Sequent Calculus and Equational Programming

Proof assistants and programming languages based on type theories usually come in two flavours: one is based on the standard natural deduction presentation of type theory and involves eliminators, while the other provides a syntax in equational style. We show here that the equational approach corresponds to the use of a focused presentation of a type theory expressed as a sequent calculus. A typed functional language is presented, based on a sequent calculus, that we relate to the syntax and internal language of Agda. In particular, we discuss the use of patterns and case splittings, as well as rules implementing inductive reasoning and dependent products and sums.Comment: In Proceedings LFMTP 2015, arXiv:1507.0759

Analysing the Double diamond design process through research & implementation

“Analysing the Double diamond design process through research & implementation” aims to clarify and discuss the Double diamond design process, its origin, use and usefulness in design today. The thesis also intends to discuss the position, skill-set and responsibilities designers are faced with when working for a start-up in comparison to a larger company. The Double diamond design process itself is viewed through the lens of a case study project with a small company/start-up called Eye Caramba Oy. As the Double diamond model originated through the study of design practices in large established companies on a strategic level it was seen ft to balance that with its use on a small project and on a highly practical level. As the Design council (the creators of the Double diamond design process) urge users to alter or modify the process to suit their projects there are a vast amount of process model variations available. For the case study an original process model was made based on a project example. This detailed model added a layer to the discussion regarding proper use and modification of the Double diamond design process. As discussions and subsequent conclusions were the result of comparing a small project with a vast pool of research, they should not be viewed as conclusive but rather as important discussions for young designers entering an ever-changing market

The Present People

In modern political thought, one of the most recalcitrant, and increasingly pressing, questions of modern democracy is whether, and in what sense, the people can be present. While the presence of the people has, and continues to be, the sine qua non of the democratic form of government, it has also been for a long time held that the people cannot be present literally or in fact. According to the conventional narrative, this absence has been seen as a necessary acquiescence to the problem posed by the modern state, territorially expansive and populous, precluding an assembly democracy in which all can be physically present. The paradox which thus underpins modern democracy is that the people, being represented, is present in some sense, while not present literally or in fact.This thesis argues that the conventional narrative of the paradox of presence of modern democracy remains incomplete. It argues that in posing the question of what it means to speak of the presence of the people, contemporary political theory and intellectual history has so far neglected the question of time. Turning to the history of political thought of early modernity, the thesis contends that in the political thinking of Thomas Hobbes, Samuel Pufendorf and Robert Filmer, the critique of the democratic assembly was indeed framed primarily as one of time, rather than size and space. The democratic assembly, it was suggested, could not be present often enough to ensure the continuance of political order. Taking this problem of presence as a point of departure, the thesis traces its constitutive role in the political thought of some of the key thinkers of modern political thinking, including John Locke, Jean-Jacques Rousseau, as well as some of the central theorists of representative government from the end of the eighteenth century. It argues that while the question of time gradually came to be lost from the vocabulary of modern political thought, the problem continued to underpin and structure modern thinking on democracy and popular sovereignty. The imperative which thus continues to underpin modern democratic thought, though largely implicit, is that the people, understood as a political unity, must be made present often enough to ensure the continuance of political order.The thesis suggests that bringing this imperative to the fore allows political theory a greater understanding of the paradox of presence which imbues modern political thinking on democracy and popular sovereignty

International Protection and the Sovereign Decision - A Geneology of the Responsibility to Protect

In the wake of the 2005 World Summit ratification of the responsibility to protect doctrine, the cases of Darfur and Syria have revealed the decisionary discretion of the collective international responsibility to protect inscribed within the doctrine. Through an engagement with the decisionist theory of Carl Schmitt and the work of Giorgio Agamben, this essay seeks to return the question of the decision regarding intervention under the responsibility to protect doctrine to its proper place as the functioning of power. Through the genealogical method of Michel Foucault, the diverse elements of the doctrine could be traced to show the decision as the articulation of a certain relation of power. Inscribed within the legal anomie where international humanitarian and human rights law no longer applies, the doctrine would prescribe a collective international responsibility to protect only in relation to a figure of bare life, such that the fate of the latter would remain subject to the decision of the Security Council. This decision can, as such, always take the form of an abstention on action, sustaining the legal anomie wherein sovereign power would exist without legal restrictions

Vertex operators, solvable lattice models and metaplectic Whittaker functions

We show that spherical Whittaker functions on an $n$-fold cover of the general linear group arise naturally from the quantum Fock space representation of $U_q(\widehat{\mathfrak{sl}}(n))$ introduced by Kashiwara, Miwa and Stern (KMS). We arrive at this connection by reconsidering solvable lattice models known as `metaplectic ice' whose partition functions are metaplectic Whittaker functions. First, we show that a certain Hecke action on metaplectic Whittaker coinvariants agrees (up to twisting) with a Hecke action of Ginzburg, Reshetikhin, and Vasserot. This allows us to expand the framework of KMS by Drinfeld twisting to introduce Gauss sums into the quantum wedge, which are necessary for connections to metaplectic forms. Our main theorem interprets the row transfer matrices of this ice model as `half' vertex operators on quantum Fock space that intertwine with the action of $U_q(\widehat{\mathfrak{sl}}(n))$. In the process, we introduce new symmetric functions termed \textit{metaplectic symmetric functions} and explain how they relate to Whittaker functions on an $n$-fold metaplectic cover of GL$_r$. These resemble \textit{LLT polynomials} introduced by Lascoux, Leclerc and Thibon; in fact the metaplectic symmetric functions are (up to twisting) specializations of \textit{supersymmetric LLT polynomials} defined by Lam. Indeed Lam constructed families of symmetric functions from Heisenberg algebra actions on the Fock space commuting with the $U_q(\widehat{\mathfrak{sl}}(n))$-action. We explain that half vertex operators agree with Lam's construction and this interpretation allows for many new identities for metaplectic symmetric and Whittaker functions, including Cauchy identities. While both metaplectic symmetric functions and LLT polynomials can be related to vertex operators on the $q$-Fock space, only metaplectic symmetric functions are connected to solvable lattice models.Comment: v3 changes: minor edit

Eisenstein series and automorphic representations

We provide an introduction to the theory of Eisenstein series and automorphic forms on real simple Lie groups G, emphasising the role of representation theory. It is useful to take a slightly wider view and define all objects over the (rational) adeles A, thereby also paving the way for connections to number theory, representation theory and the Langlands program. Most of the results we present are already scattered throughout the mathematics literature but our exposition collects them together and is driven by examples. Many interesting aspects of these functions are hidden in their Fourier coefficients with respect to unipotent subgroups and a large part of our focus is to explain and derive general theorems on these Fourier expansions. Specifically, we give complete proofs of the Langlands constant term formula for Eisenstein series on adelic groups G(A) as well as the Casselman--Shalika formula for the p-adic spherical Whittaker function associated to unramified automorphic representations of G(Q_p). In addition, we explain how the classical theory of Hecke operators fits into the modern theory of automorphic representations of adelic groups, thereby providing a connection with some key elements in the Langlands program, such as the Langlands dual group LG and automorphic L-functions. Somewhat surprisingly, all these results have natural interpretations as encoding physical effects in string theory. We therefore also introduce some basic concepts of string theory, aimed toward mathematicians, emphasising the role of automorphic forms. In particular, we provide a detailed treatment of supersymmetry constraints on string amplitudes which enforce differential equations of the same type that are satisfied by automorphic forms. Our treatise concludes with a detailed list of interesting open questions and pointers to additional topics which go beyond the scope of this book.Comment: 326 pages. Detailed and example-driven exposition of the subject with highlighted applications to string theory. v2: 375 pages. Substantially extended and small correction

Sum rules and physical limitations for passive metamaterials

Bandwidth is an important parameter in many metamaterial applications. It has been shown that Herglotz functions and sum rules offer a powerful methodology to analyze the trade-off between bandwidth and design parameters. Here, this approach is described for the temporal dispersion of constitutive relations and high-impedance surfaces

Area Based Alarm System using 3D Cameras

Depth map cameras provide new ways of designing surveillance systems. In this thesis we evaluate three different cameras from two different depth sensor techniques, and propose a complete method for detecting thefts over a counter in a retail environment. Our algorithm covers pre-processing with noise reduction and background segmentation using the reflected signals amplitude as a confidence measurement. A plane is fitted both to the 3D points of the top of the retail counter as well as to the 3D points on the side (cashiers side) of the retail counter. The algorithm determines which foreground pixels are on the wrong side of both these planes. By running this result through a few methods to improve rigidity, we show that it is possible to detect thefts with a very high detection rate and low false positive rate. Finally we present the results from our testing of different versions on a database of activities with known ground-truth (theft/no theft)

Sum rules and physical bounds on passive metamaterials

Frequency dependence of the permittivity and permeability is inevitable in metamaterial applications such as cloaking and perfect lenses. In this paper, Herglotz functions are used as a tool to construct sum rules from which we derive physical bounds suited for metamaterial applications, where the material parameters are often designed to be negative or near zero in the frequency band of interest. Several sum rules are presented that relate the temporal dispersion of the material parameters with the difference between the static and instantaneous parameter values, which are used to give upper bounds on the bandwidth of the application. This substantially advances the understanding of the behavior of metamaterials with extraordinary material parameters, and reveals a beautiful connection between properties in the design band (finite frequencies) and the low- and high-frequency limit