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.

Rhapsody in fractional

This paper studies several topics related with the concept of “fractional” that are not directly related with Fractional Calculus, but can help the reader in pursuit new research directions. We introduce the concept of non-integer positional number systems, fractional sums, fractional powers of a square matrix, tolerant computing and FracSets, negative probabilities, fractional delay discrete-time linear systems, and fractional Fourier transform.

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

Energy Resource Management under the Influence of the Weekend Transition Considering an Intensive use of Electric Vehicles

Energy resource scheduling is becoming increasingly important, as the use of distributed resources is intensified and of massive electric vehicle is envisaged. The present paper proposes a methodology for day-ahead energy resource scheduling for smart grids considering the intensive use of distributed generation and Vehicle-to-Grid (V2G). This method considers that the energy resources are managed by a Virtual Power Player (VPP) which established contracts with their owners. It takes into account these contracts, the users' requirements subjected to the VPP, and several discharge price steps. The full AC power flow calculation included in the model takes into account network constraints. The influence of the successive day requirements on the day-ahead optimal solution is discussed and considered in the proposed model. A case study with a 33-bus distribution network and V2G is used to illustrate the good performance of the proposed method.

Novel Prostate Specific Antigen plastic antibody designed withcharged binding sites for an improved protein binding and itsapplication in a biosensor of potentiometric transduction

This work shows that the synthesis of protein plastic antibodies tailored with selected charged monomersaround the binding site enhances protein binding. These charged receptor sites are placed over a neutralpolymeric matrix, thus inducing a suitable orientation the protein reception to its site. This is confirmed bypreparing control materials with neutral monomers and also with non-imprinted template. This concepthas been applied here to Prostate Specific Antigen (PSA), the protein of choice for screening prostate can-cer throughout the population, with serum levels >10 ng/mL pointing out a high probability of associatedcancer.Protein Imprinted Materials with charged binding sites (C/PIM) have been produced by surfaceimprinting over graphene layers to which the protein was first covalently attached. Vinylben-zyl(trimethylammonium chloride) and vinyl benzoate were introduced as charged monomers labellingthe binding site and were allowed to self-organize around the protein. The subsequent polymerizationwas made by radical polymerization of vinylbenzene. Neutral PIM (N/PIM) prepared without orientedcharges and non imprinted materials (NIM) obtained without template were used as controls.These materials were used to develop simple and inexpensive potentiometric sensor for PSA. Theywere included as ionophores in plasticized PVC membranes, and tested over electrodes of solid or liq-uid conductive contacts, made of conductive carbon over a syringe or of inner reference solution overmicropipette tips. The electrodes with charged monomers showed a more stable and sensitive response,with an average slope of -44.2 mV/decade and a detection limit of 5.8 × 10−11mol/L (2 ng/mL). The cor-responding non-imprinted sensors showed lower sensitivity, with average slopes of -24.8 mV/decade.The best sensors were successfully applied to the analysis of serum, with recoveries ranging from 96.9to 106.1% and relative errors of 6.8%.

Rhapsody in Fractional

This paper studies several topics related with the concept of “fractional” that are not directly related with Fractional Calculus, but can help the reader in pursuit new research directions. We introduce the concept of non-integer positional number systems, fractional sums, fractional powers of a square matrix, tolerant computing and FracSets, negative probabilities, fractional delay discrete-time linear systems, and fractional Fourier transform.

Neural Mechanisms of Exercise: Anti-Depression, Neurogenesis, and Serotonin Signaling

Depression is associated with decreased serotonin metabolism and functioning in the central nervous system, evidenced by both animal models of depression and clinical patient studies. Depression is also accompanied by decreased hippocampal neurogenesis in diverse animal models. Neurogenesis is mainly defined in dentate gyrus of hippocampus as well as subventricular zone. Moreover, hypothalamus, amygdala, olfactory tubercle, and piriform cortex are reported with evidences of adult neurogenesis. Physical exercise is found to modulate adult neurogenesis significantly, and results in mood improvement. The cellular mechanism such as adult neurogenesis upregulation was considered as one major mood regulator following exercise. The recent advances in molecular mechanisms underlying exercise-regulated neurogenesis have widen our understanding in brain plasticity in physiological and pathological conditions, and therefore better management of different psychiatric disorders.

Neural Mechanisms of Exercise: Effects on Gut Miccrobiota and Depression

Microbiota is a set of microorganisms resident in gut ecosystem that reacts to psychological stressful stimuli, and is involved in depressed or anxious status in both animals and human being. Interestingly, a series of studies have shown the effects of physical exercise on gut microbiota dynamics, suggesting that gut microbiota regulation might act as one mediator for the effects of exercise on the brain. Recent studies found that gut microbiota dynamics are also regulated by metabolism changes, such as through physical exercise or diet change. Interestingly, physical exercise modulates different population of gut bacteria in compared to food restriction or rich diet, and alleviates gut syndromes to toxin intake. Gut microbiota could as well contribute to the beneficial effects of exercise on cognition and emotion, either directly through serotonin signaling or indirectly by modulating metabolism and exercise performance.

FAS -670A>G genetic polymorphism Is associated with Treatment Resistant Depression

Background Hippocampal neurogenesis has been suggested as a downstream event of antidepressants (AD) mechanism of action and might explain the lag time between AD administration and the therapeutic effect. Despite the widespread use of AD in the context of Major Depressive Disorder (MDD) there are no reliable biomarkers of treatment response phenotypes, and a significant proportion of patients display Treatment Resistant Depression (TRD). Fas/FasL system is one of the best-known death-receptor mediated cell signaling systems and is recognized to regulate cell proliferation and tumor cell growth. Recently this pathway has been described to be involved in neurogenesis and neuroplasticity. Methods Since FAS -670A>G and FASL -844T>C functional polymorphisms never been evaluated in the context of depression and antidepressant therapy, we genotyped FAS -670A>G and FASL -844T>C in a subset of 80 MDD patients to evaluate their role in antidepressant treatment response phenotypes. Results We found that the presence of FAS -670G allele was associated with antidepressant bad prognosis (relapse or TRD: OR=6.200; 95% CI: [1.875–20.499]; p=0.001), and we observed that patients carrying this allele have a higher risk to develop TRD (OR=10.895; 95% CI: [1.362–87.135]; p=0.008).Moreover, multivariate analysis adjusted to potentials confounders showed that patients carrying G allele have higher risk of early relapse (HR=3.827; 95% CI: [1.072–13.659]; p=0.039). FAS mRNA levels were down-regulated among G carriers, whose genotypes were more common in TRD patients. No association was found between FASL-844T>C genetic polymorphism and any treatment phenotypes. Limitations Small sample size. Patients used antidepressants with different mechanisms of action. Conclusion To the best of our knowledge this is the first study to evaluate the role of FAS functional polymorphism in the outcome of antidepressant therapy. This preliminary report associates FAS -670A>G genetic polymorphism with Treatment Resistant Depression and with time to relapse. The current results may possibly be given to the recent recognized role of Fas in neurogenesis and/or neuroplasticity.

Interlimb Coordination During Step-to-Step Transition and Gait Performance

Most energy spent in walking is due to step-to-step transitions. During this phase, the interlimb coordination assumes a crucial role to meet the demands of postural and movement control. The authors review studies that have been carried out regarding the interlimb coordination during gait, as well as the basic biomechanical and neurophysiological principles of interlimb coordination. The knowledge gathered from these studies is useful for understanding step-to-step transition during gait from a motor control perspective and for interpreting walking impairments and inefficiency related to pathologies, such as stroke. This review shows that unimpaired walking is characterized by a consistent and reciprocal interlimb influence that is supported by biomechanical models, and spinal and supraspinal mechanisms. This interlimb coordination is perturbed in subjects with stroke.

Matrix fractional systems

This paper addresses the matrix representation of dynamical systems in the perspective of fractional calculus. Fractional elements and fractional systems are interpreted under the light of the classical Cole–Cole, Davidson–Cole, and Havriliak–Negami heuristic models. Numerical simulations for an electrical circuit enlighten the results for matrix based models and high fractional orders. The conclusions clarify the distinction between fractional elements and fractional systems.