HIGHLIGHTED
PUBLICATIONS
Quantifying the degree of average contraction of
Collatz orbits,
Carletti,
T. & Fanelli,
D., Bollettino
dell'Unione
Matematica
Italiana, 2017
Arithmetics is the
branch of mathematics
dealing with integer
numbers; additions,
subtraction,
multiplications,
divisions, even
numbers (divisible by
2) and odd numbers
(not divisible by 2),
are all souvenirs of
our primary school
years. Everything
seems so evident and
simple that one could
not expect unsolved
problems still exist
in arithmetics, even
more if their
statements do not
involve complicated
expressions. But look
at this intriguing
problem.
Let n_0 be any integer
number, if it is even
divide it by 2 and
call the result
n_1=n_0/2, otherwise
let n_1=3n_0+1; do the
same for n_1 and so on
obtaining new integer
numbers, the
trajectory starting
from n_0. To warm up,
let us take n_0=1, it
is odd then
n_1=3x1+1=4, which is
even and so n_2=4/2=2,
which is also even and
thus n_3=2/2=1. We are
back to our initial
number. The case n_0=2
is straightforward, so
let us do the same
with n_0=3; then one
easily get: n_1=10,
n_2=5, n_3=16, n_4=8,
n_5=4, n_6=4, n_7=2
and n_8 =1. Wow! We
end up again at 1.
The natural question
is thus: does any
initial integer n_0
will end up at 1 after
a finite number of
operations (division
by 2 and
multiplication by 3
followed by adding 1)?
Despite its
simplicity, this is an
open question since
almost a century;
mathematicians believe
it is true and named
it the Collatz
conjecture. In this
paper, we provide a
novel argument to
support the validity
of the Collatz
conjecture.
More information: https://link.springer.com/article/10.1007/s405740170145x
Theory
of Turing
Patterns on Time
Varying Networks,
Petit,
J.,В Lauwens, B.,
Fanelli, D. &
Carletti, T.,
Physical Review
Letters, 119,
148301, 2017
Networks are
everywhere. The brain,
Internet and the
cyberworld, foodwebs,
social contacts and
commuting fall within
the vast realm of
network science.
Networks are often
dynamical entities,
and their ability to
change in time
drastically affects
the behaviour of a
scrutinized system
(e.g. how constitutive
elements diffuse and
interact), in terms of
resilience,
vulnerability to
attacks or degree of
synchronization. As
rigorously
demonstrated in the
paper by Petit et al,
selforganized motifs
(e.g. non uniform
distribution across
the nodes) can indeed
emerge from noise, as
follows a spontaneous
drive triggered by the
inherent network
dynamics. This
observation translates
in a new route to
pattern formation that
bears applied and
fundamental interests,
from neuroscience to
biology, via chemistry
and physics, to
ecology and social
systems.Relevant is
for instance the
application to
epidemics spreading,
as mediated by the
rapidly evolving
networks of pairwise
social contacts.
Pathogens need in fact
some time to settle
and eventually reach
the virulent stage.
During this latent
period, individuals
carrying the virus
experience a multitude
of interactions [in
the bus/underground,
at work/shops/sportвЂ¦],
so contributing to
reshape the underlying
networks of contacts.
As discussed in the
paper, the unavoidable
variability of the
network structure [an
ingredient so far
largely omitted in the
relevant literature]
can shape the response
of the system and
possibly impact on the
propagation of the
infection. The theory
developed covers a
wide range of possible
settings, from
periodic to random
modulation of the
network structure and
allows for quite
general interactions
terms.
More information:
https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.119.148301
Shifts
of community
composition and
population density
substantially
affect ecosystem
function despite
invariant
richness,
Spaak,
J. W., Baert, J.
M.,В Baird, D. J.,
Eisenhauer, N.,
Maltby, L., Pomati,
F., Radchuk, V.,
Rohr, J. R., Van den
Brink, P. J., De
Laender, F., Ecology
Letters 20,
10,В 1315вЂ“1324, 2017
Impacts of
environmental change
are typically measured
by comparing the
observed number of
species with some
reference no impact'
value.
We show that
this approach severely
underestimates such
impacts, because
environmental change
can affect population
sizes and the
composition of
biological
communities, even if
does not affect the
number of species.
Our results, which are
based on mathematical
analyses of a
mechanistic model and
statistical modelling
of phytoplankton data
both sustain the same
conclusion: When
solely relying on the
number of species
present as an
indicator of
environmental quality,
effects of up to 80%
can go unnoticed. Our
findings have
farreaching
implications for the
field of
BiodiversityEcosystem
Function research and
environmental
monitoring and
assessment.
More information: http://onlinelibrary.wiley.com/doi/10.1111/ele.12828/full
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