Conceptually, fair use is a refinement of the basic balance copyright strikes between author and civil interests. It is important to note, though, that what counts as fair use is generally not well delineated in copyright laws around the world. In the U.S., the law lists four basic guideli...
At first glance, this looks like a somewhat arbitrary problem (as many of Erdös’s problems initially do), as the function is not obviously related to any other well-known function or problem. However, it turns out that this problem is closely related to the parity barrier in sieve theor...
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...
Analytically, this is not a particularly pleasant equation to try to solve; one can substitute the second equation into the first to obtain a single equation but the inverse derivative is difficult to work with and seems to create ill-posedness (somewhat reminiscent of the ill-posedness of the...
they are nothing but parametrized functions\varvec{f}_{\varvec{\theta }}(\varvec{x})of some data vector\varvec{x}, and their ‘learning’ is nothing but an iterative, algorithmic fitting of the parameters to data. Hence, what could be special about them as a scientific tool or model...
The section Relative Error and Ulps describes how it is measured. Since most floating-point calculations have rounding error anyway, does it matter if the basic arithmetic operations introduce a little bit more rounding error than necessary? That question is a main theme throughout this section. ...
two rigid walls. This is also the formulation that conceptually has the best correspondence to 2D formulations in other physics fields. The object does, however, not have to be “long” in thezdirection. This is a fundamental difference from the 2D approximations for most other physics fields....
Deep learning is a form of machine learning that uses a model of computing that's very much inspired by the structure of the brain. Hence we call this model aneural network. The basic foundational unit of a neural network is theneuron, which is actually conceptually quite simple. ...
Let be a field, and let be a finite extension of that field; in this post we will denote such a relationship by . We say that is a Galois extension of if the cardinality of the automorphism group of fixing is as large as it can be, namely the degree of the extension. In that cas...
However, we only have a partial explanation at present of the interesting behaviour of the real zeroes at negative t, for instance the surviving zeroes at extremely negative values of appear to lie on the curve where the quantity is close to a half-integer, where ...