What Do Symmetries Tell Us About Structure?

Mathematicians, physicists, and philosophers of physics often look to the symmetries of an object for insight into the structure and constitution of the object. My aim in this paper is to explain why this practice is successful. In order to do so, I present a collection of results that are closely related to (and in a sense, generalizations of) Beth’s and Svenonius’ theorems

On the Structure of Classical Mechanics

Jill North (North, 2009) has recently argued that Hamiltonian mechanics ascribes less structure to the world than Lagrangian mechanics does. I will argue that North's argument is not sound. In doing so, I will present some obstacles that must be navigated by anyone interested in comparing the amounts of structure that different physical theories ascribe to the world

Advanced Message Routing for Scalable Distributed Simulations

The Joint Forces Command (JFCOM) Experimentation Directorate (J9)'s recent Joint Urban Operations (JUO) experiments have demonstrated the viability of Forces Modeling and Simulation in a distributed environment. The JSAF application suite, combined with the RTI-s communications system, provides the ability to run distributed simulations with sites located across the United States, from Norfolk, Virginia to Maui, Hawaii. Interest-aware routers are essential for communications in the large, distributed environments, and the current RTI-s framework provides such routers connected in a straightforward tree topology. This approach is successful for small to medium sized simulations, but faces a number of significant limitations for very large simulations over high-latency, wide area networks. In particular, traffic is forced through a single site, drastically increasing distances messages must travel to sites not near the top of the tree. Aggregate bandwidth is limited to the bandwidth of the site hosting the top router, and failures in the upper levels of the router tree can result in widespread communications losses throughout the system. To resolve these issues, this work extends the RTI-s software router infrastructure to accommodate more sophisticated, general router topologies, including both the existing tree framework and a new generalization of the fully connected mesh topologies used in the SF Express ModSAF simulations of 100K fully interacting vehicles. The new software router objects incorporate the scalable features of the SF Express design, while optionally using low-level RTI-s objects to perform actual site-to-site communications. The (substantial) limitations of the original mesh router formalism have been eliminated, allowing fully dynamic operations. The mesh topology capabilities allow aggregate bandwidth and site-to-site latencies to match actual network performance. The heavy resource load at the root node can now be distributed across routers at the participating sites

Morita Equivalence

Logicians and philosophers of science have proposed various formal criteria for theoretical equivalence. In this paper, we examine two such proposals: definitional equivalence and categorical equivalence. In order to show precisely how these two well-known criteria are related to one another, we investigate an intermediate criterion called Morita equivalence.Comment: 30 page

Mutual Translatability, Equivalence, and the Structure of Theories

This paper presents a simple pair of first-order theories that are not definitionally (nor Morita) equivalent, yet are mutually conservatively translatable and mutually 'surjectively' translatable. We use these results to clarify the overall geography of standards of equivalence and to show that the structural commitments that theories make behave in a more subtle manner than has been recognized

Fault tolerant quantum computation with very high threshold for loss errors

Many proposals for fault tolerant quantum computation (FTQC) suffer detectable loss processes. Here we show that topological FTQC schemes, which are known to have high error thresholds, are also extremely robust against losses. We demonstrate that these schemes tolerate loss rates up to 24.9%, determined by bond percolation on a cubic lattice. Our numerical results show that these schemes retain good performance when loss and computational errors are simultaneously present.Comment: 4 pages, comments still very welcome. v2 is a reasonable approximation to the published versio

Pipes and Connections

This document describes the low-level Pipe and ConnectionManager objects of the Mesh- Router system. The overall MeshRouter framework provides a general scheme for interest- limited communications among a number of client processes. This generality is achieved by a carefully factorized, object-oriented software implementation. Within this framework, the Pipe and ConnectionManager (base) classes dened in this note specify the interfaces for i) ac- tual `bits on the wire' communications and ii) dynamic client insertions during overall system execution. Two specic implementations of the Pipe class are described in detail: a `Memo- ryPipe' linking objects instanced on a single processor and a more general 'rtisPipe' providing inter-processor communications built entirely from the standard RTI-s library used in current JSAF applications. Initialization procedures within the overall MeshRouter system are dis- cussed, with particular attention given to dynamic management of inter-processor connections. Prototype RTI-s router processes are discussed, and simple extensions of the standard system conguration data les are presented

Extension, Translation, and the Cantor-Bernstein Property

The purpose of this paper is to examine in detail a particularly interesting pair of first-order theories. In addition to clarifying the overall geography of notions of equivalence between theories, this simple example yields two surprising conclusions about the relationships that theories might bear to one another. In brief, we see that theories lack both the Cantor-Bernstein and co-Cantor-Bernstein properties

ASSET, ACTIVITY, AND INCOME DIVERSIFICATION AMONG AFRICAN AGRICULTURALISTS: SOME PRACTICAL ISSUES

This paper starts from the premise that diversification of assets, activities, and incomes is important to African rural households, in that diversification into nonfarm income constitutes on average about 45 percent of incomes, and the push and pull factors driving that diversification are bound to persist. From that premise, we noted that the empirical study of diversification has been beset by practical problems and issues relating to (1) definitions and concepts, (2) data collection, and to (3) measurement of the nature and extent of diversification. The paper addressed each of those problems. Two points are of special interest to the overall conceptualization of diversification research. The first is that empirical studies have exhibited a wide variety - bordering on confusion - of systems of classification of assets, activities, and incomes as pertains to diversification behavior. We argued that the classification should conform to that used in standard practice of national accounts and macro input-output table construction, classifying activities into economic sectors that have standard definitions, and the classification of which does not depend on the location or functional type (wage- or self-employment) of the activity. We further argued that given a sectoral classification, it is useful to make a functional and locational categorization of the activity, and keep each of these three dimensions of the activity - sectoral, functional, and locational - separate and distinct so as to avoid confusion. The second is that it is useful to have an image of a production function in mind when analyzing the components of diversification behavior: (1) assets are the factors of production, representing the capacity of the household to diversify; (2) activities are the ex ante production flows of asset services; (3) incomes are the ex post flows of incomes, and it is crucial to note that the goods and services produced by activities need to be valued by prices, formed by markets at meso and macro levels, in order to be the measured outcomes called incomes. "Livelihoods" is a term used frequently in recent diversification research, and while its meaning differs somewhat over studies, it generally means household and community behavior, with respect to holdings and use of assets and the productive activities to which the assets are applied. The link between livelihoods and incomes needs to be made by valuing the output of livelihood activities at market (and/or virtual) prices. That valuation permits an analytical link between household/community behavior (thus a micro view of diversification) and the aggregate functioning of markets (thus a link with the meso and macro levels and the policies pertaining thereto).Agribusiness, O, Q12,