Thomas Decomposition of Algebraic and Differential Systems

In this paper we consider disjoint decomposition of algebraic and non-linear partial differential systems of equations and inequations into so-called simple subsystems. We exploit Thomas decomposition ideas and develop them into a new algorithm. For algebraic systems simplicity means triangularity, squarefreeness and non-vanishing initials. For differential systems the algorithm provides not only algebraic simplicity but also involutivity. The algorithm has been implemented in Maple

Laver and set theory

In this commemorative article, the work of Richard Laver is surveyed in its full range and extent.Accepted manuscrip

Where Graph Topology Matters: The Robust Subgraph Problem

Robustness is a critical measure of the resilience of large networked systems, such as transportation and communication networks. Most prior works focus on the global robustness of a given graph at large, e.g., by measuring its overall vulnerability to external attacks or random failures. In this paper, we turn attention to local robustness and pose a novel problem in the lines of subgraph mining: given a large graph, how can we find its most robust local subgraph (RLS)? We define a robust subgraph as a subset of nodes with high communicability among them, and formulate the RLS-PROBLEM of finding a subgraph of given size with maximum robustness in the host graph. Our formulation is related to the recently proposed general framework for the densest subgraph problem, however differs from it substantially in that besides the number of edges in the subgraph, robustness also concerns with the placement of edges, i.e., the subgraph topology. We show that the RLS-PROBLEM is NP-hard and propose two heuristic algorithms based on top-down and bottom-up search strategies. Further, we present modifications of our algorithms to handle three practical variants of the RLS-PROBLEM. Experiments on synthetic and real-world graphs demonstrate that we find subgraphs with larger robustness than the densest subgraphs even at lower densities, suggesting that the existing approaches are not suitable for the new problem setting.Comment: 13 pages, 10 Figures, 3 Tables, to appear at SDM 2015 (9 pages only

A Network of Experience: Community Building and Social Restructuring in Fluxus

My thesis argues that the group dynamic of Fluxus and the artwork produced by the group functioned as agents in the cultivation and maintenance of a Fluxus community that developed an experimental, object-based approach to societal formation. I argue that a primary goal of Fluxus was to use their artistic production and their association to establish alternative modes of social interaction that were simultaneously plagiarizing and criticizing conventional social and political institutions

What\u27s So Special About Kruskal\u27s Theorem and the Ordinal \u3cem\u3eT\u3c/em\u3e\u3csub\u3eo\u3c/sub\u3e? A Survey of Some Results in Proof Theory

This paper consists primarily of a survey of results of Harvey Friedman about some proof theoretic aspects of various forms of Krusal\u27s tree theorem, and in particular the connection with the ordinal Ƭo. We also include a fairly extensive treatment of normal functions on the countable ordinals, and we give a glimpse of Veblen Hierarchies, some subsystems of second-order logic, slow-growing and fast-growing hierarchies including Girard\u27s result, and Goodstein sequences. The central theme of this paper is a powerful theorem due to Kruskal, the tree theorem , as well as a finite miniaturization of Kruskal\u27s theorem due to Harvey Friedman. These versions of Kruskal\u27s theorem are remarkable from a proof-theoretic point of view because they are not provable in relatively strong logical systems. They are examples of so-called natural independence phenomena , which are considered by more logicians as more natural than the mathematical incompleteness results first discovered by Gödel. Kruskal\u27s tree theorem also plays a fundamental role in computer science, because it is one of the main tools for showing that certain orderings on trees are well founded. These orderings play a crucial role in proving the termination of systems of rewrite rules and the correctness of Knuth-Bandix completion procedures. There is also a close connection between a certain infinite countable ordinal called Ƭoand Kruskal\u27s theorem. Previous definitions of the function involved in this connection are known to be incorrect, in that, the function is not monotonic. We offer a repaired definition of this function, and explore briefly the consequences of its existence

Corporeal Analysis: The Performing Body as Analytic Site

A framework of corporeal analysis posits that the physicality of the performer can be construed as a primary analytical parameter in a work. This dissertation seeks to set up such a method of analysis largely through anecdata and autoethnography with the aim of eliciting a deeper space for additional performer-driven analyses that prioritize the bodily knowledge of performers and their physical understandings of a work. Centering around David Bird’s 2013 work for solo piccolo and “no-less-than twenty-nine spatialized piccolos,” Atolls, three main aspects of corporeal analysis will be explored. These are: performance physicality as expressive connective tissue between flutist and audience, the construction of hypothetical geographic and atmospheric conditions implied within a work through the body as a barometer, and the sounds of pain and trauma activated through the physicality of sonic and metaphorical aspects of the work. An extended conclusion applies offshoots of these modes of analysis to Brian Ferneyhough’s solo work from the contemporary canon, Cassandra’s Dream Song through a study of salivary sounds in the work, and Bethany Younge’s Oxygen and Reality for piccolo, electronics, balloons, and lights through an exploration of prosthesis and adaptive technologies in performance

Who Shapes the Text?: Sherpas and Sahibs on Mount Everest

Also CSST Working Paper #56.http://deepblue.lib.umich.edu/bitstream/2027.42/51213/1/446.pd

Sing to the Lord a new song : Memory, Music, Epistemology, and the Emergence of Gregorian Chant as Corporate Knowledge

Following the Christianization of the crumbling Roman Empire, a wide array of disparate Christian traditions arose. A confusion of liturgical rites and musical styles expressed the diversity of this nascent Christendom; however, it also exemplified a sometimes threatening disunity. Into this frame, the Carolingian Empire made a decisive choice. Charlemagne, with a desire to consolidate power, forged stronger bonds withRome by transporting the liturgy ofRome to the Frankish North. The outcome of this transmission was the birth of a composite form of music exhibiting the liturgical properties ofRome but also shaped by the musical sensibilities of the Franks—Gregorian chant. This Frankish project of liturgical adoption and the appearance of Gregorian chant raises two important questions: How did the Carolingians transmit and incorporate Roman chant, and why did they feel drawn to this tradition in the first place? This thesis utilizes musicological studies by scholars like Leo Treitler and Anna Maria Busse Burger, epistemological arguments by analytic philosopher Richard Fumerton, and memorial scholarship by Mary Carruthers and Maurice Halbwachs to provide an analysis of Gregorian chant’s emergence. My investigation into the medieval art of memoria reveals that chant was transmitted through the use of the principles of music theory as mnemonic devices. Modal theory itself becomes a mnemonic by creating an abstract musical location in which the singer and listener can meet. Further, the impulse that drove this project was the desire for a collective memory that would resolve underlying tensions of group identity within 8th- and 9th-century early Christendom. This desire finds its resolution in modal theory itself because the musical location of chant is also a public location where corporate identity is articulated. Finally, I interpret both musical and memorial functions of chant via epistemic scholarship, showing that they both exhibit a remarkable structural similarity to the principles of acquaintance epistemology, thus unifying the questions of “how” and “why” in chant into a single answer. The quest for self-knowledge becomes part of the particular object used to make it—a material testament to a way of knowing

Special Libraries, July-August 1962

Volume 53, Issue 6https://scholarworks.sjsu.edu/sla_sl_1962/1005/thumbnail.jp