On the M\"obius Function and Topology of General Pattern Posets

We introduce a formal definition of a pattern poset which encompasses several previously studied posets in the literature. Using this definition we present some general results on the M\"obius function and topology of such pattern posets. We prove our results using a poset fibration based on the embeddings of the poset, where embeddings are representations of occurrences. We show that the M\"obius function of these posets is intrinsically linked to the number of embeddings, and in particular to so called normal embeddings. We present results on when topological properties such as Cohen-Macaulayness and shellability are preserved by this fibration. Furthermore, we apply these results to some pattern posets and derive alternative proofs of existing results, such as Bj\"orner's results on subword order.Comment: 28 Page

Investigating the Kinematics of Coronal Mass Ejections with the Automated CORIMP Catalog

Studying coronal mass ejections (CMEs) in coronagraph data can be challenging due to their diffuse structure and transient nature, compounded by the variations in their dynamics, morphology, and frequency of occurrence. The large amounts of data available from missions like the Solar and Heliospheric Observatory (SOHO) make manual cataloging of CMEs tedious and prone to human error, and so a robust method of detection and analysis is required and often preferred. A new coronal image processing catalog called CORIMP has been developed in an effort to achieve this, through the implementation of a dynamic background separation technique and multiscale edge detection. These algorithms together isolate and characterise CME structure in the field-of-view of the Large Angle Spectrometric Coronagraph (LASCO) onboard SOHO. CORIMP also applies a Savitzky-Golay filter, along with quadratic and linear fits, to the height-time measurements for better revealing the true CME speed and acceleration profiles across the plane-of-sky. Here we present a sample of new results from the CORIMP CME catalog, and directly compare them with the other automated catalogs of Computer Aided CME Tracking (CACTus) and Solar Eruptive Events Detection System (SEEDS), as well as the manual CME catalog at the Coordinated Data Analysis Workshop (CDAW) Data Center and a previously published study of the sample events. We further investigate a form of unsupervised machine learning by using a k-means clustering algorithm to distinguish detections of multiple CMEs that occur close together in space and time. While challenges still exist, this investigation and comparison of results demonstrates the reliability and robustness of the CORIMP catalog, proving its effectiveness at detecting and tracking CMEs throughout the LASCO dataset.Comment: 23 pages, 11 figures, 1 tabl

A dichotomy result for prime algebras of Gelfand-Kirillov dimension two

Let $k$ be an uncountable field. We show that a finitely generated prime Goldie $k$-algebra of quadratic growth is either primitive or satisfies a polynomial identity, answering a question of Small in the affirmative.Comment: 10 page

Noetherian algebras over algebraically closed fields

Let $k$ be an uncountable algebraically closed field and let $A$ be a countably generated left Noetherian $k$-algebra. Then we show that $A \otimes_k K$ is left Noetherian for any field extension $K$ of $k$. We conclude that all subfields of the quotient division algebra of a countably generated left Noetherian domain over $k$ are finitely generated extensions of $k$. We give examples which show that $A\otimes_k K$ need not remain left Noetherian if the hypotheses are weakened.Comment: 10 page

Sonic Pictures

Winning essay of the American Society for Aesthetics' inaugural Peter Kivy Prize. Extends Kivy's notion of sonic picturing through engagement with recent work in philosophy of perception. Argues that sonic pictures are more widespread and more aesthetically and artistically important than even Kivy envisioned. Topics discussed include: the nature of sonic pictures; the nature of sounds; what we can (and more importantly, cannot) conclude from musical listening; sonic pictures in film; beatboxing as an art of sonic picturing; and cover songs as sonic pictures. To be published in the Journal of Aesthetics and Art Criticism

On the M\"obius Function of Permutations With One Descent

The set of all permutations, ordered by pattern containment, is a poset. We give a formula for the M\"obius function of intervals $[1,\pi]$ in this poset, for any permutation $\pi$ with at most one descent. We compute the M\"obius function as a function of the number and positions of pairs of consecutive letters in $\pi$ that are consecutive in value. As a result of this we show that the M\"obius function is unbounded on the poset of all permutations. We show that the M\"obius function is zero on any interval $[1,\pi]$ where $\pi$ has a triple of consecutive letters whose values are consecutive and monotone. We also conjecture values of the M\"obius function on some other intervals of permutations with at most one descent

The Effect of Silica Surface Area on Microparticle Retention Systems

Retention of fines and fillers has always been a concern in the paper industry. There has been many different types of retention aids in the past, but they lack performance under the vigorous conditions in today\u27s paper mills. High shear forces associated with high speed paper of recycled materials into the mill brought along with it high fines content and a lot of anionic trash which readily reacts with cationic polymers. Consequently, the dosage must be increased which can lead to poor formation and increased chemical cost. A new retention aid was needed to combat these problems. Microparticle retention systems were developed by a group of papermakers, scientist, and process control experts in the late 1970\u27s. A dramatic improvement in retention and drainage was achieved, which allowed higher filler loading, increased machine speeds, and better formation. To this date, continuing research is being done on the improvement of microparticle retention aids as well as developing new retention aids. This paper deals with microparticle retention systems in a different way. Normally, the dosage of microparticle, anionic silica in this research, to the system is on a weight basis, i.e., pounds of microparticle per ton of paper. In this study, silica dosage will be done on a surface area basis. Silica particles have a very high specific surface area, which can range anywhere from around 500m2/g to 1200m2/g. Using this information and the typical dosage rate on a weight basis, a surface area dosage can be calculated. For example, 600m2/g X 1.0 lb./ton = 272,155m2/ton and 1200m2/g X 0.5lb./ton X 272,155m2/ton . Both give the same surface area dosage, but different only half of the weight basis dosage is needed for the high surface area silica. Therefore, the objective of this thesis is to test the hypothesis that equivalent retention will be obtained when equal surface area dosage is applied to the system. A two level, three variable factorial design was used to test the effects of surface area of microparticle, surface area dosage, and polymer dosage. Two different furnishes were used, a fine paper grade and a wood containing grade. Both grades are similar to those found in industry. All retention studies were carried out using a Britt Dynamic Drainage Jar. Percent fines and ash retention was measured. The results for the fine paper furnish showed no conclusive trends other than an effect of polymer dosage on fines retention. The variability in the system was extremely high. The wood containing furnish, however showed several promising results. Again, the polymer dosage was found to have a large effect on the system. There was an interaction between surface area dosage and polymer dosage. At low polymer dosages, the surface area dosage had an effect on retention, but at high polymer dosage, there was not an improved retention response as the surface area dosage increased. Finally, the wood containing furnish followed the hypothesis that equivalent retention will be obtained at equal surface area dosage. Many chemical suppliers pride themselves on the high surface area of their microparticle and the improved performance it offers. The results of this thesis show that this may not be exactly true. The dosage needed to get the same retention with a high surface area microparticle may be less, but not necessarily improved performance. If retention could be measured as a function of surface area added to the system per ton of paper, a mill could determine what is the most economical microparticle to use. For example, a supplier could supply a low surface area microparticle at a very low price, while the another supplier is offering a high surface area microparticle at an extremely high price. The mill would have to use a lot more of the low surface area microparticle to get the retention they want, but it sill may be more economical

Intervals of Permutations with a Fixed Number of Descents are Shellable

The set of all permutations, ordered by pattern containment, is a poset. We present an order isomorphism from the poset of permutations with a fixed number of descents to a certain poset of words with subword order. We use this bijection to show that intervals of permutations with a fixed number of descents are shellable, and we present a formula for the M\"obius function of these intervals. We present an alternative proof for a result on the M\"obius function of intervals $[1,\pi]$ such that $\pi$ has exactly one descent. We prove that if $\pi$ has exactly one descent and avoids 456123 and 356124, then the intervals $[1,\pi]$ have no nontrivial disconnected subintervals; we conjecture that these intervals are shellable