Conceptual modelling: Towards detecting modelling errors in engineering applications

Rapid advancements of modern technologies put high demands on mathematical modelling of engineering systems. Typically, systems are no longer “simple” objects, but rather coupled systems involving multiphysics phenomena, the modelling of which involves coupling of models that describe different phenomena. After constructing a mathematical model, it is essential to analyse the correctness of the coupled models and to detect modelling errors compromising the final modelling result. Broadly, there are two classes of modelling errors: (a) errors related to abstract modelling, eg, conceptual errors concerning the coherence of a model as a whole and (b) errors related to concrete modelling or instance modelling, eg, questions of approximation quality and implementation. Instance modelling errors, on the one hand, are relatively well understood. Abstract modelling errors, on the other, are not appropriately addressed by modern modelling methodologies. The aim of this paper is to initiate a discussion on abstract approaches and their usability for mathematical modelling of engineering systems with the goal of making it possible to catch conceptual modelling errors early and automatically by computer assistant tools. To that end, we argue that it is necessary to identify and employ suitable mathematical abstractions to capture an accurate conceptual description of the process of modelling engineering systems

Synthesis of Recursive ADT Transformations from Reusable Templates

Recent work has proposed a promising approach to improving scalability of program synthesis by allowing the user to supply a syntactic template that constrains the space of potential programs. Unfortunately, creating templates often requires nontrivial effort from the user, which impedes the usability of the synthesizer. We present a solution to this problem in the context of recursive transformations on algebraic data-types. Our approach relies on polymorphic synthesis constructs: a small but powerful extension to the language of syntactic templates, which makes it possible to define a program space in a concise and highly reusable manner, while at the same time retains the scalability benefits of conventional templates. This approach enables end-users to reuse predefined templates from a library for a wide variety of problems with little effort. The paper also describes a novel optimization that further improves the performance and scalability of the system. We evaluated the approach on a set of benchmarks that most notably includes desugaring functions for lambda calculus, which force the synthesizer to discover Church encodings for pairs and boolean operations

Existential Types for Relaxed Noninterference

Information-flow security type systems ensure confidentiality by enforcing noninterference: a program cannot leak private data to public channels. However, in practice, programs need to selectively declassify information about private data. Several approaches have provided a notion of relaxed noninterference supporting selective and expressive declassification while retaining a formal security property. The labels-as-functions approach provides relaxed noninterference by means of declassification policies expressed as functions. The labels-as-types approach expresses declassification policies using type abstraction and faceted types, a pair of types representing the secret and public facets of values. The original proposal of labels-as-types is formulated in an object-oriented setting where type abstraction is realized by subtyping. The object-oriented approach however suffers from limitations due to its receiver-centric paradigm. In this work, we consider an alternative approach to labels-as-types, applicable in non-object-oriented languages, which allows us to express advanced declassification policies, such as extrinsic policies, based on a different form of type abstraction: existential types. An existential type exposes abstract types and operations on these; we leverage this abstraction mechanism to express secrets that can be declassified using the provided operations. We formalize the approach in a core functional calculus with existential types, define existential relaxed noninterference, and prove that well-typed programs satisfy this form of type-based relaxed noninterference

Conceptual modelling: Towards detecting modelling errors in engineering applications

Rapid advancements of modern technologies put high demands on mathematical modelling of engineering systems. Typically, systems are no longer “simple” objects, but rather coupled systems involving multiphysics phenomena, the modelling of which involves coupling of models that describe different phenomena. After constructing a mathematical model, it is essential to analyse the correctness of the coupled models and to detect modelling errors compromising the final modelling result. Broadly, there are two classes of modelling errors: (a) errors related to abstract modelling, eg, conceptual errors concerning the coherence of a model as a whole and (b) errors related to concrete modelling or instance modelling, eg, questions of approximation quality and implementation. Instance modelling errors, on the one hand, are relatively well understood. Abstract modelling errors, on the other, are not appropriately addressed by modern modelling methodologies. The aim of this paper is to initiate a discussion on abstract approaches and their usability for mathematical modelling of engineering systems with the goal of making it possible to catch conceptual modelling errors early and automatically by computer assistant tools. To that end, we argue that it is necessary to identify and employ suitable mathematical abstractions to capture an accurate conceptual description of the process of modelling engineering system

Solving Tree Problems with Category Theory

Artificial Intelligence (AI) has long pursued models, theories, and techniques to imbue machines with human-like general intelligence. Yet even the currently predominant data-driven approaches in AI seem to be lacking humans' unique ability to solve wide ranges of problems. This situation begs the question of the existence of principles that underlie general problem-solving capabilities. We approach this question through the mathematical formulation of analogies across different problems and solutions. We focus in particular on problems that could be represented as tree-like structures. Most importantly, we adopt a category-theoretic approach in formalising tree problems as categories, and in proving the existence of equivalences across apparently unrelated problem domains. We prove the existence of a functor between the category of tree problems and the category of solutions. We also provide a weaker version of the functor by quantifying equivalences of problem categories using a metric on tree problems.Comment: 10 pages, 4 figures, International Conference on Artificial General Intelligence (AGI) 201

Yukawa unification in SO(10) with light sparticle spectrum

We investigate supersymmetric SO(10) GUT model with \mu<0. The requirements of top-bottom-tau Yukawa unification, correct radiative electroweak symmetry breaking and agreement with the present experimental data may be met when the soft masses of scalars and gauginos are non-universal. We show how appropriate non-universalities can easily be obtained in the SO(10) GUT broken to the Standard Model. We discuss how values of BR(b-->s \gamma) and (g-2)_\mu simultaneously in a good agreement with the experimental data can be achieved in SO(10) model with \mu<0. In the region of the parameter space preferred by our analysis there are two main mechanisms leading to the LSP relic abundance consistent with the WMAP results. One is the co-annihilation with the stau and the second is the resonant annihilation via exchange of the Z boson or the light Higgs scalar. A very interesting feature of SO(10) models with negative \mu is that they predict relatively light sparticle spectra. Even the heaviest superpartners may easily have masses below 1.5 TeV in contrast to multi-TeV particles typical for models with positive \mu.Comment: 23 pages, 5 figure

SUSY parameter determination at the LHC using cross sections and kinematic edges

We study the determination of supersymmetric parameters at the LHC from a global fit including cross sections and edges of kinematic distributions. For illustration, we focus on a minimal supergravity scenario and discuss how well it can be constrained at the LHC operating at 7 and 14 TeV collision energy, respectively. We find that the inclusion of cross sections greatly improves the accuracy of the SUSY parameter determination, and allows to reliably extract model parameters even in the initial phase of LHC data taking with 7 TeV collision energy and 1/fb integrated luminosity. Moreover, cross section information may be essential to study more general scenarios, such as those with non-universal gaugino masses, and distinguish them from minimal, universal, models.Comment: 22 pages, 8 figure

Superpartner spectrum of minimal gaugino-gauge mediation

We evaluate the sparticle mass spectrum in the minimal four-dimensional construction that interpolates between gaugino and ordinary gauge mediation at the weak scale. We find that even in the hybrid case -- when the messenger scale is comparable to the mass of the additional gauge particles -- both the right-handed as well as the left-handed sleptons are lighter than the bino in the low-scale mediation regime. This implies a chain of lepton production and, consequently, striking signatures that may be probed at the LHC already in the near future.Comment: 8 pages, 3 figures; V2: refs and a few comments added; V3 title change

Needle & knot : binder boilerplate tied up

To lighten the burden of programming language mechanization, many approaches have been developed that tackle the substantial boilerplate which arises from variable binders. Unfortunately, the existing approaches are limited in scope. They typically do not support complex binding forms (such as multi-binders) that arise in more advanced languages, or they do not tackle the boilerplate due to mentioning variables and binders in relations. As a consequence, the human mechanizer is still unnecessarily burdened with binder boilerplate and discouraged from taking on richer languages. This paper presents Knot, a new approach that substantially extends the support for binder boilerplate. Knot is a highly expressive language for natural and concise specification of syntax with binders. Its meta-theory constructively guarantees the coverage of a considerable amount of binder boilerplate for well-formed specifications, including that for well-scoping of terms and context lookups. Knot also comes with a code generator, Needle, that specializes the generic boilerplate for convenient embedding in COQ and provides a tactic library for automatically discharging proof obligations that frequently come up in proofs of weakening and substitution lemmas of type-systems. Our evaluation shows, that Needle & Knot significantly reduce the size of language mechanizations (by 40% in our case study). Moreover, as far as we know, Knot enables the most concise mechanization of the POPLmark Challenge (1a + 2a) and is two-thirds the size of the next smallest. Finally, Knot allows us to mechanize for instance dependentlytyped languages, which is notoriously challenging because of dependent contexts and mutually-recursive sorts with variables