Syntax for free: representing syntax with binding using parametricity

We show that, in a parametric model of polymorphism, the type ∀ α. ((α → α) → α) → (α → α → α) → α is isomorphic to closed de Bruijn terms. That is, the type of closed higher-order abstract syntax terms is isomorphic to a concrete representation. To demonstrate the proof we have constructed a model of parametric polymorphism inside the Coq proof assistant. The proof of the theorem requires parametricity over Kripke relations. We also investigate some variants of this representation

Quantum Inequalities and Singular Energy Densities

There has been much recent work on quantum inequalities to constrain negative energy. These are uncertainty principle-type restrictions on the magnitude and duration of negative energy densities or fluxes. We consider several examples of apparent failures of the quantum inequalities, which involve passage of an observer through regions where the negative energy density becomes singular. We argue that this type of situation requires one to formulate quantum inequalities using sampling functions with compact support. We discuss such inequalities, and argue that they remain valid even in the presence of singular energy densities.Comment: 18 pages, LaTex, 2 figures, uses eps

Circadian rhythms mediate infection risk in \u3ci\u3eDaphnia dentifera\u3c/i\u3e

Biological rhythms mediate important within-host processes such as metabolism, immunity, and behavior which are often linked to combating disease exposure. For many hosts, exposure to pathogens occurs while feeding. However, the link between feeding rhythms and infection risk is unclear because feeding behavior is tightly coupled with immune and metabolic processes which may decrease susceptibility to infection. Here, we use the Daphnia dentifera–Metschnikowia bicuspidata host–pathogen system to determine how rhythms in feeding rate and immune function mediate infection risk. The host is known to have a nocturnal circadian rhythm in feeding rate, yet we found that they do not exhibit a circadian rhythm in phenoloxidase activity. We found that the time of day when individuals are exposed to pathogens affects the probability of infection with higher infection prevalence at night, indicating that infection risk is driven by a host\u27s circadian rhythm in feeding behavior. These results suggest that the natural circadian rhythm of the host should be considered when addressing epidemiological dynamics

Scalar Field Quantum Inequalities in Static Spacetimes

We discuss quantum inequalities for minimally coupled scalar fields in static spacetimes. These are inequalities which place limits on the magnitude and duration of negative energy densities. We derive a general expression for the quantum inequality for a static observer in terms of a Euclidean two-point function. In a short sampling time limit, the quantum inequality can be written as the flat space form plus subdominant correction terms dependent upon the geometric properties of the spacetime. This supports the use of flat space quantum inequalities to constrain negative energy effects in curved spacetime. Using the exact Euclidean two-point function method, we develop the quantum inequalities for perfectly reflecting planar mirrors in flat spacetime. We then look at the quantum inequalities in static de~Sitter spacetime, Rindler spacetime and two- and four-dimensional black holes. In the case of a four-dimensional Schwarzschild black hole, explicit forms of the inequality are found for static observers near the horizon and at large distances. It is show that there is a quantum averaged weak energy condition (QAWEC), which states that the energy density averaged over the entire worldline of a static observer is bounded below by the vacuum energy of the spacetime. In particular, for an observer at a fixed radial distance away from a black hole, the QAWEC says that the averaged energy density can never be less than the Boulware vacuum energy density.Comment: 27 pages, 2 Encapsulated Postscript figures, uses epsf.tex, typeset in RevTe

Circadian rhythms mediate infection risk in \u3ci\u3eDaphnia dentifera\u3c/i\u3e

Biological rhythms mediate important within-host processes such as metabolism, immunity, and behavior which are often linked to combating disease exposure. For many hosts, exposure to pathogens occurs while feeding. However, the link between feeding rhythms and infection risk is unclear because feeding behavior is tightly coupled with immune and metabolic processes which may decrease susceptibility to infection. Here, we use the Daphnia dentifera–Metschnikowia bicuspidata host–pathogen system to determine how rhythms in feeding rate and immune function mediate infection risk. The host is known to have a nocturnal circadian rhythm in feeding rate, yet we found that they do not exhibit a circadian rhythm in phenoloxidase activity. We found that the time of day when individuals are exposed to pathogens affects the probability of infection with higher infection prevalence at night, indicating that infection risk is driven by a host\u27s circadian rhythm in feeding behavior. These results suggest that the natural circadian rhythm of the host should be considered when addressing epidemiological dynamics

Dependent Types for Pragmatics

This paper proposes the use of dependent types for pragmatic phenomena such as pronoun binding and presupposition resolution as a type-theoretic alternative to formalisms such as Discourse Representation Theory and Dynamic Semantics.Comment: This version updates the paper for publication in LEU

Coeffects: Unified static analysis of context-dependence

Monadic effect systems provide a unified way of tracking effects of computations, but there is no unified mechanism for tracking how computations rely on the environment in which they are executed. This is becoming an important problem for modern software – we need to track where distributed computations run, which resources a program uses and how they use other capabilities of the environment. We consider three examples of context-dependence analysis: liveness analysis, tracking the use of implicit parameters (similar to tracking of resource usage in distributed computation), and calculating caching requirements for dataflow programs. Informed by these cases, we present a unified calculus for tracking context dependence in functional languages together with a categorical semantics based on indexed comonads. We believe that indexed comonads are the right foundation for constructing context-aware languages and type systems and that following an approach akin to monads can lead to a widespread use of the concept

Propositions as Sessions

Continuing a line of work by Abramsky (1994), by Bellin and Scott (1994), and by Caires and Pfenning (2010), among others, this paper presents CP, a calculus in which propositions of classical linear logic correspond to session types. Continuing a line of work by Honda (1993), by Honda, Kubo, and Vasconcelos (1998), and by Gay and Vasconcelos (2010), among others, this paper presents GV, a linear functional language with session types, and presents a translation from GV into CP. The translation formalises for the first time a connection between a standard presentation of session types and linear logic, and shows how a modification to the standard presentation yield a language free from deadlock, where deadlock freedom follows from the correspondence to linear logic. Note. Please read this paper in colour! The paper uses colour to highlight the relation of types to terms and source to target. 1

On the Stability of the Mean-Field Glass Broken Phase under Non-Hamiltonian Perturbations

We study the dynamics of the SK model modified by a small non-hamiltonian perturbation. We study aging, and we find that on the time scales investigated by our numerical simulations it survives a small perturbation (and is destroyed by a large one). If we assume we are observing a transient behavior the scaling of correlation times versus the asymmetry strength is not compatible with the one expected for the spherical model. We discuss the slow power law decay of observable quantities to equilibrium, and we show that for small perturbations power like decay is preserved. We also discuss the asymptotically large time region on small lattices.Comment: 34 page