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The time function method is one of the most commonly used methods for predicting surface dynamic displacements in coal mine areas. In which, the accuracy and reliability of the predicted displacements, to a large extent, depends on the selected mathematical functions for describing the “S”-typed dynamic subsidence at a single surface point (referred to as time functions). Nearly all of the existing studies primarily improve or introduce “S”-shaped growth functions with a single object to minimizing the fitting residuals between the in-situ monitored and the model-fitted subsidence. Such a strategy, however, would result in “overfitting” (or over-parameterization), thereby increasing the complexity of the constructed time function model and the difficulty of model parameter inversion. To this end, the optimal selection of time functions was analyzed in this paper using two indicators of fitting residual and model complexity, rather than the former one in existing studies. More specifically, time-series subsidence observations at 103 field points in seven coal mining areas with different geological mining conditions were selected to be observation samples for ensuring the applicability of the optimal time function. Then, 12 common “S-shaped” growth models were chosen to candidates, and the theoretical analysis and Akaike information criterion (AIC) were further used to analyze the optimal selection of time function from the chosen 12 “S”-shaped models. The results show that: ① Among the 12 selected models, the mean mis-fitting error of the five four-parameter models is about 3.51 cm, which is obviously smaller than that of the two-parameter Knothe model (14.10 cm), but just slightly smaller than the six three-parameter models (4.78 cm); ② In the view of making a trade-off between fitting residuals and model complexity (assessing by the AIC), the AICs of the six three-parameter models are smaller than those of the four-parameter and two-parameter models.This indicates that the three-parameters models are preferrable to describe the temporal evolution of subsidence at a single point, and the four-parameter and two-parameters models may be over-fitted and under-fitted, respectively; ③ Among the six selected models, the optimal selection of time function is related to the lithology of the overburden rock strata; that is, Hossfeld model, which has not been introduced into the time function method, is preferrable under soft and medium-hard overburden strata, whereas Weibull model is preferrable under hard overburden strata.

Objective To investigate the clinical and electroencephalographic (EEG) features of children with eating-induced reflex epilepsy. Methods A retrospective analysis was performed for the clinical features, EEG findings, treatment, and prognosis of three children with eating-induced reflex epilepsy who attended Department of Pediatrics in our hospital from 2014 to 2024. Results There were two boys among the three children. Two children had normal intellectual development before the onset of the disease, while one was diagnosed with intellectual disability. All three children had normal cranial MRI results, and whole-exome genetic testing and copy number variation testing were performed for two children and their families, which yielded negative results. In case 1, the child had focal seizures and later developed into focal secondary bilateral tonic-clonic seizures, and EEG monitoring showed bilateral Rolandic discharges in the interictal period, but without eating-induced seizures. In case 2, the child had focal epileptic spasms during wakefulness and generalized myoclonic seizures during sleep, and EEG monitoring showed the coexistence of multifocal discharges and generalized discharges in the interictal period, drinking water induced three clusters of predominantly right-sided generalized multiphase slow waves with epileptic spasms, as well as several spontaneous generalized myo-clonic seizures during sleep. In case 3, the child had coexistence of focal epileptic spasms and generalized tonic seizures, and EEG monitoring showed the coexistence of multifocal discharges and generalized discharges, eating induced a cluster of predominantly left posterior multiphase slow waves with epileptic spasms. All three children received more than two anti-seizure medications (ASMs) and failed to achieve the control of seizures, and they presented with varying degrees of intellectual disability after disease onset. Conclusion Eating-induced reflex epilepsy is slightly more common in boys and is often accompanied by intellectual disability after disease onset. The coexistence of spontaneous seizures and induced seizures is often observed in this disease, with epileptic spasms being the more common type of eating-induced seizures. EEG manifestations in the interictal period include focal discharges, generalized discharges, or the coexistence of both types of discharges. ASMs have a poor therapeutic effect on this disease.