Markovian approach to tackle competing pathogens in simplicial complex

2022 ◽  
Vol 417 ◽  
pp. 126773
Author(s):  
Yanyi Nie ◽  
Wenyao Li ◽  
Liming Pan ◽  
Tao Lin ◽  
Wei Wang
Author(s):  
Benson Farb ◽  
Dan Margalit

This chapter considers the Dehn–Lickorish theorem, which states that when g is greater than or equal to 0, the mapping class group Mod(Sɡ) is generated by finitely many Dehn twists about nonseparating simple closed curves. The theorem is proved by induction on genus, and the Birman exact sequence is introduced as the key step for the induction. The key to the inductive step is to prove that the complex of curves C(Sɡ) is connected when g is greater than or equal to 2. The simplicial complex C(Sɡ) is a useful combinatorial object that encodes intersection patterns of simple closed curves in Sɡ. More detailed structure of C(Sɡ) is then used to find various explicit generating sets for Mod(Sɡ), including those due to Lickorish and to Humphries.


10.37236/1245 ◽  
1996 ◽  
Vol 3 (1) ◽  
Author(s):  
Art M. Duval

Björner and Wachs generalized the definition of shellability by dropping the assumption of purity; they also introduced the $h$-triangle, a doubly-indexed generalization of the $h$-vector which is combinatorially significant for nonpure shellable complexes. Stanley subsequently defined a nonpure simplicial complex to be sequentially Cohen-Macaulay if it satisfies algebraic conditions that generalize the Cohen-Macaulay conditions for pure complexes, so that a nonpure shellable complex is sequentially Cohen-Macaulay. We show that algebraic shifting preserves the $h$-triangle of a simplicial complex $K$ if and only if $K$ is sequentially Cohen-Macaulay. This generalizes a result of Kalai's for the pure case. Immediate consequences include that nonpure shellable complexes and sequentially Cohen-Macaulay complexes have the same set of possible $h$-triangles.


Information ◽  
2021 ◽  
Vol 12 (3) ◽  
pp. 103
Author(s):  
Casey C. Bennett

This paper discusses the creation of an agent-based simulation model for interactive robotic faces, built based on data from physical human–robot interaction experiments, to explore hypotheses around how we might create emergent robotic personality traits, rather than pre-scripted ones based on programmatic rules. If an agent/robot can visually attend and behaviorally respond to social cues in its environment, and that environment varies, then idiosyncratic behavior that forms the basis of what we call a “personality” should theoretically be emergent. Here, we evaluate the stability of behavioral learning convergence in such social environments to test this idea. We conduct over 2000 separate simulations of an agent-based model in scaled-down, abstracted forms of the environment, each one representing an “experiment”, to see how different parameters interact to affect this process. Our findings suggest that there may be systematic dynamics in the learning patterns of an agent/robot in social environments, as well as significant interaction effects between the environmental setup and agent perceptual model. Furthermore, learning from deltas (Markovian approach) was more effective than only considering the current state space. We discuss the implications for HRI research, the design of interactive robotic faces, and the development of more robust theoretical frameworks of social interaction.


2013 ◽  
Vol 20 (01) ◽  
pp. 123-140
Author(s):  
Teng Zou ◽  
Bin Zhu

For any positive integer n, we construct an n-repetitive generalized cluster complex (a simplicial complex) associated with a given finite root system by defining a compatibility degree on the n-repetitive set of the colored root system. This simplicial complex includes Fomin-Reading's generalized cluster complex as a special case when n=1. We also introduce the intermediate coverings (called generalized d-cluster categories) of d-cluster categories of hereditary algebras, and study the d-cluster tilting objects and their endomorphism algebras in those categories. In particular, we show that the endomorphism algebras of d-cluster tilting objects in the generalized d-cluster categories provide the (finite) coverings of the corresponding (usual) d-cluster tilted algebras. Moreover, we prove that the generalized d-cluster categories of hereditary algebras of finite representation type provide a category model for the n-repetitive generalized cluster complexes.


2002 ◽  
Vol 109 (2) ◽  
pp. 159-174 ◽  
Author(s):  
Sara Faridi

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