Related papers: A Monadic Calculus with Episodic Flows
This study presents data format of episodic memory for artificial intelligence and cognitive science. The data format, named cognitive-logs, enables rigour and flexible logical reasoning. Cognitive-logs consist of a set of relational and…
Statistics and Optimization are foundational to modern Machine Learning. Here, we propose an alternative foundation based on Abstract Algebra, with mathematics that facilitates the analysis of learning. In this approach, the goal of the…
Type-and-effect systems incorporate information about the computational effects, e.g., state mutation, probabilistic choice, or I/O, a program phrase may invoke alongside its return value. A semantics for type-and-effect systems involves a…
Algorithmic approach is based on the assumption that any quantum evolution of many particle system can be simulated on a classical computer with the polynomial time and memory cost. Algorithms play the central role here but not the…
The theory of computation is based on abstract computing automata which can be classified into a three-class hierarchy: Finite Automata (FA), Push-down Automata (PDA) and the Turing Machines (TM). Each class corresponds to grammar/language…
Describing systems in terms of choices and their resulting costs and rewards offers the promise of freeing algorithm designers and programmers from specifying how those choices should be made; in implementations, the choices can be realized…
In some complex domains, certain problem-specific decompositions can provide advantages over monolithic designs by enabling comprehension and specification of the design. In this paper we present an intuitive and tractable approach to…
Atomic structures and adatom geometries of surfaces encode information about the thermodynamics and kinetics of the processes that lead to their formation, and which can be captured by a generative physical model. Here we develop a workflow…
The importance of algorithms and data structures in computer science curricula has been amply recognized. For many students, however, gaining a good understanding of algorithms remains a challenge. Because of the automated nature of…
These course notes are about computing modular forms and some of their arithmetic properties. Their aim is to explain and prove the modular symbols algorithm in as elementary and as explicit terms as possible, and to enable the devoted…
We present applications of modal analysis techniques to study, model, and control canonical aerodynamic flows. To illustrate how modal analysis techniques can provide physical insights in a complementary manner, we selected four fundamental…
We offer a view of mathematics as an experimental science where axioms play the role of foundational theories like general relativity and quantum mechanics in physics. Under this view, axioms are provisional and inferred from experience…
We provide an algorithm that factorizes one-dimensional quantum walks into a protocol of two basic operations: A fixed conditional shift that transports particles between cells and suitable coin operators that act locally in each cell. This…
In this paper we present a formal computational framework for modeling manipulation actions. The introduced formalism leads to semantics of manipulation action and has applications to both observing and understanding human manipulation…
This paper describes a categorical interpretation of the Wolfram Language and introduces a simple implementation of monadic types and the "do" notation. The monadic style of programming combined with the many built in functions of the…
In this paper we argue that one-way quantum computation can be seen as a form of phase transition with the available information about the solution of the computation being the order parameter. We draw a number of striking analogies between…
Canonical functions are a powerful concept with numerous applications in the study of groups, monoids, and clones on countable structures with Ramsey-type properties. In this short note, we present a proof of the existence of canonical…
Notions of computation can be modelled by monads. Algebraic effects offer a characterization of monads in terms of algebraic operations and equational axioms, where operations are basic programming features, such as reading or updating the…
We present a family of logics for reasoning about agents' positions and motion in the plane which have several potential applications in the area of multi-agent systems (MAS), such as multi-agent planning and robotics. The most general…
Amortized analysis is a program cost analysis technique for data structures in which the cost of operations is specified in aggregate, under the assumption of continued sequential use. Typically, amortized analyses are presented…