The joint Laplace transforms for killed diffusion occupation times

The approach of Li and Zhou(2014)is adopted to find the Laplace transform of occupation time over interval(0,a)and joint occupation times over semi-infinite intervals(-∞,a)and(b,∞)for a time-homogeneous diffusion process up to an independent exponential time e_(q)for 0<a<b.The results are expressed in terms of solutions to the differential equations associated with the diffusion generator.Applying these results,we obtain explicit expressions on the Laplace transform of occupation time and joint occupation time for Brownian motion with drift.

Nonlinear Time History Analysis for the Different Column Orientations under Seismic Wave Synthetic Approach

The significant impact of earthquakes on human lives and the built environment underscores the extensive human and economic losses caused by structural collapses. Over the years, researchers have focused on improving seismic design to mitigate earthquake-induced damages and enhance structural performance. In this study, a specific reinforced concrete (RC) frame structure at Kyungpook National University, designed for educational purposes, is analyzed as a representative case. Utilizing SAP 2000, the research conducts a nonlinear time history analysis to assess the structural performance under seismic conditions. The primary objective is to evaluate the influence of different column section designs, while maintaining identical column section areas, on structural behavior. The study employs two distinct seismic waves from Abeno (ABN) and Takatori (TKT) for the analysis, comparing the structural performance under varying seismic conditions. Key aspects examined include displacement, base shear force, base moment, joint radians, and layer displacement angle. This research is anticipated to serve as a valuable reference for seismic restraint reinforcement work on RC buildings, enriching the methods used for evaluating structures through nonlinear time history analysis based on the synthetic seismic wave approach.

VARIATIONAL ANALYSIS FOR THE MAXIMAL TIME FUNCTION IN NORMED SPACES

For a general normed vector space,a special optimal value function called a maximal time function is considered.This covers the farthest distance function as a special case,and has a close relationship with the smallest enclosing ball problem.Some properties of the maximal time function are proven,including the convexity,the lower semicontinuity,and the exact characterizations of its subdifferential formulas.

ESTIMATION OF AVERAGE DIFFERENTIAL ENTROPY FOR A STATIONARY ERGODIC SPACE-TIME RANDOM FIELD ON A BOUNDED AREA

In this paper,we mainly discuss a discrete estimation of the average differential entropy for a continuous time-stationary ergodic space-time random field.By estimating the probability value of a time-stationary random field in a small range,we give an entropy estimation and obtain the average entropy estimation formula in a certain bounded space region.It can be proven that the estimation of the average differential entropy converges to the theoretical value with a probability of 1.In addition,we also conducted numerical experiments for different parameters to verify the convergence result obtained in the theoretical proofs.

TSCND:Temporal Subsequence-Based Convolutional Network with Difference for Time Series Forecasting

Time series forecasting plays an important role in various fields, such as energy, finance, transport, and weather. Temporal convolutional networks (TCNs) based on dilated causal convolution have been widely used in time series forecasting. However, two problems weaken the performance of TCNs. One is that in dilated casual convolution, causal convolution leads to the receptive fields of outputs being concentrated in the earlier part of the input sequence, whereas the recent input information will be severely lost. The other is that the distribution shift problem in time series has not been adequately solved. To address the first problem, we propose a subsequence-based dilated convolution method (SDC). By using multiple convolutional filters to convolve elements of neighboring subsequences, the method extracts temporal features from a growing receptive field via a growing subsequence rather than a single element. Ultimately, the receptive field of each output element can cover the whole input sequence. To address the second problem, we propose a difference and compensation method (DCM). The method reduces the discrepancies between and within the input sequences by difference operations and then compensates the outputs for the information lost due to difference operations. Based on SDC and DCM, we further construct a temporal subsequence-based convolutional network with difference (TSCND) for time series forecasting. The experimental results show that TSCND can reduce prediction mean squared error by 7.3% and save runtime, compared with state-of-the-art models and vanilla TCN.

The Emergence of Time from Quantum Information Dynamics

This paper presents a novel framework for understanding time as an emergent phenomenon arising from quantum information dynamics. We propose that the flow of time and its directional arrow are intrinsically linked to the growth of quantum complexity and the evolution of entanglement entropy in physical systems. By integrating principles from quantum mechanics, information theory, and holography, we develop a comprehensive theory that explains how time can emerge from timeless quantum processes. Our approach unifies concepts from quantum mechanics, general relativity, and thermodynamics, providing new perspectives on longstanding puzzles such as the black hole information paradox and the arrow of time. We derive modified Friedmann equations that incorporate quantum information measures, offering novel insights into cosmic evolution and the nature of dark energy. The paper presents a series of experimental proposals to test key aspects of this theory, ranging from quantum simulations to cosmological observations. Our framework suggests a deeply information-theoretic view of the universe, challenging our understanding of the nature of reality and opening new avenues for technological applications in quantum computing and sensing. This work contributes to the ongoing quest for a unified theory of quantum gravity and information, potentially with far-reaching implications for our understanding of space, time, and the fundamental structure of the cosmos.

Seasonal Characteristics of Forecasting Uncertainties in Surface PM_(2.5)Concentration Associated with Forecast Lead Time over the Beijing-Tianjin-Hebei Region

Forecasting uncertainties among meteorological fields have long been recognized as the main limitation on the accuracy and predictability of air quality forecasts.However,the particular impact of meteorological forecasting uncertainties on air quality forecasts specific to different seasons is still not well known.In this study,a series of forecasts with different forecast lead times for January,April,July,and October of 2018 are conducted over the Beijing-Tianjin-Hebei(BTH)region and the impacts of meteorological forecasting uncertainties on surface PM_(2.5)concentration forecasts with each lead time are investigated.With increased lead time,the forecasted PM_(2.5)concentrations significantly change and demonstrate obvious seasonal variations.In general,the forecasting uncertainties in monthly mean surface PM_(2.5)concentrations in the BTH region due to lead time are the largest(80%)in spring,followed by autumn(~50%),summer(~40%),and winter(20%).In winter,the forecasting uncertainties in total surface PM_(2.5)mass due to lead time are mainly due to the uncertainties in PBL heights and hence the PBL mixing of anthropogenic primary particles.In spring,the forecasting uncertainties are mainly from the impacts of lead time on lower-tropospheric northwesterly winds,thereby further enhancing the condensation production of anthropogenic secondary particles by the long-range transport of natural dust.In summer,the forecasting uncertainties result mainly from the decrease in dry and wet deposition rates,which are associated with the reduction of near-surface wind speed and precipitation rate.In autumn,the forecasting uncertainties arise mainly from the change in the transport of remote natural dust and anthropogenic particles,which is associated with changes in the large-scale circulation.

Clinical efficacy and safety of kyphoplasty for the treatment of osteoporotic vertebral compression fractures at different surgical timings based on the theory of“dynamic-static integration”

Objective:To investigate the clinical efficacy and safety of percutaneous kyphoplasty at different surgical timings in the treatment of osteoporotic vertebral compression fracture(OVCF)based on the theory of“dynamic-static integration”.Methods:Patients with OVCF who underwent percutaneous kyphoplasty in our hospital were selected and divided into Groups A,B,and C for those undergoing surgery within 7,7—21,and>21 days of fracture occurrence.The variations in the amount of bone cement injected,pre-and post-operative pain levels,functional activity,deformity correction of the injured vertebrae,bone cement leakage,and vertebral body height loss were compared among the three groups.Results:Regarding pain relief and functional activity,the postoperative Visual Analog Scale and Oswestry Disability Index scores of the three groups significantly improved.Furthermore,the deformities of the injured vertebrae in the three groups were significantly corrected,with Groups A and B exhibiting superior correction compared to Group C.Moreover,the bone cement leakage rates in groups A and C were higher than that in Group B.At the 3-month follow-up,the loss of vertebral height in Group C was significantly higher than those in groups A and B.Conclusion:Kyphoplasty is effective for OVCF treatment.Early surgery can effectively restore the vertebral height of the injured vertebra,reduce kyphosis,and reduce height loss of the injured vertebra after surgery;nevertheless,treatment within 1—3 weeks of the fracture can reduce the occurrence of bone cement leakage,making the surgery safer.Therefore,surgical treatment within 1—3 weeks of fracture is safer and can achieve satisfactory therapeutic effects.From the perspective of traditional Chinese medicine,PKP surgery can transform the fracture end from a micromotion state to a fixed state,which fully embodies the theory of“dynamic-static integration”.

Deep Learning for Financial Time Series Prediction:A State-of-the-Art Review of Standalone and HybridModels

Financial time series prediction,whether for classification or regression,has been a heated research topic over the last decade.While traditional machine learning algorithms have experienced mediocre results,deep learning has largely contributed to the elevation of the prediction performance.Currently,the most up-to-date review of advanced machine learning techniques for financial time series prediction is still lacking,making it challenging for finance domain experts and relevant practitioners to determine which model potentially performs better,what techniques and components are involved,and how themodel can be designed and implemented.This review article provides an overview of techniques,components and frameworks for financial time series prediction,with an emphasis on state-of-the-art deep learning models in the literature from2015 to 2023,including standalonemodels like convolutional neural networks(CNN)that are capable of extracting spatial dependencies within data,and long short-term memory(LSTM)that is designed for handling temporal dependencies;and hybrid models integrating CNN,LSTM,attention mechanism(AM)and other techniques.For illustration and comparison purposes,models proposed in recent studies are mapped to relevant elements of a generalized framework comprised of input,output,feature extraction,prediction,and related processes.Among the state-of-the-artmodels,hybrid models like CNNLSTMand CNN-LSTM-AM in general have been reported superior in performance to stand-alone models like the CNN-only model.Some remaining challenges have been discussed,including non-friendliness for finance domain experts,delayed prediction,domain knowledge negligence,lack of standards,and inability of real-time and highfrequency predictions.The principal contributions of this paper are to provide a one-stop guide for both academia and industry to review,compare and summarize technologies and recent advances in this area,to facilitate smooth and informed implementation,and to highlight future research directions.

A Novel Method for Linear Systems of Fractional Ordinary Differential Equations with Applications to Time-Fractional PDEs

This paper presents an efficient numerical technique for solving multi-term linear systems of fractional ordinary differential equations(FODEs)which have been widely used in modeling various phenomena in engineering and science.An approximate solution of the system is sought in the formof the finite series over the Müntz polynomials.By using the collocation procedure in the time interval,one gets the linear algebraic system for the coefficient of the expansion which can be easily solved numerically by a standard procedure.This technique also serves as the basis for solving the time-fractional partial differential equations(PDEs).The modified radial basis functions are used for spatial approximation of the solution.The collocation in the solution domain transforms the equation into a system of fractional ordinary differential equations similar to the one mentioned above.Several examples have verified the performance of the proposed novel technique with high accuracy and efficiency.

Different timing for abdominal paracentesis catheter placement and drainage in severe acute pancreatitis complicated by intraabdominal fluid accumulation

BACKGROUND Non-surgical methods such as percutaneous drainage are crucial for the treatment of patients with severe acute pancreatitis(SAP).However,there is still an ongoing debate regarding the optimal timing for abdominal paracentesis catheter place-ment and drainage.AIM To explore the influence of different timing for abdominal paracentesis catheter placement and drainage in SAP complicated by intra-abdominal fluid accumu-lation.METHODS Using a retrospective approach,184 cases of SAP complicated by intra-abdominal fluid accumulation were enrolled and categorized into three groups based on the timing of catheter placement:group A(catheter placement within 2 d of symptom onset,n=89),group B(catheter placement between days 3 and 5 after symptom onset,n=55),and group C(catheter placement between days 6 and 7 after symptom onset,n=40).The differences in progression rate,mortality rate,and the number of cases with organ dysfunction were compared among the three groups.RESULTS The progression rate of group A was significantly lower than those in groups B and groups C(2.25%vs 21.82%and 32.50%,P<0.05).Further,the proportion of patients with at least one organ dysfunction in group A was significantly lower than those in groups B and groups C(41.57%vs 70.91%and 75.00%,P<0.05).The mortality rates in group A,group B,and group C were similar(P>0.05).At postoperative day 3,the levels of C-reactive protein(55.41±19.32 mg/L vs 82.25±20.41 mg/L and 88.65±19.14 mg/L,P<0.05),procalcitonin(1.36±0.51 ng/mL vs 3.20±0.97 ng/mL and 3.41±0.98 ng/mL,P<0.05),tumor necrosis factor-alpha(15.12±6.63 pg/L vs 22.26±9.96 pg/L and 23.39±9.12 pg/L,P<0.05),interleukin-6(332.14±90.16 ng/L vs 412.20±88.50 ng/L and 420.08±87.65ng/L,P<0.05),interleukin-8(415.54±68.43 ng/L vs 505.80±66.90 ng/L and 510.43±68.23ng/L,P<0.05)and serum amyloid A(270.06±78.49 mg/L vs 344.41±81.96 mg/L and 350.60±80.42 mg/L,P<0.05)were significantly lower in group A compared to those in groups B and group C.The length of hospital stay in group A was significantly lower than those in groups B and group C(24.50±4.16 d vs 35.54±6.62 d and 38.89±7.10 d,P<0.05).The hospitalization expenses in group A were also significantly lower than those in groups B and groups C[2.70(1.20,3.55)ten-thousand-yuan vs 5.50(2.98,7.12)ten-thousand-yuan and 6.00(3.10,8.05)ten-thousand-yuan,P<0.05).The incidence of complications in group A was markedly lower than that in group C(5.62%vs 25.00%,P<0.05),and similar to group B(P>0.05).CONCLUSION Percutaneous catheter drainage for the treatment of SAP complicated by intra-abdominal fluid accumulation is most effective when performed within 2 d of onset.

Research on the Damping Mechanism of Time-Delay Coupled Negative Stiffness Dynamic Absorber in Nonlinear Vibration Damping System

A study was conducted on the effect of time delay and structural parameters on the vibration reduction of a time delayed coupled negative stiffness dynamic absorber in nonlinear vibration reduction systems. Taking dynamic absorbers with different structural and control parameters as examples, the effects of third-order nonlinear coefficients, time-delay control parameters, and negative stiffness coefficients on reducing the replication of the main system were discussed. The nonlinear dynamic absorber has a very good vibration reduction effect at the resonance point of the main system and a nearby area, and when 1 increases to a certain level, the stable region of the system continues to increase. The amplitude curve of the main system of a nonlinear dynamic absorber will generate Hop bifurcation and saddle node bifurcation in the region far from the resonance point, resulting in almost periodic motion and jumping phenomena in the system. For nonlinear dynamic absorbers with determined structural parameters, time-delay feedback control can be adopted to control the amplitude of the main system. For different negative stiffness coefficients, there exists a minimum damping point for the amplitude of the main system under the determined system structural parameters and time-delay feedback control parameters.

The Influence of the Implementation of Trade Facilitation Systems on the Time Required for Creating Delivery Orders: A Case Study of Tema Port

This study evaluated the impact of Ghana’s Integrated Customs Management System (ICUMS), implemented within the National Single Window initiative, on the efficiency of issuing Delivery Orders (DO) at Tema Port. Filling a gap in the existing literature, the research employed a quantitative approach to assess a specific time-related aspect of the cargo clearance process. Employing an Independent t-test on a dataset spanning 2026 Delivery Orders (924 pre-ICUMS and 1102 post-ICUMS) from July 2020 to July 2023, the study investigated ICUMS’s effectiveness in reducing DO issuance time. Results indicate a noteworthy decrease in average DO issuance time, from 11 days pre-implementation to approximately 9 days post-implementation, a reduction validated by statistical analysis through the independent t-test. In light of these findings, the study recommends ongoing refinement of the implementation, reinforcement of trade facilitation measures, and the adoption of best practices from successful global ports. Continuous stakeholder training and regular assessments of ICUMS performance are also endorsed. The study’s implications support the theoretical framework for Single Window systems and carry significant policy implications, emphasizing the need for collaborative efforts to streamline trade facilitation processes driven by Information Technology. Practically, the results serve as a management tool for stakeholders, highlighting areas for targeted interventions to reduce DO issuance times. Methodologically, this research contributes by applying robust statistical analysis to a specific component within the Time Release Study framework, offering a nuanced understanding of trade facilitation systems’ effectiveness in improving cargo clearance processes.

Dependence of Lower Molding Temperature Limit and Molding Time on Molding Mechanism in Dental Thermoforming

Effectiveness and safety of a sports mouthguard depend on its thickness and material, and the thermoforming process affects these. The purpose of this study was to clarify the effects of differences in molding mechanisms on the lower molding temperature limit and molding time in dental thermoforming. Ethylene vinyl acetate resin mouthguard sheet and two thermoforming machines;vacuum blower molding machine and vacuum ejector/pressure molding machine were used. The molding pressures for suction molding were −0.018 MPa for vacuum blower molding and −0.090 MPa for vacuum ejector molding, and for pressure molding was set to 0.090 MPa or 0.450 MPa. Based on the manufacturer’s standard molding temperature of 95˚C, the molding temperature was lowered in 2.5˚C increments to determine the lower molding temperature limit at which no molding defects occurred. In order to investigate the difference in molding time depending on the molding mechanism, the duration of molding pressure was adjusted in each molding machine, and the molding time required to obtain a sample without molding defects was measured. The molding time of each molding machine were compared using one-way analysis of variance. The lower molding temperature limit was 90.0˚C for the vacuum blower machine, 77.5˚C for the vacuum ejector machine, 77.5˚C for the pressure molding machine at 0.090 MPa, and 67.5˚C for the pressure molding machine at 0.45 MPa. The lower molding temperature limit was higher for lower absolute values of molding pressure. The molding time was shorter for pressure molding than for suction molding. Significant differences were observed between all conditions except between the pressure molding machine at 0.090 MPa and 0.45 MPa (P < 0.01). A comparison of the differences in lower molding temperature limit and molding time due to molding mechanisms in dental thermoforming revealed that the lower molding temperature limit depends on the molding pressure and that the molding time is longer for suction molding than for pressure molding.

Propagation Dynamics of Forced Pulsating Waves for a Time Periodic Lotka-Volterra Cooperative System with Nonlocal Effects in Shifting Habitats

In this paper, we will concern the existence, asymptotic behaviors and stability of forced pulsating waves for a Lotka-Volterra cooperative system with nonlocal effects under shifting habitats. By using the alternatively-coupling upper-lower solution method, we establish the existence of forced pulsating waves, as long as the shifting speed falls in a finite interval where the endpoints are obtained from KPP-Fisher speeds. The asymptotic behaviors of the forced pulsating waves are derived. Finally, with proper initial, the stability of the forced pulsating waves is studied by the squeezing technique based on the comparison principle.

Storage time affects the level and diagnostic efficacy of plasma biomarkers for neurodegenerative diseases

Several promising plasma biomarker proteins,such as amyloid-β(Aβ),tau,neurofilament light chain,and glial fibrillary acidic protein,are widely used for the diagnosis of neurodegenerative diseases.However,little is known about the long-term stability of these biomarker proteins in plasma samples stored at-80°C.We aimed to explore how storage time would affect the diagnostic accuracy of these biomarkers using a large cohort.Plasma samples from 229 cognitively unimpaired individuals,encompassing healthy controls and those experiencing subjective cognitive decline,as well as 99 patients with cognitive impairment,comprising those with mild cognitive impairment and dementia,were acquired from the Sino Longitudinal Study on Cognitive Decline project.These samples were stored at-80°C for up to 6 years before being used in this study.Our results showed that plasma levels of Aβ42,Aβ40,neurofilament light chain,and glial fibrillary acidic protein were not significantly correlated with sample storage time.However,the level of total tau showed a negative correlation with sample storage time.Notably,in individuals without cognitive impairment,plasma levels of total protein and tau phosphorylated protein threonine 181(p-tau181)also showed a negative correlation with sample storage time.This was not observed in individuals with cognitive impairment.Consequently,we speculate that the diagnostic accuracy of plasma p-tau181 and the p-tau181 to total tau ratio may be influenced by sample storage time.Therefore,caution is advised when using these plasma biomarkers for the identification of neurodegenerative diseases,such as Alzheimer's disease.Furthermore,in cohort studies,it is important to consider the impact of storage time on the overall results.

Application of Time-Tracking Platform in the Reperfusion Treatment of Patients with Acute Ischemic Stroke in Primary Hospitals

Objective To explore the application effect of time tracking platform in improving the reperfusion treatment of patients with acute ischemic stroke in primary hospitals. Methods and Results Patients with acute ischemic stroke who carried out emergency intravenous thrombolysis and arterial thrombectomy in our hospital in 2021, 2022 and 2023 were selected. The time tracking mode was implemented, and the patients were recorded at each time node of the hospital and the whole-process digital management was conducted. Compared the mean DNT (Door to Needle Time) of intravenous thrombolysis in emergency stroke patients in 2021, 2022 and 2023, the total number of hospital cases within 4.5 h of onset, the total number of thrombolysis cases within 4.5 h of onset, the number of intravenous thrombolysis in 60 minutes of acute ischemic stroke, and the number of thrombolysis cases. The results show that from 2021 to 2023 our emergency stroke patients with intravenous thrombolysis average DNT shortened year by year, to the hospital within 4.5 h after the onset of the difference is statistically significant (all P < 0.05) conclusion through the application of stroke time tracking platform, is beneficial to shorten the treatment time of each link, can effectively reduce the hospital time delay, improve the rate of thrombolysis, improve the reperfusion of stroke centers in primary hospitals.

A Time Neighborhood Method for the Verification of Landfalling Typhoon Track Forecast

Landfalling typhoons can cause disasters over large regions.The government and emergency responders need to take measures to mitigate disasters according to the forecast of landfall position,while slight timing error can be ignored.The reliability of operational model forecasts of typhoon landfall position needs to be evaluated beforehand,according to the forecasts and observation of historical cases.In the evaluation of landfalling typhoon track,the traditional method based on point-to-point matching methods could be influenced by the predicted typhoon translation speed.Consequently,the traditional track evaluation method may result in a large track error even if the predicted landfall position is close to observation.The purpose of this paper is to address the above issue using a simple evaluation method of landfalling typhoon track forecast based on the time neighborhood approach.In this new method,the timing error was lessened to highlight the importance of the position error during the landfall of typhoon.The properties of the time neighborhood method are compared with the traditional method based on numerical forecast results of 12 landfalling typhoon cases.Results demonstrated that the new method is not sensitive to the sampling frequency,and that the difference between the time neighborhood and traditional method will be more obvious when the moving speed of typhoon is moderate(between 15−30 km h^(−1)).The time neighborhood concept can be easily extended to a broader context when one attempts to examine the position error more than the timing error.

Efficient Finite Difference/Spectral Method for the Time Fractional Ito Equation Using Fast Fourier Transform Technic

A finite difference/spectral scheme is proposed for the time fractional Ito equation.The mass conservation and stability of the numerical solution are deduced by the energy method in the L^(2)norm form.To reduce the computation costs,the fast Fourier transform technic is applied to a pair of equivalent coupled differential equations.The effectiveness of the proposed algorithm is verified by the first numerical example.The mass conservation property and stability statement are confirmed by two other numerical examples.

Planck Quantised General Relativity Theory Written on Different Forms

This paper is a brief review of our work on the Planck quantized version of general relativity theory. It demonstrates several straightforward methods to rewrite the same equations that we have already presented in other papers. We also explore a relatively new general relativity-inspired field equation based on the original Newtonian mass, which is very different from today’s kilogram mass. Additionally, we examine two other field equations based on collision space-time, where both energy and matter can be described simply as space and time. We are thereby fulfilling Einstein’s dream of a theory where energy and mass are not needed, or are just aspects of space and time. If this is extended beyond the 4-dimensional space-time formalism of general relativity theory to a 6-dimensional framework with 3 space dimensions and 3 time dimensions, this ultimately reveals that they are two sides of the same coin. In reality, it is a three-dimensional space-time theory, where space and time are just two sides of the same coin.