Analytical and Quantitative Cytology and Histology the International Academy of Cytology and American Society of Cytology, 2004
To introduce a new mathematical method based on the principles of fractal geometry analysis that ... more To introduce a new mathematical method based on the principles of fractal geometry analysis that permits more realistic quantification of some of the physical (morphologic) aspects of irregular bodies appearing under microscopy. The principles of the method were tested on microscopic images of irregular collagen deposition in liver tissue. The method uses an ad hoc rectified meter implemented in a computer-assisted planar image analysis system that has been adapted to give metric measures of irregular outlines and surfaces that can be used to produce an index capable of quantifying the typical wrinkledness of biologic objects. Prototypical example measures of liver fibrosis were made on biopsy specimens showing chronic hepatitis C virus-related disease. Measurements were also made of the microscopic images of the abnormal deposition of lipid droplets in hepatocytes, a case of amyloid deposition in an osteoarthromuscular structure and a cytologic specimen of human dendritic cells. The proposed computer-aided method permits rapid measurements of the image of a whole biopsy section digitized at high magnification. The snapshot measurement of liver fibrosis deposition offered by a biopsy pattern is a valid means of more rigorously identifying the staging of the process. This method can measure liver fibrosis during chronic liver disease as well as any other irregular biologic structure that cannot be correctly quantified using traditional Euclidean-based metric methodologies.
Observations which are realizations from some continuous process are frequent in sciences, engine... more Observations which are realizations from some continuous process are frequent in sciences, engineering, economics, and other fields. We consider a linear model where the responses are random functions in a suitable Sobolev space. The process can't be observed directly. With smoothing procedures from the original data, both the response curves and their derivatives can be reconstructed, even separately. From these functions we estimate the vector of functional parameters and we prove a functional version of the Gauss-Markov theorem. We also obtain experimental designs which are optimal for the estimation of the considered model. The advantages of this theory are finally showed in a real data-set.
In this paper some new properties and computational tools for finding KL-optimum designs are prov... more In this paper some new properties and computational tools for finding KL-optimum designs are provided. KL-optimality is a general criterion useful to select the best experimental conditions to discriminate between statistical models. A KL-optimum design is obtained from a minimax optimization problem, which is defined on a infinitedimensional space. In particular, continuity of the KL-optimality criterion is proved under mild conditions; as a consequence, the first-order algorithm converges to the set of KL-optimum designs for a large class of models. It is also shown that KL-optimum designs are invariant to any scale-position transformation. Some examples are given and discussed, together with some practical implications for numerical computation purposes. * The final publication is available at Springer via http://dx.
Given a strongly stationary Markov chain and a finite set of stop- ping rules, we prove the exist... more Given a strongly stationary Markov chain and a finite set of stop- ping rules, we prove the existence of a polynomial algorithm which projects the Markov chain onto a minimal Markov chain without redundant information. Markov complexity is hence defined and tested on some classical problems.
We face a generalization of the problem of finding the distribution of how long it takes to reach... more We face a generalization of the problem of finding the distribution of how long it takes to reach a "target" set T of states in Markov chain. The graph problems of finding the number of paths that go from a state to a target set and of finding the n-length path connections are shown to belong to this generalization. We explore how the state space of the Markov chain can be reduced by collapsing together those states that behaves in the same way or in almost the same way for the purposes of calculating the distribution of the hitting time of T . We prove the existence and the uniqueness of an optimal projection for this aim which extends the results given in, together with the existence of a polynomial algorithm which reaches this optimum.
The aim of this work is to present a MP test for extreme monotone randomized models. In particula... more The aim of this work is to present a MP test for extreme monotone randomized models. In particular it tests whether the extreme event of a sample comes from the same distribution as the other data. The application we present concerns the detection of epidemics of listeriosis in Lombardy from 2005 to 2011.
On a weakly Blackwell space we show how to define a Markov chain approximating problem, for the t... more On a weakly Blackwell space we show how to define a Markov chain approximating problem, for the target problem. The approximating problem is proved to converge to the optimal reduced problem under different pseudometrics. A computational example of compression of information is discussed.
Given a strongly stationary Markov chain and a finite set of stopping rules, we prove the existen... more Given a strongly stationary Markov chain and a finite set of stopping rules, we prove the existence of a polynomial algorithm which projects the Markov chain onto a minimal Markov chain without redundant information. Markov complexity is hence defined and tested on some classical problems.
This paper deals with the process of crystallization.We first present two major models that descr... more This paper deals with the process of crystallization.We first present two major models that describe this phenomenon either as a birth-and-growth process or in terms of a Johnson-Mehl random tessellation. Then, we estimate the parameters of these models and we establish the asymptotic law of the estimators for the geometrical aspect of this phenomenon. Simulations of these laws are also provided in some cases.
ABSTRACT In this paper, we face a generalization of the problem of finding the distribution of ho... more ABSTRACT In this paper, we face a generalization of the problem of finding the distribution of how long it takes to reach a “target” set $T$ of states in Markov chain. The graph problems of finding the number of paths that go from a state to a target set and of finding the $n$-length path connections are shown to belong to this generalization. This paper explores how the state space of the Markov chain can be reduced by collapsing together those states that behave in the same way for the purposes of calculating the distribution of the hitting time of $T$. We prove the existence and the uniqueness of a optimal projection for this aim which extends the results given in [G. Aletti and E. Merzbach, J. Eur. Math. Soc. (JEMS) 8 (2006) 49–75], together with the existence of a polynomial algorithm which reaches this optimum. Some applied examples are presented. Markov complexity is defined an tested on some classical problems to demonstrate the deeper understanding that is made possible by this approach.
Analytical and Quantitative Cytology and Histology the International Academy of Cytology and American Society of Cytology, 2004
To introduce a new mathematical method based on the principles of fractal geometry analysis that ... more To introduce a new mathematical method based on the principles of fractal geometry analysis that permits more realistic quantification of some of the physical (morphologic) aspects of irregular bodies appearing under microscopy. The principles of the method were tested on microscopic images of irregular collagen deposition in liver tissue. The method uses an ad hoc rectified meter implemented in a computer-assisted planar image analysis system that has been adapted to give metric measures of irregular outlines and surfaces that can be used to produce an index capable of quantifying the typical wrinkledness of biologic objects. Prototypical example measures of liver fibrosis were made on biopsy specimens showing chronic hepatitis C virus-related disease. Measurements were also made of the microscopic images of the abnormal deposition of lipid droplets in hepatocytes, a case of amyloid deposition in an osteoarthromuscular structure and a cytologic specimen of human dendritic cells. The proposed computer-aided method permits rapid measurements of the image of a whole biopsy section digitized at high magnification. The snapshot measurement of liver fibrosis deposition offered by a biopsy pattern is a valid means of more rigorously identifying the staging of the process. This method can measure liver fibrosis during chronic liver disease as well as any other irregular biologic structure that cannot be correctly quantified using traditional Euclidean-based metric methodologies.
Observations which are realizations from some continuous process are frequent in sciences, engine... more Observations which are realizations from some continuous process are frequent in sciences, engineering, economics, and other fields. We consider a linear model where the responses are random functions in a suitable Sobolev space. The process can't be observed directly. With smoothing procedures from the original data, both the response curves and their derivatives can be reconstructed, even separately. From these functions we estimate the vector of functional parameters and we prove a functional version of the Gauss-Markov theorem. We also obtain experimental designs which are optimal for the estimation of the considered model. The advantages of this theory are finally showed in a real data-set.
In this paper some new properties and computational tools for finding KL-optimum designs are prov... more In this paper some new properties and computational tools for finding KL-optimum designs are provided. KL-optimality is a general criterion useful to select the best experimental conditions to discriminate between statistical models. A KL-optimum design is obtained from a minimax optimization problem, which is defined on a infinitedimensional space. In particular, continuity of the KL-optimality criterion is proved under mild conditions; as a consequence, the first-order algorithm converges to the set of KL-optimum designs for a large class of models. It is also shown that KL-optimum designs are invariant to any scale-position transformation. Some examples are given and discussed, together with some practical implications for numerical computation purposes. * The final publication is available at Springer via http://dx.
Given a strongly stationary Markov chain and a finite set of stop- ping rules, we prove the exist... more Given a strongly stationary Markov chain and a finite set of stop- ping rules, we prove the existence of a polynomial algorithm which projects the Markov chain onto a minimal Markov chain without redundant information. Markov complexity is hence defined and tested on some classical problems.
We face a generalization of the problem of finding the distribution of how long it takes to reach... more We face a generalization of the problem of finding the distribution of how long it takes to reach a "target" set T of states in Markov chain. The graph problems of finding the number of paths that go from a state to a target set and of finding the n-length path connections are shown to belong to this generalization. We explore how the state space of the Markov chain can be reduced by collapsing together those states that behaves in the same way or in almost the same way for the purposes of calculating the distribution of the hitting time of T . We prove the existence and the uniqueness of an optimal projection for this aim which extends the results given in, together with the existence of a polynomial algorithm which reaches this optimum.
The aim of this work is to present a MP test for extreme monotone randomized models. In particula... more The aim of this work is to present a MP test for extreme monotone randomized models. In particular it tests whether the extreme event of a sample comes from the same distribution as the other data. The application we present concerns the detection of epidemics of listeriosis in Lombardy from 2005 to 2011.
On a weakly Blackwell space we show how to define a Markov chain approximating problem, for the t... more On a weakly Blackwell space we show how to define a Markov chain approximating problem, for the target problem. The approximating problem is proved to converge to the optimal reduced problem under different pseudometrics. A computational example of compression of information is discussed.
Given a strongly stationary Markov chain and a finite set of stopping rules, we prove the existen... more Given a strongly stationary Markov chain and a finite set of stopping rules, we prove the existence of a polynomial algorithm which projects the Markov chain onto a minimal Markov chain without redundant information. Markov complexity is hence defined and tested on some classical problems.
This paper deals with the process of crystallization.We first present two major models that descr... more This paper deals with the process of crystallization.We first present two major models that describe this phenomenon either as a birth-and-growth process or in terms of a Johnson-Mehl random tessellation. Then, we estimate the parameters of these models and we establish the asymptotic law of the estimators for the geometrical aspect of this phenomenon. Simulations of these laws are also provided in some cases.
ABSTRACT In this paper, we face a generalization of the problem of finding the distribution of ho... more ABSTRACT In this paper, we face a generalization of the problem of finding the distribution of how long it takes to reach a “target” set $T$ of states in Markov chain. The graph problems of finding the number of paths that go from a state to a target set and of finding the $n$-length path connections are shown to belong to this generalization. This paper explores how the state space of the Markov chain can be reduced by collapsing together those states that behave in the same way for the purposes of calculating the distribution of the hitting time of $T$. We prove the existence and the uniqueness of a optimal projection for this aim which extends the results given in [G. Aletti and E. Merzbach, J. Eur. Math. Soc. (JEMS) 8 (2006) 49–75], together with the existence of a polynomial algorithm which reaches this optimum. Some applied examples are presented. Markov complexity is defined an tested on some classical problems to demonstrate the deeper understanding that is made possible by this approach.
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Papers by Giacomo Aletti