Related papers: Escrows are optics
In object systems, classes take the role of modules, and interfaces consist of methods. Because methods are encapsulated in objects, interfaces in object systems do not allow abstracting over \emph{where} methods are implemented. This…
Conditional independence has been widely used in AI, causal inference, machine learning, and statistics. We introduce categoroids, an algebraic structure for characterizing universal properties of conditional independence. Categoroids are…
Simple optics are defined using actions of monoidal categories. Compound optics arise, for instance, as natural transformations between polynomial functors. Since a monoidal category is a special case of a bicategory, we formulate complex…
When formalizing mathematics in (generalized predicative) constructive type theories, or more practically in proof assistants such as Coq or Agda, one is often using setoids (types with explicit equivalence relations). In this note we…
As algorithmic trading and electronic markets continue to transform the landscape of financial markets, detecting and deterring rogue agents to maintain a fair and efficient marketplace is crucial. The explosion of large datasets and the…
Bimorphic lenses are a simplification of polymorphic lenses that (like polymorphic lenses) have a type defined by 4 parameters, but which are defined in a monomorphic type system (i.e. an ordinary category with finite products). We show…
We consider an economic environment with one buyer and one seller. For a bundle $(t,q)\in [0,\infty[\times [0,1]=\mathbb{Z}$, $q$ refers to the winning probability of an object, and $t$ denotes the payment that the buyer makes. We consider…
Market manipulation is a strategy used by traders to alter the price of financial securities. One type of manipulation is based on the process of buying or selling assets by using several trading strategies, among them spoofing is a popular…
We introduce a framework where the announcements of a clearinghouse about the allocation process are opaque in the sense that there can be more than one outcome compatible with a realization of type reports. We ask whether desirable…
The goal of this article is to understand some interesting features of sequences of arbitrage operations, which look relevant to various processes in Economics and Finances. In the second part of the paper, analysis of sequences of…
A weak asynchronous system is a trace monoid with a partial action on a set. A polygonal morphism between weak asynchronous systems commutes with the actions and preserves the independence of events. We prove that the category of weak…
A growing body of work in economics and computation focuses on the trade-off between implementability and simplicity in mechanism design. The goal is to develop a theory that not only allows to design an incentive structure easy to grasp…
Since categories are graphs with additional "structure", one should start from fuzzy graphs in order to define a theory of fuzzy categories. Thus is makes sense to introduce categories whose morphisms are associated with a plausibility…
An open market is a subset of an entire equity market composed of a certain fixed number of top capitalization stocks. Though the number of stocks in the open market is fixed, the constituents of the market change over time as each…
We define a concept which we call multiplicity. First, multiplicity of a morphism is defined. Then the multiplicity of an object over another object is defined to be the minimum of the multiplicities of all morphisms from one to another.…
The present work investigates a type of morphisms between encryption schemes, called bridges. By associating an encryption scheme to every such bridge, we define and examine their security. Inspired by the bootstrapping procedure used by…
Cloaking is a method of making obstacles undetectable. Here we cloak unit cells of a magnetic pattern squeezed into an otherwise periodic pattern from a magnetically driven colloidal flow. We apply a time-periodic external magnetic field…
Lenses, optics and dependent lenses (or equivalently morphisms of containers, or equivalently natural transformations of polynomial functors) are all widely used in applied category theory as models of bidirectional processes. From the…
In voting theory, bribery is a form of manipulative behavior in which an external actor (the briber) offers to pay the voters to change their votes in order to get her preferred candidate elected. We investigate a model of bribery where the…
Comparison-based algorithms are algorithms for which the execution of each operation is solely based on the outcome of a series of comparisons between elements. Comparison-based computations can be naturally represented via the following…