Graphs Identified by Logics with Counting

We classify graphs and, more generally, finite relational structures that are identified by C2, that is, two-variable first-order logic with counting. Using this classification, we show that it can be decided in almost linear time whether a structure is identified by C2. Our classification implies that for every graph identified by this logic, all vertex-colored versions of it are also identified. A similar statement is true for finite relational structures. We provide constructions that solve the inversion problem for finite structures in linear time. This problem has previously been shown to be polynomial time solvable by Martin Otto. For graphs, we conclude that every C2-equivalence class contains a graph whose orbits are exactly the classes of the C2-partition of its vertex set and which has a single automorphism witnessing this fact. For general k, we show that such statements are not true by providing examples of graphs of size linear in k which are identified by C3 but for which the orbit partition is strictly finer than the Ck-partition. We also provide identified graphs which have vertex-colored versions that are not identified by Ck.Comment: 33 pages, 8 Figure

Image, brand and price info: do they always matter the same?

We study attention processes to brand, price and visual information about products in online retailing websites, simultaneously considering the effects of consumers’ goals, purchase category and consumers’ statements. We use an intra-subject experimental design, simulated web stores and a combination of observational eye-tracking data and declarative measures. Image information about the product is the more important stimulus, regardless of the task at hand or the store involved. The roles of brand and price information are dependent on the product category and the purchase task involved. Declarative measures of relative brand importance are found to be positively related with its observed importance

Randomisation and Derandomisation in Descriptive Complexity Theory

We study probabilistic complexity classes and questions of derandomisation from a logical point of view. For each logic L we introduce a new logic BPL, bounded error probabilistic L, which is defined from L in a similar way as the complexity class BPP, bounded error probabilistic polynomial time, is defined from PTIME. Our main focus lies on questions of derandomisation, and we prove that there is a query which is definable in BPFO, the probabilistic version of first-order logic, but not in Cinf, finite variable infinitary logic with counting. This implies that many of the standard logics of finite model theory, like transitive closure logic and fixed-point logic, both with and without counting, cannot be derandomised. Similarly, we present a query on ordered structures which is definable in BPFO but not in monadic second-order logic, and a query on additive structures which is definable in BPFO but not in FO. The latter of these queries shows that certain uniform variants of AC0 (bounded-depth polynomial sized circuits) cannot be derandomised. These results are in contrast to the general belief that most standard complexity classes can be derandomised. Finally, we note that BPIFP+C, the probabilistic version of fixed-point logic with counting, captures the complexity class BPP, even on unordered structures

Compact Labelings For Efficient First-Order Model-Checking

We consider graph properties that can be checked from labels, i.e., bit sequences, of logarithmic length attached to vertices. We prove that there exists such a labeling for checking a first-order formula with free set variables in the graphs of every class that is \emph{nicely locally cwd-decomposable}. This notion generalizes that of a \emph{nicely locally tree-decomposable} class. The graphs of such classes can be covered by graphs of bounded \emph{clique-width} with limited overlaps. We also consider such labelings for \emph{bounded} first-order formulas on graph classes of \emph{bounded expansion}. Some of these results are extended to counting queries

On Second-Order Monadic Monoidal and Groupoidal Quantifiers

We study logics defined in terms of second-order monadic monoidal and groupoidal quantifiers. These are generalized quantifiers defined by monoid and groupoid word-problems, equivalently, by regular and context-free languages. We give a computational classification of the expressive power of these logics over strings with varying built-in predicates. In particular, we show that ATIME(n) can be logically characterized in terms of second-order monadic monoidal quantifiers

Contraction Bidimensionality: the Accurate Picture

We provide new combinatorial theorems on the structure of graphs that are contained as contractions in graphs of large treewidth. As a consequence of our combinatorial results we unify and significantly simplify contraction bidimensionality theory -- the meta algorithmic framework to design efficient parameterized and approximation algorithms for contraction closed parameters

Increased DHA Production in Seed Oil Using a Selective Lysophosphatidic Acid Acyltransferase

Metabolic engineering of the omega-3 (ω3) long chain polyunsaturated fatty acid biosynthesis pathway has generated fish oil-like levels of pharmaceutically and nutritionally important docosahexaenoic acid (DHA) in plant seeds. However, the majority of DHA has been accumulated at the sn-1 and sn-3 positions of triacylglycerol (TAG) in these engineered seeds, leaving only a minor amount (∼10%) at sn-2 position and indicating a strong discrimination (or, a very poor specificity) for DHA by seed lysophosphatidic acid acyltransferases (LPAATs), which mediate the acylation of sn-2 position of glycerol backbone. In order to increase the level of DHA at sn-2 position of TAG and to increase overall DHA level in seeds, we attempted to discover DHA-preferring LPAATs. Several LPAATs for acylation of the sn-2 position of the TAG glycerol backbone were investigated for substrate preference for DHA. In transiently expressing these LPAATs in Nicotiana benthamiana, a Mortierella alpina LPAAT had the highest substrate specificity for accumulating DHA onto oleoyl-lysophosphatidic acid (oleoyl-LPA), while the plant LPAATs tested showed lower preference for DHA. In a competition assay with a pool of four ω3 acyl-Coenzyme A (CoA) substrates involved in the DHA biosynthesis pathway, LPAATs from both M. alpina and Emiliania huxleyi showed a high preference for DHA-CoA acylation onto oleoyl-LPA. When docosahexaenoyl-LPA was used as the acyl receiver, M. alpina LPAAT also showed a high preference for DHA-CoA. Stable overexpression of M. alpina LPAAT in an Arabidopsis line that expressed the DHA biosynthesis pathway significantly increased both the total DHA levels and the distribution of DHA onto the sn-2 position of seed TAG. LC-MS analysis of the seed TAG species also confirmed that overexpression of M. alpina LPAAT increased di-DHA and tri-DHA TAGs, suggesting that the M. alpina LPAAT could enrich DHA at the TAG sn-2 position, leading to a metabolic engineering of oil seed for channeling DHA into the sn-2 position of TAG and to a higher DHA level

CuInSe2 thin films produced by rf sputtering in Ar/H2 atmospheres

Structural, compositional, optical, and electrical properties of CuInSe2thin filmsgrown by rf reactive sputtering from a Se excess target in Ar/H2 atmospheres are presented. The addition of H2 to the sputtering atmospheres allows the control of stoichiometry of films giving rise to remarkable changes in the film properties. Variation of substrate temperature causes changes in film composition because of the variation of hydrogen reactivity at the substrate. Measurements of resistivity at variable temperatures indicate a hopping conduction mechanism through gap states for films grown at low temperature (100–250 °C), the existence of three acceptor levels at about 0.046, 0.098, and 0.144 eV above valence band for films grown at intermediate temperature (250–350 °C), and a pseudometallic behavior for film grown at high temperatures (350–450 °C). Chalcopyrite polycrystalline thin films of CuInSe2 with an average grain size of 1 μm, an optical gap of 1.01 eV, and resistivities from 10− 1 to 103 Ω cm can be obtained by adding 1.5% of H2 to the sputtering atmosphere and by varying the substrate temperature from 300 to 400 °C

The GALNT9, BNC1 and CCDC8 genes are frequently epigenetically dysregulated in breast tumours that metastasise to the brain.

Tumour metastasis to the brain is a common and deadly development in certain cancers; 18-30 % of breast tumours metastasise to the brain. The contribution that gene silencing through epigenetic mechanisms plays in these metastatic tumours is not well understood