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Markov Processes and Related Fields
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Optimal asynchronous estimation of 2D Gaussian-Markov processes
PublicationW artykule rozważa się problem estymacji trajektorii dwuwymiarowych ciągłoczasowych procesów Gaussa-Markowa na podstawie zaszumionych pomiarów wykonywanych w nierównomiernie rozłożonych chwilach czasu. W przypadku takiego problemu, w każdym cyklu pracy algorytmu należy dokonać dyskretnoczasowej predykcji (analogicznie jak w przypadku filtru Kalmana). Niestety zadanie to może być złożone obliczeniowo. Aby rozwiązać ten problem,...
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COMPARATIVE ANALYSIS OF RESULTS OF APPLICATION OF MARKOV AND SEMI-MARKOV PROCESSES TO RELIABILITY MODELS OF MULTI-STATE TECHNICAL OBJECTS
PublicationDuring rational operation of technical objects and systems various operational decisions are made and decision-making process itself should be consisted in selecting that considered most favourable out of all possible to be taken. Choice of such decision is possible after taking into account many different information items but it never be completely correct without accounting for data and indices dealing with reliability. In...
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Application of semi-Markov processes for evaluation of diesel engines reliability with regards to diagnostics
PublicationThe paper presents semi-Markov models of technical state transitions for diesel engines, useful for determination of their reliability, as a result of the conducted statistical empirical studies. Interpretation of technical states provided for this sort of engines refers to ship main engines, i.e. engines employed in propulsion systems of sea-going ships. The considerations recognize diesel engine as a diagnosed system (SDN), of...
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Necessity for and possibility of application of the theory of semi-markov processes to determine reliability of diagnising systems
PublicationW opracowaniu uzasadniono konieczność określenia niezawodności systemów diagnozujących (SDG) do sformułowania diagnozy o stanie dowolnego urządzenia technicznego jako systemu diagnozowanego (SDN). Wykazano, że znajomość niezawodności SDG umożliwia określenie wiarygodności diagnozy. Przyjęto, że wiarygodność diagnozy może być określona jako właściwość diagnozy określająca stopień rozpoznania przez system diagnozujący (SDG) rzeczywistego...
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USEFULNESS OF SEMI-MARKOV PROCESSES AS MODELS OF THE OPERATION PROCESSES FOR MARINE MAIN ENGINES AND OTHER MACHINES OF SHIP POWER PLANTS
PublicationThe paper describes the properties of semi-Markov processes and the opportunities and benefits from their use as models of the operation processes for marine combustion engines and other machines of ship power plants. The emphasis is put on the importance of the theory of semi-Markov processes for development of the theory of marine combustion engines and other machines of ship power plants, as well as for development of the operational...
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Assesment of operation of ship main diesel engine using the theory of semi-markovian and markov processes.
PublicationTo precisely determine the task it is necessary to specify also its duration time, apart from conditions in which it will be realized. When considering propulsion engine, i.e. the main element of ship propulsion system, especially important becomes not only the problem which amount of energy could be at one's disposal but also within which time interval it could be delivered. Therefore apart from applying the commonly used reliability...
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Application of theory of semi-Markov processes to determining distribution of probabilistic process of marine accidents resulting from colission of ships
PublicationIn this paper is presented possible application of the theory of semi-Markov processes to elaborating an eight-state model of the process of occurrence of serviceability state and unserviceability states of sea-going ships making critical manoeuvres during their entering and leaving the ports. In the analysis it was taken into account that sea-going ships are in service for a very long time t (t → ∞). The model was elaborated to...
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APPLICATION OF THE THEORY OF SEMI-MARKOV PROCESSES TO DETERMINE A LIMITING DISTRIBUTION OF THE PROCESS OF CHANGES OF ABILITY AND INABILITY STATES OF FUEL SUPPLY SYSTEMS IN HEAVY FUEL DIESEL ENGINES
PublicationThe paper presents applicability of the theory of semi-Markov processes to determine a limiting distribution of the process of changes of technical states of fuel systems for marine engines running on heavy fuel oils. The proposed study of this process includes the components of such fuel systems like: 1 - injectors, 2 - high pressure hoses, 3 - injection pumps, 4 - low pressure hoses, 5 – fine filters, 6 - coarse filters, 7 – fuel-feed...
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A model of fuel combustion process in the marine reciprocating engine work space taking into account load and wear of crankshaft-piston assembly and the theory of semi-Markov processes
PublicationThe ar ticle analyses the operation of reciprocal internal combu stion engines, with mar ine engines u sed a s an example. The analysis takes into account types of energy conversion in the work spaces (cylinders) of these engines, loads of their crankshaft-piston assemblies, and types of fuel combustion which can take place in these spaces during engine operation. It is highlighted that the analysed time-dependent loads of marine...
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Application of the theory of semi-markov processes to the development of a reliability model of an automotiv vrhicle = Zastosowanie teorii procesów semi-Markowa do opracowania modelu niezawodnościowego samochodu
PublicationW artykule przedstawiono możliwość zastosowania teorii procesów semi-Markowa (semimarkowskich) do opisu niezawodności samochodu, na przykładzie samochodu osobowego. W rozważaniach uwzględniony został samochód, w którym wyróżniono takie węzły konstrukcyjne (zespoły funkcjonalne) jak: silnik z układami zasilania czynnikami energetycznymi (paliwem, olejem smarowym i cieczą chłodzącą), sprzęgło, skrzynia biegów, wał napędowy, most...
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The Matter of Decision-Making Control Over Operation Processes of Marine Power Plant Systems with the Use of their Models in the form of Semi-Markov Decision-Making Processes
PublicationThe article presents the possibility to control the real operation process of an arbitrary device installed in the marine power plant based on the four-state semi-Markov process, being the model of the process, which describes the transition process of operational states of the device and the transition process of its technical states. All these states are precisely defined for the ship main engine (SG). A hypothesis is proposed...
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Możliwość oszacowania niezawodności silników o zapłonie samoczynnym z zastosowaniem teorii procesów semi-Markowa oraz podejmowania decyzji eksploatacyjnych z uwzględnieniem wiarygodności diagnozy o stanie technicznym tego rodzaju silników spalinowych = Possibility of estimating the reliability of diesel engines by applying the theory of semi-Markov processes and making operational decisions by considering reliability of diagnosis on technical state of this sort of combustion engines/
PublicationThe paper presents semi-Markov models of technical state transitions for diesel engines, useful for determining reliability of the engines. A possibility of application of a three-state model with a simplified matrix function, or even a two-state model, to determine reliability of the engines, has been described herein on examples of known from literature semi-Markov models, for the case when appropriate diagnosing systems (SDG)...
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Types of Markov Fields and Tilings
PublicationThe method of types is one of the most popular techniques in information theory and combinatorics. However, thus far the method has been mostly applied to one-dimensional Markov processes, and it has not been thoroughly studied for general Markov fields. Markov fields over a finite alphabet of size m ≥ 2 can be viewed as models for multi-dimensional systems with local interactions. The locality of these interactions is represented...
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Usage of Memi-Markov Process in Operation Evaluation of Diesel Engine
PublicationIn paper, the proposition of quantitative evaluation of operation using semi-Markov processes theories has been presented. Basic assumptions, essential for creating mathematical model on example of diesel engine were shown. Special attention was given to practical aspects of using established mathematical model. Example of characteristic of analysed process - temporary distribution of probability was assigned.
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TEORIA DECYZYJNYCH PROCESÓW SEMI-MARKOWA I JEJ ZASTOSOWANIE W PROJEKTOWANIU I EKSPLOATACJI OKRĘTOWYCH SILNIKÓW GŁÓWNYCH I INNYCH URZĄDZEŃ SIŁOWNI OKRĘTOWYCH
PublicationW referacie zaprezentowano znaczenie teorii procesów semi-Markowa w naukach technicznych, zwłaszcza w teorii niezawodności urządzeń technicznych, teorii bezpieczeństwa ich działania oraz statystycznej teorii podejmowania decyzji eksploatacyjnych. W referacie wyeksponowano także przydatność teorii procesów semi-Markowa w teorii i praktyce eksploatacji wspomnianych urządzeń technicznych na przykładzie tak istotnych urządzeń w transporcie...
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The semi-Markov model of the process of appearance of sea-going ship propupsion system ability and inability states in application to determining the reliablity of these systems
PublicationThe article presents possible application of the theory of semi-Markov processes in creating the eight-state model of the process of appearance of the propulsion systems ability and inability states on sea-going vessels performing transportation tasks in a relatively long operating time t (t → ∞). The model has been proved to be able to be successfully used for determining the reliability of the abovementioned systems. The probability...
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Four-state stochastic model of changes in the reliability states of a motor vehicle
PublicationThe properties of semi-Markov processes have been generally characterized and the applicability of the theory of such processes to the determining of the reliability of motor cars and other road vehicles has been explained. A formal description of the process of changes in the motor vehicle technical states considered as reliability states and a model of this process in the form of a one-dimensional stochastic process have been...
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Determination of probabilities defining safety of a sea-going ship during performance of a transportation task in stormy weather conditions
PublicationThe paper presents the possibility of applying the theory of semi-Markov processes to determine the limiting distribution for the process of changes of technical states being reliability states of the systems of sea-going ships significantly affecting safety of such ships, which include main engine, propeller and steering gear. The distribution concerns the probabilities of occurrence of the said states defined for a long time...
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A Method for The Assessing of Reliability Characteristics Relevant to an Assumed Position-Fixing Accuracy in Navigational Positioning Systems
PublicationThis paper presents a method which makes it possible to determine reliability characteristics of navigational positioning systems, relevant to an assumed value of permissible error in position fixing. The method allows to calculate: availability , reliability as well as operation continuity of position fixing system for an assumed, determined on the basis of formal requirements - both worldwide and national, position-fixing accuracy....
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Features of load and wear of main propulsion devices on sea-going ships with piston combustion engines and their impact on changes in technical states of the systems
PublicationThe paper presents the specificity of operation of propulsion systems of seagoing ships which causes the need to control the load on them, especially on their engines called main engines. The characteristics of the load on the propulsion systems, especially on the main engines as well as on the shaft lines and propellers driven by the engines, along with the process of wear in tribological joints (sliding tribological systems)...
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PROBLEMY RACJONALNEGO ZASTOSOWANIA SYSTEMÓW DIAGNOZUJĄCYCH DO PODEJMOWANIA DECYZJI W FAZIE EKSPLOATACJI URZĄDZEŃ ENERGETYCZNYCH Z UWZGLĘDNIENIEM ZAGADNIEŃ KWANTOWYCH
PublicationW rozdziale przedstawiono najistotniejsze problemy pojawiające się w fazie projektowania, wytwarzania i eksploatacji systemów diagnozujących (SDG) urządzeń energetycznych (będących systemami diagnozowanymi – SDN), w przypadku przysposabiania ich do opracowania finalnej diagnozy eksploatacyjnej. Przestawiono opisową i formalną interpretację pojęcia systemu diagnozującego (SDG). Zaproponowano modele procesu diagnozowania urządzeń...
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ISSUE OF MAKING DECISIONS WITH REGARD TO SHIP TRAFFIC SAFETY IN DIFFERENT SITUATIONS AT SEA
PublicationThe paper refers to the possibilities of making operational decisions that would enable to ensure safety to a ship in the event of application of the statistical decision theory with consideration of an expected value of consequences as a criterion for making such a decision. General description includes conditions for carrying out transportation tasks by ships and it has been shown that following this description it is possible...
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Markov Model of Disease Development and Recovery
PublicationMarkov models are commonly used to simulate diseases and allow modeling of multiple health states and outcomes. Starting with the well known Le Bras multistate model (cascading failure model) with time-independent transitions we will see how simple Markov mortality models may be pressed into the service of survival and event history analysis. We will focus on more complex models which will be able to take into account remission,...
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Simple SIR models with Markovian control
PublicationWe consider a random dynamical system, where the deterministic dynamics are driven by a finite-state space Markov chain. We provide a comprehensive introduction to the required mathematical apparatus and then turn to a special focus on the susceptible-infected-recovered epidemiological model with random steering. Through simulations we visualize the behaviour of the system and the effect of the high-frequency limit of the driving...
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A note on a Wiener-Wintner theorem for mean ergodic Markov amenable semigroups
PublicationWe prove a Wiener-Wintner ergodic type theorem for a Markov representation of a right amenable semitopological semigroup.
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Międzysektorowa mobilność zatrudnienia oraz płac a efektywność rynku pracy.
PublicationCelem artykułu jest uzyskanie odpowiedzi na pytanie, czy ocenę efektywności funkcjonowania rynków pracy, rozumianej jako zdolność rynków do „oczyszczania się”, można przedstawić za pomocą analizy międzysektorowej mobilności płac oraz zatrudnienia. W połowie lat 90. XX wieku Paul Krugman dowodził, iż negatywne szoki gospodarcze skutkują w krajach europejskich wzrostem bezrobocia, natomiast w USA wzrostem rozpiętości płac. Tymczasem...
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Hybrid of Neural Networks and Hidden Markov Models as a modern approach to speech recognition systems
PublicationThe aim of this paper is to present a hybrid algorithm that combines the advantages ofartificial neural networks and hidden Markov models in speech recognition for control purpos-es. The scope of the paper includes review of currently used solutions, description and analysis of implementation of selected artificial neural network (NN) structures and hidden Markov mod-els (HMM). The main part of the paper consists of a description...
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Average Redundancy of the Shannon Code for Markov Sources
PublicationIt is known that for memoryless sources, the average and maximal redundancy of fixed–to–variable length codes, such as the Shannon and Huffman codes, exhibit two modes of behavior for long blocks. It either converges to a limit or it has an oscillatory pattern, depending on the irrationality or rationality, respectively, of certain parameters that depend on the source. In this paper, we extend these findings, concerning the Shannon...
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Karol Flisikowski dr inż.
PeopleKarol Flisikowski works as Associate Professor at the Department of Statistics and Econometrics, Faculty of Management and Economics, Gdansk University of Technology. He is responsible for teaching descriptive and mathematical statistics (in Polish and English), as well as scientific research in the field of social statistics. He has been a participant in many national and international conferences, where he has presented the results...
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Limits Theorems for Random Walks on Homeo(S1)
PublicationThe central limit theorem and law of the iterated logarithm for Markov chains corresponding to random walks on the space Homeo(S1) of circle homeomorphisms for centered Lipschitz functions and every starting point are proved.
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The use of Markov chains in the social convergence analysis
PublicationThe main goal of this article is to analyze the social convergence process using Markov chains. In this research, term social convergence refers to the reduction of dispersion in the standard of living among countries. The use of Markov chains in the social convergence analysis allowed describing movements of observational units within the distribution and providing more details about the mechanism of the convergence process. A...
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Generalized Dobrushin Coefficients on Banach Spaces
PublicationThe asymptotic behavior of iterates of bounded linear operators (not necessarily positive), acting on Banach spaces, is studied. Through the Dobrushin ergodicity coefficient, we generalize some ergodic theorems obtained earlier for classical Markov semigroups acting on L1 (or positive operators on abstract state spaces).
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Survival time prognosis under a Markov model of cancer development
PublicationIn this study we look at a breast cancer data set of women from Pomerania region collected in year 1987-1992 in the Medical University of Gdańsk. We analyze the clinical risk factors in conjunction with Markov model of cancer development. We evaluate Artificial Neural Network (ANN) survival time prediction via a simulation study.
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On mixing in the class of quadratic stochastic operators
PublicationWe study different types of limit behavior of quadratic stochastic operators acting on ℓ^1 (or ℓ^1_d) spaces in both strong and uniform topologies. The main motif of the paper is to express the uniform and strong asymptotic stability of the quadratic stochastic operator in terms of convergence of the associated (linear) nonhomogeneous Markov chain. We also examine which type of uniform convergence of iterates of the quadratic...
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Asymptotic behaviour in the set of nonhomogeneous chains of stochastic operators
PublicationWe study different types of asymptotic behaviour in the set of (infinite dimensional) nonhomogeneous chains of stochastic operators acting on L1(μ) spaces. In order to examine its structure we consider different norm and strong operator topologies. To describe the nature of the set of nonhomogeneous chains of Markov operators with a particular limit behaviour we use the category theorem of Baire. We show that the geometric structure...
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Asymptotic properties of quadratic stochastic operators acting on the L1 space
PublicationQuadratic stochastic operators can exhibit a wide variety of asymptotic behaviours and these have been introduced and studied recently in the ℓ1 space. It turns out that in principle most of the results can be carried over to the L1 space. However, due to topological properties of this space one has to restrict in some situations to kernel quadratic stochastic operators. In this article we study the uniform and strong asymptotic...
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Application possibilities of LBN for civil engineering issues
PublicationBayesian Networks (BN) are efficient to represent knowledge and for the reasoning in uncertainty. However the classic BN requires manual definition of the network structure by an expert, who also defines the values entered into the conditional probability tables. In practice, it can be time-consuming, hence the article proposes the use of Learning Bayesian Networks (LBN). The aim of the study is not only to present LBN, which can...
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A Noether theorem for stochastic operators on Schatten classes
PublicationWe prove that a stochastic (Markov) operator S acting on a Schatten class C_1 satisfies the Noether condition S'(A) = A and S'(A^2) = A^2, where A is a Hermitian bounded linear operator on a complex Hilbert space H, if and only if, S(E(G)XE(G)) = E(G)S(X)E(G) holds true for every Borel subset G of the real line R, where E(G) denotes the orthogonal projection coming from the spectral resolution of A. Similar results are obtained...
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Melody Harmonization with Interpolated Probabilistic Models
PublicationMost melody harmonization systems use the generative hidden Markov model (HMM), which model the relation between the hidden chords and the observed melody. Relations to other variables, such as the tonality or the metric structure, are handled by training multiple HMMs or are ignored. In this paper, we propose a discriminative means of combining multiple probabilistic models of various musical variables by means of model interpolation....
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Equivalence of equicontinuity concepts for Markov operators derived from a Schur-like property for spaces of measures
PublicationVarious equicontinuity properties for families of Markov operators have been – and still are – used in the study of existence and uniqueness of invariant probability for these operators, and of asymptotic stability. We prove a general result on equivalence of equicontinuity concepts. It allows comparing results in the literature and switching from one view on equicontinuity to another, which is technically convenient in proofs....
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Machine Learning-Based Wetland Vulnerability Assessment in the Sindh Province Ramsar Site Using Remote Sensing Data
PublicationWetlands provide vital ecological and socioeconomic services but face escalating pressures worldwide. This study undertakes an integrated spatiotemporal assessment of the multifaceted vulnerabilities shaping Khinjhir Lake, an ecologically significant wetland ecosystem in Pakistan, using advanced geospatial and machine learning techniques. Multi-temporal optical remote sensing data from 2000 to 2020 was analyzed through spectral...
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Examining Influence of Distance to Microphone on Accuracy of Speech Recognition
PublicationThe problem of controlling a machine by the distant-talking speaker without a necessity of handheld or body-worn equipment usage is considered. A laboratory setup is introduced for examination of performance of the developed automatic speech recognition system fed by direct and by distant speech acquired by microphones placed at three different distances from the speaker (0.5 m to 1.5 m). For feature extraction from the voice signal...
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Positron scattering on molecular hydrogen: Analysis of experimental and theoretical uncertainties
PublicationExperiments performed in recent years on positron scattering from molecular hydrogen indicated a rise of the total cross section in the limit of zero energy, but essentially disagree on the amplitude of this rise. Mitroy and collaborators [J.-Y. Zhang et al., Phys. Rev. Lett. 103, 223202 (2009)] predicted a scattering length somewhat different from values deduced experimentally. Using a Markov chain Monte Carlo modified effective...
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A comparative study of English viseme recognition methods and algorithms
PublicationAn elementary visual unit – the viseme is concerned in the paper in the context of preparing the feature vector as a main visual input component of Audio-Visual Speech Recognition systems. The aim of the presented research is a review of various approaches to the problem, the implementation of algorithms proposed in the literature and a comparative research on their effectiveness. In the course of the study an optimal feature vector construction...
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A comparative study of English viseme recognition methods and algorithm
PublicationAn elementary visual unit – the viseme is concerned in the paper in the context of preparing the feature vector as a main visual input component of Audio-Visual Speech Recognition systems. The aim of the presented research is a review of various approaches to the problem, the implementation of algorithms proposed in the literature and a comparative research on their effectiveness. In the course of the study an optimal feature vector...
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On reliability assessment of ship machinery system in different autonomy degree; A Bayesian-based approach
PublicationAnalyzing the reliability of autonomous ships has recently attracted attention mainly due to epistemic uncertainty (lack of knowledge) integrated with automatic operations in the maritime sector. The advent of new random failures with unrecognized failure patterns in autonomous ship operations requires a comprehensive reliability assessment specifically aiming at estimating the time in which the ship can be trusted to be left unattended....
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EXAMINING INFLUENCE OF VIDEO FRAMERATE AND AUDIO/VIDEO SYNCHRONIZATION ON AUDIO-VISUAL SPEECH RECOGNITION ACCURACY
PublicationThe problem of video framerate and audio/video synchronization in audio-visual speech recognition is considered. The visual features are added to the acoustic parameters in order to improve the accuracy of speech recognition in noisy conditions. The Mel-Frequency Cepstral Coefficients are used on the acoustic side whereas Active Appearance Model features are extracted from the image. The feature fusion approach is employed. The...
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EXAMINING INFLUENCE OF VIDEO FRAMERATE AND AUDIO/VIDEO SYNCHRONIZATION ON AUDIO-VISUAL SPEECH RECOGNITION ACCURACY
PublicationThe problem of video framerate and audio/video synchronization in audio-visual speech recogni-tion is considered. The visual features are added to the acoustic parameters in order to improve the accuracy of speech recognition in noisy conditions. The Mel-Frequency Cepstral Coefficients are used on the acoustic side whereas Active Appearance Model features are extracted from the image. The feature fusion approach is employed. The...
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Towards More Realistic Probabilistic Models for Data Structures: The External Path Length in Tries under the Markov Model
PublicationTries are among the most versatile and widely used data structures on words. They are pertinent to the (internal) structure of (stored) words and several splitting procedures used in diverse contexts ranging from document taxonomy to IP addresses lookup, from data compression (i.e., Lempel- Ziv'77 scheme) to dynamic hashing, from partial-match queries to speech recognition, from leader election algorithms to distributed hashing...