Gamma-homology of algebras over an operad

The purpose of this paper is to study generalizations of Gamma-homology in the context of operads. Good homology theories are associated to operads under appropriate cofibrancy hypotheses, but this requirement is not satisfied by usual operads outside the characteristic zero context. In that case, the idea is to pick a cofibrant replacement Q of the given operad P. We can apply to P-algebras the homology theory associated to Q in order to define a suitable homology theory on the category of P-algebras. We make explicit a small complex to compute this homology when the operad P is binary and Koszul. In the case of the commutative operad P=Com, we retrieve the complex introduced by Robinson for the Gamma-homology of commutative algebras.Comment: 24 pages, correction in the definition of c_{i,j}, typos correcte

Leibniz homology of Lie algebras as functor homology

We prove that Leibniz homology of Lie algebras can be described as functor homology in the category of linear functors from a category associated to the Lie operad.Comment: 26 page

Real-Time Digital Signal Processing Demonstration Platform

In order to demonstrate various digital signal processing (DSP) algorithms to students or potential students, a program was developed that runs in real-time on low cost, commercially available hardware. The program includes several common DSP algorithms such as lowpass filter, highpass filter, echo, reverb, quantization, aliasing, simple speech recognition, and fast Fourier transform (FFT). The program allows the user to easily switch between algorithms, to adjust the parameters of the algorithms, and to immediately hear the results. The demonstration hardware consists of the TMS320C5515 eZdsp USB Stick, a powered microphone, an audio source such as an MP3 player or cellphone, and speakers. Undergraduate electrical engineering students were shown the demonstration and were surveyed to determine which algorithms they found most interesting. The C language source code for the software is available from the author for free, so this program can be modified by instructors who wish to make their own demonstrations or used as a convenient starting point for student projects

Operads with compatible CL-shellable partition posets admit a Poincar\'e-Birkhoff-Witt basis

In 2007, Vallette built a bridge across posets and operads by proving that an operad is Koszul if and only if the associated partition posets are Cohen-Macaulay. Both notions of being Koszul and being Cohen-Macaulay admit different refinements: our goal here is to link two of these refinements. We more precisely prove that any (basic-set) operad whose associated posets admit isomorphism-compatible CL-shellings admits a Poincar\'e-Birkhoff-Witt basis. Furthermore, we give counter-examples to the converse

Prairie Paupers: North Dakota Poor Farms, 1879-1973

This study examines the history of county poor farms in North Dakota and places them within the wider perspective of poor relief in the United States. North Dakota inherited its system of poor relief from the Elizabethan and American colonial poor laws. Poorhouses were a part of poor relief practices that also included local responsibility, outdoor relief, indenture of paupers, the poor list, expulsion of non-resident paupers, pauper burial, discouragement of vagrancy, and family responsibility for the poor. Chapter One outlines Elizabethan poor laws and poor relief in the American colonies. The increase in numbers of poor farms in the nineteenth century is examined in light of policies which discouraged relief applications. The growth of private charity and the role of reform movements in the United States is documented within the context of the poor relief apparatus. Chapter Two is a study of the Dakota laws concerning pauper relief and the application of the law. The establishment of county hospitals, poorhouses, and other relief practices in response to changing population pressures shows a modest adaptation of inherited poor-relief practices. The drought and depression period of the 1890s is the background for a limited involvement by the state government. Chapter Three charts the growth of Progressive changes in poor relief, particularly the protection of children. Children were present in poorhouses in the state until the 1940s. New Deal programs changed the nature of poor relief from a local to a federal responsibility during the Great Depression. Poor farms were discontinued as a result of the rise of the federal welfare state. Chapters Four through Seventeen contain the histories of fourteen North Dakota poorhouses, drawn from original records. The poor farms were discontinued by 1973 and were replaced by modern nursing homes and welfare programs

Using Practical Examples in Teaching Digital Logic Design

Digital logic design is often taught from the bottom up starting with the simplest components (transistors and gates), proceeding through combinational and sequential logic circuits, and if there is time may finish up with the basic components of microprocessors. With the bottom up approach, it may be a fairly long time before students see a complete system that performs a recognizable function. Most of the standard example circuits, such as binary adders, decoders, multiplexers, etc., are parts used in a larger system. While knowledge of the standard circuits is crucial for building more complex circuits, these standard circuits might not capture the students’ interest as much as a complete system. Therefore, this paper describes three proposed example circuits that are simple enough to cover in the first logic design course, but yet are complete systems that perform useful functions. The proposed circuits are a game show buzz-in system that determines which of two contestants rings in first, a standard 12-hour digital clock, and a car alarm that could honk a car horn if someone enters the car without resetting the alarm. The proposed circuits can be used as examples or homework problems in addition to the standard circuits to increase students’ interest in the material and to show how useful the design techniques can be. Surveys were given to the students after the proposed circuits and the standard circuits were covered to assess the level of student interest generated by the examples. The results of the surveys are presented in the paper along with detailed descriptions of the circuits

Effect of radiance-to-reflectance transformation and atmosphere removal on maximum likelihood classification accuracy of high-dimensional remote sensing data

Many analysis algorithms for high-dimensional remote sensing data require that the remotely sensed radiance spectra be transformed to approximate reflectance to allow comparison with a library of laboratory reflectance spectra. In maximum likelihood classification, however, the remotely sensed spectra are compared to training samples, thus a transformation to reflectance may or may not be helpful. The effect of several radiance-to-reflectance transformations on maximum likelihood classification accuracy is investigated in this paper. We show that the empirical line approach, LOWTRAN7, flat-field correction, single spectrum method, and internal average reflectance are all non-singular affine transformations, and that non-singular affine transformations have no effect on discriminant analysis feature extraction and maximum likelihood classification accuracy. (An affine transformation is a linear transformation with an optional offset.) Since the Atmosphere Removal Program (ATREM) and the log residue method are not affine transformations, experiments with Airborne Visible/Infrared Imaging Spectrometer (AVIRIS) data were conducted to determine the effect of these transformations on maximum likelihood classification accuracy. The average classification accuracy of the data transformed by ATREM and the log residue method was slightly less than the accuracy of the original radiance data. Since the radiance-to-reflectance transformations allow direct comparison of remotely sensed spectra with laboratory reflectance spectra, they can be quite useful in labeling the training samples required by maximum likelihood classification, but these transformations have only a slight effect or no effect at all on discriminant analysis and maximum likelihood classification accuracy