The Experts below are selected from a list of 309 Experts worldwide ranked by ideXlab platform
Wojciech Szpankowski - One of the best experts on this subject based on the ideXlab platform.
-
un Expected Behavior of digital search tree profile
Symposium on Discrete Algorithms, 2009Co-Authors: Michael Drmota, Wojciech SzpankowskiAbstract:A digital search tree (DST) -- one of the most fundamental data structures on words -- is a digital tree in which keys (strings, words) are stored directly in (internal) nodes. Such trees find myriad of applications from the popular Lempel-Ziv'78 data compression scheme to distributed hash tables. The profile of a DST measures the number of nodes at the same distance from the root; it is a function of the number of stored strings and the distance from the root. Most parameters of DST (e.g., height, fill-up) can be expressed in terms of the profile. However, from the inception of DST, the analysis of the profile has been elusive and it has become a prominent open problem in the area of analysis of algorithms. We make here the first, but decisive, step towards solving this problem. We present a precise analysis of the average profile when stored strings are generated by a biased memoryless source. The main technical difficulty of analyzing the profile lies in solving a sophisticated recurrence equation. We present such a solution for the Poissonized version of the problem (i.e., when the number of stored strings is generated by a Poisson distribution) in the Mellin transform domain. To accomplish it, we introduce a novel functional operator that allows us to express the solution in an explicit form, and then using analytic algorithmics tools to extract the asymptotic Behavior of the profile. This analysis is surprisingly demanding but once it is carried out it reveals unusually intriguing and interesting Behavior. The average profile undergoes several phase transitions when moving from the root to the longest path. At first, it resembles a full tree until it abruptly starts growing polynomially and it oscillates in this range. Our results are derived by methods of analytic algorithmics such as generating functions, Mellin transform, Poissonization and de-Poissonization, the saddle-point method, singularity analysis and uniform asymptotic analysis.
-
SODA - Un)Expected Behavior of digital search tree profile
2009Co-Authors: Michael Drmota, Wojciech SzpankowskiAbstract:A digital search tree (DST) -- one of the most fundamental data structures on words -- is a digital tree in which keys (strings, words) are stored directly in (internal) nodes. Such trees find myriad of applications from the popular Lempel-Ziv'78 data compression scheme to distributed hash tables. The profile of a DST measures the number of nodes at the same distance from the root; it is a function of the number of stored strings and the distance from the root. Most parameters of DST (e.g., height, fill-up) can be expressed in terms of the profile. However, from the inception of DST, the analysis of the profile has been elusive and it has become a prominent open problem in the area of analysis of algorithms. We make here the first, but decisive, step towards solving this problem. We present a precise analysis of the average profile when stored strings are generated by a biased memoryless source. The main technical difficulty of analyzing the profile lies in solving a sophisticated recurrence equation. We present such a solution for the Poissonized version of the problem (i.e., when the number of stored strings is generated by a Poisson distribution) in the Mellin transform domain. To accomplish it, we introduce a novel functional operator that allows us to express the solution in an explicit form, and then using analytic algorithmics tools to extract the asymptotic Behavior of the profile. This analysis is surprisingly demanding but once it is carried out it reveals unusually intriguing and interesting Behavior. The average profile undergoes several phase transitions when moving from the root to the longest path. At first, it resembles a full tree until it abruptly starts growing polynomially and it oscillates in this range. Our results are derived by methods of analytic algorithmics such as generating functions, Mellin transform, Poissonization and de-Poissonization, the saddle-point method, singularity analysis and uniform asymptotic analysis.
-
un Expected Behavior of typical suffix trees
Symposium on Discrete Algorithms, 1992Co-Authors: Wojciech SzpankowskiAbstract:Suffix tree is a data structure widely used in algorithms on words and data compression. Despite this, very little is known about its typical Behavior. Recently, Chang and Lawler have designed a sublinear Expected time algorithm for approximate string matching using simple estimates of some parameters of suffix trees. It seems that any further advances in such an endover are subject to better understanding of suffix trees Behavior. In this paper, we use a novel technique called string ruler approach to provide a characterization of several basic parameters of suffix trees (dependency among symbols are allowed !). These findings are used to :(i) settle in the negative the conjecture of Wyner and Ziv regarding the typical Behavior of the universal data compression scheme of Lampel and Ziv; (ii) prove an open problem regarding the length of a block in the Lampel-Ziv parsing algorithm; (iii) provide new insights and generalizations of string matching algorithms, particularly the one by Chang and Lawler.
-
SODA - Un)Expected Behavior of typical suffix trees
1992Co-Authors: Wojciech SzpankowskiAbstract:Suffix tree is a data structure widely used in algorithms on words and data compression. Despite this, very little is known about its typical Behavior. Recently, Chang and Lawler have designed a sublinear Expected time algorithm for approximate string matching using simple estimates of some parameters of suffix trees. It seems that any further advances in such an endover are subject to better understanding of suffix trees Behavior. In this paper, we use a novel technique called string ruler approach to provide a characterization of several basic parameters of suffix trees (dependency among symbols are allowed !). These findings are used to :(i) settle in the negative the conjecture of Wyner and Ziv regarding the typical Behavior of the universal data compression scheme of Lampel and Ziv; (ii) prove an open problem regarding the length of a block in the Lampel-Ziv parsing algorithm; (iii) provide new insights and generalizations of string matching algorithms, particularly the one by Chang and Lawler.
Ramandeep S Johal - One of the best experts on this subject based on the ideXlab platform.
-
Expected Behavior of quantum thermodynamic machines with prior information.
Physical review. E Statistical nonlinear and soft matter physics, 2012Co-Authors: George Thomas, Ramandeep S JohalAbstract:We estimate the Expected Behavior of the quantum model of a heat engine when we have incomplete information about external macroscopic parameters such as the magnetic field controlling the intrinsic energy scales of the working medium. We explicitly derive the prior probability distribution for these unknown parameters ai (i=1,2). Based on a few simple assumptions, the prior probability distribution is found to be of the form Π(ai)∝1/ai. By calculating the Expected values of various physical quantities related to this engine, we find that the Expected Behavior of the quantum model exhibits thermodynamiclike features. This leads us to a surprising proposal that incomplete information quantified as an appropriate prior distribution can lead us to expect classical thermodynamic Behavior in quantum models.
-
Expected Behavior of quantum thermodynamic machines with prior information
Physical Review E, 2012Co-Authors: George Thomas, Ramandeep S JohalAbstract:We estimate the Expected Behavior of the quantum model of a heat engine when we have incomplete information about external macroscopic parameters such as the magnetic field controlling the intrinsic energy scales of the working medium. We explicitly derive the prior probability distribution for these unknown parameters ${a}_{i}\phantom{\rule{0.28em}{0ex}}\phantom{\rule{4pt}{0ex}}(i=1,2)$. Based on a few simple assumptions, the prior probability distribution is found to be of the form $\ensuremath{\Pi}({a}_{i})\ensuremath{\propto}1/{a}_{i}$. By calculating the Expected values of various physical quantities related to this engine, we find that the Expected Behavior of the quantum model exhibits thermodynamiclike features. This leads us to a surprising proposal that incomplete information quantified as an appropriate prior distribution can lead us to expect classical thermodynamic Behavior in quantum models.
George Thomas - One of the best experts on this subject based on the ideXlab platform.
-
Expected Behavior of quantum thermodynamic machines with prior information.
Physical review. E Statistical nonlinear and soft matter physics, 2012Co-Authors: George Thomas, Ramandeep S JohalAbstract:We estimate the Expected Behavior of the quantum model of a heat engine when we have incomplete information about external macroscopic parameters such as the magnetic field controlling the intrinsic energy scales of the working medium. We explicitly derive the prior probability distribution for these unknown parameters ai (i=1,2). Based on a few simple assumptions, the prior probability distribution is found to be of the form Π(ai)∝1/ai. By calculating the Expected values of various physical quantities related to this engine, we find that the Expected Behavior of the quantum model exhibits thermodynamiclike features. This leads us to a surprising proposal that incomplete information quantified as an appropriate prior distribution can lead us to expect classical thermodynamic Behavior in quantum models.
-
Expected Behavior of quantum thermodynamic machines with prior information
Physical Review E, 2012Co-Authors: George Thomas, Ramandeep S JohalAbstract:We estimate the Expected Behavior of the quantum model of a heat engine when we have incomplete information about external macroscopic parameters such as the magnetic field controlling the intrinsic energy scales of the working medium. We explicitly derive the prior probability distribution for these unknown parameters ${a}_{i}\phantom{\rule{0.28em}{0ex}}\phantom{\rule{4pt}{0ex}}(i=1,2)$. Based on a few simple assumptions, the prior probability distribution is found to be of the form $\ensuremath{\Pi}({a}_{i})\ensuremath{\propto}1/{a}_{i}$. By calculating the Expected values of various physical quantities related to this engine, we find that the Expected Behavior of the quantum model exhibits thermodynamiclike features. This leads us to a surprising proposal that incomplete information quantified as an appropriate prior distribution can lead us to expect classical thermodynamic Behavior in quantum models.
Lawrence E. Holloway - One of the best experts on this subject based on the ideXlab platform.
-
ACC - Qualitative diagnosis of condition systems for multiple subsystem failures
2007 American Control Conference, 2007Co-Authors: J. Ashley, Lawrence E. Holloway, Ratnesh KumarAbstract:Condition systems are a form of Petri nets that interact with each other and the external environment through condition signals. Some of these condition signals may be unobservable. In previous work, fault diagnosis was defined in terms of observed Behavior versus Expected Behavior of subsystem models under a single fault assumption, where the Expected Behavior is defined through condition system models, and approximate methods were presented for detection and diagnosis. In this paper, we present an exact diagnosis method for a system that may experience multiple subsystem faults.
-
ETFA - Exploiting causal structure in the refined diagnosis of condition systems
2006 IEEE Conference on Emerging Technologies and Factory Automation, 2006Co-Authors: J. Ashley, Lawrence E. HollowayAbstract:A condition system is a collection of Petri nets that interact with each other and the external environment through condition signals. Some of these condition signals may be unobservable. In previous work, fault diagnosis was defined in terms of observed Behavior versus Expected Behavior of subsystem models, where the Expected Behavior is defined through condition system models, and approximate methods were presented for detection and diagnosis. We have also presented a method to determine a best possible diagnosis within the constraints of observability. However this method requires significant state space exploration. In this paper, we wish to exploit the causal structure imposed on the system by a partition of subsystem models in order to reduce (in certain situations) the amount of work required to perform a diagnosis.
-
exploiting causal structure in the refined diagnosis of condition systems
Emerging Technologies and Factory Automation, 2006Co-Authors: J. Ashley, Lawrence E. HollowayAbstract:A condition system is a collection of Petri nets that interact with each other and the external environment through condition signals. Some of these condition signals may be unobservable. In previous work, fault diagnosis was defined in terms of observed Behavior versus Expected Behavior of subsystem models, where the Expected Behavior is defined through condition system models, and approximate methods were presented for detection and diagnosis. We have also presented a method to determine a best possible diagnosis within the constraints of observability. However this method requires significant state space exploration. In this paper, we wish to exploit the causal structure imposed on the system by a partition of subsystem models in order to reduce (in certain situations) the amount of work required to perform a diagnosis.
-
Qualitative Diagnosis of Condition Systems
Discrete Event Dynamic Systems, 2004Co-Authors: J. Ashley, Lawrence E. HollowayAbstract:A condition system is a collection of Petri nets that interact with each other and the external environment through condition signals. Some of these condition signals may be unobservable. In this paper, a system fault is defined in terms of observed Behavior versus Expected Behavior, where the Expected Behavior is defined through condition system models. A diagnosis of this fault localizes the subsystem that is the source of the discrepancy between output and Expected observations. We show that the structure of the interacting subsystems define a diagnostic causal model that captures the causal structure of subsystem dependencies. The diagnostic causal model can then be used to determine a set of subsystems that might be the source of a fault.
-
diagnosis of condition systems using diagnostic causal networks
Systems Man and Cybernetics, 2001Co-Authors: J. Ashley, Lawrence E. HollowayAbstract:A condition system is a collection of Petri nets that interact with each other and the external environment through condition signals. Some of these condition signals may be unobservable. In this paper, a system failure is defined in terms of observed Behavior versus Expected Behavior, where the Expected Behavior is defined through condition system models. A. diagnosis of this failure localizes the subsystem that is the source of the discrepancy between output and Expected observations. We show that the structure of the interacting subsystems define a diagnostic causal model that captures the causal structure of subsystem dependencies. The diagnostic causal model can then be used to determine a set of subsystems that might be the source of a failure.
Michael Drmota - One of the best experts on this subject based on the ideXlab platform.
-
un Expected Behavior of digital search tree profile
Symposium on Discrete Algorithms, 2009Co-Authors: Michael Drmota, Wojciech SzpankowskiAbstract:A digital search tree (DST) -- one of the most fundamental data structures on words -- is a digital tree in which keys (strings, words) are stored directly in (internal) nodes. Such trees find myriad of applications from the popular Lempel-Ziv'78 data compression scheme to distributed hash tables. The profile of a DST measures the number of nodes at the same distance from the root; it is a function of the number of stored strings and the distance from the root. Most parameters of DST (e.g., height, fill-up) can be expressed in terms of the profile. However, from the inception of DST, the analysis of the profile has been elusive and it has become a prominent open problem in the area of analysis of algorithms. We make here the first, but decisive, step towards solving this problem. We present a precise analysis of the average profile when stored strings are generated by a biased memoryless source. The main technical difficulty of analyzing the profile lies in solving a sophisticated recurrence equation. We present such a solution for the Poissonized version of the problem (i.e., when the number of stored strings is generated by a Poisson distribution) in the Mellin transform domain. To accomplish it, we introduce a novel functional operator that allows us to express the solution in an explicit form, and then using analytic algorithmics tools to extract the asymptotic Behavior of the profile. This analysis is surprisingly demanding but once it is carried out it reveals unusually intriguing and interesting Behavior. The average profile undergoes several phase transitions when moving from the root to the longest path. At first, it resembles a full tree until it abruptly starts growing polynomially and it oscillates in this range. Our results are derived by methods of analytic algorithmics such as generating functions, Mellin transform, Poissonization and de-Poissonization, the saddle-point method, singularity analysis and uniform asymptotic analysis.
-
SODA - Un)Expected Behavior of digital search tree profile
2009Co-Authors: Michael Drmota, Wojciech SzpankowskiAbstract:A digital search tree (DST) -- one of the most fundamental data structures on words -- is a digital tree in which keys (strings, words) are stored directly in (internal) nodes. Such trees find myriad of applications from the popular Lempel-Ziv'78 data compression scheme to distributed hash tables. The profile of a DST measures the number of nodes at the same distance from the root; it is a function of the number of stored strings and the distance from the root. Most parameters of DST (e.g., height, fill-up) can be expressed in terms of the profile. However, from the inception of DST, the analysis of the profile has been elusive and it has become a prominent open problem in the area of analysis of algorithms. We make here the first, but decisive, step towards solving this problem. We present a precise analysis of the average profile when stored strings are generated by a biased memoryless source. The main technical difficulty of analyzing the profile lies in solving a sophisticated recurrence equation. We present such a solution for the Poissonized version of the problem (i.e., when the number of stored strings is generated by a Poisson distribution) in the Mellin transform domain. To accomplish it, we introduce a novel functional operator that allows us to express the solution in an explicit form, and then using analytic algorithmics tools to extract the asymptotic Behavior of the profile. This analysis is surprisingly demanding but once it is carried out it reveals unusually intriguing and interesting Behavior. The average profile undergoes several phase transitions when moving from the root to the longest path. At first, it resembles a full tree until it abruptly starts growing polynomially and it oscillates in this range. Our results are derived by methods of analytic algorithmics such as generating functions, Mellin transform, Poissonization and de-Poissonization, the saddle-point method, singularity analysis and uniform asymptotic analysis.
