BACKGROUND Kidney volume (KV) becomes clinically relevant in autosomal dominant polycystic kidney disease (ADPKD) management. KV can be conveniently estimated (ceKV) using ellipsoid volume equations with three axes measurements; however, the accuracy and reliability are unknown. METHODS KVs of 347 kidneys in 177 consecutive ADPKD patients were determined with a volumetric method (standard-KV)...

A FORTRAN IV algorithm is given for determining the hydrodynamic parameters of a macromolecule in solution for any specified value ofthe two axial ratios (a/b, D/c) ofthe equivalent triaxial ellipsoid model of semi-axes a > b > c for its gross conformafion. Ellipsoid model Axial ratios Elliptic integrals Myoglobin I . I N T R O D U C T I O N The ellipsoid of revolution (i.e. an ellipsoid with t...

In the Colonel Blotto game, which was initially introduced by Borel in 1921, two colonels simultaneously distribute their troops across different battlefields. The winner of each battlefield is determined independently by a winner-take-all rule. The ultimate payoff of each colonel is the number of battlefields he wins. The Colonel Blotto game is commonly used for analyzing a wide range of appli...

It is an important problem to compute the geodesics on a surface in many fields. To find the geodesics in practice, however, the traditional discrete algorithms or numerical approaches can only find a list of discrete points. The first author proposed in 2010 a new, elegant and accurate method, the geodesic-like method, for approximating geodesics on a regular surface. This paper will present b...

We propose a new method for unconstrained optimization of a smooth and strongly convex function, which attains the optimal rate of convergence of Nesterov’s accelerated gradient descent. The new algorithm has a simple geometric interpretation, loosely inspired by the ellipsoid method. We provide some numerical evidence that the new method can be superior to Nesterov’s accelerated gradient descent.

We give a deterministic 2 algorithm for computing an M-ellipsoid of a convex body, matching a known lower bound. This has several interesting consequences including improved deterministic algorithms for volume estimation of convex bodies and for the shortest and closest lattice vector problems under general norms.

We present ellipsoid algorithms for convexly constrained estimation and design problems. The proposed polynomial time algorithms yield both an estimate of the complete set of feasible solutions and a point estimate in the interior. Optimal cutting hyperplanes are derived, and a computation-ally eecient sequential cut algorithm is proven to provide estimation performance achieving the best exist...

Associated with each body K in Euclidean n-space Rn is an ellipsoid 02K called the Legendre ellipsoid of K . It can be defined as the unique ellipsoid centered at the body’s center of mass such that the ellipsoid’s moment of inertia about any axis passing through the center of mass is the same as that of the body. In an earlier paper the authors showed that corresponding to each convex body K ⊂...

We describe a new proof of the complete integrability of the two related dynamical systems: the billiard inside the ellipsoid and the geodesic flow on the ellipsoid (in Euclidean, spherical or hyperbolic space). The proof is based on the construction of a metric on the ellipsoid whose nonparameterized geodesics coincide with those of the standard metric. This new metric is induced by the hyperb...

We propose new techniques for the solution of the LP relaxation and the Lagrangean dual in combinatorial optimization problems. Our techniques find the optimal solution value and the optimal dual multipliers of the LP relaxation and the Lagrangean dual in polynomial time using as a subroutine either the Ellipsoid algorithm or the recent algorithm of Vaidya. Moreover, in problems of a certain st...