Determinantal process starting from an orthogonal symmetry is a Pfaffian process

When the number of particles $N$ is finite, the noncolliding Brownian motion (BM) and the noncolliding squared Bessel process with index $\nu > -1$ (BESQ$^{(\nu)}$) are determinantal processes for arbitrary fixed initial configurations. In the present paper we prove that, if initial configurations are distributed with orthogonal symmetry, they are Pfaffian processes in the sense that any multitime correlation functions are expressed by Pfaffians. The $2 \times 2$ skew-symmetric matrix-valued correlation kernels of the Pfaffians processes are explicitly obtained by the equivalence between the noncolliding BM and an appropriate dilatation of a time reversal of the temporally inhomogeneous version of noncolliding BM with finite duration in which all particles start from the origin, $N \delta_0$, and by the equivalence between the noncolliding BESQ$^{(\nu)}$ and that of the noncolliding squared generalized meander starting from $N \delta_0$.Comment: v2: AMS-LaTeX, 17 pages, no figure, corrections made for publication in J.Stat.Phy

Bilateral Implantation of a New Refractive Multi-Segmented Multifocal Intraocular Lens in Cataract or Refractive Lens Exchange Patients

Purpose: To evaluate the safety and efficacy of a new multi-segmented refractive multifocal intraocular lens (IOL) after phacoemulsification and refractive lens exchange (RLE).Patients and Methods: In this prospective, multicenter clinical trial, 63 presbyopic subjects who had cataract or where RLE candidates were bilaterally implanted with the Precizon Presbyopia IOL (Ophtec BV, Groningen, the Netherlands) after phacoemulsification. The study was conducted at 6 clinical centers in Germany, the Netherlands, Belgium, Turkey and Spain. Subjects were evaluated at baseline and at 1 day, 1 week, 1 and 3 months post-operatively for monocular and binocular uncorrected (UDVA) and corrected distance visual acuity (CDVA), uncorrected (UIVA) and distance-corrected intermediate visual acuity (DCIVA), uncorrected (UNVA), corrected (CNVA) and distance-corrected near visual acuity (DCNVA), contrast sensitivity and quality of vision.Results: Three months postoperatively, binocular UDVA and CDVA of >= 20/40 was achieved in 98.4% (60/61) and 100%, respectively. Binocular UIVA and DCIVA of >= 20/40 was achieved in 96.7% (59/61) and 93.4% (57/61) respectively. Binocular UNVA, CNVA and DCNVA of >= 20/40 was achieved in 93.4% (57/61), 98.4% (60/61) and 95% (57/60) subjects, respectively. Complete spectacle independence was achieved in 80% (49/61) patients; 93% of patients reported that they were quite or very satisfied with the outcomes of the procedure.Conclusion: Precizon Presbyopia IOL implantation is a safe and effective method to provide good visual acuity at all distances in presbyopic and cataract patients