Violator Spaces: Structure and Algorithms

Sharir and Welzl introduced an abstract framework for optimization problems, called LP-type problems or also generalized linear programming problems, which proved useful in algorithm design. We define a new, and as we believe, simpler and more natural framework: violator spaces, which constitute a proper generalization of LP-type problems. We show that Clarkson's randomized algorithms for low-dimensional linear programming work in the context of violator spaces. For example, in this way we obtain the fastest known algorithm for the P-matrix generalized linear complementarity problem with a constant number of blocks. We also give two new characterizations of LP-type problems: they are equivalent to acyclic violator spaces, as well as to concrete LP-type problems (informally, the constraints in a concrete LP-type problem are subsets of a linearly ordered ground set, and the value of a set of constraints is the minimum of its intersection).Comment: 28 pages, 5 figures, extended abstract was presented at ESA 2006; author spelling fixe

Geometric models of the aortic and pulmonary roots: suggestions for the Ross procedure

Objective: To discuss geometric factors, which may influence long-term results relating to homograft competence following the Ross procedure, we describe the 3D morphology of the pulmonary and aortic roots. Materials: Measurements were made on 25 human aortic and pulmonary roots. Inter-commissural distances and the heights of the sinuses were measured. For geometrical reconstruction the three commissures and their vertical projections at the root base were used as reference points. Results: In the pulmonary root, the three inter-commissural distances were of similar dimensions (17.9±1.6mm, 17.5±1.4mm and 18.6±1.5mm). In the aortic root, the right inter-commissural distance was greatest (18.8±1.9mm), followed by the non-coronary (17.4±2.0mm) and left coronary sinus commissures (15.2±1.9mm). The mean height of the left pulmonary sinus was greatest (20±1.7mm) followed by the anterior (17.5±1.4mm) and right pulmonary sinus (18±1.66mm). In the aortic root, the height of the right coronary sinus was the greatest (19.4±1.9mm) followed by the heights of the non-coronary (17.7±1.8mm) and left coronary sinus (17.4±1.4mm). Measured differences between parameters determine the tilt angle and direction of the root vector. The tilt angle in the pulmonary root averaged 16.26°, respectively; for the aortic roots, it was 5.47°. Conclusions: Herein we suggest that the left pulmonary sinus is best implanted in the position of the right coronary sinus, the anterior pulmonary in the position of the non-coronary sinus and the right pulmonary sinus in the position of the left coronary sinus. In this way, the direction of the pulmonary root vector will be parallel to that of the aortic root vecto

Incidence and pathophysiology of atrioventricular block following mitral valve replacement and ring annuloplasty

Background: In this retrospective study we evaluate the causative mechanisms underlying postoperative atrioventricular block (AVB) following mitral valve replacement and mitral valve annuloplasty. Methods: Between January 1990 and December 2003, 391 patients underwent mitral valve replacement or ring annuloplasty and quadrangular resection. Exclusion criteria were preoperative AV block, two or three valvular procedures, reoperations and procedures combined with coronary artery bypass grafting. The presence of the postoperative AVB was compared with preoperative and intraoperative variables. On 55 post-mortem specimens the relationship between the AV node, AV node artery and mitral valve annulus was investigated. Results: The mean age was 59±14 years and 44% of patients were female. Postoperatively AVB occurred in 92 (23.5%) patients. AVB III was found in 17 (4%) patents, in whom a pacemaker was implanted within median interval of 4 days. Second degree AVB occurred and first degree AVB in five (1.3%) and in 70 (18%) patients respectively. In dry dissected human hearts in 23% of investigated cases the AV node artery was discovered to run close to the annulus of the mitral valve. Conclusions: Data collected in this study showed that, sotalol and amiodarone as well as a prolonged cross-clamp time may slightly influence the 23% incidence of postoperative AVB. The morphological investigation showed that the AV node artery runs in close proximity to the annulus in 23% of cases. We speculate that damage of the AV node artery may play a role in development of AV

Advantages of subclavian artery perfusion for repair of acute type A dissection

Objective: Arterial perfusion through the right subclavian artery is proposed to avoid intraoperative malperfusion during repair of acute type A dissection. This study evaluated the clinical and neurological outcome of patients undergoing surgery of acute aortic type A dissection following subclavian arterial cannulation compared to femoral artery approach. Methods: From 1/97 to 1/03, 122 consecutive patients underwent surgery for acute type A aortic dissection. Subclavian cannulation was performed in 62 versus femoral cannulation in 60 patients. Clinical characteristics in both groups were similar. Mean age was 61 years (SD±14 years, 72% male) and mean follow-up was 3 years (±2 years). Patient outcome was assessed as the prevalence of clinical complications, especially neurological deficits, mortality at 30 days, perioperative morbidity and time of body temperature cooling and analyzed by nominal logistic regression analysis for odds ratio calculation. Results: Arterial subclavian cannulation was successfully performed without any occurrence of malperfusion in all cases. Patients undergoing subclavian cannulation showed an odds ratio of 1.98 (95% CI 1.15-3.51; P=0.0057) for an improved neurological outcome compared to patients undergoing femoral cannulation. Re-exploration rate for postoperative bleeding was significantly reduced in the subclavian group (P<0.0001), as well as occurrence of myocardial infarction (P<0.0001) and duration for body temperature cooling (P=0.004). The 30-day mortality of patients with femoral cannulation was significantly higher compared to patients with subclavian artery cannulation (24 versus 8%; P=0.0179). Conclusions: Arterial perfusion through the right subclavian artery provides an excellent approach for repair of acute type A dissection with optimized arterial perfusion body perfusion and allows for antegrade cerebral perfusion during circulatory arrest. The technique is safe and results in a significantly improved clinical and especially neurological outcom

The crust in the pamir: Insights from receiver functions

The Cenozoic convergence between India and Asia has created Earth's thickest crust in the Pamir‐Tibet Plateau by extreme crustal shortening. Here we study the crustal structure of the Pamir and western Tian Shan, the adjacent margins of the Tajik, Tarim, and Ferghana Basins, and the Hindu Kush, using data collected by temporary seismic experiments. We derive, compare, and combine independent observations from P and S receiver functions. The obtained Moho depth varies from ~40 km below the basins to a double‐normal thickness of 65–75 km underneath the Pamir and Hindu Kush. A Moho doublet—with the deeper interface down to a depth of ~90 km—coincides with the arc of intermediate‐depth seismicity underneath the Pamir, where Asian continental lower crust delaminates and rolls back. The crust beneath most of the Central and South Pamir has a low Vp/Vs ratio (<1.70), suggesting a dominantly felsic composition, probably a result of delamination/foundering of the mafic rocks of the lower crust. Beneath the Cenozoic gneiss domes of the Central and South Pamir, which represent extensional core complexes, the Vp/Vs ratios are moderate to high (~1.75), consistent with the previously observed, midcrustal low‐velocity zones, implying the presence of crustal partial melts. Even higher crustal average Vp/Vs ratios up to 1.90 are found in the sedimentary basins and along the Main Pamir Thrust. The ratios along the latter—the active thrust front of the Pamir—may reflect fluid accumulations within a strongly fractured fault system

Strong duality in conic linear programming: facial reduction and extended duals

The facial reduction algorithm of Borwein and Wolkowicz and the extended dual of Ramana provide a strong dual for the conic linear program $$(P) \sup {<c, x> | Ax \leq_K b}$$ in the absence of any constraint qualification. The facial reduction algorithm solves a sequence of auxiliary optimization problems to obtain such a dual. Ramana's dual is applicable when (P) is a semidefinite program (SDP) and is an explicit SDP itself. Ramana, Tuncel, and Wolkowicz showed that these approaches are closely related; in particular, they proved the correctness of Ramana's dual using certificates from a facial reduction algorithm. Here we give a clear and self-contained exposition of facial reduction, of extended duals, and generalize Ramana's dual: -- we state a simple facial reduction algorithm and prove its correctness; and -- building on this algorithm we construct a family of extended duals when $K$ is a {\em nice} cone. This class of cones includes the semidefinite cone and other important cones.Comment: A previous version of this paper appeared as "A simple derivation of a facial reduction algorithm and extended dual systems", technical report, Columbia University, 2000, available from http://www.unc.edu/~pataki/papers/fr.pdf Jonfest, a conference in honor of Jonathan Borwein's 60th birthday, 201

Russian Old Believers: Genetic Consequences of Their Persecution and Exile, as Shown by Mitochondrial DNA Evidence

In 1653, the Patriarch Nikon modified liturgical practices to bring the Russian Orthodox Church in line with those of the Eastern (Greek) Orthodox Church, from which it had split 200 years earlier. The Old Believers (staroveri) rejected these changes and continued to worship using the earlier practices. These actions resulted in their persecution by the Russian Orthodox Church, which forced them into exile across Siberia. Given their history, we investigate whether populations of Old Believers have diverged genetically from other Slavic populations as a result of their isolation. We also examine whether the three Old Believer populations analyzed in this study are part of a single gene pool (founder population) or are instead derived from heterogeneous sources. As part of this analysis, we survey the mitochondrial DNAs (mtDNAs) of 189 Russian Old Believer individuals from three populations in Siberia and 201 ethnic Russians from different parts of Siberia for phylogenetically informative mutations in the coding and noncoding regions. Our results indicate that the Old Believers have not significantly diverged genetically from other Slavic populations over the 200-300 years of their isolation in Siberia. However, they do show some unique patterns of mtDNA variation relative to other Slavic groups, such as a high frequency of subhaplogroup U4, a surprisingly low frequency of haplogroup H, and low frequencies of the rare East Eurasian subhaplogroup D5

The Viscous Nonlinear Dynamics of Twist and Writhe

Exploiting the "natural" frame of space curves, we formulate an intrinsic dynamics of twisted elastic filaments in viscous fluids. A pair of coupled nonlinear equations describing the temporal evolution of the filament's complex curvature and twist density embodies the dynamic interplay of twist and writhe. These are used to illustrate a novel nonlinear phenomenon: ``geometric untwisting" of open filaments, whereby twisting strains relax through a transient writhing instability without performing axial rotation. This may explain certain experimentally observed motions of fibers of the bacterium B. subtilis [N.H. Mendelson, et al., J. Bacteriol. 177, 7060 (1995)].Comment: 9 pages, 4 figure

Modeling DNA Structure, Elasticity and Deformations at the Base-pair Level

We present a generic model for DNA at the base-pair level. We use a variant of the Gay-Berne potential to represent the stacking energy between neighboring base-pairs. The sugar-phosphate backbones are taken into account by semi-rigid harmonic springs with a non-zero spring length. The competition of these two interactions and the introduction of a simple geometrical constraint leads to a stacked right-handed B-DNA-like conformation. The mapping of the presented model to the Marko-Siggia and the Stack-of-Plates model enables us to optimize the free model parameters so as to reproduce the experimentally known observables such as persistence lengths, mean and mean squared base-pair step parameters. For the optimized model parameters we measured the critical force where the transition from B- to S-DNA occurs to be approximately $140{pN}$. We observe an overstretched S-DNA conformation with highly inclined bases that partially preserves the stacking of successive base-pairs.Comment: 15 pages, 25 figures. submitted to PR

Analysis and modelling of tsunami-induced tilt for the 2007, M = 7.6, Tocopilla and the 2010, M = 8.8 Maule earthquakes, Chile, from long-base tiltmeter and broadband seismometer records

We present a detailed study of tsunami-induced tilt at in-land sites, to test the interest and feasibility of such analysis for tsunami detection and modelling. We studied tiltmeter and broadband seismometer records of northern Chile, detecting a clear s