Indeed, Reichardt (2004) has shown that there are simple problems for which the algorithm will get stuck in a local minimum, in which there are exponentially many eigenvalues all exponentially close to the ground state energy, so applying the adiabatic theorem, even for these simple problems, will take exponential time, and we are back to square one.
First-order reasoning systems, on the one hand, have reached considerable strength in some niches, but in many areas of mathematics they still cannot reliably solve relatively simple problems, for example, when reasoning about sets, relations, or functions.
It presents the real life stakes of these identities in Don's life as simple problems for Tony to solve.
Launched in April, AdWhirl solves a simple problem for iPhone developers.
Though geometric optimal control and numerical continuation provide a nice way to design efficient approaches for many aerospace applications, the answer to "how to select a reasonably simple problem for the continuation procedure" for general optimal control problems remains open.
A mathematician of extraordinary creativity, he has a taste for simple problems of timeless beauty, which he has solved by developing elegant and powerful new methods that offer deep insights.
Designed for solving simple problems of the mate-in-two variety, the program would examine every possible move until a solution was found.
The collection includes both simple problems suitable for initial testing, and more complex problems with realistic size and quality of data.
Results are generated for the simple problem of a periodic bi-material beam, and then for the more complex examples of square, diamond, and hexagonal honeycomb lattices.
A suite of simulations will be conducted utilizing different linear solvers for the simple problem of the bouyant rise of a warm bubble.
