A simultaneous generalization of independence and disjointness in boolean algebras

We give a definition of some classes of boolean algebras generalizing free boolean algebras; they satisfy a universal property that certain functions extend to homomorphisms. We give a combinatorial property of generating sets of these algebras, which we call n-independent. The properties of these classes (n-free and omega-free boolean algebras) are investigated. These include connections to hypergraph theory and cardinal invariants on these algebras. Related cardinal functions, $n$Ind, which is the supremum of the cardinalities of n-independent subsets; i_n, the minimum size of a maximal n-independent subset; and i_omega, the minimum size of an omega-independent subset, are introduced and investigated. The values of i_n and i_omega on P(omega)/fin are shown to be independent of ZFC.Comment: Sumbitted to Orde

Associative polynomial functions over bounded distributive lattices

The associativity property, usually defined for binary functions, can be generalized to functions of a given fixed arity n>=1 as well as to functions of multiple arities. In this paper, we investigate these two generalizations in the case of polynomial functions over bounded distributive lattices and present explicit descriptions of the corresponding associative functions. We also show that, in this case, both generalizations of associativity are essentially the same.Comment: Final versio

Formal modelling as a component of user centred design

User centred design approaches typically focus understanding on context and producing sketch designs. These sketches are often non functional (e.g., paper) prototypes. They provide a means of exploring candidate design possibilities using techniques such as cooperative evaluation. This paper describes a further step in the process using formal analysis techniques. The sketch design of a device is enhanced into a specification that is then analysed using formal techniques, thus providing a systematic approach to checking plausibility and consistency during early design stages. Once analysed, a further prototype is constructed using an executable form of the specification, providing the next candidate for evaluation with potential users. The technique is illustrated through an example based on a pill dispenser.We are grateful to Nuno Rodrigues, João Vilaça and Nuno Dias from IPCA (Polytechnic Institute of Cavado and Ave) who developed the first prototypeof the pill dispenser. José C. Campos, Paolo Masci and Michael Harrison werefunded by project NORTE-01-0145-FEDER-000016, financed by the North Por-tugal Regional Operational Programme (NORTE 2020), under the PORTUGAL2020 Partnership Agreement, and through the European Regional DevelopmentFund (ERDF)

Central Exclusive Production in QCD

We investigate the theoretical description of the central exclusive production process, h1+h2 -> h1+X+h2. Taking Higgs production as an example, we sum logarithmically enhanced corrections appearing in the perturbation series to all orders in the strong coupling. Our results agree with those originally presented by Khoze, Martin and Ryskin except that the scale appearing in the Sudakov factor, mu=0.62 \sqrt{\hat{s}}, should be replaced with mu=\sqrt{\hat{s}}, where \sqrt{\hat{s}} is the invariant mass of the centrally produced system. We confirm this result using a fixed-order calculation and show that the replacement leads to approximately a factor 2 suppression in the cross-section for central system masses in the range 100-500 GeV.Comment: 41 pages, 19 figures; minor typos fixed; version published in JHE

Multi-objective optimization of genome-scale metabolic models: the case of ethanol production

Ethanol is among the largest fermentation product used worldwide, accounting for more than 90% of all biofuel produced in the last decade. However current production methods of ethanol are unable to meet the requirements of increasing global demand, because of low yields on glucose sources. In this work, we present an in silico multi-objective optimization and analyses of eight genome-scale metabolic networks for the overproduction of ethanol within the engineered cell. We introduce MOME (multi-objective metabolic engineering) algorithm, that models both gene knockouts and enzymes up and down regulation using the Redirector framework. In a multi-step approach, MOME tackles the multi-objective optimization of biomass and ethanol production in the engineered strain; and performs genetic design and clustering analyses on the optimization results. We find in silico E. coli Pareto optimal strains with a knockout cost of 14 characterized by an ethanol production up to 19.74mmolgDW−1h−1 (+832.88% with respect to wild-type) and biomass production of 0.02h−1 (−98.06% ). The analyses on E. coli highlighted a single knockout strategy producing 16.49mmolgDW−1h−1 (+679.29% ) ethanol, with biomass equals to 0.23h−1 (−77.45% ). We also discuss results obtained by applying MOME to metabolic models of: (i) S. aureus; (ii) S. enterica; (iii) Y. pestis; (iv) S. cerevisiae; (v) C. reinhardtii; (vi) Y. lipolytica. We finally present a set of simulations in which constrains over essential genes and minimum allowable biomass were included. A bound over the maximum allowable biomass was also added, along with other settings representing rich media compositions. In the same conditions the maximum improvement in ethanol production is +195.24%

Complexity of equational theory of relational algebras with standard projection elements

The class $\mathsf{TPA}$ of t rue p airing a lgebras is defined to be the class of relation algebras expanded with concrete set theoretical projection functions. The main results of the present paper is that neither the equational theory of $\mathsf{TPA}$ nor the first order theory of $\mathsf{TPA}$ are decidable. Moreover, we show that the set of all equations valid in $\mathsf{TPA}$ is exactly on the $\Pi ^1_1$ level. We consider the class $\mathsf{TPA}^-$ of the relation algebra reducts of $\mathsf{TPA}$’s, as well. We prove that the equational theory of $\mathsf{TPA}^-$ is much simpler, namely, it is recursively enumerable. We also give motivation for our results and some connections to related work

Evaluation of Allelic Expression of Imprinted Genes in Adult Human Blood

Imprinted genes are expressed from only one allele in a parent-of-origin dependent manner. Loss of imprinted (LOI) expression can result in a variety of human disorders and is frequently reported in cancer. Biallelic expression of imprinted genes in adult blood has been suggested as a useful biomarker and is currently being investigated in colorectal cancer. In general, the expression profiles of imprinted genes are well characterised during human and mouse fetal development, but not in human adults

Turing Patterns Inside Cells

Concentration gradients inside cells are involved in key processes such as cell division and morphogenesis. Here we show that a model of the enzymatic step catalized by phosphofructokinase (PFK), a step which is responsible for the appearance of homogeneous oscillations in the glycolytic pathway, displays Turing patterns with an intrinsic length-scale that is smaller than a typical cell size. All the parameter values are fully consistent with classic experiments on glycolytic oscillations and equal diffusion coefficients are assumed for ATP and ADP. We identify the enzyme concentration and the glycolytic flux as the possible regulators of the pattern. To the best of our knowledge, this is the first closed example of Turing pattern formation in a model of a vital step of the cell metabolism, with a built-in mechanism for changing the diffusion length of the reactants, and with parameter values that are compatible with experiments. Turing patterns inside cells could provide a check-point that combines mechanical and biochemical information to trigger events during the cell division process

Human oocyte-derived methylation differences persist in the placenta revealing widespread transient imprinting

Thousands of regions in gametes have opposing methylation profiles that are largely resolved during the post-fertilization epigenetic reprogramming. However some specific sequences associated with imprinted loci survive this demethylation process. Here we present the data describing the fate of germline-derived methylation in humans. With the exception of a few known paternally methylated germline differentially methylated regions (DMRs) associated with known imprinted domains, we demonstrate that sperm-derived methylation is reprogrammed by the blastocyst stage of development. In contrast a large number of oocyte-derived methylation differences survive to the blastocyst stage and uniquely persist as transiently methylated DMRs only in the placenta. Furthermore, we demonstrate that this phenomenon is exclusive to primates, since no placenta-specific maternal methylation was observed in mouse. Utilizing single cell RNA-seq datasets from human preimplantation embryos we show that following embryonic genome activation the maternally methylated transient DMRs can orchestrate imprinted expression. However despite showing widespread imprinted expression of genes in placenta, allele-specific transcriptional profiling revealed that not all placenta-specific DMRs coordinate imprinted expression and that this maternal methylation may be absent in a minority of samples, suggestive of polymorphic imprinted methylation

A statistical method for excluding non-variable CpG sites in high-throughput DNA methylation profiling

<p>Abstract</p> <p>Background</p> <p>High-throughput DNA methylation arrays are likely to accelerate the pace of methylation biomarker discovery for a wide variety of diseases. A potential problem with a standard set of probes measuring the methylation status of CpG sites across the whole genome is that many sites may not show inter-individual methylation variation among the biosamples for the disease outcome being studied. Inclusion of these so-called "non-variable sites" will increase the risk of false discoveries and reduce statistical power to detect biologically relevant methylation markers.</p> <p>Results</p> <p>We propose a method to estimate the proportion of non-variable CpG sites and eliminate those sites from further analyses. Our method is illustrated using data obtained by hybridizing DNA extracted from the peripheral blood mononuclear cells of 311 samples to an array assaying 1505 CpG sites. Results showed that a large proportion of the CpG sites did not show inter-individual variation in methylation.</p> <p>Conclusions</p> <p>Our method resulted in a substantial improvement in association signals between methylation sites and outcome variables while controlling the false discovery rate at the same level.</p