On the number of critical equilibria separating two equilibria

It is shown that two arbitrary equilibria in the general equilibrium model without sign restrictions on endowments can be joined by a continuous equilibrium path that contains at most two critical equilibria. This property is strengthened by showing that regular equilibria having an index equal to one, a necessary condition for stability, can be joined by a path containing no critical equilibrium. These properties follow from the real-algebraic nature of the set of critical equilibria in any fiber of the equilibrium manifold.Equilibrium prices, equilibrium manifold, equilibrium path, critical equilibrium, catastrophe

Equilibrium Data Sets and Compatible Utility Rankings

Sets consisting of finite collections of prices and endowments such that total resources are constant, or collinear, or approximately collinear, can always be viewed as subsets of some equilibrium manifold. The additional requirement that such collections of price-endowment data are compatible with some individual preference rankings is reduced to the existence of solutions to some set of linear inequalities and equalities. This characterization enables us to give simple proofs of the contractibility of the set whose elements are finite equilibrium data collections compatible with given individual preference rankings and the path-connectedness of the set made of finite equilibrium data set.

General Equilibrium without Utility Functions: How far to go?

How far can we go in weakening the assumptions of the general equilibrium model? Existence of equilibrium, structural stability and finiteness of equilibria of regular economies, genericity of regular economies and an index formula for the equilibria of regular economies have been known not to require transitivity and completeness of consumers’ preferences. We show in this paper that if consumers’ non-ordered preferences satisfy a mild version of convexity already considered in the literature, then the following properties are also satisfied: 1) the smooth manifold structure and the diffeomorphism of the equilibrium manifold with a Euclidean space; 2) the diffeomorphism of the set of no-trade equilibria with a Euclidean space; 3) the openness and genericity of the set of regular equilibria as a subset of the equilibrium manifold; 4) for small trade vectors, the uniqueness, regularity and stability of equilibrium for two version of tatonnement; 5) the pathconnectedness of the sets of stable equilibria.general equilibrium; equilibrium manifold; natural projection; demand functions

Analysis of RNA Degradation in Dental Pulp to Estimate Postmortem Interval

There are several methods that are currently used to estimate a postmortem interval (PMI), including physiological, biochemical, entomological, and archeological approaches. However, these methods are not effective in estimating PMI\u27s extending from several weeks to months. The study presented here was performed to create an independent, objective biological method to estimate PMI by analyzing the degradation of 18S ribosomal RNA (rRNA) from porcine and human dental pulp. If successful, this method would overlap and extend the current PMI estimation methods. With a concept similar to that of radioactive carbon-14 dating, this method analyzed two different sized segments -- one large, labile segment and one small, stable segment - of the same rRNA strand using real-time reverse transcription polymerase chain reaction (RT-PCR). Since the larger segment acts as a larger target for degradation forces, it is expected that the larger PCR amplicons will disappear more quickly than the smaller amplicons, and it is the difference in the quantities of each amplicon that is expected to help estimate a PMI. A multiplex reaction with a designated fluorescent marker for each larger and smaller segment was used to examine both segments of the RNA within a single sample. Teeth and weather data were collected weekly. Once the dental pulp was isolated, the RNA was extracted and converted to complimentary DNA (cDNA) using reverse transcription PCR. Once in the cDNA form, the samples were analyzed using real-time PCR. Colorimetric data was also collected by taking a picture of the pulp sample, and using Adobe Photoshop to quantify the color content of each photograph. As PMI increased, the tooth pulp experienced some color and morphological changes, as well as degradation of the rRNA target which allowed for a relative estimate of time since death with porcine samples. Using the weather data collected, accumulated degree days (ADD) for each sample were calculated and helped refine the PMI estimate. Unfortunately, the human samples were not as successful, possibly due to the age of the specimens studied. One study of an 18-year old specimen produced promising results which were similar to those obtained with the porcine samples. However, due to some resource restraints, further analyses could not be performed on younger human specimens in this particular study, though it was evident that age of the human specimens had a robust effect on the method outcome. Still, this method can be of great significance to the forensic field, especially since PMI estimates get more complicated as decomposition progresses. This method can also fill the time gap between the maximum amount of time insects can be used to estimate a PMI and the minimum amount of time archeological approaches can be applied. Determining an accurate PMI estimate is crucial to recreating a possible homicide event and will be extremely beneficial to forensic investigations. Using a technique such as the one herein may assist investigations that may not have been able to be solved before without an accurate PMI estimate

The Memory Keeper: Analyzing the Importance of Collecting and Preserving Oral Histories in a Twenty-First Century University Archival Repository

Recognizing the importance of collecting and incorporating individuals’ memories into an institution’s archival repository is a fundamental task that archivists must professionally and ethically accept. Depending on the repository’s specific needs and mission goals the collection policies will differ; however, disregarding the personal stories of the working population of the university is a disservice to archival collecting. How can a user analyze the completed history of an academic institution without providing the documented input and sharing of personal experiences of faculty, staff, and students? How can a researcher evaluate theory and explore a multitude of viewpoints, if only printed media is available as research tools? How then, does a university archivist preserve the cultural memory—or “the spiritual and familial practices,” and oral traditions of an academic institution? How are oral histories represented in the historical narrative of a college or university? Unfortunately, more often than not, the oral histories of a university community remain largely uncollected and underrepresented. Collections that do have interview transcripts or recordings of individuals are more likely to document those who are in a position of authority in the university community than those who are responsible for its daily operations. Currently the University of Massachusetts Boston’s University Archives and Special Collections holds only two oral history collections regarding individual employee experiences and personal remembrances. For a University that is approaching its fiftieth year as an academic institution, why are only a handful of such stories and personal journeys preserved? Obviously, an archivist is not physically able to collect the personal stories of every individual who has been a part of the UMass Boston community, but as a keeper of memory, how does an archival institution decide what is, and is not, worth collecting and preserving

On a workflow model based on generalized communicating P systems

This paper introduces a new formal mathematical model for investigating workflows from dynamical and behavioural point of view. The model is designed on the basis of a special variant of the biology-inspired formal computational model called membrane systems, where the jobs or services are represented by membrane objects whose behaviour is defined by communication and generalization rules. The model supports running computations in a massive parallel manner, which makes it ideal to model high throughput workflow interpreters. Among the variants introduced in the literature, we have selected the Generalized Communicating P Systems, as it focuses on the communication among the membranes.Most of the workflow languages, based on different formal models like Petri nets or Communicating Sequential Processes, support several predefined structures – namely workflow patterns – to control the workflow interpretation such as conditions, loops etc. In this paper we show how these patterns are adapted into the membrane environment which, taking into account that membrane systems can be used to study complex dynamic systems’ runtime behaviour, makes this model a relevant alternative for the current model

The Probability of Condorcet Cycles and Super-Majority Rules

Majority voting aggregates individual preference profiles into a binary relation on the set of alternatives. Condorcet cycles are cycles of the aggregated binary relation. We show that the relative volume of the subset of the (n!−1)-simplex that represents profile distributions such that the aggregated preferences display Condorcet cycles is a decreasing function of the super majority levelτbounded by the expressionThis expression shows that Condorcet cycles become rare events for super majority rules larger than 53%