509 research outputs found
A Rank-Metric Approach to Error Control in Random Network Coding
The problem of error control in random linear network coding is addressed
from a matrix perspective that is closely related to the subspace perspective
of K\"otter and Kschischang. A large class of constant-dimension subspace codes
is investigated. It is shown that codes in this class can be easily constructed
from rank-metric codes, while preserving their distance properties. Moreover,
it is shown that minimum distance decoding of such subspace codes can be
reformulated as a generalized decoding problem for rank-metric codes where
partial information about the error is available. This partial information may
be in the form of erasures (knowledge of an error location but not its value)
and deviations (knowledge of an error value but not its location). Taking
erasures and deviations into account (when they occur) strictly increases the
error correction capability of a code: if erasures and
deviations occur, then errors of rank can always be corrected provided that
, where is the minimum rank distance of the
code. For Gabidulin codes, an important family of maximum rank distance codes,
an efficient decoding algorithm is proposed that can properly exploit erasures
and deviations. In a network coding application where packets of length
over are transmitted, the complexity of the decoding algorithm is given
by operations in an extension field .Comment: Minor corrections; 42 pages, to be published at the IEEE Transactions
on Information Theor
A Complete Characterization of Irreducible Cyclic Orbit Codes and their Pl\"ucker Embedding
Constant dimension codes are subsets of the finite Grassmann variety. The
study of these codes is a central topic in random linear network coding theory.
Orbit codes represent a subclass of constant dimension codes. They are defined
as orbits of a subgroup of the general linear group on the Grassmannian. This
paper gives a complete characterization of orbit codes that are generated by an
irreducible cyclic group, i.e. a group having one generator that has no
non-trivial invariant subspace. We show how some of the basic properties of
these codes, the cardinality and the minimum distance, can be derived using the
isomorphism of the vector space and the extension field. Furthermore, we
investigate the Pl\"ucker embedding of these codes and show how the orbit
structure is preserved in the embedding.Comment: submitted to Designs, Codes and Cryptograph
Robust vetoes for gravitational-wave burst triggers using known instrumental couplings
The search for signatures of transient, unmodelled gravitational-wave (GW)
bursts in the data of ground-based interferometric detectors typically uses
`excess-power' search methods. One of the most challenging problems in the
burst-data-analysis is to distinguish between actual GW bursts and spurious
noise transients that trigger the detection algorithms. In this paper, we
present a unique and robust strategy to `veto' the instrumental glitches. This
method makes use of the phenomenological understanding of the coupling of
different detector sub-systems to the main detector output. The main idea
behind this method is that the noise at the detector output (channel H) can be
projected into two orthogonal directions in the Fourier space -- along, and
orthogonal to, the direction in which the noise in an instrumental channel X
would couple into H. If a noise transient in the detector output originates
from channel X, it leaves the statistics of the noise-component of H orthogonal
to X unchanged, which can be verified by a statistical hypothesis testing. This
strategy is demonstrated by doing software injections in simulated Gaussian
noise. We also formulate a less-rigorous, but computationally inexpensive
alternative to the above method. Here, the parameters of the triggers in
channel X are compared to the parameters of the triggers in channel H to see
whether a trigger in channel H can be `explained' by a trigger in channel X and
the measured transfer function.Comment: 14 Pages, 8 Figures, To appear in Class. Quantum Gra
Yeast chassis design for dicarboxylic acids production
info:eu-repo/semantics/publishedVersio
Discovering universal statistical laws of complex networks
Different network models have been suggested for the topology underlying
complex interactions in natural systems. These models are aimed at replicating
specific statistical features encountered in real-world networks. However, it
is rarely considered to which degree the results obtained for one particular
network class can be extrapolated to real-world networks. We address this issue
by comparing different classical and more recently developed network models
with respect to their generalisation power, which we identify with large
structural variability and absence of constraints imposed by the construction
scheme. After having identified the most variable networks, we address the
issue of which constraints are common to all network classes and are thus
suitable candidates for being generic statistical laws of complex networks. In
fact, we find that generic, not model-related dependencies between different
network characteristics do exist. This allows, for instance, to infer global
features from local ones using regression models trained on networks with high
generalisation power. Our results confirm and extend previous findings
regarding the synchronisation properties of neural networks. Our method seems
especially relevant for large networks, which are difficult to map completely,
like the neural networks in the brain. The structure of such large networks
cannot be fully sampled with the present technology. Our approach provides a
method to estimate global properties of under-sampled networks with good
approximation. Finally, we demonstrate on three different data sets (C.
elegans' neuronal network, R. prowazekii's metabolic network, and a network of
synonyms extracted from Roget's Thesaurus) that real-world networks have
statistical relations compatible with those obtained using regression models
Model-guided development of an evolutionarily stable yeast chassis.
First-principle metabolic modelling holds potential for designing microbial chassis that are resilient against phenotype reversal due to adaptive mutations. Yet, the theory of model-based chassis design has rarely been put to rigorous experimental test. Here, we report the development of Saccharomyces cerevisiae chassis strains for dicarboxylic acid production using genome-scale metabolic modelling. The chassis strains, albeit geared for higher flux towards succinate, fumarate and malate, do not appreciably secrete these metabolites. As predicted by the model, introducing product-specific TCA cycle disruptions resulted in the secretion of the corresponding acid. Adaptive laboratory evolution further improved production of succinate and fumarate, demonstrating the evolutionary robustness of the engineered cells. In the case of malate, multi-omics analysis revealed a flux bypass at peroxisomal malate dehydrogenase that was missing in the yeast metabolic model. In all three cases, flux balance analysis integrating transcriptomics, proteomics and metabolomics data confirmed the flux re-routing predicted by the model. Taken together, our modelling and experimental results have implications for the computer-aided design of microbial cell factories
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