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

We introduce an efficient way, called Newton algorithm, to study arbitrary ideals in C[[x,y]], using a finite succession of Newton polygons. We codify most of the data of the algorithm in a useful combinatorial object, the Newton tree. For…

A foundational question in the theory of linear compartmental models is how to assess whether a model is structurally identifiable -- that is, whether parameter values can be inferred from noiseless data -- directly from the combinatorics…

We present a bijective algorithm with which an arbitrary permutation decomposes canonically into elementary blocks which we call families, which are sets with a specified number of ascents and descents. We show that families, arranged in an…

Control theory uses "signal-flow diagrams" to describe processes where real-valued functions of time are added, multiplied by scalars, differentiated and integrated, duplicated and deleted. These diagrams can be seen as string diagrams for…

Recurrent neural network architectures can have useful computational properties, with complex temporal dynamics and input-sensitive attractor states. However, evaluation of recurrent dynamic architectures requires solution of systems of…

Network representations of systems from various scientific and societal domains are neither completely random nor fully regular, but instead appear to contain recurring structural building blocks. These features tend to be shared by…

Time-continuous dynamical systems defined on graphs are often used to model complex systems with many interacting components in a non-spatial context. In the reverse sense attaching meaningful dynamics to given 'interaction diagrams' is a…

Behavior Trees constitute a widespread AI tool which has been successfully spun out in robotics. Their advantages include simplicity, modularity, and reusability of code. However, Behavior Trees remain a high-level decision making engine;…

Both neural networks and decision trees are popular machine learning methods and are widely used to solve problems from diverse domains. These two classifiers are commonly used base classifiers in an ensemble framework. In this paper, we…

A major ambition of systems science is to uncover the building blocks of any biological network to decipher how cellular function emerges from their interactions. Here, we introduce a graph representation of the information flow in these…

We study the category O of representations over a shifted Yangian. This category has a tensor product structure and contains distinguished modules, the positive prefundamental modules and the negative prefundamental modules. Motivated by…

Recently, deep architectures, such as recurrent and recursive neural networks have been successfully applied to various natural language processing tasks. Inspired by bidirectional recurrent neural networks which use representations that…

We initiate the systematic study of modular representations of symmetric groups that arise via the braiding in (symmetric) tensor categories over fields of positive characteristic. We determine what representations appear for certain…

Systems of dynamical interactions between competing species can be used to model many complex systems, and can be mathematically described by {\em random} networks. Understanding how patterns of activity arise in such systems is important…

Phylogenetic networks are a generalization of phylogenetic trees to leaf-labeled directed acyclic graphs that represent ancestral relationships between species whose past includes non-tree-like events such as hybridization and horizontal…

An important problem in the field of bioinformatics is to identify interactive effects among profiled variables for outcome prediction. In this paper, a logistic regression model with pairwise interactions among a set of binary covariates…

A new modeling framework for bipartite social networks arising from a sequence of partially time-ordered relational events is proposed. We directly model the joint distribution of the binary variables indicating if each single actor is…

We propose Causal Interaction Trees for identifying subgroups of participants that have enhanced treatment effects using observational data. We extend the Classification and Regression Tree algorithm by using splitting criteria that focus…

We develop several combinatorial notions about laminations, some with clear implications for parameter space. We introduce a simplified class of laminations called finite dynamical laminations (FDL). In order to count FDL, we introduce…

A new category $\mathfrak{dp}$, called of dynamical patterns addressing a primitive, nongeometrical concept of dynamics, is defined and employed to construct a $2-$category $2-\mathfrak{dp}$, where the irreducible plurality of species of…