Functional Time Series Models to Estimate Future Age-Specific Breast Cancer Incidence Rates for Women in Karachi, Pakistan

Background： Breast cancer is the most common female cancer in Pakistan. The incidence of breast cancer in Pakistan is about 2.5 times higher than that in the neighboring countries India and Iran. In Karachi, the most populated city of Pakistan, the age-standardized rate of breast cancer was 69.1 per 100,000 women during 1998-2002, which is the highest recorded rate in Asia. The carcinoma of breast in Pakistan is an enormous public health concern. In this study, we examined the recent trends of breast cancer incidence rates among the women in Karachi. Methods： We obtained the secondary data of breast cancer incidence from various hospitals. They included Jinnah Hospital, KIRAN （Karachi Institute of Radiotherapy and Nuclear Medicine）, and Civil hospital, where the data were available for the years 2004-2011. A total of 5331 new cases of female breast cancer were registered during this period. We analyzed the data in 5-year age groups 15-19, 20-24, 25-29, 30-34, 35-39, 40-44, 45-49, 50-54, 55-59, 60-64, 65-69, 70-74, 75＋. Nonparametric smoothing were used to obtained age-specific incidence curves, and then the curves are decomposed using principal components analysis to fit FTS （functional time series） model. We then used exponential smoothing statspace models to estimate the forecasts of incidence curve and construct prediction intervals. Results： The breast cancer incidence rates in Karachi increased with age for all available years. The rates increased monotonically and are relatively sharp with the age from 15 years to 50 years and then they show variability after the age of 50 years. 10-year forecasts for the female breast cancer incidence rates in Karachi show that the future rates are expected to remain stable for the age-groups 15-50 years, but they will increase for the females of 50-years and over. Hence in future, the newly diagnosed breast cancer cases in the older women in Karachi are expected to increase. Conclusion： Prediction of age related changes in breast cancer incidence rates will provide useful information for controlling the overall burden of cancer in Pakistan and also serve as a resource for health planning in future research. Moreover, these models will be the most useful for modeling and projecting future trends of other cancers and chronic diseases.

THE OPTIMAL LARGE TIME BEHAVIOR OF3D QUASILINEAR HYPERBOLIC EQUATIONS WITH NONLINEAR DAMPING

We are concerned with the large-time behavior of 3D quasilinear hyperbolic equations with nonlinear damping.The main novelty of this paper is two-fold.First,we prove the optimal decay rates of the second and third order spatial derivatives of the solution,which are the same as those of the heat equation,and in particular,are faster than ones of previous related works.Second,for well-chosen initial data,we also show that the lower optimal L^(2) convergence rate of the k(∈[0,3])-order spatial derivatives of the solution is(1+t)^(-(2+2k)/4).Therefore,our decay rates are optimal in this sense.The proofs are based on the Fourier splitting method,low-frequency and high-frequency decomposition,and delicate energy estimates.

Effects of data smoothing and recurrent neural network(RNN)algorithms for real-time forecasting of tunnel boring machine(TBM)performance

Tunnel boring machines(TBMs)have been widely utilised in tunnel construction due to their high efficiency and reliability.Accurately predicting TBM performance can improve project time management,cost control,and risk management.This study aims to use deep learning to develop real-time models for predicting the penetration rate(PR).The models are built using data from the Changsha metro project,and their performances are evaluated using unseen data from the Zhengzhou Metro project.In one-step forecast,the predicted penetration rate follows the trend of the measured penetration rate in both training and testing.The autoregressive integrated moving average(ARIMA)model is compared with the recurrent neural network(RNN)model.The results show that univariate models,which only consider historical penetration rate itself,perform better than multivariate models that take into account multiple geological and operational parameters(GEO and OP).Next,an RNN variant combining time series of penetration rate with the last-step geological and operational parameters is developed,and it performs better than other models.A sensitivity analysis shows that the penetration rate is the most important parameter,while other parameters have a smaller impact on time series forecasting.It is also found that smoothed data are easier to predict with high accuracy.Nevertheless,over-simplified data can lose real characteristics in time series.In conclusion,the RNN variant can accurately predict the next-step penetration rate,and data smoothing is crucial in time series forecasting.This study provides practical guidance for TBM performance forecasting in practical engineering.

Quantifying the natural growth rate of hepatocellular carcinoma:A real-world retrospective study in southwestern China

BACKGROUND In recent years,approximately half of the newly diagnosed cases and mortalities attributed to hepatocellular carcinoma(HCC)have been reported in China.Despite the high incidence of HCC,there remains a paucity of data regarding the natural growth pattern and the determination of optimal surveillance intervals specific to the Chinese population.AIM To quantify the natural tumor growth pattern of HCC in regional China.METHODS A retrospective analysis was performed on patients from a single institution in Southwest China who had undergone two or more serial dynamic computed tomography or magnetic resonance imaging scans between 2014 and 2020,without having received any anti-cancer therapy.Tumor growth was assessed using tumor volume doubling time(TVDT)and tumor growth rate(TGR),with volumes measured manually by experienced radiologists.Simple univariate linear regression and descriptive analysis were applied to explore associations between growth rates and clinical factors.RESULTS This study identifies the median TVDT for HCC as 163.4 d,interquartile range(IQR)72.1 to 302.3 d,with a daily TGR of 0.42%(IQR 0.206%-0.97%).HCC growth patterns reveal that about one-third of tumors grow indolently with TVDT exceeding 270 d,another one-third of tumors exhibit rapid growth with TVDT under 90 d,and the remaining tumors show intermediate growth rates,with TVDT ranging between 3 to 9 months.CONCLUSION The identified TGRs support biannual surveillance and follow-up for HCC patients in certain regions of China.Given the observed heterogeneity in HCC growth,further investigation is warranted.

Examining Potential Travel Time Savings Benefits Due to Toll Rates That Vary by Lane

By assigning different toll rates to different lanes during peak traffic hours, the demand for each lane of a road can be optimized. Lanes with lower travel times charge higher toll rates which are paid by those drivers who have higher values of travel time (VTT) and who want to avoid congestion in the other lanes. Conversely, travel time for those drivers with lower values of travel times will increase as they select the lower priced and slower lanes. This research examines toll rates that minimize the total value of travel time spent on the road under such a scenario. The optimum toll rates are dependent on the total road volume and distribution of VTT. The results show that total saved value of travel time can easily reach 11% of the total value of time spent traveling on the lanes when compared to a toll road with a uniform toll rate for all lanes. These savings vary based on many factors including the number of travelers on urgent trips.

A Fourier Series Proof That the Axial like the Transverse Optical Doppler Shift Impacts Time and Information Rates

In writings on relativity time, the various relations are only changed by the transverse shift. This paper proves that the axial Doppler shift does that as well and gives some impacts of that on common differential relations in physics. When a modulated signal lasting a time = T is subjected to an optical Doppler shift K (either axial or transverse or both), where K is shifted frequency/original frequency, the Doppler shifted signal will last T/K. This because all shifted harmonics of its Fourier series (with a fundamental period of T) will last 1/K times the period of the original harmonic. The reader can graph any Fourier series and then graph its shifted series. The reader will see the shifted period is T/K. The Fourier series of the original repeats when time is greater than T and the shifted one when time is greater than T/K, which means the original series only represents the signal from time = 0 to T and the shifted series represents the shifted signal from time = 0 to T/K. Hence, the shifted one has all of the information in T/K as the original has in T. Therefore everything in the series including information is T/K long in the shifted series. Therefore, both the axial and the transverse Doppler shift change time periods in a vacuum, independent of material involved. That has not been obvious for over 100 years the axial shift changes time from the definition of frequency = 1/time.

The Effect of Hydraulic Retention Times and Loading Rates on the Removal of Pollutants from Fish Processing Wastewater by Anaerobic Process

Anaerobic treatment model treats fish processing wastewater to be necessary for a small and medium factory that is very popular in Vietnam and other countries.Several techniques have been proposed.However,they are quite expensive and hard to operate,especially in remote areas.In this study,the hydraulic retention times(HRT)including 3,5,and 7 hours with a various organic loading rate of 1.5 to 6.5 kg COD/m3/day were investigated.Biomass concentration as mix-liquor volatile suspended solid(MLVSS)in the model is at 6,000 to 9,000 mg/L.On the basis of the result the optimal HRT with a 4.0 kg COD/m3/day organic loading rate was 8 hours which BOD5,COD removal efficiency were 92.18,87.36 percent respectively.By the end of the optimal hydraulic retention times,the total methane gas volume as a by-product was collected with 2.6 liters.

RELIABILITY ANALYSIS FOR A REPAIRABLE PARALLEL SYSTEM WITH TIME-VARYING FAILURE RATES

To solve a real problem:how to calculate the reliability of a system with time-varying failure rates in industry systems,this paper studies a model for the load-sharing parallel system with time-varying failure rates,and obtains calculating formulas of reliability and availability of the system by solving differential equations.In this paper,the failure rates are expressed in polynomial configuration.The constant,linear and Weibull failure rate are in their special form.The polynomial failure rates provide flexibility in modeling the practical time-varying failure rates.

A Co-integration Approach to Forecasting Container Carriers' Time Charter Rates

A vector autoregressive model was developed for a sample of container carrier time charter rates. Although the series of time charter rates are themselves found non-stationary, thus precluding the use of many modeling methodologies, evidence provided by co-integration tests points to the existence of stable long-term relationships between the series. An assessment of the forecasts derived from the model suggests that the spec-ification of these long-term relationships does not improve the accuracy of long-term forecasts. These results are interpreted as a corroboration of the efficient market hypothesis.

UNIFORM ESTIMATE ON FINITE TIME RUIN PROBABILITIES WITH RANDOM INTEREST RATE

We consider a discrete time risk model in which the net payout （insurance risk） {Xk, k = 1, 2,...} are assumed to take real values and belong to the heavy-tailed class L∩ D and the discount factors （financial risk） {Yk, k = 1,2,...} concentrate on [θ, L], where 0 〈 0 〈 1, L 〈 ∞, {Xk, k = 1,2,...}, and {Yk, k=1,2,...} are assumed to be mutually independent. We investigate the asymptotic behavior of the ruin probability within a finite time horizon as the initial capital tends to infinity, and figure out that the convergence holds uniformly for all n ≥ 1, which is different from Tang Q H and Tsitsiashvili G （Adv Appl Prob, 2004, 36： 1278-1299）.

Anomalies identification of Earth’s rotation rate time series (2012-2017) for possible correlation with strong earthquakes occurrence

The analysis of the Earth’s rotation rate time series,from January 1,2012 till December 31,2017,is performed using two different time series analysis methods,both based on signal decomposition joined with forecasting approach.Anomalies in the time series are detected making the comparison between the raw signal and the forecasting one at the 95% confidence interval.The two methods show consistent results and the best is selected according to the evaluation of the prediction uncertainty.Both methods highlight correlations between detected anomalies in the Earth’s rotation rate time series and the world’s earthquakes occurrence with magnitude≥7 and/or number of events≥150 per day,within a time interval of ±10 days from each earthquake event.This study brings an innovation in the analysis of such time series and helps to better understand the extent of this relationship.

TIME DECAY RATE OF SOLUTIONS TO THE HYPERBOLIC MHD EQUATIONS IN R3

In this paper, we first show the global existence, uniqueness and regularity of weak solutions for the hyperbolic magnetohydrodynamics(MHD) equations in R^3. Then we establish that the solutions with initial data belonging to H^m(R^3) ∩ L^1(R^3) have the following time decay rate:║▽~mu(x, t) ║~2+║ ▽~mb(x, t)║~ 2+ ║▽^(m+1)u(x, t)║~ 2+ ║▽^(m+1)b(x, t) ║~2≤ c(1 + t)^(-3/2-m)for large t, where m = 0, 1.

Effects of Danqu Capsules on Arterial Blood Pressure,Heart Rate and Myocardial Tension Time Index in Rats

[Objectives] To explore the effects of Danqu capsules(the prescription of Lei Zhongyi, the master of traditional Chinese medicine for the syndrome of intermingling of phlegm and static blood of coronary heart disease) on arterial blood pressure, heart rate and myocardial tension time index in rats. [Methods] A total of 50 SD rats, weighing(300±20) g, were randomly and evenly divided into Danqu capsule observation groups(low, middle and high-dose groups) and control groups(saline group and captopril group). Under anesthesia, the rats in each group were administered with 0.6, 1.2 and 2.4 g/kg of Danqu capsule suspension, 1 mL/100 g of saline and 10 mg/kg of captopril, respectively through duodena, and their systolic blood pressure, diastolic blood pressure, mean arterial pressure, pulse pressure difference and heart rate were measured and recorded by RM6240 multi-channel physiological signal acquisition and processing system before administration, 10, 20, 30, 40, 50, 60, 90 and 120 min after the administration, respectively, and the myocardial tension time index was calculated. [Results] Compared with the saline group, the systolic, diastolic and mean pressure reduced 10, 20, 30, 40, 50, 60, 90 and 120 min after the administration, and the pulse pressure difference did not change significantly in the Danqu capsule groups(low, middle and high-dose groups), and the heart rate slowed down and the myocardial tension time index reduced in the high-dose Danqu capsule group. Compared with the captopril group, the Danqu capsule groups showed similar blood pressure-reducing effect. [Conclusions]Danqu capsules have obvious effect of lowering blood pressure and myocardial tension time index. High-dose Danqu capsules has the effect of slowing down the heart rate. The blood pressure-lowering effect of Danqu capsules shows a dose-dependent manner. Clinically, they can be used in patients with coronary heart diseases and hypertension, suggesting that they should be used with caution in patients with hypotension.

Ordered Rate Constitutive Theories for Non-Classical Thermoviscoelastic Fluids with Internal Rotation Rates

The paper presents constitutive theories for non-classical thermoviscoelastic fluids with dissipation and memory using a thermodynamic framework based on entirety of velocity gradient tensor. Thus, the conservation and the balance laws used in this work incorporate symmetric as well as antisymmetric part of the velocity gradient tensor. The constitutive theories derived here hold in coand contra-variant bases as well as in Jaumann rates and are derived using convected time derivatives of Green’s and Almansi strain tensors as well as the Cauchy stress tensor and its convected time derivatives in appropriate bases. The constitutive theories are presented in the absence as well as in the presence of the balance of moment of moments as balance law. It is shown that the dissipation mechanism and the fading memory in such fluids are due to stress rates as well as moment rates and their conjugates. The material coefficients are derived for the general forms of the constitutive theories based on integrity. Simplified linear (or quasi-linear) forms of the constitutive theories are also presented. Maxwell, Oldroyd-B and Giesekus constitutive models for non-classical thermoviscoelastic fluids are derived and are compared with those derived based on classical continuum mechanics. Both, compressible and incompressible thermoviscoelastic fluids are considered.

Revisiting the Curie-Von Schweidler Law for Dielectric Relaxation and Derivation of Distribution Function for Relaxation Rates as Zipf’s Power Law and Manifestation of Fractional Differential Equation for Capacitor

The classical power law relaxation, i.e. relaxation of current with inverse of power of time for a step-voltage excitation to dielectric—as popularly known as Curie-von Schweidler law is empirically derived and is observed in several relaxation experiments on various dielectrics studies since late 19th Century. This relaxation law is also regarded as “universal-law” for dielectric relaxations;and is also termed as power law. This empirical Curie-von Schewidler relaxation law is then used to derive fractional differential equations describing constituent expression for capacitor. In this paper, we give simple mathematical treatment to derive the distribution of relaxation rates of this Curie-von Schweidler law, and show that the relaxation rate follows Zipf’s power law distribution. We also show the method developed here give Zipfian power law distribution for relaxing time constants. Then we will show however mathematically correct this may be, but physical interpretation from the obtained time constants distribution are contradictory to the Zipfian rate relaxation distribution. In this paper, we develop possible explanation that as to why Zipfian distribution of relaxation rates appears for Curie-von Schweidler Law, and relate this law to time variant rate of relaxation. In this paper, we derive appearance of fractional derivative while using Zipfian power law distribution that gives notion of scale dependent relaxation rate function for Curie-von Schweidler relaxation phenomena. This paper gives analytical approach to get insight of a non-Debye relaxation and gives a new treatment to especially much used empirical Curie-von Schweidler (universal) relaxation law.

Acoustic emission characteristics and stress release rate of coal samples in different dynamic destruction time

Considering the importance of the prediction of rock burst disasters, and in order to grasp the law of acoustic emission(AE) of coal samples in different dynamic destruction time, the SH-II AE monitoring system was adopted to monitor the failure process of coal samples. The study of the change rule of the AE numbers, energy, ‘b' value and spectrum in the micro crack propagation process of the coal samples shows that as dynamic damage time went by, AE presented high-energy counts and the accumulated counts increased during the compression phase. The AE energy and cumulative counts increased during the elastic stage. The AE blank area increased gradually and the blank lines were more and more obvious in the molding stage. The AE counts and energy showed a trend of decrease in the residual damage phase.AE ‘b' values gradually became sparse, and the large scale cracks percentage compared with micro cracks decreased and the degree of damage decreased. The AE frequency spectrum peak went from the residual damage phase to the molding phase, and finally it was nearly stable, besides the bandwidth of the main frequency is gradually narrowed. Also, the frequency peak changed from single peak frequency to bi-peak frequency and to the single peak frequency. Uniaxial compressive strength is more sensitive than the elastic modulus to dynamic damage time.

Effects of time lag and stress loading rate on permeability in low permeability reservoirs

In order to study the effect of time lag and stress loading rates on rock deformation,the conventional stepped stress loading mode was changed into a continuous mode to investigate the effect of effective pressure on permeability and porosity.The time lag effect of rock deformation illustrating the relationship between changes in permeability and steady time was studied.Permeability reduction ratios were measured under different stress loading rates which were achieved by different pump rate settings.The results show that permeability and porosity gradually decrease with increases in effective pressure.Permeability at high effective pressure attains stability quickly.Steady times at low effective pressure are very long.Reduction in permeability at lower stress loading rates is small,while,in contrast,it is large at high stress loading rates.

Estimation of key rate after setting dead time

The estimation of key rate is an important aspect of the quantum key distribution process, especially in the use of dead time. In this paper, we demonstrate a numerical simulation to estimate the average detection probability and the key rate. Using our method, the estimated average detection probability is better than the previous result. Besides, we can easily find the best dead time, especially when considering the impact of after pulse.

Effect of loading rate and time delay on the tangent modulus method(TMM)in coal and coal measured rocks

Non-destructive techniques of in-situ stress measurement from oriented cored rocks have great potential to be developed as a cost cost-effective and reliable alternative to the conventional overcoring and hydraulic fracturing methods.The tangent modulus method(TMM)is one such technique that can be applied to oriented cored rocks to measure in-situ stresses.Like the deformation rate analysis(DRA),the rock specimen is subjected to two cycles of uniaxial compression and the stress-tangent modulus curve for the two cycles is obtained from the stress-strain curve.A bending point in the tangent modulus curve of the first cycle is observed,separating it from the tangent modulus curve of the second cycle.The point of separation between the two curves is assumed to be the previously applied maximum stress.A number of experiments were conducted on coal and coal measured rocks(sandstone and limestone)to understand the effect of loading conditions and the time delay.The specimens were preloaded,and cyclic compressions were applied under three different modes of loading,four different strain rates,and time delays of up to one week.The bending point in the stress-tangent modulus curves occurred approximately at the applied pre-stress levels under all three loading modes,and no effect of loading rate was observed on the bending points in TMM.However,a clear effect of time delay was observed on the TMM,contradicting the DRA results.This could be due to the sensitivity of TMM and the range of its applicability,all of which need further investigation for the in-situ stress measurement.