An Abstraction of Whitney's Broken Circuit Theorem

We establish a broad generalization of Whitney's broken circuit theorem on the chromatic polynomial of a graph to sums of type $\sum_{A\subseteq S} f(A)$ where $S$ is a finite set and $f$ is a mapping from the power set of $S$ into an abelian group. We give applications to the domination polynomial and the subgraph component polynomial of a graph, the chromatic polynomial of a hypergraph, the characteristic polynomial and Crapo's beta invariant of a matroid, and the principle of inclusion-exclusion. Thus, we discover several known and new results in a concise and unified way. As further applications of our main result, we derive a new generalization of the maximums-minimums identity and of a theorem due to Blass and Sagan on the M\"obius function of a finite lattice, which generalizes Rota's crosscut theorem. For the classical M\"obius function, both Euler's totient function and its Dirichlet inverse, and the reciprocal of the Riemann zeta function we obtain new expansions involving the greatest common divisor resp. least common multiple. We finally establish an even broader generalization of Whitney's broken circuit theorem in the context of convex geometries (antimatroids).Comment: 18 page

The Fractal Geometry of Invention

Fractals are geometric objects of inexhaustible detail. Fractal structures have been found in the contours of mountain ranges, the patterns of veins on a leaf, and the fluctuations of the Dow Jones Industrial Average. The endeavor of inventing new technologies, consisting of a hierarchical network of practical inquiries, exhibits fractal properties as well. Among these are multiplicity, latency, and self-similarity. Multiplicity means that a single inventive idea may lead to an immense and diverse array of technological artifacts. Latency means that the potential of an inventive idea to yield practical embodiments only reveals itself in time, and may never be fully known. Self-similarity means that invention is not scale-dependent; in other words, breakthroughs and refinements may be difficult, in principle, to distinguish. Invention, as a whole, resembles an ever-expanding fractal island of promontory upon promontory. Patent law assigns a particular inventor legal rights to a portion of that intricate coastline. The fractal properties of multiplicity, latency, and self-similarity contribute to many of the perennial difficulties in patent law, including fixing the meaning of claim language, properly applying the enablement and written description requirements, and identifying “abstract ideas” that cannot be patented. Understanding the fractal properties of invention is an important step in addressing these issues

The Poetry of Logical Ideas: Towards a Mathematical Genealogy of Media Art

In this dissertation I chart a mathematical genealogy of media art, demonstrating that mathematical thought has had a significant influence on contemporary experimental moving image production. Rather than looking for direct cause and effect relationships between mathematics and the arts, I will instead examine how mathematical developments have acted as a cultural zeitgeist, an indirect, but significant, influence on the humanities and the arts. In particular, I will be narrowing the focus of this study to the influence mathematical thought has had on cinema (and by extension media art), given that mathematics lies comfortably between the humanities and sciences, and that cinema is the object par excellence of such a study, since cinema and media studies arrived at a time when the humanities and sciences were held by many to be mutually exclusive disciplines. It is also shown that many media scholars have been implicitly engaging with mathematical concepts without necessarily recognizing them as such. To demonstrate this, I examine many concepts from media studies that demonstrate or derive from mathematical concepts. For instance, Claude Shannon's mathematical model of communication is used to expand on Stuart Hall's cultural model, and the mathematical concept of the fractal is used to expand on Rosalind Krauss' argument that video is a medium that lends itself to narcissism. Given that the influence of mathematics on the humanities and the arts often occurs through a misuse or misinterpretation of mathematics, I mobilize the concept of a productive misinterpretation and argue that this type of misreading has the potential to lead to novel innovations within the humanities and the arts. In this dissertation, it is also established that there are many mathematical concepts that can be utilized by media scholars to better analyze experimental moving images. In particular, I explore the mathematical concepts of symmetry, infinity, fractals, permutations, the Axiom of Choice, and the algorithmic to moving images works by Hollis Frampton, Barbara Lattanzi, Dana Plays, T. Marie, and Isiah Medina, among others. It is my desire that this study appeal to scientists with an interest in cinema and media art, and to media theorists with an interest in experimental cinema and other contemporary moving image practices

Virtual articulation and kinematic abstraction in robotics

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2009.Cataloged from PDF version of thesis.Includes bibliographical references (p. 279-292).This thesis presents the theory, implementation, novel applications, and experimental validation of a general-purpose framework for applying virtual modifications to an articulated robot, or virtual articulations. These can homogenize various aspects of a robot and its task environment into a single unified model which is both qualitatively high-level and quantitatively functional. This is the first framework designed specifically for the mixed real/virtual case. It supports arbitrary topology spatial kinematics, a broad catalog of joints, on-line structure changes, interactive kinostatic simulation, and novel kinematic abstractions, where complex subsystems are simplified with virtual replacements in both space and time. Decomposition algorithms, including a novel method of hierarchical subdivision, enable scaling to large closed-chain mechanisms with 100s of joints. Novel applications are presented in two areas of current interest: operating high- DoF kinematic manipulation and inspection tasks, and analyzing reliable kinostatic locomotion strategies based on compliance and proprioception. In both areas virtual articulations homogeneously model the robot and its task environment, and abstractions structure complex models. For high-DoF operations the operator attaches virtual joints as a novel interface metaphor to define task motion and to constrain coordinated motion (by virtually closing kinematic chains); virtual links can represent task frames or serve as intermediate connections for virtual joints. For compliant locomotion, virtual articulations model relevant compliances and uncertainties, and temporal abstractions model contact state evolution.(cont.) Results are presented for experiments with two separate robotic systems in each area. For high-DoF operations, NASA/JPL's 36 DoF ATHLETE performs previously challenging coordinated manipulation/inspection moves, and a novel large-scale (100s of joints) simulated modular robot is conveniently operated using spatial abstractions. For compliant locomotion, two experiments are analyzed that each achieve high reliability in uncertain tasks using only compliance and proprioception: a novel vertical structure climbing robot that is 99.8% reliable in over 1000 motions, and a mini-humanoid that steps up an uncertain height with 90% reliability in 80 trials. In both cases virtual articulation models capture the essence of compliant/proprioceptive strategies at a higher level than basic physics, and enable quantitative analyses of the limits of tolerable uncertainty that compare well to experiment.by Marsette Arthur Vona, III.Ph.D

Without a parallel: reasons for the expansion of early American Methodism (1767 through 1812)

https://place.asburyseminary.edu/ecommonsatsdissertations/1681/thumbnail.jp

Hostility or tolerance? Philosophy, polyphony and the novels of Thomas Pynchon

This thesis undertakes a systematic, tripartite analysis of the interactions between the fiction and essays of Thomas Pynchon and the philosophy of Ludwig Wittgenstein, Michel Foucault and Theodor W. Adorno, resulting in a solid set of original reference-material for those undertaking work on Pynchon and philosophy, or more generally on philosophico-literary intersections. Premised upon the notion that Pynchon's literature harbours a fundamental hostility to much systematizing philosophical thought, this work avoids a dominating imposition of philosophy, or an application of philosophical thought as a validating Other, by examining those aspects of Pynchon's work that seem ill at ease with, or aggressive towards, aspects of each philosopher's thought. This is explored through the concept of an intra-textual polyvocality and relational situation of philosophical intersection; when Wittgenstein is cited, for instance, who is speaking and what are the connotations of that placement? I do not propose, therefore, a Wittgensteinian / Foucauldian / Adornian Pynchon, but rather explicitly highlight excluded aspects of thought to instead develop a complementary reading; a form of intersubjective triangulation. This polyvocality is examined from a univocal perspective. The specific conclusions of this work re-situate Pynchon, in many cases against forty years of critical consensus, as a quasi-materialist or at least anti-idealist, a regulative utopist and a practitioner of an anti-synthetic style akin to Adorno's model of negative dialectics. In a broader sense, it answers the questions regarding hostility towards philosophical thought in Pynchon's work by demonstrating that no single philosophical standpoint has yet to totally resonate with even one of his novels. Simultaneously, it also shows that a profitable approach can be found in the spaces of philosophical overlap and divergence

Hierarchy in industry architecture : transaction strategy under technological constraints

Thesis (Ph. D.)--Massachusetts Institute of Technology, Engineering Systems Division, 2010.Cataloged from PDF version of thesis.Includes bibliographical references (p. 154-163).Motivation -- Industrial firms survive, sustain and co-evolve by participating in the sector of innovation and production through industrial transactions with each other. However, it is difficult for specialized firms to be aware of and manage accordingly the kind of systemic constraints and opportunities induced by relevant but indirect transactions, as well as the technological and economic requirements of their value chains, which they cannot control or even sufficiently observe. The myopia may cause specialized firms to implement incorrect strategies, leave them vulnerable to system failures or ignorant of emerging opportunities. This implies a paradox: the simultaneous needs to specialize and to understand and manage the big picture of the eco-system. Goal -- Previous industry studies have focused on the question if a transaction with an external firm is needed rather than in-house production, and on empirical work from single industries or bilateral relationships between firms. Meanwhile, the firms' positions in the sectoral transactional network are also influential to the success and performance of firms. In this dissertation, I conduct transactional network analysis to explore how firms are organized in the sector of aggregated industries, in order to shed light on the set of previously ignored knowledge on industrial transactions, which is valuable to single firms in designing strategies and managing operations but is not available from firm- and industry-level analysis. Hierarchy in Industry Architecture -- At the sector level, existing theories often assumed hierarchical or non-hierarchical relationships among industrial firms, and quantitative evidence on variable degrees of hierarchy in industry sectors is lacking. This dissertation first identifies and defines the type of hierarchy relevant to industry studies -flow hierarchy, develops a network-based metric on the degree of hierarchy (one-way flow of transactions), and applies it to the transaction data from two industrial sectors in Japan. The empirical results show that the electronics sector exhibits a significantly lower degree of hierarchy than the automotive sector due to the presence of many transaction cycles. It shows that the simplistic hierarchy hypothesis for production sectors does not always hold. Industrial Network Model and Transaction Specificity -- I further create a network simulation model with random networks to relate sector-level hierarchy degrees to firm-level behavioral variables, and infer transaction specificity, i.e. the extent to which a firm is captive to a niche of customers positioned closely in the industrial network hierarchy. The model builds on three basic rules on market structures, i.e. hierarchy, niche, and the mapping relationship between roles and positions. Transaction specificity provides a way to quantify the tendency of a firm to fix or institutionalize its role according to its relative network position, or where the transactions of a firm are oriented in the value chains, whereas traditional studies analyze whether a transaction versus in-house production is needed. The result shows that transaction specificity in the electronics sector is quantitatively much lower than that in the automotive sector. Interviews and Firm Boundary Strategies -- I further conducted interviews with nine firms in the two sectors and found that, with decision rationales related to product modularity, innovation dynamics and asset specificity, the major electronics firms take the permeable vertical boundary strategy and diversified horizontal boundary strategy, which decrease transaction specificity so that many transaction cycles emerge in the electronics sector. My analysis shows the permeability of a firm's vertical boundary, i.e. playing multiple value chain roles, is the necessary condition for transaction cycles to emerge. Meanwhile, these two strategies are not feasible in the automotive sector according to interviews. They are also not observed in the American electronics sector. My data show the American electronics firms tend to be vertically specialized in the value chains. Social-Technical Arguments -- Linking network analysis results, interview data, and the prior work on the physical limits to product modularity, I argue that higher power level of a sector's technologies leads to higher transaction specificity, and more hierarchical transaction lows across the sector. High power technologies constrain strategic transaction choices, while lower power technologies enable a larger option space of transaction strategies, for companies to explore and exploit. Implications -- For academics, the use of network analysis permits transaction cost analysis, or more general analysis of transaction-related decisions, to be extended from the boundary of a firm to the architecture of a sector comprising related industries. It gives us a bird's-eye view to observe firm-level transaction behaviors and create new knowledge on transaction specificity. In addition, the analysis of the physical properties of product technologies allows us to interpret the difference in transaction specificities and hierarchy degrees of different sectors, which economic and sociology theories cannot explain. For industry practitioners, this research suggests that firms' choices for industrial transactions are under some predictable constraints from product technologies. A better understanding of the linkages between industry architecture, firm transaction strategy, and product technology, in turn can guide companies to tailor transaction strategies to implicit technological constraints and to adequately explore strategic options made feasible by technologies.by Jianxi Luo.Ph.D

Annual report of the Board of Regents of the Smithsonian Institution, showing the operations, expenditures, and condition of the institution for the year 1863.

Annual Report of the Smithsonian Institution. 28 June. HMD 83, 38-1, v4, 416p. [1201] Research related to the American Indian; North American archaeology; aboriginal inhabitants of the Californian peninsula

Fourth Annual Workshop on Space Operations Applications and Research (SOAR 90)

The proceedings of the SOAR workshop are presented. The technical areas included are as follows: Automation and Robotics; Environmental Interactions; Human Factors; Intelligent Systems; and Life Sciences. NASA and Air Force programmatic overviews and panel sessions were also held in each technical area