escalating care pathway and conceptual framework to manage noncompressible hemorrhage and hemorrhage-induced traumatic cardiac arrest utilizing an integrated endovascular and extracorporeal approach is proposed based on prior literature and recent developments in selective abdominopelvic perfusion. Market dynamics remain an important consideration for fielding new technologies; development of specialized medical devices would benefit from versatile, multi-use capabilities to serve broader patient populations to enable economically sustainable employment within healthcare systems.

Abstract: Clearing dying cardiomyocytes by efferocytosis is required for inflammation resolution and cardiac repair after myocardial infarction (MI). Whether the three functional stages of efferocytosis (recognition, engulfment and degradation) are coordinated by the local cellular neighborhood in the human infarcted myocardium is unknown. We analyzed 24 human cardiac Visium spatial transcriptomic samples (20 MI, 4 control; 94,029 spots; 19 independent donors) from a published multi-omic map of human MI^[4]. Multiview interaction-based spatial transcriptomics (MISTy) identified 12 gene programs with spot-level neighborhood dependency; donor-level aggregation showed positive neighborhood gains for 22 of 23 programs after Benjamini-Hochberg correction (FDR < 0.05), including all three efferocytosis stages[5]. Efferocytosis module activity tracked macrophage proportions (Spearman rho = 0.41-0.44). Controlling for macrophage abundance removed the engulfment-related association but left a degradation-related association with endothelial and fibroblast proportions, indicating niche-dependent regulation of the degradation stage. Distance-stratified analysis showed neighborhood effects beyond direct cell-cell contact, without simple short-range dominance. Mendelian randomization linked NR1H3, STAU1, CTSS and ITGAV expression to MI risk (FDR < 0.05)[14], and connectivity-map analysis nominated niclosamide as a candidate for reversing the efferocytosis-degradation program[15]. Model-based in silico perturbation attributed the neighborhood dependency to vascular-stromal neighbors; virtual knockout of NR1H3 predicted coordinated downregulation of efferocytosis genes. Efferocytosis subprograms are thus spatially decoupled in the human infarcted myocardium, with degradation as a niche-regulated step, providing spatial and genetic leads for targeting infarct repair.

Abstract: The digitization of an ever-developing network of cybersecurity threats has weighted traditional packet filter rule-based firewalls and signature based intrusion detection systems towards being less effective against zero day vulnerabilities, ransomware, polymorphic malware, and Advanced Persistent Threat (APTs) attacks. Emerging technologies like Artificial Intelligence (AI) and Machine Learning (ML) have potential to be game changers for proactive and adaptive defence of cyberspace. This review investigates AI powered cybersecurity systems: machine learning algorithms, deep learning architectures, Reinforcement Learning, and Explainable Artificial Intelligence (XAI). Also investigated will be applications within Cloud Computing, Healthcare, Maritime Systems and National Critical Infrastructure. Further discussions will include feature engineering, Transformer based Zero Shot Learning (ZSL), SOAR integration, blockchain-based forensic integrity, adversarial AI and quantum computing concerns. The results demonstrated positive trends through AI powered cybersecurity systems improving detection Accuracy, lowering False Positives, reducing incident response time and enhancing Autonomous Defence capabilities. However, challenges around Explainability, Ethical Governance, Scalability of Computation, and Adversarial Resistance are expressed as possible major concerns. A conclusion point will outlining future research directions to develop, build and maintain resilient, transparent and quantum resistant Cybersecurity Ecosystems.

Abstract: We examine how fundamental thermodynamic principles constrain the mathematical structure of real linear evolution operators governing isolated discrete dynamical systems (\( \dot{u} = M u \)). Using a bottom-up, deductive approach, we evaluate an unconstrained linear operator against macroscopic conservation of energy and the second law of thermodynamics. We prove that exact energy conservation requires vanishing column sums (\( \sum_i M_{ij} = 0 \)), while ensuring a non-negative entropy production rate (\( \dot{S} \ge 0 \)) necessitates non-negative off-diagonal entries (\( M_{ij} \ge 0 \) for \( i \neq j \)), establishing \( M \) as a Metzler matrix. We explicitly demonstrate through a counterexample that off-diagonal non-negativity alone is insufficient to guarantee global thermodynamic consistency, which additionally requires detailed balance relative to a positive stationary state \( u^* \). Building on these results, we establish that the standard graph Laplacian operator naturally satisfies both constraints via structural weight symmetry and detailed balance relative to a uniform state. Finally, we highlight the dual role of off-diagonal non-negativity in independently enforcing both the thermodynamic second law and the positive invariance of state space (state positivity).