相关论文: The Logarithmic Spiral Conjecture
Logarithmic spirals are conjectured to be optimal escape paths from a half plane ocean. Assuming this, we find the rate of increase for both min-max and min-mean interpretations of "optimal". For the one-dimensional analog, which we call…
Two general methods for establishing the logarithmic behavior of recursively defined sequences of real numbers are presented. One is the interlacing method, and the other one is based on calculus. Both methods are used to prove logarithmic…
In deterministic optimization, line searches are a standard tool ensuring stability and efficiency. Where only stochastic gradients are available, no direct equivalent has so far been formulated, because uncertain gradients do not allow for…
In deterministic optimization, line searches are a standard tool ensuring stability and efficiency. Where only stochastic gradients are available, no direct equivalent has so far been formulated, because uncertain gradients do not allow for…
When the sequence of regular polygons with consecutively increasing numbers of sides is joined edge-to-edge in a single direction while minimizing bending, the resulting structure assumes the shape of a logarithmic spiral. This paper proves…
We introduce a geometric construction which relates to the pentagram map much in the way that a logarithmic spiral relates to a circle. After introducing the construction, we establish some basic geometric facts about it, and speculate on…
A new pattern search method for bound constrained optimization is introduced. The proposed algorithm employs the coordinate directions, in a suitable way, with a nonmonotone line search for accepting the new iterate, without using…
There are several scoring rules that one can choose from in order to score probabilistic forecasting models or estimate model parameters. Whilst it is generally agreed that proper scoring rules are preferable, there is no clear criterion…
The LL(finite) parsing strategy for parsing of LL(k) grammars where k needs not to be known is presented. The strategy parses input in linear time, uses arbitrary but always minimal lookahead necessary to disambiguate between alternatives…
Often a non-linear mechanical problem is formulated as a non-linear differential equation. A new method is introduced to find out new solutions of non-linear differential equations if one of the solutions of a given non-linear differential…
The Collatz conjecture is explored using polynomials based on a binary numeral system. It is shown that the degree of the polynomials, on average, decreases after a finite number of steps of the Collatz operation, which provides a weak…
In this paper, we study a general Syracuse problem. We give some necessary conditions concerning the existence of eventual non trivial cycles. Some properties based on linear logarithmic forms are established. New general conjectures are…
We introduce two topological non-$\Sigma$ operad structures on planar line arrangements subject to a certain geometric order condition, ensuring a well-defined notion of particle ordering on a distinguished line. This is interpreted in…
Modelling real world systems frequently requires the solution of systems of nonlinear equations. A number of approaches have been suggested and developed for this computational problem. However, it is also possible to attempt solutions…
We consider the problem of minimizing a sum of several convex non-smooth functions. We introduce a new algorithm called the selective linearization method, which iteratively linearizes all but one of the functions and employs simple…
Second order spiral splines are $C^2$ unit-speed planar curves that can be used to interpolate a list $Y$ of $n+1$ points in $\R ^2$ at times specified in some list $T$, where $n\geq 2$. Asymptotic methods are used to develop a fast…
We present a polynomial-time algorithm that determines, given some choice rule, whether there exists an obviously strategy-proof mechanism for that choice rule.
This paper is about line search for the generalized alternating projections (GAP) method. This method is a generalization of the von Neumann alternating projections method, where instead of performing alternating projections, relaxed…
We study the version of the C-Planarity problem in which edges connecting the same pair of clusters must be grouped into pipes, which generalizes the Strip Planarity problem. We give algorithms to decide several families of instances for…
We use the methods of empirical mathematics to show that iterative logarithmic operations will result in an attractor point on the complex plane. Moreover, we demonstrate that different bases converge onto different attractors. Finally, we…