Enrico Rogora | Università degli Studi "La Sapienza" di Roma (original) (raw)

Papers by Enrico Rogora

Geometriae Dedicata, 1997

In this paper I give a classification of irreducible projective varieties of dimension less than ... more In this paper I give a classification of irreducible projective varieties of dimension less than or equal to four, according to a new classification scheme. No assumption is made about singularities.

La ricerca in biologia è oggi in grande espansione e la sua importanza è sempre più grande. Model... more La ricerca in biologia è oggi in grande espansione e la sua importanza è sempre più grande. Modelli teorici per la biologia molecolare, per la filogenetica e per numerose altre branche della biologia, devono confrontarsi con quantità di dati sterminate. La necessità di operare riduzioni drastiche della massa dei dati senza perdere informazioni essenziali, è cruciale. L’approccio utilizzato nella fisica statistica nel passaggio dalle leggi microscopiche a quelle macroscopiche è certamente una guida importante, ma l’esigenza di nuovi punti di vista, che tengano in considerazione la specificità dei problemi delle scienze naturali è sempre più avvertita dai ricercatori. Qual è il ruolo della matematica in queste sfide? Come è sempre stato, alla matematica si richiede il linguaggio per una formulazione rigorosama flessibile di teorie efficaci e di validi modelli che permettano di interpretare i dati osservati e di prevedere l’evoluzione di aspetti rilevanti di un sistema. Nella fisica i modelli classici basati sulle equazioni differenziali e sulle equazioni differenziali stocastiche hanno avuto grande successo, ma nuovi strumenti matematici sembrano necessari per la biologia.

The heartbeat time series of subjects with atrial fibrillation is modeled using a non stationary ... more The heartbeat time series of subjects with atrial fibrillation is modeled using a non stationary sequence of random variables. The mean and standard deviation are estimated by using a segmentation of the data. We find that they are linearly related and then we use a lognormal model to analyze the data. The autocorrelation function of the residuals shows to be significantly close to zero.

Physical Review E, 2006

Spectral analysis of heart rate sequences is commonly used to investigate neuroauthonomic control... more Spectral analysis of heart rate sequences is commonly used to investigate neuroauthonomic control of heart rate by means of two indexes, the low and the high frequency power. For tilt test data of normal subjects we compare the spectral indexes with new indexes defined within the framework of symbolic analysis. We define two classes of binary words of length 4: the first class is related to "acceleration" of heart rate and the second class to "stationary behavior". The new indexes measure the change in frequency of the two classes before and after the tilt. Data analysis of 13 normal subjects shows that the behavior of the new indexes is in agreement with that of spectral ones.

Physica A-statistical Mechanics and Its Applications, 2005

Heartbeat intervals during atrial fibrillation are commonly believed to form a series of almost i... more Heartbeat intervals during atrial fibrillation are commonly believed to form a series of almost independent variables. The series extracted from 24 hours Holter recordings show a non stationary behavior. Because of non stationarity it is difficult to give a quantitative measure of independence. In this paper we use and compare two methods for this. The first is a classical method which models a non stationary series using a linear Gaussian state space model. In this framework the independence is tested on the stationary sequence of the residuals. The second method codes data into permutations and tests the uniformity of their distribution. This test assumes as null hypothesis a weaker form of independence which we call symbolic independence. We discuss some advantages of symbolic independence in the context of heartbeat series. We analyze the time series of heartbeat intervals from 24 hours Holter recordings of 9 subjects with chronic atrial fibrillation and find that the detrended series is a zero or one memory process for 83% of regular segments and is symbolically independent for 93% of segments.

Chaos Solitons & Fractals, 2007

We study the time reversal properties of time series by means of a ternary coding of the differen... more We study the time reversal properties of time series by means of a ternary coding of the differentiated series. For the symbolic series obtained in this way we show that suitable pairs of ternary words have the same probability if the time series is reversible. This provides tests in which time reversibility is rejected if the estimated probabilities are significantly different. We apply one of these tests to the human heartbeat series extracted from 24-hours Holter recordings of 19 healthy subjects. Data analysis shows a highly significant prevalence of irreversibility. Our symbolic approach to time reversal gives further support to the suitability of non linear modeling of the normal heartbeat.

International Journal of Bifurcation and Chaos, 2005

We study probability distributions of permutations and binary words, which arise in symbolic anal... more We study probability distributions of permutations and binary words, which arise in symbolic analysis of time series and their differences. Under the assumptions that the series is stationary and independent we show that these probability distributions are universal and we derive a recursive algorithm for computing the distribution of binary words. This provides a general framework for performing chi square tests of goodness of fit of empirical distributions versus universal ones. We apply these methods to analyze heartbeat time series; in particular we measure the extent to which atrial fibrillation can be modeled as an independent sequence.

Geometriae Dedicata, 1997

In this paper I give a classification of irreducible projective varieties of dimension less than ... more In this paper I give a classification of irreducible projective varieties of dimension less than or equal to four, according to a new classification scheme. No assumption is made about singularities.

La ricerca in biologia è oggi in grande espansione e la sua importanza è sempre più grande. Model... more La ricerca in biologia è oggi in grande espansione e la sua importanza è sempre più grande. Modelli teorici per la biologia molecolare, per la filogenetica e per numerose altre branche della biologia, devono confrontarsi con quantità di dati sterminate. La necessità di operare riduzioni drastiche della massa dei dati senza perdere informazioni essenziali, è cruciale. L’approccio utilizzato nella fisica statistica nel passaggio dalle leggi microscopiche a quelle macroscopiche è certamente una guida importante, ma l’esigenza di nuovi punti di vista, che tengano in considerazione la specificità dei problemi delle scienze naturali è sempre più avvertita dai ricercatori. Qual è il ruolo della matematica in queste sfide? Come è sempre stato, alla matematica si richiede il linguaggio per una formulazione rigorosama flessibile di teorie efficaci e di validi modelli che permettano di interpretare i dati osservati e di prevedere l’evoluzione di aspetti rilevanti di un sistema. Nella fisica i modelli classici basati sulle equazioni differenziali e sulle equazioni differenziali stocastiche hanno avuto grande successo, ma nuovi strumenti matematici sembrano necessari per la biologia.

The heartbeat time series of subjects with atrial fibrillation is modeled using a non stationary ... more The heartbeat time series of subjects with atrial fibrillation is modeled using a non stationary sequence of random variables. The mean and standard deviation are estimated by using a segmentation of the data. We find that they are linearly related and then we use a lognormal model to analyze the data. The autocorrelation function of the residuals shows to be significantly close to zero.

Physical Review E, 2006

Spectral analysis of heart rate sequences is commonly used to investigate neuroauthonomic control... more Spectral analysis of heart rate sequences is commonly used to investigate neuroauthonomic control of heart rate by means of two indexes, the low and the high frequency power. For tilt test data of normal subjects we compare the spectral indexes with new indexes defined within the framework of symbolic analysis. We define two classes of binary words of length 4: the first class is related to "acceleration" of heart rate and the second class to "stationary behavior". The new indexes measure the change in frequency of the two classes before and after the tilt. Data analysis of 13 normal subjects shows that the behavior of the new indexes is in agreement with that of spectral ones.

Physica A-statistical Mechanics and Its Applications, 2005

Heartbeat intervals during atrial fibrillation are commonly believed to form a series of almost i... more Heartbeat intervals during atrial fibrillation are commonly believed to form a series of almost independent variables. The series extracted from 24 hours Holter recordings show a non stationary behavior. Because of non stationarity it is difficult to give a quantitative measure of independence. In this paper we use and compare two methods for this. The first is a classical method which models a non stationary series using a linear Gaussian state space model. In this framework the independence is tested on the stationary sequence of the residuals. The second method codes data into permutations and tests the uniformity of their distribution. This test assumes as null hypothesis a weaker form of independence which we call symbolic independence. We discuss some advantages of symbolic independence in the context of heartbeat series. We analyze the time series of heartbeat intervals from 24 hours Holter recordings of 9 subjects with chronic atrial fibrillation and find that the detrended series is a zero or one memory process for 83% of regular segments and is symbolically independent for 93% of segments.

Chaos Solitons & Fractals, 2007

We study the time reversal properties of time series by means of a ternary coding of the differen... more We study the time reversal properties of time series by means of a ternary coding of the differentiated series. For the symbolic series obtained in this way we show that suitable pairs of ternary words have the same probability if the time series is reversible. This provides tests in which time reversibility is rejected if the estimated probabilities are significantly different. We apply one of these tests to the human heartbeat series extracted from 24-hours Holter recordings of 19 healthy subjects. Data analysis shows a highly significant prevalence of irreversibility. Our symbolic approach to time reversal gives further support to the suitability of non linear modeling of the normal heartbeat.

International Journal of Bifurcation and Chaos, 2005

We study probability distributions of permutations and binary words, which arise in symbolic anal... more We study probability distributions of permutations and binary words, which arise in symbolic analysis of time series and their differences. Under the assumptions that the series is stationary and independent we show that these probability distributions are universal and we derive a recursive algorithm for computing the distribution of binary words. This provides a general framework for performing chi square tests of goodness of fit of empirical distributions versus universal ones. We apply these methods to analyze heartbeat time series; in particular we measure the extent to which atrial fibrillation can be modeled as an independent sequence.