A separated representation involving multiple time scales within the Proper Generalized Decomposition framework

Solutions of partial differential equations can exhibit multiple time scales. Standard discretization techniques are constrained to capture the finest scale to accurately predict the response of the system. In this paper, we provide an alternative route to circumvent prohibitive meshes arising from the necessity of capturing fine-scale behaviors. The proposed methodology is based on a time-separated representation within the standard Proper Generalized Decomposition, where the time coordinate is transformed into a multi-dimensional time through new separated coordinates, each representing one scale, while continuity is ensured in the scale coupling. For instance, when considering two different time scales, the governing Partial Differential Equation is commuted into a nonlinear system that iterates between the so-called microtime and macrotime, so that the time coordinate can be viewed as a 2D time. The macroscale effects are taken into account by means of a finite element-based macro-discretization, whereas the microscale effects are handled with unidimensional parent spaces that are replicated throughout the time domain. The resulting separated representation allows us a very fine time discretization without impacting the computational efficiency. The proposed formulation is explored and numerically verified on thermal and elastodynamic problems.

Out with “Fine Time,” in with Financial Waivers: Recent Developments in Massachusetts Probation Fines and Fees Policies

The criminal justice system routinely imposes financial sanctions on probation clients. These fines, fees, and restitution debts often amount to more than what many clients can reasonably afford to pay. Until recently, Massachusetts courts have incarcerated clients solely for their inability to pay these debts in a practice known as “fine time”. In 2018, the state passed a landmark criminal justice reform bill that restricted the types of cases in which fine time can be ordered. Clients that can establish that payment would lead to financial hardship can now petition the court for a financial waiver accompanied by community service. The current study seeks to explore the implications of the recent reform efforts on probation services by analyzing surveys gathered from a sample of 121 Massachusetts probation officers in 2020. Descriptive findings of officers’ attitudes toward fines and fees, responses to nonpayment by clients, and the use of financial waivers are presented. Officers’ perceptions and practices align with the recent reform efforts, suggesting support among probation personnel for policies that limit punitive responses to nonpayment of legal debts by their supervisees. Possible directions for future research and policy development are discussed.

The Advanced Multilevel Predictor-Corrector Quasi-Static Method for Pin-Resolved Neutron Kinetics Simulation

The Advanced Multilevel Predictor-Corrector Quasi-static Method (AML-PCQM) is proposed in this work. The four computational levels, including transport, Multi-Group (MG) Coarse Mesh Finite Difference (CMFD), One-Group (1G) CMFD, and Exact Point-Kinetics Equation (EPKE), are coupled with a new dynamic iteration strategy. In each coupling algorithm, the original Transient Fixed Source Problem (TFSP) is solved in the predictor process using coarse time step, and then the flux distribution is factorized to the functions of amplitude and shape in the next corrector process. Finally, multiple fine time steps are used to adjust the predicted solution. Two heterogeneous single assembly problems with the prompt control rod withdrawal event are used to verify the AML-PCQM scheme’s accuracy and efficiency. The numerical results obtained by different cases are compared and analyzed. The final results indicate that the AML-PCQM performs the remarkable advantages of efficiency and accuracy with the reference cases.

High Repetition Rate and Coherent Free-Electron Laser Oscillator in the Tender X-ray Range Tailored for Linear Spectroscopy

Fine time-resolved analysis of matter—that is, spectroscopy and photon scattering—in the linear response regime requires fs-scale pulsed, high repetition rate, fully coherent X-ray sources. A seeded Free-Electron Laser, driven by a linac based on Super Conducting cavities, generating 108–1010 coherent photons at 2–5 keV with 0.2–1 MHz of repetition rate, can address this need. The scheme proposed is a Free-Electron Laser Oscillator at 3 keV, working with a cavity based on X-ray mirrors. The whole chain of the X-ray generation is here described by means of start-to-end simulations.

VIP neurons desynchronize cortical assemblies

Neural synchronization on fast timescales has been linked to critical aspects of sensation, cognition and action, and impairments in synchronization are associated with neurological disease. Although the strength and spatial scale of neural synchronization varies dramatically with sensory and behavioral context, the circuit mechanisms that regulate the magnitude and spatial spread of neural oscillations are largely unknown. As in humans, monkeys, and cats, we found that in the mouse primary visual cortex (V1) the stimulus properties and behavioral state powerfully modulate gamma band synchronization. To reveal the underlying circuit that mediates this dependence, we used multi-site multi-electrode electrophysiology and cell type specific optogenetic suppression of vasoactive intestinal peptide (VIP) interneurons in awake mice. Our results show that VIP neurons potently control the gain and behavioral state-dependence of gamma band network synchronization by desynchronizing local and global networks on fine time scales. Importantly, VIP neurons preferentially decouple spatially separated cortical ensembles when they are processing non-matched stimulus features. Based on these data, we propose that cortical disinhibition by VIP interneurons fine-tunes the strength and spatial architecture of gamma-oscillating neural assemblies, which may facilitate the downstream generation of coherent visual percepts.

Detecting the dominant contributions of runoff variance across the source region of the Yellow River using a new decomposition framework

Quantifying the contributions of climatic variables to runoff variance is still a great challenge to water resource management. This study adopted an extended Budyko framework to investigate the effects of terrestrial water storage changes (ΔS) on runoff variance across the source region of the Yellow River, China, during the period of 2003–2014. A new decomposition framework based on the extended Budyko framework was proposed to effectively quantify the contributions of different climatic variables including precipitation, PET and ΔS to runoff variance. The results demonstrated that the extended Budyko framework showed a better performance in presenting the water and energy balance than the original Budyko framework, especially at fine time scales. Meanwhile, the variance in runoff estimated by the new decomposition framework was close to that of runoff observations, indicating that this framework can effectively capture the variation in runoff during 2003–2014. It was also found that precipitation was the most important factor that contributed to runoff changes, while PET made a slightly smaller contribution compared to precipitation. Notably, the results also emphasized the important effects of ΔS on runoff variance at fine time scales, which was useful to better understand the interactions between atmospheric and hydrological processes for regions.