67 research outputs found
On countings and enumerations of block-parallel automata networks
When we focus on finite dynamical systems from both the
computability/complexity and the modelling standpoints, automata networks seem
to be a particularly appropriate mathematical model on which theory shall be
developed. In this paper, automata networks are finite collections of entities
(the automata), each automaton having its own set of possible states, which
interact with each other over discrete time, interactions being defined as
local functions allowing the automata to change their state according to the
states of their neighbourhoods. The studies on this model of computation have
underlined the very importance of the way (i.e. the schedule) according to
which the automata update their states, namely the update modes which can be
deterministic, periodic, fair, or not. Indeed, a given network may admit
numerous underlying dynamics, these latter depending highly on the update modes
under which we let the former evolve. In this paper, we pay attention to a new
kind of deterministic, periodic and fair update mode family introduced recently
in a modelling framework, called the block-parallel update modes by duality
with the well-known and studied block-sequential update modes. More precisely,
in the general context of automata networks, this work aims at presenting what
distinguish block-parallel update modes from block-sequential ones, and at
counting and enumerating them: in absolute terms, by keeping only
representatives leading to distinct dynamics, and by keeping only
representatives giving rise to distinct isomorphic limit dynamics. Put
together, this paper constitutes a first theoretical analysis of these update
modes and their impact on automata networks dynamics
Complexity of fixed point counting problems in Boolean Networks
A Boolean network (BN) with components is a discrete dynamical system
described by the successive iterations of a function . This model finds applications in biology, where fixed points play a
central role. For example, in genetic regulations, they correspond to cell
phenotypes. In this context, experiments reveal the existence of positive or
negative influences among components: component has a positive (resp.
negative) influence on component meaning that tends to mimic (resp.
negate) . The digraph of influences is called signed interaction digraph
(SID), and one SID may correspond to a large number of BNs (which is, in
average, doubly exponential according to ). The present work opens a new
perspective on the well-established study of fixed points in BNs. When
biologists discover the SID of a BN they do not know, they may ask: given that
SID, can it correspond to a BN having at least/at most fixed points?
Depending on the input, we prove that these problems are in or
complete for , ,
\textrm{NP}^{\textrm{#P}} or . In particular, we prove
that it is -complete (resp. -complete) to
decide if a given SID can correspond to a BN having at least two fixed points
(resp. no fixed point).Comment: 43 page
COVID-19 symptoms at hospital admission vary with age and sex: results from the ISARIC prospective multinational observational study
Background:
The ISARIC prospective multinational observational study is the largest cohort of hospitalized patients with COVID-19. We present relationships of age, sex, and nationality to presenting symptoms.
Methods:
International, prospective observational study of 60â109 hospitalized symptomatic patients with laboratory-confirmed COVID-19 recruited from 43 countries between 30 January and 3 August 2020. Logistic regression was performed to evaluate relationships of age and sex to published COVID-19 case definitions and the most commonly reported symptoms.
Results:
âTypicalâ symptoms of fever (69%), cough (68%) and shortness of breath (66%) were the most commonly reported. 92% of patients experienced at least one of these. Prevalence of typical symptoms was greatest in 30- to 60-year-olds (respectively 80, 79, 69%; at least one 95%). They were reported less frequently in children (â€â18 years: 69, 48, 23; 85%), older adults (â„â70 years: 61, 62, 65; 90%), and women (66, 66, 64; 90%; vs. men 71, 70, 67; 93%, each Pâ<â0.001). The most common atypical presentations under 60 years of age were nausea and vomiting and abdominal pain, and over 60 years was confusion. Regression models showed significant differences in symptoms with sex, age and country.
Interpretation:
This international collaboration has allowed us to report reliable symptom data from the largest cohort of patients admitted to hospital with COVID-19. Adults over 60 and children admitted to hospital with COVID-19 are less likely to present with typical symptoms. Nausea and vomiting are common atypical presentations under 30 years. Confusion is a frequent atypical presentation of COVID-19 in adults over 60 years. Women are less likely to experience typical symptoms than men
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