Related papers: Fitting an Elephant with Four non-Zero Parameters
Many biological systems perform close to their physical limits, but promoting this optimality to a general principle seems to require implausibly fine tuning of parameters. Using examples from a wide range of systems, we show that this…
This paper describes the formulation and experimental testing of a novel method for the estimation and approximation of submanifold models of animal motion. It is assumed that the animal motion is supported on a configuration manifold $Q$…
Using information theory, we propose an estimation method for traits parameters in a Darwinian evolution model for species with on trait or multiple traits. We use the Fisher's information to obtain the errors on the estimation for one…
Many-body systems undergoing quantum phase transitions reveal substantial growth of non-classical correlations between different parties of the system. This behavior is manifested by characteristic divergences of the von Neumann entropy.…
We study some problems in metric Diophantine approximation over local fields of positive characteristic.
The ability of animals to interact with complex dynamics is unmatched in robots. Especially important to the interaction performances is the online adaptation of body dynamics, which can be modeled as an impedance behaviour. However, the…
This paper initiates a novel research direction in the theory of Diophantine equations: define an appropriate version of the equation's size, order all polynomial Diophantine equations starting from the smallest ones, and then solve the…
If robots are to become ubiquitous, they will need to be able to adapt to complex and dynamic environments. Robots that can adapt their bodies while deployed might be flexible and robust enough to meet this challenge. Previous work on…
Spacetime nonmetricity can be studied experimentally through its couplings to fermions and photons. We use recent high-precision searches for Lorentz violation to deduce first constraints involving the 40 independent nonmetricity components…
Animals and robots exist in a physical world and must coordinate their bodies to achieve behavioral objectives. With recent developments in deep reinforcement learning, it is now possible for scientists and engineers to obtain sensorimotor…
In this paper, we consider the Dirichlet problem associated to an elliptic Kirchhoff-type equation depending on two parameters. Under rather general and natural assumptions, we prove that, for certain values of the parameters, the problem…
We provide an accurate calculation of the energy spectrum of three atoms interacting through a contact force in a one-dimensional harmonic trap, considering both spinful fermions and spinless bosons. We use fermionic energies as a benchmark…
Modern machine learning often operates in the regime where the number of parameters is much higher than the number of data points, with zero training loss and yet good generalization, thereby contradicting the classical bias-variance…
This paper attempts to explain the mystery behind an 18th elephant that appears in many popular legends involving the division of a herd of 17 elephants into groups in the ratio 1/2:1/3:1/9.
We consider the frog model with geometric lifetime (parameter $1-p$) on homogeneous trees of dimension $d$. In 2002, \cite{alves2002-2} proved that there exists a critical lifetime parameter $p_c\in(0,1)$ above which infinitely many frogs…
Many authors studied the problem that rational triangle pairs (triangle-parallelogram pairs) with the same area and the same perimeter. They investigated this problem by solving the rational solutions of the corresponding Diophantine…
Fitting a simplifying model with several parameters to real data of complex objects is a highly nontrivial task, but enables the possibility to get insights into the objects physics. Here, we present a method to infer the parameters of the…
All fields of science depend on mathematical models. Occam's razor refers to the principle that good models should exclude parameters beyond those minimally required to describe the systems they represent. This is because redundancy can…
This paper puts forth a new formulation and algorithm for the elastic matching problem on unparametrized curves and surfaces. Our approach combines the frameworks of square root normal fields and varifold fidelity metrics into a novel…
A random forest prediction can be computed by the scalar product of the labels of the training examples and a set of weights that are determined by the leafs of the forest into which the test object falls; each prediction can hence be…