Statistical Code Research Articles

Study protocol for Vitality: a proof-of-concept randomised controlled trial of exercise training or complex mental and social activities to promote cognition in adults with chronic stroke

IntroductionCerebrovascular disease—such as stroke—is the second most common cause of dementia (ie, vascular dementia). Specifically, a stroke increases one’s risk for dementia by a factor of two. Thus, stroke survivors...

Design and Characterization of a Low-Cost FPGA-Based TDC

We present a field-programmable gate array (FPGA) implementation of a time-to-digital converter (TDC) based on a low-cost, low-area Spartan 6 device. The converter is based on a tapped delay line model. Several implementation details are discussed with a particular focus on critical blocks such as the input stage and thermometer-to-binary decoding techniques. We implemented a tap filtering technique to improve the differential nonlinearity (DNL) of the single delay line while keeping a good LSB value of 25.57 ps with a single-shot precision (SSP) between 0.69 - 1.46 LSB. Measured DNL and integral nonlinearity (INL) lie in the range between -0.90 + 1.23 and -0.43 ÷ 2.96 LSB, respectively. Measured DNL and INL lie in the range between -0.90 ÷ 1.23 and -0.43 ÷ 2.96 LSB, respectively. We then implemented an interpolating TDC to overcome the limitations of a single delay line in terms of linearity and measurement range. The interpolating TDC uses the sliding scale technique, where the time interval to be measured is asynchronous with respect to the FPGA clock, achieving DNL and INL in the range -0.072 ÷ 0.070 and -0.755 ÷ 0.872 LSB. SSP is in the 1.096 ÷ 2.815 range. Moreover, we present a novel comparison between the DNLs obtained with two different methods: statistical code density test and using a finely controlled delay source. Finally, we present the results of a Monte Carlo simulation used to investigate the effects of nonlinear propagation of the signal through the delay line.

Pre-equilibrium Effects of the Hot Nuclei De-excitation via GDR Emission --- Theoretical Approach

The hot rotating nuclei could be formed in the complete and incomplete fusion reaction of two heavy ions. At low bombarding energies the reaction goes via compound nucleus formation and subsequent evaporation of charged particles, neutrons and $\gamma$-rays. However, with increasing the energy of the projectile, the emission of particles during the equilibration process becomes more and more probable. This effect can be estimated by the Heavy-Ion Phase-Space Exploration (HIPSE) code which describes the production of clusters of various size from nucleons initially in the target or projectile. This dynamic evolution finalizes with the compound nuclei, quasi-fission or multi-fragmentation products. The hot rotating nuclei produced in fusion reaction can de-excitate by evaporation of particles and emission of $\gamma$-rays from the Giant Dipole Resonance, or by fission into two fragments. These processes, evaporation and fission, are described within statistical codes such as GEMINI++ or in dynamical approaches by solving the transport equations of Langevin type. In the present article we will concentrate on the possible effect of the pre-equilibrium emission on the strength function of the effective Giant Dipole Resonance, which can be described within Thermal Shape Fluctuation Model (TSFM) approach.

Implementing and testing theoretical fission fragment yields in a Hauser-Feshbach statistical decay framework

We implement fission fragment yields, calculated using Brownian shape-motion on a macroscopic-microscopic potential energy surface in six dimensions, into the Hauser-Feshbach statistical decay code CGMF. This combination allows us to test the impact of utilizing theoretically-calculated fission fragment yields on the subsequent prompt neutron and γ-ray emission. We draw connections between the fragment yields and the total kinetic energy TKE of the fission fragments and demonstrate that the use of calculated yields can introduce a difference in the 〈TKE〉 and, thus, the prompt neutron multiplicity v, as compared with experimental fragment yields. We deduce the uncertainty on the 〈TKE〉 and v from this procedure and identify possible applications.

Удосконалення методу ієрархічної інтерполяції на основі використання нейронних мереж

Given the convergence of networks, the amount of transmitting information increases in geometric progression, in turn, technical implementation does not allow the use of a wide range of compression methods, as well as the development of new technical units, that is, the system, it is standardized and certified, therefore, each new block will change the entire structure of the system itself. Therefore, in order for the system to be able to use additional features, it is possible, on the basis of technical implementation already, to use a software product that is already embedded in technical units. Based on this, it was decided to stay on the methodology, using additional software or software and hardware. In the framework of this article, an interpolation image compression method is considered, designed to solve a given problem.The method of hierarchical interpolation in combination with the modifiers of the algorithms of statistical coding and algorithms, based on neural measurements (ANN), constitute the proposed information technology for video information compression, which meets all the above requirements.

Low-energy nuclear reaction of the N14+Tm169 system: Incomplete fusion

Excitation functions of reaction residues produced in the $^{14}\mathrm{N}+^{169}\mathrm{Tm}$ system have been measured to high precision at energies above the fusion barrier, ranging from $1.04{V}_{B}$ to $1.30{V}_{B}$, and analyzed in the framework of the statistical model code pace4. Analysis of $\ensuremath{\alpha}$-emitting channels points toward the onset of incomplete fusion even at slightly above-barrier energies where complete fusion is supposed to be one of the dominant processes. The onset and strength of incomplete fusion have been deduced and studied in terms of various entrance channel parameters. Present results together with the reanalysis of existing data for various projectile-target combinations conclusively suggest strong influence of projectile structure on the onset of incomplete fusion. Also, a strong dependence on the Coulomb effect $({Z}_{P}{Z}_{T})$ has been observed for the present system along with different projectile-target combinations available in the literature. It is concluded that the fraction of incomplete fusion linearly increases with ${Z}_{P}{Z}_{T}$ and is found to be more for larger ${Z}_{P}{Z}_{T}$ values, indicating significantly important linear systematics.

Study of incomplete fusion reaction dynamics in [formula omitted] system and its dependence on various entrance channel parameters

The excitation functions for the evaporation residues populated in the interaction of C13+165Ho system have been measured at projectile energies ≈ 4–7 MeV/nucleon. Stacked foil activation technique followed by off-line γ-ray spectroscopy have been employed in the present work. The experimentally measured cross-sections are analyzed in the frame work of statistical model code PACE4, which takes into account only the complete fusion reaction cross-sections. The evaporation residues populated via xn and pxn channels were found to be in good agreement with the PACE4 predictions, while a significant enhancement in the measured cross-sections over PACE4 predictions is observed in case of α-emitting channels, which may be attributed to the incomplete fusion process. For the better understanding of incomplete fusion dynamics, the incomplete fusion fraction has also been deduced and its sensitivity with various entrance channel parameters like: projectile energy, mass-asymmetry, projectile structure in terms of Qα-value and Coulomb effect has been studied in the present work. The incomplete fusion fraction is found to increase with increasing the projectile energy and a strong projectile structure dependent mass-asymmetry systematic is also observed. The incomplete fusion fraction is also found to be small for more negative Qα-value projectile (13C) induced reactions as compared to less negative Qα-value projectiles (12C, 16O and 20Ne) induced reactions with the same target nucleus 165Ho. An interesting trend is obtained on further investigation of incomplete fusion dependence on Coulomb effect (ZPZT).

Fission time scale from pre-scission neutron and α multiplicities in the O16 + Pt194 reaction

Pre- and post-scission $\ensuremath{\alpha}$-particle multiplicities have been measured for the reaction $^{16}O+^{194}Pt$ at 98.4 MeV forming $^{210}Rn$ compound nucleus. $\ensuremath{\alpha}$ particles were measured at various angles in coincidence with the fission fragments. Moving source technique was used to extract the pre- and post-scission contributions to the particle multiplicity. Study of the fission mechanism using the different probes are helpful in understanding the detailed reaction dynamics. The neutron multiplicities for this reaction have been reported earlier. The multiplicities of neutrons and $\ensuremath{\alpha}$ particles were reproduced using standard statistical model code joanne2 by varying the transient (${\ensuremath{\tau}}_{tr}$) and saddle to scission (${\ensuremath{\tau}}_{ssc}$) times. This code includes deformation dependent-particle transmission coefficients, binding energies and level densities. Fission time scales of the order of 50--65 $\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}21}$ s are required to reproduce the neutron and $\ensuremath{\alpha}$-particle multiplicities.

Systematic study of low-energy incomplete fusion: Role of entrance channel parameters

An attempt has been made to investigate the role of various entrance channel parameters in low-energy ($\ensuremath{\approx}4\text{--}7$ MeV/nucleon) incomplete fusion reactions through excitation function measurements. The analysis of measured excitation functions, in the framework of statistical model code pace4, reveals that the $xn$/$pxn$ channels are populated, predominantly, via complete fusion processes. However, in the production of $\ensuremath{\alpha}$-emitting channels, even after correcting for the precursor decay contribution, a significant enhancement as compared to statistical model predictions has been observed, which may be attributed due to the contribution of breakup processes. The observed enhancement is found to increase with projectile energy. Further, the comparison of present work with literature data reveals the dependence of incomplete fusion on mass-asymmetry of interacting partners, $\ensuremath{\alpha}\text{\ensuremath{-}}Q$ value of the projectile, and also on ${Z}_{P}{Z}_{T}$ (the Coulomb factor). From the present analysis, it may be concluded that a single entrance channel parameter (i.e., mass asymmetry or ${Z}_{P}{Z}_{T}$ or $\ensuremath{\alpha}\text{\ensuremath{-}}Q$ value) is not able to explain, completely, the yields of the low-energy incomplete fusion component. Therefore, a combination of these parameters and/or a parameter which can incorporate all gross features of interacting partners should be chosen to get a systematics for such reactions.

Proton capture reaction cross section measurements on Er162 as a probe of statistical model calculations

It is crucial to measure reaction cross sections relevant to the astrophysical $\ensuremath{\gamma}$ process so that theoretical reaction rates can be tested and validated with experimental data. The total cross sections for the $^{162}\mathrm{Er}(p,\ensuremath{\gamma})^{163}\mathrm{Tm}$ and the $^{162}\mathrm{Er}(p,n)^{162}\mathrm{Tm}$ reactions have been measured by the activation method in center-of-mass energies from 3.973 to 8.944 MeV and from 5.962 to 8.944 MeV, respectively. The nucleus $^{162}\mathrm{Er}$ is the heaviest $p$ nuclide to be measured by the activation method using $\ensuremath{\gamma}$-ray spectroscopy, so far. It is important to note that the energy range for the $(p,\ensuremath{\gamma})$ reaction measurement covers a large fraction of the astrophysically relevant energy region between 2.71 and 5.34 MeV. The targets were prepared by evaporating $28.2%$ isotopically enriched $^{162}\mathrm{Er}_{2}{\mathrm{O}}_{3}$ powder onto carbon backing foils, and bombarded with proton beams provided by the FN Tandem Accelerator at the University of Notre Dame. The reaction yields have been determined by the observed activity of produced radioactive isotopes, which was detected offline by a high-purity germanium detector. The results are presented and compared with calculations from two statistical model codes: non-smoker and talys.

Influence of incomplete fusion on complete fusion at energies above the Coulomb barrier

In the present work, excitation functions of several reaction residues in the system 19F+169Tm, populated via the complete and incomplete fusion processes, have been measured using off-line γ-ray spectroscopy. The analysis of excitation functions has been done within the framework of statistical model code pace4. The excitation functions of residues populated via xn and pxn channels are found to be in good agreement with those estimated by the theoretical model code, which confirms the production of these residues solely via complete fusion process. However, a significant enhancement has been observed in the cross-sections of residues involving α-emitting channels as compared to the theoretical predictions. The observed enhancement in the cross-sections has been attributed to the incomplete fusion processes. In order to have a better insight into the onset and strength of incomplete fusion, the incomplete fusion strength function has been deduced. At present, there is no theoretical model available which can satisfactorily explain the incomplete fusion reaction data at energies ≈4–6 MeV/nucleon. In the present work, the influence of incomplete fusion on complete fusion in the 19F+169Tm system has also been studied. The measured cross-section data may be important for the development of reactor technology as well. It has been found that the incomplete fusion strength function strongly depends on the α-Q value of the projectile, which is found to be in good agreement with the existing literature data. The analysis strongly supports the projectile-dependent mass-asymmetry systematics. In order to study the influence of Coulomb effect () on incomplete fusion, the deduced strength function for the present work is compared with the nearby projectile–target combinations. The incomplete fusion strength function is found to increase linearly with , indicating a strong influence of Coulomb effect in the incomplete fusion reactions.

Transport properties of isospin asymmetric nuclear matter using the time-dependent Hartree-Fock method

Background: The study of deep-inelastic reactions of nuclei provide a vehicle to investigate nuclear transport phenomena for a full range of equilibration dynamics. These inquires provide us the ingredients to model such phenomena and help answer important questions about the nuclear Equation of State (EOS) and its evolution as a function of neutron-to-proton $(N/Z)$ ratio. Purpose: The motivation is to examine the real-time dynamics of nuclear transport phenomena and its dependence on $(N/Z)$ asymmetry from a microscopic point of view to avoid any pre-conceived assumptions about the involved processes. Method: Time-dependent Hartree-Fock (TDHF) method in full 3D is employed to calculate deep-inelastic reactions of $^{78}$Kr+$^{208}$Pb and $^{92}$Kr+$^{208}$Pb systems at 8.5~MeV$/A$. The impact parameter and energy-loss dependence of relevant observables are calculated. In addition, density constrained TDHF method is used to compute excitation energies of the primary fragments. The statistical deexcitation code GEMINI is utilized to examine the final reaction products. Results: The kinetic energy loss and sticking times as a function of impact parameter are calculated. Final properties of the fragments (charge, mass, scattering angle, kinetic energy) are computed. Conclusions: We find a smooth dependence of the energy loss, $E_\mathrm{loss}$, on the impact parameter for both systems. On the other hand the transfer properties for low $E_\mathrm{loss}$ values are very different for the two systems but become similar in the higher $E_\mathrm{loss}$ regime. The mean life time of the charge equilibration process, obtained from the final $(N-Z)/A$ value of the fragments, is shown to be $\sim 0.5$~zs. This value is slightly larger (but of the same order) than the value obtained from reactions at Fermi energies.

Effects of symmetry energy and effective k -mass splitting on central Ru96(Zr96)+Zr96(Ru96) collisions at 50 to 400 MeV/nucleon

The isospin mixing between projectile and target in central $^{96}\mathrm{Ru}(^{96}\mathrm{Zr})+^{96}\mathrm{Zr}(^{96}\mathrm{Ru})$ collisions at 50 to 400 MeV/nucleon is investigated within the isospin-dependent quantum molecular dynamics model in combination with the statistical decay code gemini. Four groups of parameters, which provide different density dependences of symmetry energy and effective $k$-mass splitting, are applied in the model. Calculations within the same effective $k$-mass splittings show that the isospin mixing is more likely to take place for soft symmetry energy than hard symmetry energy. Calculations within similar symmetry energies show that the isospin mixing is more likely to take place for ${m}_{n}^{*}l{m}_{p}^{*}$ than ${m}_{n}^{*}g{m}_{p}^{*}$. Significantly, the effects of effective $k$-mass splitting on the isospin mixing become stronger with increasing incident energies, while those of symmetry energy are similar at different incident energies.

Abstract 4227: The Family Life, Activity, Sun, Health and Eating Study: A public use data resource for individual and dyadic analyses of cancer preventive behaviors

Abstract The NCI’s Family Life, Activity, Sun, Health, and Eating (FLASHE) study was designed to examine multilevel factors that relate to cancer preventive behaviors within parent-adolescent dyads. The neighborhood, home and school environments, parenting, psychosocial variables and demographics were assessed. Outcomes were diet and physical activity behaviors, in addition to sleep, sun safety, and tobacco use. This presentation will describe the FLASHE resources that are available to facilitate individual and dyad-level analyses related to cancer preventive behaviors. The FLASHE study involved two cross-sectional, web-based surveys of adolescents (12-17 years old) and their parents that were administered between April -October 2014. One survey focused on diet and another focused on physical activity and other cancer-preventive behaviors. These surveys included constructs and items that were informed by: existing literature, input from scientific experts, and cognitive testing with 18 parent-adolescent pairs. A subset of adolescents also wore an accelerometer for seven days to objectively assess physical activity. A total of 1,573 parent-adolescent dyads completed all surveys. Of these dyads, 38% were mother-daughter dyads, 36% mother-son, 13% father-son, and 12% father-daughter. Parents were predominantly female (75%), married (72%), and home-owners (72%), and 47% had a 4-year college degree. The majority of parents (70%) and adolescents (64%) were non-Hispanic White. Approximately 16% of parents and adolescents were non-Hispanic Black, and 7% of parents (10% of adolescents) were Hispanic. Several resources are available for FLASHE data users. Survey datasets are available for free download. Separate datasets for parents and adolescents facilitate individual-level analyses on parents’ or adolescents’ health behaviors. Datasets can also be merged to conduct dyadic analyses, such as examining associations in health behavior constructs within dyad members. Additional resources include: a methodology report, data users guide, list of FLASHE constructs with references, sample statistical code for conducting a dyadic analysis (Actor-Partner Interdependence Model), and an introductory webinar on dyadic data. These materials will be accompanied by a forthcoming journal theme issue focused on the FLASHE study, including topics such as: study development and methodology, physical activity and diet assessment, and individual and dyadic approaches to examining FLASHE data. Data on parent- and adolescent-reported constructs included in FLASHE offer multiple opportunities to study research questions among individuals and dyads and related cancer prevention behaviors. Researchers interested in these areas can access FLASHE data and resources online to examine their own research questions. Citation Format: Linda C. Nebeling, Laura Dwyer, April Oh, Erin Hennessy. The Family Life, Activity, Sun, Health and Eating Study: A public use data resource for individual and dyadic analyses of cancer preventive behaviors [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2017; 2017 Apr 1-5; Washington, DC. Philadelphia (PA): AACR; Cancer Res 2017;77(13 Suppl):Abstract nr 4227. doi:10.1158/1538-7445.AM2017-4227

E1 and M1 strength functions from average resonance capture data

The average resonance capture (ARC) data measured at different filter beam facilities are re-analyzed. They include all measurements made between 1970 and 1990, but only partially exploited. Updated spectroscopic information on the states of interest as well as on $s$-wave resonance spacing are used to extract the $E1$ and $M1$ photon strength function. This re-evaluation aims at providing experimental information on the $E1$ and $M1$ strength function around the neutron binding energy and in doing so provides also constraints for existing models used in statistical reaction codes. The revised data are compared to the photon strength function extracted from other experimental methods, such as photoneutron data and Oslo-method data. We also compare the ARC data with recent quasiparticle random phase approximation calculations based on the D1M Gogny force. The ratio of the $E1$ to $M1$ strength functions is also analyzed and proposed as a new stringent test for the future elaboration of theoretical models for the dipole strength function.

. The two-hierarchical structural slotting to improve the information’s integrity in telecommunication systems

The article substantiates the problem of the integrity ensure for the state video information resource in modern image processing methods at the state institutions. There is the analysis of the existing error localization technologies in the recovery process. It is proposed to develop an equalization redistribution method for statistical codes in order to ensure code positioning. The binary elements sequence structural characterization accounted in the fixed-length code constructs (slots) formation. The two-hierarchical scheme structural slotting conducting is proposed due to the binomial code formation nature. The recovery error propagation localization within the binary elements sequence set that has certain structural characteristics is justified. It is proposed to use the last binomial code forming feature for positioning transforms in of cyber attack conditions. Thus, the two-hierarchical structural slotting method with variable length codes redistribution has been developed. It allows increasing the state video information resource integrity. The scientific and applied research direction is defined: the image processing time costs reduction taking into the codes stream structural features account and the state video information resource confidentiality increasing with binominal coding.

Reporting guidance considerations from a statistical perspective: overview of tools to enhance the rigour of reporting of randomised trials and systematic reviews

ObjectiveResearch waste has received considerable attention from the biomedical community. One noteworthy contributor is incomplete reporting in research publications. When detailing statistical methods and results, ensuring analytic methods and findings...

Experience of Introduction of National Principles Governing the Activity of the State Statistics Bodies of Ukraine

The paper analyzes the role of the Fundamental Principles of Official Statistics in the development of the Ukrainian statistical system and its adaptation to international standards.
 The adoption and implementation of the Fundamental Principles, their subsequent development in the European Statistics Code of Practice (2005) and explanation in the National Principles Governing the Activity of the State Statistics Bodies of Ukraine (2010) served as a clear benchmark for setting priorities in the state statistical activity. It should be noted that not all of the principles could be equally easy implemented in the existing statistical practice. Even today two decades after the adoption of the Fundamental Principles of Official Statistics, there is still a number of debating points in their practical implementation.
 Special attention is given to the compilation of the National Principles Governing the Activity of the State Statistics Bodies of Ukraine that are based on the European Statistics Code of Practice and incorporate PARIS21 system of indicators. The principles have been developed and implemented with the goal to create the basis for further strengthening of the institutional capacity of national statistical office, to implement the best practices of the European statistics, and on this basis to enhance user confidence in the official statistics and ensure high-quality statistical information.

Spin distributions and cross sections of evaporation residues in the Si28+Yb176 reaction

Background: Non-compound-nucleus fission in the preactinide region has been an active area of investigation in the recent past. Based on the measurements of fission-fragment mass distributions in the fission of $^{202}\mathrm{Po}$, populated by reactions with varying entrance channel mass asymmetry, the onset of non-compound-nucleus fission was proposed to be around ${Z}_{p}{Z}_{t}\ensuremath{\sim}1000$ [Phys. Rev. C 77, 024606 (2008)], where ${Z}_{p}$ and ${Z}_{t}$ are the projectile and target proton numbers, respectively.Purpose: The present paper is aimed at the measurement of cross sections and spin distributions of evaporation residues in the $^{28}\mathrm{Si}+^{176}\mathrm{Yb}$ reaction (${Z}_{p}{Z}_{t}=980$) to investigate the hindrance which, in turn, would give information about the contribution from non-compound-nucleus fission in this reaction.Method: Evaporation-residue cross sections were measured in the beam energy range of 129--166 MeV using the hybrid recoil mass analyzer (HYRA) operated in the gas-filled mode. Evaporation-residue cross sections were also measured by the recoil catcher technique followed by off-line $\ensuremath{\gamma}$-ray spectrometry at few intermediate energies. $\ensuremath{\gamma}$-ray multiplicities of evaporation residues were measured to infer about their spin distribution. The measurements were carried out using NaI(Tl) detector-based 4\ensuremath{\pi}-spin spectrometer from the Tata Institute of Fundamental Research, Mumbai, coupled to the HYRA.Results: Evaporation-residue cross sections were significantly lower compared to those calculated using the statistical code pace2 [Phys. Rev. C 21, 230 (1980)] with the coupled-channel code ccfus [Comput. Phys. Commun. 46, 187 (1987)] at beam energies close to the entrance channel Coulomb barrier. At higher beam energies, experimental cross sections were close to those predicted by the model. Average $\ensuremath{\gamma}$-ray multiplicities or angular momentum values of evaporation residues were in agreement with the calculations of the code ccfus + pace2 within the experimental uncertainties at all the beam energies.Conclusions: Deviation of evaporation-residue cross sections from the fusion + statistical model predictions at beam energies close to the entrance channel Coulomb barrier indicates hindrance at these beam energies which would lead to non-compound-nucleus fission. However, reasonable agreement of average angular momentum values of evaporation residues at these beam energies with those calculated using the coupled-channel with the statistical codes ccfus + pace2 suggests that suppression at beam energies close to the entrance channel Coulomb barrier where populated $l$ waves are low is not $l$ dependent.

Investigation of incomplete fusion dynamics at energy 4–8 MeV/nucleon

The recoil-catcher activation technique followed by the offline γ-ray spectroscopy has been adopted for the excitation function measurement of residues populated in 12,13C induced reactions with 175Lu target at lower projectile energies ≈4–8 MeV/nucleon. The independent cross-sections for some of the populated residues have been estimated by subtracting the contributions of higher charge precursor isobars from the measured cumulative cross-sections. The measured excitation functions are compared with theoretical predictions based on statistical model code PACE-4. This comparison reveals that complete fusion process solely contributes in the formation of xn-pxn channels and an enhancement in the measured cross-sections of α-emitting channels from the theoretical predictions may be attributed to the incomplete fusion process. The incomplete fusion probability is found to be higher in case of C12 than for a one neutron rich projectile C13 throughout the incident energy region. Present findings obtained for 12,13C + 175Lu systems have been compared with informations extracted from previously studied systems and projectile structure is found to strongly affect the incomplete fusion dynamics in terms of projectile α-Q-value along with projectile-target mass-asymmetry. Moreover, it may be pointed out that Morgenstern's mass-asymmetry systematic is probably the projectile structure dependent systematic. A substantial contribution to incomplete fusion coming from collision trajectories with ℓ≤ℓcrit is also observed, contrary to the SUMRULE model assumptions.