5,147 research outputs found
Unveiling the nature of out-of-equilibrium phase transitions in a system with long-range interactions
Recently, there has been some vigorous interest in the out-of-equilibrium
quasistationary states (QSSs), with lifetimes diverging with the number N of
degrees of freedom, emerging from numerical simulations of the ferromagnetic XY
Hamiltonian Mean Field (HMF) starting from some special initial conditions.
Phase transitions have been reported between low-energy magnetized QSSs and
large-energy unexpected, antiferromagnetic-like, QSSs with low magnetization.
This issue is addressed here in the Vlasov N \rightarrow \infty limit. It is
argued that the time-asymptotic states emerging in the Vlasov limit can be
related to simple generic time-asymptotic forms for the force field. The
proposed picture unveils the nature of the out-of-equilibrium phase transitions
reported for the ferromagnetic HMF: this is a bifurcation point connecting an
effective integrable Vlasov one-particle time-asymptotic dynamics to a partly
ergodic one which means a brutal open-up of the Vlasov one-particle phase
space. Illustration is given by investigating the time-asymptotic value of the
magnetization at the phase transition, under the assumption of a sufficiently
rapid time-asymptotic decay of the transient force field
A Simple Iterative Algorithm for Parsimonious Binary Kernel Fisher Discrimination
By applying recent results in optimization theory variously known as optimization transfer or majorize/minimize algorithms, an algorithm for binary, kernel, Fisher discriminant analysis is introduced that makes use of a non-smooth penalty on the coefficients to provide a parsimonious solution. The problem is converted into a smooth optimization that can be solved iteratively with no greater overhead than iteratively re-weighted least-squares. The result is simple, easily programmed and is shown to perform, in terms of both accuracy and parsimony, as well as or better than a number of leading machine learning algorithms on two well-studied and substantial benchmarks
Computational thinking and robotics in education
After the computational thinking sessions in the previous 2016-2018 editions of TEEM Conference, the fourth edition of this track has been organized in the current 2019 edition. Computational thinking is still a very significant topic, especially, but not only, in pre-university education. In this edition, the robotic has a special role in the track, with a strength relationship with the STEM and
STEAM education of children at the pre-university levels, seeding the future of our society
Ince's limits for confluent and double-confluent Heun equations
We find pairs of solutions to a differential equation which is obtained as a
special limit of a generalized spheroidal wave equation (this is also known as
confluent Heun equation). One solution in each pair is given by a series of
hypergeometric functions and converges for any finite value of the independent
variable , while the other is given by a series of modified Bessel functions
and converges for , where denotes a regular singularity.
For short, the preceding limit is called Ince's limit after Ince who have used
the same procedure to get the Mathieu equations from the Whittaker-Hill ones.
We find as well that, when tends to zero, the Ince limit of the
generalized spheroidal wave equation turns out to be the Ince limit of a
double-confluent Heun equation, for which solutions are provided. Finally, we
show that the Schr\"odinger equation for inverse fourth and sixth-power
potentials reduces to peculiar cases of the double-confluent Heun equation and
its Ince's limit, respectively.Comment: Submitted to Journal of Mathmatical Physic
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