The dynamics of synaptic interactions within spiking neuron networks play a fundamental role in shaping emergent collective behavior. This paper studies a finite-size network of quadratic integrate-and-fire neurons interconnected via a general synaptic function that accounts for synaptic dynamics and time delays. Through asymptotic analysis, we transform this integrate-and-fire network into the Kuramoto-Sakaguchi model, whose parameters are explicitly expressed via synaptic function characteristics. This reduction yields analytical conditions on synaptic activation rates and time delays determining whether the synaptic coupling is attractive or repulsive. Our analysis reveals alternating stability regions for synchronous and partially synchronous firing, dependent on slow synaptic activation and time delay. We also demonstrate that the reduced microscopic model predicts the emergence of synchronization, weakly stable cyclops states, and non-stationary regimes remarkably well in the original integrate-and-fire network and its theta neuron counterpart. Our reduction approach promises to open the door to rigorous analysis of rhythmogenesis in networks with synaptic adaptation and plasticity.

This study proposes a direct synthesis-based two-degree-of-freedom (2-DOF) controller for various types of integrating processes with time delays. This 2-DOF controller includes a proportional-integral-derivative (PID) controller to enhance load disturbance rejection performance and a set-point filter to improve servo response performance. The main PID controller parameters are expressed as process model parameters and a single adjustment variable, while the set-point filter is composed of PID controller parameters with weighted factors. The adjustment variable is tuned to achieve an optimal balance between response performance and robustness, based on the maximum magnitude of the sensitivity function (Ms). Controller parameters for various Ms values and guidelines for setting these parameters are provided in a consistent formulaic form using a curve-fitting method. These parameter-setting formulas facilitate the accurate implementation of PID controllers with specified Ms values and allow the controller design to be extended to processes with larger dimensionless time delays for a given Ms value. Although a 2-DOF controller was proposed, the adjustment variable for setting the parameters of the main PID controller and the set-point filter was solely the desired time constant. The proposed method was applied to various integrating processes with time delays, and its performance was compared with existing methods reported in the literature, based on performance indices such as settling time, overshoot, integral of absolute error, total variation in input usage, and global performance index. Simulations were conducted using six examples of various integrating processes with time delays to verify the effectiveness and applicability of the proposed controller.

Viral infection develops in the organism due to virus replication inside infected cells and its transmission from infected to uninfected cells through the extracellular matrix or cell junctions. In this work, we model infection spreading in tissue with a delay reaction-diffusion system of equations for the concentrations of uninfected cells, infected cells and virus. We prove the wave existence, determine its speed of propagation and introduce a simplified one-equation model obtained from the complete model using a quasi-stationary approximation.

Background ST-elevation myocardial infarction (STEMI) requires swift intervention, with primary percutaneous coronary intervention (PCI) being essential to limit myocardial damage. The key factor affecting PCI effectiveness is the door-to-balloon (DTB) time. This observational study evaluated DTB times in STEMI patients at a tertiary care center who underwent primary angioplasty, examining adherence to benchmarks and identifying factors contributing to delays. Methodology This prospective observational study was conducted from March 2017 to August 2018 at Fortis Hospital Mulund, Mumbai, India. It included 171 STEMI patients aged 18 and older who underwent primary angioplasty. Patients with non-ST elevation myocardial infarction (NSTEMI), those who received thrombolysis, or had medical contraindications to primary angioplasty were excluded. Data on key time intervals were collected via direct observation and then analyzed using SPSS for Windows, Version 15 (Released 2006; SPSS Inc., Chicago, United States). Qualitative data were summarized using frequency and percentages, whereas quantitative data were presented as mean (±SD). T-test was applied to compare the mean duration between the two groups, i.e., DTB time ≤90 minutes and DTB time >90 minutes, and a p-value <0.05 was considered statistically significant. Results The participants had a mean age of 56.5 (±13.1) years and were predominantly male (78.4%). The mean DTB time was 70.21 (±29.16) minutes, with 79.5% achieving ≤90 minutes. Patient-related delays (48.6%) were mainly due to consent issues (31.4%), which was the most predominant cause. Hospital-related delays (51.4%) included catheterization laboratory occupancy (14.3%) and diagnostic delays (14.3%). Patients with DTB times >90 minutes had significantly longer durations in all procedural steps except door-to-ECG time. Conclusion This study underscores the complex challenges in achieving timely DTB times for STEMI patients undergoing primary angioplasty. Overcoming these barriers through targeted interventions is essential for optimizing management and enhancing outcomes. Insights into delay factors inform evidence-based strategies to improve the timeliness and effectiveness of STEMI care delivery.

The issues of state estimations based on distributed observers for linear time-invariant (LTI) systems with multiple sensors are discussed in this paper. We deal with the scenario when the information exchange has known time delays, and aim at designing a distributed observer for each subsystem such that each distributed observer can estimate the system state asymptotically by rejecting the time delay. To begin with, by rewriting the target system in a connecting form, a subsystem which is affected by the time-delay states of other nodes is established. And then, for this subsystem, a distributed observer with time delay is constructed. Moreover, an equivalent state transformation is made for the observer error dynamic system based on the observable canonic decomposition theorem. Further, in order to ensure that the distributed observer error dynamic system is asymptotically stable even if there exists a time delay, a linear matrix inequality (LMI) which is relative to the Laplace matrix is elaborately set up, and a special Lyapunov function candidate based on the LMI is considered. Next, based on the Lyapunov function and Lyapunov stability theory, we prove that the error dynamic system of the distributed observer is asymptotically stable, and the observer gain is determined by a feasible solution of the LMI. Finally, a simulation example is given to illustrate the effectiveness of the proposed method.

The detection of the liquid-to-ice transition is an important challenge for many applications. In this paper, a method for multi-parameter characterization of the liquid-to-ice phase transition is proposed and tested. The method is based on the fundamental properties of bulk acoustic waves (BAWs). BAWs with shear vertical (SV) or shear horizontal (SH) polarization cannot propagate in liquids, only in solids such as ice. BAWs with longitudinal (L) polarization, however, can propagate in both liquids and solids, but with different velocities and attenuations. Velocities and attenuations for L-BAWs and SV-BAWs are measured in ice using parameters such as time delay and wave amplitude at a frequency range of 1-37 MHz. Based on these measurements, relevant parameters for Rayleigh surface acoustic waves and Poisson\'s modulus for ice are determined. The homogeneity of the ice sample is also detected along its length. A dual sensor has been developed and tested to analyze two-phase transitions in two liquids simultaneously. Distilled water and a 0.9% solution of NaCl in water were used as examples.

Introduction: The oxygen uptake (V˙O2) vs power output relationship from ramp incremental exercise is used to prescribe aerobic exercise. As power output increases, there is a delay in V˙O2 that contributes to a misalignment of V˙O2 from power output; the mean response time (MRT). If the MRT is not considered in exercise prescription, ramp incremental-identified power outputs will elicit V˙O2 values that are higher than intended. We compared three methods of determining MRT (exponential modeling (MRTEXP), linear modeling (MRTLIN), and the steady-state method (MRTSS)) and evaluated their accuracy at predicting the V˙O2 associated with power outputs approximating 75% and 85% of gas exchange threshold and 15% of the difference between gas exchange threshold and maximal V˙O2 (Δ15). Methods: Ten males performed a 30-W∙min-1 ramp incremental and three 30-min constant power output cycle ergometer trials with intensities at 75% gas exchange threshold, 85% gas exchange threshold, and ∆15. At each intensity, the measured steady-state V˙O2 during each 30-min test was compared to the V˙O2 predicted after adjustment by each of the three MRTs. Results: For all three MRT methods, predicted V˙O2 was not different (p = 1.000) from the measured V˙O2 at 75%GET (MRTEXP, 31 mL, MRTLIN, -35 mL, MRTSS 11 mL), 85%gas exchange threshold (MRTEXP -14 mL, MRTLIN -80 mL, MRTSS -32 mL). At Δ15, predicted V˙O2 based on MRTEXP was not different (p = .767) from the measured V˙O2, but was different for MRTLIN (p < .001) and MRTSS (p = .03). Conclusion: Given that the intensity is below gas exchange threshold, all model predictions implemented from the current study matched the exercise prescription.

OBJECTIVE: The main objective of this work is to design an efficient numerical scheme is proposed for solving singularly perturbed time delayed parabolic problems with two parameters.
RESULTS: The scheme is constructed via the implicit Euler and non-standard finite difference method to approximate the time and space derivatives, respectively. Besides, to enhance the accuracy and order of convergence of the method Richardson extrapolation technique is employed. Intensive numerical experimentation has been done on some model examples. Further, the layer behavior of the solutions is presented using graphs and observed to agree with the existing theories. Finally, error analysis of the scheme is done and observed that the proposed method is parameter uniform convergent with the order of convergence ( Δ t ) 2 + h 2 .

OBJECTIVE: To propose a straightforward and time-efficient quality assurance (QA) approach of beam time delay for respiratory-gated radiotherapy and validate the proposed method on typical respiratory gating systems, Catalyst™ and AlignRT™.
METHODS: The QA apparatus was composed of a motion platform and a Winston-Lutz cube phantom (WL3) embedded with metal balls. The apparatus was first scanned in CT-Sim and two types of QA plans specific for beam on and beam off time delay, respectively, were designed. Static reference images and motion testing images of the WL3 cube were acquired with EPID. By comparing the position differences of the embedded metal balls in the motion and reference images, beam time delays were determined. The proposed approach was validated on three linacs with either Catalyst™ or AlignRT™ respiratory gating systems. To investigate the impact of energy and dose rate on beam time delay, a range of QA plans with Eclipse (V15.7) were devised with varying energy and dose rates.
RESULTS: For all energies, the beam on time delays in AlignRT™ V6.3.226, AlignRT™ V7.1.1, and Catalyst™ were 92.13 ± $ \\pm $ 5.79 ms, 123.11 ± $ \\pm $ 6.44 ms, and 303.44 ± $ \\pm $ 4.28 ms, respectively. The beam off time delays in AlignRT™ V6.3.226, AlignRT™ V7.1.1, and Catalyst™ were 121.87 ± $ \\pm $ 1.34 ms, 119.33 ± $ \\pm $ 0.75 ms, and 97.69 ± $ \\pm $ 2.02 ms, respectively. Furthermore, the beam on delays decreased slightly as dose rates increased for all gating systems, whereas the beam off delays remained unaffected.
CONCLUSIONS: The validation results demonstrate the proposed QA approach of beam time delay for respiratory-gated radiotherapy was both reproducible and time-efficient to practice for institutions to customize accordingly.

Graphene Nano Scrolls (GNSs) and Zigzag graphene nanoscrolls (ZGNSs) are semi-one-dimensional materials with exceptional electrical and optical properties, making them attractive to be used in nanoelectronics and complementary metal-oxide-semiconductor (CMOS) technology. With in CMOS device technology, time delay is a crucial issue in the design and implementation of CMOS based ZGNSs. Current paper focus is on ZGNSs application in the channel area of metal-oxide-semiconductor field-effect transistors (MOSFETs) in CMOS technology. We studied analytically, the importance of different parameters on time delay reduction, resulting in faster switching and higher frequency in integrated circuits (ICs). The results of this research demonstrates that, the ZGNS-based CMOS proves considerable variations in the current due to the geometrical parameters, such as chirality number, channel length, and nanoscroll length which can be engineered to produce faster ICs.