Probability and statistics: selected problems

Probability and Statistics—Selected Problems is a unique book for senior undergraduate and graduate students to fast review basic materials in Probability and Statistics. Descriptive statistics are presented first, and probability is reviewed secondly. Discrete and continuous distributions are presented. Sample and estimation with hypothesis testing are presented in the last two chapters. The solutions for proposed excises are listed for readers to references.

Conditional probability applied to the definition of limestone geochemical facies: A new Methodological Approach

A new method, based on linear correlation and phase diagrams was successfully developed for processes like the sedimentary process, where the deposition phase can have different time duration - represented by repeated values in a series - and where the erosion can play an important rule deleting values of a series. The sampling process itself can be the cause of repeated values - large strata twice sampled - or deleted values: tiny strata fitted between two consecutive samples. What we developed was a mathematical procedure which, based upon the depth chemical composition evolution, allows the establishment of frontiers as well as the periodicity of different sedimentary environments. The basic tool isn't more than a linear correlation analysis which allow us to detect the existence of eventual evolution rules, connected with cyclical phenomena within time series (considering the space assimilated to time), with the final objective of prevision. A very interesting discovery was the phenomenon of repeated sliding windows that represent quasi-cycles of a series of quasi-periods. An accurate forecast can be obtained if we are inside a quasi-cycle (it is possible to predict the other elements of the cycle with the probability related with the number of repeated and deleted points). We deal with an innovator methodology, reason why it's efficiency is being tested in some case studies, with remarkable results that shows it's efficacy. Keywords: sedimentary environments, sequence stratigraphy, data analysis, time-series, conditional probability.

Modified Discrete PSO to Increase the Delivered Energy Probability in Distribution energy Systems

This paper proposes a PSO based approach to increase the probability of delivering power to any load point by identifying new investments in distribution energy systems. The statistical failure and repair data of distribution components is the main basis of the proposed methodology that uses a fuzzyprobabilistic modeling for the components outage parameters. The fuzzy membership functions of the outage parameters of each component are based on statistical records. A Modified Discrete PSO optimization model is developed in order to identify the adequate investments in distribution energy system components which allow increasing the probability of delivering power to any customer in the distribution system at the minimum possible cost for the system operator. To illustrate the application of the proposed methodology, the paper includes a case study that considers a 180 bus distribution network.

DC Fuzzy Multicriteria Approach to Increase the Probability of Delivering Power in Distribution Networks

This paper proposes a methodology to increase the probability of delivering power to any load point through the identification of new investments. The methodology uses a fuzzy set approach to model the uncertainty of outage parameters, load and generation. A DC fuzzy multicriteria optimization model considering the Pareto front and based on mixed integer non-linear optimization programming is developed in order to identify the adequate investments in distribution networks components which allow increasing the probability of delivering power to all customers in the distribution network at the minimum possible cost for the system operator, while minimizing the non supplied energy cost. To illustrate the application of the proposed methodology, the paper includes a case study which considers an 33 bus distribution network.

Increase of the Delivered Power Probability in Distribution Networks using Pareto DC Programming

A methodology to increase the probability of delivering power to any load point through the identification of new investments in distribution network components is proposed in this paper. The method minimizes the investment cost as well as the cost of energy not supplied in the network. A DC optimization model based on mixed integer non-linear programming is developed considering the Pareto front technique in order to identify the adequate investments in distribution networks components which allow increasing the probability of delivering power for any customer in the distribution system at the minimum possible cost for the system operator, while minimizing the energy not supplied cost. Thus, a multi-objective problem is formulated. To illustrate the application of the proposed methodology, the paper includes a case study which considers a 180 bus distribution network

Erros de medicação num serviço de internamento hospitalar : estudo de prevalência

RESUMO - Os erros de medicação (EM) são uma das principais causas de eventos adversos, estimando-se serem as causas não relacionados com procedimentos cirúrgicos mais frequentes. Estes podem ser classificados por erros latentes ou erros ativos. Objetivos Definiram-se como principais objetivos deste estudo, determinar a prevalência de EM ativos num internamento hospitalar evitados e não evitados, nos momentos da prescrição escrita, transcrição, distribuição e administração, bem como a sua relação com algumas variáveis, como o Grupo farmacológico, Via de administração, Especialidade médica do prescritor e Área médica do médico responsável pelo episódio de internamento (MREI). Metodologia O estudo foi do tipo observacional descritivo de abordagem quantitativa, transversal com recrutamento prospetivo. Foi utilizado um instrumento de observação (check-list) para o registo de todos os EM e das variáveis em cada fase. Resultados Foram observadas 513 unidades amostrais com uma prevalência de 98,2% de EM, num total de 1655 erros dos quais 75% foram evitados. Nas variáveis Grupo farmacológico e Área médica do MREI não foram encontradas relações estatísticas relevantes. Obteve-se um OR=1,97 [1,18;3,27] para medicamentos orais quando comparados aos endovenosos nos erros de prescrição (EP) e um OR=7 [2,77;17,71] quando comparados com os endovenosos na transcrição dos Serviços Farmacêuticos (TSF). A anestesiologia apresentou um OR=0,41 [0,27;0,63] nos EP comparativamente às outras especialidades. Do total de EM observaram-se 30% de erros de prescrição (EP), 20% de erros na transcrição do internamento, 36% de erros na TSF, 2% de erros na distribuição e 12% de erros na administração. Os erros mais prevalentes foram a identificação do prescritor ilegível (16%) e a identificação do doente omissa na TSF (16%). Conclusão Apesar da elevada prevalência de EM observados, a maioria dos erros foram corrigidos e não chegaram ao doente. Tendo em conta os EM observados, a utilização de meios informáticos e o aumento da adesão dos enfermeiros ao procedimento de identificação dos doentes poderão permitir a redução do número de EM em cerca de 80%, reduzindo também a probabilidade de ocorrência de eventos adversos relacionados com os erros ativos na utilização de medicamentos.

Tracking error of exchange-traded funds: Evidence from the UK

This paper is mainly concerned with the tracking accuracy of Exchange Traded Funds (ETFs) listed on the London Stock Exchange (LSE) but also evaluates their performance and pricing efficiency. The findings show that ETFs offer virtually the same return but exhibit higher volatility than their benchmark. It seems that the pricing efficiency, which should come from the creation and redemption process, does not fully hold as equity ETFs show consistent price premiums. The tracking error of the funds is generally small and is decreasing over time. The risk of the ETF, daily price volatility and the total expense ratio explain a large part of the tracking error. Trading volume, fund size, bid-ask spread and average price premium or discount did not have an impact on the tracking error. Finally, it is concluded that market volatility and the tracking error are positively correlated.

Restriction site-associated DNA sequencing, genotyping error estimation and de novo assembly optimization for population genetic inference.

Restriction site-associated DNA sequencing (RADseq) provides researchers with the ability to record genetic polymorphism across thousands of loci for nonmodel organisms, potentially revolutionizing the field of molecular ecology. However, as with other genotyping methods, RADseq is prone to a number of sources of error that may have consequential effects for population genetic inferences, and these have received only limited attention in terms of the estimation and reporting of genotyping error rates. Here we use individual sample replicates, under the expectation of identical genotypes, to quantify genotyping error in the absence of a reference genome. We then use sample replicates to (i) optimize de novo assembly parameters within the program Stacks, by minimizing error and maximizing the retrieval of informative loci; and (ii) quantify error rates for loci, alleles and single-nucleotide polymorphisms. As an empirical example, we use a double-digest RAD data set of a nonmodel plant species, Berberis alpina, collected from high-altitude mountains in Mexico.

Resolución No. 076. Por medio de la cual se dejan sin efecto las renovaciones de unas matriculas mercantiles por error operativo

Servicios registrales

Autonomic prediction of error-related ERP components in perceptual and conceptual tasks in older and younger adults

In studies of cognitive processing, the allocation of attention has been consistently linked to subtle, phasic adjustments in autonomic control. Both autonomic control of heart rate and control of the allocation of attention are known to decline with age. It is not known, however, whether characteristic individual differences in autonomic control and the ability to control attention are closely linked. To test this, a measure of parasympathetic function, vagal tone (VT) was computed from cardiac recordings from older and younger adults taken before and during performance of two attentiondemanding tasks - the Eriksen visual flanker task and the source memory task. Both tasks elicited event-related potentials (ERPs) that accompany errors, i.e., error-related negativities (ERNs) and error positivities (Pe's). The ERN is a negative deflection in the ERP signal, time-locked to responses made on incorrect trials, likely generated in the anterior cingulate. It is followed immediately by the Pe, a broad, positive deflection which may reflect conscious awareness of having committed an error. Age-attenuation ofERN amplitude has previously been found in paradigms with simple stimulus-response mappings, such as the flanker task, but has rarely been examined in more complex, conceptual tasks. Until now, there have been no reports of its being investigated in a source monitoring task. Age-attenuation of the ERN component was observed in both tasks. Results also indicated that the ERNs generated in these two tasks were generally comparable for young adults. For older adults, however, the ERN from the source monitoring task was not only shallower, but incorporated more frontal processing, apparently reflecting task demands. The error positivities elicited by 3 the two tasks were not comparable, however, and age-attenuation of the Pe was seen only in the more perceptual flanker task. For younger adults, it was Pe scalp topography that seemed to reflect task demands, being maximal over central parietal areas in the flanker task, but over very frontal areas in the source monitoring task. With respect to vagal tone, in the flanker task, neither the number of errors nor ERP amplitudes were predicted by baseline or on-task vagal tone measures. However, in the more difficult source memory task, lower VT was marginally associated with greater numbers of source memory errors in the older group. Thus, for older adults, relatively low levels of parasympathetic control over cardiac response coincided with poorer source memory discrimination. In both groups, lower levels of baseline VT were associated with larger amplitude ERNs, and smaller amplitude Pe's. Thus, low VT was associated in a conceptual task with a greater "emergency response" to errors, and at the same time, reduced awareness of having made them. The efficiency of an individual's complex cognitive processing was therefore associated with the flexibility of parasympathetic control of heart rate, in response to a cognitively challenging task.

Developmental and individual differences in novelty and error detection in 10-year-old children and young adults /

Event-related potentials were recorded from 10-year-old children and young adults in order to examine the developmental dififerences in two frontal lobe functions: detection of novel stimuli during an auditory novelty oddball task, and error detection during a visual flanker task. All participants showed a parietally-maximal P3 in response to auditory stimuli. In children, novel stimuli generated higher P3 amplitudes at the frontal site compared with target stimuli, whereas target stimuli generated higher P3 amplitudes at the parietal site compared with novel stimuli. Adults, however, had higher P3 amplitude to novel tones compared with target tones at each site. Children also had greater P3 amplitude at more parietal sites than adults during the novelty oddball and flanker tasks. Furthermore, children and adults did not show a significant reduction in P3 amplitude from the first to second novel stimulus presentation. No age differences were found with respect to P3 latency to novel and target stimuli. These findings suggest that the detection of novel and target stimuli is mature in 10-year-olds. Error trials typically elicit a negative ERP deflection (the ERN) with a frontal-central scalp distribution that may reflect response monitoring. There is also evidence of a positive ERP peak (the Pe) with a posterior scalp distribution which may reflect subjective recognition of a response. Both children and adults showed an ERN and Pe maximal at frontal-central sites. Children committed more errors, had smaller ERN across sites, and had a larger Pe at the parietal site than adults. This suggests that response monitoring is still immature in 10-year-olds whereas recognition of and emotional responses to errors may be similar in children and adults.

Generator Matrix Based Search for Extremal Self-Dual Binary Error-Correcting Codes

Self-dual doubly even linear binary error-correcting codes, often referred to as Type II codes, are codes closely related to many combinatorial structures such as 5-designs. Extremal codes are codes that have the largest possible minimum distance for a given length and dimension. The existence of an extremal (72,36,16) Type II code is still open. Previous results show that the automorphism group of a putative code C with the aforementioned properties has order 5 or dividing 24. In this work, we present a method and the results of an exhaustive search showing that such a code C cannot admit an automorphism group Z6. In addition, we present so far unpublished construction of the extended Golay code by P. Becker. We generalize the notion and provide example of another Type II code that can be obtained in this fashion. Consequently, we relate Becker's construction to the construction of binary Type II codes from codes over GF(2^r) via the Gray map.

Top-down and Bottom-up influences on ACC activation: Evaluation of a proposed model of the feedback-related negativity

The Feedback-Related Negativity (FRN) is thought to reflect the dopaminergic prediction error signal from the subcortical areas to the ACC (i.e., a bottom-up signal). Two studies were conducted in order to test a new model of FRN generation, which includes direct modulating influences of medial PFC (i.e., top-down signals) on the ACC at the time of the FRN. Study 1 examined the effects of one’s sense of control (top-down) and of informative cues (bottom-up) on the FRN measures. In Study 2, sense of control and instruction-based (top-down) and probability-based expectations (bottom-up) were manipulated to test the proposed model. The results suggest that any influences of medial PFC on the activity of the ACC that occur in the context of incentive tasks are not direct. The FRN was shown to be sensitive to salient stimulus characteristics. The results of this dissertation partially support the reinforcement learning theory, in that the FRN is a marker for prediction error signal from subcortical areas. However, the pattern of results outlined here suggests that prediction errors are based on salient stimulus characteristics and are not reward specific. A second goal of this dissertation was to examine whether ACC activity, measured through the FRN, is altered in individuals at-risk for problem-gambling behaviour (PG). Individuals in this group were more sensitive to the valence of the outcome in a gambling task compared to not at-risk individuals, suggesting that gambling contexts increase the sensitivity of the reward system to valence of the outcome in individuals at risk for PG. Furthermore, at-risk participants showed an increased sensitivity to reward characteristics and a decreased response to loss outcomes. This contrasts with those not at risk whose FRNs were sensitive to losses. As the results did not replicate previous research showing attenuated FRNs in pathological gamblers, it is likely that the size and time of the FRN does not change gradually with increasing risk of maladaptive behaviour. Instead, changes in ACC activity reflected by the FRN in general can be observed only after behaviour becomes clinically maladaptive or through comparison between different types of gain/loss outcomes.

A Study of Ordered Gene Problems Featuring DNA Error Correction and DNA Fragment Assembly with a Variety of Heuristics, Genetic Algorithm Variations, and Dynamic Representations

Ordered gene problems are a very common classification of optimization problems. Because of their popularity countless algorithms have been developed in an attempt to find high quality solutions to the problems. It is also common to see many different types of problems reduced to ordered gene style problems as there are many popular heuristics and metaheuristics for them due to their popularity. Multiple ordered gene problems are studied, namely, the travelling salesman problem, bin packing problem, and graph colouring problem. In addition, two bioinformatics problems not traditionally seen as ordered gene problems are studied: DNA error correction and DNA fragment assembly. These problems are studied with multiple variations and combinations of heuristics and metaheuristics with two distinct types or representations. The majority of the algorithms are built around the Recentering- Restarting Genetic Algorithm. The algorithm variations were successful on all problems studied, and particularly for the two bioinformatics problems. For DNA Error Correction multiple cases were found with 100% of the codes being corrected. The algorithm variations were also able to beat all other state-of-the-art DNA Fragment Assemblers on 13 out of 16 benchmark problem instances.

We need to have a conversation about OpenURL, a close look at a corpus of error reports from the 2013 academic year. Or, How I learned to stop worrying and give up on clean metadata.

Presented at Access 2014, winner of poster contest.