Uniform-in-Time Continuum Limit of the Winfree Model on an Infinite Cylinder and Emergent Dynamics

We study a uniform-in-time continuum limit of the lattice Winfree model (LWM) on an inifinite cylinder under restricted initial datum and suitable assumptions on system functions such as natural frequency functions and the coupling strength function. Roughly speaking, the continuum Winfree model (CWM) is an integro-differential equation for the temporal evolution of a Winfree phase field over an infinite cylinder. For bounded measurable initial phase field and natural frequency functions, we can establish a unique global existence of classical solutions to the CWM in a large coupling regime. At the same time, we can also see that a classical solution to the CWM can be obtained as an L-1 -limit of a sequence of lattice solutions to the LWM under a suitable framework. This provides a good approximation of solution to the CWM as a sequence of solutions to the LWM. Moreover, we verify that the continuum limit of a sequence of equilibria to the LWM tends to a unique stationary profile of the CWM.N

On the emerging asymptotic patterns of the Winfree model with frustrations

We study the emergence of asymptotic patterns in Winfree ensemble such as the partial/complete phase-locking and bump states under the effect of heterogeneous frustrations. Although the Winfree model is the first model for the synchronization of limit-cycle oscillators, there is little literature on the mathematical validity of asymptotic patterns compared to the vast literature of the well-studied Kuramoto model. Recently, it has received a renewed attention in nonlinear dynamics and statistical physics communities due to its diverse asymptotic patterns that it can generate. In particular, we provide a rigorous result on the existence of bump states in a homogeneous ensemble with the same natural frequency. Our provided results exhibit the robustness of emerging asymptotic patterns with respect to frustrations. We derive several sufficient frameworks for the unique existence of an equilibrium state, bump states and uniform stability with respect to initial data.N

Collective behaviors of a Winfree ensemble on an infinite cylinder

The Winfree model is the first phase model for synchronization and it exhibits diverse asymptotic patterns that cannot be observed in the Kuramoto model. In this paper, we propose a Winfree type model describing the aggregation of particles on the surface of an infinite cylinder. For a special case, our proposed model is in fact equivalent to the complex Winfree model. For the proposed model, we present a sufficient framework leading to the complete oscillator death and uniform l(p)-stability in a large coupling regime. We also derive the corresponding kinetic model via uniform-in-time mean-field limit. In addition, we also provide several numerical simulations for the particle and compare them with analytical results.Y

Uniform-in-time continuum limit of the lattice Winfree model and emergent dynamics

&lt;p style='text-indent:20px;'&gt;We study a uniform-in-time continuum limit of the lattice Winfree model(LWM) and its asymptotic dynamics which depends on system functions such as natural frequency function and coupling strength function. The continuum Winfree model(CWM) is an integro-differential equation for the temporal evolution of Winfree phase field. The LWM describes synchronous behavior of weakly coupled Winfree oscillators on a lattice lying in a compact region. For bounded measurable initial phase field, we establish a global well-posedness of classical solutions to the CWM under suitable assumptions on coupling function, and we also show that a classical solution to the CWM can be obtained as a &lt;inline-formula&gt;&lt;tex-math id="M1"&gt;\begin{document}$L^1$\end{document}&lt;/tex-math&gt;&lt;/inline-formula&gt;-limit of a sequence of lattice solutions. Moreover, in the presence of frustration effect, we show that stationary states and bump states can emerge from some admissible class of initial data in a large and intermediate coupling regimes, respectively. We also provide several numerical examples and compare them with analytical results.&lt;/p&gt;</jats:p

Machine Learning-Based Causality Analysis of Human Resource Practices on Firm Performance

An organization&rsquo;s human resource management practices are essential for its competitive advantage. This study specifically examined human resource (HR) practices that predict corporate performance (employee turnover and firm sales) based on a backpropagation neural network (BPN)-based causality analysis. This study aims to test how to optimize human resource practices to improve organizational performance. This study elucidated the effect of HR practices and organizational-level factors on predicting employee turnover and firm sales. The BPN-based causality analysis revealed the relative importance of explanatory variables on firm performance. To test the model, it employed the Human Capital Corporate Panel open data on Korean companies&rsquo; HR practices and other characteristics. The analysis identifies causal relationships between specific HR practices and firm performance. The results show that compensation-related HR practices are most influential in predicting firm sales and employee turnover. Moreover, training-related HR practices were modest, and talent acquisition and performance management practices had relatively weak effects on the two outcomes. The study provides insights into how human resource practices can be optimized to improve firm performance and enhance organizational effectiveness. The findings of this study contribute to the growing body of research on the use of machine learning in HR management and suggest practical implications for managers&rsquo; insights to optimize HR practices