Maximal chain descent orders

This paper introduces a partial order on the maximal chains of any finite bounded poset $P$ which has a CL-labeling $\lambda$. We call this the maximal chain descent order induced by $\lambda$, denoted $P_{\lambda}(2)$. As a first example, letting $P$ be the Boolean lattice and $\lambda$ its standard EL-labeling gives $P_{\lambda}(2)$ isomorphic to the weak order of type A. We discuss in depth other seemingly well-structured examples: the max-min EL-labeling of the partition lattice gives maximal chain descent order isomorphic to a partial order on certain labeled trees, and particular cases of the linear extension EL-labelings of finite distributive lattices produce maximal chain descent orders isomorphic to partial orders on standard Young tableaux. We observe that the order relations which one might expect to be the cover relations, those given by the "polygon moves" whose transitive closure defines the maximal chain descent order, are not always cover relations. Several examples illustrate this fact. Nonetheless, we characterize the EL-labelings for which every polygon move gives a cover relation, and we prove many well known EL-labelings do have the expected cover relations. One motivation for $P_{\lambda}(2)$ is that its linear extensions give all of the shellings of the order complex of $P$ whose restriction maps are defined by the descents with respect to $\lambda$. This yields strictly more shellings of $P$ than the lexicographic ones induced by $\lambda$. Thus, the maximal chain descent order $P_{\lambda}(2)$ might be thought of as encoding the structure of the set of shellings induced by $\lambda$.Comment: 48 pages, 21 figure

Frog Model Wakeup Time on the Complete Graph

The frog model is a system of random walks where active particles set sleeping particles in motion. On the complete graph with n vertices it is equivalent to a well-understood rumor spreading model. We given an alternate and elementary proof that the wakeup time, that is, the expected time for every particle to be activated, is &Theta(log n). Additionally, we give an explicit distributional equation for the wakeup time as a mixture of geometric random variables

Reaction-Based Indicator Displacement Assay (RIA) for the Selective Colorimetric and Fluorometric Detection of Peroxynitrite

Using the self-assembly of aromatic boronic acids with Alizarin Red S (ARS), we developed a new chemosensor for the selective detection of peroxynitrite. Phenylboronic acid (PBA), benzoboroxole (BBA) and 2-(N, N-dimethylaminomethyl) phenylboronic acid (NBA) were employed to bind with ARS to form the complex probes. In particular, the ARS-NBA system with a high binding affinity can preferably react with peroxynitrite over hydrogen peroxide and other ROS/RNS due to the protection of the boron via the solvent-insertion B-N interaction. Our simple system produces a visible colorimetric change and on-off fluorescence response towards peroxynitrite. By coupling a chemical reaction that leads to an indicator displacement, we have developed a new sensing strategy, referred to herein as RIA (Reaction-based Indicator displacement Assay).China Scholarship Council (CSC)University of Bath Full Fees ScholarshipChemistr

Victory or repudiation? Predicting winners in civil wars using international financial markets

We develop a method to estimate which side will win a civil war using data from international financial markets. The key insight we deliver is that, for typical sovereign debt contracts, the probability of debt repayment will equal the probability of victory in a civil war. We test our predictor for standard outcomes in civil wars, including when the incumbent government loses (the Chinese Nationalists), when a new government is installed by a foreign power and decides to repudiate debt (the restoration of Ferdinand VII of Spain), and when there is a secession (the U.S. Confederacy). For China, markets were predicting a Communist victory three years before it happened. For the U.S. markets never gave the South much more than a 40 percent chance of maintaining the Confederacy. For Spain, markets considered the restoration of Ferdinand VII as likely (probabilities above 50%) as soon as France declared its intention to send military forces to the area.SCOPUS: ar.jinfo:eu-repo/semantics/publishe