Decision Making under Uncertainty through Extending Influence Diagrams with Interval-valued Parameters

Influence Diagrams (IDs) are one of the most commonly used graphical and mathematical decision models for reasoning under uncertainty. In conventional IDs, both probabilities representing beliefs and utilities representing preferences of decision makers are precise point-valued parameters. However, it is usually difficult or even impossible to directly provide such parameters. In this paper, we extend conventional IDs to allow IDs with interval-valued parameters (IIDs), and develop a counterpart method of Copper’s evaluation method to evaluate IIDs. IIDs avoid the difficulties attached to the specification of precise parameters and provide the capability to model decision making processes in a situation that the precise parameters cannot be specified. The counterpart method to Copper’s evaluation method reduces the evaluation of IIDs into inference problems of IBNs. An algorithm based on the approximate inference of IBNs is proposed, extensive experiments are conducted. The experimental results indicate that the proposed algorithm can find the optimal strategies effectively in IIDs, and the interval-valued expected utilities obtained by proposed algorithm are contained in those obtained by exact evaluating algorithms

PersLay: A Neural Network Layer for Persistence Diagrams and New Graph Topological Signatures

Persistence diagrams, the most common descriptors of Topological Data Analysis, encode topological properties of data and have already proved pivotal in many different applications of data science. However, since the (metric) space of persistence diagrams is not Hilbert, they end up being difficult inputs for most Machine Learning techniques. To address this concern, several vectorization methods have been put forward that embed persistence diagrams into either finite-dimensional Euclidean space or (implicit) infinite dimensional Hilbert space with kernels. In this work, we focus on persistence diagrams built on top of graphs. Relying on extended persistence theory and the so-called heat kernel signature, we show how graphs can be encoded by (extended) persistence diagrams in a provably stable way. We then propose a general and versatile framework for learning vectorizations of persistence diagrams, which encompasses most of the vectorization techniques used in the literature. We finally showcase the experimental strength of our setup by achieving competitive scores on classification tasks on real-life graph datasets

Single-particle potential from resummed ladder diagrams

A recent work on the resummation of fermionic in-medium ladder diagrams to all orders is extended by calculating the complex single-particle potential $U(p,k_f)+ i\,W(p,k_f)$ for momenta $pk_f$. The on-shell single-particle potential is constructed by means of a complex-valued in-medium loop that includes corrections from a test-particle of momentum $\vec p$ added to the filled Fermi sea. The single-particle potential $U(k_f,k_f)$ at the Fermi surface as obtained from the resummation of the combined particle and hole ladder diagrams is shown to satisfy the Hugenholtz-Van-Hove theorem. The perturbative contributions at various orders $a^n$ in the scattering length are deduced and checked against the known analytical results at order $a^1$ and $a^2$. The limit $a\to\infty$ is studied as a special case and a strong momentum dependence of the real (and imaginary) single-particle potential is found. This indicates an instability against a phase transition to a state with an empty shell inside the Fermi sphere such that the density gets reduced by about 5%. For comparison, the same analysis is performed for the resummed particle-particle ladder diagrams alone. In this truncation an instability for hole-excitations near the Fermi surface is found at strong coupling. For the set of particle-hole ring diagrams the single-particle potential is calculated as well. Furthermore, the resummation of in-medium ladder diagrams to all orders is studied for a two-dimensional Fermi gas with a short-range two-body contact-interaction.Comment: 28 pages, 19 figures, to be published in European Physical Journal

The Kinetic Basis of Morphogenesis

It has been shown recently (Shalygo, 2014) that stationary and dynamic patterns can arise in the proposed one-component model of the analog (continuous state) kinetic automaton, or kinon for short, defined as a reflexive dynamical system with active transport. This paper presents extensions of the model, which increase further its complexity and tunability, and shows that the extended kinon model can produce spatio-temporal patterns pertaining not only to pattern formation but also to morphogenesis in real physical and biological systems. The possible applicability of the model to morphogenetic engineering and swarm robotics is also discussed.Comment: 8 pages. Submitted to the 13th European Conference on Artificial Life (ECAL-2015) on March 10, 2015. Accepted on April 28, 201