QPCF: higher order languages and quantum circuits

qPCF is a paradigmatic quantum programming language that ex- tends PCF with quantum circuits and a quantum co-processor. Quantum circuits are treated as classical data that can be duplicated and manipulated in flexible ways by means of a dependent type system. The co-processor is essentially a standard QRAM device, albeit we avoid to store permanently quantum states in between two co-processor's calls. Despite its quantum features, qPCF retains the classic programming approach of PCF. We introduce qPCF syntax, typing rules, and its operational semantics. We prove fundamental properties of the system, such as Preservation and Progress Theorems. Moreover, we provide some higher-order examples of circuit encoding

Elaboration in Dependent Type Theory

To be usable in practice, interactive theorem provers need to provide convenient and efficient means of writing expressions, definitions, and proofs. This involves inferring information that is often left implicit in an ordinary mathematical text, and resolving ambiguities in mathematical expressions. We refer to the process of passing from a quasi-formal and partially-specified expression to a completely precise formal one as elaboration. We describe an elaboration algorithm for dependent type theory that has been implemented in the Lean theorem prover. Lean's elaborator supports higher-order unification, type class inference, ad hoc overloading, insertion of coercions, the use of tactics, and the computational reduction of terms. The interactions between these components are subtle and complex, and the elaboration algorithm has been carefully designed to balance efficiency and usability. We describe the central design goals, and the means by which they are achieved

On the alleged simplicity of impure proof

Roughly, a proof of a theorem, is “pure” if it draws only on what is “close” or “intrinsic” to that theorem. Mathematicians employ a variety of terms to identify pure proofs, saying that a pure proof is one that avoids what is “extrinsic,” “extraneous,” “distant,” “remote,” “alien,” or “foreign” to the problem or theorem under investigation. In the background of these attributions is the view that there is a distance measure (or a variety of such measures) between mathematical statements and proofs. Mathematicians have paid little attention to specifying such distance measures precisely because in practice certain methods of proof have seemed self- evidently impure by design: think for instance of analytic geometry and analytic number theory. By contrast, mathematicians have paid considerable attention to whether such impurities are a good thing or to be avoided, and some have claimed that they are valuable because generally impure proofs are simpler than pure proofs. This article is an investigation of this claim, formulated more precisely by proof- theoretic means. After assembling evidence from proof theory that may be thought to support this claim, we will argue that on the contrary this evidence does not support the claim

Perspectives for proof unwinding by programming languages techniques

In this chapter, we propose some future directions of work, potentially beneficial to Mathematics and its foundations, based on the recent import of methodology from the theory of programming languages into proof theory. This scientific essay, written for the audience of proof theorists as well as the working mathematician, is not a survey of the field, but rather a personal view of the author who hopes that it may inspire future and fellow researchers

The role of information systems in the prevention and detection of transnational and international crime

© Cambridge University Press 2014. All around the world criminal activity remains at the forefront of governmental concerns, not only as a problem that distorts the very fabric of society within the confines of national jurisdictions, but also as a problem that cuts across national borders to exhibit a global dimension. The international dimension of criminal activity remains critical and is generally characterized by a complexity that is unique and requires action on many different levels. Criminals set out to mask their illegal activities and deliberately generate complexity as a means of concealment. In doing so, they exploit new developments in technology that assist them in achieving their ends. This criminality exhibits forms of innovation that stretch far beyond traditional criminal activity (e.g., drug and human trafficking) and manages to attach itself within the broader fabric of society by exploiting the very latest developments. This evolution is necessary as criminals seek not only to escape arrest, prosecution and conviction, but also to enjoy the fruits of their criminality (mostly financial gains). Thus, they seek to develop ways of exploiting the various diffuse norms of social interaction (e.g., trust), financial modes of conduct (e.g., cash-based economies), technological and communication developments (e.g., Internet), and thereby minimize the possibility for detection. By limiting the resources that can be made available for prevention (or making them obsolete when developing new criminal behaviour), they participate in this co-evolution actively; and this they achieve by generating complexity

The structure of problem-solving knowledge and the structure of organisations

This work presents a model of organisational problem solving able to account for the relationships between problem complexity, tasks decentralilzation and problem solving efficiency. Whenever problem solving requires the coordination of a multiplicity of interdependent elements, the varying degrees of decentralization of cognitive and operational tasks shape the solution which can be generated, tested and selected. Suboptimality and path-dependence are shown to be ubiquitous features of organisational problem solving. At the same time, the model allows a precise exploration of the possible trade-offs between decompostion patterns and search efficiency involved in different organisational architectures.-

On the Road to Accurate Biomarkers for Cardiometabolic Diseases by Integrating Precision and Gender Medicine Approaches

The need to facilitate the complex management of cardiometabolic diseases (CMD) has led to the detection of many biomarkers, however, there are no clear explanations of their role in the prevention, diagnosis or prognosis of these diseases. Molecules associated with disease pathways represent valid disease surrogates and well-fitted CMD biomarkers. To address this challenge, data from multi-omics types (genomics, epigenomics, transcriptomics, proteomics, metabolomics, microbiomics, and nutrigenomics), from human and animal models, have become available. However, individual omics types only provide data on a small part of molecules involved in the complex CMD mechanisms, whereas, here, we propose that their integration leads to multidimensional data. Such data provide a better understanding of molecules related to CMD mechanisms and, consequently, increase the possibility of identifying well-fitted biomarkers. In addition, the application of gender medicine also helps to identify accurate biomarkers according to gender, facilitating a differential CMD management. Accordingly, the impact of gender differences in CMD pathophysiology has been widely demonstrated, where gender is referred to the complex interrelation and integration of sex (as a biological and functional marker of the human body) and psychological and cultural behavior (due to ethnical, social, and religious background). In this review, all these aspects are described and discussed, as well as potential limitations and future directions in this incipient field

Effects of zinc oxide filler on the curing and mechanical response of alkyd coatings

The mechanical properties of an alkyd resin filled with zinc oxide pigment were studied at different concentrations over a wide range of time scales using dynamic mechanical analysis, quartz crystal rheometry and nanoindentation. The motivation for this work stems from the interest in accessing the long-term properties of paint coatings by studying the mechanical properties of historic paints. In this foundational work, we compare three different modalities of mechanical measurements and systematically determine the effect of pigment filler loading on the measured properties. Quantitative agreement between the methods is obtained when the characteristic time scales of each of the methods is taken into account. While nanoindentation is the technique most readily applied to historic paint samples, the rheometric quartz crystal microbalance (rheo-QCM) is the best suited for obtaining mechanistic information from measurements of paint properties over time, provided that appropriate thin-film samples can be produced. In these studies we find that ZnO increases the rate of oxidation of the alkyd during the initial stages of cure by an amount that depends on the ZnO content