As part of the NASA IMPACT program to model mechanical interactions with bodies in space such as comets, asteroids, and other Near Earth Objects (NEOs), the Colorado School of Mines team is designing a motor stage apparatus to interact with JSC-1A regolith simulant surfaces. This initial study involved development and testing of a prototype motor stage apparatus which was used to drive three types of probes into JSC-1A surfaces while collecting force data under standard Earth atmospheric conditions. The probes used were a conical-tipped probe, a wedge-tipped probe, and an anchoring probe. Main goals of the prototype system were to acquire general force trends for each interaction, and to isolate the most important design features for a more-complex in-vacuum system. Our data revealed force interactions that were very small in magnitude—on the order of tenths of Newtons—and more complex than our simple stiff beam probe and mount model could accurately predict. Our results lead us to recommend a more complex experimental model that can accurately represent deflection in the probes while also allowing for better measurement of regolith movement near the tip of the probes. Specifically, we recommend the following design features for the in-vacuum system: a load cell capable of measuring at very low ranges (thousandths of Newtons), reliability of structural axis alignment between trials, a robust mounting system that can accommodate each different type of probe, and consistency of sample preparation between trials.
Linear regression is one of the most widely used statistical methods available today. It is used by data analysts and students in almost every discipline. However, for the standard ordinary least squares method, there are several strong assumptions made about data that is often not true in real world data sets. This can cause numerous problems in the least squares model. One of the most common issues is a model overfitting the data. Ridge Regression and LASSO are two methods used to create a better and more accurate model. I will discuss how overfitting arises in least squares models and the reasoning for using Ridge Regression and LASSO include analysis of real world example data and compare these methods with OLS and each other to further infer the benefits and drawbacks of each method.
This is the template for DAM (discrete and argumentative mathematics).
We prove theorem $2.1$ using the method of proof by way of contradiction. This theorem states that for any set $A$, that in fact the empty set is a subset of $A$, that is $\emptyset \subset A$.
In this paper I demonstrate a novel design for an optoelectronic State Machine which replaces input/output forming logic found in conventional state machines with BDD based optical logic while still using solid state memory in the form of flip-flops in order to store states. This type of logic makes use of waveguides and ring resonators to create binary switches. These switches in turn can be used to create combinational logic which can be used as input/output forming logic for a state machine. Replacing conventional combinational logic with BDD based optical logic allows for a faster range of state machines that can certainly outperform conventional state machines as propagation delays within the logic described are in the order of picoseconds as opposed to nanoseconds in digital logic.