Oscillation analysis of numerical solutions for nonlinear delay differential equations of population dynamics

This paper is concerned with oscillations of numerical solutions for the nonlinear delay differential equation of population dynamics. The equation proposed by Mackey and Glass for a ”dynamic disease” involves respiratory disorders and its solution resembles the envelope of lung ventilation for pathological breathing, called Cheyne-Stokes respiration. Some conditions under which the numerical solution is oscillatory are obtained. The properties of non-oscillatory numerical solutions are investigated. To verify our results, we give numerical experiments

Forward and Backward Information Retention for Accurate Binary Neural Networks

Weight and activation binarization is an effective approach to deep neural network compression and can accelerate the inference by leveraging bitwise operations. Although many binarization methods have improved the accuracy of the model by minimizing the quantization error in forward propagation, there remains a noticeable performance gap between the binarized model and the full-precision one. Our empirical study indicates that the quantization brings information loss in both forward and backward propagation, which is the bottleneck of training accurate binary neural networks. To address these issues, we propose an Information Retention Network (IR-Net) to retain the information that consists in the forward activations and backward gradients. IR-Net mainly relies on two technical contributions: (1) Libra Parameter Binarization (Libra-PB): simultaneously minimizing both quantization error and information loss of parameters by balanced and standardized weights in forward propagation; (2) Error Decay Estimator (EDE): minimizing the information loss of gradients by gradually approximating the sign function in backward propagation, jointly considering the updating ability and accurate gradients. We are the first to investigate both forward and backward processes of binary networks from the unified information perspective, which provides new insight into the mechanism of network binarization. Comprehensive experiments with various network structures on CIFAR-10 and ImageNet datasets manifest that the proposed IR-Net can consistently outperform state-of-the-art quantization methods

Noise expresses exponential growth under regime switching

Consider a given system under regime switching whose solution grows at most polynomially, and suppose that the system is subject to environmental noise in some regimes. Can the regime switching and the environmental noise work together to make the system change signicantly? The answer is yes. In this paper, we will show that the regime switching and the environmental noise will make the original system whose solution grows at most polynomially become a new system whose solution will grow exponentially. In other words, we reveal that the regime switching and the environmental noise will exppress the exponential growth

Independent Association of Serum Fibroblast Growth Factor 21 Levels With Impaired Liver Enzymes in Hyperthyroid Patients

Fibroblast growth factor 21 (FGF21) is identified as a potential biomarker for liver diseases. However, information is limited regarding serum FGF21 and impaired liver function in hyperthyroidism. We aim to determine the potential association of serum FGF21 levels with impaired liver enzymes in hyperthyroid patients. In this case-control study, 105 normal subjects and 122 overt hyperthyroid patients were included. Among them, 41 hyperthyroid patients who obtained euthyroid status after thionamide treatment received second visit. Serum FGF21 levels were determined using the ELISA method. Compared to the normal subjects, patients with hyperthyroidism had significantly elevated serum liver enzymes, including alanine transaminase (ALT) (p < 0.001), aspartate aminotransferase (AST) (p < 0.001) levels, as well as FGF21 levels (p < 0.001). Further analysis showed serum FGF21 (p < 0.05), as well as thyroid hormone (TH) free T3 (p < 0.05), free T4 (p < 0.05) levels were higher in hyperthyroid patients with impaired liver enzymes than in those with normal liver enzymes. After reversal of hyperthyroid state, elevated serum FGF21 levels in hyperthyroid patients declined significantly (p < 0.001), with a concomitant decrease in serum ALT (p < 0.001), AST (p < 0.001) levels. Correlation analysis showed close correlation between FGF21 and ALT (p < 0.002), AST (p < 0.012), free T3 (p < 0.001), free T4 (p < 0.001). Further logistic regression analysis revealed FGF21 is significantly associated with elevated ALT [Odds Ratio, OR 1.79, (95% confidence interval, CI), (1.30–2.47), P < 0.001], AST [1.59 (1.07–2.34), p < 0.020]. After adjustment of potential confounders, the association between FGF21 and elevated ALT remained significant [1.42 (1.01–1.99), p < 0.043]. In conclusion, serum FGF21 is independently associated with impaired liver enzymes in hyperthyroid patients

Higher fibrinogen and neutrophil-to-lymphocyte ratio are associated with the early poor response to intravenous thrombolysis in acute ischemic stroke

BackgroundInflammation and platelet activation play pivotal roles in acute ischemic stroke (AIS) pathogenesis. Early response to thrombolysis is a vital indicator for the long-term prognosis of AIS. However, the correlation between fibrinogen or the neutrophil-to-lymphocyte ratio (NLR) and the early response to intravenous thrombolysis in patients with AIS remains unclear.MethodsAIS patients undergoing intravenous thrombolysis were enrolled between January 2018 and May 2023. Blood cell counts were sampled before thrombolysis. A good response was defined as a National Institutes of Health Stroke Scale (NIHSS) score decreased ≥4 or complete recovery 24 h after thrombolysis treatment. A poor response was defined as any increase in the NIHSS score or a decrease in the NIHSS score <4 at the 24 h after thrombolysis treatment compared with that at admission. Logistic regression analysis was performed to explore the relationship of the fibrinogen level and NLR with a poor thrombolysis response. Receiver operating characteristic (ROC) analysis was used to assess the ability of the fibrinogen level and NLR to discriminate poor responders.ResultsAmong 700 recruited patients, 268 (38.29%) were diagnosed with a good response, and 432 (61.71%) were diagnosed with a poor response to intravenous thrombolysis. A binary logistic regression model indicated that an elevated fibrinogen level (odds ratio [OR], 1.693; 95% confidence interval [CI] 1.325–2.122, P < 0.001) and NLR (OR, 1.253; 95% CI, 1.210–2.005, P = 0.001) were independent factors for a poor response. The area under the curve (AUC) values for the fibrinogen level, NLR and fibrinogen level combined with the NLR for a poor response were 0.708, 0.605, and 0.728, respectively.ConclusionsOur research indicates that the levels of fibrinogen and NLR at admission can be used as a prognostic factor to predict early poor response to intravenous thrombolysis