Biconed graphs, edge-rooted forests, and h-vectors of matroid complexes

A well-known conjecture of Richard Stanley posits that the $h$-vector of the independence complex of a matroid is a pure ${\mathcal O}$-sequence. The conjecture has been established for various classes but is open for graphic matroids. A biconed graph is a graph with two specified `coning vertices', such that every vertex of the graph is connected to at least one coning vertex. The class of biconed graphs includes coned graphs, Ferrers graphs, and complete multipartite graphs. We study the $h$-vectors of graphic matroids arising from biconed graphs, providing a combinatorial interpretation of their entries in terms of `edge-rooted forests' of the underlying graph. This generalizes constructions of Kook and Lee who studied the M\"obius coinvariant (the last nonzero entry of the $h$-vector) of graphic matroids of complete bipartite graphs. We show that allowing for partially edge-rooted forests gives rise to a pure multicomplex whose face count recovers the $h$-vector, establishing Stanley's conjecture for this class of matroids.Comment: 15 pages, 3 figures; V2: added omitted author to metadat

Generalized Bockstein maps and Massey products

Given a profinite group G of finite p-cohomological dimension and a pro-p quotient H of G by a closed normal subgroup N, we study the filtration on the Iwasawa cohomology of N by powers of the augmentation ideal in the group algebra of H. We show that the graded pieces are related to the cohomology of G via analogues of Bockstein maps for the powers of the augmentation ideal. For certain groups H, we relate the values of these generalized Bockstein maps to Massey products relative to a restricted class of defining systems depending on H. We apply our study to give a new proof of the vanishing of triple Massey products in Galois cohomology.Comment: 41 page

Collusive Bidding in the Market for Corporate Control

Part I of this article examines the historical evolution of antitrust laws, specifically as they have been applied to the market for corporate control. Part II examines the current judicial opinions advanced which reject the application of antitrust laws to the market for corporate control, including the supposed nonapplicability of antitrust laws to the sale of stock and the implied revocation of the antitrust laws by virtue of the enaction of the Williams Act. Part III addresses the inability of the Securities and Exchange Commission to regulate the market for corporate control via the Williams Act in that there is no inherent conflict between the Commission\u27s disclosure requirements and the policy of antitrust laws. Part IV analyzes the quantitative economic effects of the diminution of competition in the market for corporate control and examine its aggregate effect on shareholders

The epidemiology and outcomes of central nervous system infections in Far North Queensland, tropical Australia; 2000-2019

Background: The epidemiology of central nervous system (CNS) infections in tropical Australia is incompletely defined. Methods: A retrospective study of all individuals in Far North Queensland, tropical Australia, who were diagnosed with a CNS infection between January 1, 2000, and December 31, 2019. The microbiological aetiology of the infection was correlated with patients' demographic characteristics and their clinical course. Results: There were 725 cases of CNS infection during the study period, meningitis (77.4%) was the most common, followed by brain abscess (11.6%), encephalitis (9.9%) and spinal infection (1.1%). Infants (24.3%, p<0.0001) and Aboriginal and Torres Strait Islander Australians (175/666 local residents, 26.3%, p<0.0001) were over-represented in the cohort. A pathogen was identified in 513 cases (70.8%); this was viral in 299 (41.2%), bacterial in 175 (24.1%) and fungal in 35 (4.8%). Cryptococcal meningitis (24 cases) was diagnosed as frequently as pneumococcal meningitis (24 cases). There were only 2 CNS infections with a S. pneumoniae serotype in the 13-valent pneumococcal vaccine after its addition to the National Immunisation schedule in 2011. Tropical pathogens-including Cryptococcus species (9/84, 11%), Mycobacterium tuberculosis (7/84, 8%) and Burkholderia pseudomallei (5/ 84, 6%)-were among the most common causes of brain abscess. However, arboviral CNS infections were rare, with only one locally acquired case-a dengue infection in 2009-diagnosed in the entire study period. Intensive Care Unit admission was necessary in 14.3%; the overall case fatality rate was 4.4%. Conclusion: Tropical pathogens cause CNS infections as commonly as traditional bacterial pathogens in this region of tropical Australia. However, despite being highlighted in the national consensus guidelines, arboviruses were identified very rarely. Prompt access to sophisticated diagnostic and supportive care in Australia's well-resourced public health system is likely to have contributed to the cohort's low case-fatality rate

FuelCell2009-85041 Influence of Ammonia on Membrane-Electrode Assemblies in Polymer Electrolyte Fuel Cells

Abstract An experimental investigation of contamination of polymer electrolyte fuel cell (PEFC) membranes and catalyst layers with ammonia (NH 3 ) is reported. Cyclic voltammetry (CV) scans and electrochemical impedance spectroscopy (EIS) analyses show that trace amounts of ammonia can significantly contaminate both the polymer electrolyte membrane (PEM) and the catalyst layers. The results show that the catalyst layer contamination can be reversed under certain conditions, while the membrane recovery tends to be much slower, and permanent effects of ammonia contamination is observed. Mechanisms of contamination of the polymer electrolyte and catalyst layers, and performance degradation of the PEFC are also postulated. Introduction Ammonia (NH 3 ) is a potential hydrogen carrier due to its high hydrogen capacity (18% by weight) 1 . To generate hydrogen for fuel cell applications, ammonia is reformed, either by cracking 2-3 or through metal hydride reaction