8 research outputs found
Towards Machine Wald
The past century has seen a steady increase in the need of estimating and
predicting complex systems and making (possibly critical) decisions with
limited information. Although computers have made possible the numerical
evaluation of sophisticated statistical models, these models are still designed
\emph{by humans} because there is currently no known recipe or algorithm for
dividing the design of a statistical model into a sequence of arithmetic
operations. Indeed enabling computers to \emph{think} as \emph{humans} have the
ability to do when faced with uncertainty is challenging in several major ways:
(1) Finding optimal statistical models remains to be formulated as a well posed
problem when information on the system of interest is incomplete and comes in
the form of a complex combination of sample data, partial knowledge of
constitutive relations and a limited description of the distribution of input
random variables. (2) The space of admissible scenarios along with the space of
relevant information, assumptions, and/or beliefs, tend to be infinite
dimensional, whereas calculus on a computer is necessarily discrete and finite.
With this purpose, this paper explores the foundations of a rigorous framework
for the scientific computation of optimal statistical estimators/models and
reviews their connections with Decision Theory, Machine Learning, Bayesian
Inference, Stochastic Optimization, Robust Optimization, Optimal Uncertainty
Quantification and Information Based Complexity.Comment: 37 page
RESULTS OF SHOULDER STABILIZATION BY A MODIFIED BRISTOW - LATARJET PROCEDURE WITH ARTHROSCOPY
The authors describe the minimally invasive technique for Bristow-Latarjet bone unfree autoplasty with arthroscopy in patients with bone loss more than 25% of anterior-posterior diameter of the glenoid, the poor quality of the capsule or deep defects of Hill-Sachs. The analysis of the early results of treatment in 19 patients and midterm results - in 13 soldiers operated in 2011-2014. Features of the proposed technique are the shortening of surgical approach and the reduction of subscapularis muscle damage. In addition, arthroscopic support allows to attain the precision location of the graft relative to the articular surface of scapula, at the same time restoring the damaged anatomy SLAP, rotator cuff tendons and posterior labrum and restore shoulder ligaments tension and isolate bone graft from the joint cavity, contributing to a better articulation of the humeral head and reducing the risk of nonunion and resorption
On the impact of running intersection inequalities for globally solving polynomial optimization problems
The beginnings of the Soviet encyclopedia. The utopia and misery of mathematics in the political turmoil of the 1920s
Global Optimization of Mixed-Integer Quadratically Constrained Quadratic Programs (MIQCQP) through Piecewise-Linear and Edge-Concave Relaxations
We propose a deterministic global optimization approach, whose novel contributions are rooted in the edge-concave and piecewise-linear underestimators, to address nonconvex mixed-integer quadratically-constrained quadratic programs (MIQCQP) to Δ-global optimality. The facets of low-dimensional (n †3) edge-concave aggregations dominating the termwise relaxation of MIQCQP are introduced at every node of a branch-and-bound tree. Concave multivariable terms and sparsely distributed bilinear terms that do not participate in connected edge-concave aggregations are addressed through piecewise-linear relaxations. Extensive computational studies are presented for point packing problems, standard and generalized pooling problems, and examples from GLOBALLib (Meeraus, Globallib. http://www.gamsworld.org/global/globallib. htm). © 2012 Springer and Mathematical Optimization Society