Deciding first-order properties of nowhere dense graphs

Nowhere dense graph classes, introduced by Nesetril and Ossona de Mendez, form a large variety of classes of "sparse graphs" including the class of planar graphs, actually all classes with excluded minors, and also bounded degree graphs and graph classes of bounded expansion. We show that deciding properties of graphs definable in first-order logic is fixed-parameter tractable on nowhere dense graph classes. At least for graph classes closed under taking subgraphs, this result is optimal: it was known before that for all classes C of graphs closed under taking subgraphs, if deciding first-order properties of graphs in C is fixed-parameter tractable, then C must be nowhere dense (under a reasonable complexity theoretic assumption). As a by-product, we give an algorithmic construction of sparse neighbourhood covers for nowhere dense graphs. This extends and improves previous constructions of neighbourhood covers for graph classes with excluded minors. At the same time, our construction is considerably simpler than those. Our proofs are based on a new game-theoretic characterisation of nowhere dense graphs that allows for a recursive version of locality-based algorithms on these classes. On the logical side, we prove a "rank-preserving" version of Gaifman's locality theorem.Comment: 30 page

On Symmetric Circuits and Fixed-Point Logics

We study properties of relational structures, such as graphs, that are decided by families of Boolean circuits. Circuits that decide such properties are necessarily invariant to permutations of the elements of the input structures. We focus on families of circuits that are symmetric, i.e., circuits whose invariance is witnessed by automorphisms of the circuit induced by the permutation of the input structure. We show that the expressive power of such families is closely tied to definability in logic. In particular, we show that the queries defined on structures by uniform families of symmetric Boolean circuits with majority gates are exactly those definable in fixed-point logic with counting. This shows that inexpressibility results in the latter logic lead to lower bounds against polynomial-size families of symmetric circuits.This research was supported by EPSRC grant EP/H026835

The Complexity of Admissibility in Omega-Regular Games

Iterated admissibility is a well-known and important concept in classical game theory, e.g. to determine rational behaviors in multi-player matrix games. As recently shown by Berwanger, this concept can be soundly extended to infinite games played on graphs with omega-regular objectives. In this paper, we study the algorithmic properties of this concept for such games. We settle the exact complexity of natural decision problems on the set of strategies that survive iterated elimination of dominated strategies. As a byproduct of our construction, we obtain automata which recognize all the possible outcomes of such strategies

Solving linear programs without breaking abstractions

We show that the ellipsoid method for solving linear programs can be implemented in a way that respects the symmetry of the program being solved. That is to say, there is an algorithmic implementation of the method that does not distinguish, or make choices, between variables or constraints in the program unless they are distinguished by properties definable from the program. In particular, we demonstrate that the solvability of linear programs can be expressed in fixed-point logic with counting (FPC) as long as the program is given by a separation oracle that is itself definable in FPC. We use this to show that the size of a maximum matching in a graph is definable in FPC. This settles an open problem first posed by Blass, Gurevich and Shelah [Blass et al. 1999]. On the way to defining a suitable separation oracle for the maximum matching program, we provide FPC formulas defining canonical maximum flows and minimum cuts in undirected capacitated graphs.Research supported by EPSRC grant EP/H026835.This is the author accepted manuscript. The final version is available from ACM via http://dx.doi.org/10.1145/282289

The impacts of urease inhibitor and method of application on the bioavailability of urea fertiliser in ryegrass (Lolium perenne L.)

The use of urea fertiliser has been associated with relatively poor nitrogen (N) use efficiency (NUE) due to heavy N losses such as gaseous emissions of ammonia (NH₃) and nitrous oxide (N₂O) and nitrate (NO₃⁻) leaching into surface and ground waters. Improving N use-efficiency of applied urea is therefore critical to maximise its uptake and to minimise its footprint on the environment. The study was conducted under laboratory-glasshouse conditions (Chapter 2-4)and lysimiter-field plot studies (Chapter 5). In chapter 2, Two glasshouse-based experimentswere conducted to investigate the potential of incorporating urea fertiliser with ureaseinhibitor, (N-(n-butyl) thiophosphoric triamide (nBTPT) or ‘Agrotain’) to enhance fertiliser N uptake efficiency. Urea, with or without Agrotain, was applied to Ryegrass (Lolium perenne L.) grown in standard plant trays maintained at soil moisture contents of 75–80% field capacity, at rates equivalent to 25 or 50 kg Nha⁻¹. These treatments were compared with other common forms of N fertilisers (ammonium nitrate, ammonium sulphate and sodium nitrate). In a separate pot experiment, granular ¹⁵N urea (10 atom %) with or without Agrotain, was applied at 25 kg Nh⁻¹ to track N use-efficiency and the fate of ¹⁵N-labelled fertiliser. In both experiments, Agrotain-treated urea improved bioavailability (defined as the fraction of total soil N that can interact with a biological target in the plant or that can be taken up by plant) of added N and resulted in significantly higher herbage DM yield and N uptake than urea alone or other forms of N fertilisers. Results from the ¹⁵N experiment support the suggestion that a delay in urea hydrolysis by Agrotain provided an opportunity for direct plant uptake of an increased proportion of the applied urea-N than in the case of urea alone. In chapter 3, two more glasshouse-based experiments were conducted to investigate if urea applied in fine particle application (FPA), with or without Agrotain, had any effect on fertiliser-N uptake efficiency (defined as the difference in N uptake between the fertiliser treatment and the control as a percentage of the amount of N applied) under optimum soil moisture (75-80% field capacity) and temperature (25 °C) conditions, in comparison with other common forms of N fertilisers applied, either in FPA or in granular form. In a separate pot experiment, ¹⁵N urea (10 atom %), with or without Agrotain, was applied to either shoots or leaves only or to the soil surface (avoiding the shoots and leaves) to determine urea hydrolysis, herbage DM and ¹⁵N uptake. In both experiments, herbage DM yield and N uptake were significantly greater in the FPA treatments than in those receiving granular application. Agrotain-treated urea FPA resulted in significantly higher N response efficiency (difference between the dry matter produced by the various fertiliser treatments and the control, divided by the amount of N applied) than urea FPA alone or other forms of N fertilisers. Results from the ¹⁵N experiment support the idea that Agrotain treatment improves the N response of urea applied in FPA form due to a delay in hydrolysis of urea, thus providing herbage an extended opportunity to absorb added urea directly through leaves, cuticles and roots. A further glasshouse-based study was conducted to investigate the effect of Agrotain and irrigation on urea hydrolysis and its movement in a Typic Haplustepts silt loam soil (Chapter 4). A total of 72 repacked soil cores (140 mm inner diameter and 100 mm deep) were used - half (36) of these cores were adjusted to soil moisture contents of 80% field capacity (FC) and the remaining 36 cores to 50% FC. Granular urea, with or without Agrotain, was applied at a rate equivalent to 100 kg N ha⁻¹. Twelve pots were destructively sampled at each day after 1, 2, 3, 4, 7, and 10 days of treatment application to determine urea hydrolysis and its lateral and vertical movement in different soil layers. Agrotain-treated urea delayed urea hydrolysis compared with urea alone during the first 7 days of its application. This delay in urea hydrolysis by Agrotain enabled added urea to disperse and move away from the surface soil layer to the sub-surface soil layer both vertically and laterally. In contrast, most urea in the absence of Agrotain hydrolysed within 2 days of its application. Irrigation after 1 day resulted in further urea movement from the surface soil layer (0-10 mm) to the sub-soil layer (30-50 mm) in Agrotain-treated urea. These results suggest that Agrotain delayed urea hydrolysis and allowed more time for rainfall or irrigation to move the added urea from the surface layer to sub-soil layers where it is likely to make good contact with plant roots. This distribution of urea in the rooting zone (0-200 mm) has the potential to enhance N use efficiency and minimise N losses via ammonia (NH₃) volatilisation from surface-applied urea. Finally, a field study using lysimeters (300 mm inner diameter and 400 mm deep), and small field plots (1 m² in area) was established using a silt loam Typic Haplustepts soil (Soil Survey Staff 1998) to investigate the effect of FPA and granular applications of urea, with or without Agrotain, on N losses and N use efficiency (Chapter 5). The five treatments were: control (no N) and ¹⁵N-labelled urea (10 atom %), with or without Agrotain, applied to lysimeters or mini plots (un-labelled urea), either in granular form to the soil surface or in FPA form (through a spray) at a rate equivalent to 100 kg N ha⁻¹. Gaseous emissions of NH₃ and N₂O, NO₃⁻ leaching, herbage production, N response efficiency, total N uptake and total recovery of applied ¹⁵N in the plant and soil were determined up to 63 days. Urea-alone and urea with Agrotain, applied in FPA form, was more effective than its granular form and reduced N2O emissions by 5-12% and NO3- leaching losses by 31-55%. Urea-alone applied in FPA form had no significant effect in reducing NH₃ losses compared with granular form. However, urea with Agrotain applied in FPA form reduced NH₃ emissions by 69% compared with the equivalent granular treatment. Urea-alone and with Agrotain applied in FPA form increased herbage dry matter production by 27% and 38%, and N response efficiency compared with the equivalent granular urea application, respectively. Urea applied in FPA form resulted in significantly higher ¹⁵N recovery in the shoots compared with granular treatments – this was improved further when urea in FPA form was applied with Agrotain. Thus, treating urea with Agrotain in FPA under field conditions has the potential to delay its hydrolysis, minimise N losses and improve N use efficiency and herbage production. The lower dry matter production and N-response efficiency to urea applied in FPA form in Chapter 3 are probably because of additional factors such as lower application rates (25 kg N ha⁻¹ ) or lack of interception of urea by the leaves. Applying urea in FPA form is a good management strategy and I conclude that combining FPA urea with Agrotain has the potential to increase N use efficiency and herbage production further

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

Towards the specification and verification of modal properties for structured systems

System specification formalisms should come with suitable property specification languages and effective verification tools. We sketch a framework for the verification of quantified temporal properties of systems with dynamically evolving structure. We consider visual specification formalisms like graph transformation systems (GTS) where program states are modelled as graphs, and the program behavior is specified by graph transformation rules. The state space of a GTS can be represented as a graph transition system (GTrS), i.e. a transition system with states and transitions labelled, respectively, with a graph, and with a partial morphism representing the evolution of state components. Unfortunately, GTrSs are prohibitively large or infinite even for simple systems, making verification intractable and hence calling for appropriate abstraction techniques

EFFECT OF OILSEED CAKES ALONE OR IN COMBINATION WITH TRICHODERMA SPECIES FOR THE CONTROL OF CHARCOAL ROT OF SUNFLOWER (HELIANTHUS ANNUS L.)

Abstract Seed treatment with oil seed cakes like Cotton cake, Mustard cake (Black and yellow) and Taramera cake alone or in combination with Trichoderma harzianum and T. resei significantly reduced colonization of roots by charcoal rot fungus (Macrophomina phaseolina) and significantly increased growth of sunflower (Helianthus annus L.) plants. Highest reduction in charcoal rot of sunflower was observed when seeds of sunflower were coated with cotton cake and T. resei followed by Taramera cake and T. harzianum and Mustard cake in combination with T. harzianum

Disconnection clauses: an inevitable symptom of regionalism?

‘Disconnection clauses’ are legal provisions inserted into multilateral conventions to ensure that certain parties to the convention are not required to apply the rules of the convention because other relevant rules have already been agreed to among themselves. A disconnection clause can also be described more generally as a ‘conflict clause’ because it signals to all parties that parallel and potentially conflicting treaty obligations exist. This paper presents a discussion of the disconnection clause which argues that while these clauses make it possible for a limited group of parties to enhance the objectives of a treaty by taking measures that correspond to their special circumstance, this practice also creates a possibility that the inter se agreement will undermine the original treaty regime. The actual impact of a particular disconnection clause depends on how the clause is crafted, along with the changing nature of the regime that it refers to. The potential for a disconnection clause to undermine the object and purpose of the original treaty can therefore be removed during its design. Nevertheless, without full disclosure when negotiating the convention, any clause that seeks to replace treaty provisions with an alternative regime that would be applicable only between certain parties may, at worst, be creating different standards for different parties and, at best, be opaque and incoherent. This paper first describes the various types of disconnection clause, focusing on their purpose and development. It then assesses the main legal and political controversies surrounding these clauses before assessing whether these clauses could potentially create more legal problems than they are intended to solve or whether they are simply a practical response to deepening regionalism

Role of early contrast enhanced CT scan in severity prediction of acute pancreatitis

Abstract Severe pancreatitis occurs in approximately 15-25% of patients with acute pancreatitis. The objective of our study was to compare the CTSeverity Index (CTSI) with a clinical score (BISAP score) to predict severity of acute pancreatitis. Forty-eight consecutive patients with acutepancreatitis who underwent contrast enhanced CT scan within 72 hours of presentation were included. Results of our study showed that both CTSI and BISAP score were reliable predictors of mortality (p value = 0.019 and \u3c0.001 respectively) and need for mechanical ventilation (p value = .002 and .006 respectively). Positive predictive value of CTSI to predict recovery without intervention was 91.4% as compared to 78% for that of BISAP score. Receiver Operating Characteristics (ROC) Curves showed CT scan was superior to BISAP Score in predicting need of percutaneous or surgical intervention. Early CT scan may be utilized for prediction of clinical course of patients with acute pancreatitis