Decidability of Univariate Real Algebra with Predicates for Rational and Integer Powers

We prove decidability of univariate real algebra extended with predicates for rational and integer powers, i.e., $(x^n \in \mathbb{Q})$ and $(x^n \in \mathbb{Z})$. Our decision procedure combines computation over real algebraic cells with the rational root theorem and witness construction via algebraic number density arguments.Comment: To appear in CADE-25: 25th International Conference on Automated Deduction, 2015. Proceedings to be published by Springer-Verla

Psychological functioning in adolescents referred to specialist gender identity clinics across Europe : a clinical comparison study between four clinics

Adolescents seeking professional help with their gender identity development often present with psychological difficulties. Existing literature on psychological functioning of gender diverse young people is limited and mostly bound to national chart reviews. This study examined the prevalence of psychological functioning and peer relationship problems in adolescents across four European specialist gender services (The Netherlands, Belgium, the UK, and Switzerland), using the Child Behavioural Checklist (CBCL) and the Youth Self-Report (YSR). Differences in psychological functioning and peer relationships were found in gender diverse adolescents across Europe. Overall, emotional and behavioural problems and peer relationship problems were most prevalent in adolescents from the UK, followed by Switzerland and Belgium. The least behavioural and emotional problems and peer relationship problems were reported by adolescents from The Netherlands. Across the four clinics, a similar pattern of gender differences was found. Birth-assigned girls showed more behavioural problems and externalising problems in the clinical range, as reported by their parents. According to self-report, internalising problems in the clinical range were more prevalent in adolescent birth-assigned boys. More research is needed to gain a better understanding of the difference in clinical presentations in gender diverse adolescents and to investigate what contextual factors that may contribute to this

Machine-Checked Proofs For Realizability Checking Algorithms

Virtual integration techniques focus on building architectural models of systems that can be analyzed early in the design cycle to try to lower cost, reduce risk, and improve quality of complex embedded systems. Given appropriate architectural descriptions, assume/guarantee contracts, and compositional reasoning rules, these techniques can be used to prove important safety properties about the architecture prior to system construction. For these proofs to be meaningful, each leaf-level component contract must be realizable; i.e., it is possible to construct a component such that for any input allowed by the contract assumptions, there is some output value that the component can produce that satisfies the contract guarantees. We have recently proposed (in [1]) a contract-based realizability checking algorithm for assume/guarantee contracts over infinite theories supported by SMT solvers such as linear integer/real arithmetic and uninterpreted functions. In that work, we used an SMT solver and an algorithm similar to k-induction to establish the realizability of a contract, and justified our approach via a hand proof. Given the central importance of realizability to our virtual integration approach, we wanted additional confidence that our approach was sound. This paper describes a complete formalization of the approach in the Coq proof and specification language. During formalization, we found several small mistakes and missing assumptions in our reasoning. Although these did not compromise the correctness of the algorithm used in the checking tools, they point to the value of machine-checked formalization. In addition, we believe this is the first machine-checked formalization for a realizability algorithm.Comment: 14 pages, 1 figur

Profits and Fractal Properties: Notes on Marx, Countertendencies and Simulation Models

© 2017 Informa UK Limited, trading as Taylor & Francis Group. There are new reasons for revisiting Marx’s elaboration on the rate of profit because contemporary debates provide findings from the MEGA Project, long-term data on the rate of profit, and tools for dealing with complexity and non-equilibrium systems. This article proposes that the interplay between the tendency and the countertendencies of the rate of profit to fall can be translated into a simple system of equations, one based on each chapter of Section Three of Capital—as if Marx sought to mathematically formalise his insights. This article reviews previous debates, presents data and runs a simulation model, showing that the rate of profit behaves as fractals.Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES, Brazil), grant (BEX 0840/14-9

Thermal States as Universal Resources for Quantum Computation with Always-On Interactions

Measurement-based quantum computation utilizes an initial entangled resource state and proceeds with subsequent single-qubit measurements. It is implicitly assumed that the interactions between qubits can be switched off so that the dynamics of the measured qubits do not affect the computation. By proposing a model spin Hamiltonian, we demonstrate that measurement-based quantum computation can be achieved on a thermal state with always-on interactions. Moreover, computational errors induced by thermal fluctuations can be corrected and thus the computation can be executed fault tolerantly if the temperature is below a threshold value

Solvable Lie algebras are not that hypo

We study a type of left-invariant structure on Lie groups, or equivalently on Lie algebras. We introduce obstructions to the existence of a hypo structure, namely the 5-dimensional geometry of hypersurfaces in manifolds with holonomy SU(3). The choice of a splitting g^*=V_1 + V_2, and the vanishing of certain associated cohomology groups, determine a first obstruction. We also construct necessary conditions for the existence of a hypo structure with a fixed almost-contact form. For non-unimodular Lie algebras, we derive an obstruction to the existence of a hypo structure, with no choice involved. We apply these methods to classify solvable Lie algebras that admit a hypo structure.Comment: 21 pages; v2: presentation improved, typos corrected, notational conflicts eliminated. To appear in Transformation Group

Efficient coupling into slow light photonic crystal waveguide without transition region: Role of evanescent modes

We show that efficient coupling between fast and slow photonic crystal waveguide modes is possible, provided that there exist strong evanescent modes to match the waveguide fields across the interface. Evanescent modes are required when the propagating modes have substantially different modal fields, which occurs, for example, when coupling an index-guided mode and a gap-guided mode. ©2009 Optical Society of America

Efficient slow-light coupling in a photonic crystal waveguide without transition region

We consider the coupling into a slow mode that appears near an inflection point in the band structure of a photonic crystal waveguide. Remarkably, the coupling into this slow mode, which has a group index ng > 1000, can be essentially perfect without any transition region. We show that this efficient coupling occurs thanks to an evanescent mode in the slow medium, which has appreciable amplitude and helps satisfy the boundary conditions but does not transport any energy. © 2008 Optical Society of America