scholarly journals Recursive Formula for the Random String Word Detection Probability, Overlaps and Probability Extremes

2019 ◽  
Vol 11 (2) ◽  
pp. 171
Author(s):  
V. I. Ilyevsky
Keyword(s):  
Probability Theory ◽  
Molecular Biology ◽  
Detection Probability ◽  
Numerical Evaluation ◽  
Recursive Formula ◽  
Discrete Mathematics ◽  
Random String ◽  
Detection Probabilities ◽  
Word Detection ◽  
First Time

In this paper, for the first time ever, the properties of the word detection probability in a random string have been investigated. The formerly known methods led to numerical evaluation of the researched probabilities only. The present work derives the simplest algorithm for calculation of the word’s at least once detection probability in a random string. A recursive formula that considers the overlap capability has been deduced for the probability under study. This formula is being used for the proposition on comparison of the word detection probabilities in a random string for the words with different periods. The result allows determining the structure of words that have maximum and minimum detection probabilities. In particular, words having equal number of alphabetic characters have been studied. It has been established, that for the words in question detection probability is minimal for the ideally symmetrical words that have irreducible period - and maximal for the words devoid of the overlap feature. These results will be useful for molecular genetics, as well as for students studying discrete mathematics, probability theory and molecular biology.

scholarly journals Analysis of Low Probability of Detection Capability for Chaotic Standard Map-Based FH-OFDMA System

2021 ◽  
Vol 11 (5) ◽  
pp. 2198
Author(s):  
Junwoo Jung ◽  
Jaesung Lim ◽  
Sungyeol Park ◽  
Haengik Kang ◽  
Seungbok Kwon
Keyword(s):  
Detection Probability ◽  
Probability Of Detection ◽  
Lower Probability ◽  
Symbol Sequence ◽  
Ofdma System ◽  
Standard Map ◽  
Detection Probabilities ◽  
Low Probability ◽  
Transmitted Symbol ◽  
Basic Symbol

A frequency hopping orthogonal frequency division multiple access (FH-OFDMA) can provide low probability of detection (LPD) and anti-jamming capabilities to users against adversary detectors. To obtain an extreme LPD capability that cannot be provided by the basic symbol-by-symbol (SBS)-based FH pattern, we proposed two FH patterns, namely chaotic standard map (CSM) and cat map for FH-OFDMA systems. In our previous work, through analysis of complexity to regenerate the transmitted symbol sequence, at the point of adversary detectors, we found that the CSM had a lower probability of intercept than the cat map and SBS. It is possible when a detector already knows symbol and frame structures, and the detector has been synchronized to the FH-OFDMA system. Unlike the previous work, here, we analyze whether the CSM provides greater LPD capability than the cat map and SBS by detection probability using spectrum sensing technique. We analyze the detection probability of the CSM and provide detection probabilities of the cat map and SBS compared to the CSM. Based on our analysis of the detection probability and numerical results, it is evident that the CSM provides greater LPD capability than both the cat map and SBS-based FH-OFDMA systems.

scholarly journals Detection of contaminant plumes released from landfills

2006 ◽  
Vol 3 (3) ◽  
pp. 819-857
Author(s):  
N. B. Yenigül ◽  
A.T. Hendsbergen ◽  
A. M. M. Elfeki ◽  
F. M. Dekking
Keyword(s):  
Simulation Model ◽  
Contaminant Transport ◽  
Analytical Model ◽  
Detection Probability ◽  
Average Concentration ◽  
Contaminant Plume ◽  
Contaminant Plumes ◽  
Heterogeneous Aquifer ◽  
Monitoring Well ◽  
Detection Probabilities

Abstract. Contaminant leaks released from landfills are a significant threat to groundwater quality. The groundwater detection monitoring systems installed in the vicinity of such facilities are vital. In this study the detection probability of a contaminant plume released from a landfill has been investigated by means of both a simulation and an analytical model for both homogeneous and heterogeneous aquifer conditions. The results of the two models are compared for homogeneous aquifer conditions to illustrate the errors that might be encountered with the simulation model. For heterogeneous aquifer conditions contaminant transport is modelled by an analytical model using effective (macro) dispersivities. The results of the analysis show that the simulation model gives the concentration values correctly over most of the plume length for homogeneous aquifer conditions, and that the detection probability of a contaminant plume at given monitoring well locations match quite well. For heterogeneous aquifer conditions the approximating analytical model based on effective (macro) dispersivities yields the average concentration distribution satisfactorily. However, it is insufficient in monitoring system design since the discrepancy between the detection probabilities of contaminant plumes at given monitoring well locations computed by the two models is significant, particularly with high dispersivity and heterogeneity.

scholarly journals Detection Probability Analysis of True Random Coding Photon Counting Lidar

Photonics ◽  
2021 ◽  
Vol 8 (12) ◽  
pp. 545
Author(s):  
Yang Yu ◽  
Zhangjun Wang ◽  
Kuntai Ma ◽  
Chao Chen ◽  
Xiufen Wang ◽  
...  
Keyword(s):  
Theoretical Model ◽  
Detection Probability ◽  
Effective Means ◽  
Photon Number ◽  
Photon Counting ◽  
Sequence Length ◽  
Random Coding ◽  
Working Principle ◽  
The Impact ◽  
First Time

With the wide application of lidar in the future, the problem of crosstalk between lidars will become more serious. True random coding photon counting lidar with high anti-crosstalk ability will play an important role in solving this problem. In this paper, based on the working principle of Gm-APD, the detection probability theoretical model of true random coding photon counting lidar is built, and the impact of jitter on detection probability is considered for the first time. The influence of mean echo photon number, mean pulse count density, sequence length and pulse width on detection probability is analyzed. Monte Carlo simulation and experimental results are highly consistent with the theoretical model, which proves the correctness of the detection probability theoretical model. This theoretical model provides an effective means to evaluate the system performance.

The Patterns of Large Numbers

2019 ◽  
pp. 43-66
Author(s):  
Steven J. Osterlind
Keyword(s):  
Probability Theory ◽  
Central Limit Theorem ◽  
Limit Theorem ◽  
French Revolution ◽  
Central Limit ◽  
Historical Context ◽  
Binomial Theorem ◽  
The Central Limit Theorem ◽  
Large Numbers ◽  
First Time

This chapter advances the historical context for quantification by describing the climate of the day—social, cultural, political, and intellectual—as fraught with disquieting influences. Forces leading to the French Revolution were building, and the colonists in America were fighting for secession from England. During this time, three important number theorems came into existence: the binomial theorem, the law of large numbers, and the central limit theorem. Each is described in easy-to-understand language. These are fundamental to how numbers operate in a probability circumstance. Pascal’s triangle is explained as a shortcut solving some binomial expansions, and Jacob Bernoulli’s Ars Conjectandi, which presents the study of measurement “error” for the first time, is discussed. In addition, the central limit theorem is explained in terms of its relevance to probability theory, and its utility today.

Estimating detection probabilities of tagged fish migrating past fixed receiver stations using only local information

2010 ◽  
Vol 67 (4) ◽  
pp. 641-658 ◽  
Author(s):  
Michael C. Melnychuk ◽  
Carl J. Walters
Keyword(s):  
Detection Probability ◽  
Radio Telemetry ◽  
Model Parameters ◽  
Migration Routes ◽  
Mark Recapture ◽  
The Pacific ◽  
Detection Probabilities ◽  
Acoustic Tags ◽  
Attenuation Models ◽  
Local Detection

We developed a method to predict the probability of detecting acoustic tags crossing a receiver station using only detection information at that station. This method is suitable for acoustic or radio telemetry studies in which individually tagged animals migrate past fixed stations (where a station may consist of one or more receivers). It is based on fitting attenuation models to sequences of detections and missed transmissions of individually coded tags in fish migrating past stations of the Pacific Ocean Shelf Tracking Project (POST). We used estimated attenuation model parameters from detected fish at each station to predict the number of fish that crossed the station undetected, which in turn was used to calculate the local detection probability. This estimator was correlated (r = 0.54–0.81 in river and coastal habitats) with mark–recapture estimates of detection probability (pmr) that use nonlocal detection information at stations further along migration routes. This local detection probability estimate can be used as a covariate of pmr in mark–recapture models and can predict approximate values of pmr at final detection stations where pmr is not estimable because of the lack of recaptures further along migration routes.

scholarly journals Estimating Detection Probability and Density from Point-Count Surveys: A Combination of Distance and Double-Observer Sampling

The Auk ◽  
2006 ◽  
Vol 123 (3) ◽  
pp. 735-752 ◽  
Author(s):  
Michelle L. Kissling ◽  
Edward O. Garton
Keyword(s):  
Detection Probability ◽  
Survey Methods ◽  
Effective Area ◽  
Survey Method ◽  
Density Estimates ◽  
Point Count ◽  
Detection Probabilities ◽  
Fixed Radius ◽  
Count Surveys ◽  
Double Observer

Abstract Point counts are the method most commonly used to estimate abundance of birds, but they often fail to account properly for incomplete and variable detection probabilities. We developed a technique that combines distance and double-observer sampling to estimate detection probabilities and effective area surveyed. We applied this paired-observer, variable circular-plot (POVCP) technique to point-count surveys (n = 753) conducted in closed-canopy forests of southeast Alaska. Distance data were analyzed for each species to model a detection probability for each observer and calculate an estimate of density. We then multiplied each observer's density estimates by a correction factor to adjust for detection probabilities <1 at plot center. We compared analytical results from four survey methods: single-observer fixed-radius (50-m) plot; single-observer, variable circular-plot (SOVCP); double-observer fixed-radius (50-m) plot; and POVCP. We examined differences in detection probabilities at plot center, effective area surveyed, and densities for five bird species: Pacific-slope Flycatcher (Empidonax difficilis), Winter Wren (Troglodytes troglodytes), Golden-crowned Kinglet (Regulus satrapa), Hermit Thrush (Catharus guttatus), and Townsend's Warbler (Dendroica townsendi). Average detection probabilities for paired observers increased ≈8% (SE = 2.9) for all species once estimates were corrected for birds missed at plot center. Density estimators of fixed-radius survey methods were likely negatively biased, because the key assumption of perfect detection was not met. Density estimates generated using SOVCP and POVCP were similar, but standard errors were much lower for the POVCP survey method. We recommend using POVCP when study objectives require precise estimates of density. Failure to account for differences in detection probabilities and effective area surveyed results in biased population estimators and, therefore, faulty inferences about the population in question. Estimaciones de la Densidad y de las Probabilidades de Detección a Partir de Muestreos Utilizando Conteos en Puntos: Una Combinación de Muestreos de Distancia y de Doble Observador

scholarly journals Contribution to identify the causal gents of Dutch elm disease in the Czech Republic

2008 ◽  
Vol 43 (No. 4) ◽  
pp. 142-145 ◽  
Author(s):  
M. Dvořák ◽  
M. Tomšovský ◽  
L. Jankovský ◽  
D. Novotný
Keyword(s):  
Czech Republic ◽  
North America ◽  
Molecular Biology ◽  
The Other ◽  
Dutch Elm Disease ◽  
The Czech Republic ◽  
Ophiostoma Ulmi ◽  
Other Hand ◽  
Subspecies Level ◽  
First Time

This study provides new data on Dutch elm disease in the Czech Republic. <I>Ophiostoma novo-ulmi</I> is reported for the first time in the area of the Czech Republic, as well as both subspecies ssp. <I>novo-ulmi</I> (indigenous in the area of the Ukraine and Moldavia), and ssp. <I>Americana</I> indigenous in North America. The majority of the recorded strains belonged to <I>O. n.-u.</I> ssp. <I>novo-ulmi</I>, while <I>O. n.-u.</I> ssp. <I>Americana</I> and hybrids of these two subspecies were found less frequently. On the other hand, <I>Ophiostoma ulmi</I> was not found at all in the investigated samples. Identification on the subspecies level was performed by methods of molecular biology, i.e. PCR and RFLP of gene regions<I> cu</I> and <I>col1</I>.

Factors influencing detection probabilities of frogs in the monsoonal tropics of northern Australia: implications for the design of monitoring studies

2013 ◽  
Vol 40 (5) ◽  
pp. 393 ◽  
Author(s):  
P. L. Dostine ◽  
S. J. Reynolds ◽  
A. D. Griffiths ◽  
G. R. Gillespie
Keyword(s):  
Detection Probability ◽  
Individual Species ◽  
Sampling Effort ◽  
Northern Australia ◽  
Wet Season ◽  
Factors Influencing ◽  
Detection Probabilities ◽  
High Detection ◽  
Frog Species ◽  
A Site

Context Failure to acknowledge potential bias from imperfect detection of cryptic organisms such as frogs may compromise survey and monitoring programmes targeting these species. Aims The aims of the present study were to identify proximate factors influencing detection probabilities of a range of frog species in monsoonal northern Australia, and to estimate the number of repeat censuses required at a site to have confidence that non-detected species are absent. Methods Data on detection or non-detection of frog species based on calling individuals were recorded during 10 wet-season censuses of 29 survey sites in the Darwin region. Factors influencing detection probabilities were identified using occupancy models; model selection was based on the Akaike information criterion. Sampling effort for individual species was calculated using model predictions at different stages of the wet season. Key results The covariate water temperature featured in the best-supported models for 7 of the 14 frog species. Six of these species were more likely to be detected when water temperatures were below 30°C. Detection probabilities were also correlated with the number of days since the commencement of the wet season, time since last significant rainfall, air temperature and time after sunset. Required sampling effort for individual species varied throughout the wet season. For example, a minimum of two repeat censuses was required for detection of Litoria caerulea in the early wet season, but this number increased to 13 in the middle stage of the wet season. Conclusions Variability in environmental conditions throughout the wet season leads to variability in detection probabilities of frog species in northern Australia. Lower water temperatures, mediated by rainfall immediately before or during surveys, enhances detectability of a range of species. For most species, three repeat surveys under conditions resulting in a high detection probability are sufficient to determine presence at a site. Implications Survey and monitoring programmes for frogs in tropical northern Australia will benefit from the results of the present study by allowing targeting of conditions of high detection probability for individual species, and by incorporating sufficient repeat censuses to provide accurate assessment of the status of individual species at a site.

Randomized switching in the two-envelope problem

2009 ◽  
Vol 465 (2111) ◽  
pp. 3309-3322 ◽  
Author(s):  
Mark D. McDonnell ◽  
Derek Abbott
Keyword(s):  
Probability Theory ◽  
Decision Theory ◽  
New Approach ◽  
Switching Strategy ◽  
It Impacts ◽  
State Switching ◽  
Economics Literature ◽  
First Time ◽  
Deterministic Switching

The two-envelope problem is a conundrum in decision theory that is subject to longstanding debate. It is a counterintuitive problem of decidability between two different states, in the presence of uncertainty, where a player’s payoff must be maximized in some fashion. The problem is a significant one as it impacts on our understanding of probability theory, decision theory and optimization. It is timely to revisit this problem, as a number of related two-state switching phenomena are emerging in physics, engineering and economics literature. In this paper, we discuss this wider significance, and offer a new approach to the problem. For the first time, we analyse the problem by adopting Cover’s switching strategy—this is where we randomly switch states with a probability that is a smoothly decreasing function of the observed value of one state. Surprisingly, we show that the player’s payoff can be increased by this strategy. We also extend the problem to show that a deterministic switching strategy, based on a thresholded decision once the amount in an envelope is observed, is also workable.

Detection Probability of Airborne AIS

2013 ◽  
Vol 401-403 ◽  
pp. 1204-1207 ◽  
Author(s):  
She Xiang Ma ◽  
Jin Sun ◽  
Yong Qiang Guan
Keyword(s):  
Calculation Method ◽  
Detection Probability ◽  
Probability Model ◽  
Complicated Structure ◽  
Transmission Distance ◽  
Detection Probabilities ◽  
Simulation Results ◽  
The Relationship ◽  
Maximum Transmission

Aiming at the small coverage of shore-based AIS and complicated structure of space-based AIS, airborne AIS is chosen to increase the coverage effectively. This paper gives the calculation method of the maximum transmission distance, and then establishes the detection probability model of the airborne AIS. The relationship between reporting interval, ship densities and detection probabilities is established. At the end of the paper, simulation results of the model are given.

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