Search Results (185)

Comparing fault-tolerant controllers for redundant manipulators requires reducing several incommensurable criteria—tracking degradation, detection latency, reconfiguration time, energy, real-time feasibility, constraint violation—to a single ordering. In practice, this is done with weighted sums whose functional form is never justified and whose weights are never audited, so that reported rankings may be artifacts of the aggregation rule. This paper supplies the missing theory; it proposes no new controller and takes the controllers being compared as given. Faults of eight kinds are written as one perturbation of the rigid-body dynamics, and post-fault task capability is characterized by the Chebyshev radius of the zonotope of attainable task velocities, which is concave in the effectiveness vector and norm-equivalent to the classical locked-joint measure. Six axioms on the aggregation step—normalization, strict monotonicity, homogeneity, continuity, non-compensability and multiplicative compounding—reduce the admissible functionals, within the quasi-arithmetic class, to the weighted geometric mean alone, excluding the weighted arithmetic mean the field currently uses. Three consequences are made computable: the score is Lipschitz with constant one in logarithmic coordinates; the exact ${\ell }^1$ distance from the nominal weights to the weight vectors that reverse a pairwise comparison has a closed form; and the effect of misspecifying the normalization constants is bounded by an explicit exponent. Distribution-free bounds give the episodes needed before a difference may be reported: 738 to state one controller’s score to within $0.05$ at $95\%$ confidence and 343 to state which of two controllers scores higher under paired sampling. A campaign of $\mathrm{32,000}$ episodes verifies every bound; shows that the excluded arithmetic mean reverses the reported ranking on three of the five plants; and quantifies how the ranking responds to the detection thresholds, the weights, and the fault distribution. Full article

This paper presents the nonlinear chaotic dynamics of a power system model within an incommensurate fractional-order framework. Equilibrium points are derived and analyzed using Jacobian-based local stability theory adapted to fractional-order systems. Furthermore, bifurcation analysis is employed to examine how variations in system parameters and incommensurate fractional orders influence the emergence of period-doubling cascades and chaotic motion. The study investigates multistability phenomena characterized by the coexistence of multiple attractors under identical system parameters. The simulation is run in MATLAB R2020a, and nonlinear tools such as time series, bifurcation diagrams, Lyapunov exponents, and phase portraits in 2D and 3D projections are used to visualize the findings. Full article

This paper proposes an entropy–topological method for the analysis of multicomponent complex systems that accounts for the relative incompatibility of system parameters, in particular physical, chemical, and other mechanisms, with configurational, thermodynamic, and other system properties. The relevance of the study is determined by the insufficient formalization of existing approaches to the description of multicomponent complex systems and the need for a universal quantitative criterion characterizing their structural and functional organization. The scientific novelty of the proposed approach lies in the decomposition of the total entropy into a spectrum of interrelated constituents and in representing the system as a multilayer network structure augmented by its thermodynamic parameters. This representation makes it possible to investigate a wide range of mutually incommensurable properties of a complex system, including its structure, information content, functionality, physicochemical features, surface phenomena (including interfaces with a supersystem), the capacity for thermodynamic imbalance, and kinetic behavior, depending on the intrinsic nature of the system under consideration. The practical applicability of the method is demonstrated through an analysis of the functional properties of geopolymer materials produced from metallurgical waste, for which an aggregated quality index is introduced that links entropy-based parameters with operational performance characteristics. The obtained results extend the capabilities of thermodynamic and information-theoretic modeling of certain classes of complex systems. Full article

In the 2020 screen-based performance Extraterritorial صوت, artists Dena Al-Adeeb, Sholeh Asgary, Leyya Mona Tawil, and Daiane Lopes da Silva develop a feminist refugee praxis through video, sound, and choreography to reclaim “post-apocalyptic landscapes … where ghosts reside at the end of the world.” Filmed along the San Francisco Bay shoreline, the work brings bodies, rocky terrain, synthetic material, and the spectral into relation with layered histories of displacement, settler colonialism, and (neo)colonial violence. Through an analysis of choreography, cinematic form, and material interaction, the essay develops “steadfastness” as an analytic for examining how performance cultivates practices of remaining within the ongoing coloniality of the postapocalypse. The analysis proceeds across three interrelated dimensions. First, it examines material persistence through the dancers’ sustained contact with shifting ground and Mylar emergency blankets, foregrounding how histories of extraction, Indigenous dispossession, and humanitarian governance endure through embodied and environmental relations. Second, it examines temporal duration, showing how delay and recurrence interrupt accelerative temporalities and cultivate an unfinished present by rendering slow violence discernible as an ongoing condition. Third, it turns to spectral persistence, where ancestral relations and colonial violence continue to inhabit bodies and landscapes while unsettling dominant regimes of visibility. Working within the incommensurable frictions between Indigenous sovereignty and SWANA (Southwest Asian and North African) displacement, these dimensions establish steadfastness as a choreographic analytic that foregrounds the labor through which livability is sustained within the postapocalypse. Full article

In this article, we consider a class of nonhomogeneous neutral linear systems with Caputo-type fractional derivatives, having incommensurate orders of differentiation and distributed delays. The main goal is to investigate the influence of the Perron condition on the stability properties of the corresponding homogeneous neutral linear system, when the nonhomogeneous system satisfies this condition. We first prove that, for any partially absolutely continuous initial functions, the investigated nonhomogeneous system has a unique global absolutely continuous solution. Furthermore, if the nonhomogeneous system satisfies the Perron condition, we establish that the fundamental and the extended fundamental matrices of the corresponding homogeneous system are uniformly bounded under certain boundedness conditions, which are also used in the classical case for systems with first-order derivatives. This uniform boundedness implies that the zero solution of the homogeneous system is uniformly stable. Finally, it is proved that the extended fundamental matrix $Q(t,s)$ tends to zero as $\mathrm{t}\to \infty$, thereby demonstrating that the zero solution of the investigated homogeneous system is uniformly asymptotically stable. Full article

This paper investigates distributed optimization-assisted output consensus for nonlinear multi-agent systems with mutually incommensurate Caputo orders, unavailable velocity-like states, bounded disturbances, measurement noise, and actuator saturation. A mixed-power exact penalty flow generates practical optimal references from local costs and intermittent neighbor broadcasts. The penalty gain and a smoothing bias bound are determined from a public interval, topology information, and certified local gradient data without prior knowledge of the aggregate optimizer. An autonomous decaying threshold provides event-triggered communication, an initial condition-independent fixed-time practical certificate for the integer-order optimizer, and exclusion of finite-time event accumulation. The physical layer is analyzed with established Caputo quadratic inequalities and agentwise Mittag–Leffler comparison. Fractional reference and command filters, a composite observer, and two-gain anti-saturation compensation form the output feedback controller, while the physical result is formulated as a finite-horizon regional verification certificate. Numerical studies include same-model and communication budget comparisons, a recent method-inspired optimizer benchmark, certificate tightening, and robustness tests for initialization, the fractional order, measurement noise, and the integration step size. Full article

The sustainability of biomass utilization as a fuel is commonly assessed through thermodynamic and ecological methods—energy, exergy, and emergy analyses—applied in isolation, each with only partial scope. Their integration through multicriteria analysis has been proposed for the sugar industry, but has not yet been formalized as a reproducible, auditable, and generalizable protocol: neither the logical sequence linking balances and decision-making, nor an explicit sustainability rule, nor the treatment of the incommensurability between thermodynamic and ecological accounting has been established. This work formalizes such a protocol in three stages: (i) definition of fuel alternatives and screening of criteria through the Delphi method; (ii) characterization of each alternative through three coupled balances—energy (quantity), exergy (quality), and emergy (environmental cost); and (iii) integration through the Analytic Hierarchy Process (AHP) into a single sustainability ranking with an explicit decision rule, supported by a robustness layer based on Monte Carlo simulation and multi-method comparison. The protocol is demonstrated in the Cuban sugar industry using two steam generators (G.V. VU-40 and Retal-type steam generator) and variants of bagasse, agricultural harvest residues (AHR), and marabou (Dichrostachys cinerea). In the demonstration, AHP weighting ranked the emergy criterion above the exergy and energy criteria (priority vectors 0.539, 0.297, and 0.164, respectively; consistency ratio 0.008), and the bagasse alternative emerged as the most sustainable in both technologies despite not being the most efficient. The robustness analysis confirmed that this verdict is stable: bagasse Pareto-dominates the independent emergy indicators and remains the best alternative in more than 95% of the weight space. The contribution of the work is methodological—the formalization and generalization of the protocol—while the case study illustrates its operation and does not constitute a statistical validation. Full article

Multi-objective optimization provides the mathematical foundation for reasoning about trade-offs in complex decision problems, from engineering design to resource allocation. Software testing exemplifies such problems: practitioners must simultaneously optimize for fault detection capability, code coverage, execution cost, and test suite diversity—objectives that are fundamentally incommensurable. Since the early 2000s, multi-objective evolutionary algorithms (MOEAs) such as NSGA-II, MOEA/D, and their many-objective extensions (MOSA; DynaMOSA) have served as the dominant mathematical framework for navigating these trade-offs through Pareto-front approximation with hand-crafted fitness functions. However, the recent emergence of reinforcement learning (RL) and large language models (LLMs) is shifting the optimization paradigm from numerical Pareto-front approximation toward neural, semantically aware decision making over learned representations. This paper presents a systematic mapping study of multi-objective optimization algorithms, tracing their evolution from classical Pareto-based methods toward AI-driven and hybrid approaches, with software testing as the primary application domain. We survey 120+ papers published from 2000 to 2025 and propose a novel five-level taxonomy (L1–L5) that classifies optimization approaches along the intelligence spectrum: classical MOEAs, ML-guided MOEAs, RL-driven optimization, LLM-driven optimization, and hybrid neuro-evolutionary systems. For each level, we analyze the mathematical problem formulations (Pareto optimality conditions, Markov decision processes, and neural loss landscapes), objective function design, algorithmic convergence properties, and computational complexity. We further conduct a cross-cutting mathematical analysis comparing these paradigms along dimensions of convergence, diversity, scalability, and interpretability. Our survey identifies critical open mathematical challenges: the lack of formal convergence guarantees for LLM-driven optimization, the under-exploration of many-objective ($m\ge 4$) formulations in AI-driven testing, the sample complexity of reinforcement learning for combinatorial test optimization, and the absence of standardized benchmarks with known Pareto-optimal frontiers. We conclude by outlining a research roadmap for the next generation of multi-objective optimization systems that combine the complementary mathematical strengths of neural function approximation and evolutionary diversity preservation. Full article

The development of artificial intelligence has proceeded within a disciplinary culture whose positivist epistemological foundations generate a constitutive blind spot: the systematic exclusion of tacit, embodied, relational and contextually situated knowledge from what counts as knowledge at all. This article argues that this exclusion is not a technical limitation, but a structural condition of AI systems as currently built, with serious consequences for individuals, institutions and the social order. The method is interdisciplinary and critically synthetic, integrating the anthropology of science and technology, the philosophy of language and the literary-philosophical tradition of techno-critique. Three original contributions are advanced. First, the Faustian framework is reformulated as a collective rather than individual pact: the AI contract implicates a civilisation. Second, the prevalent reductionist critique is refined: the error is not quantification of incommensurable goods but the enforcement of total orderings upon value landscapes that admit only partial orderings. Third, the stochastic parrot objection is reconciled with the Faustian analysis through the concept of institutional amplification: AI’s danger resides not in its intelligence but in the authority conferred upon its incomprehension. The article concludes that Mephistopheles, not Faustus, is the more precise figure for AI itself, and asks whether the defunding of humanities disciplines, those best placed to navigate the moral challenges AI presents, constitutes the most consequential characteristic deletion of all. Full article

Complex nonlinear dynamical systems, often associated with high-entropy time series, have been widely employed to describe and predict intricate dynamic phenomena in real-world systems. Motivated by the need to better understand such complex dynamics in network-based epidemic processes, this paper investigates bifurcation dynamics in a fractional-order extension of the classical Susceptible–Latent–Breaking–Out model for computer virus propagation. The proposed framework incorporates two distinct transmission-related time delays and employs Caputo fractional derivatives of incommensurate orders, with the delays associated with infection rate and latent period selected as the primary bifurcation parameters. Due to the combined influence of multiple delays and incommensurate fractional exponents, the resulting system exhibits a complexity that goes beyond most existing models in the literature. By linearizing the model around its endemic equilibrium and analyzing the associated characteristic roots, we characterize how the system’s qualitative behavior depends on the magnitudes of the time delays, and establish explicit sufficient conditions for bifurcation to occur. In particular, the endemic equilibrium remains asymptotically stable as long as each delay stays below a certain critical value; once any delay exceeds its threshold, the system undergoes a Hopf bifurcation, leading to sustained periodic oscillations in virus prevalence. Numerical simulations are provided to support the analytical results, and they show strong agreement between predicted and observed system responses. These findings enhance theoretical insight into bifurcation mechanisms in fractional-order delay models of epidemic dynamics on networks, and may offer useful guidance for designing containment strategies in large-scale interconnected systems. Full article

Maximizing the dominant Lyapunov exponent ${\lambda }_1$ of an incommensurate fractional-order chaotic system, while respecting the dynamical conditions for a strange attractor, is a non-convex, gradient-free problem on a history-dependent landscape. Existing metaheuristic studies typically use hard-cutoff penalties that distort the fitness landscape and integer-order Lyapunov estimators that can be biased for strongly fractional regimes. This paper presents a constraint-faithful optimization framework combining (i) subtractive-hinge penalties that vanish on the feasible set, (ii) a memory-consistent Grünwald–Letnikov variational Lyapunov estimator with adaptive tail-sum truncation, (iii) joint search over parameters and incommensurate orders by the Marine Predators Algorithm, and (iv) a fractional conditional Lyapunov exponent (FCLE) that recovers the integer-order limit. Applied with a fixed configuration to the fractional-order Lorenz, Ma–Chen financial, Iqbal–Wang, and Hyper–Chen systems, the framework converges to feasible attractors with enlarged Lyapunov spectra. Dissipativity is rigorously verified; all selected optima have strictly negative Lyapunov trace at the reported precision. FCLE analysis on the optimized Lorenz attractor recovers the integer-order identity $c_{min}={\lambda }_1$ under full-state coupling, and shows that single-state x-coupling raises the threshold to ≈9${\lambda }_1^{*}$. The optimized fractional-order Lorenz attractor is employed as the random-number generator of a recent chaos-based image-encryption scheme, where it yields strong statistical results across standard benchmarks. Full article

In the present work, we study a class of nonhomogeneous linear systems with fractional derivatives in Caputo’s sense of incommensurate order and distributed delays, satisfying the Perron condition. More precisely we study the impact of the Perron condition on the boundedness of the fundamental and extended fundamental matrices of the corresponding homogeneous system. We prove that if the nonhomogeneous system satisfies the Perron condition, then the fundamental matrix $C(t,s)$ and the extended fundamental matrix $Q(t,s)$ of the homogeneous system are uniformly bounded. As a consequence we obtain that the boundedness of the matrix $Q(t,s)$ is a necessary and sufficient condition for the uniform stability of the zero solution of the homogeneous system. Furthermore, we also prove that the extended fundamental matrix $Q(t,s)$ tends to zero when $t\to \infty$, which is a necessary and sufficient condition for the uniform asymptotic stability of the zero solution of the homogeneous system under study. Full article

Structural superlubricity enables ultralow friction and wear–free sliding by cancellation of lateral forces at incommensurate, weakly interacting interfaces. However, edge–induced friction remains non–negligible. In this work, we systematically quantify edge–induced friction in atomically smooth single–crystal graphite/graphite interfaces using a controlled edge–contact architecture. By introducing holes with well–defined geometries and sizes, we systematically vary the total contact edge length while preserving the crystallinity and atomically smooth morphology of the interior graphite surface. The results reveal that friction enhancement in the patterned graphite/graphite interface is dominated by edge–mediated interactions at the hole boundary, demonstrating that total edge length, rather than real contact area, is the primary parameter governing interfacial friction. This outcome diverges from conventional contact–area–dependent friction theories, bringing to light the paramount importance of edge contributions in structurally superlubric interfaces. We show that engineering the hole perimeter provides a route to tuning friction in layered materials without changing material composition or external operating conditions. Full article

AMn₇O₁₂ perovskites (with A = divalent elements) show complex structural and magnetic transitions including incommensurate orbital density waves and coupled/decoupled modulated spin helicity originating from charge-ordered Mn³⁺/Mn⁴⁺ cations with the 3:1 ratio at the B perovskite sites and unusual apically compressed Jahn–Teller distortions of MnO₆ octahedra. The same Mn³⁺:Mn⁴⁺ ratio can be achieved in RCuMn₆O₁₂ compositions, where R is a trivalent rare-earth cation. Therefore, the comparison in behavior of AMn₇O₁₂ and RCuMn₆O₁₂ is of interest. In this work, the A-site-ordered quadruple perovskite NdCuMn₆O₁₂ was prepared by a high-pressure high-temperature method. Its structural properties were investigated by synchrotron powder X-ray diffraction between 100 K and 350 K and laboratory powder X-ray diffraction between 5 K and 300 K. It shows a first-order structural phase transition from Im-3 symmetry (at high temperatures) to R-3 symmetry near 292 K. The structural transition is accompanied by charge (Mn³⁺/Mn⁴⁺) and unusual orbital (on the Jahn–Teller active Mn³⁺ cations located in MnO₆ octahedra) orders. However, no additional structural/orbital modulations were found at lower temperatures in comparison with AMn₇O₁₂. Magnetic properties were investigated by temperature- and field-dependent magnetization and specific heat measurements, where a ferrimagnetic transition was found near 120 K. In addition, low-temperature magnetic anomalies were observed near 20 K, probably originating from the Nd sublattice. Full article

In her approach to religious pluralism, Jeanine Diller has advocated for partialism, the view that multiple religious engagement is needed for knowledge of the Ultimate. In this article, I expound on partialism, which I interpret as a transreligious view that posits a noetic threshold for knowledge of the Ultimate. Given this interpretation, I argue that there are two central ambiguities that the partialist needs to clarify. First, the partialist needs to explain whether the noetic threshold should be understood in a metaconceptual or perspectival manner. Second, the partialist needs to explain whether a tradition’s noetic contributions are commensurable or incommensurable. I identify some of the advantages and disadvantages of each option, and I conclude with some future directions for partialist transreligious pluralism. Full article