A counterexample to Thiagarajan's conjecture on regular event structures

We provide a counterexample to a conjecture by Thiagarajan (1996 and 2002) that regular event structures correspond exactly to event structures obtained as unfoldings of finite 1-safe Petri nets. The same counterexample is used to disprove a closely related conjecture by Badouel, Darondeau, and Raoult (1999) that domains of regular event structures with bounded $\natural$-cliques are recognizable by finite trace automata. Event structures, trace automata, and Petri nets are fundamental models in concurrency theory. There exist nice interpretations of these structures as combinatorial and geometric objects. Namely, from a graph theoretical point of view, the domains of prime event structures correspond exactly to median graphs; from a geometric point of view, these domains are in bijection with CAT(0) cube complexes. A necessary condition for both conjectures to be true is that domains of regular event structures (with bounded $\natural$-cliques) admit a regular nice labeling. To disprove these conjectures, we describe a regular event domain (with bounded $\natural$-cliques) that does not admit a regular nice labeling. Our counterexample is derived from an example by Wise (1996 and 2007) of a nonpositively curved square complex whose universal cover is a CAT(0) square complex containing a particular plane with an aperiodic tiling. We prove that other counterexamples to Thiagarajan's conjecture arise from aperiodic 4-way deterministic tile sets of Kari and Papasoglu (1999) and Lukkarila (2009). On the positive side, using breakthrough results by Agol (2013) and Haglund and Wise (2008, 2012) from geometric group theory, we prove that Thiagarajan's conjecture is true for regular event structures whose domains occur as principal filters of hyperbolic CAT(0) cube complexes which are universal covers of finite nonpositively curved cube complexes

A Counterexample to Thiagarajan\u27s Conjecture on Regular Event Structures

We provide a counterexample to a conjecture by Thiagarajan (1996 and 2002) that regular prime event structures correspond exactly to those obtained as unfoldings of finite 1-safe Petri nets. The same counterexample is used to disprove a closely related conjecture by Badouel, Darondeau, and Raoult (1999) that domains of regular event structures with bounded natural-cliques are recognizable by finite trace automata. Event structures, trace automata, and Petri nets are fundamental models in concurrency theory. There exist nice interpretations of these structures as combinatorial and geometric objects and both conjectures can be reformulated in this framework. Namely, the domains of prime event structures correspond exactly to pointed median graphs; from a geometric point of view, these domains are in bijection with pointed CAT(0) cube complexes. A necessary condition for both conjectures to be true is that domains of respective regular event structures admit a regular nice labeling. To disprove these conjectures, we describe a regular event domain (with bounded natural-cliques) that does not admit a regular nice labeling. Our counterexample is derived from an example by Wise (1996 and 2007) of a nonpositively curved square complex whose universal cover is a CAT(0) square complex containing a particular plane with an aperiodic tiling

Transitions: An Institutionalist Perspective

A transition to a new technological regime is complete (and stable) when accompanied with a co-stabilization between the mode of regulation and the regime of accumulation. Key to understanding the dynamics of transitions are the factors, including institutions, that “regulate” and stabilize the regime of accumulation over time. However, the available frameworks for institutional analysis employ arbitrary and narrow definition of institutions, focus mainly on the policy domain, and do not pay sufficient attention to the evolutionary characteristics of change as manifested in emergence of numerous institutions that underlie transitions. This paper consists of three parts. The first part critically reviews and synthesizes some of the main approaches for conducting institutional analysis. The second part rearticulates the concept of “transitions”, or technological regime shifts, from a systems perspective to make a case for investigating transitions as multi-level, multi-scale, and multi-system phenomena best understood in their institutional contexts. The third part proposes a framework for examining institutional change and demonstrates how this framework may be used to identify the key factors and conditions whose convergence might result in transitions in a given subsystem. Examples are drawn from the Dutch waste management subsystem to demonstrate how this framework should be operationalized.economics of technology ;

1-Safe Petri nets and special cube complexes: equivalence and applications

Nielsen, Plotkin, and Winskel (1981) proved that every 1-safe Petri net $N$ unfolds into an event structure $\mathcal{E}_N$. By a result of Thiagarajan (1996 and 2002), these unfoldings are exactly the trace regular event structures. Thiagarajan (1996 and 2002) conjectured that regular event structures correspond exactly to trace regular event structures. In a recent paper (Chalopin and Chepoi, 2017, 2018), we disproved this conjecture, based on the striking bijection between domains of event structures, median graphs, and CAT(0) cube complexes. On the other hand, in Chalopin and Chepoi (2018) we proved that Thiagarajan's conjecture is true for regular event structures whose domains are principal filters of universal covers of (virtually) finite special cube complexes. In the current paper, we prove the converse: to any finite 1-safe Petri net $N$ one can associate a finite special cube complex ${X}_N$ such that the domain of the event structure $\mathcal{E}_N$ (obtained as the unfolding of $N$) is a principal filter of the universal cover $\widetilde{X}_N$ of $X_N$. This establishes a bijection between 1-safe Petri nets and finite special cube complexes and provides a combinatorial characterization of trace regular event structures. Using this bijection and techniques from graph theory and geometry (MSO theory of graphs, bounded treewidth, and bounded hyperbolicity) we disprove yet another conjecture by Thiagarajan (from the paper with S. Yang from 2014) that the monadic second order logic of a 1-safe Petri net is decidable if and only if its unfolding is grid-free. Our counterexample is the trace regular event structure $\mathcal{\dot E}_Z$ which arises from a virtually special square complex $\dot Z$. The domain of $\mathcal{\dot E}_Z$ is grid-free (because it is hyperbolic), but the MSO theory of the event structure $\mathcal{\dot E}_Z$ is undecidable

On the evolution of decoys in plant immune systems

The Guard-Guardee model for plant immunity describes how resistance proteins (guards) in host cells monitor host target proteins (guardees) that are manipulated by pathogen effector proteins. A recently suggested extension of this model includes decoys, which are duplicated copies of guardee proteins, and which have the sole function to attract the effector and, when modified by the effector, trigger the plant immune response. Here we present a proof-of-principle model for the functioning of decoys in plant immunity, quantitatively developing this experimentally-derived concept. Our model links the basic cellular chemistry to the outcomes of pathogen infection and resulting fitness costs for the host. In particular, the model allows identification of conditions under which it is optimal for decoys to act as triggers for the plant immune response, and of conditions under which it is optimal for decoys to act as sinks that bind the pathogen effectors but do not trigger an immune response.Comment: 15 pages, 6 figure

Community next steps for making globally unique identifiers work for biocollections data

Biodiversity data is being digitized and made available online at a rapidly increasing rate but current practices typically do not preserve linkages between these data, which impedes interoperation, provenance tracking, and assembly of larger datasets. For data associated with biocollections, the biodiversity community has long recognized that an essential part of establishing and preserving linkages is to apply globally unique identifiers at the point when data are generated in the field and to persist these identifiers downstream, but this is seldom implemented in practice. There has neither been coalescence towards one single identifier solution (as in some other domains), nor even a set of recommended best practices and standards to support multiple identifier schemes sharing consistent responses. In order to further progress towards a broader community consensus, a group of biocollections and informatics experts assembled in Stockholm in October 2014 to discuss community next steps to overcome current roadblocks. The workshop participants divided into four groups focusing on: identifier practice in current field biocollections; identifier application for legacy biocollections; identifiers as applied to biodiversity data records as they are published and made available in semantically marked-up publications; and cross-cutting identifier solutions that bridge across these domains. The main outcome was consensus on key issues, including recognition of differences between legacy and new biocollections processes, the need for identifier metadata profiles that can report information on identifier persistence missions, and the unambiguous indication of the type of object associated with the identifier. Current identifier characteristics are also summarized, and an overview of available schemes and practices is provided