41 research outputs found
On a class of rational matrices and interpolating polynomials related to the discrete Laplace operator
Let \dlap be the discrete Laplace operator acting on functions (or rational
matrices) , where is the two
dimensional lattice of size embedded in . Consider a rational
matrix , whose inner entries
satisfy \dlap\mathcal{H}_{ij}=0. The matrix is thus the
classical finite difference five-points approximation of the Laplace operator
in two variables. We give a constructive proof that is the
restriction to of a discrete harmonic polynomial in two
variables for any . This result proves a conjecture formulated in the
context of deterministic fixed-energy sandpile models in statistical mechanics.Comment: 18 pag, submitted to "Note di Matematica
Heterogeneous Mean Field for neural networks with short term plasticity
We report about the main dynamical features of a model of leaky-integrate-and
fire excitatory neurons with short term plasticity defined on random massive
networks. We investigate the dynamics by a Heterogeneous Mean-Field formulation
of the model, that is able to reproduce dynamical phases characterized by the
presence of quasi-synchronous events. This formulation allows one to solve also
the inverse problem of reconstructing the in-degree distribution for different
network topologies from the knowledge of the global activity field. We study
the robustness of this inversion procedure, by providing numerical evidence
that the in-degree distribution can be recovered also in the presence of noise
and disorder in the external currents. Finally, we discuss the validity of the
heterogeneous mean-field approach for sparse networks, with a sufficiently
large average in-degree
Average synaptic activity and neural networks topology: a global inverse problem
The dynamics of neural networks is often characterized by collective behavior
and quasi-synchronous events, where a large fraction of neurons fire in short
time intervals, separated by uncorrelated firing activity. These global
temporal signals are crucial for brain functioning. They strongly depend on the
topology of the network and on the fluctuations of the connectivity. We propose
a heterogeneous mean--field approach to neural dynamics on random networks,
that explicitly preserves the disorder in the topology at growing network
sizes, and leads to a set of self-consistent equations. Within this approach,
we provide an effective description of microscopic and large scale temporal
signals in a leaky integrate-and-fire model with short term plasticity, where
quasi-synchronous events arise. Our equations provide a clear analytical
picture of the dynamics, evidencing the contributions of both periodic (locked)
and aperiodic (unlocked) neurons to the measurable average signal. In
particular, we formulate and solve a global inverse problem of reconstructing
the in-degree distribution from the knowledge of the average activity field.
Our method is very general and applies to a large class of dynamical models on
dense random networks
On a class of rational matrices and interpolating polynomials related to the discrete Laplace operator
Let \dlap be the discrete Laplace operator acting on functions(or rational matrices) ,where is the two dimensional lattice of size embedded in . Consider a rational matrix , whose inner entries satisfy \dlap\mathcal{H}_{ij}=0. The matrix is thus theclassical finite difference five-points approximation of theLaplace operator in two variables. We give a constructive proofthat is the restriction to of adiscrete harmonic polynomial in two variables for any L>2. Thisresult proves a conjecture formulated in the context ofdeterministic fixed-energy sandpile models in statisticalmechanics
Metric Features of a Dipolar Model
The lattice spin model, with nearest neighbor ferromagnetic exchange and long
range dipolar interaction, is studied by the method of time series for
observables based on cluster configurations and associated partitions, such as
Shannon entropy, Hamming and Rohlin distances. Previous results based on the
two peaks shape of the specific heat, suggested the existence of two possible
transitions. By the analysis of the Shannon entropy we are able to prove that
the first one is a true phase transition corresponding to a particular melting
process of oriented domains, where colored noise is present almost
independently of true fractality. The second one is not a real transition and
it may be ascribed to a smooth balancing between two geometrical effects: a
progressive fragmentation of the big clusters (possibly creating fractals), and
the slow onset of a small clusters chaotic phase. Comparison with the nearest
neighbor Ising ferromagnetic system points out a substantial difference in the
cluster geometrical properties of the two models and in their critical
behavior.Comment: 20 pages, 15 figures, submitted to JPhys
Rohlin Distance and the Evolution of Influenza A virus: Weak Attractors and Precursors
The evolution of the hemagglutinin amino acids sequences of Influenza A virus
is studied by a method based on an informational metrics, originally introduced
by Rohlin for partitions in abstract probability spaces. This metrics does not
require any previous functional or syntactic knowledge about the sequences and
it is sensitive to the correlated variations in the characters disposition. Its
efficiency is improved by algorithmic tools, designed to enhance the detection
of the novelty and to reduce the noise of useless mutations. We focus on the
USA data from 1993/94 to 2010/2011 for A/H3N2 and on USA data from 2006/07 to
2010/2011 for A/H1N1 . We show that the clusterization of the distance matrix
gives strong evidence to a structure of domains in the sequence space, acting
as weak attractors for the evolution, in very good agreement with the
epidemiological history of the virus. The structure proves very robust with
respect to the variations of the clusterization parameters, and extremely
coherent when restricting the observation window. The results suggest an
efficient strategy in the vaccine forecast, based on the presence of
"precursors" (or "buds") populating the most recent attractor.Comment: 13 pages, 5+4 figure
Infographic consensus recommendations on the classification, definition and diagnostic criteria of hip-related pain in young and middle-aged active adults from the International Hip-related Pain Research Network, Zurich 2018
**Please note that there are multiple authors for this article therefore only the name of the first 30 including Federation University Australia affiliate “Michael Drew" is provided in this record*
Patient-reported outcome measures for hip-related pain: A review of the available evidence and a consensus statement from the International Hip-related Pain Research Network, Zurich 2018
Hip-related pain is a well-recognised complaint among active young and middle-aged active adults. People experiencing hip-related disorders commonly report pain and reduced functional capacity, including difficulties in executing activities of daily living. Patient-reported outcome measures (PROMs) are essential to accurately examine and compare the effects of different treatments on disability in those with hip pain. In November 2018, 38 researchers and clinicians working in the field of hip-related pain met in Zurich, Switzerland for the first International Hip-related Pain Research Network meeting. Prior to the meeting, evidence summaries were developed relating to four prioritised themes. This paper discusses the available evidence and consensus process from which recommendations were made regarding the appropriate use of PROMs to assess disability in young and middle-aged active adults with hip-related pain. Our process to gain consensus had five steps: (1) systematic review of systematic reviews; (2) preliminary discussion within the working group; (3) update of the more recent high-quality systematic review and examination of the psychometric properties of PROMs according to established guidelines; (4) formulation of the recommendations considering the limitations of the PROMs derived from the examination of their quality; and (5