Physical Sciences and Mathematics Commons^™

Why Rectified Linear Neurons Are Efficient: Symmetry-Based, Complexity-Based, And Fuzzy-Based Explanations, Olac Fuentes, Justin Parra, Elizabeth Y. Anthony, Vladik Kreinovich

Departmental Technical Reports (CS)

Traditionally, neural networks used a sigmoid activation function. Recently, it turned out that piecewise linear activation functions are much more efficient -- especially in deep learning applications. However, so far, there have been no convincing theoretical explanation for this empirical efficiency. In this paper, we show that, by using different uncertainty techniques, we can come up with several explanations for the efficiency of piecewise linear neural networks. The existence of several different explanations makes us even more confident in our results -- and thus, in the efficiency of piecewise linear activation functions.

Z-Numbers: How They Describe Student Confidence And How They Can Explain (And Improve) Laplacian And Schroedinger Eigenmap Dimension Reduction In Data Analysis, Vladik Kreinovich, Olga Kosheleva, Michael Zakharevich

Departmental Technical Reports (CS)

Experts have different degrees of confidence in their statements. To describe these different degrees of confidence, Lotfi A. Zadeh proposed the notion of a Z-number: a fuzzy set (or other type of uncertainty) supplemented by a degree of confidence in the statement corresponding to fuzzy sets. In this chapter, we show that Z-numbers provide a natural formalization of the competence-vs-confidence dichotomy, which is especially important for educating low-income students. We also show that Z-numbers provide a natural theoretical explanation for several empirically heuristic techniques of dimension reduction in data analysis, such as Laplacian and Schroedinger eigenmaps, and, moreover, show how …

Why Deep Learning Methods Use Kl Divergence Instead Of Least Squares: A Possible Pedagogical Explanation, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In most applications of data processing, we select the parameters that minimize the mean square approximation error. The same Least Squares approach has been used in the traditional neural networks. However, for deep learning, it turns out that an alternative idea works better -- namely, minimizing the Kullback-Leibler (KL) divergence. The use of KL divergence is justified if we predict probabilities, but the use of this divergence has been successful in other situations as well. In this paper, we provide a possible explanation for this empirical success. Namely, the Least Square approach is optimal when the approximation error is normally …

Why Triangular Membership Functions Are Often Efficient In F-Transform Applications: Relation To Interval Uncertainty\\ And Haar Wavelets, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

Fuzzy techniques describe expert opinions. At first glance, we would therefore expect that the more accurately the corresponding membership functions describe the expert's opinions, the better the corresponding results. In practice, however, contrary to these expectations, the simplest -- and not very accurate -- triangular membership functions often work the best. In this paper, on the example of the use of membership functions in F-transform techniques, we provide a possible theoretical explanation for this surprising empirical phenomenon.

Beyond Integration: A Symmetry-Based Approach To Reaching Stationarity In Economic Time Series, Songsak Sriboonchitta, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

Many efficient data processing techniques assume that the corresponding process is stationary. However, in areas like economics, most processes are not stationery: with the exception of stagnation periods, economies usually grow. A known way to apply stationarity-based methods to such processes -- integration -- is based on the fact that often, while the process itself is not stationary, its first or second differences are stationary. This idea works when the trend polynomially depends on time. In practice, the trend is usually non-polynomial: it is often exponentially growing, with cycles added. In this paper, we shod how integration techniques can be …

Why Sparse?, Thongchai Dumrongpokaphan, Olga Kosheleva, Vladik Kreinovich, Aleksandra Belina

Departmental Technical Reports (CS)

In many situations, a solution to a practical problem is sparse, i.e., corresponds to the case when most of the parameters describing the solution are zeros, and only a few attain non-zero values. This surprising empirical phenomenon helps solve the corresponding problems -- but it remains unclear why this phenomenon happens. In this paper, we provide a possible theoretical explanation for this mysterious phenomenon.

How To Best Apply Neural Networks In Geosciences: Towards Optimal "Averaging" In Dropout Training, Afshin Gholamy, Justin Parra, Vladik Kreinovich, Olac Fuentes, Elizabeth Y. Anthony

Departmental Technical Reports (CS)

The main objectives of geosciences is to find the current state of the Earth -- i.e., solve the corresponding inverse problems -- and to use this knowledge for predicting the future events, such as earthquakes and volcanic eruptions. In both inverse and prediction problems, often, machine learning techniques are very efficient, and at present, the most efficient machine learning technique is deep neural training. To speed up this training, the current learning algorithms use dropout techniques: they train several sub-networks on different portions of data, and then "average" the results. A natural idea is to use arithmetic mean for this …

Why Taylor Models And Modified Taylor Models Are Empirically Successful: A Symmetry-Based Explanation, Mioara Joldes, Christoph Lauter, Martine Ceberio, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In this paper, we show that symmetry-based ideas can explain the empirical success of Taylor models and modified Taylor models in representing uncertainty.

How To Store Tensors In Computer Memory: An Observation, Martine Ceberio, Vladik Kreinovich

Departmental Technical Reports (CS)

In this paper, after explaining the need to use tensors in computing, we analyze the question of how to best store tensors in computer memory. Somewhat surprisingly, with respect to a natural optimality criterion, the standard way of storing tensors turns out to be one of the optimal ones.

How To Make A Proof Of Halting Problem More Convincing: A Pedagogical Remark, Benjamin W. Robertson, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

As an example of an algorithmically undecidable problem, most textbooks list the impossibility to check whether a given program halts on given data. A usual proof of this result is based on the assumption that the hypothetical halt-checker works for all programs. To show that a halt-checker is impossible, we design an auxiliary program for which the existence of such a halt-checker leads to a contradiction. However, this auxiliary program is usually very artificial. So, a natural question arises: what if we only require that the halt-checker work for reasonable programs? In this paper, we show that even with such …

Statistics As Unbiased Estimators: Exploring The Teaching Of Standard Deviation, Nicholas H. Wasserman, Stephanie Casey, Joe Champion, Maryann Huey

Mathematics Faculty Publications and Presentations

This manuscript presents findings from a study about the knowledge for and planned teaching of standard deviation. We investigate how understanding variance as an unbiased (inferential) estimator – not just a descriptive statistic for the variation (spread) in data – is related to teachers’ instruction regarding standard deviation, particularly around the issue of division by n-1. In this regard, the study contributes to our understanding about how knowledge of mathematics beyond the current instructional level, what we refer to as nonlocal mathematics, becomes important for teaching. The findings indicate that acquired knowledge of nonlocal mathematics can play a role …

Facing The Sun, Frank Prendergast, Muiris O'Sullivan, Ken Williams, Gabriel Cooney

Articles

December 2017 marked 50 years since archaeologist Michael J. O’Kelly first observed the solar illumination of the burial chamber in the Neolithic passage tomb at Newgrange during the period of the winter solstice. O’Kelly subsequently recorded direct sunlight entering Newgrange through the ‘especially contrived slit which lies under the roof-box at the outer end of the passage roof’ on 21 December 1969. The discovery of this historic phenomenon, dating back over 5,000 years, captured the public interest and imagination at that time and ever since. In this major article published in the Winter 2017 edition of Archaeology Ireland (date of …

Deep Subaru Hyper Suprime-Cam Observations Of Milky Way Satellites Columba I And Triangulum Ii*, Jeffrey Carlin, David Sand, Ricardo Muñoz, Kristine Spekkens, Beth Willman, Denija Crnojević, Duncan Forbes, Jonathan Hargis, Evan Kirby, Annika Peter, Aaron Romanowsky, Jay Strader

Faculty Publications

We present deep, wide-field Subaru Hyper Suprime-Cam photometry of two recently discovered satellites of the Milky Way (MW): Columba I (Col I) and Triangulum II (Tri II). The color–magnitude diagrams of both objects point to exclusively old and metal-poor stellar populations. We re-derive structural parameters and luminosities of these satellites, and find for Col I and for Tri II, with corresponding half-light radii of pc and pc. The properties of both systems are consistent with observed scaling relations for MW dwarf galaxies. Based on archival data, we derive upper limits on the neutral gas content of these dwarfs, and find …

Eigenstate–Specific Temperatures In Two–Level Paramagnetic Spin Lattices, Mark Masthay, Calley N. Eads, Amber N. Johnson, R. Gerald Keil, Phillip Miller, Ross E. Jones, Joe D. Mashburn, Harry B. Fannin

Chemistry Faculty Publications

Increasing interest in the thermodynamics of small and/or isolated systems, in combination with recent observations of negative temperatures of atoms in ultracold optical lattices, has stimulated the need for estimating the conventional, canonical temperature Tconvc of systems in equilibrium with heat baths using eigenstate-specific temperatures (ESTs). Four distinct ESTs—continuous canonical, discrete canonical, continuous microcanonical, and discrete microcanonical—are accordingly derived for two-level paramagnetic spin lattices (PSLs) in external magnetic fields. At large N, the four ESTs are intensive, equal to Tconvc, and obey all four laws of thermodynamics. In contrast, for N < 1000, the ESTs of most PSL eigenstates are non-intensive, differ from Tconvc, and violate each of the thermodynamic laws. Hence, in spite of their similarities to Tconvc at large N, the ESTs …

Fluorescent Surface Mapping Of Mastodon Tusk, Clare Laubenthal, Joshua Sebree

Mastodon Tusk Project Posters

The subject of study is a Mammut americanum (American Mastodon) tusk. The tusk is currently damaged and in need of repair. To better understand the tusk and the preservation materials previously used, fluorescence spectrometry was used to make a surface map of the tusk. This data will be useful to the conservationists as they plan the care and restoration of the tusk.

Energy-Dispersive X-Ray (Edx) Mapping Of Lead In Mastodon Tusk Using Sem, Nicholas Bonde, Katherine Plotzke

Mastodon Tusk Project Posters

The composition and location of lead within a prehistoric mastodon tusk was mapped using Energy Dispersive X-ray (EDX) spectroscopy analysis via a Scanning Electron Microscope (SEM). This analysis was intended to provide information on the distribution of lead throughout the tusk. Data collected from this analysis has provided insights into the sources of the lead.

An In Between Study: The Usage Of Cross-Sectional Sem And Raman Spectroscopy To Map The Surface Interfacing Of A Mastodon Tusk And Its Lacquers, Katherine Plotzke

Mastodon Tusk Project Posters

A microscopy study utilizing a DXR2 SmartRaman and Evex Mini-Scanning Electron Microscope (SEM) was done on the UNI Museum’s Mammut americanum (American Mastodon) tusk. A map of the surface interfacing was generated and provided information about the elemental composition and layer interconnectedness. Additionally, this project will also aid in the future restoration work on the tusk funded by the Roy J. Carver Charitable Trust.

What Is The Red Plaster In The Mastodon Tusk?, Tray Hickie

Mastodon Tusk Project Posters

During the first visit to the tusk, Dr. Sebree found the crack that had been filled with a strange plaster that was not known at the time.

After seeing the plaster glow from the small flashlight Dr. Sebree had with him, identifying this material seemed like an interesting project.

Due to the fact that the plaster’s makeup is unknown, but identifying the material it was made of, future attempts to restore and preserve the fossil can be done more safely in the event that the material is harmful

Initial x-ray analysis of the mastodon tusk revealed many unexpected surprises.

In …

Classification Of Tusk Layers By Means Of Raman Spectroscopy, Treasure Divis, Vaughn Koch

Mastodon Tusk Project Posters

The American Mastodon tusk was donated to the University of Northern Iowa, and Dr. J. Cable took the lead on preserving it for museum display at UNI. Dr. Cable’s notes stated that it would be possible to preserve the entire tusk, because the outside was “covered with a hard enamel-like substance”. Some notes were taken as to what materials were used to preserve the tusk early on, but their exact composition was not noted.

• Glazed and varnished between 1933 and 1960

• 1960 – canned patching plaster on chipping areas, glazing liquid (brown), two coats of varnish (satin finish …

Carbonization Studies On Mammut Americanum Tusk, Nina Jocic

Mastodon Tusk Project Posters

Many preservation attempts have been made on the tusk that the University of Northern Iowa acquired. Due to the poor preservation attempts a lot of damage has happened and has caused the tusk to be in a way of disrepair. The Carver grant is very keen on the future preservation of the tusk. The sublimation of nucleobases will be able to help guide the type of preservation methods used in order to preserve the nucleobases and possible DNA still in the tusk. The extraction of nucleobases will not only help with the future preservation of tusk but it will also …

Analysis Of Mammut Americanum Tusk For Asbestos, Madeline C. Roach, Joshua A. Sebree

Mastodon Tusk Project Posters

On September 23, 1933, a tusk was discovered in a gravel pit four miles south of Hampton, Iowa. After careful analysis, the tusk was determined to belong to a Mastodon americanus.1 The University of Northern Iowa museum records note that the tusk was patched with a prepared patching plaster in the 1960’s.2 In the United States at the time Alvar was the most commonly used consolidate to form a plaster. It was either mixed with acetone, alcohol and other solvents, or asbestos.3 The museum record notes indicate that the patching plaster was prepared in a can, like a spackling compound.2 …

Sem Topology Of Enamel, Tami Wallin

Mastodon Tusk Project Posters

The topology of the enamel is an important topic to study how, on a microscopic level, the surface of the tusk is rough or smooth so that the correct restoration material and method are applied to the tusk. The method of study to find this information will be the SEM; which with the back scattered electrons will tell me the topography and chemical composition on the surface of the mastodon tusk fragment that will be tested, shown in the image below. SEM has better spacial resolution than optical microscopes do with the measuring tool provided by the program and the …

4th Annual Sustainability Report, Saint Mary's College Of California

Sustainability Report

No abstract provided.

A Customized Quantitative Pcr Microrna Panel Provides A Technically Robust Context For Studying Neurodegenerative Disease Biomarkers And Indicates A High Correlation Between Cerebrospinal Fluid And Choroid Plexus Microrna Expression, Wang-Xia Wang, David W. Fardo, Gregory A. Jicha, Peter T. Nelson

Sanders-Brown Center on Aging Faculty Publications

MicroRNA (miRNA) expression varies in association with different tissue types and in diseases. Having been found in body fluids including blood and cerebrospinal fluid (CSF), miRNAs constitute potential biomarkers. CSF miRNAs have been proposed as biomarkers for neurodegenerative diseases; however, there is a lack of consensus about the best candidate miRNA biomarkers and there has been variability in results from different research centers, perhaps due to technical factors. Here, we sought to optimize technical parameters for CSF miRNA studies. We examined different RNA isolation methods and performed miRNA expression profiling with TaqMan® miRNA Arrays. More specifically, we developed a customized …

Ella Savesthe Beach, Leena Aly, Maddie Hodgdon

Environmental Studies Student Projects

The intention of this project is to start educating children on the consequences of polluting our planet with seemingly harmless waste such as plastics. Many do not realize how small plastic objects can be fatal to many animals. We asked elementary school children to collect trash as part of their participation. Then the trash was used to make a poster featuring Ella the crab. This poster is paired with a children’s story book, where Ella and her animal friends are featured dealing with the consequences of littering. The story book depicts how people’s behavior in natural areas can harm innocent …

Colin The Cormorant, Chelsey Jankauskas, Samantha Schultz

Environmental Studies Student Projects

Colin the Cormorant was an art project created to represent the effects of pollution on local organisms, such as Colin the Cormorant. We hope by seeing this sculpture people think twice about how they dispose of their trash. Colin is made from trash collected at Fortunes Rocks Beach in Biddeford Pool. We chose to make a cormorant because we frequently see cormorants around the Biddeford Pool area and they are a seabird that has been impacted by various types of pollution (garbage, air pollution, etc.).

The Route To Water Security For Texas: The 2015–2016 Texas Water Roadmap Forums, Rudolph A. Rosen, Rabi Mohtar, Luis A. Cifuentes, Stephen Frayser, Gwendolyn Hustvedt, Wesley Patrick, Chara Ragland, Susan V. Roberts, Jorge Vanegas, Cindy Wall, James Wall

Water Resources Science and Technology Faculty Publications

Three forums were held between February 2015 and November 2016, bringing together Texas water experts from business, industry, government, academia, research, and the investment community in impartially facilitated sessions to deter-mine ways to secure Texas’ water future through accelerating growth of infrastructure, technologies, research, education, and sustainable use. Consensus emerged after the first forum that Texas is approaching a water crisis reflecting matters of supply, allocation, and quality that demands immediate action to ensure water security and equitable access to this vital resource. Participant focus rested on new technology acceleration and investment, workforce education, research underway and desired by segments …

Stationary Analysis Of A Multiserver Queue With Multiple Working Vacation And Impatient Customers, P. Manoharan, Shakir Majid

Applications and Applied Mathematics: An International Journal (AAM)

We consider an M/M/c queue with multiple working vacation and impatient customers. The server serves the customers at a lower rate rather than completely halts the service during this working vacation period. The impatience of the customer’s arises when they arrive during the working vacation period, where the service rate of the customer’s is lower than the normal busy period. The queue is analyzed for multiple working vacation policies. The policy of a MWV demands the server to keep taking vacation until it finds at least a single customer waiting in the system at an instant vacation completion. On returning …

Transient Solution Of M[X1],M[X2]/G1,G2/1 With Priority Services, Modified Bernoulli Vacation, Bernoulli Feedback, Breakdown, Delaying Repair And Reneging, G. Ayyappan, J. Udayageetha

Applications and Applied Mathematics: An International Journal (AAM)

This paper considers a queuing system which facilitates a single server that serves two classes of units: high priority and low priority units. These two classes of units arrive at the system in two independent compound Poisson processes. It aims to decipher average queue size and average waiting time of the units. Under the pre-emptive priority rule, the server provides a general service to these arriving units. It is further assumed the server may take a vacation after serving the last high priority unit present in the system or at the service completion of each low priority unit present in …

Analysis Of A M/M/C Queue With Single And Multiple Synchronous Working Vacations, Shakir Majid, P. Manoharan

Applications and Applied Mathematics: An International Journal (AAM)

We consider a M/M/c queuing system with synchronous working vacation and two different policies of working vacation i.e. a multiple working vacation policy and a single working policy. During a working vacation the server does not completely halts the service rather than it will render service at a lower rate. In synchronous vacation policy all the servers leave for a vacation simultaneously, when the server finds the system empty after finishing serving a customer. In multiple working vacation (MWV) policy the servers continue to take vacation till they find the system nonempty at a vacation completion instant. Single working vacation …