Computer Science and Mathematics

Abstract: This paper examines the local asymptotic behavior of the distance \( \left\lVert T\left(t+\xi \left(t\right)\right)-T\left(t\right)\right\lVert \) near the origin, where \( {\left(T\left(t\right)\right)}_{t\gt 0} \) is a semigroup on a commutative Banach algebra and \( \xi ∶\left]0,+\infty \right[\rightarrow \left]0,+\infty \right[ \) is a continuous function satisfying \( \operatorname{\underset{t\rightarrow 0^{+}}{\lim⁡\inf}\ }{\frac{\xi \left(t\right)}{t}\gt 0} \). Our first main result establishes that if the closed subalgebra A generated by the semigroup \( {\left(T\left(t\right)\right)}_{t\gt 0} \) is nonunital, then \( \operatorname{\underset{t\rightarrow 0^{+}}{\lim⁡\sup}}{\left\lVert T\left(t+\xi \left(t\right)\right)-T\left(t\right)\right\lVert \gt 0} \). As an application, we derive an exact asymptotic formula for the disk algebra \( A(\bar{\mathbb{D}}) \). Considering the semigroup \( {\left(T\left(t\right)\right)}_{t\gt 0} \) on \( A(\bar{\mathbb{D}}) \), given by \( \left(T\left(t\right)f\right)\left(z\right)=f\left(e^{-t}z\right) \) for \( f\in A(\bar{\mathbb{D}}),\ z\in \mathbb{D} \), and assuming that \( \lim_{t\rightarrow 0^{+}}{\frac{\xi \left(t\right)}{t}=\mathrm{\gamma }\ } \)finite, we prove that \( \operatorname{\underset{t\rightarrow 0^{+}}{\lim⁡\sup}}{\left\lVert T\left(t+\xi \left(t\right)\right)-T\left(t\right)\right\lVert =\frac{\gamma }{{\left(1+\gamma \right)}^{1+\frac{1}{\gamma }}}} \). Furthermore, the closed subalgebra generated by this semigroup is nonunital.

Abstract: The JSSP is recognized as one of the most difficult combinatorial optimization problems because it can be classified as an NP-hard problem. In this study, three metaheuristics are presented and evaluated. The first metaheuristic, EGD-ILS, is a new hybrid metaheuristic. The first phase constructs a feasible solution via Gradient Descent on a convex energy function, with a fixed operation sequence. We provide a mathematical proof of convergence for this phase to a feasible solution. The second phase applies an Iterated Local Search to explore the solution space and minimize the makespan. This separation of objectives guarantees convergence of the initial phase and simplifies parameter tuning. The second metaheuristic, termed Priority-based Metaheuristic, constructs schedules according to priority scheduling rules based on ILS. On the other hand, the third metaheuristic, which is termed Permutational Coding-based Metaheuristic, is built on the idea of coding each operation as a permutation of the operations. In order to test the performance of the three metaheuristics, computational tests are conducted in MATLAB using the standard benchmark to investigate the performance of the problems solved. Experiments on standard FT and LA benchmarks show that EGD-ILS achieves competitive results with reduced computation time.

Abstract: The powerful earthquake that struck Japan on 11 March 2011 produced one of the most destructive and catastrophic tsunamis in recent times. Despite Japan’s extensive tsunami preparedness and mitigation measures, the event caused more than 18,000 fatalities and severe damage to coastal infrastructure. Accurate estimation of tsunami wave heights is therefore essential for coastal hazard assessment. In this study, time-series water-level data associated with the 2011 tsunami were obtained from NOAA for 24 tide gauges distributed across the Pacific Ocean. Several probability distributions were fitted to the observed data, with the Weibull and Generalized Extreme Value (GEV) distributions providing comparable fits. The fitted models were used to estimate maximum wave heights for return levels of 5, 10, 25, 50, and 100 years at selected coastal locations. Although the GEV distribution generally provided a better fit, the Weibull distribution was selected for further analysis because it can be applied directly to the observed data. Comparison with observed maximum wave heights showed that the conventional Weibull distribution did not consistently capture the upper tail. Therefore, a modified Weibull distribution was proposed by introducing an additional constant. Parameter sensitivity analysis demonstrated that the transformation parameter substantially increases the estimated upper-tail wave heights, indicating its potential for improved extreme tsunami-wave estimation. Further validation using independent datasets and formal statistical tests is required.

Abstract: A single-valued neutrosophic extension of adaptive-agent-based network models for the study of host–guest interactions in migration contexts is proposed. Unlike the classical formulation developed by Chuang, Chou, and D’Orsogna, each agent is described by a single-valued neutrosophic attitude ⟨T, I, F⟩ ∈ [0, 1]³, quantifying, respectively, the propensity toward integration-oriented acceptance (T), indeterminacy (I), and segregation-oriented rejection (F). Compared with a purely scalar attitude model, this framework separates acceptance, refusal, and undecidedness, which is crucial in migration contexts where an observed moderate position may correspond either to a genuine compromise or to unresolved ambiguity. Moreover, it captures key characteristics of social interactions more effectively. The proposed model contributes in three main directions. First, the network structure is extended from the Erdős-Rényi random baseline to Watts-Strogatz small-world and Barabási–Albert-type scale-free topologies. Second, the utility function is made capacity-dependent: agents with higher socioeconomic reward and higher neutrosophic scores can maintain more social connections without a proportional loss of effectiveness. Third, the rewiring process is refined by combining multi-agent Q-learning with a Dezert-Smarandache-inspired trust aggregation mechanism. This allows agents to learn whether keeping, adding, or deleting social ties is advantageous over the long term, while candidate selection combines pairwise similarity with trust, prestige, and degree-based visibility. Numerical simulations compare random, small-world, and scale-free networks, examine the evolution of an integration index, and illustrate how the model can be used to scan migrant-fraction sensitivity and possible neighbourhood-tipping thresholds.

Abstract: Monitoring and forecasting environmental thresholds in data-scarce ecosystems poses a critical challenge for resource management. In this study, we evaluate four forecasting paradigms—Seasonal Autoregressive Integrated Moving Average (SARIMA), Light Gradient Boosting Machine (LightGBM), Long Short-Term Memory (LSTM) networks, and Echo State Networks (ESNs)—to model and reconstruct historical landing dynamics of a shallow-water shrimp fishery. The historical time series exhibits severe data gaps, including continuous unmonitored periods spanning up to six years. To assess real-time deployment feasibility, all models were benchmarked on an embedded NVIDIA Jetson Orin Nano edge platform using walk-forward validation (h=1). Empirical results demonstrate that the ESN architecture captures the non-linear temporal dynamics of the fishery, achieving the highest predictive accuracy (MAE=1.37t, RMSE=1.96t, and RMSSE=0.70). A bidirectional forecasting-backcasting reconstruction strategy filled the multi-year gaps and confirmed that the landing decline occurred abruptly after 2013. For edge computing applications, the ESN achieved low latency, executing sub-millisecond inference (0.27ms) and a fast training time per fold (424.44ms) while consuming less energy than LSTM. These findings indicate that projecting dynamics into a high-dimensional fixed reservoir provides a computationally efficient solution for continuous time-series reconstruction and landing trend detection under severe data and hardware constraints.

Abstract: Futures markets exhibit nonlinear interactions, multi-scale dynamics, and non-stationary behaviour, rendering traditional linear risk models inadequate for tracing extreme-event transmission or measuring systemic fragility. We propose an integrated entropy–multifractal framework to measure systemic risk across three levels. At the micro level, High-Order Moment Multiscale Entropy quantifies local complexity. At the meso level, Weighted Cross Permutation Entropy and Multifractal Detrended Cross-Correlation Analysis identify directional contagion and tail co-movement. At the macro level, Multidimensional Scaling, Multivariate Permutation Entropy, and rolling-window analysis capture network structure, regime shifts, and time-varying risk.Using daily data from 16 global futures and financial variables (2018–2025), the empirical analysis yields three findings. Micro-level results show a structural divergence: emerging-market assets are extremely unpredictable, whereas developed-market assets maintain stable volatility. Meso-level findings reveal a stable causal hierarchy: energy markets transmit risk to agricultural commodities, while US–China equity co-movement is driven by common factors, not direct contagion. Macro-level results show that common factors dominate the futures system, with geopolitical risk isolated as exogenous; system complexity decays monotonically with horizon, and the complexity gradient signals crises in advance.We further propose and validate three risk indicators: the Fractal Vulnerability Index, the Causal Contagion Index, and the Systemic Chaos Indicator. These findings inform horizon-dependent portfolio construction, early-warning system design, and macro-prudential risk monitoring in futures markets.

Abstract: Water allocation in capacity-constrained canal trees with conveyance losses requires local limits and guaranteed service to be considered simultaneously. We develop a deterministic three-stage lexicographic model for a rooted tree with fixed routes. Stage 1 maximizes the minimum service ratio, Stage 2 maximizes weighted seasonal satisfaction subject to that guarantee, and Stage 3 minimizes temporal service-ratio variation while preserving the preceding optima. The nonnegative packing structure yields the Stage-1 optimum in closed form from capacity-to-full-load ratios; the loss-aware path operator is equivalent to node balance and determines unique gross flows. In five exact benchmarks, the maximum discrepancy between the closed-form and linear-programming solutions was 1.11×10⁻¹⁶, with zero operator–balance residual. Scaling tests with up to 500 users and 1022 edges yielded a maximum discrepancy of 2.22×10⁻¹⁶. In the three-period test, the temporal variation ranged from 0.40 to 1.05 over the Stage-2 optimal face, and Stage 3 attained 0.40. The price of fairness was 3.29% in the controlled Gone Abat Jap scenario. The results provide a model-specific analytical characterization and a reproducible computational framework for loss-aware allocation on fixed-route irrigation trees.

Abstract: Dynamic roll-on/roll-off terminals require an executable decision between yard planning and vessel stowage: which yard lane to release, how many accessible vehicles to move, and which ferry lane to receive the ordered batch. We formulate this interface as state-aware hierarchical batch control. Each action selects one yard queue, a FIFO-prefix length, and one receiving lane/deck, while complete enumeration screens compatibility, residual capacities, discharge order, slot continuity, and a transverse-moment envelope. All controllers receive the same physical execution-time budget, with one setup-time unit plus one unit per moved vehicle. A two-step beam model-predictive controller (HBC-MPC) minimizes the first-stage cost plus the optimal feasible second-stage cost and terminal backlog. We prove FIFO integrity, modeled action safety, recursive admissibility, completeness, and dominance of the endogenous feasible set over any included fixed size. The study uses 180 paired synthetic paths across three fleet regimes, three arrival intensities, and 20 seeds, yielding 1080 policy runs. Every final and intermediate feasibility audit passes. HBC-MPC loads 63.33 vehicles per sailing on average, versus 62.87 for myopic endogenous and largest-feasible control, 62.74 for fixed-four with cleanup, 44.53 for strict fixed-four, and 41.80 for strict fixed-six. Its mean weighted waiting area is 204.47, and its gain over strong adaptive baselines is modest but positive. The evidence supports state-dependent batching; predictive lookahead provides an additional benefit at substantially higher computation.

Abstract: This paper addresses the fixed-time adaptive stabilization problem for a class of underactuated mechanical systems governed by Euler-Lagrange dynamics with matched parametric uncertainty. Unlike conventional adaptive schemes that guarantee only asymptotic convergence and usually assume stable internal dynamics, we develop a framework that (i) drives the actuated coordinates and the parameter-adaptive sliding manifold to the origin in a fixed time whose upper bound is independent of the initial condition, and (ii) supplies an explicit Lyapunov certificate for the zero dynamics induced by underactuation, thereby removing the minimum-phase assumption. The controller couples partial feedback linearization with a recursive fixed-time backstepping design and an online \( \sigma \)-modified adaptation law that preserves the structural properties of Euler–Lagrange systems. A composite Lyapunov function handles the coupled actuated/unactuated dynamics and yields a differential inequality of the form \( \dot V \le -\alpha V^{p}-\beta V^{q} \) with 0 < p < 1 and q > 1, which certifies fixed-time reaching on the actuated channel. A separate internal-dynamics certificate establishes input-to-state stability of the unactuated coordinate with respect to the actuated error, so all closed-loop signals are globally bounded and the full state converges to the origin under matched uncertainty. Numerical studies on the translational oscillator with rotational actuator (TORA) and the cart–pole show the initial-condition-independent settling of the actuated channel and quantify the advantage over an asymptotic adaptive baseline.

Abstract: Accurate and computationally efficient numerical modelling of shallow-water flows is essential for flood prediction and hydrodynamic risk assessment. This study develops an implicit finite-difference scheme for the numerical solution of the two-dimensional shallow water equations. First, the main numerical approaches used for shallow-water modelling, including finite-difference, finite-volume, finite-element, and discontinuous Galerkin methods, are analysed in terms of accuracy, stability, treatment of discontinuities, and computational requirements. Based on this analysis, an implicit finite-difference formulation is developed that uses central approximations for spatial derivatives and averages flow variables at cell boundaries. The nonlinear terms are treated using Newton linearization, resulting in an iterative scheme that allows larger time steps than explicit formulations constrained by the Courant-Friedrichs-Lewy condition. The proposed method is implemented in MATLAB as a computational module for two-dimensional hydrodynamic simulations. Its performance is demonstrated on a test problem that describes the propagation of an initially localised disturbance in a rectangular computational domain with rigid boundaries. The numerical results demonstrate stable wave propagation, conservation of the modelled flow dynamics, and physically consistent boundary reflections. The developed approach provides a computational basis for further integration of shallow-water hydrodynamic models with spatial data and geographic information systems for flood forecasting and risk assessment.

Abstract: Compressible rotational gas–particle flows at high Mach numbers are ubiquitous in advanced powder processing technologies, including cyclone separators, supersonic jet mills, and pneumatic conveying systems. Accurate predictive modelling remains profoundly challenging due to long-range nonlocal particle interactions, anomalous diffusion and viscoelastic memory effects, and shock discontinuities that render classical local models inadequate. To address these challenges, we develop a rigorous mathematical framework that replaces the classical Laplacian with a nonlocal integral operator constructed from symmetrized neural kernels, coupled with a Caputo fractional time derivative of order β∈(0,1) to model subdiffusive transport and rheological memory. A generalised Voronovskaya-type theorem for neural kernel operators furnishes sharp pointwise error bounds and convergence rates even in the presence of discontinuities, rigorously justifying the neural operator approximation. Employing a Lyapunov-Schmidt reduction adapted to this fractional nonlocal setting, we establish the existence, uniqueness, and linear stability of multi-bubble solutions representing interacting coherent structures. The asymptotic expansion of the reduced energy functional yields a novel scaling law λ_m ∼ C_sm^1/s, where s∈(1/2,1) is the fractional exponent — fundamentally different from the classical local case s=1, where λ_m∼Cm. The framework is validated against experimental and LES data for a Stairmand cyclone separator, achieving RMSE values of 12.39–19.32% across Mach numbers M=1.0, 2.0, 5.0. The fractional model outperforms classical semi-empirical correlations by up to 70% in predictive accuracy. This work bridges advanced functional analysis with engineering practice, providing a solid foundation for reliable simulations and design optimisation of powder processing equipment, and paving the way for physics-informed neural operator architectures with guaranteed stability and convergence in industrial compressible multiphase flow applications.

Abstract: This paper extends the optimal investment control framework by incorporating fractional Brownian motion to capture long-range dependence and memory effects in asset prices. Replacing the standard Brownian component with a fractional Brownian motion governed by the Hurst parameter H, we employ the Wick–Itô calculus to derive the associated Hamilton–Jacobi–Bellman (HJB) equation. The resulting nonlinear PDE contains a time-dependent diffusion coefficient that reduces to the classical model when H = ½. We apply a linearized generalized Newton method to construct an iterative sequence for the value function, and prove its convergence via the contraction mapping theorem. The proposed framework provides a dynamic optimal investment ratio π*(t) that adjusts to market memory, offering a more realistic strategy for portfolio management under both jump and long-memory risks.

Abstract: This paper establishes a local fixed point theorem for multivalued mappings in zero-complete strong partial (b)-metric spaces and develops a framework for modelling multistage processes with several admissible terminal states. The contractive condition is formulated using a Bianchini–Grandolfi gauge function and the associated excess functional. Unlike global principles, the theorem requires contractive assumptions only within a prescribed closed ball. A localization condition keeps the successive approximations inside this ball, while an adapted chain estimate proves that the iterative sequence is zero-Cauchy. The proof does not require the family of partial (b)-metric balls to form a topological basis; the ball serves only as a localization set, and the limiting argument relies on zero-completeness and the zero-closedness of the mapping values. The main theorem guarantees a fixed point for a multivalued mapping and, under an additional condition, uniqueness in the single-valued case. Its consequences include local and global principles for linear set-valued contractions, a partial metric version, and a local Banach-type theorem. A further contribution is a method for constructing strong partial (b)-metrics from bounded metric spaces and prescribed nonempty target families. A nonlinear transformation of the original metric is combined with the transformed distances from the target family. Thus, the self-distance of each point is determined by its position relative to that family and vanishes precisely on it. This provides a natural model for processes with several distinct but equally stable terminal states. The theory is illustrated through a finite model of linguistic enrichment. Twenty formulations of the same mathematical statement are arranged into successive levels of grammatical, terminological, logical, and stylistic refinement. A weighted revision graph generates the generalized distance, while the self-distance represents the remaining effort required to reach a stable formulation. A multivalued revision mapping allows several admissible improvements at every stage. The model admits two distinct stable formulations: a concise formal version and a more explanatory, pedagogically oriented version. Both require no further essential revision but remain distinct. This demonstrates that stabilization need not imply uniqueness and that different enrichment trajectories may lead to different acceptable terminal texts. More generally, the example shows how generalized fixed point methods can describe local, nonunique, and multistage stabilization processes in language dynamics and related nonlinear systems.

Abstract: We develop a theory of informational privacy for parametric deterministic dynamical systems observed in real time through a noisy channel. Starting from the Kullback–Leibler divergence between the law of observations and a reference law, we define the absolute privacy factor as the exponential of the negative KL rate. We then construct a relative Fisher metric on the space-time parameter manifold and an associated relative informational energy functional whose stationary curves are characterized as eigenfunctions of a variational eigenvalue problem, with eigenvalues quantifying the leakage-per-unit-work trade-off. The spectral problem is analyzed in full in the linear Gaussian setting via the Galerkin method, yielding a finite-dimensional approximation with monotone convergence. A sharp lower bound on the privacy factor in terms of the first eigenvalue establishes the fundamental privacy-efficiency trade-off intrinsic to the system. The resulting framework provides a constructive and deterministic solution: the first eigenfunction of the spectral problem is the optimal perturbation of a nominal parameter trajectory that, for a prescribed kinetic budget, maximises the time over which an observer—accessing only the observables—cannot determine the nominal parameter with statistical certainty.

Abstract: We introduce Hybrid Physics-Aware Sparse Neural Networks (Hy-PAS), a framework for solving ordinary and partial differential equations that reinterprets classical meshless partition-of-unity approximation as a structurally sparse neural network. Each trainable parameter of Hy-PAS corresponds to a concrete physical or numerical quantity a node position, a kernel width, or a nodal amplitude so that the trained model is directly interpretable and its basis adapts to the solution during optimization. The construction recovers radial-basis-function collocation as a special case when node positions and widths are frozen, and connects to physics-informed neural networks (PINNs), the Deep Ritz method, and finite-basis PINNs. We implement Hy-PAS together with a dense PINN and the Sparse, Physics-based, and partially Interpretable Neural Network (SPINN) in a common PyTorch training and evaluation harness, and benchmark all three on seven problems spanning ordinary, elliptic, parabolic, hyperbolic, and nonlinear PDEs, including the lid-driven cavity flow at Re=100. Across three random seeds per configuration, Hy-PAS attains the lowest relative L₂ error on four of the seven benchmarks using roughly an order of magnitude fewer trainable parameters than the dense PINN, while SPINN is most accurate on the Helmholtz and heat problems and PINN on the viscous Burgers problem. A parameter-scaling study shows Hy-PAS reaching ∼10−4 relative L2 error with a few hundred parameters and saturating, whereas the dense PINN plateaus near 10−1 even at 5×104 parameters. Ablations quantify the requirement that kernel smoothness match the differential order of the operator and a genuinely sparse operating regime in which accuracy is flat from 11% to 44% kernel–collocation connectivity. We report all results honestly, including the benchmarks on which Hy-PAS is not the most accurate method, and provide the full implementation for reproduction.

Abstract: FEFLOW is used to provide a design stage analysis of seepage flow through a tailings storage facility constructed by on-dam cycloning, including phreatic surface level, drain flows, and water balance. Significant differences between simulation results and measurements of dam crest piezometer data and foundation flows highlight possible structural issues with hydraulic conductivity gradient of the tailings beaches, hydraulic conductivity of the downstream shells, and internal erosion. Partial saturation of tailings beach material is accounted for by solving Richards’ transient flow equation throughout facility staged construction, using MATLAB seepage analysis of an idealized 1D staged construction processes as an initial benchmark for setting FEFLOW time stepping and mesh size parameters. Seepage analysis of an idealized 2D staged construction process is used to clarify the importance of solving Richards’ transient flow equation for accurate tailings dam phreatic surface location.

Abstract: Classical turbulence closures systematically fail in high-Mach rotating flows because they introduce excessive dissipation and cannot capture the non-equilibrium effects that govern the dynamics. This limitation severely compromises the predictive reliability of thermal-hydraulic simulations for gas-cooled nuclear reactors. To overcome this challenge, we develop a rigorous numerical framework that seamlessly integrates a structure-preserving Lattice Boltzmann Method with a Physics-Informed Neural Network correction, grounded in hypocoercive stability theory. At the heart of our approach lies the Santos-Andrade inequality, a novel stability criterion that explicitly quantifies the competing influences of rotation, compressibility, and neural-network corrections, thereby offering a mathematically certified threshold for stable data-driven closures. We derive second-order convergence estimates for the semi-discrete LBM–PINN scheme and validate the framework against the canonical Taylor-Couette flow at Mach numbers 5.0 and 10.0. At Ma=10.0, classical closures — Smagorinsky, RANS, and SAS — fail catastrophically, producing unphysical constant temperature and pressure fields. In striking contrast, the Smagorinsky+PINN scheme uniquely restores a realistic radial temperature gradient and delivers a physically plausible Nusselt number of 17.14. The observed Lipschitz constant Lθ≈2.96 lies comfortably below the stability limit, confirming the practical utility of the Santos-Andrade criterion for high-fidelity nuclear thermal-hydraulic simulations.

Abstract: Collusion is inherently unstable because individual firms have incentives to deviate from cooperative agreements. We study a novel hybrid oligopoly market structure, termed a failed cartel, in which one firm abandons a cartel agreement while the remaining firms continue to coordinate their production decisions. We further reinterpret the Cournot–Stackelberg hybrid structure as a natural punitive benchmark following cartel breakdown, in which the remaining firms abandon cooperation and compete while facing the deviating firm as a common Stackelberg follower. From a game-theoretic perspective, each firm’s quantity choice depends on its own action, its rivals’ actions, and the resulting market state. While simple inverse demand and cost functions permit equilibrium analysis by classical profit maximization, nonlinear specifications used in oligopoly research, such as isoelastic inverse demand, generally do not yield explicit reaction functions or closed-form equilibria. We therefore represent strategic adjustment as an iterative game generated by firms’ reaction mappings: at each stage, firms revise their production quantities in response to the current market configuration. Tripled fixed points of the resulting mapping characterize equilibrium and provide conditions for existence, uniqueness, stability, and convergence of successive quantity adjustments. Numerical comparisons, ranging from an illustrative triopoly to the asymptotic regime with many firms, characterize how the failed-cartel and punitive Cournot–Stackelberg structures differ from classical markets in terms of output, prices, profits, consumer surplus, and total welfare.

Abstract: Adaptive systems that couple inference to irreversible commitment are governed by a rate-capacity law analogous to Shannon's: agency persists only while the induced informational flux R_self remains below the integrative capacity C_self. We define Recoverable Self-Coding (RSC), a structural framework in which the self - human, organizational, or artificial - is a self-decoder whose feasibility is tracked by a small set of measurable parameters: the capacity ratio CR = R_self/C_self, the margin M = C_self - R_self, the accessible-option entropy H_self, an exploration temperature T, and a finite integration horizon. Sustained CR > 1 makes state evolution non-invertible: options are eliminated faster than they can be reconstituted, and recovery cannot be restored by effort, intelligence, or optimization. We show that the parameters are directly estimable from open longitudinal event streams, verifying the construct on four open cohorts - synthetic health records (~1,900 units), the MIMIC-IV and eICU demonstration cohorts, and ~40,000 ICU stays from the PhysioNet/CinC 2019 sepsis challenge - where critically ill patients concentrate at the feasibility boundary CR ≈ 1 and outcome-labelled populations (sepsis; death in unit) sit measurably deeper into infeasibility without any fitted model. Applications are developed for healthcare capacity monitoring; for human agency under rate shocks - episodes, from a serious diagnosis to AI adoption, that abruptly multiply the induced flux against slow-adapting personal capacity; and for operational systems whose certification backlogs are directly observable. Annealing - regulated exploration followed by feasibility-paced consolidation - emerges as the admissible dynamics for staying recoverable under acceleration.

Abstract: Multicollinearity and heteroscedasticity are common problems in linear regression analysis that can adversely affect the stability, precision, and efficiency of parameter estimates. Although the generalised Liu-type estimator is useful for reducing the effect of multicollinearity, its performance depends largely on the appropriate selection of its shrinkage parameters. This study developed and evaluated improved generalised Liu-type estimators by modifying the shrinkage parameters (k) and (d) of the existing generalised two-parameter Liu estimator. Three improved parameter combinations, namely (k₁d₁), (k₂d₂), and (k₃d₃), were proposed and assessed using their mean square error properties. A Monte Carlo simulation study with 1,000 replications was conducted using sample sizes of (n=10, 20, 30, 50, 75,100), correlation levels ranging from (ρ = 0.7, 0.75 0.8, 0.85, 0.9, 0.95, 0.99) different error variances, and varying levels of heteroscedasticity. The performance of the estimators was evaluated using the mean square error (MSE) criterion and ranking procedure. The results showed that the improved estimators generally outperformed the original generalised Liu-type estimators in small and moderate sample sizes. In particular, the (k₂d₂), improvement based on 1/(Max⁡(VIF_s )) frequently produced the minimum mean square error under moderate and severe multicollinearity. The (k₃d₃) improvement was particularly useful in very small samples, whereas the original estimators remained competitive under extremely high multicollinearity and large sample sizes. The Portland Cement data application supported the simulation findings, with the second improvement emerging as the best overall alternative. The study concludes that the proposed improved generalised Liu-type estimators provide useful alternatives for regression models affected by multicollinearity and heteroscedasticity.