Related papers: The cocked hat
In this article, a new solution for the convex hull problem has been presented. The convex hull is a widely known problem in computational geometry. As nature is a rich source of ideas in the field of algorithms, the solution has been…
We apply an old method for constructing points-and-lines configurations in the plane to study some recent questions in incidence geometry.
We study the famous mathematical puzzle of prisoners and hats. We introduce a framework in which various variants of the problem can be formalized. We examine three particular versions of the problem (each one in fact a class of problems)…
A novel approach to an old symmetry problem is developed. A new proof is given for the following symmetry problem, studied earlier.
This paper serves as the announcement of my program---a joke version of the Langlands Program. In connection with this program, I discuss an old hat puzzle, introduce a new hat puzzle, and offer a puzzle for the reader.
The long standing issue known as the hot QCD collinear singularity problem has been proven to rely on an incorrect sequence of two mathematical operations. Here, the original derivation of this problem is entirely revisited within the…
In a previous paper (q-alg/9501022) we suggested some algorithms that could be useful in solving the problem of knot classification. Here we continue this discussion by answering questions raised in that paper and by commenting on practical…
This paper describes a problem arising in sea exploration, where the aim is to schedule the expedition of a ship for collecting information about the resources on the seafloor. The aim is to collect data by probing on a set of carefully…
In this paper we study the Three Hat Problem which appeared in Puzzle Corner of the Technology Review magazine. This puzzle gives a scenario in which three players wearing hats are sitting together and each hat can be seen by everyone…
We explore the resolution of claims problems with history. At a given period of time, a group of agents holds claims over an insufficient endowment, as they did in previous periods. The solution to the present-period problem might be…
We discuss some old common knowledge puzzles and introduce a lot of new common knowledge puzzles.
By some new recursive algorithms, in this paper, we will give some improvements on Waring's problem.
We survey the history of the capset problem in the context of related results on progression-free sets, discuss recent progress, and mention further directions to explore.
We are witnessing the rise of autonomous cars, which will likely revolutionize the way we travel. Arguably, the maritime domain lags behind, as ships operate on many more degrees of freedom (thus, a much larger search space): there is less…
We study solutions of the mean curvature flow which are defined for all negative curvature times, usually called ancient solutions. We give various conditions ensuring that a closed convex ancient solution is a shrinking sphere. Examples of…
This note presents an interesting counterexample to a basic covering problem.
We study a new type of K-armed bandit problem where the expected return of one arm may depend on the returns of other arms. We present a new algorithm for this general class of problems and show that under certain circumstances it is…
We consider a novel variant of the contextual bandit problem (i.e., the multi-armed bandit with side-information, or context, available to a decision-maker) where the context used at each decision may be corrupted ("useless context"). This…
There is a serious problem with one of the assumptions made in the security proof of the SURF scheme. This problem turns out to be easy in the regime of parameters needed for the SURF scheme to work. We give afterwards the old version of…
The Halting Problem is ill-conceived and ill-defined.