Statistical Model Description Research Articles

ПРОСТОРОВИЙ ІНСТРУМЕНТАРІЙ В ПОЛІТИЧНИХ ДОСЛІДЖЕННЯХ: ОГЛЯД СТАТТІ «ПРОСТОРОВИЙ АНАЛІЗ ДЛЯ ПОЛІТОЛОГІВ» ДЖЕСІКІ ДІ САЛЬВАТОРЕ Й АНДРЕА РУДЖЕРІ

The purpose of the article is to review the work of Jessica Dі Salvatore and Andrea Ruggeri, "Spatial analysis for political scientists", taking into account the fact that the progress of modern scientific and practical discourse proves that spatial analysis as a methodological toolkit of geography and interdisciplinary geopolitical and political science research is slowly spreading in the Ukrainian academic space. The results. The apparent advantage of Jessica Di Salvatore's work in co-authorship with Andrea Ruggeri is that the authors, in a relatively concise form, outlined the main difficulties that may arise for researchers in political science, electoral, and political geography when conducting spatial analysis. In the first part of the article, the authors present a brief description of the basics of spatial analysis: a description of data formats and their relationships in space. Readers will benefit from a description and illustrative example of the construction of the W spatial matrix, as well as comments on the relevance of the data and the importance of taking context into account. The second part, with a description of statistical models, is more difficult to understand, requires more reader preparation, and requires an additional search to get acquainted with examples of studies that analyze the relevance of using specific models and their advantages and disadvantages. With some reservations about the uneven depth of coverage of the theoretical foundations and practical applications of geospatial analytics models, we find the article "Spatial analysis for political scientists" by Jessica Dі Salvatore and Andrea Ruggeri to be beneficial for both novice and seasoned researchers with an appropriate level of academic training. It is worth noting that this review is particularly relevant for those interested in the application of spatial analysis in the context of interdisciplinary research, as it provides a comprehensive analysis of the results and the subject field of specific investigations. Practical implications. By expanding the analysis of this work to not only highlight its main content, but also to provide a critical analysis in the context of its potential application in educational and research activities, we believe that our review, at the very least, stimulates other researchers to delve deeper into this and other thematic works. This is crucial for the application of spatial analysis by fellow geographers, political scientists, and interdisciplinary intelligence specialists in real-world scenarios.

Cancellation of the Sigma Mode in the Thermal Pion Gas by Quark Pauli Blocking

In this study, we calculate the pressure of the interacting pion gas using the Beth–Uhlenbeck approach to the relativistic virial expansion with Breit–Wigner phase shifts for the σ- and ϱ-meson resonances. The repulsive phase shift δ02 is taken from the quark interchange model of Barnes and Swanson, which is in very good agreement with the experimental data. In this work we show that the cancellation of the attractive (I = 0) and repulsive (I = 2) isospin channel contributions to the scalar ππ interaction in the low-energy region that is known for the vacuum phase shifts also takes place at a finite temperature. This happens despite the strong medium dependence of these phase shifts that enters our model by the temperature dependence of the σ-meson and constituent quark masses, because for these masses the relation Mσ(T)≈2mq(T) holds and the scattering length approximation is valid as long as the strong decay channel σ→ππ is open. Exploiting the Nambu–Jona-Lasinio model for describing the dynamical breaking of chiral symmetry in the vacuum and its restoration at a finite temperature, we justify with our approach that the σ-meson should be absent from the hadron resonance gas description at low temperatures because the above cancellation holds. However, since this cancellation breaks down in the vicinity of the hadronization transition, where due to chiral symmetry restoration the decay channel σ→ππ closes and the σ-meson becomes a good resonance, the latter should be included into the statistical model description of chemical freeze-out in heavy-ion collisions.

Nuclear level density of 69Zn from gamma gated particle spectrum and its implication on 68Zn(n, γ)69Zn capture cross section

Evaporated α-spectra have been measured in coincidence with low energy discrete γ-rays from residual nucleus 68Zn populated by αn evaporation from compound nucleus 73Ge produced in the reaction 64Ni(9Be,αn)68Zn at E(9Be) = 30 MeV. Low energy γ-gated α-particle spectra, for the first time, have been used to extract the nuclear level density (NLD) for the intermediate 69Zn nucleus in the excitation energy range of E ≈ 4-20 MeV. The slope of present NLD data as a function of excitation energy for 69Zn matches nicely with the slope determined from RIPL estimates for NLD at low energies and the NLD from neutron resonance data at neutron separation energy Sn. The extracted inverse NLD parameter (k = A/a˜) has been used to determine the nuclear level density parameter value a at neutron separation energy Sn for 69Zn. The cross section of 68Zn(n,γ) capture reaction as a function of neutron energy is then estimated employing the derived a(Sn) in the reaction code TALYS. It is found that the estimated neutron capture cross section agrees well with the available experimental data without any normalization. The present result indicates that experimentally derived nuclear level density parameter can constrain the statistical model description of astrophysical capture cross section and optimize the uncertainties associated with astrophysical reaction rate.

Quest for consistent modelling of statistical decay of the compound nucleus

A statistical model description of heavy ion induced fusion–fission reactions is presented where shell effects, collective enhancement of level density, tilting away effect of compound nuclear spin and dissipation are included. It is shown that the inclusion of all these effects provides a consistent picture of fission where fission hindrance is required to explain the experimental values of both pre-scission neutron multiplicities and evaporation residue cross-sections in contrast to some of the earlier works where a fission hindrance is required for pre-scission neutrons but a fission enhancement for evaporation residue cross-sections.

Examination of level density prescriptions for the interpretation of high-energyγ-ray spectra

High energy $\gamma$-ray spectra measured by our group involving the compound nuclei (CN) $^{63}$Cu at excitation energy ($E^*$) $\sim$ 36 MeV with average angular momentum ($J$) = 12 - 17 $\hbar$, $^{97}$Tc at $E^* \sim$ 29 - 50 MeV with $J$ = 12 - 14 $\hbar$, $^{113}$Sb at $E^*$ = 109 MeV and 121 MeV with $J$ = 49 - 59 $\hbar$ and $^{201}$Tl at $E^*$ = 39.5, 47.5 MeV with $J$ = 18 - 24 $\hbar$ have been analyzed utilizing the level density prescriptions of (i)Ignatyuk, Smirenkin and Tishin (IST), (ii)Budtz-Jorgensen and Knitter (BJK), and (iii) Kataria, Ramamurthy and Kapoor (KRK). These three prescriptions have been tested for correct statistical model description of high energy $\gamma$-rays in the light of extracting the giant dipole resonance (GDR) parameters at low excitation energy and spin where shell effects might play an important role as well as at high excitation energy where shell effects have melted. Interestingly, only the IST level density prescription could explain the high energy $\gamma$-ray spectra with reasonable GDR parameters for all the four nuclei.

SHARE with CHARM

SHARE with CHARM program (SHAREv3) implements the statistical hadronization model description of particle production in relativistic heavy-ion collisions. Given a set of statistical parameters, SHAREv3 program evaluates yields and therefore also ratios, and furthermore, statistical particle abundance fluctuations. The physical bulk properties of the particle source is evaluated based on all hadrons produced, including the fitted yields. The bulk properties can be prescribed as a fit input complementing and/or replacing the statistical parameters. The modifications and improvements in the SHARE suite of programs are oriented towards recent and forthcoming LHC hadron production results including charm hadrons. This SHAREv3 release incorporates all features seen previously in SHAREv1.x and v2.x and, beyond, we include a complete treatment of charm hadrons and their decays, which further cascade and feed lighter hadron yields. This article is a complete and self-contained manual explaining and introducing both the conventional and the extended capabilities of SHARE with CHARM. We complement the particle list derived from the Particle Data Group tabulation composed of up, down, strange $u,d,s$ quarks (including resonances) with hadrons containing charm $c,\bar c$ quarks. We provide a table of the charm hadron decays including partial widths. The branching ratios of each charm hadron decays add to unity, which is achieved by including some charm hadron decay channels based on theoretical consideration in the absence of direct experimental information. A very successful interpretation of all available LHC results has been already obtained using this program.

Linking statistical bias description to multiobjective model calibration

In the absence of model deficiencies, simulation results at the correct parameter values lead to an unbiased description of observed data with remaining deviations due to observation errors only. However, this ideal cannot be reached in the practice of environmental modeling, because the required simplified representation of the complex reality by the model and errors in model input lead to errors that are reflected in biased model output. This leads to two related problems: First, ignoring bias of output in the statistical model description leads to bias in parameter estimates, model predictions and, in particular, in the quantification of their uncertainty. Second, as there is no objective choice of how much bias to accept in which output variable, it is not possible to design an “objective” model calibration procedure. The first of these problems has been addressed by introducing a statistical (Bayesian) description of bias, the second by suggesting the use of multiobjective calibration techniques that cannot easily be used for uncertainty analysis. We merge the ideas of these two approaches by using the prior of the statistical bias description to quantify the importance of multiple calibration objectives. This leads to probabilistic inference and prediction while still taking multiple calibration objectives into account. The ideas and technical details of the suggested approach are outlined and a didactical example as well as an application to environmental data are provided to demonstrate its practical feasibility and computational efficiency.

Phase Diagram and Heavy-Ion Collisions: Overview

The physics of the QCD phase diagram is discussed in view from heavy-ion collisions, compact astrophysical phenomena, lattice QCD and chiral effective models. We find that (T,mu_B) region probed in heavy-ion collisions and the black hole formation processes covers most of the critical point locations predicted in recent lattice QCD Monte-Carlo simulations and chiral effective models of QCD. We also discuss the consistency of the statistical model results and dynamical model description.

A comparative analysis of statistical hadron production

We perform a systematic comparison of the statistical model parametrization of hadron abundances observed in high-energy pp, AA and e + e − collisions. The basic aim of the study is to test if the quality of the description depends on the nature of the collision process. In particular, we want to see if nuclear collisions, with multiple initial interactions, lead to “more thermal” average multiplicities than elementary pp collisions or e + e − annihilation. Such a comparison is meaningful only if it is based on data for the same or similar hadronic species and if the analyzed data has quantitatively similar errors. When these requirements are maintained, the quality of the statistical model description is found to be the same for the different initial collision configurations.

Segmentation of DNA sequences into twostate regions and melting fork regions

The accurate prediction and characterization of DNA melting domains by computationaltools could facilitate a broad range of biological applications. However, no algorithm formelting domain prediction has been available until now. The main challenges include thedifficulty of mathematically mapping a qualitative description of DNA melting domains toquantitative statistical mechanics models, as well as the absence of ‘gold standards’ and aneed for generality. In this paper, we introduce a new approach to identify the twostateregions and melting fork regions along a given DNA sequence. Compared with an ad hocsegmentation used in one of our previous studies, the new algorithm is based on boundaryprobability profiles, rather than standard melting maps. We demonstrate that a moredetailed characterization of the DNA melting domain map can be obtained using our newmethod, and this approach is independent of the choice of DNA melting model. Weexpect this work to drive our understanding of DNA melting domains one stepfurther.

Craniofacial reconstruction using a combined statistical model of face shape and soft tissue depths: Methodology and validation

Forensic facial reconstruction aims at estimating the facial outlook associated with an unidentified skull specimen. Estimation is generally based on tabulated average values of soft tissue thicknesses measured at a sparse set of landmarks on the skull. Traditional ‘plastic’ methods apply modeling clay or plasticine on a cast of the skull, approximating the estimated tissue depths at the landmarks and interpolating in between. Current computerized techniques mimic this landmark interpolation procedure using a single static facial surface template. However, the resulting reconstruction is biased by the specific choice of the template and no face-specific regularization is used during the interpolation process. We reduce the template bias by using a flexible statistical model of a dense set of facial surface points, combined with an associated sparse set of skull-based landmarks. This statistical model is constructed from a facial database of ( N = 118) individuals and limits the reconstructions to statistically plausible outlooks. The actual reconstruction is obtained by fitting the skull-based landmarks of the template model to the corresponding landmarks indicated on a digital copy of the skull to be reconstructed. The fitting process changes the face-specific statistical model parameters in a regularized way and interpolates the remaining landmark fit error using a minimal bending thin-plate spline (TPS)-based deformation. Furthermore, estimated properties of the skull specimen (BMI, age and gender, e.g.) can be incorporated as conditions on the reconstruction by removing property-related shape variation from the statistical model description before the fitting process. The proposed statistical method is validated, both in terms of accuracy and identification success rate, based on leave-one-out cross-validation tests applied on the facial database. Accuracy results are obtained by statistically analyzing the local 3D facial surface differences of the reconstructions and their corresponding ground truth. Identification success rate is obtained by comparing, based on correlation, Euclidean distance matrix (EDM) signatures of the reconstructed and the original 3D facial surfaces in the database. A subjective identification success rate is quantified based on face-pool tests. Finally a qualitative comparison is made between facial reconstructions of a real-case skull, based on two typical static face models and our statistical model, showing the shortcomings of current face models and the improved performance of the statistical model.

Statistically Deformable Face Models for Cranio-Facial Reconstruction

Forensic facial reconstruction aims at estimating the facial outlook associated to an unknown skull specimen. Estimation is based on tabulated average values of soft tissue thicknesses measured at a sparse set of landmarks on the skull. Traditional 'plastic' methods apply modeling clay or plasticine on a cast of the skull approximating the estimated tissue depths at the landmarks and interpolating in between. Current computerized techniques mimic this landmark interpolation procedure using a single facial surface template. However, the resulting reconstruction is biased by the specific choice of the template and no face specific regularization is present. We reduce the bias by using a flexible statistical model of a dense set of facial surface points combined with an associated sparse set of skull landmarks. The statistical model also provides a probability value, which can be used to regularize the reconstruction towards more plausible outlooks. The reconstruction is obtained by fitting the model skull landmarks to the corresponding landmarks indicated on a digital copy of the skull to be reconstructed. The fitting process alternates between changing the face-specific statistical model parameters and interpolating the remaining landmark fit error using a minimal bending Thin-Plate Spline (TPS) based deformation. Furthermore, estimated properties of the skull specimen (BMI, age and gender e.g.) can be incorporated as conditions on the reconstruction by removing property-related shape variation from the statistical model description before the fitting process. This iterative statistical model based reconstruction process is shown by experiment to converge to a realistic reconstruction of the face, independent of the initial template.

Statistical model description of particle multiplicities in heavy ion collisions

The application of statistical thermal models to a description of particles production in heavy ion collisions is discussed. A relation of the equation of state obtained form the phenomenological analysis of particle multiplicities in heavy ion collisions with a recent findings in Monte Carlo simulation of Lattice Gauge Theory at finite temperature and chemical potential is discussed. A connection of chemical freezeout with a critical condition in heavy ion collisions is indicated.

Statistical hadronization probed by resonances

We study to what extent a measurement of the ${m}_{\ensuremath{\perp}}$ spectra for hadrons and their resonances can resolve ambiguities in the statistical model description of particle production. We describe in a quantitative analysis how physical assumptions about the freeze-out geometry and dynamics influence the particle spectra. Considering ratios of ${m}_{\ensuremath{\perp}}$ distribution of resonance-particle ratios (such as ${K}^{*}/K,$ ${\ensuremath{\Sigma}}^{*}/\ensuremath{\Lambda},{\ensuremath{\eta}}^{\ensuremath{'}}/\ensuremath{\eta})$ we observe significant sensitivity to fireball freeze-out geometry and flow dynamics.

Canonical constraints on particle production

We discuss the statistical model description of particle production in heavy-ion collisions. We put particular emphasis on the interpretation of the enhancement of particles that carry a non-vanishing quantum number related to U(1) internal symmetry. We argue that the basic features of experimental data showing enhancement of strange mesons and baryons are well described by the model.

Statistical model description of K+ and K− production between 1–10 A·GeV

The excitation functions of K + and K − mesons in heavy ion collisions are studied within a statistical model assuming chemical and thermal equilibrium with exact strangeness conservation. At low incident energies the associate production of kaons, i.e., the production of a K + together with a hyperon and the production of a K − together with a K +, implies specific features: different threshold energies and different dependences of K + and K − yields on baryon number density. It is shown that the experimentally observed equality of the K + and K − rates at energies s − s th ≤0 is due to a crossing of the two excitation functions. Furthermore, the independence of the K + to K − ratio on the number of participating nucleons observed at 1 and 10 A·GeV is consistent with this model.

A C-code for combining a Langevin fission dynamics of hot nuclei with a statistical model including evaporation of light particles and giant dipole γ-quanta

We present a C-code calculating the decay of highly excited and rotating atomic nuclei by fission and light particle (neutrons, protons, α-particles, giant dipole γ-quanta) evaporation. The program calculates the distributions of the relevant observables, their averages, variances and correlations. The most important output parameters are: fission (respectively survival) probabilities, pre-scission neutron and charged-particle multiplicities and spectra, pre-scission gamma-multiplicities and spectra, average energies of these particles, scission lifetime distributions, and excitation energies at scission. For this purpose a dynamical Langevin equation for an overdamped fission process is combined with a statistical model description. In the dynamical part of the model the evaporation of light particles and giant dipole γ-quanta is accounted for by coupling a Monte Carlo algorithm to the fission dynamics. In the statistical part of the model a fission width consistent with the dynamical description is used besides the standard way of calculating the light particle emission. The code provides also the possibility to investigate the influence of different nuclear friction form factors on the observable quantities.

Similarities and differences in fission and evaporation of hot nuclei and hot metallic clusters

Similarities and differences in the decay of hot nuclei and hot metallic clusters are discussed. A liquid-drop model description explains why symmetric fission is the dominant decay mode for heavy nuclei, whereas hot metallic clusters prefer strongly asymmetric fission, which looks more like an evaporation process of light charged particles. Critical (appearance) sizes of multiply-charged clusters are calculated by equating the rates for neutral monomer and charged-particle evaporation. The time scale of cluster decay due to multiple-cluster atom emission is determined by calculating shrinking and cooling rates. It is compared with the time scale of particle emission during fission of hot nuclei, where friction plays a crucial role. It is probable that viscosity is also of importance in symmetric fission of clusters. The latter is predicted to be possible due to shell effects, in particular for clusters with closed shells. The increase (as compared to a purely statistical model description) of fission times of clusters due to friction is predicted to be an order of magnitude larger than the corresponding well established effect in fission of hot nuclei.

New data on prefission neutrons

The spectra of neutrons emitted in fission of232Th,235U and238U induced by 2.9- and 14.7- MeV neutrons (below and above the chance fission threshold, respectively) were measured by the time-of-flight method. Two effects were observed in the prefission neutron spectra: the high-energy wing is related to the nonequilibrium mechanism of emission up to the well pronounced upper boundary of ɛmax=8.5 MeV; in the lower-energy wing e < 2 MeV, neutron yield exceeds conventional statistical model description. The latter effect was attributed to the fission process dynamics.

Path-integral approach to the critical behaviour of two-dimensional systems

A path-integral approach to the critical behaviour of two-dimensional systems is presented. The method, based on a decoupling change of path-integral variables, enables one to compute critical exponents in a simple and systematic way. Thus, it provides a new tool to be used in the field-theoretical description of certain statistical mechanics models.