On the (co)homology of the poset of weighted partitions

We consider the poset of weighted partitions $\Pi_n^w$, introduced by Dotsenko and Khoroshkin in their study of a certain pair of dual operads. The maximal intervals of $\Pi_n^w$ provide a generalization of the lattice $\Pi_n$ of partitions, which we show possesses many of the well-known properties of $\Pi_n$. In particular, we prove these intervals are EL-shellable, we show that the M\"obius invariant of each maximal interval is given up to sign by the number of rooted trees on on node set $\{1,2,\dots,n\}$ having a fixed number of descents, we find combinatorial bases for homology and cohomology, and we give an explicit sign twisted $\mathfrak{S}_n$-module isomorphism from cohomology to the multilinear component of the free Lie algebra with two compatible brackets. We also show that the characteristic polynomial of $\Pi_n^w$ has a nice factorization analogous to that of $\Pi_n$.Comment: 50 pages, final version, to appear in Trans. AM

The Myrtles : Les Myrtes

https://digitalcommons.library.umaine.edu/mmb-ps/2302/thumbnail.jp

Seeing Beyond: Real-time Ultrasound Image Integration in Augmented Reality Based Telementoring

Ultrasound imaging, when aptly integrated with augmented reality based medical telementoring, may be beneficial as an assistive tool in a range of trauma procedures including removal of foreign objects from blast injuries and central or peripheral venous access. Expected benefits include reduced procedure completion time, higher efficiency, and higher incision accuracy. This paper describes the implementation strategy selected for the integration of real time ultrasound imaging in the trainee view of a telementoring system. The proposed strategy augments the view of the trainee surgeon by displaying the ultrasound image directly below and parallel to the ultrasound transducer. The developed system features a fiducial marker based tracking approach employing a triplanar geometric fixture. An experiment was designed to demonstrate the system function and validate its performance

Real-Time Hand Shape Classification

The problem of hand shape classification is challenging since a hand is characterized by a large number of degrees of freedom. Numerous shape descriptors have been proposed and applied over the years to estimate and classify hand poses in reasonable time. In this paper we discuss our parallel framework for real-time hand shape classification applicable in real-time applications. We show how the number of gallery images influences the classification accuracy and execution time of the parallel algorithm. We present the speedup and efficiency analyses that prove the efficacy of the parallel implementation. Noteworthy, different methods can be used at each step of our parallel framework. Here, we combine the shape contexts with the appearance-based techniques to enhance the robustness of the algorithm and to increase the classification score. An extensive experimental study proves the superiority of the proposed approach over existing state-of-the-art methods.Comment: 11 page

Five-Torsion in the Homology of the Matching Complex on 14 Vertices

J. L. Andersen proved that there is 5-torsion in the bottom nonvanishing homology group of the simplicial complex of graphs of degree at most two on seven vertices. We use this result to demonstrate that there is 5-torsion also in the bottom nonvanishing homology group of the matching complex $M_{14}$ on 14 vertices. Combining our observation with results due to Bouc and to Shareshian and Wachs, we conclude that the case $n=14$ is exceptional; for all other $n$, the torsion subgroup of the bottom nonvanishing homology group has exponent three or is zero. The possibility remains that there is other torsion than 3-torsion in higher-degree homology groups of $M_n$ when $n \ge 13$ and $n \neq 14$.Comment: 11 page

Nature of catalytically active sites in the supported WO3/ZrO2 solid acid system: a current perspective

Tungstated zirconia (WO3/ZrO2) is one of the most well-studied solid acid catalyst systems and continues to attract the attention of both academia and industry. Understanding and controlling the properties of WO3/ZrO2 catalysts has been a topic of considerable interest over almost the past three decades, with a particular focus on discovering the relationship between catalytic activity and the molecular structure of the surface acid site. Amorphous tungsten oxide (WOx) species on ZrO2 surfaces were previously proposed to be very active for different acidic reactions such as alcohol dehydration and alkane isomerization. Recent developments in electron optical characterization and in situ spectroscopy techniques have allowed researchers to isolate the size, structure, and composition of the most active catalytic species, which are shown to be three-dimensional distorted Zr-WOx clusters (0.8–1.0 nm). Complementary theoretical calculations of the Brønsted acidity of these Zr-WOx clusters have confirmed that they possess the lowest deprotonation energy values. This new insight provides a foundation for the future characterization and theory of acidic supported metal oxide catalytic materials that will, hopefully, lead to the design of more active and selective catalysts. This perspective presents an up-to-date, comprehensive summary of the leading models of WO3/ZrO2 solid acid catalysts

Weighted partitions

In this extended abstract we consider the poset of weighted partitions Π _n^w, introduced by Dotsenko and Khoroshkin in their study of a certain pair of dual operads. The maximal intervals of Π _n^w provide a generalization of the lattice Π _n of partitions, which we show possesses many of the well-known properties of Π _n. In particular, we prove these intervals are EL-shellable, we compute the Möbius invariant in terms of rooted trees, we find combinatorial bases for homology and cohomology, and we give an explicit sign twisted S_n-module isomorphism from cohomology to the multilinear component of the free Lie algebra with two compatible brackets. We also show that the characteristic polynomial of Π _n^w has a nice factorization analogous to that of Π _n

Extracellular Matrix Disparities in an \u3ci\u3eNkx2-5\u3c/i\u3e Mutant Mouse Model of Congenital Heart Disease

Congenital heart disease (CHD) affects almost one percent of all live births. Despite diagnostic and surgical reparative advances, the causes and mechanisms of CHD are still primarily unknown. The extracellular matrix plays a large role in cell communication, function, and differentiation, and therefore likely plays a role in disease development and pathophysiology. Cell adhesion and gap junction proteins, such as integrins and connexins, are also essential to cellular communication and behavior, and could interact directly (integrins) or indirectly (connexins) with the extracellular matrix. In this work, we explore disparities in the expression and spatial patterning of extracellular matrix, adhesion, and gap junction proteins between wild type and Nkx2-5+/R52G mutant mice. Decellularization and proteomic analysis, Western blotting, histology, immunostaining, and mechanical assessment of embryonic and neonatal wild type and Nkx2-5 mutant mouse hearts were performed. An increased abundance of collagen IV, fibronectin, and integrin β-1 was found in Nkx2-5 mutant neonatal mouse hearts, as well as increased expression of connexin 43 in embryonic mutant hearts. Furthermore, a ventricular noncompaction phenotype was observed in both embryonic and neonatal mutant hearts, as well as spatial disorganization of ECM proteins collagen IV and laminin in mutant hearts. Characterizing such properties in a mutant mouse model provides valuable information that can be applied to better understanding the mechanisms of congenital heart disease

Normal Ordering for Deformed Boson Operators and Operator-valued Deformed Stirling Numbers

The normal ordering formulae for powers of the boson number operator $\hat{n}$ are extended to deformed bosons. It is found that for the `M-type' deformed bosons, which satisfy $a a^{\dagger} - q a^{\dagger} a = 1$, the extension involves a set of deformed Stirling numbers which replace the Stirling numbers occurring in the conventional case. On the other hand, the deformed Stirling numbers which have to be introduced in the case of the `P-type' deformed bosons, which satisfy $a a^{\dagger} - q a^{\dagger} a = q^{-\hat{n}}$, are found to depend on the operator $\hat{n}$. This distinction between the two types of deformed bosons is in harmony with earlier observations made in the context of a study of the extended Campbell-Baker-Hausdorff formula.Comment: 14 pages, Latex fil