Related papers: Escrows are optics
Consider an exchange mechanism which accepts diversified offers of various commodities and redistributes everything it receives. We impose certain conditions of fairness and convenience on such a mechanism and show that it admits unique…
Fong developed `decorated cospans' to model various kinds of open systems: that is, systems with inputs and outputs. In this framework, open systems are seen as the morphisms of a category and can be composed as such, allowing larger open…
We describe a pricing structure for the provision of IT services that ensures trust without requiring repeated interactions between service providers and users. It does so by offering a pricing structure that elicits truthful reporting of…
To a semi-cosimplicial object (SCO) in a category we associate a system of partial shifts on the inductive limit. We show how to produce an SCO from an action of the infinite braid monoid $\mathbb{B}^+_\infty$ and provide examples. In…
In this paper, we investigate a class of information-flow security properties called opacity in partial-observed discrete-event systems. Roughly speaking, a system is said to be opaque if the intruder, which is modeled by a passive…
General cryptographic schemes are presented where keys can be one-time or ephemeral. Processes for key exchange are derived. Public key cryptographic schemes based on the new systems are easily established. Authentication and signature…
We propose to use transformation optics to generate a general illusion such that an arbitrary object appears to be like some other object of our choice. This is achieved by using a remote device that transforms the scattered light outside a…
Financial structures such as securitisations, insurance contracts, and other hierarchical claims systems can be interpreted as deterministic allocation mechanisms acting on stochastic inflow processes. This paper develops a general…
We use formal methods to specify, design, and monitor continuous double auctions, which are widely used to match buyers and sellers at exchanges of foreign currencies, stocks, and commodities. We identify three natural properties of such…
Opacity is a property expressing whether a system may reveal its secret to a passive observer (an intruder) who knows the structure of the system but has a limited observation of its behavior. Several notions of opacity have been studied,…
Optics are bidirectional data accessors that capture data transformation patterns such as accessing subfields or iterating over containers. Profunctor optics are a particular choice of representation supporting modularity, meaning that we…
The notion of a spherical space over an arbitrary base scheme is introduced as a generalization of a spherical variety over an algebraically closed field. It is studied how the sphericity condition behaves in families. In particular it is…
Entropy can signify different things: For instance, heat transfer in thermodynamics or a measure of information in data analysis. Many entropies have been introduced and it can be difficult to ascertain their different importance and…
This paper investigates an important class of information-flow security property called opacity for stochastic control systems. Opacity captures whether a system's secret behavior (a subset of the system's behavior that is considered to be…
Relations between some kinds of formal and standard smoothness, for morphisms of schemes, are clarified in surprisingly simple and direct ways, bypassing much of the customarily employed machinery. Even the deep local-to-global property of…
Trades based on bilateral (indivisible) contracts can be represented by a network. Vertices correspond to agents while arcs represent the non-price elements of a bilateral contract. Given prices for each arc, agents choose the incident arcs…
Two structures are said to be equimorphic if each embeds in the other. Such structures cannot be expected to be isomorphic, and in this paper we investigate the special case of linear orders, here also called chains. In particular we…
A prototype model of stock market is introduced and studied numerically. In this self-organized system, we consider only the interaction among traders without external influences. Agents trade according to their own strategy, to accumulate…
Forking is a central notion of model theory, generalizing linear independence in vector spaces and algebraic independence in fields. We develop the theory of forking in abstract, category-theoretic terms, for reasons both practical (we…
A pattern of interaction that arises again and again in programming is a "handshake", in which two agents exchange data. The exchange is thought of as provision of a service. Each interaction is initiated by a specific agent--the client or…