A Singular Perturbation Approach to the Fitzhugh-Nagumo PDE for Modeling Cardiac Action Potentials.

The study of cardiac action potentials has many medical applications. Dr. Dennis Noble first used mathematical models to study cardiac action potentials in the 1960s. We begin our study of cardiac action potentials with one form of the Fitzhugh-Nagumo partial differential equation. We use the non-classical method to produce a closed form solution for the decoupled Fitzhugh Nagumo equation. Using voltage recording data of action potentials in a cardiac myocyte and in purkinje fibers, we estimate parameter values for the closed form solution with standard linear and non-linear regression methods. Results are limited, thus leading us to perturb the solution to obtain a better fit. We turn to singular perturbation theory to justify our pole-based approach. Finally, we test our model on independent action potential data sets to evaluate our model and to draw conclusions on how our model can be applied

How do Stream Confluences Influence Aquatic Invertebrate Taxonomic and Functional Diversity?

Aquatic communities, species that live and interact with each other, each have a unique composition and function (i.e collection of decomposers, predators, and grazers). Broad ecological theory provides a variety of models that can predict communities and their functions across riverscapes. For example, the River Continuum Concept (RCC) explains general shifts in stream communities and their function along longitudinal (upstream to downstream) gradients, but it fails to consider the more narrow effects of tributaries and confluences. Conversely, dendritic stream networks theory helps explain the potential role of river confluences and how they connect communities, but fails to explain general longitudinal shifts in communities. This discontinuity between models begs for a way to integrate the role of confluences (dendritic theory) into a broader landscape model (RCC). I hypothesized that river confluences would have a different influence on community diversity and function than expected under the RCC. To explore this, I sampled aquatic insects at tributaries along a watershed to test predictions that stream confluences would (1) increase insect diversity (number of species), (2) abruptly change specific species abundance, and (3) change the overall community function through increasing and decreasing insect functional feeding groups. I collected aquatic insects in two watersheds in the Beartooth-Absaroka Wilderness, sampling above and below four stream confluences in each watershed. Aquatic insect samples were identified to genus level and given a functional feeding group score. I will examine pairwise upstream/downstream differences with and without intervening confluences to compare community diversity, composition, and functional diversity. Streams ecosystems are often ranked as one of the most imperiled ecosystems in the world. Developing aquatic community theories and models as we work to restore these ecosystems is important in understanding how pristine aquatic ecosystems should function

Hohenzollern Prussia: Claiming a Legacy of Legitimacy

Prussia has been seen since the Second World War as a militaristic pariah and because of its scattered and desperate nature it has been vilified as the root cause of Nazism. Modern authors like Christopher Clark, Philip Dwyer, and others have helped to perpetuate these ideas in contemporary literature. These ideas contradict works by older historians who wrote and asserted that Prussian expansion was based on dynastic claims. These earlier historians asserted that Prussian actions followed a series of dynastic claims that gave credibility to Prussian expansion without upsetting the political norms of the time. By examining the actions and written accounts of Prussia\u27s monarchs I will show that in contrast to the accepted Anglo-America theory of Prussian militarism as expressed by authors like Dwyer, that Prussia was in fact, a legally expanding state growing through the legitimate and internationally recognized means of dynastic claims. To validate my thesis I will use archival evidence such as the written testaments of Prussia\u27s rules and the historic actions these rules took through 150 years of history, from 1640 to 1786. This research will prove that the current historiography on the subject is badly tainted by post Nazi views on expansion, freedom of action, and other international norms. The application of modern norms on international affairs regarding events occurring in the 17th and 18th century fails to view Prussian actions as it was seen by Prussia\u27s peers during that time. Instead of viewing Prussia as aggressive and expansionistic, other states saw its growth as legitimate expansion via a series of dynastic claims that Prussia held. These claims were recognized as a legitimate international form of expansion. This thesis will thus prove that Prussian expansion from 1640-1786 was only based on dynastic claims

Comparing Dominant and Non-Dominant Torque and Work Using Biodex 3 Isokinetic Protocol for Knee Flexors and Extensors

INTRODUCTION. There is often a misconception when looking at comparing dominant and non-dominant limbs of any sort. Although there will be a lack of control in non-dominant limbs compared to dominant, the amount of torque and power associated with each limb may be equal; even so, there may be an instance of bilateral deficit, where even though the dominant limb may be used to do work on a specific limb, the non-dominant limb may still receive strength benefits. PURPOSE. The main purpose of this study is to directly relate ability (torque and total work) in both dominant and non-dominate limbs with a focus on knee flexion and extension. METHODS. Participants: Four (N = 4; 4 males, 0 females) volunteers were utilized for this study. The average age of the participants were 24.5 + 1.73 years old, average height was 71.75 + 3.20” (inches or 182.245 centimeters), and average weight was 183.26 + 45.78 pounds (83.3 kilograms). Methodology: Upon arriving to the lab, each participant was measured for height (recorded in inches) and weight (recorded in kilograms), as well as age was recorded (years). Each participant was added into the system when they attempted to perform the protocol. The protocol utilized isokinetic concentric/concentric contractions on the knee for three separate speeds or sets (30/s, 60/s, and 90/s); each set included 5 repetitions. Upon completion of each set (5 repetitions) the participant would be allowed 10 seconds of rest. Following the same protocol, all participants would complete the test using their non-dominate leg. RESULTS. The value and percent difference associated with dominant and non-dominant extension (both torque and work) were rather large. As seen in the percent difference section, the value of each percent difference were at least 7.83% (min) and as high as 27.43% (max). There was also a noticeable percent difference associated with 90/s in flexion for both torque and work between dominant and non-dominant with values at torque = 19.97% and work = 16.23%. DISCUSSION. This study may help provide insight into how dominant and non-dominant limbs may be trained and how they may be equal even without training. This may be untrue due to many variables, but this study has allowed a certain insight into how dominant and non-dominant limbs may be equal in gross motor movements. Results that find non-dominant to dominant differences may be errors due the tester and/or the participant; it may be due to the participant because of situational awareness, they may learn the protocol and movements with one leg and adjust using the other

MatlabMPI

The true costs of high performance computing are currently dominated by software. Addressing these costs requires shifting to high productivity languages such as Matlab. MatlabMPI is a Matlab implementation of the Message Passing Interface (MPI) standard and allows any Matlab program to exploit multiple processors. MatlabMPI currently implements the basic six functions that are the core of the MPI point-to-point communications standard. The key technical innovation of MatlabMPI is that it implements the widely used MPI ``look and feel'' on top of standard Matlab file I/O, resulting in an extremely compact (~250 lines of code) and ``pure'' implementation which runs anywhere Matlab runs, and on any heterogeneous combination of computers. The performance has been tested on both shared and distributed memory parallel computers (e.g. Sun, SGI, HP, IBM, Linux and MacOSX). MatlabMPI can match the bandwidth of C based MPI at large message sizes. A test image filtering application using MatlabMPI achieved a speedup of ~300 using 304 CPUs and ~15% of the theoretical peak (450 Gigaflops) on an IBM SP2 at the Maui High Performance Computing Center. In addition, this entire parallel benchmark application was implemented in 70 software-lines-of-code, illustrating the high productivity of this approach. MatlabMPI is available for download on the web (www.ll.mit.edu/MatlabMPI).Comment: Download software from http://www.ll.mit.edu/MatlabMPI, 12 pages including 7 color figures; submitted to the Journal of Parallel and Distributed Computin

Re-examining balinese subaks through the lens of cultural multilevel selection

Unidad de excelencia María de Maeztu MdM-2015-0552Overcoming environmental challenges requires understanding when and why individuals adopt cooperative behaviors, how individual behaviors and interactions among resource users change over time, and how group structure and group dynamics impact behaviors, institutions, and resource conditions. Cultural multilevel selection (CMLS) is a theoretical framework derived from theories of cultural evolution and cultural group selection that emphasizes pressures affecting different levels of social organization as well as conflicts among these levels. As such, CMLS can be useful for understanding many environmental challenges. With this paper, we use evidence from the literature and hypothetical scenarios to show how the framework can be used to understand the emergence and persistence of sustainable social-ecological systems. We apply the framework to the Balinese system of rice production and focus on two important cultural traits (synchronized cropping and the institutions and rituals associated with water management). We use data from the literature that discusses bottom-up (self-organized, complex adaptive system) and top-down explanations for the system and discuss how (1) the emergence of group structure, (2) group-level variation in cropping strategies, institutions, and rituals, and (3) variation in overall yields as a result of different strategies and institutions, could have allowed for the spread of group-beneficial traits and the increasing complexity of the system. We also outline cultural transmission mechanisms that can explain the spread of group-beneficial traits in Bali and describe the kinds of data that would be required to validate the framework in forward-looking studies