Search Results (483)

Fractional calculus and distribution theory share a common conceptual origin in the symbolic interpretation of differentiation and integration. Despite this connection, most developments in fractional calculus have traditionally been formulated within the framework of ordinary functions, while the systematic use of distributions remains limited. In this work, a novel distributional framework is developed by constructing a fractional Taylor representation of the product of Euler gamma and Riemann zeta functions in terms of fractional derivatives of the Dirac delta distribution. The proposed formulation enables the derivation of new fractional identities via Laplace transformation and facilitates the analytical solution of fractional differential equations containing such functions. Closed-form solutions are obtained in both classical and generalized distributional senses, allowing the extension of solutions from the positive real axis to the entire real line. Furthermore, the framework is applied to fractional operators of Erdélyi–Kober type, yielding new integral and derivative transforms. Fractional differential and integral equations with singular terms arise naturally in several engineering models involving memory effects, impulsive responses, and anomalous transport phenomena. However, the presence of nonremovable singularities—such as those associated with Euler gamma and Riemann zeta functions—significantly restricts the applicability of classical analytical methods. Overall, the proposed distributional framework bridges the gap between abstract fractional calculus and practical engineering models by enabling analytical solutions of fractional systems with singular memory kernels that were previously inaccessible using classical methods. Full article

Mechanistic tumor growth models are widely used to describe disease progression and treatment response, but their utility depends on accurate estimation of parameters governing the underlying biological processes. In this study, we employ a Physics-Informed Neural Network (PINN) to estimate the parameters of a tumor growth model that captures both tumor dynamics and drug effects. We introduce a piecewise PINN that splits the time domain at dosing events to handle non-smooth dose-driven dynamics, and we incorporate drug injection by representing the pharmacokinetic subsystem analytically via an impulse-response function. The approach is evaluated on synthetic tumor-volume trajectories generated from known parameter sets and dosing schedules from an experimental cohort of 54 mice. Across the cohort, the PINN accurately reconstructs total tumor volume and robustly estimates the tumor proliferation rate a, with inferred values closely aligned with the true values ($R^2=0.841$). The framework was also able to estimate the drug killing effect parameter b. This consistency is further supported by forward ODE simulations using the PINN-estimated parameters. Within the evaluated setting, performance depended on the model structure, parameter identifiability, and training configuration, underscoring the need for careful loss weighting and further validation. Overall, the results demonstrate the feasibility of piecewise PINNs for parameter inference in tumor growth models and support their further study in realistic therapeutic settings. Full article

This study investigates the forward discount puzzle by examining the dynamic relationships among excess returns arising from interest rate parity deviations, interest rate differentials, and the USD/JPY exchange rate. The empirical analysis employs correlation analysis, the Autoregressive Distributed Lag (ARDL) cointegration test, and variance decomposition together with impulse response functions derived from a Toda–Yamamoto augmented Vector Autoregressive (VAR) model, using data spanning January 2001 to September 2025. The correlation results indicate that the spot exchange rate is negatively related to both the swap rate and the interest rate differential. Impulse response analysis shows that the USD/JPY rate responds positively to swap rate shocks in the medium to long run, while responding negatively to interest rate differential shocks in the short run. Variance decomposition results are consistent with the impulse response analysis and underscore the dominant bilateral linkage between the exchange rate and the swap rate. The long-run ARDL estimates further reveal that the swap rate is positively associated with dollar appreciation, whereas both the interest rate differential and relative output are negatively related. Overall, although short-run arbitrage appears temporarily, the cointegration and dynamic results provide robust evidence that the forward discount puzzle persists for a substantial period rather than interest rate parity holding. Full article

Laser powder bed fusion has attracted increasing attention for the production of metallic substrates intended for surface functionalization by advanced physical vapor deposition coatings. This study investigates the influence of the substrate manufacturing route on the performance of titanium–aluminum–silicon nitride-coated AISI 316L stainless steel, with particular emphasis on substrates produced by laser powder bed fusion. Conventionally manufactured and additively manufactured AISI 316L substrates were coated with a titanium–aluminum–silicon nitride layer using high-power impulse magnetron sputtering. The substrates were characterized by tensile testing and microhardness measurements, while coating thickness and uniformity were evaluated using the crater ball method. The mechanical integrity of the coating–substrate system was assessed by progressive load scratch testing. The additively manufactured substrate exhibited a significantly higher yield strength (411 MPa) compared to the conventionally manufactured material (257 MPa), together with increased microhardness. The titanium–aluminum–silicon nitride coating showed a uniform thickness of 4.47 µm and a well-defined coating–substrate interface. Scratch tests revealed a delayed onset of coating damage on additively manufactured substrates, with the transition to severe adhesive failure occurring at higher normal loads compared to the conventionally manufactured substrate. These results demonstrate that AISI 316L stainless steel produced by laser powder bed fusion provides a mechanically robust substrate for titanium–aluminum–silicon nitride coatings deposited by high-power impulse magnetron sputtering, with favorable coating response under progressive loading conditions. Full article

Indonesia’s financial system is bank-centric, with banks managing approximately 78% of the nation’s financial assets; therefore, the effectiveness of monetary policy transmission depends on banks’ responsiveness to the central bank’s interest rate policy (the BI Rate). However, a policy-relevant anomaly persists: deposit rate pricing is more strongly anchored to the Deposit Insurance benchmark (IDIC Rate) than to the BI Rate. This study argues that this research is significant because it identifies a “Dual Benchmark System” that traditional single-anchor models fail to address, representing a critical friction in emerging market transmission. This study examines this dual-benchmark paradigm and the associated asymmetric risks using a panel VAR with a Generalized Impulse Response Function (GIRF) on quarterly data for 63 commercial banks from 2010 to 2024. The results indicate that IDIC Rate shocks have a larger and more persistent effect on deposit rates than BI Rate shocks, generating asymmetric transmission risks. This dominance creates a structural “price ceiling” that keeps funding costs high, ultimately raising lending rates for borrowers and distorting deposit growth rates. Furthermore, this analysis reveals that external policy signals are far more influential than internal financial performance. This suggests that under the Basel III framework and prevailing financial regulations, banks prioritize liquidity compliance and safety net protection over internal operational efficiency. Macroeconomic shocks remain weaker than policy shocks and dissipate more quickly. This finding reveals a potential systemic coordination risk, implying an urgent need for tighter policy coordination between the Central Bank and the IDIC to reduce structural frictions, maintain transmission effectiveness, and protect long-term financial stability. Full article

The high-dimensional stochastic space caused by a large number of random variables remains a significant challenge hindering the practical application of stochastic process simulation in engineering. Although various dimension reduction techniques have been developed, their direct integration into time-domain simulation frameworks remains limited. To address this issue, this paper proposes two efficient time-domain dimension reduction methods for simulating stationary stochastic processes. The methods reduce the number of input random variables required for simulation to a single variable, while the randomness of the output stochastic process remains unchanged. The proposed methods are theoretically motivated by spectral decomposition of processes using two distinct strategies and explicitly incorporate the decay characteristics of the impulse response function associated with the stochastic process. Based on this, the random orthogonal functions can be naturally introduced to simulate the stationary stochastic process, which effectively resolves the high-dimensional random variables encountered in conventional time-domain simulations. Furthermore, the incorporation of a number-theoretic method enables uncertainty quantification of stochastic process samples. Numerical simulations demonstrate that the proposed methods reduce the random variable dimension from 2400 to 1 (99.95% reduction). Relative error of the simulated power spectral density remains below 2%, while computational time is reduced by approximately 4% compared with the conventional time-domain methods. These results demonstrate the effectiveness and practical applicability of the proposed approach in engineering stochastic process simulation. Full article

This paper examines the short-run transmission of monetary policy to bank credit granted to the non-financial corporate sector in Morocco, a bank-based emerging economy. Using monthly macro-financial data over the period of 2014–2024, the study estimates a reduced-form VAR model to analyze the dynamic interactions between the policy rate, bank credit, banks’ holdings of sovereign securities, credit risk indicators, and short-term market spreads. Impulse response functions and forecast error variance decompositions indicate that a one-standard-deviation monetary policy shock is associated with a small and short-lived response of non-financial corporations bank credit at a monthly horizon, accounting for only a limited share of its forecast error variance, while the same shock is more strongly reflected in market spreads and banks’ balance-sheet reallocations toward sovereign assets, alongside temporary movements in credit risk indicators. Overall, these results are consistent with a reduced-form transmission pattern in which monetary policy appears to affect bank credit primarily through indirect financial channels related to risk perception, portfolio reallocation, and balance-sheet management, rather than through immediate changes in aggregate credit volumes. This interpretation is conditional on the VAR specification and short-run horizon considered, and suggests an attenuation of the interest rate–credit channel in a bank-dominated emerging economy, rather than evidence of a structural breakdown of monetary transmission. Full article

The neuronal cell adhesion molecule NrCAM is widely expressed in the nervous system across the lifespan and has important physiological functions in the development of neuronal circuits through axonal growth and guidance and formation and maintenance of synapses in the cortex. NrCAM gene polymorphisms are associated with vulnerability to neuropsychiatric disorders such as schizophrenia, as well as vulnerability to substance use disorders. We investigated the effects of acute and chronic stress and the effects of systemic administration of AMPAR antagonist CNQX and NMDAR antagonist MK-801 on delay discounting in male NrCAM knockout (KO) mice and their wild-type littermate controls (WT). Under the no-stress condition, no discounting differences were found. Acute stress increased discounting and impulsivity in WTs but not in NrCAM KO mice. Chronic stress increased discounting and impulsivity in both genotypes. CNQX increased impulsive choice in WT controls but not in NrCAM KOs; impulsive choice decreased in both genotypes after MK-801 administration. Relative to WTs, NrCAM KOs had more neuronal activation in the prelimbic and orbitofrontal cortices. In NrCAM KO mice, a low dose of MK-801 decreased neuronal activation in the ventral orbitofrontal cortex and increased activation in the accumbens shell and core. These results indicate differential effects of genotype, stress, and response to glutamatergic drugs and support a role for NrCAM in stress-induced behavioral alterations relevant to addiction and psychiatric disorders. Full article

This study investigates volatility spillovers from the stock markets of the United States, Germany, China, and Japan to the UK stock market using daily data from major benchmark indices (FTSE 100, S&P 500, DAX, Shanghai Composite, and Nikkei 225) and Brent crude oil prices. Using a novel two-stage bootstrap framework, we first model time-varying conditional volatilities with GARCH-family models and compare them with long-memory FIGARCH specifications to account for persistent volatility dynamics. These volatilities are then incorporated into a VAR-X model, treating Brent crude oil price volatility as an endogenous or exogenous variable in robustness checks. To overcome limitations of traditional VARs, bootstrap-corrected GIRFs are employed to trace dynamic, order-invariant impacts across key sub-periods: the global financial crisis, Brexit, COVID-19, and the Ukraine war. We also benchmark our results against the Diebold–Yilmaz connectedness index and conduct rigorous out-of-sample forecasting and Value-at-Risk backtesting. Results reveal heterogeneous spillovers: US and German shocks trigger strong, immediate, and persistent UK market volatility, reflecting deep integration; Chinese shocks are delayed and gradual, while Japanese shocks are muted or short-lived. Spillover intensity is time-varying, peaking during global crises. Our model outperforms standard benchmarks in out-of-sample volatility forecasting and risk management applications. The study offers critical insights for investors seeking international diversification and for policymakers aiming to manage systemic risk in an interconnected global financial system. Full article

The interplay between fiscal and monetary policy is critical for small open economies exposed to global volatility, yet the regime-dependent nature of this transmission often remains underexplored. This study investigates whether the Hungarian economy operated under fiscal or monetary dominance from 2010 to 2024, a period marked by significant external shocks. Adopting a Markov Regime-Switching VAR (MS-VAR) framework tailored to an open-economy context, the research estimates state-dependent reaction functions and Impulse Response Functions (IRFs) for both the central bank and the fiscal authority. The model explicitly controls for exogenous geopolitical and economic crises and is validated through rigorous stationarity and regime-selection tests. Empirical results reveal that Hungary predominantly operated under fiscal dominance, with the fiscal authority exhibiting non-Ricardian behavior and no significant response to debt accumulation across the sample. Conversely, the Magyar Nemzeti Bank demonstrated regime-switching behavior: a “Passive” stance accommodating fiscal expansion from 2013 to 2019, followed by a forced shift to an “Active” regime in 2022 characterized by aggressive responses to inflation and high-interest rate volatility. These findings suggest that in small open economies, policy dominance is frequently dictated by external constraints, with the burden of macroeconomic stabilization falling disproportionately on monetary policy during crisis episodes. Full article

Background/Objectives: The effects of online physical activity (PA) interventions on executive function (EF) and Attention-Deficit Hyperactivity Disorder (ADHD) symptoms are promising; nonetheless, their benefits for Latinx youth remain unclear. Methods: This study explores levels of adherence, cognitive and behavioral outcomes and acceptability of an online PA intervention, Zing Performance, among a Latinx youth sample; only a few of the participants completed their condition (n = 6). Results: There was wide variability in adherence levels at mid-treatment (n = 5) and high-level adherence at post-treatment (n = 2). A Mann–Whitney test yielded a statistically significant (p = 0.004) improvement in the treatment group’s inattention symptoms at mid-treatment (n = 5), compared to the Waitlist Control; (WLC; n = 6). EF and hyperactivity/impulsivity were not significantly different. Further, pre-, mid- and post-participant trajectory data revealed that one participant benefited significantly from treatment, one participant demonstrated little to no response to treatment, and most of the WLC participants remained in the severity ranges throughout the 12 weeks. The parents of the two children who completed treatment reported high levels of acceptability informally and on the quantitative measure. Conclusions: Exploratory findings support further investigation of Zing among Latinx families with cultural consideration to study procedures. The lessons learned from this study are valuable for future research procedures and interventions with this marginalized population. Full article

The clinical management of major depressive disorder is constrained by a trial-and-error approach. The clinical management of major depressive disorder is constrained by a trial-and-error approach. While computational methods have focused on static binary classification (e.g., responder vs. non-responder), they ignore the dynamic nature of recovery. Building upon the recently proposed prognostic theory of treatment response, this article presents a methodological framework for its operationalisation. We define a multi-modal data architecture for the theory’s core constructs—the Patient State Vector (PSV), Therapeutic Impulse Function (TIF), and Predicted Recovery Trajectory (PRT)—transforming them from abstract concepts into specified computational inputs. To model the asynchronous interactions between these components, we specify a Time-Aware Long Short-Term Memory (LSTM) architecture, providing explicit mathematical formulations for time-decay gates to handle irregular clinical sampling. Furthermore, we outline a synthetic validation protocol to benchmark this dynamic approach against static baselines. By integrating these technical specifications with a translational pipeline for Explainable AI (XAI) and ethical governance, this paper provides the necessary blueprint to transition psychiatry from theoretical prognosis to empirical forecasting. Full article

This study examines the systemic operational risk in Morocco’s banking sector using a Panel VAR model based on data from three banks over ten years. The model includes real GDP, interbank rate (TMP), and bank credit, alongside indicators of operational, credit, and liquidity risks. The Impulse Response Functions (IRF) show that operational risk shocks reduce GDP and affect TMP with a lag, confirming their systemic impact. Forecast Error Variance Decomposition (FEVD) reveals that GDP significantly explains the variance in operational risk. To strengthen the analysis, a dynamic panel GMM model is used to address endogeneity. The GMM results demonstrate that systemic operational risk in Moroccan banks is both persistent and procyclical, highlighting how macro-financial dynamics such as growth, inflation, and monetary conditions, directly shape banks’ resilience. These findings provide new empirical evidence on the determinants of systemic operational risk in emerging markets. This dual approach supports the integration of operational risk into Morocco’s macroprudential policy frameworks. Full article

A description of the Kibble–Zurek mechanism with linear response theory has been done previously, but ad hoc hypotheses were used, such as the rate-dependent impulse window via the Zurek equation in the context of no driving in the relaxation time. In this work, I present a new framework where such hypotheses are unnecessary while preserving all the characteristics of the phenomenon. The Kibble-Zurek scaling obtained for the excess work is close to 2/5, a result that holds for open and thermally isolated systems with relaxation time that diverges at the critical point and the first zero of the relaxation function is finite. I exemplify the results using four different but significant types of scaling functions. Full article

With the explosive growth of global data traffic, long-distance fiber optic transmission systems are continuously evolving towards higher capacity and longer distances. However, to overcome the high complexity of fiber dispersion compensation algorithms, various dispersion compensation techniques have emerged. This paper aims to systematically review and summarize dispersion compensation algorithms in long-distance fiber optic transmission. First, we briefly introduce the physical mechanism of fiber dispersion. Then, this paper focuses on digital domain compensation algorithms, dividing them into two major categories: compensation algorithms without penalty and with penalty. For compensation algorithms without penalty, we elaborate on traditional block processing strategies such as Overlap-Save (OLS), and various enhanced strategies combining intelligent filter segmentation and optimized frequency domain workflows. For compensation algorithms with penalty, we focus on analyzing a scheme that redesigns chromatic dispersion compensation (CDC) algorithm into a hardware-friendly structure using geometric clustering of taps, and finite-impulse-response (FIR) filters based on frequency response approximating the ideal inverse chromatic dispersion (CD) transfer function. By numerical simulation, we analyze the core principles, computational complexity, and compensation performance of each type of algorithm. Finally, this paper summarizes the limitations and development trends of existing dispersion compensation algorithms, pointing out that low-complexity and small-scale deployment algorithm structures will be an important research direction in the future. Full article