On a matrix with integer eigenvalues and its relation to conditional Poisson sampling

A special non-symmetric N × N matrix with eigenvalues 0, 1, 2, . . . ,N − 1 is presented. The matrix appears in sampling theory. Its right eigenvectors, if properly normalized, give the inclusion probabilities of the Conditional Poisson design (for all different fixed sample sizes). The explicit expressions for the right eigenvectors become complicated for N large. Nevertheless, the left eigenvectors have a simple analytic form. An inversion of the left eigenvector matrix produces the right eigenvectors − the inclusion probabilities. Finally, a more general matrix with similar properties is defined and expressions for its left and right eigenvectors are derived

Stochastic Calculus for a Time-changed Semimartingale and the Associated Stochastic Differential Equations

It is shown that under a certain condition on a semimartingale and a time-change, any stochastic integral driven by the time-changed semimartingale is a time-changed stochastic integral driven by the original semimartingale. As a direct consequence, a specialized form of the Ito formula is derived. When a standard Brownian motion is the original semimartingale, classical Ito stochastic differential equations driven by the Brownian motion with drift extend to a larger class of stochastic differential equations involving a time-change with continuous paths. A form of the general solution of linear equations in this new class is established, followed by consideration of some examples analogous to the classical equations. Through these examples, each coefficient of the stochastic differential equations in the new class is given meaning. The new feature is the coexistence of a usual drift term along with a term related to the time-change.Comment: 27 pages; typos correcte

Mixtures in non stable Levy processes

We analyze the Levy processes produced by means of two interconnected classes of non stable, infinitely divisible distribution: the Variance Gamma and the Student laws. While the Variance Gamma family is closed under convolution, the Student one is not: this makes its time evolution more complicated. We prove that -- at least for one particular type of Student processes suggested by recent empirical results, and for integral times -- the distribution of the process is a mixture of other types of Student distributions, randomized by means of a new probability distribution. The mixture is such that along the time the asymptotic behavior of the probability density functions always coincide with that of the generating Student law. We put forward the conjecture that this can be a general feature of the Student processes. We finally analyze the Ornstein--Uhlenbeck process driven by our Levy noises and show a few simulation of it.Comment: 28 pages, 3 figures, to be published in J. Phys. A: Math. Ge

Enhanced external counter pulsation in treatment of refractory angina pectoris: two year outcome and baseline factors associated with treatment failure

<p>Abstract</p> <p>Background</p> <p>Enhanced external counter pulsation (EECP) is a non-invasive treatment option for patients with refractory angina pectoris ineligible to further traditional treatment. The aim of this study was to evaluate the effect of EECP on patients at a Scandinavian medical centre and to investigate if outcome can be predicted by analysing baseline factors.</p> <p>Methods</p> <p>86 consecutive patients (70 male, 16 female) were treated with EECP and followed for two years post treatment. Canadian cardiovascular society (CCS) class was analysed, and medication and adverse clinical events were researched prior to EECP, at the end of the treatment, and at six, 12 and 24 months thereafter. Patients responding to therapy by improving at least one CCS class were compared with those who failed to respond. Any differences in background factors were recorded and analysed.</p> <p>Results</p> <p>79% of the patients responded to therapy by improving at least one CCS class. In general, the CCS class improved by one class after EECP treatment (3.05 before versus 2.14 after treatment). A total of 61.5% of the initial responders showed sustained improvement at the 12 month follow-up while 29% presented sustained improvement after 24 months. Treatment was most effective among patients suffering from CCS class III-IV angina pectoris, while patients suffering from CCS class II angina pectoris improved transiently but failed to show sustained improvement after the 12 month follow-up. Diabetes mellitus and calcium channel antagonists were more common among the non-responders (<it>p </it>< 0.05).</p> <p>Conclusion</p> <p>This study confirms the safety and efficiency of EECP as a treatment option for patients suffering from refractory angina pectoris. The therapy is most beneficial in patients suffering from severe angina (CCS III-IV) while sustained response to therapy could not be verified among patients suffering from CCS class II angina pectoris.</p

One year follow-up of patients with refractory angina pectoris treated with enhanced external counterpulsation

BACKGROUND: Enhanced external counterpulsation (EECP) is a non-invasive technique that has been shown to be effective in reducing both angina and myocardial ischemia in patients not responding to medical therapy and without revascularization alternatives. The aim of the present study was to assess the long-term outcome of EECP treatment at a Scandinavian centre, in relieving angina in patients with chronic refractory angina pectoris. METHODS: 55 patients were treated with EECP. Canadian cardiovascular society (CCS) class, antianginal medication and adverse clinical events were collected prior to EECP, at the end of the treatment, and at six and 12 months after EECP treatment. Clinical signs and symptoms were recorded. RESULTS: EECP treatment significantly improved the CCS class in 79 ± 6% of the patients with chronic angina pectoris (p < 0.001). The reduction in CCS angina class was seen in patients with CCS class III and IV and persisted 12 months after EECP treatment. There was no significant relief in angina in patients with CCS class II prior to EECP treatment. 73 ± 7% of the patients with a reduction in CCS class after EECP treatment improved one CCS class, and 22 ± 7% of the patients improved two CCS classes. The improvement of two CCS classes could progress over a six months period and tended to be more prominent in patients with CCS class IV. In accordance with the reduction in CCS classes there was a significant decrease in the weekly nitroglycerin usage (p < 0.05). CONCLUSION: The results from the present study show that EECP is a safe treatment for highly symptomatic patients with refractory angina. The beneficial effects were sustained during a 12-months follow-up period

20-Year Risks of Breast-Cancer Recurrence after Stopping Endocrine Therapy at 5 Years

The administration of endocrine therapy for 5 years substantially reduces recurrence rates during and after treatment in women with early-stage, estrogen-receptor (ER)-positive breast cancer. Extending such therapy beyond 5 years offers further protection but has additional side effects. Obtaining data on the absolute risk of subsequent distant recurrence if therapy stops at 5 years could help determine whether to extend treatment

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Res. Lett. Inf. Math. Sci., 2005, Vol.8, pp155-163

this paper we present a special non-symmetric matrix A with these eigenvalues. The matrix A is simple but not the matrix P of its right eigenvectors. The right eigenvectors of A are of special interest in sampling theory. They give inclusion probabilities of an important sampling design the Conditional Poisson (CP) design. They are di#cult to calculate in general and simple explicit analytic formulae are not available. In the literature (Chen, 1997, Aires, 1999, Traat et al., 2004, Bondesson et al., 2004), some recursive formulae and algorithms for their calculation are presented. In this paper we develop an eigenvector approach. The eigenvector, properly normalized, corresponding to the eigenvalue n 1 (n = 1, 2, . . . , N) represents the inclusion probabilities of the CP design with fixed sample size n. Consequently, the matrix P yields the inclusion probabilities for all possible sample sizes, simultaneously. Surprisingly, in spite of the complexity of P, the matrix Q = P -1 of left eigenvectors has a simple form. The matrix Q is presented in this paper. The inclusion probabilities of the CP design can now be obtained by just inverting