Elucidating protein-ligand binding kinetics based on returning probability theory.

The returning probability (RP) theory, a rigorous diffusion-influenced reaction theory, enables us to analyze the binding process systematically in terms of thermodynamics and kinetics using molecular dynamics (MD) simulations. Recently, the theory was extended to atomistically describe binding processes by adopting the host-guest interaction energy as the reaction coordinate. The binding rate constants can be estimated by computing the thermodynamic and kinetic properties of the reactive state existing in the binding processes. Here, we propose a methodology based on the RP theory in conjunction with the energy representation theory of solution, applicable to complex binding phenomena, such as protein-ligand binding. The derived scheme of calculating the equilibrium constant between the reactive and dissociate states, required in the RP theory, can be used for arbitrary types of reactive states. We apply the present method to the bindings of small fragment molecules [4-hydroxy-2-butanone (BUT) and methyl methylthiomethyl sulphoxide (DSS)] to FK506 binding protein (FKBP) in an aqueous solution. Estimated binding rate constants are consistent with those obtained from long-timescale MD simulations. Furthermore, by decomposing the rate constants to the thermodynamic and kinetic contributions, we clarify that the higher thermodynamic stability of the reactive state for DSS causes the faster binding kinetics compared with BUT.

Uniform probability in cosmology.

Problems with uniform probabilities on an infinite support show up in contemporary cosmology. This paper focuses on the context of inflation theory, where it complicates the assignment of a probability measure over pocket universes. The measure problem in cosmology, whereby it seems impossible to pick out a uniquely well-motivated measure, is associated with a paradox that occurs in standard probability theory and crucially involves uniformity on an infinite sample space. This problem has been discussed by physicists, albeit without reference to earlier work on this topic. The aim of this article is both to introduce philosophers of probability to these recent discussions in cosmology and to familiarize physicists and philosophers working on cosmology with relevant foundational work by Kolmogorov, de Finetti, Jaynes, and other probabilists. As such, the main goal is not to solve the measure problem, but to clarify the exact origin of some of the current obstacles. The analysis of the assumptions going into the paradox indicates that there exist multiple ways of dealing consistently with uniform probabilities on infinite sample spaces. Taking a pluralist stance towards the mathematical methods used in cosmology shows there is some room for progress with assigning probabilities in cosmological theories.

Generalized measurement error: Intrinsic and incidental measurement error.

In this paper, we generalize the notion of measurement error on deterministic sample datasets to accommodate sample data that are random-variable-valued. This leads to the formulation of two distinct kinds of measurement error: intrinsic measurement error, and incidental measurement error. Incidental measurement error will be recognized as the traditional kind that arises from a set of deterministic sample measurements, and upon which the traditional measurement error modelling literature is based, while intrinsic measurement error reflects some subjective quality of either the measurement tool or the measurand itself. We define calibrating conditions that generalize common and classical types of measurement error models to this broader measurement domain, and explain how the notion of generalized Berkson error in particular mathematicizes what it means to be an expert assessor or rater for a measurement process. We then explore how classical point estimation, inference, and likelihood theory can be generalized to accommodate sample data composed of generic random-variable-valued measurements.

Application of probability theory to neonatal cardiac evaluation.

Based on probability theory, a methodology that allows diagnosing neonatal cardiac dynamics was previously developed; however, diagnostic applications of this method are required to validate it to the neonatal cardiac dynamics was conducted, allowing to differentiate normal from pathological dynamics. The hourly maximum and minimum heart rate values from 39 continuous and ambulatory electrocardiographic records with a minimum length of 21 hours were taken, from newborns between 0 and 10 days of life, 9 clinically within normality limits and 30 with cardiac pathologies. The probability of occurrence of heart rates in ranges of 5 beats/minute was calculated. The distributions of probability were analysed, and finally the diagnosis was determined by the physical-mathematical methodology. Then, a statistical validation of sensitivity, specificity, and diagnostic agreement was performed. Normal registries showed probability distributions with absent or minimal presence of heart rates of the ranges between 125 and 135 beats/minute, while the abnormal ones had values within these ranges, as well as absence or minimal presence of heart rates from 75 beats/minute to 85 beats/minute. The sensitivity and specificity were 100%, and the Kappa coefficient had a value of 1. Hereby, it is concluded that through an application of a physical-mathematical methodology of neonatal cardiac diagnosis, it is possible to differentiate normality from disease.

La venganza como rechazo de la responsabilidad. la ira de Dios / La muerte lenta de Luciana B / Revenge as rejection of responsibility

Dos novelas sucesivas del escritor y matemático argentino Guillermo Martínez, "Crímenes imperceptibles" (2004) y "La muerte lenta de Luciana B." (2007) fueron llevadas al cine. En ambas se abordan las categorías lógico-matemáticas de azar y necesidad, permitiendo abrir una brecha entre ellas para conjeturar una hipótesis clínica sobre la responsabilidad subjetiva de los personajes. Este trabajo pone el foco en la versión "La ira de Dios" (Schindel, 2022), introduciendo la cuestión de las leyes del azar, la respuesta de un sujeto a ese encuentro con el azar, para concluir con la venganza como rechazo de la responsabilidad.

Two successive novels by Argentine writer and mathematician Guillermo Martínez, "Imperceptible Crimes" (2004) and "The Slow Death of Luciana B." (2007) were made into movies. In both, the logical-mathematical categories of chance and necessity are addressed, allowing a gap to be opened between them to conjecture a clinical hypothesis about the subjective responsibility of the characters. This work focuses on the version "The Wrath of God" (Schindel, 2022), introducing the question of the laws of chance, the response of a subject to that encounter with chance, to conclude with revenge as a rejection of the responsibility

Estrategia de predicción pacientes con casos de coronavirus; reporte de experiencia Pereira, Risaralda, marzo-abril 2020 / Prediction strategy for patients with coronavirus cases; experience report Pereira, Risaralda, March- April 2020

Resumen Introducción: la infección por COVID 19 corresponde actualmente al evento infeccioso con mayor impacto en salud púbica a nivel mundial, en Colombia, al 30 de abril de 2020 se registraron 6465 casos acumulados, 360 defunciones y 2186 casos recuperados, dado el aumento en los casos reportados mediante los sistemas de vigilancia epidemiológica se precisa de herramientas que faciliten el diagnóstico oportuno y la predicción en el comportamiento de los casos a nivel nacional. Objetivos: proponer un modelo estadístico que permita predecir la probabilidad de cursar con diagnóstico de COVID-19 en la población atendida por sospecha de infección por el mismo en una institución de tercer nivel del municipio de Pereira- Risaralda entre marzo y abril de 2020. Materiales y métodos: se presenta un estudio descriptivo de corte trasversal en el cual se analizaron 82 casos, se realizó un modelo predictivo basado en compuertas lógicas AND y OR, y análisis por estadística descriptiva e inferencial. Resultados: de los 82 registros analizados se encontró una relación hombre: mujer de 1:2; el 6% de los pacientes tuvo alta probabilidad para diagnóstico de COVID 19, el 20% tuvo probabilidad intermedia y el 72% registró baja probabilidad para COVID19, la concordancia del modelo con los resultados de las pruebas fue inferior a 0,5. Conclusiones: el modelo estadístico planteado fue insuficiente para lograr la predicción de la totalidad de los casos de COVID-19 basados en el perfil de riego de la población, se precisan nuevas investigaciones con tamaños de muestra superiores, diseños y análisis distintos. MÉD.UIS.2022;35(1): 57-69.

Abstract Introduction: COVID 19 infection currently corresponds to the infectious event with the greatest impact on public health worldwide, in Colombia, as of April 30, 2020, 6465 accumulated cases, 360 deaths and 2186 recovered cases were registered, given the increase in cases reported through epidemiological surveillance systems, tools are needed to facilitate timely diagnosis and prediction in the behavior of cases at the national level. Objectives: to propose a statistical model that allows predicting the probability of a diagnosis of COVID-19 in the population treated for suspected coronavirus infection in a third-level institution in the population of Pereira-Risaralda between March and April 2020. Materials and methods: a descriptive cross-sectional study is presented, in which 82 cases were analyzed, a predictive model based on AND and OR logic gates, analyzes by descriptive and inferential statistics were performed. Results: of the 82 records analyzed, a male: female ratio of 1: 2 was found; 6% of the patients had a high probability for the diagnosis of COVID 19, 20% had an intermediate probability and 72% had a low probability for COVID19, the agreement of the model with the test results was less than 0.5. Conclusions: the proposed statistical model was insufficient to achieve the prediction of all the cases of COVID-19 based on the irrigation profile of the population. New investigations are required with larger sample sizes associated with longitudinal designs and combined statistical analyzes that allow to refine the proposed model. MÉD.UIS.2022;35(1): 57-69.

Clarifying the relationship between coherence and accuracy in probability judgments.

Bayesian approaches presuppose that following the coherence conditions of probability theory makes probabilistic judgments more accurate. But other influential theories claim accurate judgments (with high "ecological rationality") do not need to be coherent. Empirical results support these latter theories, threatening Bayesian models of intelligence; and suggesting, moreover, that "heuristics and biases" research, which focuses on violations of coherence, is largely irrelevant. We carry out a higher-power experiment involving poker probability judgments (and a formally analogous urn task), with groups of poker novices, occasional poker players, and poker experts, finding a positive relationship between coherence and accuracy both between groups and across individuals. Both the positive relationship in our data, and past null results, are captured by a sample-based Bayesian approximation model, where a person's accuracy and coherence both increase with the number of samples drawn. Thus, we reconcile the theoretical link between accuracy and coherence with apparently negative empirical results.

Constructive Biases in Clinical Judgment.

With a pair of oppositely valenced stimuli, rating the first one sometimes leads to a more extreme evaluation for the second (e.g., if the second is negatively valenced, rating the first stimulus would lead to a more negative rating for the second). We considered an evaluation bias in the case of clinical diagnosis relating to eating disorders. A population sample which included experienced clinical psychologists and psychiatrists showed partial evidence of an evaluation bias, when judging descriptions of individuals designed to be consistent with eating disorders or not. Quantum probability theory, the probability rules from quantum mechanics without any of the physics, is particularly well-suited to modeling the evaluation bias (and constructive influences generally), because a measurement (or judgment) can change the state of the system. We applied a previous quantum model to the present result, an extension of the model embodying noisy processes, and belief adjustment model. We discuss how model fits inform an examination of rationality in the observed behavior.

Modern Statistical Tendencies used in Investigations in the Medical Sciences / endencias estadísticas modernas utilizadas en investigaciones en las ciencias médicas

Introduction: The name Statistics was probably used in Egypt in 1549. The term Statistics, which was connected to the development of sovereign states, was coined in Germany in 1749 and used to designate the systematic collection of demographic and economic data by states. Objective: To present the most relevant and current statistical techniques in clinical medicine and epidemiology, as well as to show examples of the use of these techniques. Material and Methods: Review of the literature on the subject; presentation of some examples developed in class by professors of the subject Research Methodology and Statistics in Medical Sciences. Development: From the very beginnig, Statistics was used to characterize data based on their properties, as well as to develop information summary measures. In the modern era, procedures and techniques were designated to facilitate valid inferences to the universe from the sampling theory, whose foundation is the probability theory. Conclusions: There is a need for the application of modern techniques and especially the multivariate ones used to explain biological phenomena, which cannot be explained by one or two variables. This makes possible that our universities, scientific research centers, and companies conduct studies using statistical techniques that involve many variables, which are supposed to be related to the variable under study(AU)

Introducción: El nombre de Estadística probablemente se usó en Egipto en 1549. El término Estadística se acuñó en Alemania en 1749, conectado con el desarrollo de estados soberanos y designando la recopilación sistemática de datos demográficos y económicos por estados. Objetivo: Presentar las técnicas estadísticas más relevantes en el campo de la clínica médica y la epidemiología actualmente y mostrar ejemplos del uso de dichas técnicas. Material y métodos: Revisión de la literatura sobre el tema, algunos ejemplos desarrollados en clases por profesores de la asignatura Metodología de la investigación y Estadística en carreras de Ciencias Médicas. Desarrollo: En sus inicios la Estadística caracterizaba los datos basados en sus propiedades, desarrollaron medidas de resumen de información. En la era moderna se diseñaron procedimientos y técnicas para realizar inferencias válidas al universo a partir de la teoría del muestreo, cuyo fundamento es la teoría de probabilidades. Conclusiones: Necesidad de la aplicación de las técnicas modernas y especialmente las multivariadas para explicar los fenómenos biológicos, que no pueden ser explicados por una o dos variables, esto hace que nuestras universidades, centros de investigaciones científicas y empresas realicen sus estudios, utilizando técnicas estadísticas que envuelvan muchas variables que se suponen se relacionen con la variable objeto de estudio(AU)

States of ignorance and ignorance of states: Examining the Quantum Principal Principle.

Earman (2018) has recently argued that the Principal Principle, a principle of rationality connecting objective chance and credence, is a theorem of quantum probability theory. This paper critiques Earman's argument, while also offering a positive proposal for how to understand the status of the Principal Principle in quantum probability theory.

The similarity-updating model of probability judgment and belief revision.

People often take nondiagnostic information into account when revising their beliefs. A probability judgment decreases due to nondiagnostic information represents the well-established "dilution effect" observed in many domains. Surprisingly, the opposite of the dilution effect called the "confirmation effect" has also been observed frequently. The present work provides a unified cognitive model that allows both effects to be explained simultaneously. The suggested similarity-updating model incorporates two psychological components: first, a similarity-based judgment inspired by categorization research, and second, a weighting-and-adding process with an adjustment following a similarity-based confirmation mechanism. Four experimental studies demonstrate the model's predictive accuracy for probability judgments and belief revision. The participants received a sample of information from one of two options and had to judge from which option the information came. The similarity-updating model predicts that the probability judgment is a function of the similarity of the sample to the options. When one is presented with a new sample, the previous probability judgment is updated with a second probability judgment by taking a weighted average of the two and adjusting the result according to a similarity-based confirmation. The model describes people's probability judgments well and outcompetes a Bayesian cognitive model and an alternative probability-theory-plus-noise model. The similarity-updating model accounts for several qualitative findings, namely, dilution effects, confirmation effects, order effects, and the finding that probability judgments are invariant to sample size. In sum, the similarity-updating model provides a plausible account of human probability judgment and belief revision. (PsycInfo Database Record (c) 2021 APA, all rights reserved).

Minimizing Population Health Loss in Times of Scarce Surgical Capacity During the Coronavirus Disease 2019 Crisis and Beyond: A Modeling Study.

OBJECTIVES: Coronavirus disease 2019 has put unprecedented pressure on healthcare systems worldwide, leading to a reduction of the available healthcare capacity. Our objective was to develop a decision model to estimate the impact of postponing semielective surgical procedures on health, to support prioritization of care from a utilitarian perspective. METHODS: A cohort state-transition model was developed and applied to 43 semielective nonpediatric surgical procedures commonly performed in academic hospitals. Scenarios of delaying surgery from 2 weeks were compared with delaying up to 1 year and no surgery at all. Model parameters were based on registries, scientific literature, and the World Health Organization Global Burden of Disease study. For each surgical procedure, the model estimated the average expected disability-adjusted life-years (DALYs) per month of delay. RESULTS: Given the best available evidence, the 2 surgical procedures associated with most DALYs owing to delay were bypass surgery for Fontaine III/IV peripheral arterial disease (0.23 DALY/month, 95% confidence interval [CI]: 0.13-0.36) and transaortic valve implantation (0.15 DALY/month, 95% CI: 0.09-0.24). The 2 surgical procedures with the least DALYs were placing a shunt for dialysis (0.01, 95% CI: 0.005-0.01) and thyroid carcinoma resection (0.01, 95% CI: 0.01-0.02). CONCLUSION: Expected health loss owing to surgical delay can be objectively calculated with our decision model based on best available evidence, which can guide prioritization of surgical procedures to minimize population health loss in times of scarcity. The model results should be placed in the context of different ethical perspectives and combined with capacity management tools to facilitate large-scale implementation.

Voevodsky's unfinished project: Filling the gap between pure and applied mathematics.

In a series of lectures given in 2003, soon after receiving the Fields Medal for his results in the Algebraic Geometry, Vladimir Voevodsky (1966-2017) identifies two strategic goals for mathematics, which he plans to pursue in his further research. The first goal is to develop a ''computerised library of mathematical knowledge,'' which supports an automated proof-verification. The second goal is to ''bridge pure and applied mathematics.'' Voevodsky's research towards the first goal brought about the new Univalent foundations of mathematics. In view of the second goal Voevodsky in 2004 started to develop a mathematical theory of Population Dynamics, which involved the Categorical Probability theory. This latter project did not bring published results and was abandoned by Voevodsky in 2009 when he decided to focus his efforts on the Univalent foundations and closely related topics. In the present paper, which is based on Voevodsky's archival sources, I present Voevodsky's views of mathematics and its relationships with natural sciences, critically discuss these views, and suggest how Voevodsky's ideas and approaches in the applied mathematics can be further developed and pursued. A special attention is given to Voevodsky's original strategy to bridge the persisting gap between pure and applied mathematics where computers and the computer-assisted mathematics play a major role.

Information overload for (bounded) rational agents.

Bayesian inference offers an optimal means of processing environmental information and so an advantage in natural selection. We consider the apparent, recent trend in increasing dysfunctional disagreement in, for example, political debate. This is puzzling because Bayesian inference benefits from powerful convergence theorems, precluding dysfunctional disagreement. Information overload is a plausible factor limiting the applicability of full Bayesian inference, but what is the link with dysfunctional disagreement? Individuals striving to be Bayesian-rational, but challenged by information overload, might simplify by using Bayesian networks or the separation of questions into knowledge partitions, the latter formalized with quantum probability theory. We demonstrate the massive simplification afforded by either approach, but also show how they contribute to dysfunctional disagreement.

Do children have Bayesian intuitions?

Can children solve Bayesian problems, given that these pose great difficulties even for most adults? We present an ecological framework in which Bayesian intuitions emerge from a match between children's numerical competencies and external representations of numerosity. Bayesian intuition is defined here as the ability to determine the exact Bayesian posterior probability by minds untutored in probability theory or in Bayes' rule. As we show, Bayesian intuitions do not require processing of probabilities or Arabic numbers, but basically the ability to count tokens in icon arrays and to understand what to count. A series of experiments demonstrates for the first time that icon arrays elicited Bayesian intuitions in children as young as second-graders for 22% to 32% of all problems; fourth-graders achieved 50% to 60%. Most surprisingly, icon arrays elicited Bayesian intuitions in children with dyscalculia, a specific learning disorder that has been attributed to genetic causes. These children could solve an impressive 50% of Bayesian problems, a level similar to that of children without dyscalculia. By seventh grade, children solved about two thirds of Bayesian problems with natural frequencies alone, without the additional help of icon arrays. We identify four non-Bayesian rules. On the basis of these results, we propose a common solution for the phylogenetic, the ontogenetic, and the 1970s puzzles in the Bayesian literature and argue for a revision of how to teach statistical thinking. In accordance with recent work on infants' numerical abilities, these findings indicate that children have more numerical ability than previously assumed. (PsycInfo Database Record (c) 2021 APA, all rights reserved).

Random variation and systematic biases in probability estimation.

A number of recent theories have suggested that the various systematic biases and fallacies seen in people's probabilistic reasoning may arise purely as a consequence of random variation in the reasoning process. The underlying argument, in these theories, is that random variation has systematic regressive effects, so producing the observed patterns of bias. These theories typically take this random variation as a given, and assume that the degree of random variation in probabilistic reasoning is sufficiently large to account for observed patterns of fallacy and bias; there has been very little research directly examining the character of random variation in people's probabilistic judgement. We describe 4 experiments investigating the degree, level, and characteristic properties of random variation in people's probability judgement. We show that the degree of variance is easily large enough to account for the occurrence of two central fallacies in probabilistic reasoning (the conjunction fallacy and the disjunction fallacy), and that level of variance is a reliable predictor of the occurrence of these fallacies. We also show that random variance in people's probabilistic judgement follows a particular mathematical model from frequentist probability theory: the binomial proportion distribution. This result supports a model in which people reason about probabilities in a way that follows frequentist probability theory but is subject to random variation or noise.

A novel family of lifetime distribution with applications to real and simulated data.

The paper investigates a new scheme for generating lifetime probability distributions. The scheme is called Exponential- H family of distribution. The paper presents an application of this family by using the Weibull distribution, the new distribution is then called New Flexible Exponential distribution or in short NFE. Various statistical properties are derived, such as quantile function, order statistics, moments, etc. Two real-life data sets and a simulation study have been performed so that to assure the flexibility of the proposed model. It has been declared that the proposed distribution offers nice results than Exponential, Weibull Exponential, and Exponentiated Exponential distribution.

Conditionals and testimony.

Conditionals and conditional reasoning have been a long-standing focus of research across a number of disciplines, ranging from psychology through linguistics to philosophy. But almost no work has concerned itself with the question of how hearing or reading a conditional changes our beliefs. Given that we acquire much-perhaps most-of what we believe through the testimony of others, the simple matter of acquiring conditionals via others' assertion of a conditional seems integral to any full understanding of the conditional and conditional reasoning. In this paper we detail a number of basic intuitions about how beliefs might change in response to a conditional being uttered, and show how these are backed by behavioral data. In the remainder of the paper, we then show how these deceptively simple phenomena pose a fundamental challenge to present theoretical accounts of the conditional and conditional reasoning - a challenge which no account presently fully meets.

The Effect of Information Formats and Incidental Affect on Prior and Posterior Probability Judgments.

Background. Interpreting medical test results involves judging probabilities, including making Bayesian inferences such as judging the positive and negative predictive values. Although prior work has shown that experience formats (e.g., slide shows of representative patient cases) produce more accurate Bayesian inferences than description formats (e.g., verbal statistical summaries), there are disadvantages of using the experience format for real-world medical decision making that may be solved by presenting relevant information in a 2 × 2 table format. Furthermore, medical decisions are often made in stressful contexts, yet little is known about the influence of acute stress on the accuracy of Bayesian inferences. This study aimed to a) replicate the description-experience format effect on probabilistic judgments; b) examine judgment accuracy across description, experience, and a new 2 × 2 table format; and c) assess the effect of acute stress on probability judgments. Method. The study employed a 2 (stress condition) × 3 (format) factorial between-subjects design. Participants (N = 165) completed a Bayesian inference task in which information about a medical screening test was presented in 1 of 3 formats (description, experience, 2 × 2 table), following a laboratory stress induction or a no-stress control condition. Results. Overall, the 2 × 2 table format produced the most accurate probability judgments, including Bayesian inferences, compared with the description and experience formats. Stress had no effect on judgment accuracy. Discussion. Given its accuracy and practicality, a 2 × 2 table may be better suited than description or experience formats for communicating probabilistic information in medical contexts.