5,306 research outputs found
Positive trigonometric polynomials for strong stability of difference equations
We follow a polynomial approach to analyse strong stability of linear
difference equations with rationally independent delays. Upon application of
the Hermite stability criterion on the discrete-time homogeneous characteristic
polynomial, assessing strong stability amounts to deciding positive
definiteness of a multivariate trigonometric polynomial matrix. This latter
problem is addressed with a converging hierarchy of linear matrix inequalities
(LMIs). Numerical experiments indicate that certificates of strong stability
can be obtained at a reasonable computational cost for state dimension and
number of delays not exceeding 4 or 5
A CDCL-style calculus for solving non-linear constraints
In this paper we propose a novel approach for checking satisfiability of
non-linear constraints over the reals, called ksmt. The procedure is based on
conflict resolution in CDCL style calculus, using a composition of symbolical
and numerical methods. To deal with the non-linear components in case of
conflicts we use numerically constructed restricted linearisations. This
approach covers a large number of computable non-linear real functions such as
polynomials, rational or trigonometrical functions and beyond. A prototypical
implementation has been evaluated on several non-linear SMT-LIB examples and
the results have been compared with state-of-the-art SMT solvers.Comment: 17 pages, 3 figures; accepted at FroCoS 2019; software available at
<http://informatik.uni-trier.de/~brausse/ksmt/
Increasing the Numeric Expressiveness of the Planning Domain Definition Language
The technology of artificial intelligence (AI) planning is being adopted across many different disciplines. This has resulted in the wider use of the Planning Domain Definition Language (PDDL), where it is being used to model planning problems of different natures. One such area where AI planning is particularly attractive is engineering, where the optimisation problems are mathematically rich. The example used throughout this paper is the optimisation (minimisation) of machine tool measurement uncertainty. This planning problem highlights the limits of PDDL's numerical expressiveness in the absence of the square root function. A workaround method using the Babylonian algorithm is then evaluated before the extension of PDDL to include more mathematics functions is discussed
Uncovering protein interaction in abstracts and text using a novel linear model and word proximity networks
We participated in three of the protein-protein interaction subtasks of the
Second BioCreative Challenge: classification of abstracts relevant for
protein-protein interaction (IAS), discovery of protein pairs (IPS) and text
passages characterizing protein interaction (ISS) in full text documents. We
approached the abstract classification task with a novel, lightweight linear
model inspired by spam-detection techniques, as well as an uncertainty-based
integration scheme. We also used a Support Vector Machine and the Singular
Value Decomposition on the same features for comparison purposes. Our approach
to the full text subtasks (protein pair and passage identification) includes a
feature expansion method based on word-proximity networks. Our approach to the
abstract classification task (IAS) was among the top submissions for this task
in terms of the measures of performance used in the challenge evaluation
(accuracy, F-score and AUC). We also report on a web-tool we produced using our
approach: the Protein Interaction Abstract Relevance Evaluator (PIARE). Our
approach to the full text tasks resulted in one of the highest recall rates as
well as mean reciprocal rank of correct passages. Our approach to abstract
classification shows that a simple linear model, using relatively few features,
is capable of generalizing and uncovering the conceptual nature of
protein-protein interaction from the bibliome. Since the novel approach is
based on a very lightweight linear model, it can be easily ported and applied
to similar problems. In full text problems, the expansion of word features with
word-proximity networks is shown to be useful, though the need for some
improvements is discussed
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