Uma Simulação computacional do passeio aleatório simples

Em 1828 foi observado um fenômeno no microscópio em que se visualizava minúsculos grãos de pólen mergulhados em um líquido em repouso que mexiam-se de forma aleatória, desenhando um movimento desordenado. A questão era compreender este movimento. Após cerca de 80 anos, Einstein (1905) desenvolveu uma formulação matemática para explicar este fenômeno, tratado por movimento Browniano, teoria cada vez mais desenvolvida em muitas das áreas do conhecimento, inclusive recentemente em modelagem computacional. Objetiva-se pontuar os pressupostos básicos inerentes ao passeio aleatório simples considerando experimentos com e sem problema de valor de contorno para melhor compreensão ao no uso de algoritmos aplicados a problemas computacionais. Foram explicitadas as ferramentas necessárias para aplicação de modelos de simulação do passeio aleatório simples nas três primeiras dimensões do espaço. O interesse foi direcionado tanto para o passeio aleatório simples como para possíveis aplicações para o problema da ruína do jogador e a disseminação de vírus em rede de computadores. Foram desenvolvidos algoritmos do passeio aleatório simples unidimensional sem e com o problema do valor de contorno na plataforma R. Similarmente, implementados para os espaços bidimensionais e tridimensionais,possibilitando futuras aplicações para o problema da disseminação de vírus em rede de computadores e como motivação ao estudo da Equação do Calor, embora necessita um maior embasamento em conceitos da Física e Probabilidade para dar continuidade a tal aplicação.

Capture probability of a survey trawl for red king crab (Paralithodes camtschaticus)

The relative abundance of Bristol Bay red king crab (Paralithodes camtschaticus) is estimated each year for stock assessment by using catch-per-swept-area data collected on the Alaska Fisheries Science Center’s annual eastern Bering Sea bottom trawl survey. To estimate survey trawl capture efficiency for red king crab, an experiment was conducted with an auxiliary net (fitted with its own heavy chain-link footrope) that was attached beneath the trawl to capture crabs escaping under the survey trawl footrope. Capture probability was then estimated by fitting a model to the proportion of crabs captured and crab size data. For males, mean capture probability was 72% at 95 mm (carapace length), the size at which full vulnerability to the survey trawl is assigned in the current management model; 84.1% at 135 mm, the legal size for the fishery; and 93% at 184 mm, the maximum size observed in this study. For females, mean capture probability was 70% at 90 mm, the size at which full vulnerability to the survey trawl is assigned in the current management model, and 77% at 162 mm, the maximum size observed in this study. The precision of our estimates for each sex decreased for juveniles under 60 mm and for the largest crab because of small sample sizes. In situ data collected from trawl-mounted video cameras were used to determine the importance of various factors associated with the capture of individual crabs. Capture probability was significantly higher when a crab was standing when struck by the footrope, rather than crouching, and higher when a crab was hit along its body axis, rather than from the side. Capture probability also increased as a function of increasing crab size but decreased with increasing footrope distance from the bottom and when artificial light was provided for the video camera.

Daily rainfall along the United States Pacific Coast appears to conform to a square-root normal probability distribution

EXTRACT (SEE PDF FOR FULL ABSTRACT): As part of a study of climatic influences on landslide initiation, a statistical analysis of long-term (>40 years) records of daily rainfall from 24 Pacific coastal stations, from San Diego to Cape Flattery, disclosed an unexpected result - the square root of the daily rainfall closely approximates a normal distribution function. ... This paper illustrates the use of the square-root-normal distribution to analyze variations in precipitation along the mainland United States Pacific Coast with examples of orographic enhancement, rain shadows, and increase in precipitation frequency with geographic latitude.

Evaluation of quality of shark livers using bio-chemical properties and organoleptic score sheet

Shark livers are considered as an important raw material providing a quality fish oil. It has been reported to aid white — blood-cell production and act as an active ingredient in hemorrhoid treatments. It is also reported that liver oil as a good supplement of vitamin A and poly-unsaturated fatty acids which are important to the development of brain cells in human. Freshness of livers is very important to extract better quality oil. In Sri Lanka, the annual shark production amounts to 8000t, however the quality of livers collected from landing sites has not being measured yet. Present study was conducted to evaluate the quality of silky (Charcarninus fakiformis) shark livers available in Negombo and Beruwala landing sites in the West Coast of Sri Lanka and also to study the relationship between organoleptic and bio-chemical correlation on freshness of shark livers. Liver samples which were collected from landing sites in the West coast of Sri Lanka, were evaluated for external and internal colour, texture and odour. Total volatile nitrogen (TVN), pH value, free fatty acid (FFA%) and peroxide (PV) values of livers were also determined to assess quality. According to the organoleptic scoring system 4.3% of liver samples were categorized as best in quality while 30.4%, 56.5% and 8.7% rated as good, medium and poor in quality respectively at the Negombo and Beruwala landing sites. Bio-chemical analysis showed that the better quality livers had the highest score for sensory evaluation and low values for TVN, FFA and peroxide value while low quality livers gave low score for sensory evaluation and high TVN, FFA, peroxide values. Correlation coefficient of organoleptic scores against total volatile nitrogen value, pH value, free fatty acid % and peroxide value of shark livers were determined by statistical analysis. Organoleptic score of shark livers was found to be highly.

Response probability distribution of built-up vibro-acoustic systems

The vibro-acoustic response of built-up structures, consisting of stiff components with low modal density and flexible components with high modal density, is sensitive to small imperfections in the flexible components. In this paper, the uncertainty of the response is considered by modeling the low modal density master system as deterministic and the high modal density subsystems in a nonparametric stochastic way, i.e., carrying a diffuse wave field, and by subsequently computing the response probability density function. The master system's mean squared response amplitude follows a singular noncentral complex Wishart distribution conditional on the subsystem energies. For a single degree of freedom, this is equivalent to a chi-square or an exponential distribution, depending on the loading conditions. The subsystem energies follow approximately a chi-square distribution when their relative variance is smaller than unity. The results are validated by application to plate structures, and good agreement with Monte Carlo simulations is found. © 2012 Acoustical Society of America.

Outage probability of the gaussian MIMO free-space optical channel with PPM

Atmospheric effects can significantly degrade the reliability of free-space optical communications. One such effect is scintillation, caused by atmospheric turbulence, refers to random fluctuations in the irradiance and phase of the received laser beam. In this paper we inv stigate the use of multiple lasers and multiple apertures to mitigate scintillation. Since the scintillation process is slow, we adopt a block fading channel model and study the outage probability under the assumptions of orthogonal pulse-position modulation and non-ideal photodetection. Assuming perfect receiver channel state information (CSI), we derive the signal-to-noise ratio (SNR) exponents for the cases when the scintillation is lognormal, exponential and gammagamma distributed, which cover a wide range of atmospheric turbulence conditions. Furthermore, when CSI is also available at the transmitter, we illustrate very large gains in SNR are possible (in some cases larger than 15 dB) by adapting the transmitted power. Under a long-term power constraint, we outline fundamental design criteria via a simple expression that relates the required number of lasers and apertures for a given code rate and number of codeword blocks to completely remove system outages. Copyright © 2009 IEEE.