Search Results (1,070)

This paper develops a dynamic asset allocation strategy for defined contribution pension funds using a stochastic control framework under the Heston stochastic volatility model. By solving the associated Hamilton–Jacobi–Bellman partial differential equation, we derive optimal equity allocations that adapt to changing market volatility and investor risk aversion using a constant relative risk aversion utility function (parameter $\gamma$). The strategy increases equity exposure during stable periods and reduces it during volatile regimes, capturing both myopic and intertemporal hedging demands. We test the model using historical U.S. data from 2006 to 2025 and benchmark its performance against a traditional static 60/40 stock–bond portfolio, as well as rule-based strategies such as volatility targeting and constant proportion portfolio insurance. Our results show that with moderate risk aversion, the dynamic strategy achieves long-term wealth comparable to the 60/40 benchmark while substantially reducing drawdown risk. As risk aversion increases, drawdown risk is further reduced and risk-adjusted returns remain competitive. Although higher aversion yields lower final wealth, certainty-equivalent returns are highest at moderate aversion levels. These results demonstrate that volatility responsive dynamic policies grounded in realistic stochastic volatility modeling can substantially enhance downside protection and risk-adjusted utility, especially for long-horizon, risk-averse pension participants. Full article

This paper considers the pricing of a subscription service in a heterogeneous market with consumers having different discount rates. We show that in the case of a non-zero enrollment/cancellation cost, solutions of the Hamilton–Jacobi–Bellman equation naturally contain an equivalent of the well-known Preisach operator, a fundamental model of hysteresis in engineering applications. Singular perturbation expansions are used to approximate the optimal solution, assuming that enrollment/cancellation costs are small, relative to the total subscription cost. As a case study, we consider and compare markets with one and two consumers. Full article

Background and Objectives: The dopamine D2 receptor (DRD2) plays a central role in fronto-striatal circuits regulating cognitive control and reward processing. The rs1076560 polymorphism alters receptor isoform expression, potentially modifying impulsivity and vulnerability to stimulant use disorders. We examined gene–environment interactions between rs1076560 and stimulant dependence in relation to impulsivity, ADHD traits, and hedonic capacity. Methods: A total of 517 men (235 stimulant-dependent, 282 controls) completed the Barratt Impulsiveness Scale (BIS-11), Adult ADHD Self-Report Scale (ASRS v1.1), and Snaith–Hamilton Pleasure Scale (SHAPS). Genotyping for rs1076560 was performed using real-time PCR, and two-way ANOVAs tested genotype-by-group effects. Results: Significant genotype-by-group interactions were observed across all BIS-11 subscales and ASRS scores. In the stimulant-dependent group, C/C homozygotes showed the highest levels of attentional impulsivity and attentional dysregulation compared to both A/C and C/C controls. In contrast, within the control group, A/A homozygotes demonstrated higher motor impulsivity, non-planning impulsivity, and BIS-11 total scores than C/C controls. No significant main effects or interactions were found for SHAPS scores. Conclusions: DRD2 rs1076560 moderates impulsivity-related traits through dopaminergic pathways relevant to executive dysfunction in stimulant use disorders. These findings highlight a neurobiological mechanism of addiction vulnerability and may inform precision approaches in neurology and psychiatry. Full article

Background: Sleep disturbances in the multiple sclerosis (MS) population are increasingly recognized, but the factors driving this association remain understudied. This study aimed to determine the prevalence and associations of poor sleep quality in the relapsing–remitting MS (RRMS) population receiving disease-modifying therapy (DMT). Methods: We conducted a cross-sectional study that enrolled 399 individuals diagnosed with RRMS on DMT. Data on patient demographics, clinical presentation, and treatment were systematically evaluated. Sleep-related outcomes were assessed using validated questionnaires—the Pittsburgh Sleep Quality Index (PSQI), Insomnia Severity Index (ISI), Epworth Sleepiness Scale (ESS), Fatigue Severity Scale (FSS), STOP-Bang questionnaire, and Hamilton Anxiety Rating Scale (HAM-A). Independent associations of poor sleep were examined using log-binomial regression to estimate risk ratios (RR). Results: Poor sleep was reported in 42% of the participants in our cohort. In multivariable analysis, only insomnia severity (RR = 1.07; 95% CI 1.05–1.09, p < 0.001) and anxiety (RR = 1.02; 95% CI 1.01–1.04, p = 0.001) remained independently associated with poor sleep. Conclusions: Sleep disturbances are common among patients with RRMS. Insomnia severity and anxiety, rather than demographic or disease-related characteristics, showed independent associations with impaired sleep. Routine screening and targeted interventions addressing insomnia and anxiety may improve sleep quality and, consequently, overall quality of life in this population. Full article

This paper investigates a robust optimal reinsurance and investment problem for an insurance company operating in a Markov-modulated financial market. The insurer’s surplus process is modeled by a diffusion process with jumps, which is correlated with financial risky assets through a common shock structure. The economic regime switches according to a continuous-time Markov chain. To address model uncertainty concerning both diffusion and jump components, we formulate the problem within a robust optimal control framework. By applying the Girsanov theorem for semimartingales, we derive the dynamics of the wealth process under an equivalent martingale measure. We then establish the associated Hamilton–Jacobi–Bellman (HJB) equation, which constitutes a coupled system of nonlinear second-order integro-differential equations. An explicit form of the relative entropy penalty function is provided to quantify the cost of deviating from the reference model. The theoretical results furnish a foundation for numerical solutions using actor–critic reinforcement learning algorithms. Full article

Background: Older adults are a vulnerable population wherein their advancing age leads to limitations in physical and mental functionality that can compromise quality of life. Objective: The objective of this study was to analyze the relationship between mental health factors and quality of life in older adult users of long-term care services in Mexico. Methods: The present cross-sectional study was conducted with a convenience sample of 131 older adult users of long-term care services (three residential care homes and a day center) in Morelia, Michoacán, Mexico. A questionnaire including the World Health Organization Quality of Life Older Adults Scale (WHO-QoL-Old), Geriatric Depression Scale (GDS), Hamilton Anxiety Rating Scale (HARS), Cognitive Reserve Questionnaire (CRQ), and sociodemographic variables was administered. The analysis of the relationship between variables was performed using bivariate analysis (comparisons between groups and Pearson correlations). Due to the type of sampling, the representativeness of the sample obtained was not evaluated. Results: Depression and anxiety were found to inversely influence overall quality of life and its dimensions, while cognitive reserve is a factor that favors quality of life. Also, as related to cognitive reserve, level of education was found to be a factor that favors quality of life. Conclusions: Older adult users of long-term care services are a vulnerable group, given the negative impact on their quality of life that some mental health conditions could have, such as depression, anxiety, and low cognitive reserve. Full article

Background/Objectives: Electroconvulsive therapy (ECT) is used for treatment-resistant depression (TRD). Despite high effectiveness, its most prevalent side effect is memory loss, particularly autobiographical memory deficits. Some patients and physicians might associate post-ECT improvement in depressive symptoms with a higher risk of autobiographical amnesia or even consider this side effect ECT’s mechanism of action. Here, we aimed to study the association between improvement in depressive symptoms and the severity of autobiographical amnesia, as well as identify factors associated with the degree of memory loss. Methods: In this prospective naturalistic observational pilot study, we included 20 patients who underwent ECT for TRD. Attending psychiatrists decided on the electrode placement. Electrical dosage was based on the seizure-titration procedure. Depressive symptoms (Hamilton Depression Scale-21) and autobiographical memory (AMI-SF) were assessed before and after the full course of ECT. The correlation between symptomatic improvements and severity of memory loss was studied using Spearman’s correlation. Demographic and clinical baseline data were examined to look for associations with the decline in autobiographical memory. Results: Symptomatic improvement was not correlated with autobiographical memory loss (r = −0.14, p = 0.58) or any of its domains. Suicidal ideation at baseline was associated with a stronger decline in autobiographical memory (r = −0.53, p = 0.016). Patients treated with bilateral electrode placement had worse amnesia than those treated with right unilateral treatment, though the difference was not significant (MD = −17.4 vs. −13.1, p = 0.2). Conclusions: ECT improved depressive symptoms irrespective of autobiographical amnesia severity. Patients with suicidal ideation at baseline might experience worse post-ECT amnesia than those without. Full article

The intelligent transformation of the wastewater treatment industry, as a core component of the modern environmental governance system, is of decisive significance for achieving sustainable development goals. This study focuses on the issue of multi-stakeholder collaborative governance in the intelligent transformation of the wastewater treatment industry, with differential game theory as the core framework. A tripartite game model involving the government, wastewater treatment enterprises, and digital twin platforms is developed to depict the dynamic interrelations and mutual influences of strategy choices, thereby capturing the coordination mechanisms among government regulation, enterprise technology adoption, and platform support in the transformation process. Based on the dynamic optimization properties of differential games, the Hamilton–Jacobi–Bellman (HJB) equation is employed to derive the long-term equilibrium strategies of the three parties, presenting the evolutionary paths under Nash non-cooperative games, Stackelberg games, and tripartite cooperative games. Furthermore, the Sobol global sensitivity analysis is applied to identify key parameters influencing system performance, while the response surface method (RSM) with central composite design (CCD) is used to quantify parameter interaction effects. The findings are as follows: (1) compared with Nash non-cooperative and Stackelberg games, the tripartite cooperative strategy based on the differential game model achieves global optimization of system performance, demonstrating the efficiency-enhancing effect of dynamic collaboration; (2) the most sensitive parameters are β, α, μ₃, and η₃, with β having the highest sensitivity index (ST_i = 0.459), indicating its dominant role in system performance; (3) significant synergistic enhancement effects are observed among α–β, α–μ₃, and β–μ₃, corresponding, respectively, to the “technology stability–benefit conversion” gain effect, the “technology decay–platform compensation” dynamic balance mechanism, and the “benefit conversion–platform empowerment” performance threshold rule. Full article

Aluminum doping can improve the phase stability of metastable compound Sm₂Fe₁₇C_x with a high carbon content (x > 1.5). We investigated the preferential site substitution of Al, chemical bonding, and structural stability in Sm₂(Fe,Al)₁₇C₃ using first-principle calculations. Our results reveal a strong correlation between the preferential substitution of Fe by Al and the atomic site chemical environment, which affects the overall phase stability. Specifically, Al preferentially occupies the 9d site in Sm₂(Fe,Al)₁₇C₃. At the same time, Al prefers the site 6c in its parent phase Sm₂(Fe,Al)₁₇. Partial replacement of Fe with Al leads to a more negative formation energy, indicating enhanced thermodynamic stability. Crystal Orbital Hamilton Population (COHP) and Crystal Orbital Bond Index (COBI) analysis suggest that insertion of carbon weakens the bonding strength of Sm-Fe (18f) and Sm-Fe (18h), resulting in metastability of Sm₂Fe₁₇C_x. Doping Al strengthens Al-Fe, Al-Sm, Sm-Fe (18f, 18h) and Fe–C bonding in Sm₂(Fe,Al)₁₇C₃, as revealed by calculated COHP and COBI. These effects contribute to improved phase stability in the Al-doped 2:17 interstitial compound. Full article

Introduction: Major depressive disorder (MDD) is a common and often treatment-resistant condition, with many patients showing only partial or minimal response to standard therapies. Repetitive transcranial magnetic stimulation (rTMS) is a well-established, non-invasive treatment for depression, though individual response varies considerably. While demographic and clinical predictors have been explored, the impact of personality styles on rTMS outcomes remains underinvestigated. Herein, we aimed to explore whether personality styles influence treatment response to rTMS. Methods: This retrospective study included 63 in- and outpatients with depressive episodes treated with intermittent theta-burst stimulation (iTBS) between September 2020 and December 2022. Patients were assessed before and after treatment using the 21-item Hamilton Depression Rating Scale (HAMD-21) and the self-reported Major Depression Inventory (MDI). Personality styles were evaluated using the German Persönlichkeits-Stil-und-Störungs-Inventar (PSSI), a dimensional measure of 14 personality styles. Statistical analyses included paired-samples t-tests to assess symptom change and linear regression models to examine whether personality styles predicted treatment outcomes. Effect sizes were reported as Cohen’s d. Results: Patients showed a significant reduction in depressive symptoms following iTBS (HAMD-21: t(62) = 10.86, p < 0.001, d = 1.37. MDI: t(62) = 8.55, p < 0.001, d = 1.06). Stepwise regression for the MDI identified critical–negativistic (NT) and reserved–schizoid (SZ) styles as significant predictors, explaining approximately 16% of the variance (R² = 0.159, p = 0.007). When entered simultaneously in a regression model for the HAMD-21, these same traits also predicted symptom change, though the effect was smaller (R² = 0.108, p = 0.033). Higher scores of critical–negativistic (NT) style were associated with better improvement, whereas higher scores of reserved–schizoid (SZ) style were associated with less improvement. Conclusions: This study confirms the overall efficacy of rTMS in reducing depressive symptoms. While SZ and NT traits showed some predictive value for treatment response—particularly on self-reported outcomes—their influence was modest and inconsistent. Based on our findings, there is no reason why patients with depression and specific personality styles, or even comorbid personality disorders, should be denied rTMS treatment. Full article

As global copper demand continues to grow, China, being the largest copper consumer, faces increasingly complex challenges in ensuring the security of its supply chain. However, a substantive gap remains: prevailing assessments rely on static index systems and discrete scenario analyses that seldom model uncertainty-driven, continuous-time strategic interactions, leaving the conditions for self-enforcing cooperation and the attendant policy trade-offs insufficiently identified. This study models the interaction between Chinese copper importers and foreign suppliers as a continuous-time stochastic differential game, with feedback Nash equilibria derived from a Hamilton–Jacobi–Bellman system. The supply security utility is specified as a diffusion process perturbed by Brownian shocks, while regulatory intensity and profit-sharing are treated as structural parameters shaping its drift and volatility—thereby delineating the parameter region for self-enforcing cooperation and clarifying how sudden disturbances reconfigure equilibrium security. The research findings reveal the following: (i) the mean and variance of supply security utility progressively strengthen over time under the influence of both parties’ maintenance efforts, while stochastic disturbances causing actual fluctuations remain controllable within the contract period; (ii) spontaneous cooperation can be achieved under scenarios featuring strong regulation of domestic importers, weak regulation of foreign suppliers, and a profit distribution ratio slightly favoring foreign suppliers, thereby reducing regulatory costs; this asymmetry is beneficial because stricter oversight of domestic importers curbs the primary deviation risk, lighter oversight of foreign suppliers avoids cross-border enforcement frictions, and a modest supplier-favored profit-sharing ratio sustains participation—together expanding the self-enforcing cooperation set; (iii) sudden events exert only short-term impacts on supply security with controllable long-term effects; however, an excessively stringent regulatory environment can paradoxically reduce long-term supply security. Security effort levels demonstrate positive correlation with supply security, while regulatory intensity must be maintained within a moderate range to balance incentives and constraints. Full article

By extending the four-dimensional semi-Riemann geometry to higher-dimensional Finsler/Hamilton geometry, the canonical quantization of the fundamental metric tensor of general relativity, i.e., an approach that tackles a geometric quantity, is derived. With this quantization, the smooth continuous Finsler structure is transformed into a quantized Hamilton structure through the kinematics of a free-falling quantum particle with a positive mass, along with the introduction of the relativistic generalized uncertainty principle (RGUP) that generalizes quantum mechanics by integrating gravity. This transformation ensures the preservation of the positive one-homogeneity of both Finsler and Hamilton structures, while the RGUP dictates modifications in the noncommutative relations due to integrating consequences of relativistic gravitational fields in quantum mechanics. The anisotropic conformal transformation of the resulting metric tensor and its inverse in higher-dimensional spaces has been determined, particularly highlighting their translations to the four-dimensional fundamental metric tensor and its inverse. It is essential to recognize the complexity involved in computing the fundamental inverse metric tensor during a conformal transformation, as it is influenced by variables like spatial coordinates and directional orientation, making it a challenging task, especially in tensorial terms. We conclude that the derivations in this study are not limited to the structure in tangent and cotangent bundles, which might include both spacetime and momentum space, but are also applicable to higher-dimensional contexts. The theoretical framework of quantization of general relativity based on quantizing its metric tensor is primarily grounded in the four-dimensional metric tensor and its inverse in pseudo-Riemannian geometry. Full article

This study explores a stochastic guarantee cost control (GCC) for time-varying systems with random parameters and asymmetric saturation actuators by employing the integral reinforcement learning (IRL) method in the dynamic event-triggered (DET) mode. Firstly, a modified Hamilton–Jacobi–Isaac (HJI) equation is formulated, and then the worst-case disturbance policy and the asymmetric saturation optimal control signal can be obtained. Secondly, the multivariate probabilistic collocation method (MPCM) is used to evaluate the value function at designated sampling points. The purpose of introducing the MPCM is to simplify the computational complexity of stochastic dynamic programming (SDP) methods. Furthermore, the DET mode is utilized to solve the SDP problem to reduce the computational burden on communication resources. Finally, the Lyapunov stability theorem is applied to analyze the stability of time-varying systems, and the simulation shows the feasibility of the designed method. Full article

We study stochastic production planning in capacity-constrained manufacturing systems, where feasible operating states are restricted to a convex safe-operating region. The objective is to minimize the total cost that combines a quadratic production effort with an inventory holding cost, while automatically halting production when the state leaves the safe region. We derive the associated Hamilton–Jacobi–Bellman (HJB) equation, establish the existence and uniqueness of the value function under broad conditions, and prove a concavity property of the transformed value function that yields a robust gradient-based optimal feedback policy. From an operations perspective, the stopping mechanism encodes hard capacity and safety limits, ensuring bounded risk and finite expected costs. We complement the analysis with numerical methods based on finite differences and illustrate how the resulting policies inform real-time decisions through two application-inspired examples: a single-product case calibrated with typical process-industry parameters and a two-dimensional example motivated by semiconductor fabrication, where interacting production variables must satisfy joint safety constraints. The results bridge rigorous stochastic control with practical production planning and provide actionable guidance for operating under uncertainty and capacity limits. Full article

In real-world applications, finite time convergence to a desired Lyapunov stable equilibrium is often necessary. This notion of stability is known as finite time stability and refers to systems in which the state trajectory reaches an equilibrium in finite time. This paper explores the notion of finite time stability in probability within the context of nonlinear stochastic dynamical systems. Specifically, we introduce sufficient conditions based on Lyapunov methods, utilizing Lyapunov functions that satisfy scalar differential inequalities involving fractional powers for guaranteeing finite time stability in probability. Then, we address the finite time optimal control problem by developing a framework for designing optimal feedback control laws that achieve finite time stochastic stability of the closed-loop system using a Lyapunov function that also serves as the solution to the steady-state stochastic Hamilton–Jacobi–Bellman equation. Full article