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Background In addition to tricuspid regurgitation (TR) and right ventricular (RV) enlargement, patients with Ebstein anomaly are at risk for left ventricular (LV) dysfunction and dyssynchrony. We studied the impact of the cone tricuspid valve reconstruction operation on LV size, function, and dyssynchrony. Methods All Ebstein anomaly patients who had both pre- and postoperative cardiovascular magnetic resonance (CMR) studies were retrospectively identified. From cine images, RV and LV volumes and ejection fractions (EF) were calculated, and LV circumferential and longitudinal strain were measured by feature tracking. To quantify LV dyssynchrony, temporal offsets (TOs) were computed among segmental circumferential strain versus time curves using cross-correlation analysis and patient-specific reference curves. An LV dyssynchrony index was calculated as the standard deviation of the TOs. Results Twenty patients (65% female) were included with a median age at cone operation of 16 years, and a median time between pre- and postoperative CMR of 2.8 years. Postoperatively, there was a decline in the TR fraction (56 ± 19% vs. 5 ± 4%, p  < 0.001), RV end-diastolic volume (EDV) (242 ± 110 ml/m 2 vs. 137 ± 82 ml/m 2 , p  < 0.001), and RV stroke volume (SV) (101 ± 35 vs. 51 ± 7 ml/m 2 , p  < 0.001). RV EF was unchanged. Conversely, there was an increase in both LV EDV (68 ± 13 vs. 85 ± 13 ml/m 2 , p  < 0.001) and LV stroke volume (37 ± 8 vs. 48 ± 6 ml/m 2 , p  < 0.001). There was no change in LV EF, or global circumferential and longitudinal strain but basal septal circumferential strain improved (16 ± 7% vs. 22 ± 5%, p  = 0.04). LV contraction become more synchronous (dyssynchrony index: 32 ± 17 vs. 21 ± 9 msec, p  = 0.02), and the extent correlated with the reduction in RV EDV and TR. Conclusions In patients with the Ebstein anomaly, the cone operation led to reduced TR and RV stroke volume, increased LV stroke volume, improved LV basal septal strain, and improved LV synchrony. Our data demonstrates that the detrimental effect of the RV on LV function can be mitigated by the cone operation.

Cone reconstruction for Ebstein’s anomaly, although effective, is challenging in neonatal cases. Very few reports have discussed recurrent regurgitation. Herein, we report a successful redo tricuspid valve repair for recurrent regurgitation 5 years after cone reconstruction. A 5-year-old boy underwent cone reconstruction for Ebstein’s anomaly in the neonatal period. Although tricuspid regurgitation reduced initially, it subsequently worsened. The mechanisms of regurgitation are dilatation of the anteroseptal commissure, indentation in the septal leaflet, and foreshortening of the anterior leaflet. Augmentation of the anterior leaflet using an elliptic autologous pericardium and mending of the gaping commissure and indentation markedly reduced the regurgitation.

The 1998 arrest of General Augusto Pinochet in London and subsequent extradition proceedings sent an electrifying wave through the international community. This legal precedent for bringing a former head of state to trial outside his home country signaled that neither the immunity of a former head of state nor legal amnesties at home could shield participants in the crimes of military governments. It also allowed victims of torture and crimes against humanity to hope that their tormentors might be brought to justice. In this meticulously researched volume, Naomi Roht-Arriaza examines the implications of the litigation against members of the Chilean and Argentine military governments and traces their effects through similar cases in Latin American and Europe. Roht-Arriaza discusses the difficulties in bringing violators of human rights to justice at home, and considers the role of transitional justice in transnational prosecutions and investigations in the national courts of countries other than those where the crimes took place. She traces the roots of the landmark Pinochet case and follows its development and those of related cases, through Spain, the United Kingdom, elsewhere in Europe, and then through Chile, Argentina, Mexico, and the United States. She situates these transnational cases within the context of an emergent International Criminal Court, as well as the effectiveness of international law and of the lawyers, judges, and activists working together across continents to make a new legal paradigm a reality. Interviews and observations help to contextualize and dramatize these compelling cases. These cases have tremendous ramifications for the prospect of universal jurisdiction and will continue to resonate for years to come. Roht-Arriaza's deft navigation of these complicated legal proceedings elucidates the paradigm shift underlying this prosecution as well as the traction gained by advocacy networks promoting universal jurisdiction in recent decades.

This paper proposes three strong second order cone programming (SOCP) relaxations for the AC optimal power flow (OPF) problem. These three relaxations are incomparable to each other and two of them are incomparable to the standard SDP relaxation of OPF. Extensive computational experiments show that these relaxations have numerous advantages over existing convex relaxations in the literature: (i) their solution quality is extremely close to that of the standard SDP relaxation (the best one is within 99.96% of the SDP relaxation on average for all the IEEE test cases) and consistently outperforms previously proposed convex quadratic relaxations of the OPF problem, (ii) the solutions from the strong SOCP relaxations can be directly used as a warm start in a local solver such as IPOPT to obtain a high quality feasible OPF solution, and (iii) in terms of computation times, the strong SOCP relaxations can be solved an order of magnitude faster than the standard SDP relaxation. For example, one of the proposed SOCP relaxations together with IPOPT produces a feasible solution for the largest instance in the IEEE test cases (the 3375-bus system) and also certifies that this solution is within 0.13% of global optimality, all this computed within 157.20 seconds on a modest personal computer. Overall, the proposed strong SOCP relaxations provide a practical approach to obtain feasible OPF solutions with extremely good quality within a time framework that is compatible with the real-time operation in the current industry practice.

Given a proper cone K in a finite dimensional real Hilbert space H, we present some results characterizing Z-transformations that keep K invariant. We show for example, that when K is irreducible, nonnegative multiples of the identity transformation are the only such transformations. And when K is reducible, they become ‘nonnegative diagonal’ transformations. We apply these results to symmetric cones in Euclidean Jordan algebras, and, in particular, obtain conditions on the Lyapunov transformation LA and the Stein transformation SA that keep the semidefinite cone invariant.

We first provide an inner-approximation hierarchy described by a sum-of-squares (SOS) constraint for the copositive (COP) cone over a general symmetric cone. The hierarchy is a generalization of that proposed by Parrilo (Structured semidefinite programs and semialgebraic geometry methods in Robustness and optimization, Ph.D. Thesis, California Institute of Technology, Pasadena, CA, 2000) for the usual COP cone (over a nonnegative orthant). We also discuss its dual. Second, we characterize the COP cone over a symmetric cone using the usual COP cone. By replacing the usual COP cone appearing in this characterization with the inner- or outer-approximation hierarchy provided by de Klerk and Pasechnik (SIAM J Optim 12(4):875–892, https://doi.org/10.1137/S1052623401383248, 2002) or Yıldırım (Optim Methods Softw 27(1):155–173, https://doi.org/10.1080/10556788.2010.540014, 2012), we obtain an inner- or outer-approximation hierarchy described by semidefinite but not by SOS constraints for the COP matrix cone over the direct product of a nonnegative orthant and a second-order cone. We then compare them with the existing hierarchies provided by Zuluaga et al. (SIAM J Optim 16(4):1076–1091, https://doi.org/10.1137/03060151X, 2006) and Lasserre (Math Program 144:265–276, https://doi.org/10.1007/s10107-013-0632-5, 2014). Theoretical and numerical examinations imply that we can numerically increase a depth parameter, which determines an approximation accuracy, in the approximation hierarchies derived from de Klerk and Pasechnik (SIAM J Optim 12(4):875–892, https://doi.org/10.1137/S1052623401383248, 2002) and Yıldırım (Optim Methods Softw 27(1):155–173, https://doi.org/10.1080/10556788.2010.540014, 2012), particularly when the nonnegative orthant is small. In such a case, the approximation hierarchy derived from Yıldırım (Optim Methods Softw 27(1):155–173, https://doi.org/10.1080/10556788.2010.540014, 2012) can yield nearly optimal values numerically. Combining the proposed approximation hierarchies with existing ones, we can evaluate the optimal value of COP programming problems more accurately and efficiently.

We introduce a first-order method for solving very large convex cone programs. The method uses an operator splitting method, the alternating directions method of multipliers, to solve the homogeneous self-dual embedding, an equivalent feasibility problem involving finding a nonzero point in the intersection of a subspace and a cone. This approach has several favorable properties. Compared to interior-point methods, first-order methods scale to very large problems, at the cost of requiring more time to reach very high accuracy. Compared to other first-order methods for cone programs, our approach finds both primal and dual solutions when available or a certificate of infeasibility or unboundedness otherwise, is parameter free, and the per-iteration cost of the method is the same as applying a splitting method to the primal or dual alone. We discuss efficient implementation of the method in detail, including direct and indirect methods for computing projection onto the subspace, scaling the original problem data, and stopping criteria. We describe an open-source implementation, which handles the usual (symmetric) nonnegative, second-order, and semidefinite cones as well as the (non-self-dual) exponential and power cones and their duals. We report numerical results that show speedups over interior-point cone solvers for large problems, and scaling to very large general cone programs.

In this note, we prove a representation theorem for the symmetric cone automorphisms in the spin algebra Ln.

Amenability is a notion of facial exposedness for convex cones that is stronger than being facially dual complete (or ‘nice’) which is, in turn, stronger than merely being facially exposed. Hyperbolicity cones are a family of algebraically structured closed convex cones that contain all spectrahedral cones (linear sections of positive semidefinite cones) as special cases. It is known that all spectrahedral cones are amenable. We establish that all hyperbolicity cones are amenable. As part of the argument, we show that any face of a hyperbolicity cone is a hyperbolicity cone. As a corollary, we show that the intersection of two hyperbolicity cones, not necessarily sharing a common relative interior point, is a hyperbolicity cone.

In this paper, we investigate the generalized polynomial complementarity problem, which is a subclass of generalized complementarity problems with the involved map pairs being two polynomials. Based on the analysis on two structured tensor pairs located in the heading items of polynomials involved, and by using the degree theory, we achieve several results on the nonemptiness and compactness of solution sets. When generalized polynomial complementarity problems reduce to polynomial complementarity problems (or tensor complementarity problems), our results reduce to the existing ones. In particular, one of our results broadens the one proposed in a very recent paper to guarantee the nonemptiness and compactness of solution sets to generalized polynomial complementarity problems. Furthermore, we establish several existence and uniqueness results, which enrich the theory of generalized complementarity problems with the observation that some known conditions to guarantee the existence and uniqueness of solutions may not hold for a lot of generalized polynomial complementarity problems.