相关论文: Interactions that reshape the interfaces of the in…

We extend our earlier work on the compositional structure of cybernetic systems in order to account for the embodiment of such systems. All their interactions proceed through their bodies' boundaries: sensations impinge on their surfaces,…

Invariants for complicated objects such as those arising in phylogenetics, whether they are invariants as matrices, polynomials, or other mathematical structures, are important tools for distinguishing and working with such objects. In this…

We define an algorithm k which takes a connected graph G on a totally ordered vertex set and returns an increasing tree R (which is not necessarily a subtree of G). We characterize the set of graphs G such that k(G)=R. Because this set has…

We explore the relationship between polynomial functors and (rooted) trees. In the first part we use polynomial functors to derive a new convenient formalism for trees, and obtain a natural and conceptual construction of the category…

Bipartite learning is a machine learning task that aims to predict interactions between pairs of instances. It has been applied to various domains, including drug-target interactions, RNA-disease associations, and regulatory network…

This monograph is a study of the category of polynomial endofunctors on the category of sets and its applications to modeling interaction protocols and dynamical systems. We assume basic categorical background and build the categorical…

We show that the problem of constructing tree-structured descriptions of data layouts that are optimal with respect to space or other criteria from given sequences of displacements, can be solved in polynomial time. The problem is relevant…

"Interaction trees" (ITrees) are a general-purpose data structure for representing the behaviors of recursive programs that interact with their environments. A coinductive variant of "free monads," ITrees are built out of uninterpreted…

Rooted phylogenetic networks provide an explicit representation of the evolutionary history of a set $X$ of sampled species. In contrast to phylogenetic trees which show only speciation events, networks can also accommodate reticulate…

The output of a machine learning algorithm can usually be represented by one or more multivariate functions of its input variables. Knowing the global properties of such functions can help in understanding the system that produced the data…

Dynamic regression trees are an attractive option for automatic regression and classification with complicated response surfaces in on-line application settings. We create a sequential tree model whose state changes in time with the…

Finding interactions between variables in large and high-dimensional datasets is often a serious computational challenge. Most approaches build up interaction sets incrementally, adding variables in a greedy fashion. The drawback is that…

Dynamical systems---by which we mean machines that take time-varying input, change their state, and produce output---can be wired together to form more complex systems. Previous work has shown how to allow collections of machines to…

We study systems of interacting reinforced stochastic processes, where agents' decisions evolve under reinforcement, network-mediated interactions, and environmental influences. In competitive environments with irreducible networks, we…

The study of abstraction and composition - the focus of category theory - naturally leads to sophisticated diagrams which can encode complex algebraic semantics. Consequently, these diagrams facilitate a clearer visual comprehension of…

The Learnable Tree Filter presents a remarkable approach to model structure-preserving relations for semantic segmentation. Nevertheless, the intrinsic geometric constraint forces it to focus on the regions with close spatial distance,…

Recent years have witnessed the rise of compositional semantics as a foundation for formal verification of complex systems. In particular, interaction trees have emerged as a popular denotational semantics. Interaction trees achieve…

We investigate the dynamics of forward or backward self-similar systems (iterated function systems) and the topological structure of their invariant sets. We define a new cohomology theory (interaction cohomology) for forward or backward…

Discrete statistical models supported on labelled event trees can be specified using so-called interpolating polynomials which are generalizations of generating functions. These admit a nested representation. A new algorithm exploits the…

This paper studies the problem of modeling multi-agent dynamical systems, where agents could interact mutually to influence their behaviors. Recent research predominantly uses geometric graphs to depict these mutual interactions, which are…