16,269 research outputs found
Towards a genome-wide transcriptogram: the Saccharomyces cerevisiae case
A genome modular classification that associates cellular processes to modules could lead to a method to quantify the differences in gene expression levels in different cellular stages or conditions: the transcriptogram, a powerful tool for assessing cell performance, would be at hand. Here we present a computational method to order genes on a line that clusters strongly interacting genes, defining functional modules associated with gene ontology terms. The starting point is a list of genes and a matrix specifying their interactions, available at large gene interaction databases. Considering the Saccharomyces cerevisiae genome we produced a succession of plots of gene transcription levels for a fermentation process. These plots discriminate the fermentation stage the cell is going through and may be regarded as the first versions of a transcriptogram. This method is useful for extracting information from cell stimuli/responses experiments, and may be applied with diagnostic purposes to different organisms
Statistical equilibrium of tetrahedra from maximum entropy principle
Discrete formulations of (quantum) gravity in four spacetime dimensions build
space out of tetrahedra. We investigate a statistical mechanical system of
tetrahedra from a many-body point of view based on non-local, combinatorial
gluing constraints that are modelled as multi-particle interactions. We focus
on Gibbs equilibrium states, constructed using Jaynes' principle of constrained
maximisation of entropy, which has been shown recently to play an important
role in characterising equilibrium in background independent systems. We apply
this principle first to classical systems of many tetrahedra using different
examples of geometrically motivated constraints. Then for a system of quantum
tetrahedra, we show that the quantum statistical partition function of a Gibbs
state with respect to some constraint operator can be reinterpreted as a
partition function for a quantum field theory of tetrahedra, taking the form of
a group field theory.Comment: v3 published version; v2 18 pages, 4 figures, improved text in
sections IIIC & IVB, minor changes elsewher
Generalized Gibbs Ensembles in Discrete Quantum Gravity
Maximum entropy principle and Souriau's symplectic generalization of Gibbs states have provided crucial insights leading to extensions of standard equilibrium statistical mechanics and thermodynamics. In this brief contribution, we show how such extensions are instrumental in the setting of discrete quantum gravity, towards providing a covariant statistical framework for the emergence of continuum spacetime. We discuss the significant role played by information-theoretic characterizations of equilibrium. We present the Gibbs state description of the geometry of a tetrahedron and its quantization, thereby providing a statistical description of the characterizing quanta of space in quantum gravity. We use field coherent states for a generalized Gibbs state to write an effective statistical field theory that perturbatively generates 2-complexes, which are discrete spacetime histories in several quantum gravity approaches
Smeared phase transitions in percolation on real complex networks
Percolation on complex networks is used both as a model for dynamics on
networks, such as network robustness or epidemic spreading, and as a benchmark
for our models of networks, where our ability to predict percolation measures
our ability to describe the networks themselves. In many applications,
correctly identifying the phase transition of percolation on real-world
networks is of critical importance. Unfortunately, this phase transition is
obfuscated by the finite size of real systems, making it hard to distinguish
finite size effects from the inaccuracy of a given approach that fails to
capture important structural features. Here, we borrow the perspective of
smeared phase transitions and argue that many observed discrepancies are due to
the complex structure of real networks rather than to finite size effects only.
In fact, several real networks often used as benchmarks feature a smeared phase
transition where inhomogeneities in the topological distribution of the order
parameter do not vanish in the thermodynamic limit. We find that these smeared
transitions are sometimes better described as sequential phase transitions
within correlated subsystems. Our results shed light not only on the nature of
the percolation transition in complex systems, but also provide two important
insights on the numerical and analytical tools we use to study them. First, we
propose a measure of local susceptibility to better detect both clean and
smeared phase transitions by looking at the topological variability of the
order parameter. Second, we highlight a shortcoming in state-of-the-art
analytical approaches such as message passing, which can detect smeared
transitions but not characterize their nature.Comment: 10 pages, 8 figure
Strengthening weak measurements of qubit out-of-time-order correlators
For systems of controllable qubits, we provide a method for experimentally
obtaining a useful class of multitime correlators using sequential generalized
measurements of arbitrary strength. Specifically, if a correlator can be
expressed as an average of nested (anti)commutators of operators that square to
the identity, then that correlator can be determined exactly from the average
of a measurement sequence. As a relevant example, we provide quantum circuits
for measuring multiqubit out-of-time-order correlators using optimized
control-Z or ZX-90 two-qubit gates common in superconducting transmon
implementations.Comment: 12 pages, 6 figures, published versio
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