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Physical Sciences and Mathematics Commons™
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Articles 1 - 11 of 11
Full-Text Articles in Physical Sciences and Mathematics
Investigating The Spatial Complexity Of Various Pke-Peks Schematics, Jacob Patterson
Investigating The Spatial Complexity Of Various Pke-Peks Schematics, Jacob Patterson
Rose-Hulman Undergraduate Research Publications
With the advent of cloud storage, people upload all sorts of information to third party servers. However, uploading plaintext does not seem like a good idea for users who wish to keep their data private. Current solutions to this problem in literature involves integrating Public Key Encryption and Public key encryption with keyword search techniques. The intent of this paper is to analyze the spatial complexities of various PKE-PEKS schemes at various levels of security and discuss potential avenues for improvement.
Inverse Laplace Transform And Post Inversion Formula, Qinmao Zhang
Inverse Laplace Transform And Post Inversion Formula, Qinmao Zhang
Mathematical Sciences Technical Reports (MSTR)
This paper is dedicated to a general numerical approach to inverse Laplace transforms based on the Post Inversion Formula, which is a theoretical equivalent to the inverse Laplace transform. Though most approaches are too computationally intensive to be of practical use, we introduce an efficient algorithm to compute it based on the Parker-Sochacki method (PSM). This paper also contains some example MATLAB code and algorithm analysis.
Important Considerations For Human Activity Recognition Using Sensor Data, Matt Buckner
Important Considerations For Human Activity Recognition Using Sensor Data, Matt Buckner
Rose-Hulman Undergraduate Research Publications
Automated human activity recognition has received much attention in recent years due to increasing focus on interconnected devices in The Internet of Things (IoT) and the miniaturization and proliferation of sensor systems with the adoption of smartphones. In this work, we focus on the current status of human activity recognition across multiple studies, including methodology, accuracy of results, and current challenges to implementation. We include some preliminary work we have completed on a sensor system for classifying treadmill usage.
Real Time Activity Recognition Of Treadmill Usage Via Machine Learning, Nathan Blank, Matt Buckner, Christian Owen, Anna Scott
Real Time Activity Recognition Of Treadmill Usage Via Machine Learning, Nathan Blank, Matt Buckner, Christian Owen, Anna Scott
Rose-Hulman Undergraduate Research Publications
Our objective is to provide real-time classification of treadmill usage patterns based on accelerometer and magnetometer measurements. We collected data from treadmills in the Rose-Hulman Student Recreation Center (SRC) using Shimmer3 sensor units. We identified useful data features and classifiers for predicting treadmill usage patterns. We also prototyped a proof of concept wireless, real-time classification system.
Topological And Hq Equivalence Of Prime Cyclic P-Gonal Actions On Riemann Surfaces (Corrected), Sean A. Broughton
Topological And Hq Equivalence Of Prime Cyclic P-Gonal Actions On Riemann Surfaces (Corrected), Sean A. Broughton
Mathematical Sciences Technical Reports (MSTR)
Two Riemann surfaces S1 and S2 with conformal G-actions have topologically equivalent actions if there is a homeomorphism h : S1 -> S2 which intertwines the actions. A weaker equivalence may be defined by comparing the representations of G on the spaces of holomorphic q-differentials Hq(S1) and Hq(S2). In this note we study the differences between topological equivalence and Hq equivalence of prime cyclic actions, where S1/G and S2/G have genus zero.
Mathematical Modeling Of Quadcopter Dynamics, Qikai Huang (Bruce Wingo)
Mathematical Modeling Of Quadcopter Dynamics, Qikai Huang (Bruce Wingo)
Mathematical Sciences Technical Reports (MSTR)
Recently, Google, Amazon and others are attempting to develop delivery drones for commercial use, in particular Amazon Prime Air promising 30 minute delivery. One type of commonly used drone proposed for such purposes is a quadcopter. Quadcopters have been around for some time with original development in the 1920’s. They are popular now because they are mechanically simple and provide a good vehicle for unmanned flight. By controlling the speed of the four propellers, a quadcopter can roll, change pitch, change yaw, and accelerate. This research will focus on the study of classical mechanics theories on rigid body motion using …
An Investigation Of Minimal Surfaces In So(3), Luke Bohn
An Investigation Of Minimal Surfaces In So(3), Luke Bohn
Rose-Hulman Undergraduate Research Publications
Classical minimal surface theory can be thought of as dealing with the shapes of soap films stretched across wires in Euclidean space R3. This article will examine such structures in an abstract three-dimensional space, the Lie Group SO(3). This is the space of possible rotations in R3, where each rotation is expressed as three angles: two to indicate the axis of rotation and one to indicate the amount of rotation. The properties of the space SO(3) may result in minimal surfaces that behave differently than they do in R3.
Counting Solutions To Discrete Non-Algebraic Equations Modulo Prime Powers, Abigail Mann
Counting Solutions To Discrete Non-Algebraic Equations Modulo Prime Powers, Abigail Mann
Mathematical Sciences Technical Reports (MSTR)
As society becomes more reliant on computers, cryptographic security becomes increasingly important. Current encryption schemes include the ElGamal signature scheme, which depends on the complexity of the discrete logarithm problem. It is thought that the functions that such schemes use have inverses that are computationally intractable. In relation to this, we are interested in counting the solutions to a generalization of the discrete logarithm problem modulo a prime power. This is achieved by interpolating to p-adic functions, and using Hensel's lemma, or other methods in the case of singular lifting, and the Chinese Remainder Theorem.
Statistical Analysis Of Binary Functional Graphs Of The Discrete Logarithm, Mitchell Orzech
Statistical Analysis Of Binary Functional Graphs Of The Discrete Logarithm, Mitchell Orzech
Mathematical Sciences Technical Reports (MSTR)
The increased use of cryptography to protect our personal information makes us want to understand the security of cryptosystems. The security of many cryptosystems relies on solving the discrete logarithm, which is thought to be relatively difficult. Therefore, we focus on the statistical analysis of certain properties of the graph of the discrete logarithm. We discovered the expected value and variance of a certain property of the graph and compare the expected value to experimental data. Our finding did not coincide with our intuition of the data following a Gaussian distribution given a large sample size. Thus, we found the …
Mathematical Modeling Of Quadcopter Dynamics, Qikai Huang (Bruce Wingo)
Mathematical Modeling Of Quadcopter Dynamics, Qikai Huang (Bruce Wingo)
Rose-Hulman Undergraduate Research Publications
Recently, Google, Amazon and others are attempting to develop delivery drones for commercial use, in particular Amazon Prime Air promising 30 minute delivery. One type of commonly used drone proposed for such purposes is a quadcopter. Quadcopters have been around for some time with original development in the 1920’s. They are popular now because they are mechanically simple and provide a good vehicle for unmanned flight. By controlling the speed of the four propellers, a quadcopter can roll, change pitch, change yaw, and accelerate. This research will focus on the study of classical mechanics theories on rigid body motion using …
Variance Of Clusterings On Graphs, Thomas Vlado Mulc
Variance Of Clusterings On Graphs, Thomas Vlado Mulc
Mathematical Sciences Technical Reports (MSTR)
Graphs that represent data often have structures or characteristics that can represent some relationships in the data. One of these structures is clusters or community structures. Most clustering algorithms for graphs are deterministic, which means they will output the same clustering each time. We investigated a few stochastic algorithms, and look into the consistency of their clusterings.