Define Probability Distributions Research Articles

Improving safety in complex systems: A review of integration of functional resonance analysis method with semi‐quantitative and quantitative approaches

AbstractFunctional resonance analysis method (FRAM) is extensively employed in analyzing and managing performance variabilities. Additionally, semi‐quantitative and quantitative methods have been increasingly integrated with the FRAM to analyze complex socio‐technical systems to improve safety levels. This review article presents a comprehensive and updated survey of current literature focused on semi‐quantitative and quantitative methods employed for quantifying performance variabilities and exploring aggregation/propagation rules. A total of 1659 studies published between 2012 and March 2024 from various scientific databases were systematically examined using preferred reporting items for systematic review and meta‐analysis, identifying 29 studies that met inclusion criteria. The identified studies were categorized into four groups based on the quantitative methods employed: Monte Carlo simulation, fuzzy logic, cognitive reliability and error analysis method, and miscellaneous approaches. While different methodologies had unique strengths, they commonly relied on expert judgment for data collection, whether for defining probability distributions in Monte Carlo simulations, membership functions, and fuzzy rule bases in fuzzy inference systems, or selecting common performance conditions, determining their interrelationships, and assigning scores. Addressing bias from expert judgment in assessing performance variabilities can be achieved by using suitable experts' opinions integration techniques, and leading safety indicators in the analysis.

Generation of true quantum random numbers with on-demand probability distributions via single-photon quantum walks

Random numbers are at the heart of diverse fields, ranging from simulations of stochastic processes to classical and quantum cryptography. The requirement for true randomness in these applications has motivated various proposals for generating random numbers based on the inherent randomness of quantum systems. The generation of true random numbers with arbitrarily defined probability distributions is highly desirable for applications, but it is very challenging. Here we show that single-photon quantum walks can generate multi-bit random numbers with on-demand probability distributions, when the required “coin” parameters are found with the gradient descent (GD) algorithm. Our theoretical and experimental results exhibit high fidelity for various selected distributions. This GD-enhanced single-photon system provides a convenient way for building flexible and reliable quantum random number generators. Multi-bit random numbers are a necessary resource for high-dimensional quantum key distribution.

Speech and lexico-semantic errors during direct cortical stimulation mapping of the language-dominant hemisphere: effects of object and action naming.

In this retrospective study, the authors aimed to establish the stereotactically defined probability distribution for speech (i.e., anarthria, speech arrest) and lexico-semantic errors (i.e., anomia) through direct cortical stimulation (DCS) by using two tasks: action naming and object naming. They also analyzed the patterns of interindividual variability in the localization of the language sites involved, and investigated whether any patient or lesion location factors were associated with greater variability. Eighty-one Italian-speaking patients who underwent awake surgery between 2010 and 2021 for low- and high-grade gliomas in eloquent areas of the language-dominant hemisphere were entered in the analyses. The intraoperative DCS protocol included automatic speech tasks, object naming, and action naming. The position of the tags, as depicted on the intraoperative video or photograph, was transposed into Montreal Neurological Institute space. Subsequently, a 2D scatterplot and cluster analysis were performed. Associations between various clinical and radiological characteristics and the quantity of positive stimulated sites were determined by univariate analyses using binary logistic regression. Associated variables (p < 0.2) were included in stepwise multivariate logistic regression with backward elimination (p < 0.05). A total of 1380 cortical sites were stimulated, with a positive response in 511 cases (37%). Most anarthric errors were triggered when stimulating the left precentral gyrus, and most speech arrest errors were elicited when stimulating the left posterior inferior frontal gyrus. Anomias were found in the left inferior frontal gyrus and in the posterior part of the left temporal lobe for object naming. DCS to the left dorsal premotor cortex elicited anomic errors for action naming. Anomias were also elicited during DCS to the left posterior temporal lobe, with both object and action naming. The distribution of speech and lexico-semantic errors is in line with the current literature. The action-naming results are new and mostly involve the dorsal premotor cortex. These findings stress the importance of maximizing the use of different language tasks during surgery, because even when looking for the same type of errors, different tasks may be better suited to map specific brain regions. DCS with action and object naming identifies more positive sites than object naming alone.

Generalized entropies of subdivision-corona networks

The entropy of a graph is an information-theoretic quantity which expresses the complexity of a graph. Entropy functions have been used successfully to capture different aspects of graph complexity. The generalized graph entropies result from applying information measures to a graph using various schemes for defining probability distributions over the elements of the graph. In this paper, we investigate the complexity of a class of composite graphs based on subdivision graphs and corona product evaluating the generalized graph entropies, and we present explicit formulae for the complexity of subdivision-corona type product graphs.

Chemodynamical ages of small-scale kinematic structures of the galactic disc in the solar neighbourhood from ∼250 000 K and M dwarfs

ABSTRACT We combine photometric metallicities with astrometry from Gaia DR3 to examine the chemodynamic structure of ∼250 000 K dwarfs in the solar neighbourhood (SN). In kinematics, we observe ridges/clumps of ‘kinematic groups’, like studies of more massive main-sequence stars. Here, we note clear differences in both metallicity and vertical velocity as compared with the surrounding regions in velocity space and hypothesize this is due to differences in mean age. To test this, we develop a method to estimate the age distribution of subpopulations of stars. In this method, we use GALAH data to define probability distributions of W versus [M/H] in age bins of 2 Gyr and determine optimal age distributions as the best-fitting weighted sum of these distributions. This process is then validated using the GALAH subset. We estimate the probable age distribution for regions in the kinematic plane, where we find significant substructure that is correlated with the kinematic groups. Most notably, we find an age gradient across the Hercules streams that is correlated with birth radius. Finally, we examine the bending and breathing modes as a function of age. From this, we observe potential hints of an increase in the bending amplitude with age, which will require further analysis in order to confirm it. This is one of the first studies to examine these chemodynamics in the SN using primarily low-mass stars and we hope these findings can better constrain dynamical models of the Milky Way due to the increase in resolution the sample size provides.

Risk Assessment and Management of Underground Metro Construction (Bengaluru Scenario)

Construction projects are characterized as very complex projects, where uncertainties are part of it. Risk is an uncertain event or condition that, if it occurs, has a positive or a negative impact on one or more project objectives, such as time, cost, scope or quality. Risk management includes the process concerned with the conducting the risk identification, analysis, responses and management planning and control on a project The study aims at carrying out the risk assessment and management process in the construction of Bangalore Underground Metro project. At first, the risks associated with the project and also with the similar projects in past are identified and listed based on the historic reviews, interviews and literature review. A questionnaire survey is prepared for the risks that are listed and probability and impact of these risks on the projects are found out, and risks are prioritized based on the risk index score which forms the probability-impact matrix and risk register is formed. A schedule is prepared in Primavera P6, and then integrated with Primavera Risk Analysis (PERT Master) software which analyze the schedule for the risk events assigned to the activities and for the defined probability distributions and then schedule of the project is simulated using the Monte Carlo simulation for the both pre mitigated and the post mitigated analysis, and then results are compared. Response strategies are suggested for the moderate to higher priorities risks.

In situ stress field in the Athabasca oil sands deposits: Field measurement, stress-field modeling, and engineering implications

In situ stress is one of the key engineering parameters that ensures caprock integrity in steam-assisted gravity drainage (SAGD) operations. Massive steam injections during an SAGD operation leads to significant changes in the pore pressure, temperature, stress, and volumetric strain in the rock formations. These changes trigger deformation and stress redistribution in the overburdened strata, which could lead to a containment breach of the caprock through shear or tensile failure. To ensure subsurface steam containment, both to satisfy public safety considerations and instill confidence that the steam containment will continue over the necessary timescales, the Alberta government requires every SAGD operator to measure the in situ stress conditions in the oil sands reservoir and its caprock. Minifrac test is a suggested method that can measure the minimum principal stress with high confidence. A safety factor (SF) of 80% is used to determine the maximum operation pressure (MOP) for safe SAGD operations; in other words, MOP = 80%*σmin, where σmin is the minimum principal stress at the base of the caprock. In most cases, this 80% SF safeguards the SAGD injection pressure to always remain lower than the σmin at the base of the caprock, ensuring that no tensile fractures are initiated at the caprock.In this study, we compiled a database containing in excess of 100 minifrac datasets across the Athabasca oil sands region and constructed an in situ stress map. Based on our in situ stress dataset, we developed a quantitative risk model to analyze the effects of uncertainties on the probability of exceedance (i.e., the probability that the MOP exceeds the fracture pressure at the base of the caprock). The risk model involves defining probability distributions to quantify the uncertainties at the shallowest depth and minimum stress gradient. The output of the risk model was a set of predictions of exceedance probabilities, which were computed using Monte Carlo simulations. Through a statistical analysis of this in situ database and risk-based simulation analysis, this study demonstrates the reliability of a SF of 80%.

REVIEW OF THEORETICAL APPROACHES TO USING OF ARTIFICIAL INTELLIGENCE FOR PLANNING PROBLEMS IN ECONOMICS

Artificial intelligence methods and technologies are increasingly included in human's everyday life. Managing actors in the context of their activities, from the planning stage to the decision-making stage, are faced with the need to operate with big data, non-linear, exponentially growing, critically overloaded data scenarios. In these conditions, the need to introduce artificial intelligence technologies is due to the exhaustion of the intellectual and analytical capabilities of a person. The article discusses a variety of methods and approaches of artificial intelligence, examines the content of key algorithms, models and theories, their strengths and weaknesses in such important areas of the economy as planning and decision-making. The focus is on their classification. Due to the dependence of the planning process on environmental factors, both classical and non-classical planning environments are discussed. If the environment is fully observable, deterministic and static (external changes are ignored) and discrete in terms of time and action, then we are dealing with a classical planning environment. In the case of a partially observable or stochastic environment, we get a non-classical planning environment. The simplest and most intuitive approach to the planning process algorithms is a Total Order Planning. A scheduling algorithm with parallel execution of actions or without specifying the sequence of their execution is a Partial Order Planning algorithm. Recent research into the development of efficient algorithms has sparked interest in one of the earliest planning approaches – Prepositional Logic Planning. With the Critical Path Method, a schedule of activities is drawn up as part of a plan with zero critical travel time margin for each activity, taking into account the calculation of the time margin for each activity and sequence of activities. A forward-looking planning method for solving complex problems is a hierarchical decomposition based on a Hierarchical Task Networks. The influence of time and resource factors on planning procedures is separately highlighted. Approaches and methods used in a non-classical planning environment: compatible planning, conditional planning, continuous planning, multi-agent planning. Special attention is paid to the issues of constructing planning models in conditions of uncertainty based on the theoretical-probabilistic (stochastic) approaches. Bayesian networks are used to represent vagueness. The Relational Probability Model includes certain constraints on the presentation means, thereby guaranteeing a fully defined probability distributions. The main tasks of probabilistic representation in temporal models are: filtering, forecasting, smoothing, determining a probabilistic explanation. By combining these algorithms and additional enhancements, three large blocks of temporal models can be obtained: Hidden Markov Models, Kalman Filter, and Dynamic Bayesian Network. Decision theory allows the agent to determine the sequence of actions to be performed. A simpler formal system for solving decision-making problems is decision-making networks. The use of expert systems containing information about utility creates additional opportunities. Sequential multiple decision problems in an uncertain environment, such as Markov Decision Processes, are defined using transition models. When several agents interact simultaneously, game theory is used to describe the rational behavior of agents. As we can see, planning has recently become one of the most interesting and relevant directions in the field of artificial intelligence research. There is still a long way to go: it is necessary to develop a clear vision of the problem of choosing the appropriate specific methods depending on the type of task, perhaps by creating completely new methods and approaches.

A grey Bayesian inference framework for structural damage assessment

Real-life civil structures often stay in a grey situation due to lack of knowledge and measurements. In a poor information condition, classic Bayesian inference is practically difficult to perform owing to intractable likelihood functions. Under such circumstance, a structure should be defined as a grey system. Thereby, a grey Bayesian inference framework has been proposed by incorporating the grey theory with approximate Bayesian computation for damage assessment purposes. Structural parameters are represented by interval grey variables, whose grey kernels and degrees of greyness are used to define probability distributions for sampling. A grey population Monte Carlo sampler has also been developed by introducing interval grey numbers and an evolutionary particle pool into the particle filtering process. A novel particle interchange mechanism is simultaneously proposed for effective particle interflow. Meanwhile, stochastic response surfaces are used to correlate structural parameters with responses for fast response computation. Also, likelihood calculation is replaced with a distance measure between simulated and measured samples. Lastly, the proposed inference strategy has been verified against both the numerical and experimental beams having the different damage scenarios. The damage locations and severities were successfully identified by the changes in the grey intervals and kernels.

Reconceptualising Atrial Fibrillation Using Renewal Theory: A Novel Approach to the Assessment of Atrial Fibrillation Dynamics.

Despite a century of research, the mechanisms of AF remain unresolved. A universal motif within AF research has been unstable re-entry, but this remains poorly characterised, with competing key conceptual paradigms of multiple wavelets and more driving rotors. Understanding the mechanisms of AF is clinically relevant, especially with regard to treatment and ablation of the more persistent forms of AF. Here, the authors outline the surprising but reproducible finding that unstable re-entrant circuits are born and destroyed at quasi-stationary rates, a finding based on a branch of mathematics known as renewal theory. Renewal theory may be a way to potentially unify the multiple wavelet and rotor theories. The renewal rate constants are potentially attractive because they are temporally stable parameters of a defined probability distribution (the exponential distribution) and can be estimated with precision and accuracy due to the principles of renewal theory. In this perspective review, this new representational architecture for AF is explained and placed into context, and the clinical and mechanistic implications are discussed.

Projected Pólya Tree

One way of defining probability distributions for circular variables (directions in two dimensions) is to radially project probability distributions, originally defined on R 2 , to the unit circle. Projected distributions have proved to be useful in the study of circular and directional data. Although any bivariate distribution can be used to produce a projected circular model, these distributions are typically parametric. In this article, we consider a bivariate Pólya tree on R 2 and project it to the unit circle to define a new Bayesian nonparametric model for circular data. We study the properties of the proposed model, obtain its posterior characterization and show its performance with simulated and real datasets. Supplemental materials for this article are available online.

Complexity of subdivision-vertex and subdivision-edge join graphs

The entropy of a graph is an information-theoretic quantity which expresses the complexity of a graph. The generalized graph entropies result from applying information measures to a graph using various schemes for defining probability distributions over the elements of the graph. In this paper, the first Zagreb index of a class of composite graphs, namely, subdivision-vertex and subdivision-edge join graphs are investigated in order to evaluate the generalized graph entropies, and explicit formulae for the generalized graph entropy of subdivision-vertex and subdivision-edge join graphs are presented.

Statistics on the Stiefel manifold: Theory and applications

A Stiefel manifold of the compact type is often encountered in many fields of engineering including, signal and image processing, machine learning, numerical optimization and others. The Stiefel manifold is a Riemannian homogeneous space but not a symmetric space. In previous work, researchers have defined probability distributions on symmetric spaces and performed statistical analysis of data residing in these spaces. In this paper, we present original work involving definition of Gaussian distributions on a homogeneous space and show that the maximum-likelihood estimate of the location parameter of a Gaussian distribution on the homogeneous space yields the Fréchet mean (FM) of the samples drawn from this distribution. Further, we present an algorithm to sample from the Gaussian distribution on the Stiefel manifold and recursively compute the FM of these samples. We also prove the weak consistency of this recursive FM estimator. Several synthetic and real data experiments are then presented, demonstrating the superior computational performance of this estimator over the gradient descent based nonrecursive counter part as well as the stochastic gradient descent based method prevalent in literature.

Stochastic Work Flow Bridges Gap Between Subsurface and Surface Disciplines

This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper SPE 187462, “Bridging the Gap Between Subsurface and Surface Disciplines—A Tool for the Modern Facilities Engineer,” by Z. Cristea, SPE, Stochastic Asset Management, and T. Cristea, Independent, prepared for the 2017 SPE Annual Technical Conference and Exhibition, San Antonio, Texas, USA, 9–11 October. The paper has not been peer reviewed. This paper presents an unbiased stochastic data-driven work flow in which surface and subsurface uncertainties are accounted for and their effects on facilities design and operational decisions are quantified. Unlike the traditional approach in facilities design where the most-conservative values are used typically as design input variables, the proposed work flow accounts for life-cycle variability and correlations of relevant input data. Introduction Traditional, deterministic facilities-design methodologies, based on deterministic (single-point) conservative conditions and design margins, might not recognize the full spectrum of operational conditions throughout a field’s life cycle, resulting in significant residual risk and waste of resources during operations. Despite efforts to standardize the process of project delivery as much as possible, industry projects remain heavily customized, intermittent (high-variety, low-volume) processes, with a high rate of diversification and complexity. On the other hand, facilities operations are expected to be high-volume, low-variety, ideally continuous processes. In the proposed work flow, deterministic models are established to account for dependencies between design input variables (static variables such as bottomhole pressure and temperature) and the desired objective (static results, such as the chemical-injection rate). However, in field situations, the analyzed variables change because of subsurface and surface events with different levels of uncertainty (e.g., condensate banking, lean gas injection, water breakthrough). Stochastic algorithms are used to create probability distribution functions (PDFs) for all analyzed design input variables (stochastic variables). Stochastic algorithms then are applied on the deterministic model, sampling from the previously defined probability distributions. Stochastic results are assembled into insightful charts and used to analyze the most-relevant variables and their correlations affecting the model objectives. Example Case Equipment and Processes. A deterministic model is created to calculate the baseline methanol-injection rate (QMEOH) required to mitigate the hydrate-formation risk in a wet-gas field. Both the deterministic and subsequent probabilistic modeling work is performed in a system designed for statistical computation and graphics. Design-basis input data (static variables), considered to be conservative and covering all operational scenarios, are used in the deterministic model. Furthermore, the deterministic model assumes chemical injection as a mass/continuous process. In the field, parameters such as bottomhole pressure and flow rates of different phases change over time. These changes are caused by subsurface and surface events that can be predicted with different levels of uncertainty. PDFs are created for all relevant parameters. Similar probability distributions are created for all relevant variables.

Eliminate Decision Bias in Facilities Planning

This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper SPE 187283, “Eliminate Decision Bias in Facilities Planning,” by Z. Cristea, Stochastic Asset Management, and T. Cristea, Consultant, prepared for the 2017 SPE Annual Technical Conference and Exhibition, San Antonio, Texas, USA, 8–11 October. The paper has not been peer reviewed. The complete paper holds the traditional facilities-planning methodologies, heavily based on design-basis documents and biased toward the most-conservative conditions, fail to recognize the entirety of operational conditions throughout the oilfield life cycle, leading to significant residual risk and the wastage of resources in the operations stage. An integrated stochastic approach is proposed, accounting for both subsurface and surface uncertainties and their interrelations throughout field life. Introduction The authors discuss an unbiased, data-driven stochastic work flow addressing the effect of subsurface uncertainties on surface-facilities design and operational decisions. Unlike classical design approaches, in which the most-conservative values are typically used as design input variables and assembled into design-basis documents, the stochastic work flow accounts for design-input-variable distribution and combination throughout the entire system life cycle. An example case is provided in which a flow-assurance risk is managed and chemical consumption optimized in a wet-gas field development. Theory and Definitions Oil and gas engineering projects are typically processes of high variety, low volume, and intermittent productivity, and with a high rate of diversification and complexity. Conversely, oilfield-facilities operations are expected to be continuous, characterized by high volumes and low variety. This expectation is reflected in the approach toward facilities design, where single-point, “conservative” design conditions are proposed and assembled as facilities design-basis documents. This approach frequently fails to recognize the risks and uncertainties associated with oilfield developments. In the proposed work flow, deterministic models are established to account for the dependencies between design input variables {static variables [i.e., bottomhole pressure (BHP) and bottomhole temperature (BHT)]} and the desired objective [static results (i.e., chemical- injection rate)]. In the provided example, the analyzed variables change because of subsurface and surface events with different levels of uncertainty (i.e., condensate banking, lean-gas injection, water breakthrough). Stochastic algorithms are used to create probability-distribution functions (PDFs) for all analyzed design input variables (stochastic variables). Stochastic algorithms are then applied in the deterministic model, sampling from the previously defined probability distributions. Stochastic results are assembled into insightful charts and used to analyze the most-relevant variables and correlations affecting the objective function.

A network-based detection scheme for the jet stream core

Abstract. The polar and subtropical jet streams are strong upper-level winds with a crucial influence on weather throughout the Northern Hemisphere midlatitudes. In particular, the polar jet is located between cold arctic air to the north and warmer subtropical air to the south. Strongly meandering states therefore often lead to extreme surface weather. Some algorithms exist which can detect the 2-D (latitude and longitude) jets' core around the hemisphere, but all of them use a minimal threshold to determine the subtropical and polar jet stream. This is particularly problematic for the polar jet stream, whose wind velocities can change rapidly from very weak to very high values and vice versa. We develop a network-based scheme using Dijkstra's shortest-path algorithm to detect the polar and subtropical jet stream core. This algorithm not only considers the commonly used wind strength for core detection but also takes wind direction and climatological latitudinal position into account. Furthermore, it distinguishes between polar and subtropical jet, and between separate and merged jet states. The parameter values of the detection scheme are optimized using simulated annealing and a skill function that accounts for the zonal-mean jet stream position (Rikus, 2015). After the successful optimization process, we apply our scheme to reanalysis data covering 1979–2015 and calculate seasonal-mean probabilistic maps and trends in wind strength and position of jet streams. We present longitudinally defined probability distributions of the positions for both jets for all on the Northern Hemisphere seasons. This shows that winter is characterized by two well-separated jets over Europe and Asia (ca. 20° W to 140° E). In contrast, summer normally has a single merged jet over the western hemisphere but can have both merged and separated jet states in the eastern hemisphere. With this algorithm it is possible to investigate the position of the jets' cores around the hemisphere and it is therefore very suitable to analyze jet stream patterns in observations and models, enabling more advanced model-validation.

Interval and random analysis for structure–acoustic systems with large uncertain-but-bounded parameters

For the response analysis of the structure–acoustic system with uncertain-but-bounded parameters, three bounded uncertain models are introduced. One is the bounded random model in which all of the uncertain-but-bounded parameters are described as bounded random variables with well defined probability distribution. The second one is the interval model in which all of the uncertain-but-bounded parameters are described as interval variables due to the limited information. The third one is the bounded hybrid uncertain model in which the interval variables and the bounded random variables exist simultaneously. Based on the parametric Gegenbauer polynomial, which is formulated for bounded random model recently, the Gegenbauer Series Expansion Method (GSEM) is developed for the response prediction of the structure–acoustic system under these three bounded uncertain models. Within GSEM, the response of these three bounded uncertain models of the structure–acoustic system can be approximated by the unified Gegenbauer Series with different values of polynomial parameter. Then, the interval and random analysis for these three bounded uncertain models of the structure–acoustic system are conducted on the basis of Gegenbauer series. Owing to the orthogonal property of Gegenbauer polynomial, the analytical solution of the expectation and variance of Gegenbauer series with respect to the bounded random variables can be readily obtained. The bounds of Gegenbauer series with respect to the interval variables are determined by the Monte Carlo simulation. The GSEM is applied to solve a shell structure–acoustic system under these three bounded uncertain models. Inspired by the convergence behavior of GSEM, the relative improvement criterion is established to estimate the required retained order of Gegenbauer Series for large uncertain problems. The results on numerical examples show that GSEM with the estimated retained order can achieve a prescribed accuracy and good efficiency for structure–acoustic systems with large uncertain-but-bounded parameters.

Prioritizing HIV comparative effectiveness trials based on value of information: generic versus brand-name ART in the US

Background:Value of Information (VOI) analysis examines whether to acquire information before making a decision. We introduced VOI to the HIV audience, using the example of generic antiretroviral therapy (ART) in the US.Methods and Findings:We used a mathematical model and probabilistic sensitivity analysis (PSA) to generate probability distributions of survival (in quality-adjusted life years, QALYs) and cost for three potential first-line ART regimens: three-pill generic, two-pill generic, and single-pill branded. These served as input for a comparison of two hypothetical two-arm trials: three-pill generic versus single-pill branded; and two-pill generic versus single-pill branded. We modeled pre-trial uncertainty by defining probability distributions around key inputs, including 24-week HIV-RNA suppression and subsequent ART failure. We assumed that, without a trial, patients received the single-pill branded strategy. Post-trial, we assumed that patients received the most cost-effective strategy. For both trials, we quantified the probability of changing to a generic-based regimen upon trial completion and the expected VOI in terms of improved health outcomes and costs. Assuming a willingness to pay (WTP) threshold of $100 000/QALY, the three-pill trial led to more treatment changes (84%) than the two-pill trial (78%). Estimated VOI was $48 000 (three-pill trial) and $35 700 (two-pill trial) per future patient initiating ART.Conclusions:A three-pill trial of generic ART is more likely to lead to post-trial treatment changes and to provide more value than a two-pill trial if policy decisions are based on cost-effectiveness. Value of Information analysis can identify trials likely to confer the greatest impact and value for HIV care.

A practical overview on probability distributions.

Aim of this paper is a general definition of probability, of its main mathematical features and the features it presents under particular circumstances. The behavior of probability is linked to the features of the phenomenon we would predict. This link can be defined probability distribution. Given the characteristics of phenomena (that we can also define variables), there are defined probability distribution. For categorical (or discrete) variables, the probability can be described by a binomial or Poisson distribution in the majority of cases. For continuous variables, the probability can be described by the most important distribution in statistics, the normal distribution. Distributions of probability are briefly described together with some examples for their possible application.

The Possibility of Using Neural Networks in Data Analysis Connected with Observation in the Construction Process Simulation

The subject of the article is to present the possibility of applying artificial neural network in analysis of observational data on the issue of simulation concrete supplies in construction industry. Neural networks allows a quick and efficient way to model phenomena at different levels of complexity. They can be used both in processes of well and poorly structured problems, knowledge of which is limited. The advantages of neural networks were transferred to the possibilities of defining probability distributions of individual tasks in cyclical building processes.The article presents the problem of concrete supplies for construction site, its elements and parameters which describe the process. The use of simulation in decision-making system was also demonstrated. One of the stages of creating simulation models is the adoption and verification of probability distributions that describe the elements of the system. In order to learn and predict the characteristics of probability distributions neural networks were used, that enable in the efficient and effective manner the implementation of further stages of simulation modeling. The article presents the results of applying the neural network and approach that enables their use.