The main objective of AI is tocreate systems capable of performing tasks without direct human involvement. In the right environment, these systems can approximate or even surpass human capabilities in terms of
because the definition of the complexity in field theory is still not complete, the confirmation of the holographic duality of the complexity is ambiguous. To improve this situation, we approach the problem from
First suppose that , so that is non-invertible, and there is a linear dependence between the rows . Thus, one of the will lie in the hyperplane spanned by the other rows, and so one of the distances mentioned above will vanish; in fact, one expects many of the distances to vanish. ...
As it is shown in the first part of this short essay, duality plus conservation laws allow the violation of Bell’s inequalities for any spatio-temporal separation. To dig deeper into particle dualism, in the second part, a class of models is proposed as a working framework. It encompasses...
When this is the case, then there are no nonzero coefficients that satisfy the equation a1x1+a2x2+...+anxn=0. If there do exist a set of nonzero coefficients that cause this equation to be true, then this is an example of linear dependence....
As a consequence, the -entropy is of polynomial size (a fact that seems to have first been implicitly observed in Lemma 6.2 of this paper of Frantzikinakis; thanks to Ben Green for this reference). One can obtain more precise dependence on using the quantitative version of this inverse ...
This lesson introduces the matrix - the rectangular array at the heart of matrix algebra. Matrix algebra is used quite a bit in advanced statistics, largely because it provides two benefits.Compact notation for describing sets of data and sets of equations. Efficient methods for manipulating sets ...
Larger firms will likely have more resources at their disposal to make financial and people based investments in their exporting activities. Further, “larger suppliers have the resources to make investments in branding that reduce their dependence on a [channel partner]; they may be more successful...
Indeed, the unregu- lated entropy (taking the length of the geodesic all the way to the AdS boundary) is invariant, but it is also divergent, so it cannot be used directly to compute E. And as soon as we introduce a cutoff, we introduce coordinate dependence. This is truly a property...
This result has a number of applications, for instance to establishing asymptotics for linear equations in the primes, but this will not be the focus of discussion here. The purpose of this post is to record the observation that this “discrete” inverse theorem, together with an ...