Lie-Poisson Neural Networks (LPNets): Data-based computing of Hamiltonian systems with symmetries

An accurate data-based prediction of the long-term evolution of Hamiltonian systems requires a network that preserves the appropriate structure under each time step. Every Hamiltonian system contains two essential ingredients: the Poisson bracket and the Hamiltonian. Hamiltonian systems with symmetries, whose paradigm examples are the Lie-Poisson systems, have been shown to describe a broad category of physical phenomena, from satellite motion to underwater vehicles, fluids, geophysical applications, complex fluids, and plasma physics. The Poisson bracket in these systems comes from the symmetries, while the Hamiltonian comes from the underlying physics. We view the symmetry of the system as primary, hence the Lie-Poisson bracket is known exactly, whereas the Hamiltonian is regarded as coming from physics and is considered not known, or known approximately. Using this approach, we develop a network based on transformations that exactly preserve the Poisson bracket and the special functions of the Lie-Poisson systems (Casimirs) to machine precision. We present two flavors of such systems: one, where the parameters of transformations are computed from data using a dense neural network (LPNets), and another, where the composition of transformations is used as building blocks (G-LPNets). We also show how to adapt these methods to a larger class of Poisson brackets. We apply the resulting methods to several examples, such as rigid body (satellite) motion, underwater vehicles, a particle in a magnetic field, and others. The methods developed in this paper are important for the construction of accurate data-based methods for simulating the long-term dynamics of physical systems.

Long short-term memory models to quantify long-term evolution of streamflow discharge and groundwater depth in Alabama

Long short-term memory (LSTM) models have been shown to be efficient for rainfall-runoff modeling, and to a lesser extent, for groundwater depth forecasting. In this study, LSTMs were applied to quantify the spatiotemporal evolution of surface and subsurface hydrographs in Alabama in the Southeastern United States, where water sustainability has not been fully quantified across spatiotemporal scales. First, the surface water LSTM model with extensive dynamic (precipitation and other weather variables) and static (basin characteristics) inputs predicted the main characteristics of streamflow for six years at 19 gauged basins in Alabama. The model tended to underestimate extremely high streamflow but adding drainage density as an input feature slightly improved the predictions of extreme events. Second, to predict the groundwater depth evolution, a groundwater LSTM (GW-LSTM) model was proposed and applied using static inputs capturing the aquifers' hydrogeological properties and dynamic inputs of meteorological information. Three precipitation scenarios were also explored to evaluate the groundwater hydrograph evolution in the next two decades. The GW-LSTM model predicted the general trend of daily groundwater depth fluctuations (at 21 wells distributed across Alabama from 1990 to 2021) including most extremely high groundwater levels, and recovered groundwater depth for locations withheld from model training and validation. This study, therefore, extended the application of LSTMs in quantifying the spatiotemporal evolution of surface water and groundwater, two manifestations of a single integrated resource.

Identification of long-term evolution of ozone sensitivity to precursors based on two-dimensional mutual verification

Tropospheric ozone pollution has been continuously worsening in China during the past decade. Identification of long-term evolution of ozone sensitivity to precursors is essential to evaluating the impact of emission reduction measures on ozone pollution. Traditional observation-based model and 3-d numerical model are not suitable for analyzing long-term variation of ozone sensitivity to precursors. In this study, by transforming the conventional ozone isopleth plot into a VOCR isopleth plot in the functional space of NO_x and ozone concentrations, we developed a novel approach to identify ozone sensitivity to precursors by simply using long-term monitoring data of ozone, NO_x and temperature. This approach estimated ozone formation regimes (OFR) by ozone sensitivity to NO_x and temperature separately, and the convergence of OFR serves as a way of mutual verification. We found that ozone formation was generally in the VOCR-limited or transitional regime in Shanghai, the largest metropolitan area in China. However, OFR was shifted to NO_x-limited at Pudong station during 2017-19 due much to the stringent NO_x emission control. OFR was also shifted to NO_x-limited along with the increasing temperature. When temperature was over 30 °C, Shanghai was mostly in a NO_x-limited OFR. This highlights that the NO_x emission control measures need to be strengthened to reduce peak ozone levels more efficiently. Jinshan station exhibited a different trend with OFR shifted to VOCR-limited in 2017-19, which proved the effectiveness of VOCs emission control on petrochemical sector. However, OFR was shifted to NO_x-limited when temperature was over 30 °C, suggesting more stringent VOCs emissions control should be targeted on days with higher temperature.

Functional and network analyses of human exposure to long-term evolution signal

Human exposure to the electromagnetic field emitted by wireless communication systems has raised public concerns. There were claims of the potential association of some neurophysiological disorders with the exposure, but the mechanism is yet to be established. The wireless networks, recently, experience a transition from the 4th generation (4G) to 5th generation (5G), while 4G long-term evolution (LTE) is still the frequently used signal in wireless communication. In the study, exposure experiments were conducted using the LTE signal. The subjects were divided into sham and real exposure groups. Before and after the exposure experiments, they underwent functional magnetic resonance imaging. Within-session and between-session comparisons have been executed for functional connectivity and network properties. Individual specific absorption rate (SAR) was also calculated. The results indicated that acute LTE exposure beneath the safety limits modulated both the functional connection and graph-based properties. To characterize the effect of functional activity, SAR averaged over a certain tissue mass was not an appropriate metric. The potential neurophysiological effect of 5G exposure has also been discussed in the study.

Long-term monitoring of PCDD/Fs in soils in the vicinity of a hazardous waste incinerator in China: Temporal variations and environmental impacts

Campaigns from 2008 to 2016 are carried out to study temporal variations and environmental impacts of polychlorinated dibenzo-p-dioxin and dibenzofuran (PCDD/Fs) in soils in the vicinity of a new hazardous waste incinerator (HWI) in China. Results indicate that after 8-year operation of HWI, the geometrical means of both the total concentrations and the TEQ values of PCDD/Fs in soils decrease from 1280 ng·kg^-1 and 3.08 ng WHO-TEQ·kg^-1 to 568 ng·kg^-1 and 2.70 ng WHO-TEQ·kg^-1, respectively, showing generally limited impact on soils within 7.5 km. Temporal changes of PCDD/Fs congener profiles trend to profiles in combustion sources. Considering the whole studied area, results of principal component analysis between soils and emission sources show that instead of HWI, other sources including open burning, traffic, and cement plant are more responsible for PCDD/Fs accumulation. The modeling results of AERMOD indicate the dominant roles of wind velocities and directions on the deposition of PCDD/Fs emitted from HWI. The largest PCDD/Fs increase value in soils predicted by integrating AERMOD and a reservoir model is very limited after 25 years (2.03 × 10^-5 ng WHO-TEQ·kg^-1), indicating relatively minor impacts of HWI on surrounding soils, but the noticeable impact on area downwind from the stack in short distance (e.g., within 0.5 km) should be recognized.

Lennox-Gastaut syndrome in adulthood: Long-term clinical follow-up of 38 patients and analysis of their recorded seizures

Lennox-Gastaut syndrome (LGS) is a severe epileptic encephalopathy with childhood onset that usually continues through adolescence and into adulthood. In the long term, patients with this condition still have intractable seizures, intellectual disability, behavioral problems, and physical comorbidities. The aim of this study was to describe the clinical and EEG characteristics of a group of adults with Lennox-Gastaut syndrome. We identified 38 (22 females, 16 males) patients with LGS older than age 18years at their last evaluation, with mean age of 43.3±10.6years. Median follow-up was 14.4years (range: 2-40). All of our patients had 3 or more seizure types during their clinical history. The most prevalent seizure types at follow-up were atypical absences (28/38), tonic (28/38), generalized tonic-clonic (17/38), focal (11/38), and myoclonic seizures (9/38). All patients had drug-resistant seizures. Besides epilepsy, intellectual disability and behavioral problems were prominent features. Surprisingly, paroxysmal nonepileptic seizures were reported in 3 patients. Our observations confirm the poor outcome of Lennox-Gastaut syndrome through adulthood, regardless of age at seizure onset, etiology, and history of previous West syndrome.

[Long-term evolution of detorsion of the testes after acute scrotum]

OBJECTIVES

To assess the long-term evolution of the testicles preserved after testicular torsion (TT).

MATERIAL AND METHODS

We realized a prospective study by ultrasound of patients diagnosed TT that underwent orchidopexy. We reviewed 85 patients treated for acute scrotum (2004-2014), finding 49TT. We excluded from the study 15 perinatal torsions, 14 orchiectomies and 5 patients who refused to participate. We analyzed 15 patients, comparing testicular volumes between affected and contralateral testes, and the difference in volume between the two testes of the 15 cases with 14 control patients (Mann-Whitney U test).

RESULTS

15 patients underwent surgery at a mean age of 10,7 years, with an average time of 6 hours evolution [0,7-24]. The control ultrasound was performed at a mean age of 14,7 years, after a mean time of 47 months after the episode, finding a medium volume of the affected and contralateral testicle of 9,3 cc and 12,6 cc, respectively (p = 0,683). The median of the difference between the volumes was 0'8 cc [0,1-12,80]. In the control group, ultrasounds were performed at a mean age of 16 years, with an average volume of 6,64 cc on right testicle and 6,26 cc on the left, and median volume difference of 0,34 cc [0,05-4,59]; with no statistically significant difference (p = 0,270) between testicular volume differences of cases and controls.

CONCLUSION

Testicular orchidopexy in patients with TT with less than 6 hours of evolution does not affect the long-term testicular growth, compared with the contralateral testis growth and testes of the normal population.