Computing only minimal answers in disjunctive deductive databases

A method is presented for computing minimal answers in disjunctive deductive databases under the disjunctive stable model semantics. Such answers are constructed by repeatedly extending partial answers. Our method is complete (in that every minimal answer can be computed) and does not admit redundancy (in the sense that every partial answer generated can be extended to a minimal answer), whence no non-minimal answer is generated. For stratified databases, the method does not (necessarily) require the computation of models of the database in their entirety. Compilation is proposed as a tool by which problems relating to computational efficiency and the non-existence of disjunctive stable models can be overcome. The extension of our method to other semantics is also considered.Comment: 48 page

Shape Generation using Spatially Partitioned Point Clouds

We propose a method to generate 3D shapes using point clouds. Given a point-cloud representation of a 3D shape, our method builds a kd-tree to spatially partition the points. This orders them consistently across all shapes, resulting in reasonably good correspondences across all shapes. We then use PCA analysis to derive a linear shape basis across the spatially partitioned points, and optimize the point ordering by iteratively minimizing the PCA reconstruction error. Even with the spatial sorting, the point clouds are inherently noisy and the resulting distribution over the shape coefficients can be highly multi-modal. We propose to use the expressive power of neural networks to learn a distribution over the shape coefficients in a generative-adversarial framework. Compared to 3D shape generative models trained on voxel-representations, our point-based method is considerably more light-weight and scalable, with little loss of quality. It also outperforms simpler linear factor models such as Probabilistic PCA, both qualitatively and quantitatively, on a number of categories from the ShapeNet dataset. Furthermore, our method can easily incorporate other point attributes such as normal and color information, an additional advantage over voxel-based representations.Comment: To appear at BMVC 201

Random Forests for Big Data

Big Data is one of the major challenges of statistical science and has numerous consequences from algorithmic and theoretical viewpoints. Big Data always involve massive data but they also often include online data and data heterogeneity. Recently some statistical methods have been adapted to process Big Data, like linear regression models, clustering methods and bootstrapping schemes. Based on decision trees combined with aggregation and bootstrap ideas, random forests were introduced by Breiman in 2001. They are a powerful nonparametric statistical method allowing to consider in a single and versatile framework regression problems, as well as two-class and multi-class classification problems. Focusing on classification problems, this paper proposes a selective review of available proposals that deal with scaling random forests to Big Data problems. These proposals rely on parallel environments or on online adaptations of random forests. We also describe how related quantities -- such as out-of-bag error and variable importance -- are addressed in these methods. Then, we formulate various remarks for random forests in the Big Data context. Finally, we experiment five variants on two massive datasets (15 and 120 millions of observations), a simulated one as well as real world data. One variant relies on subsampling while three others are related to parallel implementations of random forests and involve either various adaptations of bootstrap to Big Data or to "divide-and-conquer" approaches. The fifth variant relates on online learning of random forests. These numerical experiments lead to highlight the relative performance of the different variants, as well as some of their limitations

Measuring constructive alignment: an alignment metric to guide good practice

We present a computational model that represents and computes the level to which an educational design is constructively aligned. The model is able to provide ‘alignment metrics’ for both holistic and individual aspects of a programme or module design. A systemic and structural perspective of teaching and learning underpins the design of the computational model whereby Bloom’s taxonomy is used as a basis for categorising the core components of a teaching system and some basic principles of generative linguistics are borrowed for representing alignment structures and relationships. The degree of alignment is computed using Set theory and linear algebra. The model presented forms the main processing framework of a software tool currently being developed to facilitate teachers to systematically and consistently produce constructively aligned programmes of teaching and learning. It is envisaged that the model will have broad appeal as it allows the quality of educational designs to be measured and works on the principle of ‘practice techniques’ and ‘learning elicited’ as opposed to content

T-equivariant disc potential and SYZ mirror construction

We develop a G-equivariant Lagrangian Floer theory by counting pearly trees in the Borel construction LG. We apply the construction to smooth moment-map fibers of toric semi-Fano manifolds and obtain the T-equivariant Landau-Ginzburg mirrors. We also apply this to the typical S^1-invariant SYZ singular fiber, which is the single-pinched torus, and compute its S^1-equivariant disc potential.First author draf

A survey on algorithmic aspects of modular decomposition

The modular decomposition is a technique that applies but is not restricted to graphs. The notion of module naturally appears in the proofs of many graph theoretical theorems. Computing the modular decomposition tree is an important preprocessing step to solve a large number of combinatorial optimization problems. Since the first polynomial time algorithm in the early 70's, the algorithmic of the modular decomposition has known an important development. This paper survey the ideas and techniques that arose from this line of research

LAF-Fabric: a data analysis tool for Linguistic Annotation Framework with an application to the Hebrew Bible

The Linguistic Annotation Framework (LAF) provides a general, extensible stand-off markup system for corpora. This paper discusses LAF-Fabric, a new tool to analyse LAF resources in general with an extension to process the Hebrew Bible in particular. We first walk through the history of the Hebrew Bible as text database in decennium-wide steps. Then we describe how LAF-Fabric may serve as an analysis tool for this corpus. Finally, we describe three analytic projects/workflows that benefit from the new LAF representation: 1) the study of linguistic variation: extract cooccurrence data of common nouns between the books of the Bible (Martijn Naaijer); 2) the study of the grammar of Hebrew poetry in the Psalms: extract clause typology (Gino Kalkman); 3) construction of a parser of classical Hebrew by Data Oriented Parsing: generate tree structures from the database (Andreas van Cranenburgh)

Ferromagnetic Potts Model: Refined #BIS-hardness and Related Results

Recent results establish for 2-spin antiferromagnetic systems that the computational complexity of approximating the partition function on graphs of maximum degree D undergoes a phase transition that coincides with the uniqueness phase transition on the infinite D-regular tree. For the ferromagnetic Potts model we investigate whether analogous hardness results hold. Goldberg and Jerrum showed that approximating the partition function of the ferromagnetic Potts model is at least as hard as approximating the number of independent sets in bipartite graphs (#BIS-hardness). We improve this hardness result by establishing it for bipartite graphs of maximum degree D. We first present a detailed picture for the phase diagram for the infinite D-regular tree, giving a refined picture of its first-order phase transition and establishing the critical temperature for the coexistence of the disordered and ordered phases. We then prove for all temperatures below this critical temperature that it is #BIS-hard to approximate the partition function on bipartite graphs of maximum degree D. As a corollary, it is #BIS-hard to approximate the number of k-colorings on bipartite graphs of maximum degree D when k <= D/(2 ln D). The #BIS-hardness result for the ferromagnetic Potts model uses random bipartite regular graphs as a gadget in the reduction. The analysis of these random graphs relies on recent connections between the maxima of the expectation of their partition function, attractive fixpoints of the associated tree recursions, and induced matrix norms. We extend these connections to random regular graphs for all ferromagnetic models and establish the Bethe prediction for every ferromagnetic spin system on random regular graphs. We also prove for the ferromagnetic Potts model that the Swendsen-Wang algorithm is torpidly mixing on random D-regular graphs at the critical temperature for large q.Comment: To appear in SIAM J. Computin