Stationary distributions and condensation in autocatalytic CRN

We investigate a broad family of non weakly reversible stochastically modeled reaction networks (CRN), by looking at their steady-state distributions. Most known results on stationary distributions assume weak reversibility and zero deficiency. We first give explicitly product-form steady-state distributions for a class of non weakly reversible autocatalytic CRN of arbitrary deficiency. Examples of interest in statistical mechanics (inclusion process), life sciences and robotics (collective decision making in ant and robot swarms) are provided. The product-form nature of the steady-state then enables the study of condensation in particle systems that are generalizations of the inclusion process.Comment: 25 pages. Some typos corrected, shortened some part

Fundamental polytopes of metric trees via parallel connections of matroids

We tackle the problem of a combinatorial classification of finite metric spaces via their fundamental polytopes, as suggested by Vershik in 2010. In this paper we consider a hyperplane arrangement associated to every split pseudometric and, for tree-like metrics, we study the combinatorics of its underlying matroid. We give explicit formulas for the face numbers of fundamental polytopes and Lipschitz polytopes of all tree-like metrics, and we characterize the metric trees for which the fundamental polytope is simplicial.Comment: 20 pages, 2 Figures, 1 Table. Exposition improved, references and new results (last section) adde

Impossibility results on stability of phylogenetic consensus methods

We answer two questions raised by Bryant, Francis and Steel in their work on consensus methods in phylogenetics. Consensus methods apply to every practical instance where it is desired to aggregate a set of given phylogenetic trees (say, gene evolution trees) into a resulting, "consensus" tree (say, a species tree). Various stability criteria have been explored in this context, seeking to model desirable consistency properties of consensus methods as the experimental data is updated (e.g., more taxa, or more trees, are mapped). However, such stability conditions can be incompatible with some basic regularity properties that are widely accepted to be essential in any meaningful consensus method. Here, we prove that such an incompatibility does arise in the case of extension stability on binary trees and in the case of associative stability. Our methods combine general theoretical considerations with the use of computer programs tailored to the given stability requirements

Characterizing the Adsorption-Bioavailability Relationship of PAHs Adsorbed to Carbon Nanomaterials in the Aquatic Environment

Concurrent with the high applicability of carbon nanomaterials (CNM) in a variety of fields and the potential use for pollution remediation, there is the inevitable release of CNMs into the environment. As a consequence of their unique physicochemical properties, CNMs entering the environment will interact with both abiotic and biotic factors. With CNM concentrations estimated to range from parts per billion to low parts per million and their high adsorption affinity for organic contaminants, there is significant concern that CNMs will act as œcontaminant transporters . Even though adsorption and desorption of contaminants from CNMs play a significant role in the ultimate fate of adsorbed compounds, currently there is little conclusive information characterizing the relationship between adsorption behavior and bioavailability of CNM-adsorbed contaminants. The goal of the present research was to establish a comprehensive understanding of the key mechanisms influencing bioavailability of CNM-adsorbed organic contaminants. To accomplish this, I utilized a systematic approach to characterize the influence of CNM morphology, contaminant physicochemical properties, and contaminant mixtures on the resulting bioavailability of the adsorbed compounds, where polycyclic aromatic hydrocarbons (PAHs) were selected as a model class of organic contaminants. Adsorption behavior of a suite of PAHs by suspended multi-walled carbon nanotubes (MWCNTs) and exfoliated graphene (GN) was characterized using batch adsorption isotherm techniques and fitting experimental data with established adsorption models. Bioavailability of CNM-adsorbed PAHs to Pimephales promelas (fathead minnow) was quantified using bile analysis via fluorescence spectroscopy. Multiple linear regression techniques were used to assess the influence of CNM type, PAH physicochemical characteristics, and concentration effects on adsorption of PAHs by MWCNTs as well as to model the relationship between adsorption behavior and the resulting bioavailability of MWCNT-adsorbed PAHs. While CNM structure and surface area differed, adsorption affinity was more influenced by PAH physicochemical characteristics. In particular, differences in adsorption of PAHs between MWCNT and GN became insignificant as hydrophobic and Ï€-Ï€ interactions with the particular PAHs increased. Similarly, bioavailability of CNM-adsorbed PAHs was less influenced by the type of CNM and more influenced by the PAHs physicochemical properties, particularly the size and morphology of the PAH molecules. A further investigation with a greater range of PAHs, showed that molecular morphology of small less hydrophobic PAHs was particularly influential on bioavailability when adsorbed to MWCNTs. Though adsorption of chemically similar PAHs was nearly identical in single-solute solutions, the resulting bioavailability was not the same and was attributed to differences in the PAH\u27s Ï€ electron system as a function of structure and aromatic makeup. Additionally, modeling the relationship between adsorption affinity (i.e. Log Kd) and resulting bioavailability of MWCNT-adsorbed PAHs, showed a direct correlation when Log Kd was greater than 2.5, where only the aqueous concentration of PAH remained bioavailable. However, lower adsorption affinity resulted in a variable amount of the MWCNT-adsorbed PAH remaining bioavailable in an unpredictable manner. The results of this work also indicated that there was a concentration effect influencing adsorption affinity and bioavailability. This was determined to largely be a function of molecular surface area coverage of MWCNT resulting in a change of the adsorption process from more heterogenous to more homogenous. Finally, adsorption of two pairs of chemically similar PAHs, (1) phenanthrene and anthracene and (2) fluoranthene and pyrene, in bi-solute mixtures confirmed that structural makeup of the molecule is signficantly influential on the adsorption-bioavailability relationship. PAHs that have increased contact with the surface of MWCNT, such as anthracene being linear to align with the curved surface of the tube or fluoranthene being more flexible to bend with the curved surface of the tube, outcompeted their chemically similar isoforms. Competitive interactions between PAHs at the surface of MWCNT decreased adsorption affinity of both PAHs within the bi-solute system thus increased bioavailability of the adsorbed PAHs. However, the effect of competition on PAH bioavailability appeared to be greater for less hydrophobic PAHs (i.e. phenanthrene and anthracene) compared with the more hydrophobic PAH pair (i.e. fluoranthene and pyrene). This was attributed to adsorption affinity of phenanthrene and anthracene dipping below Log Kd = 2.5 due to competitive interactions in a bi-solute system. Similar to the single solute studies, only when Log Kd \u3e 2.5 was bioavailability of adsorbed PAHs largely associated with just the aqueous concentration of PAH left in the system. Overall, the results of this work indicate that there is a correlation between bioavailability of CNM-adsorbed PAHs and observed adsorption behavior in aqueous systems, which is largely driven by the adsorbate\u27s physicochemical characteristics. Factors influencing CNM adsorption affinity of PAHs prior to organismal ingestion, such as concentration and competition, also influence bioavailability of the CNM-adsorbed PAHs in a similar manner. However, adsorption behavior of PAHs by CNMs in aqueous solution is not a perfect prediction of the resulting uptake of PAH into P. promelas bile, though my data does indicate an adsorption affinity threshold at which MWCNTs can significantly reduce bioavailability of the adsorbed PAHs. This work furthered our understanding in the factors that may predominantly influence the bioavailability of CNM-adsorbed organic contaminants and provided initial insight into the complex interactions that may occur after consumption on CNM-contaminant complexes that should be focused on in the future

Characterizing the Effect of Suspended Carbon Nanotubes on the Bioavailablility of Adsorbed Fluoranthene to P. Promelas

The introduction of carbon nanomaterials into the environment has increased exponentially in the last decade, causing environmental as well as health concerns. One concern is the interaction that such nanomaterials have with the biota in the aquatic ecosystem and the direct and indirect toxic effects that may result. Previous research has documented a positive influence of natural organic matter (NOM) on the stability of carbon nanotube (CNTs) suspensions in surface waters. Further, research has quantified the ability of these carbon nanomaterials to adsorb aquatic contaminants such as polycyclic aromatic hydrocarbons (PAHs). Though both CNTs and PAHs can co-occur in wastewater treatment effluents few studies have investigated the bioavailability of these adsorbed PAHs to fish. The goal of this research was to characterize the bioavailability of fluoranthene (FLU) adsorbed to suspended muliwalled-carbon nanotubes (MWNTs) in a solution containing NOM. Results indicated that while NOM was critical for producing stable MWNT suspensions, it did not influence the bioavailability of FLU to P. promelas in the absence of MWNTs. Adsorption isotherms indicated that NOM significantly influenced the adsorption of FLU to MWNTs. P. promelas were exposed for 16 hrs in moderately hard water (MHW) containing only FLU, FLU in the presence of different concentrations of NOM, and FLU adsorbed to MWNTs in the presence of NOM. Bioavailable FLU was quantified in each exposure through bile analysis using a fluorescence microplate reader. Results indicated that 2 mg/L NOM as dissolved organic carbon (DOC) were sufficient to produce a stable MWNT suspension. The bioavailability of FLU was significantly reduced in the presence of this suspension. Through comparing the concentration of FLU metabolites in the bile to the concentration of FLU added to MWNT and DOC solutions we were able to quantify the relative bioavailability of FLU adsorbed to MWNTs. Results indicate that approximately 60-90% of the FLU was adsorbed to the MWNTs and that adsorbed FLU was not bioavailable to P. promelas

The Effect of the Stress Path on Squeezing Behavior in Tunneling

Summary: The interplay between support systems and the rock when tunneling under squeezing conditions is normally studied by means of two-dimensional analyses. The present paper shows that the underlying plane strain assumption involved in a two-dimensional analysis may lead, under certain conditions, to ground pressure and deformation values that are considerably lower than those produced by stress analyses that take into account spatial effects in the vicinity of the tunnel face. The differences are due to the stress path dependency in the elasto-plastic behavior of the ground and, more specifically, to the inability of the plane strain model to map the actual radial stress history, which involves a complete radial unloading (and, later, a re-loading) of the tunnel boundary over the unsupported span. This inherent weakness of any plane strain analysis is relevant from the design standpoint, particularly for heavily squeezing conditions that require a yielding support. For the majority of tunneling conditions and methods, however, involving as they do the completion of a stiff support within a few meters of the face, the errors introduced by the plane strain assumption are not important from a practical point of vie