The present paper examines the relative out-of-sample predictive ability of GARCH, GARCH-M, EGARCH, TGARCH and PGARCH models for ten Asian markets by using three different time frames and two different methods, considering the features of volatility clustering, leverage effect and volatility persistence phenomena, for which the evidence of existence is found in the data. Five measures of comparison are employed in this research, and a further dimension is investigated based on the classification of the selected models, in order to identify the existence or lack of any differences between the recursive and rolling window methods. The empirical results reveal that asymmetric models, led by the EGARCH model, provide better forecasts compared to symmetric models in higher time frames. However, when it comes to lower time frames, symmetric GARCH models tend to outperform their asymmetric counterparts. Furthermore, linear GARCH models are penalized more by the rolling window method, while recursive method places them amongst the best performers, highlighting the importance of choosing a proper approach. In addition, this study reveals an important controversy: that one error statistic may suggest a particular model is the best, while another suggests the same model to be the worst, indicating that the performance of the model heavily depends on which loss function is used. Finally, it is proved that GARCH-type models can appropriately adapt to the volatility of Asian stock indices and provide a satisfactory degree of forecast accuracy in all selected time frames. These results are also supported by the Diebold-Mariano (DM) pairwise comparison test. Volatility is the degree of variation of a trading price series over time, and is usually measured by the standard deviation of logarithmic returns. As an important concern for traders, investors, companies and financial regulatory authorities, volatility forecasts of asset returns have been studied over the years for risk management, security valuation, portfolio diversification and monetary policy making purposes. Furthermore, volatility modelling and forecasting have especially attracted finance professionals and academics following the stock market crash in 1987, since the main reason for the crash was attributed to high volatility  and non-linear (asymmetric) GARCH family models for producing the most accurate volatility forecasts.It is broadly acknowledged by the financial literature that an increase in data frequency is accompanied by excess kurtosis, which challenges the capabilities of forecasting models due to the fat-tailed distribution on return series  model was developed and proposed by Tim Bollerslev in 1986. ARCH family models are a milestone in regression analysis in terms of estimating variance by a nonlinear estimation model. The GARCH model is based on a weighted average of past squared residuals with a few improvements compared to ARCH. First, GARCH has decaying weights on past squared residuals that stay above zero, no matter how much it falls. Second, it puts greater weight on more recent events. Third, it is superior for handling different sets of data in different frequencies. With these combined benefits, GARCH is an avant-garde model with a wide selection of extensions in predicting conditional volatility.This model can be expressed with a mean specification and a variance specification. The GARCH  can be represented as follows:Mean specificationVariance specificationi.i.d.), and Hypothetical long-run average variance: First independent variable which reflects “news” about previous period volatility: Second independent variable which reflects forecast variance from previous period: Returns of residual can also be expressed as:Most models used in finance suppose that investors should be rewarded for taking additional risk by obtaining a higher return Brooks . Engle eMean specificationVariance specificationThe The Exponential GARCH model was proposed by Nelson  based onThe Threshold GARCH model  is one of the best-known and most commonly used asymmetric models to measure and handle with possible asymmetries, such as leverage effects. This model was developed by Zakoian , but alsThe Power GARCH (PGARCH) model was developed by Ding, Granger, and Engle in 1993. The PGARCH model differentiates itself from the other asymmetric models by using conditional standard deviation instead of the conditional variance. The power parameter is defined as The leverage parameter Out-of-sample tests are widely considered as the “gold standard” of the forecast evaluation, and according to the “conventional wisdom”, the forecasts of the estimated models should be evaluated by conducting out-of-sample fit rather than generating the same set of data that was used to estimate the model’s parameters, which is called an “in-sample” forecast. Bartolomei and Sweet  and PantOut-of-sample forecasts can be estimated using two different methods which are known as recursive forecast and rolling window forecast. The recursive forecast sets a fixed initial sample data starting from For each index, forecasting models are estimated using recursive and rolling window methods and assessed by out-of-sample performance. The maximum likelihood method has been used to estimate parameters. The choice of window size for out-of-sample forecasting is controversial, since there is no satisfactory solution for the optimal length. However, to keep the competence of the estimated parameters robust and avoid non-convergence problems, adequately large estimation size is recommended, especially in the applications of richly parameterized GARCH family models , Mean Absolute Percentage Error (MAPE), Root Mean Square Error (RMSE), Quasi-Likelihood (QLIKE) and Mean Squared Error (MSE).n denotes the rank of forecasted data, MAE measures the average magnitude of the errors in a set of predictions, without considering their direction. It is the average over the test sample of the absolute differences between prediction and actual observation where all individual differences have equal weight. The mean absolute error is given by:MAPE is the sum of the individual absolute errors divided by each period separately. In other words, it is the average of the percentage errors. The advantage of the MAPE is that it is easy to interpret and helpful for comparing the performance of the estimated volatility models. The mean absolute percentage error is defined as follows:RMSE is the square root of the average of squared differences between prediction and actual observation. Since the errors are squared before they are averaged, the RMSE gives a relatively high weight to large errors. This means the RMSE is most useful when large errors are particularly undesirable. Its value can only be positive, and a value of zero  would indicate a perfect fit to the data. In general, a lower RMSE is better than a higher one. However, comparisons across different types of data would be invalid because the measure is dependent on the scale of the numbers used. The following formula is given for the root mean square error:The term quasi-likelihood function was introduced by Wedderburn  to descrPatton and Sheppard , Patton MSE is another popular accuracy measure in the empirical financial literature developed by Bollerslev et al.  to gaugeIn order to evaluate the predictive accuracy of two competing models, the Diebold-Mariano test  is employed. Diebold and Mariano  introducConsider two sets of competing forecast sequences, defined as:The accuracy of each forecast is gauged by the loss function:The loss functions adopted for this study are the absolute-error loss function:To assess whether the two competing forecasts have same predictive ability, the equal accuracy hypothesis is considered. The null hypothesis of DM test is given as:Then, the DM test statistic can be expressed as:mentclass2pt{minimAsia is divided into two regions: developed and emerging economies. The highly developed countries include Japan and the four Asian Tigers—Hong Kong, South Korea, Taiwan, and Singapore. China and Malaysia are other major economic forces which are considered an important powerhouse in the region, however, academics often classify these countries as “developing”; see Johansson and Ljungwall , Luo et In this study, ten Asian countries have been selected for investigation and their widely accepted indices have been chosen. The five developed market indices that have been added are as follows: the Nikkei 225 Index (NIKKEI) from Japan, the Hang Seng Index (HSI) from Hong Kong, the Korea Composite Stock Market Index (KOSPI) from South Korea, the Taiwan Capitalization Weighted Stock Index (TAIEX) from Taiwan, and the Straits Times Index (STI) from Singapore. The remaining five Asian countries are chosen as emerging markets and their broadly accepted stock market indices are considered as follows: the SSE Composite Index (SSE) from China, the PSE Composite Index (PSE) from the Philippines, the Stock Exchange of Thailand Index (SET) from Thailand, the Kuala Lumpur Composite Index (KLCI) from Malaysia, and the Jakarta Stock Exchange Composite Index (JCI) from Indonesia.Daily, weekly and monthly time series data is obtained from the Bloomberg database to ensure the reliability and accuracy of older data. The overall sample period covers 25 years in total, starting from November 1993 to May 2018. However, one problem was the limitation on accessing older data in higher time frames, and thus the daily and weekly data start from 1994 instead of 1993. Another challenge was non-synchronous holidays in different markets which may cause computational difficulties and negatively effect the output of the models. Therefore, the data range has been chosen separately for each market to not get exposed to data loss. The statistical software Eviews 10 was used for the quantitative analysis.The main advantage of daily data is providing more information in terms of estimating volatility for applied econometric models since they are more data-intensive than simple regression models. Weekly and monthly frequencies are also estimated, since they provide a broader framework regarding volatility, and it is crucial to understand the comparison between different frequencies. In order to satisfy stationarity, closing price series are transformed to return series in all daily, weekly and monthly time frames for each index.Return series have been obtained as shown in the following formula:mentclass2pt{minimTable Table On the other hand, based on Table A general conclusion for the daily forecasting results is that in most circumstances, the asymmetric models provide a smaller loss function than the symmetric models. Based on the error measures no specific model emerges as unconditionally best. Yet, in the presence of EGARCH, asymmetric models seem to outperform, especially in the developed markets, which contradicts the findings of Liu et al.  to some Table Table Table Based on the rolling window forecast results as presented in Table p-values are also attached for each statistic to show the level of significance.Tables from The conducted DM test results are mostly in line with the forecasting results, as can be seen from the tables below. A considerable portion of the pairwise comparisons show that the forecasting accuracy of one of the selected models is better based on the value of the error loss. Specifically, the daily results provide more significant values based on the absolute-error loss criteria for both recursive and rolling window methods. On the other hand, according to the daily results based on the squared-error loss, the NIKKEI, STI, SET, SSE and TAIEX indices cannot provide a definite forecasting accuracy between compared models due to the weakness of the DM test results.The weekly results are more indecisive compared to the daily DM test results. The DM statistics for the NIKKEI and HSI Indices are less than 1.96, and therefore the zero hypothesis cannot be rejected. Thus, the observed difference between the forecasting performance of selected models is not significant and might be due to stochastic interference, which is in line with the findings of Burda and Bélisle . The STIFinally, the forecasting comparison for the monthly return series reports significant forecasting accuracy for superior models, especially those based on the absolute-error loss. On the other hand, the DM statistics based on the squared-error criteria provide weaker results due to the smaller values for both recursive and rolling window methods: that is to say, the zero hypothesis cannot be rejected.Summarizing the results listed in the following tables shows that the DM test results are highly consistent with the empirical volatility forecasts, indicating that the evaluations, of the forecasts are strong and accurate, as the outcomes are supported by the DM test statistics.The present paper examines the volatility forecasting ability of the GARCH-type econometric models based on recursive and rolling window methods for ten Asian stock markets, inspired by the theoretical gap in model accuracy and the practical need for more comprehensive evidence for the selected markets and models. Five GARCH models are considered, namely GARCH, GARCH-M, EGARCH, TGARCH and PGARCH models where the first two represents symmetric and the remaining three represents asymmetric models. Daily, weekly and monthly return series data has been used and the evaluation of the forecasts are determined by using five different error statistics.Based on the empirical analyses, GARCH-type models can appropriately adapt to the volatility behavior of Asian stock indices and provide a satisfactory degree of forecast accuracy in all selected time frames. The superiority of asymmetric models is more evident for higher time frames, while symmetric models tend to outperform in lower time frames. More precisely, the EGARCH model generates the most accurate volatility forecasts, closely followed by the TGARCH and PGARCH models for the daily and weekly frequencies, indicating that asymmetric specification of volatility dynamics needs to be taken into account: a finding which is in line with the study of Anggita . This ouFor a better visualization of the performance of the employed models and overall conclusion, Tables Table Based on the reported values by Table Symmetric and asymmetric GARCH models can be applied to Asian stock markets. Although these models were developed and widely used in the process of researching Western financial markets, it does not obstruct the use of them in emerging or developed Asian financial markets.In terms of the time series perspective, the volatility behavior of Asian markets indicates considerable clustering and time-varying events. This is more evident during the turbulent times, such as the 1997–1998 Asian crisis and the 2008 US subprime crisis, due to the information shock on the markets reflecting the phenomenon whereby large changes tend to be followed by large changes, of either sign, and small changes tend to be followed by small changes.Given the level of risk associated with investment in stock markets, day traders, investors, financial analysts and empirical finance professionals should consider alternative error distributions while specifying predictive volatility model as less contributing error distributions implies incorrect specification, which could lead to loss of efficiency in the model. Investors should also not ignore the impact of news while forming expectations on investments.Frequency of the data and choice of forecast method have a strong effect on model performance, and therefore, depending on the investment perspective and risk sensitivity, the correct method and time frames should be applied.Through the analyses above, the following conclusion can be drawn.The out-of-sample performance of the compared volatility models in terms of the different loss functions based on the three data sets, thus suggests a bit of a challenge. It is far from evident which of the specific conditional volatility models outperforms the other. First, the ranking of models based on a specific loss function differs for the three data sets. Secondly, for the selected markets the best and worst model depends heavily on which loss function is used. To answer which model has the best out-of-sample performance, one must first consider the specific data set used and then which loss function to use as the criteria.The main limitation of this study is data availability, especially for the higher frequency of data in the emerging countries of Asia. Further research could explore a wider sample of financial markets—Vietnam, India, Russia and other countries in Asia—with more up-to-date data considering the recent COVID-19 crisis and the war between Ukraine and Russia. This would explore how the news information impacts volatility behavior across stock markets of Asia. Another agenda for future research could include a wider set of GARCH family models to test and estimate the forecasting accuracy of a wider sample.


In atrial fibrillation (AF), thromboembolic events can result from the particular conformation of the left atrial appendage (LAA) bearing increased clot formation and accumulation. Current therapies to reduce the risk of adverse events rely on surgical exclusion or percutaneous occlusion, each of which has drawbacks limiting application and efficacy. We sought to quantify the hemodynamic and structural loads of a novel potential procedure to partially invert the “dead” LAA space to eliminate the auricle apex where clots develop. A realistic left atrial geometry was first achieved from the heart anatomy of the Living Heart Human Model (LHHM) and then the left atrial appendage inversion (LAAI) was simulated by finite-element analysis. The LAAI procedure was simulated by pulling the elements at the LAA tip and prescribing a displacement motion along a predefined path. The deformed configuration was then used to develop a computational flow analysis of LAAI. Results demonstrated that the inverted LAA wall undergoes a change in the stress distribution from tensile to compressive in the inverted appendage, and this can lead to resorption of the LAA tissue as per a reduced stress/resorption relationship. Computational flow analyses highlighted a slightly nested low-flow velocity pattern for the inverted LAA with minimal differences from that of a model without inversion of the LAA apex. Our study revealed important insights into the biomechanics of LAAI and demonstrated the inversion of the stress field (from tensile to compressive), which &can ultimately lead the long-term resorption of the LAA. Atrial fibrillation (AF), the most common sustained arrhythmia, affects 3–6 million Americans and increases the risk of stroke by 4 to 6 times on average ,2. AF prThe left atrial appendage (LAA) extends from the LA and creates a side chamber, which can be a site of increased clot formation and accumulation in AF. The LAA in a low-flow state as in AF is the nidus for >90% of thrombus formation ,7, where® (LHHM) [In this study, the feasibility of resorption of the “dead” LAA space without the need of a specific device left behind was investigated by computational modeling. Specifically, the procedure for the treatment of LAA uses a suction-based catheter device to latch the distal portion of the LAA endocardium , enablin® (LHHM) . Then, t−9 kg/mm3 was used. Moreover, the biomechanical behavior of the LA tissue wall was modeled as a hyper-elastic and isotropic material using the third-order Ogden’s strain energy function:The geometry of the left atrium (LA) including the ear-shaped sac of the LAA was extrapolated from that of the LHHM representing the ideal average heart anatomy of a middle-aged healthy male. No human data was used in this study, and thus no authorization is needed by ethical committee. The LA geometry was then discretized with 33,632 triangular elements (S3) as a shell layer with uniform thickness of 2 mm . A nearlocardium .−6. Post-processing was carried out with Ensight software by overlaying the geometry of the whole LHHM heart.To model the LAAI procedure, we first simulated the catheter clamping of the LAA by constraining the element nodes at the distal apex of the LAA. Then, the inversion was simulated pulling the clamped elements inside the heart by prescribing a displacement motion along a predefined path . Specifically, the clamped nodes were coupled to the centerline end point of LAA while the motion was implemented though connector assignments of constrained nodes in ABAQUS commercial software . For each time increment, the displacement was 0.03 mm and was kept upon LAA inversion. To account for blood pressure, a uniform pressure of 1.3 mmHg was applied to LA inner surface. For boundary conditions, the distal ends of the pulmonary veins were fixed in all directions. The general contact algorithm with frictionless condition was adopted to consider the interaction of LAA tissue wall with itself during the retraction process. Simulations were carried out using ABAQUS/Explicit solver to account for the non-linear problem with large deformation and complex contact conditions. Energy was monitored to ensure the ratio of kinetic energy to internal energy remained less than 10%, and a variable mass-scaling technique was adopted to keep the time step less than 10−6 at every time step. For boundary conditions, the LAA wall was rigid with no-slip condition while flow velocity inlet  and outlet  with zero-pressure condition were set as flow conditions. For mitral valve outflow, a representative flow waveform with duration of 0.8 s at the mitral valve section was considered [Once simulation of LAAI was accomplished, the deformed configuration of the LAA was exported to generate the fluid domain and thus assess the left heart hemodynamic environment by unsteady computational flow analysis. Specifically, the inner volume of the LAA wall was meshed with 2,411,143 tetrahedral elements using the ICEM CFD . Mesh quality check was evaluated by grid-convergence index analysis to quantify the discretization error using the pressure gradient on the LAA wall as convergence parameter, as previously . The Navnsidered . AfterwaSpecifically, Flow velocity at LAA was analyzed by streamlines at mitral valve flow peak of the E-wave and early diastole for both the non-inverted and LAAI models . At the From a qualitative perspective, there was a minimal difference in the flow pattern of the LAAI model versus the non-inverted reference model . SpecifiUsing realistic left atrial anatomy as extracted from the LHHM, the LAA tip was virtually clamped, and the retraction procedure was simulated to reveal insights into the biomechanics of the inverted LAA tissue wall . The simIt has long been recognized that mechanics play a fundamental role in tissue growth and remodeling, especially in cardiac diseases. Mechanobiological control mechanisms in the myocardial wall tend to restore values of stress (or strain) toward preferred homeostatic values in response to diverse perturbations from normal conditions. For instance, hypertrophic growth of cardiomyocytes is the primary response by which the left ventricle reduces the stress on the myocardial wall imposed by pressure overload  . An incrFrom a hemodynamic perspective, the computational flow analysis revealed minimal differences in the flow patterns of the non-inverted LAA versus the LAAI , which wThere are several limitations in this numerical proof of concept study. First, for the sake of simplicity, the LAA tissue wall was assumed to be a passive and isotropic material with uniform thickness. During heart beating, contractile material force is initiated through changes in the electrical potential and depends on reference tension, the primary fiber stress ratio, the fiber-stretch velocity and the current cellular state. Second, knowledge of myofiber orientation is a crucial for model development even in a non-contracting myocardium because myocardial mechanical properties are significantly stiffer in the local myofiber direction than in a plane transverse to the myofiber direction. Our group has extensively studied and developed constitutive material law to account for the active material contraction and includes myofiber orientation as validated against in-vivo measured strain data ,36. FurtAs a proof-of-concept, this study demonstrated the feasibility of the LAAI procedure for removal of the dead space of the appendage without leaving any device behind. Although further model improvements are needed, the simulation framework here proposed can be used not only to quantify the biomechanics and hemodynamic of LAAI but also to optimize LAAI procedure development towards translation in clinical practice.


To enrich the diversity of artificial neurons, a type of quadratic neurons was proposed previously, where the inner product of inputs and weights is replaced by a quadratic operation. In this paper, we demonstrate the superiority of such quadratic neurons over conventional counterparts. For this purpose, we train such quadratic neural networks using an adapted backpropagation algorithm and perform a systematic comparison between quadratic and conventional neural networks for classificaiton of Gaussian mixture data, which is one of the most important machine learning tasks. Our results show that quadratic neural networks enjoy remarkably better efficacy and efficiency than conventional neural networks in this context, and potentially extendable to other relevant applications. In machine learning, the mainstream approach is now artificial neural networks (ANNs), especially deep neural networks. Usually, a neural network consists of several layers of neurons, each of which consists of a linear compartment in the form of the inner product of inputs and weights and a nonlinear unit known as an activation function to make a signal on (activated) or off (attenuated). Deep neural networks have been recently shown to achieve remarkable successes in various applications such as natural language processing , 2, autoClassification/clustering is one of the essential pattern recognition techniques in machine learning, and has a wide arrange of applications such as bioinformatics , 11 and In our previous study –19, a neThe main purpose of this paper is to highlight the superiority of quadratic over conventional neural networks with the classification task as an illustrative example. The rest of the paper is organized as follows. In the next section, we review the theoretical minimum error in the GMM classification and the EM algorithm that is traditionally used to reach that error bound. In the third section, we present our procedure for initializing and training the conventional and quadratic networks with an adapted backpropagation (BP) algorithm. In the fourth section, we perform numerical experiments systematically and establish the superiority of quadratic networks over the conventional counterparts in the GMM classification. Finally, in the last section we discuss relevant issues and conclude the paper.In statistical classification, the Bayes error rate is theoretically optimal. In practice, without knowing latent GMM parameters, the Bayes error rate cannot be directly calculated. To close the gap, the classic EM algorithm can be used to approximate the optimal error rate, which is the benchmark to evaluate the performance of classification neural networks.D dimensional sample vector D, N, and K represent the dimensionality of the sample vector, the sample size and the number of Gaussian components respectively. We can obtain the Bayesian inference results, a size N vector Given the mean entclass1pt{minimaNote that the inference MaxCycle according to the number of Gaussian components K, and in our experiment A solution to this problem is to perform an exclusive search so that the accuracy or loss can be optimized. By doing so, the best match will be found as our final result. More efficiently, the alternating variables method can be used as described in Algorithm 1, a common derivative-free method for numerical optimization, with the idea to maximize the accuracy by exchanging two coordinates each time and fixing all the remaining ones. We set the Then, we compute Eq. As a classic iterative method, the EM algorithm consists of the following two steps: expectation (E) and maximization (M). The E step evaluates the expectation function based on the currently available intermediate parameters, and the M step updates the intermediate parameters to maximize the expectation function. To estimate all the D vector that filled with values from the standard normal distribution, D by D identity matrix and jth iteration, To start the EM procedure, for entclass1pt{minimaTraining a neural network involves two steps: initialization which sets up network parameters appropriately, and optimization which adjusts the neural parameters iteratively. An optimizer used in the second step is illustrated in Fig. While the conventional and quadratic neural networks can be trained based on the same idea of computational optimization, they differ in specific steps, since the chain rule must be applied to different functions that summarize data . Specifically, let us formulate the forward and BP processes in the following two subsections respectively, and then describe the whole process in the third subsection.L layers in total, in each of which there is a number of neurons. A typical layer first implements affine transforms for conventional neurons and quadratic operations for quadratic neurons, and then nonlinear activations An exemplary feed-forward neural network is shown in Fig. l-th layer is the last layer of the network, i.e., An illustration of the affine layer of conventioinal and quadratic neurons is shown in Fig. N by D sample matrix N by K matrix In other words, the input to the forward process is a To optimize a neural network, we perform numerical optimization. Specifically, we first find the partial derivatives with respect to each of the parameters and update them via gradient descent search at a suitable step size (learning rate). Using the chain rule, this process was formulated as the well-known BP algorithm, which is widely used to train a neuronal network. As its name indicates, the BP process computes the partial derivatives layer-wise from the output layer to the input layer. A brief BP diagram is shown in Fig. Q stand for the cross-entropy loss value defined asN is the number of sample vectors, Let mentclasspt{minimaInitiation. Let us use a series of integers to describe a feed-forward neural network architecture of our interest,Then, the network can be randomly initialized with a vector of parameters Optimization. As shown in Fig. Using the training methods in the preceding section, we optimized conventional and quadratic neural networks to solve a number of GMM-based classification problems. At the beginning, we solved a three-class problem in the two-dimensional (2D) space to illustrate the working principle. Then, we performed a systematic comparison between conventional and quadratic neural networks on samples with different numbers of classes and dimensions. Finally, we applied all methods on three real data sets. Meanwhile, we used the EM algorithm and Bayes inference to obtain the Bayes error rate as the performance benchmark of the neural networks.K = 3) in the 2D space  spaces with We trained and tested the EM algorithm, conventional and quadratic networks with different numbers of layers/neurons in terms of the average accuracy. The resutls are summarized in Table Finally, we applied conventional and quadratic networks on three real data sets from the UCI Machine Learning repository : proteinWe trained and tested the EM algorithm, conventional and quadratic networks with different numbers of layers/neurons on each dataset 20 times. The average accuracy of and time needed by each method are shown in Table Although it has been well tested with a solid theoretical foundation, the EM algorithm needs to take an entire dataset into the memory, processes them iteratively, and is time-consuming, under the restriction that data must come from GMM. Furthermore, when new samples become available, parameters need to be adjusted again. A neural network approach can be much more desirable, effective and efficient, workable with many data models in principle thanks to its universal approximation nature. After a network is well trained, new samples can be used to fine-tune the network or processed to inference in a feed-forward fashion, being extremely efficient and generalizable to cases much more complicated than GMM. Very interestingly, compared to conventional networks, quadratic networks can deliver a performance close to that of the EM algorithm in the GMM cases and yet be orders of magnitude simpler than conventional networks for the same classification task.In conclusion, in this paper we have numerically and experimentally demonstrated the superiority of quadratic networks over conventional ones. It is underlined that the quadratic neural network of a much lighter structure rivals the conventional network of a complexity orders of magnitude more in solving the same classification problems. Clearly, the superior classification performance of quadratic networks could be translated to medical imaging tasks, especially radiomics.


We propose a coupled system of delay-algebraic equations to describe tick attaching and host grooming behaviors in the tick-host interface, and use the model to understand how this tick-host interaction impacts the tick population dynamics. We consider two critical state variables, the loads of feeding ticks on host and the engorged ticks on the ground for ticks in a particular development stage  and show that the model as a coupled system of delay differential equation and an algebraic  equation may have rich structures of equilibrium states, leading to multi-stability. We perform asymptotic analyses and use the implicit function theorem to characterize the stability of these equilibrium states, and show that bi-stability and quadri-stability occur naturally in several combinations of tick attaching and host grooming behaviours. In particular, we show that in the case when host grooming is triggered by the tick biting, the system will have three stable equilibrium states including the extinction state, and two unstable equilibrium states. In addition, the two nontrivial stable equilibrium states correspond to a low attachment rate and a large number of feeding ticks, and a high attachment rate and a small number of feeding ticks, respectively. Tick-borne diseases (TBDs) have been imposing significant public health challenges globally. The TBD transmission relies on the tick-host interaction where ticks may acquire and/or transmit the pathogen from the host by taking a blood meal from the host. There are systemic transmission and co-feeding routes, both depending on the co-occurrence of ticks  on the same host, so understanding the tick load distribution dynamics over the host and its implication for the tick population dynamics, the main focus of this study, is important. The tick load distribution process over the host is a dynamical process, governed by the tick attachment/fixation and host grooming behaviours. Our study shows that these tick and host individual behaviors, the host response to tick attaching and/or to tick feeding, and their combinations can yield a complicated tick-host interaction leading to multi-stability where tick densities can converge to a tick extinction, or a lower level tick persistence, or a higher level tick persistence equilibrium state depending on the initial conditions.Tick life cycle includes four stages: egg, larvae, nymph and adult. Larval and nymphal ticks seek blood meals from small rodents, like mice and bird, to molt into nymphal and adult stage, respectively. While it is hard to find larval and nymphal ticks on the hosts since they are small [only around 1–2 mm in size  density-dependent attachment/fixation rate, as we will consider in our model formulation.Important to the survival of an egg through the life cycle is the attachment/fixation success of the questing tick. Existing models have assumed a constant attachment success rate, so the fixation rate of an engorged tick to a host for feeding to develop into the next stage is the questing rate times the attachment/fixation success rate. However, it was reported Voordouw  that ticacquired tick resistance (ATR), by Trager  density-dependent grooming rate  in some of the proposed mathematical models. Pioneering observation of the phenomenon called y Trager , showed y Trager  for the y Trager  providedIn summary, a mathematical description of the tick population dynamics must take consideration of the tick attachment and fixation dynamics, and host grooming dynamics. Here, we develop a coupled system involving two state variables, the number of engorged nymphal ticks and the number of feeding nymphal ticks. We start with an evolution equation for the feeding tick density  governed by the density-dependent grooming rate, and subject to an initial condition involving density-dependent attachment and fixation rate. Integration along a characteristic equation leads to an algebraic equation for the total feeding  ticks. We then couple this algebraic equation with a delay differential equation for the engorged nymphal tick dynamics. Since questing nymphal ticks come from the engorged nymphal ticks with a delay after further development and production, the coupled system becomes a closed feedback system with delay.The model will be formulated in Sect. We focus on the developmental stage, nymphal stage, where questing and attaching rate of the ticks and the grooming rate of the hosts may depend on the feeding nymphal tick loads on the host.Q(t), F(t) and E(t) be the numbers of questing nymphal ticks, feeding nymphal ticks and engorged nymphal ticks, respectively, at time t. We make it explicit our standing assumptions: (i)F(t). This is to reflect the fact that the attachment success of questing ticks depends on the total amount of feeding nymphal ticks on the hosts. As the total number of hosts for nymphal ticks is relatively static, the average feeding ticks on the hosts is proportional to F(t). In what follows, we assume The attachment rate of questing nymphal ticks is a function (ii)F(t). This is to describe the host grooming behaviors, and can also be used to describe the cooperative co-feeding behaviours of the nymphal ticks (that enhances the immune-induced feeding). We also assume that The drop off rate of feeding nymphal ticks is a function Let n be the density of feeding nymphal ticks at time t with respect to feeding duration a since they attach to the host. Then we have the structured feeding tick population dynamics modelT is the average feeding duration of nymphal ticks. In this formulation, the evolution describes the grooming dynamics while the boundary condition describes the attaching behaviours.Let n over the feeding interval, i.e.,F(t). Then the dynamics for engorged nymphal ticks followsThe structured population model can be easily solved using the method of integration along characteristics Evans . Namely,mentclass2pt{minimt take the following formT of nymphal ticks, it is easy to see that the life cycle of tick population is We now link the questing nymphal ticks at the current time to engorged nymphal ticks in the past through the life cycle. Let We now show that the above coupled system of differential-algebraic system is equivalent to a coupled system of delay differential equations subject to a matching condition of the initial data.F(t), we getF satisfies the algebraic equation in system  although the right hand side is given implicitly. Alternatively, we can rewrite the algebraic equation asThere are two other approaches to establish the fundamental theory for the well-posedness of the coupled system we formulated. First of all, we can solve the algebraic equation by using the implicit function theory to obtain  in Hale , Hale an in Hale . See als in Hale  and Gour in Hale  for neutThe equilibrium of model  satisfieClearly, model  always hze model  at the zry Smith , 1995. TThe nontrivial equilibrium of model  satisfieE(t) with a non-trivial non-negative initial value on We first consider the simplest case of constant attachment rate and grooming rate, with s. Model  becomes Note also that  has infiin model . Then thin model  is reduc-Terjeki  and it hA more biologically realistic situation is when the attachment rate decreases and grooming rate increases with tick loads on the host. We consider the prototypical casece model  into13\dF of model If 1, model  has no p(ii)If 1, model  has only(iii)F being replaced by If 1, model  has two tions of  and the ssion of  with F bThe equilibrium structure is determined by When hosts groom in response to tick biting, we haveen model  becomes1ation of  for the a, but this has been reserved for the age-variable in our current study). The parameter j is related to the attach rate (r) and the handling time , that is, rj/2 at The choice of this function is motivated by the Holling type III functional response to describe the improvement of the tick’s searching for an appropriate soft and thin area of the host skin. Note that we have separated the ticks on the hosts into two classes: those questing ticks who have successfully attached to the host but not yet feeding on the host, and those who are feeding, therefore the questing functional response function is (i)When in model ;(ii)If 2, model  has no pF being replaced by If ∗, model  has two ssion of  with F bF being replaced by If 2, model  has fourmentclass2pt{minimssion of  with F bWhen For the combination of the attachment rate  and the We illustrate the case (ii3) in Fig. T is relatively small (a few days) comparing with the tick life cycle in the natural world that can be as long as 3 years.We translate the positive equilibrium F∗,model  becomes1In this section, we use feeding duration of model  at positE-coordinate:We start with the simplest case where of model  into \doat model  has two d system  with resf system . In whatIt is clear to see thattituting , we can ation of  when \doWe now consider the real part of a zero of the modified but equivalent characteristic equation Suppose that the series expansions of ation of  can be rAssume in model  in the cWe note that in the case considered in Theorem 3, the trivial equilibrium is asymptotically stable since We consider the case that ation of  becomes3equation , we obtaUsing the attachment rate function , we get3Letation of  when \doIn what follows, we will explore the solutions of The second equation of  gives34\ing with , we haveation of , we can tituting  into  is a decreasing function for Now we assume thatAssume that the following condition holdsof model  are unstA is determined by the signs of the following three terms:j) and decreasing for A isUsing the assumption , we can mentclass2pt{minimmentclass2pt{minimof model  are bothWe remark that in the case considered in the above theorem, As shown in previous studies Brauer , 2013, aHere, we formulated a novel coupled system of a differential equation and an algebraic/integral equation to characterize the tick population dynamics, with a particular focus on the tick attachment/fixation behaviors and host grooming response and the implication of this tick-host interaction on the tick population dynamics at the population level. The model formulation is particularly useful to provide insights of multi-stability in different combinations of tick-host pairs. We did consider two special cases: the case of cooperative feeding and density-dependent grooming when bi-stability occurs, and the case of cooperative feeding and grooming in response to tick biting when quadri-stability becomes a feasible scenario.We now provide a few numerical examples to show bi-stability and quadri-stability are both possible with parameters suggested from experimental settings or field observations , local stability analysis of the multiple equilibria coexisted in the coupled system is very difficult and we are only able to conduct the local stability analysis using the perturbation analysis when the feeding duration T is relatively small comparing with the long life cycle (Due to the incorporation of two time lags (Tick population dynamics and tick-borne disease transmission dynamics have been modeled intensively (see, for example, Gaff and Gross An important step forward is to expand our coupled system for the tick population dynamics to a coupled system for tick-borne disease transmission dynamics when tick population is further stratified by physiological stages and epidemic status. Separating the tick-attaching and host grooming behaviors for ticks at different stages in describing the tick-borne disease transmission dynamics is also important to understand the co-occurrence of ticks at different stages in the same host, which is critically important to understand the role of co-feeding transmission dynamics (Alekseev and Chunikhin


Traffic volatility modeling has been highly valued in recent years because of its advantages in describing the uncertainty of traffic flow during the short-term forecasting process. A few generalized autoregressive conditional heteroscedastic (GARCH) models have been developed to capture and hence forecast the volatility of traffic flow. Although these models have been confirmed to be capable of producing more reliable forecasts than traditional point forecasting models, the more or less imposed restrictions on parameter estimations may make the asymmetric property of traffic volatility be not or insufficiently considered. Furthermore, the performance of the models has not been fully evaluated and compared in the traffic forecasting context, rendering the choice of the models dilemmatic for traffic volatility modeling. In this study, an omnibus traffic volatility forecasting framework is proposed, where various traffic volatility models with symmetric and asymmetric properties can be developed in a unifying way by fixing or flexibly estimating three key parameters, namely the Box-Cox transformation coefficient  Short-term travel flow forecasting serves as an essential tool to provide useful traffic flow information in the immediate future, and hence wide supports to intelligent transportation systems (ITSs), especially advanced traveler information system, route guidance system, and proactive traffic signal control system. For instance, with accurate real-time traffic flow forecasts, a proactive signal control system is able to set up strategies to significantly reduce traffic delay, and a route guidance system is capable of providing travelers with the optimal route with a minimum travel cost. With this in mind, plenty of methods have been proposed for short-term traffic flow forecasting, which can be generally divided into two categories: (1) traditional forecasting methods that concentrate on improving the accuracy of traffic mean forecasts; and (2) traffic volatility forecasting that focus on the unpredictable part to capture the time-dependent variances.During the last couple of decades, extensive traffic flow forecasting studies have been conducted using time series models ,2,3,4, KAs the traffic reliability or uncertainty problem has been highly valued in recent years, many volatility models have been proposed for short-term traffic flow forecasting. Compared with the point forecasting models that presume a constant variance, the volatility models can not only produce accurate mean forecasts but also give more reliable forecasting confidence intervals by capturing the temporal evolution of conditional variances. Among the volatility models, the GARCH-type models, such as the fractionally integrated asymmetric power ARCH (FIAPARCH) model , the expIn this research, an omnibus traffic volatility forecasting framework based on the FGARCH model  is propoThe main contributions of this research include two aspects. First, we present a comprehensive traffic volatility forecasting framework, which can be utilized to develop effective volatility models in a flexible manner, and are capable of properly capturing the evolution of conditional variance with symmetric or asymmetric properties. Second, we conduct extensive experimental studies to fully evaluate and compare the performance of the established volatility forecasting models, including the symmetric standard GARCH  and the The remainder of this paper is organized as follows: In During the past decades, a large number of volatility methods have been developed for short-term traffic flow forecasting. In general, these methods describe the traffic volatility during the forecasting process by using the standard GARCH or its advanced extensions.The GARCH-type models were firstly proposed in the fields of finance and economics. In order to deal with the problem that the volatility of financial time series changes over time, the autoregressive conditional heteroscedastic (ARCH) model was introduced by Engle , and theDue to the standard GARCH process having a linear relationship between the conditional variance and the shocks in the past, the GARCH model is limited in perfectly describing the temporal evolution of traffic volatility. Moreover, the squared term in the standard GARCH model does not allow the asymmetric effects of traffic volatility that might exist when traffic condition changes dramatically. Therefore, Tsekeris and Stathopoulos  presenteConsidering traffic volatility may be better modeled by removing underlying traffic patterns that can be decomposed from original traffic flow data series, Zhang et al.  proposedThe aforementioned GARCH-type models describe the evolution of traffic volatility from linear to nonlinear, from symmetric effect to asymmetric effect. Though the dynamics of traffic volatility has been modeled explicitly step-by-step, the ability of capturing traffic volatility may be subject to the restrictions of the appointed GARCH-type models. For instance, the asymmetric property of volatility can be captured by EGARCH, GJR-GARCH, and asymmetric power ARCH models because of the introduced “rotation factor” in the ARCH term. However, another critical factor—“shift factor”—that can also be used to describe the asymmetric property is not considered in these models. According to Helbing et al. ,41, the To develop an effective traffic volatility model that can better capture the evolution of the conditional heteroskedasticity underlying traffic flow time series, an omnibus traffic volatility forecasting framework is presented, as depicted in Generally, the framework can be systematically deconstructed into five steps. First, a mean forecasting model is built based on a calibration dataset and the ARIMA algorithm. To achieve satisfactory mean forecasts, the stationarity test and autocorrelation test are conducted using the augmented Dickey–Fuller (ADF) test  and the The purpose of developing the mean forecasting model is to remove the sample mean from the traffic flow data and obtain the residual series for further traffic volatility modeling. One of the most widely used mean forecasting models, namely ARIMA ,20,27,31First, the stationarity of the traffic flow time series needs to be checked, which is an important assumption in modeling the ARIMA model. The ADF test  is a uniSecond, the autocorrelation of the traffic flow time series is tested with the Ljung–Box test . As a liThird, a step-wise algorithm proposed by Hyndman and Khandakar  is intro the BIC  is adoptOnce the orders of the ARIMA are optimally determined, the last subprocedure of building the mean forecasting model is to estimate the parameters refer to  for moreOnce the mean forecasting model is established, the residual series can be computed according to the observations and mean forecasts. The conditional heteroscedasticity of the residual series, also known ARCH effects, needs to be carefully checked to model the traffic volatility. In view of this, the Lagrange multiplier test  is introWhen the significant ARCH effects are checked, the subsequent step is to capture the effects with a proper volatility model. The ARCH model proposed by Engle  providesTo deal with the above issue, various GARCH-type models have been presented. Among the GARCH-type models for short-term traffic flow forecasting, the GARCH  model has been verified as the most adequate and simple representation of traffic volatility ,18,31. TThe parameter g et al. , a bettee shocks . As Helbe shocks  demonstrThe above volatility equation has a flexible form for modeling volatility by controlling the parameters entschel  for the entschel .The adequacy of the fitted models needs to be examined carefully before traffic volatility forecasting. More specifically, we need to check the validity of the established mean equation and volatility equation. The validity of the mean equation can be examined by applying the Ljung–Box test to the standardized residual series sumption .The last step of the framework is to evaluate the performance of the developed models and select the most effective one for further traffic volatility forecasting according to the evaluation results.For traffic flow mean forecasting performance evaluation, two typical measures, i.e., the mean absolute error (MAE) and the mean absolute percentage error (MAPE), are selected, which are defined as follows.In the above equations, tatistic  is adoptWith regard to traffic volatility forecasting performance evaluation, four classical measures, including the kickoff percentage (KP), the average confidence length (ACL), the volatility MAE (VMAE), and the directional accuracy, are employed. For short-term traffic flow forecasting, the KP measure indicates the probability that future observations do not lie in the forecasted confidence intervals when given the evaluation sample size. Theoretically, the better the performance is, the closer the KP is at a given significant level s study) . The ACLs study) , VMAE meIn the above equations, urrogate , where xThe proposed traffic volatility forecasting framework and developed models were tested using real traffic speed data collected from urban roads of Kunshan city, China and freeway segments of the San Diego Region, USA . To inveTo evaluate the mean forecasting performance of the developed models, the MAE and its two-sided DM test statistics were computed and compared. In this study, the parameters of the mean forecasting model can be estimated in two ways—namely separate estimation and joint estimation. The former is implemented based on a separate ARIMA modeling process, while the latter is achieved by estimating the parameters of the mean equation and volatility equation jointly. The two ways may lead to different mean forecasting performance. Therefore, it is necessary to investigate the performance difference between the two ways.As can be seen from the table, under normal traffic conditions, the two estimation ways show very similar performance, especially on weekends. However, under incident traffic conditions, there were significant differences between the performance of the two estimation ways on nearly half of the evaluation stations. More specifically, the separate estimation way achieved better performance than the joint estimation way. This implies that it is better to first estimate the parameters of the mean equation and further use the residual time series to estimate the parameters of the volatility equation when modeling traffic volatility under incident traffic conditions.Traffic on different types of roads exhibits distinct fluctuation patterns. To properly evaluate the performance of the established models under different volatility levels, we grouped the stations with different road types according to the calculated VMAE measure, as illustrated in The best rank is labeled with the red color, while the worst rank is labeled with the blue color. Note that when the DM test ranks of two models are same, the best model is further determined by the average MAE values. As indicated by the average MAE values, the developed six models show very similar mean forecasting performance. By further going through the DM test ranks, we can find that the NGARCH has better performance when the volatility levels are high and medium. Comparatively, the TGARCH shows worse performance in the same situations. It is a bit surprising that the TGARCH model shows advantages over other models under incident conditions. We can also see that the freely estimated FGARCH model takes the most advantage at the high volatility level on weekdays.To effectively evaluate the volatility forecasting performance of the developed models, the VMAE, DA, KP, and ACL measures were calculated. The four measures quantify the model performance from different perspectives. The VMAE measures the accuracy of traffic volatility forecasting. The DA gives the volatility direction accuracy of the forecasting models. KP and ACL ensure the forecasts fall into the predicted confidence interval as much as possible when the interval length is short enough. Considering the inconsistency of the measures in some cases, we also computed the ranks of the models for each measure to make a fair comparison.As seen in  Schwert .The DA measure describes the forecasting directional accuracy of the given model. In view of this, we calculated the average DA value and its rank of the six models, as shown in The absolute deviation of KP from the significance level of 0.05 was calculated to check the validity of the models at each traffic station. The calculation results include the average value and its rank on all stations of the same volatility level group, which are illustrated in The average ACL value and the rank of each developed model are presented in There are commonly two strategies for identifying the orders of the mean equation of the proposed framework. The first is an automtic identification strategy, which uses the step-wise searching algorithm  with an To investigate the impact of the two order identification strategies on the forecasting performance of the developed models, we recorded the forecasting results using the two strategies. After careful inspection and calibration, we found that the two strategies lead to similar forecasting performance for most stations. However, for several specific monitoring stations, they show significant differences. Traffic volatility forecasting plays a key role in traffic reliability or uncertainty analysis. Many GARCH-type models have been developed to capture volatility in the fields of finance and economics. However, the ability of these models to capture traffic volatility has not been fully investigated. In this study, a systematic traffic volatility forecasting framework based on an omnibus family GARCH model is proposed. Under this framework, six volatility models were developed by manually setting up or freely estimating three key parameters. The performance of the models was comprehensively evaluated and compared by using 47 traffic speed data collected from five kinds of roads under normal traffic conditions and incident conditions. A number of key findings were achieved based on the experimental results, which can provide insights into traffic volatility modeling for researchers and practitioners.The experimental results in this research reveal the potential of explicitly modeling volatility evolution properties in improving traffic volatility forecasting performance. In the future, more traffic flow datasets could be used to evaluate the effectiveness of the proposed framework. The physical explanations about how the asymmetric property of traffic volatility is associated with various traffic phenomena are also worth exploring.


Internationally, intensive psychiatric home treatment has been increasingly implemented as a community-based alternative to inpatient admission. Since 2018, the so-called Inpatient Equivalent Home Treatment  has been introduced as a particularly intensive form of home treatment that provides at least one daily treatment contact in the service users’ (SU) home environment. Prior research shows that this can be challenging in rural catchment areas. Our paper investigates to which extent the location of the SU home location within the catchment area as well as the distance between the home and the clinic influence the utilisation of inpatient treatment compared to IEHT.Routine data of one psychiatric hospital in the federal state of Brandenburg in Germany were analysed for the observational period 07/2018–06/2021. Two comparison groups were formed: SU receiving inpatient treatment and SU receiving IEHT. The SU places of residence were respectively anonymised and converted into geo-coordinates. A geographic information system (GIS) was used to visualise the places of residence, and car travel distances as well as travel times to the clinic were determined. Spatial analyses were performed to show the differences between comparison groups. In a more in-depth analysis, the proximity of SU residences to each other was examined as an indicator of possible clustering.p > 0.05). The places of residence of SU treated with IEHT were located in greater proximity to each other than those of SU treated in inpatient setting (p < 0.1).During the observational period, the location of 687 inpatient and 140 IEHT unique SU were mapped using the GIS. SU receiving treatment resided predominantly within the catchment area, and this proportion was slightly higher for SU receiving IEHT than for those treated in inpatient setting (95.3% vs. 84.7%). In the catchment area, the geographical distribution of SU place of residence was similar in the two groups. There was a general higher service provision in the more densely populated communities close to Berlin. SU with residence in peripheral communities were mainly treated within the inpatient setting. The mean travel times and distances to the place of residence only differed minimally between the two groups of SU (In especially peripheral parts of the examined catchment area, it may be more difficult to have access to IEHT rather than to inpatient services. The results raise questions regarding health equity and the planning of health care services and have important implications for the further development of intensive home treatment. Telehealth interventions such as blended-care approaches and an increase of flexibility in treatment intensity, e.g. eliminating the daily visit requirement, could ease the implementation of intensive home treatment especially in rural areas. Equal access to care services is a leading principle of health care systems . A centrAs early as 1866, the epidemiologist and psychiatrist E. Jarvis was able to prove a significant correlation between the rate of admission and the distance of service users’ (SU) place of residence to the psychiatric hospital. SU that lived close to the hospital were more likely to be treated as inpatients than those that lived further away . This soTo date, it has not been investigated to what extent the usage of (intensive) home treatment depends on the place of residence, or whether a greater distance between the place of residence and the hospital constitutes a negative predictor for outreach psychiatric service usage. Since outreach intensive care services are being internationally increasingly implemented as an alternative to inpatient psychiatric care –12, thisIn Germany, the possibility for psychiatric hospitals with a catchment area to offer the so-called Inpatient-Equivalent Home Treatment  as part of routine health care services exists since 2018-01-01 . The legIs intensive home treatment utilised equally across the catchment area studied, or are there differences depending on the place of residence?How do the distances and the car travel time from place of residence to hospital differ between SU treated in the home treatment or inpatient setting?Thus, the goal of this study is to investigate to what extent IEHT, a particular intensive form of home treatment, is utilised in a large rural catchment area in comparison to inpatient treatment, and whether this is influenced by the previously mentioned distance effects. The following research questions are explored:Analyses of the utilisation and mapping of health care services have been performed for research and planning purposes using geographic information systems (GIS) , 19. Thi2. This area is just about double the size of Berlin. 70% of the inhabitants of the catchment area live in the more densely populated communities close to Berlin [The study was performed at the Department for Psychiatry and Psychotherapy of the Brandenburg Medical University, Immanuel Hospital Rüdersdorf (IHR). Additionally, to the main site in Rüdersdorf, two satellite locations in Strausberg and Fürstenwalde belong to the hospital, and both include a day-care unit and a psychiatric outpatient centre. The IHR is responsible for the acute mental health care for the two regions Märkisch-Oderland (MOL) and Oder-Spree (LOS) that border Berlin to the east. The catchment area of the hospital includes 239.908 inhabitants (recorded 2020-12-30) and a surface of 1.550 kmAt IHR, IEHT has been offered since May 2018. During the observational period (1. July 2018–30. June 2021) the mean caseload of IEHT, i.e. the amount of SU treated simultaneously, was 7.2. Treatment contacts were usually performed by two team members working together, driving by car from one SU to the next. Depending on the distribution of SU within the catchment area, one or two different routes, a north-western and a south-eastern one, were travelled every day. The mean length of an exemplary travel route  between all residences per setting were calculated. Visual interpretation indicated differing spatial distribution especially with decreasing proximity of SU between settings. Therefore, in each setting, the 75% quantile of the paired distance was calculated for each of the residences and the distribution subsequently tested for significant differences. Thereby, particular differences in the pairwise distance outside of existing spatial clusters could be taken into account. All differences between comparison groups were tested using the Wilcoxon-Mann-Whitney-Test.Within the observation period, 831 SU were treated in the inpatient and/or the IEHT setting by the study hospital. 783 addresses of this total number of SU could be determined with the GIS, and of those, 687 SU were treated in inpatient setting and 140 SU received IEHT. 44 SU received care in both inpatient and IEHT settings. The socio-demographic characteristics of the service users are shown in Table 2) and immediately adjacent surroundings  of SU in the inpatient and 95.3% (n = 133) in the IEHT setting. Figure In the following spatial analyses only SU residing inside the catchment area were included, comprising 84,7% (p = 0.0965). Considering the 75% quantile, this result is significant with p < 0.01.The mean travel times, distances and the paired distances between the SU places of residence (as an indicator for clustering) are displayed in Table The results show that in the Brandenburg region we studied, SU generally were able to receive inpatient or inpatient-equivalent home treatment regardless of the travel time and distance to the hospital. It was not possible to prove a “Distance Decay” effect for either of the two settings or a particular primary diagnosis since the utilisation of health care services seems to increase with rising distance from the hospital rather than to diminish. Concerning the inpatient setting, the results confirm already existing evidence , 26.Stulz, Hepp and colleagues argue that the usually more severe and acute clinical condition of SU treated in the inpatient setting, often taken to the hospital as an emergency or involuntary admission, reduces the influence of distance on the usage of the inpatient setting . In contYet the present results show that the implementation of IEHT is distributed in a more complex manner. SU in the observed region were more likely to be admitted to IEHT in those areas in which other SU living close by received the same treatment. This particularly applied to densely populated territories. To date, the increased rate of utilisation of health care services in urban sectors is well documented through the typically higher prevalence of psychiatric crises in comparison to rural districts –33.Aside from this epidemiological factor, the decision whether a SU with a specific residence location could be treated with IEHT was also determined by institutional contingencies in the studied region. To facilitate admission of SU living further away from the IEHT team travel route, caseload and available staff had to be balanced so that the IEHT team could compensate for longer travel times .The possibilities to offer spatially inclusive and comprehensive home treatment services in the examined region are restricted within the current framework of the IEHT. A conceivable scenario could be to dispatch IEHT teams from satellite sites spread throughout the catchment area instead of dispatching them from the headquarters of the hospital. This would presumably increase the range of the IEHT team. Alternatively, the caseload could be diminished to such an extent that even SU that live further apart could be treated by one and the same IEHT team. Yet there are strong limitations to the feasibility of this option, since from a caseload of roughly 4–5 downwards a cost-effective service provision would be impossible in the long term. This hypothesis is also supported by health economic evaluations, which provide ambiguous, or inconclusive, evidence of the cost-effectiveness of outreach care in rural regions .To ensure the successful implementation of exhaustive intensive psychiatric outreach care in rural areas, other framework conditions than those of IEHT are necessary. Several different flexible outreach treatment models are already well established in the international scene , among tCurrently, a variety of integrated and outreach mental health service models exist in Germany, which allow for a flexible management of treatment intensity. For example, based on a global treatment budget , it was possible to implement a form of mental health home treatment in very sparsely populated regions of Schleswig-Holstein in Northern Germany that covered the entire region through a flexible control of the treatment intensity , 25, 39.A further possibility for increasing the flexibility of home treatment, and thus also for expanding its range of accessibility, would be to utilise digitalisation to reduce the number of in-person contacts with SU. In the context of the Covid-19 pandemic, the application of Video- and Telemedicine to reduce in-person contacts by intensive home treatment teams was internationally successfully tested . A curreThis is the first study that analyses the utilisation of intensive outreach versus inpatient psychiatric treatment from a geographical perspective based on routine hospital data. This study was limited to one particular region, which limits the generalisability of the results. A comparative analysis of more and different regions is thus still needed. Still, we were able to demonstrate a fundamental problem of outreach care services in larger catchment areas. The fact that the car travel route between hospital and place of residence diverges from the actual route of the IEHT team is considered a methodological limitation. The reason for this is that the SU in treatment - at least in the study region - are visited one after the other, which in many cases decreases the travel route per SU considerably. Yet the mean distance between hospital and place of residence as an indicator for the accessibility of a care service could still enable a basic comparison between the settings.The probability of a service user (= SU) to have access to and receive intensive home treatment is higher in densely populated regions of Germany than in areas with a lower population density or those located peripherally in catchment areas.Our results suggest that the range of intensive outreach treatment does not depend on the distance/travel time of the treatment team to the residence of the SU but rather on its distance to the travel route of the home treatment team.In order to present intensive outreach treatment as a truly equivalent alternative to inpatient psychiatric treatment, SU need to be able to access this form of treatment equally regardless of their place of residence within the catchment area. Making the restrictive legal framework of inpatient equivalent home treatment more flexible as well as supplementing Blended-Care approaches could contribute to increasing implementation of this concrete German form of intensive home treatment even in rural regions.


In many countries, along with rising rural labor transfer, the problem of rural domestic sewage discharge is becoming increasingly serious due to labor shortages in the villages. It is urgent to solve the environment pollution and health problems of residents which is caused by the massive discharge of domestic sewage in rural areas. Based on the survey data collected from Nanjing Agricultural University in 2020, this paper employs the ordered probit model and the CMP method, to empirically test the impact of non-agricultural employment and regional choice on farmers’ domestic sewage discharge behavior and the moderating effect of environmental cognition and the social network. The results show that: (1) There is a significantly positive correlation between non-agricultural employment and farmers’ sewage treatment behavior. (2) Environmental cognition significantly improves the participation of urban non-agricultural employment farmers in sewage treatment, and the social network has a significant role in promoting the adoption of sewage treatment behavior of local non-agricultural employment farmers. (3) Further heterogeneity analysis results show that the inhibitory effect of urban non-agricultural employment on random sewage discharge is more pronounced than that of local non-agricultural employment. Therefore, in order to effectively solve the problem of rural domestic sewage discharge, it is necessary to actively guide the sewage discharge behavior of non-agricultural employment households, strengthen the social network interaction within the village, and increase the publicity for sewage discharge knowledge. The results of the second national pollution source census in 2017 showed that the emission of rural water pollutants reached 5.9226 million tons in China, accounting for 47% of the total national water pollutants ,4. In faWith the continuous expansion of urbanization and industrialization in China, in order to obtain higher working remuneration and improve family livelihood, a large number of the rural labor force have been transferred into non-agricultural industries . The monIn theory, some scholars believe that non-agricultural employment can promote farmers’ participation in environmental governance through an income effect, which is mainly manifested in the improvement of environmental literacy and the enhanced investment ability in environmental governance caused by the increase of non-agricultural income . In addiTherefore, there have been abundant studies on the impact of non-agricultural employment on farmers’ sewage treatment behavior However, there are two aspects that need to be considered, which are to be the contributions of this paper. First, although non-agricultural employment conceptually emphasizes the professional transformation of farmers’ family members from agriculture to non-agricultural industries, it also implies in a broad sense the geographical migration of rural and urban labor . NeverthThe remainder of the paper is organized as follow. Non-agricultural employment plays an important role in strengthening farmers’ family endowments ,13. In tFurther, non-agricultural employment can be divided into local non-agricultural employment and urban non-agricultural employment according to the working distance of migrant workers. The distance of migrant households may affect their behavior decisions from different angles. Generally speaking, if the expected income of local employment is closed to urban non-agricultural employment, farmers are more inclined to engage in local non-agricultural employment with the consideration of part-time farming or family care. Hence, farmers choosing urban non-agricultural employment is mainly ascribed to the higher labor remuneration in economically developed cities. In other words, there is a strong correlation between farmers’ choice of urban non-agricultural employment and the economic development level of the living areas . FarmersAs analyzed above, when the expected income of local non-agricultural employment is lower than that of urban non-agricultural employment, the reasons why farmers still choose local non-agricultural employment may be for the consideration of part-time farming or family care. At this time, the production and life of local non-agricultural employment households are still embedded in the rural traditional acquaintance society. In the traditional acquaintance society, farmers always exchange life production information and make behavioral decisions based on the social relationship network formed by blood, kinship, and geography . First oAccordingly, Hypotheses 1 and 2 are proposed:Hypothesis 1.Households with non-agricultural employment are more willing to treat domestic sewage.Hypothesis 2.For farmers involved in local non-agricultural employment, environmental cognition positively regulates their domestic sewage treatment behavior. For farmers involved in urban non-agricultural employment, the social network positively moderates their domestic sewage treatment behavior.Jiangsu Province is located on the lower reaches of the Yangtze River and Huaihe River basins . It owns rich water resources and a high urbanization rate. By 2018, the province’s rural population reached 47.75 million, accounting for 59.5% of the province’s total population. Due to the large rural population base and the high per capita sewage discharge in the province, the domestic sewage discharge problem is more prominent in densely populated areas. In order to promote rural sewage treatment comprehensively, the Jiangsu provincial government has issued the “Jiangsu Province Groundwater Pollution Prevention and Control Implementation Plan”, “Jiangsu Province’s 14th Five-Year Plan for Soil, Groundwater and Rural Ecological Environmental Protection”, and “the provincial ecological environment special law enforcement action plan in 2022” and other related policy documents. With the continuous promotion of sewage treatment, the rate of rural domestic sewage treatment in the province reached 31.1% in 2022, but it still needs to be further strengthened.The data sources used for analysis are the China Land Economic Survey (CLES) conducted by the Department of Humanities and Social Sciences of Nanjing Agricultural University and the Jin Shanbao Institute of Modern Agricultural in Jiangsu Province in 2020. The reasons for selecting Jiangsu Province as the sample province in this paper are as follows. First, Jiangsu Province is located in a hilly area with abundant water sources. The per capita domestic sewage discharge in rural areas is relatively high and the problem of domestic sewage discharge is more prominent . Second,The explained variable in this paper is the household sewage discharge behavior. The indicator was measured by asking “How is your domestic sewage discharged”. If farmers choose to discharge it to outdoor or open ditches at will, a value of 0 is assigned. The option to discharge to the sewer is assigned a value of 1. Using a special sewage collection bucket to collect is assigned a value of 2. According to the environmental protection level of sewage discharge from low to high, the sewage discharge behavior of farmers can be divided into three categories and assigned a value of 0–2: First, “random discharge to outdoor and open ditches” = 0. The randomly scattered discharge method reflects the low participation of farmers in sewage treatment, which is not conducive to the improvement of sewage treatment effectiveness. Second, “discharge to sewer” = 1. Farmers gradually participate in the process of sewage treatment through the installation and use of water pipes, thereby curbing the pollution caused by random discharge. Third, “use a dedicated sewage collection bucket to collect” = 2. Compared with discharging into the sewer, this behavior can better reflect farmers’ stronger awareness of environmental protection and higher participation in sewage treatment. In a practical sense, it is helpful to have the assignment of three types of variables to explain the participation of farmers in sewage treatment, and improve the effectiveness of sewage treatment.Household non-agricultural employment is selected as the core explanatory variable, which is mainly because the household is the basic unit of agricultural micro-research, and the household is generally the decision-making unit for sewage discharge. Some researchers believe that the indicator could be measured by the number of family migrants . On thisAccording to the theoretical analysis, the social network and environmental cognition will positively regulate the sewage treatment behavior of farmers involved in non-agricultural employment. Drawing on the results of previous research , this paConsidering that other factors can also interfere with farmers’ sewage discharge behavior, this paper draws on the previous research results and controls factors such as farmers’ personal characteristics, family characteristics, environmental cognition, and policy understanding. The descriptive statistics of variables are shown in y, and the hidden variable of farmers’ sewage discharge behavior is denoted by y*; ix represents the core explanatory variable that is the family non-agricultural employment situation, ic represents the control variables, iα  is the column matrix of the parameters to be estimated, iε is the random error term, and r0 and r1 are the unknown tangent points. When iε ~ N  is distributed, the ordered probit model can be obtained:This paper uses Stata15.0 for empirical analysis. Since the explained variable in this paper is ordered and discrete, the ordered probit model is selected to analyze the influencing factors of farmers’ domestic sewage discharge behavior. The model is developed as follows:r0, the household sewage is discharged to outdoor and open-air ditches at will. When it is higher than r0 and less than r1, the farmer directly discharges the domestic sewage to the sewers When it is higher than r1, farmers use special sewage collection buckets to collect domestic sewage.From Equation (3), it can be found that when the household non-agricultural employment ratio is lower than There may be problems of missing variables and reverse causality between non-agricultural employment and sewage discharge behavior, which leads to biased empirical results. First, the omission variables that are difficult to measure, such as farmers’ subjective employment preference choices and living habits, may have an impact on non-agricultural employment and sewage discharge behavior, resulting in the problem of omission variables. In addition, when the village environment is seriously polluted by the farmers’ polluting behavior, farmers choose to go out to work for better life quality, which leads to an increase in the number of migrant workers. Therefore, the pollutant discharge behavior of households may adversely affect the family’s choice of migrant workers, which will lead to the problem of reverse causality. In order to solve the above problems, this paper uses the conditional mixed estimation (CMP) proposed by previous research . In the iz, and the interaction term is denoted by ix × iz. β0 is the constant term, iβ  is the parameter coefficient to be estimated, and iμ is the random error term. After adding the interaction term, the moderating effect of social network and environmental cognition can be examined through β3.Based on the above theoretical analysis, it can be seen that social network and environmental cognition may play a moderating role in the impact of non-agricultural employment on farmers’ pollutant discharge behavior. In order to test the moderating effect, this paper establishes the following moderating effect model:p value is 0.14 > 0.05, indicating that through the parallel line test, the regression equations are parallel to each other, and the ordered probit model can be used for analysis.Considering the possibility of multicollinearity among the selected variables, this paper tests the variable variance inflation factor (VIF) in the model first of all. The test results show that the VIF of all variables in this model are less than 10, which satisfies the principle of independence, so the selected explanatory variables do not have serious collinearity problems. In addition, the regression results of the model are tested by parallel lines, the chi-square value is 9.65, and the From the point of control variables, age, wealth level, and policy understanding have inhibited the random discharge of domestic sewage by farmers at a statistically significant level of 1%. With sufficient financial support and the guidance of environmental protection policies, families can better understand the importance of environmental protection for village development and choose to participate in the treatment of domestic sewage. Political status has a positive impact at the level of 5%, indicating that households with village cadres tend to choose a more environmentally friendly way of discharging domestic sewage, which further shows that village cadres have a better understanding of human settlement improvement policies than other villagers. The leaders of the village action, and the families with political identities, will also take the lead in governance. The proportion of women has a positive impact at the level of 10%. Families with a higher proportion of women may pay more attention to the issue of domestic sewage discharge, and the increase in the proportion of women in the family will also strengthen women’s decision-making power in family affairs, thereby promoting participation in sewage treatment. On the contrary, insignificant environmental perception means that although farmers are aware of certain environmental pollution problems in their villages, they cannot link pollution with domestic sewage discharge. Therefore, incomplete environmental perception may also be the reason for the random discharge of rural households. The fact that the average education level of households is not significant may be due to the failure to receive relevant knowledge of water resource protection in the process of school education, so that they cannot understand the importance of domestic sewage discharge behavior for the ecological environment.The results of the above basic estimate can only show the impact of non-agricultural employment on sewage treatment behavior from the overall parameter sign and the significance. This paper further analyzes the marginal effect of explanatory variables. As shown in Considering the potential endogeneity problem, this paper chooses the CMP method for further examination. The effective estimation of CMP requires the selection of a suitable instrumental variable. The “non-agricultural employment ratio of villages” as the instrumental variable is selected. On the one hand, the increase in the number of migrant workers in the village contributes to strengthen the connection between the village and the outside world and provides opportunities for other farmers to go out to work. At the same time, with the increase in the proportion of non-agricultural employment in villages, the atmosphere of non-agricultural employment will also affect the choice of other farmers to go out to work. On the other hand, the proportion of migrant workers at the village level does not directly affect the pollutant discharge behavior of rural households, so it satisfies the requirement of exogenous instrumental variables.First, the CMP method is used to regress the ordered probit model, and the obtained regression results are basically consistent with the basic regression results. In addition, the IV-ordered probit model is estimated in two stages using the CMP method after determining the instrumental variables. From With the above results the relevant empirical tests on the impact of non-agricultural employment on sewage discharge behavior were conducted and it was found that non-agricultural employment significantly promotes the orderly discharge behavior of farmers. However, the above results are only considered from the whole sample level, which may ignore the differences in the distance between different labors. Therefore, based on the CMP method in this paper the heterogeneity of the impact of non-agricultural employment on sewage discharge behavior under different working distances was examined in turn. The results of the heterogeneity are shown in According to the working distances in different regions, we divided the labor samples of non-agricultural employment into non-agricultural employment samples of local townships, non-agricultural employment samples that cross townships but not across counties, and non-agricultural employment samples that cross counties in order to analyze the effect of regional selection of employment on domestic sewage discharge behavior. The results of models (4) in Based on the models (4)–(6), further testing was conducted on the moderating role of environmental cognition and social network in the implementation of sewage treatment behavior of local non-agricultural employment farmers and urban non-agricultural employment farmers. The specific regression results are shown in Although the CMP method is used to alleviate the endogeneity problem, considering that there may still be problems such as measurement error in the regression is necessary in order to verify the reliability of the regression results. This paper adopts the following three methods to test the robustness: First, replace the core explanatory variables. “Average non-agricultural employment hours” was used to replace “the ratio of household non-agricultural employment”. Due to the instability of non-agricultural employment, farmers may have part-time jobs in reality. At this time, the interviewed farmers will have a certain degree of subjectivity due to the deviation of understanding when filling out the questionnaire. Therefore, setting the number of people as a measurement indicator in the questionnaire acquisition may cause a certain error, and the selection of the variable “Average non-agricultural employment time” is more objective, which helps to solve the above measurement error, and ensure the empirical result’s robustness. Second, change the estimation method. In addition to the ordered probit model, this paper also uses the probit model to study the impact of non-agricultural employment on the domestic sewage discharge behavior of farmers, and verify the robustness of the regression results through different estimation methods. Third, remove the sample. Based on the regression of the CMP method, this paper removes the sample of pure agricultural households, for better verification of the relationship between non-agricultural employment and farmers’ sewage discharge behavior. The estimation results of the alternative explanatory variables in model (11) verify that the effect of non-agricultural employment on the domestic sewage discharge behavior of farmers is significant, but the direction is inconsistent with the basic regression’s results. The possible reason is that the increase in the non-agricultural employment time will correspondingly shorten the time of farmers in the village, which will lead to changes in the degree of attachment and sense of belonging in the village. Therefore, the longer time working outside and the lower sense of village belonging of the farmers, thereby, reduce their concern for the village environment and their participation in environmental governance. After changing the model, we found that the estimation results in model (12) also show the robustness of the basic regression. Compared with the basic regression, after removing irrelevant samples, the empirical results show as being more significant and the absolute value of the correlation coefficient increases significantly in the model (13), which further demonstrates the robustness of the empirical results.On the basis of theoretical analysis, based on the survey data of 2473 farmers in Jiangsu Province, China, this paper used the ordered probit model to empirically test the impact of farmers’ non-agricultural employment and regional selection on domestic sewage discharge behavior. The moderating effects of social network and environmental cognition were also tested by constructing a moderating effect model. The results demonstrate that non-agricultural employment has a significantly positive impact on the domestic sewage discharge behavior of farmers. The results of the moderating effect analysis show that environmental cognition can significantly improve the participation of urban off-farm employment households in sewage treatment, and social network can significantly promote the adoption of sewage treatment behavior of local non-agricultural employment households. Heterogeneity analysis shows that the probability of local non-agricultural employment households to implement sewage treatment behavior is lower than that of urban off-farm employment households, and the non-agricultural employment households who cross townships but not counties are more willing to implement relatively environmentally friendly sewage disposal behaviors. Our conclusions are consistent with the previous researcher , who alsBased on the above research conclusions, this paper proposes the following policy suggestions: First, the government should guide the rural surplus labor force to engage properly in non-agricultural employment, and actively promote the local employment of farmers through the establishment of human resource platforms, expanding income channels and attracting the return of talents. While promoting non-agricultural employment, it is necessary to promote vigorously rural sewage treatment, and focus on the non-agricultural employment households with lower degree as the main promotion objects. For non-agricultural households, the government should guide and regulate their sewage discharge behaviors by providing training of environmental protection awareness and carrying out collective activities in the village to improve farmers’ adoption of sewage treatment behaviors. Second, the government should strengthen the environmental awareness level of farmers. To be more comprehensive, the government should make good use of the internet, conferences, posters, etc., to strengthen the publicity of domestic sewage discharge knowledge, thereby enhancing farmers’ awareness of sewage treatment, and strengthen the awareness of the importance of sewage treatment for village development. Third, the government should strengthen farmers’ accruing of social network. Based on the collective actions related to sewage treatment in rural areas, we can promote communication among farmers, reduce the cost for households purchasing sewage treatment equipment, and help to improve their living environment.Due to the limitation of research resource and objective conditions, this manuscript has the following shortcomings. This article uses cross-sectional data from Jiangsu Province. Compared with the national survey data, the sample size of CLES2020 is relatively small. Since we mainly focus on domestic sewage discharge in rural areas, there are certain differences in the degree of water pollution and sewage treatment status in different regions. There may be certain limitations in exploring the impact of non-agricultural employment on sewage discharge behavior through survey data in one province. Therefore, in subsequent research, we will use national large sample data to better reveal the relationship between variables.