262 research outputs found
The phase diagram of random threshold networks
Threshold networks are used as models for neural or gene regulatory networks.
They show a rich dynamical behaviour with a transition between a frozen and a
chaotic phase. We investigate the phase diagram of randomly connected threshold
networks with real-valued thresholds h and a fixed number of inputs per node.
The nodes are updated according to the same rules as in a model of the
cell-cycle network of Saccharomyces cereviseae [PNAS 101, 4781 (2004)]. Using
the annealed approximation, we derive expressions for the time evolution of the
proportion of nodes in the "on" and "off" state, and for the sensitivity
. The results are compared with simulations of quenched networks. We
find that for integer values of h the simulations show marked deviations from
the annealed approximation even for large networks. This can be attributed to
the particular choice of the updating rule.Comment: 8 pages, 6 figure
Response of Boolean networks to perturbations
We evaluate the probability that a Boolean network returns to an attractor
after perturbing h nodes. We find that the return probability as function of h
can display a variety of different behaviours, which yields insights into the
state-space structure. In addition to performing computer simulations, we
derive analytical results for several types of Boolean networks, in particular
for Random Boolean Networks. We also apply our method to networks that have
been evolved for robustness to small perturbations, and to a biological
example
The Influence of Canalization on the Robustness of Boolean Networks
Time- and state-discrete dynamical systems are frequently used to model
molecular networks. This paper provides a collection of mathematical and
computational tools for the study of robustness in Boolean network models. The
focus is on networks governed by -canalizing functions, a recently
introduced class of Boolean functions that contains the well-studied class of
nested canalizing functions. The activities and sensitivity of a function
quantify the impact of input changes on the function output. This paper
generalizes the latter concept to -sensitivity and provides formulas for the
activities and -sensitivity of general -canalizing functions as well as
canalizing functions with more precisely defined structure. A popular measure
for the robustness of a network, the Derrida value, can be expressed as a
weighted sum of the -sensitivities of the governing canalizing functions,
and can also be calculated for a stochastic extension of Boolean networks.
These findings provide a computationally efficient way to obtain Derrida values
of Boolean networks, deterministic or stochastic, that does not involve
simulation.Comment: 16 pages, 2 figures, 3 table
Phase Synchronization in Railway Timetables
Timetable construction belongs to the most important optimization problems in
public transport. Finding optimal or near-optimal timetables under the
subsidiary conditions of minimizing travel times and other criteria is a
targeted contribution to the functioning of public transport. In addition to
efficiency (given, e.g., by minimal average travel times), a significant
feature of a timetable is its robustness against delay propagation. Here we
study the balance of efficiency and robustness in long-distance railway
timetables (in particular the current long-distance railway timetable in
Germany) from the perspective of synchronization, exploiting the fact that a
major part of the trains run nearly periodically. We find that synchronization
is highest at intermediate-sized stations. We argue that this synchronization
perspective opens a new avenue towards an understanding of railway timetables
by representing them as spatio-temporal phase patterns. Robustness and
efficiency can then be viewed as properties of this phase pattern
Demographic, clinical and antibody characteristics of patients with digital ulcers in systemic sclerosis: data from the DUO Registry
OBJECTIVES: The Digital Ulcers Outcome (DUO) Registry was designed to describe the clinical and antibody characteristics, disease course and outcomes of patients with digital ulcers associated with systemic sclerosis (SSc).
METHODS: The DUO Registry is a European, prospective, multicentre, observational, registry of SSc patients with ongoing digital ulcer disease, irrespective of treatment regimen. Data collected included demographics, SSc duration, SSc subset, internal organ manifestations, autoantibodies, previous and ongoing interventions and complications related to digital ulcers.
RESULTS: Up to 19 November 2010 a total of 2439 patients had enrolled into the registry. Most were classified as either limited cutaneous SSc (lcSSc; 52.2%) or diffuse cutaneous SSc (dcSSc; 36.9%). Digital ulcers developed earlier in patients with dcSSc compared with lcSSc. Almost all patients (95.7%) tested positive for antinuclear antibodies, 45.2% for anti-scleroderma-70 and 43.6% for anticentromere antibodies (ACA). The first digital ulcer in the anti-scleroderma-70-positive patient cohort occurred approximately 5 years earlier than the ACA-positive patient group.
CONCLUSIONS: This study provides data from a large cohort of SSc patients with a history of digital ulcers. The early occurrence and high frequency of digital ulcer complications are especially seen in patients with dcSSc and/or anti-scleroderma-70 antibodies
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