6,036 research outputs found
Hilbert Lattice Equations
There are five known classes of lattice equations that hold in every infinite
dimensional Hilbert space underlying quantum systems: generalised
orthoarguesian, Mayet's E_A, Godowski, Mayet-Godowski, and Mayet's E equations.
We obtain a result which opens a possibility that the first two classes
coincide. We devise new algorithms to generate Mayet-Godowski equations that
allow us to prove that the fourth class properly includes the third. An open
problem related to the last class is answered. Finally, we show some new
results on the Godowski lattices characterising the third class of equations.Comment: 24 pages, 3 figure
Janus II: a new generation application-driven computer for spin-system simulations
This paper describes the architecture, the development and the implementation
of Janus II, a new generation application-driven number cruncher optimized for
Monte Carlo simulations of spin systems (mainly spin glasses). This domain of
computational physics is a recognized grand challenge of high-performance
computing: the resources necessary to study in detail theoretical models that
can make contact with experimental data are by far beyond those available using
commodity computer systems. On the other hand, several specific features of the
associated algorithms suggest that unconventional computer architectures, which
can be implemented with available electronics technologies, may lead to order
of magnitude increases in performance, reducing to acceptable values on human
scales the time needed to carry out simulation campaigns that would take
centuries on commercially available machines. Janus II is one such machine,
recently developed and commissioned, that builds upon and improves on the
successful JANUS machine, which has been used for physics since 2008 and is
still in operation today. This paper describes in detail the motivations behind
the project, the computational requirements, the architecture and the
implementation of this new machine and compares its expected performances with
those of currently available commercial systems.Comment: 28 pages, 6 figure
SUE: A Special Purpose Computer for Spin Glass Models
The use of last generation Programmable Electronic Components makes possible
the construction of very powerful and competitive special purpose computers. We
have designed, constructed and tested a three-dimensional Spin Glass model
dedicated machine, which consists of 12 identical boards. Each single board can
simulate 8 different systems, updating all the systems at every clock cycle.
The update speed of the whole machine is 217ps/spin with 48 MHz clock
frequency. A device devoted to fast random number generation has been developed
and included in every board. The on-board reprogrammability permits us to
change easily the lattice size, or even the update algorithm or the action. We
present here a detailed description of the machine and the first runs using the
Heat Bath algorithm.Comment: Submitted to Computer Physics Communications, 19 pages, 5 figures,
references adde
On Linear Information Systems
Scott's information systems provide a categorically equivalent, intensional
description of Scott domains and continuous functions. Following a well
established pattern in denotational semantics, we define a linear version of
information systems, providing a model of intuitionistic linear logic (a
new-Seely category), with a "set-theoretic" interpretation of exponentials that
recovers Scott continuous functions via the co-Kleisli construction. From a
domain theoretic point of view, linear information systems are equivalent to
prime algebraic Scott domains, which in turn generalize prime algebraic
lattices, already known to provide a model of classical linear logic
Shinren : Non-monotonic trust management for distributed systems
The open and dynamic nature of modern distributed systems and pervasive environments presents significant challenges to security management. One solution may be trust management which utilises the notion of trust in order to specify and interpret security policies and make decisions on security-related actions. Most trust management systems assume monotonicity where additional information can only result in the increasing of trust. The monotonic assumption oversimplifies the real world by not considering negative information, thus it cannot handle many real world scenarios. In this paper we present Shinren, a novel non-monotonic trust management system based on bilattice theory and the anyworld assumption. Shinren takes into account negative information and supports reasoning with incomplete information, uncertainty and inconsistency. Information from multiple sources such as credentials, recommendations, reputation and local knowledge can be used and combined in order to establish trust. Shinren also supports prioritisation which is important in decision making and resolving modality conflicts that are caused by non-monotonicity
Towards MKM in the Large: Modular Representation and Scalable Software Architecture
MKM has been defined as the quest for technologies to manage mathematical
knowledge. MKM "in the small" is well-studied, so the real problem is to scale
up to large, highly interconnected corpora: "MKM in the large". We contend that
advances in two areas are needed to reach this goal. We need representation
languages that support incremental processing of all primitive MKM operations,
and we need software architectures and implementations that implement these
operations scalably on large knowledge bases.
We present instances of both in this paper: the MMT framework for modular
theory-graphs that integrates meta-logical foundations, which forms the base of
the next OMDoc version; and TNTBase, a versioned storage system for XML-based
document formats. TNTBase becomes an MMT database by instantiating it with
special MKM operations for MMT.Comment: To appear in The 9th International Conference on Mathematical
Knowledge Management: MKM 201
The Parma Polyhedra Library: Toward a Complete Set of Numerical Abstractions for the Analysis and Verification of Hardware and Software Systems
Since its inception as a student project in 2001, initially just for the
handling (as the name implies) of convex polyhedra, the Parma Polyhedra Library
has been continuously improved and extended by joining scrupulous research on
the theoretical foundations of (possibly non-convex) numerical abstractions to
a total adherence to the best available practices in software development. Even
though it is still not fully mature and functionally complete, the Parma
Polyhedra Library already offers a combination of functionality, reliability,
usability and performance that is not matched by similar, freely available
libraries. In this paper, we present the main features of the current version
of the library, emphasizing those that distinguish it from other similar
libraries and those that are important for applications in the field of
analysis and verification of hardware and software systems.Comment: 38 pages, 2 figures, 3 listings, 3 table
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