Computer-aided verification in mechanism design

In mechanism design, the gold standard solution concepts are dominant strategy incentive compatibility and Bayesian incentive compatibility. These solution concepts relieve the (possibly unsophisticated) bidders from the need to engage in complicated strategizing. While incentive properties are simple to state, their proofs are specific to the mechanism and can be quite complex. This raises two concerns. From a practical perspective, checking a complex proof can be a tedious process, often requiring experts knowledgeable in mechanism design. Furthermore, from a modeling perspective, if unsophisticated agents are unconvinced of incentive properties, they may strategize in unpredictable ways. To address both concerns, we explore techniques from computer-aided verification to construct formal proofs of incentive properties. Because formal proofs can be automatically checked, agents do not need to manually check the properties, or even understand the proof. To demonstrate, we present the verification of a sophisticated mechanism: the generic reduction from Bayesian incentive compatible mechanism design to algorithm design given by Hartline, Kleinberg, and Malekian. This mechanism presents new challenges for formal verification, including essential use of randomness from both the execution of the mechanism and from the prior type distributions. As an immediate consequence, our work also formalizes Bayesian incentive compatibility for the entire family of mechanisms derived via this reduction. Finally, as an intermediate step in our formalization, we provide the first formal verification of incentive compatibility for the celebrated Vickrey-Clarke-Groves mechanism

Shortest paths in nearly conservative digraphs

We introduce the following notion: a digraph D = (V, A) with arc weights c: A → R is called nearly conservative if every negative cycle consists of two arcs. Computing shortest paths in nearly conservative digraphs is NP-hard, and even deciding whether a digraph is nearly conservative is coNP-complete. We show that the “All Pairs Shortest Path” problem is fixed parameter tractable with various parameters for nearly conservative digraphs. The results also apply for the special case of conservative mixed graphs

Discrete Convex Functions on Graphs and Their Algorithmic Applications

The present article is an exposition of a theory of discrete convex functions on certain graph structures, developed by the author in recent years. This theory is a spin-off of discrete convex analysis by Murota, and is motivated by combinatorial dualities in multiflow problems and the complexity classification of facility location problems on graphs. We outline the theory and algorithmic applications in combinatorial optimization problems

Generating natural language specifications from UML class diagrams

Early phases of software development are known to be problematic, difficult to manage and errors occurring during these phases are expensive to correct. Many systems have been developed to aid the transition from informal Natural Language requirements to semistructured or formal specifications. Furthermore, consistency checking is seen by many software engineers as the solution to reduce the number of errors occurring during the software development life cycle and allow early verification and validation of software systems. However, this is confined to the models developed during analysis and design and fails to include the early Natural Language requirements. This excludes proper user involvement and creates a gap between the original requirements and the updated and modified models and implementations of the system. To improve this process, we propose a system that generates Natural Language specifications from UML class diagrams. We first investigate the variation of the input language used in naming the components of a class diagram based on the study of a large number of examples from the literature and then develop rules for removing ambiguities in the subset of Natural Language used within UML. We use WordNet,a linguistic ontology, to disambiguate the lexical structures of the UML string names and generate semantically sound sentences. Our system is developed in Java and is tested on an independent though academic case study

Finding Connected Dense kk-Subgraphs

Given a connected graph $G$ on $n$ vertices and a positive integer $k\le n$, a subgraph of $G$ on $k$ vertices is called a $k$-subgraph in $G$. We design combinatorial approximation algorithms for finding a connected $k$-subgraph in $G$ such that its density is at least a factor $\Omega(\max\{n^{-2/5},k^2/n^2\})$ of the density of the densest $k$-subgraph in $G$ (which is not necessarily connected). These particularly provide the first non-trivial approximations for the densest connected $k$-subgraph problem on general graphs

Conjunctions of Among Constraints

Many existing global constraints can be encoded as a conjunction of among constraints. An among constraint holds if the number of the variables in its scope whose value belongs to a prespecified set, which we call its range, is within some given bounds. It is known that domain filtering algorithms can benefit from reasoning about the interaction of among constraints so that values can be filtered out taking into consideration several among constraints simultaneously. The present pa- per embarks into a systematic investigation on the circumstances under which it is possible to obtain efficient and complete domain filtering algorithms for conjunctions of among constraints. We start by observing that restrictions on both the scope and the range of the among constraints are necessary to obtain meaningful results. Then, we derive a domain flow-based filtering algorithm and present several applications. In particular, it is shown that the algorithm unifies and generalizes several previous existing results.Comment: 15 pages plus appendi

A broad distribution of the alternative oxidase in microsporidian parasites

Microsporidia are a group of obligate intracellular parasitic eukaryotes that were considered to be amitochondriate until the recent discovery of highly reduced mitochondrial organelles called mitosomes. Analysis of the complete genome of Encephalitozoon cuniculi revealed a highly reduced set of proteins in the organelle, mostly related to the assembly of ironsulphur clusters. Oxidative phosphorylation and the Krebs cycle proteins were absent, in keeping with the notion that the microsporidia and their mitosomes are anaerobic, as is the case for other mitosome bearing eukaryotes, such as Giardia. Here we provide evidence opening the possibility that mitosomes in a number of microsporidian lineages are not completely anaerobic. Specifically, we have identified and characterized a gene encoding the alternative oxidase (AOX), a typically mitochondrial terminal oxidase in eukaryotes, in the genomes of several distantly related microsporidian species, even though this gene is absent from the complete genome of E. cuniculi. In order to confirm that these genes encode functional proteins, AOX genes from both A. locustae and T. hominis were over-expressed in E. coli and AOX activity measured spectrophotometrically using ubiquinol-1 (UQ-1) as substrate. Both A. locustae and T. hominis AOX proteins reduced UQ-1 in a cyanide and antimycin-resistant manner that was sensitive to ascofuranone, a potent inhibitor of the trypanosomal AOX. The physiological role of AOX microsporidia may be to reoxidise reducing equivalents produced by glycolysis, in a manner comparable to that observed in trypanosome

Early detection of Haemonchus contortus infection in sheep using three different faecal occult blood tests

Haemonchus contortus is a blood-sucking parasite causing the presence of faecal occult blood (FOB). The objective was to study three different FOB tests in order to have a new indicator of H. contortus infection in sheep that could be included in the genetic evaluation system as an alternative selection criterion to faecal worm egg count (FEC). A total of 29 Corriedale lambs were experimentally infected with 10.000 larvae of H. contortus. Stool samples were recorded for FEC and FOB tests (Hexagon, Hematest® and Multistix®), blood for packed cell volume (PCV), haemoglobin, white and red blood cell count (RBC), and FAMACHA© for scoring anaemia. At the end of the experiment lambs were slaughtered to worm burden count. Field infection was achieved in 309 Merino lambs under natural parasite challenge. FEC data were normalized through logarithmic transformation (LnFEC). Pearson correlation was estimated to examine the relationship between all traits. The three tests were able to detect the presence of FOB at day 11. FEC, PCV and RBC decreased to sub-normal values from day 18. FAMACHA© score 3 was considered to be indicative of anaemia. Most of the correlations were of high magnitude, with the exception of Multistix® test that was moderately correlated with haematological parameters, LnFEC and FEC. In field infection, most samples were negative to FOB tests and the correlations were lower than those calculated under experimental infection. In conclusion, FOB tests were able to detect haemonchosis earlier than FEC under high experimental parasite challenge. However, they were not able to detect FOB under natural mixed parasite challenge. FAMACHA© and PCV demonstrated to be good indicators of Haemonchosis, having moderate to high correlations with FEC.Keywords: Faecal occult blood test, Faecal worm egg count, Haemonchosis, Sheep

Binets: fundamental building blocks for phylogenetic networks

Phylogenetic networks are a generalization of evolutionary trees that are used by biologists to represent the evolution of organisms which have undergone reticulate evolution. Essentially, a phylogenetic network is a directed acyclic graph having a unique root in which the leaves are labelled by a given set of species. Recently, some approaches have been developed to construct phylogenetic networks from collections of networks on 2- and 3-leaved networks, which are known as binets and trinets, respectively. Here we study in more depth properties of collections of binets, one of the simplest possible types of networks into which a phylogenetic network can be decomposed. More speci_cally, we show that if a collection of level-1 binets is compatible with some binary network, then it is also compatible with a binary level-1 network. Our proofs are based on useful structural results concerning lowest stable ancestors in networks. In addition, we show that, although the binets do not determine the topology of the network, they do determine the number of reticulations in the network, which is one of its most important parameters. We also consider algorithmic questions concerning binets. We show that deciding whether an arbitrary set of binets is compatible with some network is at least as hard as the well-known Graph Isomorphism problem. However, if we restrict to level-1 binets, it is possible to decide in polynomial time whether there exists a binary network that displays all the binets. We also show that to _nd a network that displays a maximum number of the binets is NP-hard, but that there exists a simple polynomial-time 1/3-approximation algorithm for this problem. It is hoped that these results will eventually assist in the development of new methods for constructing phylogenetic networks from collections of smaller networks

TRY plant trait database - enhanced coverage and open access

Plant traits-the morphological, anatomical, physiological, biochemical and phenological characteristics of plants-determine how plants respond to environmental factors, affect other trophic levels, and influence ecosystem properties and their benefits and detriments to people. Plant trait data thus represent the basis for a vast area of research spanning from evolutionary biology, community and functional ecology, to biodiversity conservation, ecosystem and landscape management, restoration, biogeography and earth system modelling. Since its foundation in 2007, the TRY database of plant traits has grown continuously. It now provides unprecedented data coverage under an open access data policy and is the main plant trait database used by the research community worldwide. Increasingly, the TRY database also supports new frontiers of trait-based plant research, including the identification of data gaps and the subsequent mobilization or measurement of new data. To support this development, in this article we evaluate the extent of the trait data compiled in TRY and analyse emerging patterns of data coverage and representativeness. Best species coverage is achieved for categorical traits-almost complete coverage for 'plant growth form'. However, most traits relevant for ecology and vegetation modelling are characterized by continuous intraspecific variation and trait-environmental relationships. These traits have to be measured on individual plants in their respective environment. Despite unprecedented data coverage, we observe a humbling lack of completeness and representativeness of these continuous traits in many aspects. We, therefore, conclude that reducing data gaps and biases in the TRY database remains a key challenge and requires a coordinated approach to data mobilization and trait measurements. This can only be achieved in collaboration with other initiatives