Enrico Rogora

Varieties with many lines

This paper contains a classification ofk-dimensional algebraic varieties,even non-smooth, containing a family of lines of dimension (2k−4). If the codimension of the varieties is greater than two, these are: bidimensional families ofPk−2; one dimensional families of irreducible quadrics; linear sections of the grassmannian of lines ofP4.

TESTING INDEPENDENCE IN TIME SERIES VIA UNIVERSAL DISTRIBUTIONS OF PERMUTATIONS AND WORDS

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.

Classification of Bertini's Series of Varieties of Dimension Less than or Equal to Four

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.

Guido Castelnuovo and his commitment to the University of Rome’s Faculty of Science

Besides his well-known and celebrated research activity, Guido Castelnuovo fulfilled many important institutional roles. In this paper we consider his commitment to make the University of Rome the most prestigious in Italy and one of the most advanced international research centres for mathematics.

A basic relation between invariants of matrices under the action of the special orthogonal group

The first fundamental theorem of invariant theory for the action of the special orthogonal group onm tuples of matrices by simultaneous conjugation is proved in [2]. In this paper, as a first step in the direction of establishing the second fundamental theorem, we study a basic identity betweenSO(n, K) invariants ofm matrices.

VALIDATION OF NONSTATIONARY MODEL OF ATRIOVENTRICULAR NODE CONDUCTION IN ATRIAL FIBRILLATION

In normal human heart the main pacemaker is the sinus node, located in the right atrium; the electrical activation propagates from the sinus node through the atria and then to the ventricles in such a way that each atrial contraction corresponds to a ventricular one. The only conducting pathway between the atria and the ventricles is the atrioventricular node. Atrial fibrillation is an arrhythmia characterized by rapid irregular contraction of the atrial myocardium; electrical stimulations are filtered by the atrioventricular node, which propagates some of them to the ventricles, while others are blocked. The ventricular contractions are represented by the R peaks of the ECG. The time interval between two consecutive R peaks is called RR interval; the RR intervals sequence extracted from the 24 hours Holter recording defines a time series of about 100,000 elements. In long term RR series of fibrillating subjects many qualitatively different kind of regimes may be observed in the same subject. For example, in Figure 1 two different regimes are evident in the second recording. The first regime (roughly the first 15000 beats) is similar to an RR sequence of a normal subject, while the second is typical of chronic fibrillation, as is the regime in the first