[en] The bifurcations of 2-point heterodimensional cycles are investigated in this paper. Under some generic conditions, we establish the existence of one homoclinic loop, one periodic orbit, two periodic orbits, one 2-fold periodic orbit, and the coexistence of one periodic orbit and heteroclinic loop. Some bifurcation patterns different to the case of non-heterodimensional heteroclinic cycles are revealed.

[en] This study was designed to report our experience with 'cutting' balloon angioplasty (CBA) for the treatment of short femoral bifurcation arterial stenosis. Between March 2005 and September 2007, 18 consecutive patients who were high-risk for surgery with critical limb ischemia or severe lifestyle-limiting claudication underwent 'cutting' balloon angioplasty (4-6 mm diameter/15-20-mm length) for the treatment of 27 focal (<3 cm) severe fibro-calcified stenosis of the common femoral artery (n = 14) and/or the proximal part of the superficial femoral artery (n = 6) or profunda femoris (n = 7). Baseline patient demographic data, pre- and post-procedural patient clinical data, and procedural results were recorded. Follow-up consisted of clinical check-up and color duplex ultrasonography (CDU) examination 1, 3, 6, 12, and 18 months after the procedure. All endovascular treatments were successfully performed with clinical success obtained for all patients. No complications occurred during all treatments and no patient required surgical conversion or placement of a stent because of recoil, dissection, or arterial tears. No acute vessel closure was registered. During a mean follow-up of 9.4 (range, 6-18) months, endovascular treatment (CBA) was performed for restenosis/occlusion of seven lesions (25.9%) in four patients, whereas surgical treatment (endarterectomy with patch) for restenosis/occlusion of three lesions (11.1%) was performed in two patients with a consequent reintervention rate of 37%. Primary and secondary patency rates were 84.6 and 88.4% at 6 months and 57.9 and 79.6% at 12 months, respectively. No major limb amputation was performed, with a 12-month limb salvage rate of 88.9%. CBA seems to be a valuable tool for the endovascular treatment of focal femoral bifurcation stenotic lesions for patients who are poor candidates for surgery.

[en] We investigate the collective dynamics of network-organized identical excitable nodes. We theoretically analyze the stability of the rest state and propose that there are two different transition paths: the stationary path and the oscillatory path. We find that, although the onset of collective dynamics strongly depend on the network topology, the local dynamics and how local nodes interact with each other decide the transition path and the involved bifurcation. (general)

[en] We study certain one-parameter families of partially hyperbolic maps $F_t:{\mathrm{\Sigma <!--\; ??\; -->}}_2\times <!--\; ??\; -->\mathbb{R}\to <!--\; ???\; -->{\mathrm{\Sigma <!--\; ??\; -->}}_2\times <!--\; ??\; -->\mathbb{R}$ of skew-product type generating so-called porcupine-like horseshoes. Such sets are topologically transitive and semiconjugate to the shift map in two symbols. They exhibit a very rich fiber structure characterized by the fact that the set ${\mathrm{\Sigma <!--\; ??\; -->}}_2$ is the disjoint union of two dense and uncountable subsets with opposite behavior: corresponding spines (preimage of a sequence by the semiconjugation) are nontrivial and trivial, respectively, that is, the semiconjugation is noninjective and injective, respectively. We will study the bifurcation process of creation and annihilation of nontrivial spines as the parameter t evolves. In particular, we focus on the Hausdorff dimension of these subsets of ${\mathrm{\Sigma <!--\; ??\; -->}}_2$. This study illustrates the richness of the process. (paper)

[en] We describe a simple technique to perform difficult endovascular interventions safely by using a wire-loop guidewire over the aortic bifurcation. This guidewire is then used to stabilize catheters for stenting or embolization.

[en] In order to formulate and examine the central limit theorem for a binary tree numerically, a method for generating random binary trees is presented. We first propose the correspondence between binary trees and a certain type of binary sequences (which we call Dyck sequences). Then, the method for generating random Dyck sequences is shown. Also, we propose the method of branch ordering of a binary tree by means of only the corresponding Dyck sequence. We confirm that the method is in good consistency with the topological analysis of binary trees known as the Horton-Strahler analysis. Two types of central limit theorem are numerically confirmed, and the obtained results are expressed in simple forms. Furthermore, the proposed method is available for a wide range of the topological analysis of binary trees.

[en] The existence of bifurcation points of Newtonian rotating polytropes in the interval of polytropic index 0.9989 < n ≤ 1.0795, in which asymmetric with respect to the axis of rotation solutions describing the density distribution are branched, is proved for the first time. It is shown that, in this interval of values of n, the parameter of the rotation rate at critical points ε_k takes values 0.0442 > ε_k ≥ 0.

No abstract available

[en] Two angiographic instances of anomalous external carotid artery (ECA) and internal carotid artery (ICA) anastomosis are described, each occurring at the C2-3 level and bearing remnants of proximal ICA. The ICA remnant of one patient (identifiable immediately upon bifurcation of the common carotid artery) was hypoplastic, and that of the other patient was an occluded arterial stump. These features are not typical of non-bifurcating ICA. The occipital artery originated from an anomalous connection in one instance and from the main trunk of the ECA (just past the ECA-ICA connection) in the other

No abstract available