47 research outputs found
A note on 5-cycle double covers
The strong cycle double cover conjecture states that for every circuit of
a bridgeless cubic graph , there is a cycle double cover of which
contains . We conjecture that there is even a 5-cycle double cover of
which contains , i.e. is a subgraph of one of the five 2-regular
subgraphs of . We prove a necessary and sufficient condition for a 2-regular
subgraph to be contained in a 5-cycle double cover of
Normal edge-colorings of cubic graphs
A normal -edge-coloring of a cubic graph is an edge-coloring with
colors having the additional property that when looking at the set of colors
assigned to any edge and the four edges adjacent it, we have either exactly
five distinct colors or exactly three distinct colors. We denote by
the smallest , for which admits a normal
-edge-coloring. Normal -edge-colorings were introduced by Jaeger in order
to study his well-known Petersen Coloring Conjecture. More precisely, it is
known that proving for every bridgeless cubic graph is
equivalent to proving Petersen Coloring Conjecture and then, among others,
Cycle Double Cover Conjecture and Berge-Fulkerson Conjecture. Considering the
larger class of all simple cubic graphs (not necessarily bridgeless), some
interesting questions naturally arise. For instance, there exist simple cubic
graphs, not bridgeless, with . On the other hand, the known
best general upper bound for was . Here, we improve it by
proving that for any simple cubic graph , which is best
possible. We obtain this result by proving the existence of specific no-where
zero -flows in -edge-connected graphs.Comment: 17 pages, 6 figure
Birational Mappings and Matrix Sub-algebra from the Chiral Potts Model
We study birational transformations of the projective space originating from
lattice statistical mechanics, specifically from various chiral Potts models.
Associating these models to \emph{stable patterns} and \emph{signed-patterns},
we give general results which allow us to find \emph{all} chiral -state
spin-edge Potts models when the number of states is a prime or the square
of a prime, as well as several -dependent family of models. We also prove
the absence of monocolor stable signed-pattern with more than four states. This
demonstrates a conjecture about cyclic Hadamard matrices in a particular case.
The birational transformations associated to these lattice spin-edge models
show complexity reduction. In particular we recover a one-parameter family of
integrable transformations, for which we give a matrix representationComment: 22 pages 0 figure The paper has been reorganized, splitting the
results into two sections : results pertaining to Physics and results
pertaining to Mathematic
Embodied memory: unconscious smiling modulates emotional evaluation of episodic memories.
Since Damasio introduced the somatic markers hypothesis in Damasio (1994), it has spread through the psychological community, where it is now commonly acknowledged that somatic states are a factor in producing the qualitative dimension of our experiences. Present actions are emotionally guided by those somatic states that were previously activated in similar experiences. In this model, somatic markers serve as a kind of embodied memory. Here, we test whether the manipulation of somatic markers can modulate the emotional evaluation of negative memories. Because facial feedback has been shown to be a powerful means of modifying emotional judgements, we used it to manipulate somatic markers. Participants first read a sad story in order to induce a negative emotional memory and then were asked to rate their emotions and memory about the text. Twenty-four hours later, the same participants were asked to assume a predetermined facial feedback (smiling) while reactivating their memory of the sad story. The participants were once again asked to fill in emotional and memory questionnaires about the text. Our results showed that participants who had smiled during memory reactivation later rated the text less negatively than control participants. However, the contraction of the zygomaticus muscles during memory reactivation did not have any impact on episodic memory scores. This suggests that manipulating somatic states modified emotional memory without affecting episodic memory. Thus, modulating memories through bodily states might pave the way to studying memory as an embodied function and help shape new kinds of psychotherapeutic interventions
The random field ising model: algorithmic complexity and phase transition
The random field Ising model (RFIM) is investigated from the complexity point of view. We prove that finding a ground state of the ferromagnetic RFIM is a polynomial (P) optimization problem in any dimension d. A new rigidity algorithm for the search of the ground state morphology is also given. In contrast, the problem associated to the antiferromagnetic RFIM is shown to be an NP-complete optimization problem. The absence of any sensivity to d contrasts sharply with the known results previously obtained for the frustration model of spin glasses. Our results show, in particular, the absence of a simple one to one correspondence between finite Tc phase transition and NP-completeness properties in statistical mechanics models with competing interactions
Low-energy excitations in the three-dimensional random-field Ising model
The random-field Ising model (RFIM), one of the basic models for quenched
disorder, can be studied numerically with the help of efficient ground-state
algorithms. In this study, we extend these algorithm by various methods in
order to analyze low-energy excitations for the three-dimensional RFIM with
Gaussian distributed disorder that appear in the form of clusters of connected
spins. We analyze several properties of these clusters. Our results support the
validity of the droplet-model description for the RFIM.Comment: 10 pages, 9 figure