Bounds on the Average Sensitivity of Nested Canalizing Functions

Nested canalizing Boolean (NCF) functions play an important role in biological motivated regulative networks and in signal processing, in particular describing stack filters. It has been conjectured that NCFs have a stabilizing effect on the network dynamics. It is well known that the average sensitivity plays a central role for the stability of (random) Boolean networks. Here we provide a tight upper bound on the average sensitivity for NCFs as a function of the number of relevant input variables. As conjectured in literature this bound is smaller than 4/3 This shows that a large number of functions appearing in biological networks belong to a class that has very low average sensitivity, which is even close to a tight lower bound.Comment: revised submission to PLOS ON

Canonical tree-decompositions of finite graphs I. Existence and algorithms

We construct tree-decompositions of graphs that distinguish all their k-blocks and tangles of order k, for any fixed integer k. We describe a family of algorithms to construct such decompositions, seeking to maximize their diversity subject to the requirement that they commute with graph isomorphisms. In particular, all the decompositions constructed are invariant under the automorphisms of the graph.Comment: 23 pages, 5 figure

kk-Blocks: a connectivity invariant for graphs

A $k$-block in a graph $G$ is a maximal set of at least $k$ vertices no two of which can be separated in $G$ by fewer than $k$ other vertices. The block number $\beta(G)$ of $G$ is the largest integer $k$ such that $G$ has a $k$-block. We investigate how $\beta$ interacts with density invariants of graphs, such as their minimum or average degree. We further present algorithms that decide whether a graph has a $k$-block, or which find all its $k$-blocks. The connectivity invariant $\beta(G)$ has a dual width invariant, the block-width ${\rm bw}(G)$ of $G$. Our algorithms imply the duality theorem $\beta = {\rm bw}$: a graph has a block-decomposition of width and adhesion $< k$ if and only if it contains no $k$-block.Comment: 22 pages, 5 figures. This is an extended version the journal article, which has by now appeared. The version here contains an improved version of Theorem 5.3 (which is now best possible) and an additional section with examples at the en

Developmental constraint of insect audition

BACKGROUND: Insect ears contain very different numbers of sensory cells, from only one sensory cell in some moths to thousands of sensory cells, e.g. in cicadas. These differences still await functional explanation and especially the large numbers in cicadas remain puzzling. Insects of the different orders have distinct developmental sequences for the generation of auditory organs. These sensory cells might have different functions depending on the developmental stages. Here we propose that constraints arising during development are also important for the design of insect ears and might influence cell numbers of the adults. PRESENTATION OF THE HYPOTHESIS: We propose that the functional requirements of the subadult stages determine the adult complement of sensory units in the auditory system of cicadas. The hypothetical larval sensory organ should function as a vibration receiver, representing a functional caenogenesis. TESTING THE HYPOTHESIS: Experiments at different levels have to be designed to test the hypothesis. Firstly, the neuroanatomy of the larval sense organ should be analyzed to detail. Secondly, the function should be unraveled neurophysiologically and behaviorally. Thirdly, the persistence of the sensory cells and the rebuilding of the sensory organ to the adult should be investigated. IMPLICATIONS OF THE HYPOTHESIS: Usually, the evolution of insect ears is viewed with respect to physiological and neuronal mechanisms of sound perception. This view should be extended to the development of sense organs. Functional requirements during postembryonic development may act as constraints for the evolution of adult organs, as exemplified with the auditory system of cicadas

Co-Hydroprocessing of Fossil Middle Distillate and Bio-Derived Durene-Rich Heavy Ends under Hydrotreating Conditions

Methanol-to-gasoline (MTG) and dimethyl ether-to-gasoline (DTG), as industrially approved processes for producing greenhouse gas-neutral gasoline, yield byproducts rich in heavy mono-ring aromatics such as 1,2,4,5-tetramethylbenzene (durene). Due to its tendency to crystallize and the overall poor fuel performance, the heavy fuel fraction is usually further processed using aftertreatment units designed for this purpose. This research article discusses the co-hydroprocessing (HP) of bio-derived heavy gasoline (HG) with fossil middle distillate (MD), drawing on available refinery hydrotreaters. Co-HP experiments were conducted in a laboratory-scale fixed bed reactor using an industrial CoMo/g-Al2O3 catalyst, varying the space-time between 0.7 and 4.0 cm3 Cat h cm3 Feed and the reaction temperature between 340 and 390 °C. In addition to the durene conversion, special attention was paid to the octane and cetane numbers (CN) of gasoline and MD, respectively. A six-lump model with ten parameters was developed to predict relevant fuel yields dependent on the process conditions. Under stable catalyst conditions, C10 aromatic conversions of more than 60% were obtained, while the CN remained close to that of pure MD. Harsh process conditions increased the gasoline yield up to 20% at the cost of MD, while the kerosene yield remained almost constant. With an optimized lumping model, fuel yields could be predicted with an R2 of 0.998. In this study, co-HP heavy aromatic-rich MTG/DTG fuels with fossil MD were proven to be a promising process strategy compared to a stand-alone after-treatment