Essential edges in Poisson random hypergraphs

Consider a random hypergraph on a set of N vertices in which, for k between 1 and N, a Poisson(N beta_k) number of hyperedges is scattered randomly over all subsets of size k. We collapse the hypergraph by running the following algorithm to exhaustion: pick a vertex having a 1-edge and remove it; collapse the hyperedges over that vertex onto their remaining vertices; repeat until there are no 1-edges left. We call the vertices removed in this process "identifiable". Also any hyperedge all of whose vertices are removed is called "identifiable". We say that a hyperedge is "essential" if its removal prior to collapse would have reduced the number of identifiable vertices. The limiting proportions, as N tends to infinity, of identifiable vertices and hyperedges were obtained by Darling and Norris. In this paper, we establish the limiting proportion of essential hyperedges. We also discuss, in the case of a random graph, the relation of essential edges to the 2-core of the graph, the maximal sub-graph with minimal vertex degree 2.Comment: 12 pages, 3 figures. Revised version with minor corrections/clarifications and slightly expanded introductio

Should intelligent design be taught alongside evolution in public schools?

Evolution being the creation of life through a scientific method and ID being the creation of life through a religious point of view. The overall proposing question to be discussed throughout this project is whether or not ID should be taught in schools alongside Evolution within science classes. The first phase of this project involves research of the positive teachings of ID within the school system and how it can be beneficial to students. The second part of this project involves the negative aspects of educating students the proposed theory of ID. The final phase revolves around the favored conclusion to educate students of both teachings, Evolution and ID, within the education system

Random recursive trees and the Bolthausen-Sznitman coalescent

We describe a representation of the Bolthausen-Sznitman coalescent in terms of the cutting of random recursive trees. Using this representation, we prove results concerning the final collision of the coalescent restricted to [n]: we show that the distribution of the number of blocks involved in the final collision converges as n tends to infinity, and obtain a scaling law for the sizes of these blocks. We also consider the discrete-time Markov chain giving the number of blocks after each collision of the coalescent restricted to [n]; we show that the transition probabilities of the time-reversal of this Markov chain have limits as n tends to infinity. These results can be interpreted as describing a ``post-gelation'' phase of the Bolthausen-Sznitman coalescent, in which a giant cluster containing almost all of the mass has already formed and the remaining small blocks are being absorbed.Comment: 28 pages, 2 figures. Revised version with minor alterations. To appear in Electron. J. Proba

Climate change mitigation by Greater Adelaide councils

This paper reports on carbon mitigation actions adopted by Greater Adelaide councils (n=14) in South Australia. A survey of environmental officers profiled carbon mitigation actions, emissions auditing, and motives for emissions reduction by councils. The main reasons for carbon actions were a climate change plan, showing climate leadership, and cost savings

Quantifying the Potential of Restored Natural Capital to Alleviate Poverty and Help Conserve Nature: A Case Study from South Africa

Abstract not available.

Coagulation--fragmentation duality, Poisson--Dirichlet distributions and random recursive trees

In this paper we give a new example of duality between fragmentation and coagulation operators. Consider the space of partitions of mass (i.e., decreasing sequences of nonnegative real numbers whose sum is 1) and the two-parameter family of Poisson--Dirichlet distributions $\operatorname {PD}(\alpha,\theta)$ that take values in this space. We introduce families of random fragmentation and coagulation operators $\mathrm {Frag}_{\alpha}$ and $\mathrm {Coag}_{\alpha,\theta}$, respectively, with the following property: if the input to $\mathrm {Frag}_{\alpha}$ has $\operatorname {PD}(\alpha,\theta)$ distribution, then the output has $\operatorname {PD}(\alpha,\theta+1)$ distribution, while the reverse is true for $\mathrm {Coag}_{\alpha,\theta}$. This result may be proved using a subordinator representation and it provides a companion set of relations to those of Pitman between $\operatorname {PD}(\alpha,\theta)$ and $\operatorname {PD}(\alpha\beta,\theta)$. Repeated application of the $\mathrm {Frag}_{\alpha}$ operators gives rise to a family of fragmentation chains. We show that these Markov chains can be encoded naturally by certain random recursive trees, and use this representation to give an alternative and more concrete proof of the coagulation--fragmentation duality.Comment: Published at http://dx.doi.org/10.1214/105051606000000655 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Incidence of Gunshot Wounds: Before and After Implementation of a Shall Issue Conceal Carry Law

Introduction. This study examined the incidence of gunshot wounds before and after enacting a conceal carry (CC) law in a predominately rural state. Methods. A retrospective review was conducted of all patients who were admitted with a gunshot injury to a Level I trauma center. Patient data collected included demographics, injury details, hospital course, and discharge destination. Results. Among the 238 patients included, 44.6% (n = 107) were admitted during the pre-CC period and 55.4% (n = 131) in the post-CC period. No demographic differences were noted between the two periods except for an increase in uninsured patients from 43.0% vs 61.1% (p = 0.020). Compared to pre-CC patients, post-CC patients experienced a trend toward increased abdominal injury (11.2% vs 20.6%, p = 0.051) and increased vascular injuries (11.2% vs 22.1%, p = 0.026) while lower extremity injuries decreased significantly (38.3% vs 26.0%, p = 0.041). Positive focused assessment with sonography in trauma (FAST) exams (2.2% vs 16.8, p < 0.001), intensive care unit admission (26.2% vs 42.0%, p = 0.011) and need for ventilator support (11.2% vs 22.1%, p = 0.026) all increased during the post-CC period. In-hospital mortality more than doubled (8.4% vs 18.3%, p = 0.028) across the pre- and post-CC time periods. Conclusion. Implementation of a CC law was not associated with a decrease in the overall number of penetrating injuries or a decrease in mortality

A Novel Power Sharing Control Method for Distributed Generators in DC Networks

The power sharing control method is a desirable solution to integrate multiple renewable energy generators into the grid and to keep them working synchronously. Power sharing control between different distributed generators is an important consideration for the stabilized operation of the power grid network. In this thesis work, a novel method is used with the concept of droop control technique and is designed to control power from each individual generator in DC network particularly. The proposed power sharing control method can be widely applied to grid connected network and to islanded power grid network for obtaining high efficiency of power distribution and also provides higher stability. An efficient power control method to share the load demand power is designed based on the concept of droop control. This method does not follow sequential or predefined topology of power sharing but uses the availability of power from each generator as a factor of control. The proposed controller can be applied to an individual distributed generator to regulate its output power quickly and accurately. The power sharing control method was formulated, modeled and verified by simulation studies of steady state and transient stability tests. The optimal coupling resistance for power sharing was also identified. The interaction of the controller and the communication delay was also studied. The interference of communication delay is negligible for the power sharing controller. The system is simulated in MATLAB/SIMULINK environment

Asymmetric discrimination of non-speech tonal analogues of vowels

Published in final edited form as: J Exp Psychol Hum Percept Perform. 2019 February ; 45(2): 285–300. doi:10.1037/xhp0000603.Directional asymmetries reveal a universal bias in vowel perception favoring extreme vocalic articulations, which lead to acoustic vowel signals with dynamic formant trajectories and well-defined spectral prominences due to the convergence of adjacent formants. The present experiments investigated whether this bias reflects speech-specific processes or general properties of spectral processing in the auditory system. Toward this end, we examined whether analogous asymmetries in perception arise with non-speech tonal analogues that approximate some of the dynamic and static spectral characteristics of naturally-produced /u/ vowels executed with more versus less extreme lip gestures. We found a qualitatively similar but weaker directional effect with two-component tones varying in both the dynamic changes and proximity of their spectral energies. In subsequent experiments, we pinned down the phenomenon using tones that varied in one or both of these two acoustic characteristics. We found comparable asymmetries with tones that differed exclusively in their spectral dynamics, and no asymmetries with tones that differed exclusively in their spectral proximity or both spectral features. We interpret these findings as evidence that dynamic spectral changes are a critical cue for eliciting asymmetries in non-speech tone perception, but that the potential contribution of general auditory processes to asymmetries in vowel perception is limited.Accepted manuscrip