dataesr/scientific-paragraphs-categorization huggingface dataset:
Model parameters This section provides a description of the dataset and the modified SEIR model with consideration of infection vulnerability stratification. In its most basic form, following Herbert (2000), SEIR can be written as follows: where S, E, I, R represent the fraction of susceptible, exposed, infected, recovered, respectively, β is the day -1 infectivity rate, α -1 is the daily average incubation period, γ -1 denotes the daily average recovery rate. The variables in equation system 1 are subject to the initial conditions: where σ is the initial fraction of infected people. The average infected person can infect susceptible individuals for γ -1 days; therefore, the basic reproduction number can be written as: The parameters used in SEIR model are defined in Table  1. Pandemic growth will occur as long as the value of β exceeds 1, and cumulative number of infected will grow even during the decay stage.
COVID-19 data analysis and estimating the dynamics of basic reproduction number R 0 This section describes our analysis of real data using our SEIR model with vulnerability stratification. Such analysis includes fluctuations in data and weekly cycles and our method of filtering out those fluctuations and estimating how the dynamics of basic reproduction number R 0 change over time. Obtaining parameters values is the first step of the analysis. As indicated above, the EU dataset does not include information about the dynamics of recovery; therefore, it is impossible to obtain the numbers of currently infected people (Publication Office of the European Union, 2020). The U. S. conducts daily tracking of statistics about COVID-19 dynamics  (The Covid Tracking Project, 2020). A prediction of future COVID dynamics can be obtained by solving the reversal problem based on the SEIR model.
Then, the number of infected people was calculated as the difference between cumulative infected, cumulative recovered and dead people. The results were used to obtain statistical data for the fractions of infected and recovered people I(t) and R(t). U. S. states that lacked data on the number of recovered individuals were excluded from the analysis. As mentioned in (The COVID Tracking Project, 2020): States provide very disparate definitions on what constitutes a 'recovered' COVID-19 case…Types of 'recovered' cases include those who are discharged from hospitals, released from isolation after meeting CDC guidance on symptoms cessation, or those who have not been identified as fatalities after a number of days (30 or more) post disease onset. Specifics vary for each state or territory. Therefore, the fraction of recovered individuals varies from state to state.
Our findings indicate the possibility of a second wave of the pandemic in those countries. The vulnerability stratification coefficients in the U. S. and U. K. were found to be near zero, thereby suggesting the possibility of either a second wave or a slowing down of infection propagation in those countries. Russia and Turkey evinced higher positive coefficients and are deemed to be the country's most likely to experience slowdowns. The main limitation of this study is the lack of data with which to evaluate the statistical significance of factors impacting pandemic dynamics. Changes in seasonal infection rates, the effects of preventive measures, and infection vulnerability stratification cannot be distinguished because related data are only available for a single year. In addition, the number of cases recorded depends on criteria for who is tested for coronavirus, which varies across countries.
Let g denote the Lie algebra of G. Then any Y ∈ g defines a canonical vector field Y M on M. Let then as in  [2]  the G-transverse cotangent space be given by (  2 ) T * G M := { ξ ∈ T * M | ξ(Y M (π(ξ))) = 0, ∀Y ∈ g }. A. B. , R. C. , and V. N. have been partially supported by ANR-14-CE25-0012-01 (SINGSTAR). Manuscripts available from http://www. math. psu. edu/nistor/. As before, S * M denotes the unit cosphere bundle of M. Let S * G M := S * M ∩ T * G M denote the set of unit covectors in the G-transverse cotangent space T * G M. Let then (3) σ G m (P ) : Ω M (E) := {(ξ, ρ) ∈ S * G M × G ξ | E ξρ = 0} → (x,ρ)∈ΩM (E) Hom(E 0xρ , E 1xρ ) G ξ , σ G m (P )(ξ, ρ) := π ρ (σ m (P )(ξ)) ∈ Hom(E 0xρ , E 1xρ ) G ξ , ξ ∈ (S * G M ) x , called the G-principal symbol σ G m (P ) of P. Recall also the following.
Accurate, robust, and fast fully compressible real-fluid simulation of fuel jets is today's one of the highly debated topics in various research laboratories and industries. Indeed, the use of real-fluid equations of state has proved to be computationally very expensive and is one of the current challenges. In this paper, a thermodynamic equilibrium tabulation approach is proposed to overcome most of the limitations and to make real-fluid simulations affordable in the industry. This tabulation approach is implemented in the Converge software as a closure to the fully compressible two-phase and multi-component real-fluid model (RFM). This modeling approach has been applied to the simulation of a classical cryogenic injection of liquid nitrogen (LN2) coaxially with warm hydrogen (H2) jet, in a transcritical regime using thermodynamic tables generated by two different equations of state: Peng-Robinson (PR), and Soave-Redlich-Kwong (SRK).
Another notable study has recently been done by Koukouvinis et al. [10]. In that study, the authors proposed a uniform tabulated thermodynamic approach based on NIST-database and VLE using PC-SAFT EoS for the simulation of the ECN spray A  [10]. They reported that by use of the PC-SAFT and log10(P)-T tabulation approach, the results are independent of table size when bilinear interpolation is adopted, even with linear mixing rules. As a result, to sum up, most of the available studies show that the tabulation should be highly accurate, with low-storage requirements, and a fast lookup algorithm. However, it seems not clear how to make real-fluid simulations affordable in the industry. In this study, a fully compressible multi-component two-phase real fluid model (RFM)  [1, 2, 11]  has been closed using a generalized three-dimensional (3D) tabulation method.
In this method, an in-house thermodynamic library IFPEN-Carnot is used to generate the 3D-Table (with T-P-Y as the axis for a binary mixture) based on various real fluid EoS. This thermodynamic library involves many EoS such as Peng-Robinson (PR), and Soave-Redlich-Kwong (SRK), which represent also one of its main advantages. The tabulated thermodynamic properties of the mixture are calculated as a function of temperature (T), pressure (P), and species composition (Y). Noteworthy, the uniform look-up table is constructed based on an isothermal-isobaric flash (TP flash)  [12]. This tabulation method also improves the efficiency of the tabulation approach previously developed by Yi et al. [11]  based only on PR-EoS  [1, 2]. The RFM model along with the generalized 3D tabulation method has been implemented in the CONVERGE v3 software  [13].
2-2 Thermodynamic closure, tabulation look-up, and its validation The current work has adopted a tabulation approach where the thermal and transport properties as well as the phase state and composition are tabulated before the CFD simulation. During the simulation, the various tabulated parameters are robustly interpolated over the entire range of the thermodynamic states based on three inputs for the tables which are (T, P, Ym). The coupling between the flow solver and the thermodynamic table is implemented in CONVERGE v3 software  [13]. The flow solver offers pressure-velocityenergy coupling using a modified Pressure Implicit with Splitting of Operator (PISO)  [17]. A second-order central difference scheme with flux limiter is used for the spatial discretization of each equation. The time discretization is achieved by the first-order Euler scheme.
On March 13, Nishiura and colleagues used data from 565 Japanese citizens to estimate the proportion of asymptomatic infections as 30. 8%. 66 With greater access to antibody testing, a Stanford group in Santa Clara County recruited 3330 people used lateral flow immunoassays to estimate the populationweighted seroprevalence of antibodies to SARS-CoV-2 as 2. 49% (95% CI, 1. 80-3. 17%) to 4. 16% (95% CI, 2. 58-5. 70%). 67 Another group in a northern Iran province used a cohort of 528 people to estimate the population antibody seropositivity prevalence as 33% (95% CI, 28-39%). Of the sample, 65 subjects (18%) had no symptoms, but had antibodies to SARS-CoV-2. 68 Contact tracing of 100 patients revealed similar secondary attack rates between pre-symptomatic and symptomatic exposures. 69 Byambasuren, et al.
This turns the infinite dimensional control problem into an optimisation problem over a finite dimensional parameter space. We carry out numerical simulations in the case of M = 3 countries, with parameters as in (2. 3), and piecewise constant vaccination rates: ξ i (t) =    ξ i,1 t < 50 ξ i,2 50 ≤ t < 100 ξ i,3 t ≥ 100. ( 5. 3) Time is measured in days. We seek to minimise the total cost C by optimising over the 9 parameters ξ i,j , 1 ≤ i, j ≤ 3. For a first quick implementation, we use Matlab's fmincon built-in routine to find the optimal solution, which uses an interior point method by default. Figure  4  illustrates the solution to the optimisation problem for different choices of the initial guess where the optimisation starts from. The results show that the problem is numerically unstable, as the optimum found by fmincon is highly dependent on the initial guess.
A key feature of our model is a time-varying, age-stratified vector (! ! ) governing social distancing (non-pharmaceutical interventions) including reduced contacts through personal choices and/or mandated partial lockdowns, as well as reductions in exposure contacts due to mask wearing or physical distancing. The components of the vector ! ! vary from 0, indicating pre-pandemic levels of societal interactivity and no masking, to 1, indicating complete lockdown with no interactions (Supp Fig  1b ). For data prior to November 2020, we estimated ! ! for each age group by calibrating monthly to cases, hospitalization and deaths. In 2021, we project that ! ! will continue to vary according to government policy and public behavior. We include several parameters to reflect this uncertainty. The first is the case threshold to trigger partial lockdown (" "#$ ).
Capitalizing on the strengths of this family of models, here we reconsider disclosure control and develop an application-specific model selection method. Rather than assessing models on the whole contingency table, we target the specific objective of the analysis and develop a two-stage procedure aimed at limiting a form of bias arising in the process of model selection. Under a Bayesian approach, models can be assessed and compared by evaluating their predictive accuracy on future datasets; the posterior predictive density can be used to assess the out-of-sample predictive performance of a model. Measures of predictive accuracy are often based on the log-predictive density, which represents a general summary of model fit. Therefore, an ideal measure of predictive accuracy could be the expected log-posterior predictive density for a future dataset.
This is a particularly challenging problem, recently debated in various fields, from computer science and mathematical statistics to social science and public health. Microdata from social surveys typically include values of sensitive variables (such as income, health status, political orientation, …) and values of demographic variables. Of course, such data are disseminated without direct identifiers (name, surname, etc. ), but some categorical variables might still be used as indirect identifiers, that is to say as keys for re-identification of respondents, because their values are also available from external sources in non-anonymized files. Examples of key variables include gender, ethnicity, marital status, place of residence, and so forth, also recorded in a number of administrative registers along with direct identifiers.
When the released sample includes rare combinations of values of the key variables, the risk of disclosing respondents' identities is high if those combinations of values are also rare in the population. Actually, if variables are recorded without error, a potential intruder can easily discover the identity of data subjects by matching on keys, thus gaining access to their sensitive information. Breaches of confidentiality carry very serious legal consequences and undermine trust in the statistical agency, which becomes likely to get less, or less truthful, answers (i. e. lower quality data) from future respondents. Disclosure risk estimation is a challenging inferential task since cross-classification of respondents according to the values of the key variables often results in a large contingency table with many sampling and structural zeros.
, 2014; Piironen & Vehtari, 2017). About (i) and (ii)  Piironen & Vehtari (2017) , p. 718, wrote: '[…] the unbiasedness is intrinsically unimportant for a model selection criterion' and 'it is more important to be able to rank competing models in an approximately correct order with a low variability'. They also comment that, nonetheless, most literature focuses on unbiased estimates of the model predictive accuracy and provides little guidance on how to reduce the selection-induced bias. However, the solution they provide to this problem (detailed in  Piironen & Vehtari, 2017, p. 775 ) cannot be easily implemented in many applications since it assumes that the true data generating model can be conceptualized in some way (M-completed view), which is often an unrealistic assumption. This is the case, for instance, in the presence of large datasets with a complex dependence structure or when the search for good models is pragmatically, rather than theoretically motivated, as in disclosure risk estimation.
Illustration of the Proposed Method We illustrate and test our model selection procedure in a range of contingency tables differing in size, reference population and spanning variables obtained from different sources, as detailed next. We consider two large datasets, taken here as reference pseudo-populations, from which we draw simple random samples with fraction π ¼ 0:05. Because the pseudo-populations are known, we can compute the true risk measures and assess the performance of the proposed method. The first pseudo-population is the set of N ¼ 1 150 934 individuals aged 21 and over in the 5% public use microdata sample of the US 2000 census for the state of California (IPUMS,  Ruggles et al. , 2017). The second consists of the N ¼ 794 986 individuals recorded in the 7% public use microdata sample of the Italian National Social Security  Administration, 2004 (source: Work Histories Italian Panel, WHIP).
Taking advantage of a natural reduction of the within-sample-error (the data are not used twice, because only a small subset of them-the U sample uniques-is re-used to evaluate C 1 ), we deliberately refrain from adding a data based correction for bias to C 1 , as this would exacerbate the selection-induced bias, as shown in Section 4. The applications investigated in this paper reveal that the proposed procedure is generally able to rank competing models in terms of their ability to produce good estimates of global disclosure risks in rather different settings and in a relatively simple and fast way. Outside the application discussed in the paper, the same method can be directly adapted to different inferential problems involving datasets with a similar structure, but arising in completely different fields of research.
This end heat loss is estimated in the continuum regime by comparing the experimental data to the one-dimensional analytical solution of heat transfer between concentric cylinders. Also, a portion of the heat though the gap is transfered by radiation, which is referred to by Q R. The amount of heat transferred by conduction, Q C , is calculated as  1. The total heat generation, Q T , and the portion transferred by conduction, Q C , through the gap, as well as the measured initial, p ini , and steady state, p ss , pressures in the gap, and the inner cylinder surface temperature, T exp w1 , are provided in Table  1. The accommodation coefficients on both surfaces are estimated in Ref. [21]  to be the same and their values are also presented in Table  1. Q C = Q T -Q R -Q L , see Table The temperature distribution in the gap between the cylinders was simulated using the numerical solution of the S-model kinetic equation for different values of heat flux imposed on the inner cylinder surface.
We highlight the associated tradeoffs in the paper. The remainder of this paper is structured as follows. In Section 2, we introduce semi-Markov processes (SMP) via both Approach I and Approach II. We also present the probabilistic relationships between the approaches. We continue with Section 3 focusing on inference and specify the likelihood function for both approaches. In Section 4, we illustrate inference on two available datasets and present how to implement both approaches (for both datasets) using several contemporary R software packages. For both datasets, we compare results of fully parametric models based on both approaches and highlight the implications of each modelling choice. Section 5 presents some concluding remarks. All the numerical results (tables and figures) from the paper are freely reproducible via R code in a comprehensive detailed vignette available in  [33].
Our focus in this paper is right censored data corresponding to when at the end of the observation period, not all individuals under study have reached an absorbing state. As our focus is on the fully-parametric case we now present the likelihood functions for both Approach I and Approach II. We assume there are n subjects denoted via h = 1,. , n, for which data is collected and we assume independence between subjects. For each subject, we distinguish between two cases depending on if the subject is in an absorbing state at time T or not. Note that in principle we can set T to be subject specific, but for simplicity we do not do so here. This is recorded via δ h where δ (h) = 1 implies no right censoring (subject is in an absorbing state at time T ), and δ (h) = 0 implies right censoring. Further, we record the state evolution denoted via the sequence {J} and the sojourn times denoted via the sequence {τ }.
Likelihood for Approach I The form of L (h) based on H (h) is, L (h) = N (h) k=1 p J k-1 J k f J k-1 J k (τ k ) S J N (h) (U (h) ) 1-δ (h) , (27) where for brevity we omit the (h) superscripts for the state and sojourn time sequences {J} and {τ }. To further understand (27) consider a recursive construction where each transition without censoring based on J k-1 → J k with a sojourn time of τ k has a likelihood contribution p J k-1 J k f J k-1 J k (τ k ). Further, in case of censoring the last censored transition has likelihood contribution S J N (h) (U (h) ) based on the survival function of the holding time  (7) , corresponding to the last observed state J N (h).
With Approach II, the decoupling in  (30)  allows to optimize the likelihood for each transition i → j separately if each hazard intensity transition function  (33)  has its own set of parameters θij and βij. In such a framework, the full likelihood of the SMP can be maximized separately by maximizing the likelihood of the different separate two-state models, see  [37]. Also, the inference of the SMP can be easily handled by using survival models like the Cox model as the separate likelihood arising in survival analysis. Hence Approach II enables fitting SMP models using survival analysis methods and software, see for example  [49, 19, 26]. This also applies to the case where extensions to the proportional hazard assumption are needed. The forms in (  32 ) and (  33 ) are clearly based on a proportional hazard assumption with fixed covariates where there is only a multiplicative effect on the baseline hazard functions independent of time.
An extension is to consider time-dependent covariates Z(t) as in  [6, 7]. Further, in both proportional models the effect of variables is assumed to have a linear (or log-linear) functional form. A more flexible model is to consider non-linear effects using smooth functions of the covariates such as the Generalized Additive Model (GAM) presented by  [24]. With such extensions, using Approach II is much more straightforward than using Approach I due to the decoupling and because there is ample statistical software available for survival analysis. One may also wish to incorporate random effects in the models using frailty models. In this case, both  (32)  and  (33)  could also include random effect to take into account the correlation between observations/subjects. This has been handled in  [35]  for Approach II by exploiting the decoupling of the likelihood.
Semi-Markov Application in Practice In this section, we illustrate the inference of the semi-Markov model on two real datasets. Our purpose with these examples is to help practitioners see how the mathematical details presented above interact with statistical software. In light of this, we chose datasets that have been analyzed previously with a one sided view (either Approach I or Approach II but not both). These datasets are readily available in the R ecosystem. All the numerical results including tables and figures, are freely reproducible through R codes in a comprehensible detail vignette available in  [33]. For both datasets, we compare results of full parametric models based on Approach I where we estimate sojourn time distributions and transition probabilities of the embedded chain, and based on Approach II where we estimate transition intensity functions.
To carry out estimation using Approach I we use the SemiMarkov package, see  [31]. This package implements inference using the likelihood  (26)  with  (27)  while allowing to use different parametric forms for the sojourn time distribution including exponential, Weibull, and exponentiated Weibull, see  [22]. It also supports covariates with standard inference for the covariate coefficients β ij , including the Wald test. It allows the possibility to include different covariates for each transition. While the focus of the inference with this package is Approach I, as output, the package can automatically provide the intensity transition functions αij (•), referred to as the "hazard function of the SMP". For Approach II, the decoupling in  (30)  with  (31)  allows us to use any package that implements inference for survival analysis since for each transition i → j we can maximize, L ij = n h=1 L (h) ij separately if each hazard intensity transition function (  33 ) is assumed to have its own set of parameters θij and βij.
For this we can use different R packages including flexsurv (  [26] ), survival (  [48] ), and eha (  [13] ). In the examples here, we mainly use flexsurv which offers an easy way to run different parametric forms for αij (•) including exponential, Weibull, gamma, and generalized gamma (see  [40] ) among many other forms. It also supports covariates with standard inference for the covariate coefficients βij. We note that the purpose of this section is not to be an extensive survey of all of the R packages that can be used for inference in multi-state models. For a comprehensive software survey, see the survival task view from R (  [8] ). Our focus here is to illustrate how the aforementioned packages can be used to easily carry out inference, while we also illustrate a few key points.