Bayesian inference of Gaussian mixture models with noninformative priors

This paper deals with Bayesian inference of a mixture of Gaussian distributions. A novel formulation of the mixture model is introduced, which includes the prior constraint that each Gaussian component is always assigned a minimal number of data points. This enables noninformative improper priors such as the Jeffreys prior to be placed on the component parameters. We demonstrate difficulties involved in specifying a prior for the standard Gaussian mixture model, and show how the new model can be used to overcome these. MCMC methods are given for efficient sampling from the posterior of this model.Comment: 26 pages 10 figure

Newton-Euler Dynamic Equations of Motion for a Multi-body Spacecraft

The Magnetospheric MultiScale (MMS) mission employs a formation of spinning spacecraft with several flexible appendages and thruster-based control. To understand the complex dynamic interaction of thruster actuation, appendage motion, and spin dynamics, each spacecraft is modeled as a tree of rigid bodies connected by spherical or gimballed joints. The method presented facilitates assembling by inspection the exact, nonlinear dynamic equations of motion for a multibody spacecraft suitable for solution by numerical integration. The building block equations are derived by applying Newton's and Euler's equations of motion to an "element" consisting of two bodies and one joint (spherical and gimballed joints are considered separately). Patterns in the "mass" and L'force" matrices guide assembly by inspection of a general N-body tree-topology system. Straightforward linear algebra operations are employed to eliminate extraneous constraint equations, resulting in a minimum-dimension system of equations to solve. This method thus combines a straightforward, easily-extendable, easily-mechanized formulation with an efficient computer implementation

America First as a Foreign Policy : Multilateralism and Security Policy

President Donald Trump has redefined America’s foreign policy around his mantra, “America First.” This has led to attempts at renegotiating international treaties and reversing American Foreign policy toward inter-governmental organizations (IGOs). His actions, specifically on security policy issues including Iran and the Joint Comprehensive Plan of Action (JCPOA), as well as the North Atlantic Treaty Organization (NATO), have led to multiple short-term as well as potential long-term consequences. These include a level of uncertainty surrounding President Trump’s meaning of “America First” and a difficulty in understanding and/or anticipating his actions and intentions due to the lack of a clear foreign policy direction. Additionally, Trump’s actions have led to a substantial increase in tensions between the US and Iran, which has already caused multiple casualties. This paper aims to address the following questions: What does this mean for the United States? How are foreign leaders perceiving these changes made by the Trump Administration, and how does it help or hurt US interests abroad? Ultimately, Trump has approached foreign policy with his Realist mindset, causing him to question multilateralism and even bilateralism. His tendency to withdraw or threaten to withdraw from agreements and treaties has caused panic and fear amongst our allies who are unsure of the American commitment and has contributed to a lack of trust in America

Simulating Attitudes and Trajectories of Multiple Spacecraft

A computer program called "42" simulates the attitudes and trajectories of multiple spacecraft flying in formation anywhere in the Solar System

Inevitable Forces: Deciphering the Environment

My work is a response to my surroundings, the relationship between man and nature, and my perception of human impact on the environment. I compare the sprawl of cities that overtake the surrounding countryside to the spreading of microscopic bacteria and disease. My observation of the destruction of the environment and other uncontrollable events that perpetuate fear, such as passage of time, death, and growth, is visualized through the combination of two opposing forces: structure (controlled) and organic (uncontrolled). My use of printmaking processes parallels these concepts of control or lack of control. Lithography, intaglio, silkscreen and relief are closely linked to the use of hand-drawn elements and the hand of the artist. The use of the artist\u27s hand directs the work back to my futile individual attempts to structure and control aspects of nature (both micro and macroscopic) that provoke apprehension