149,637 research outputs found
S-duality in Abelian gauge theory revisited
Definition of the partition function of U(1) gauge theory is extended to a
class of four-manifolds containing all compact spaces and certain
asymptotically locally flat (ALF) ones including the multi-Taub--NUT spaces.
The partition function is calculated via zeta-function regularization with
special attention to its modular properties. In the compact case, compared with
the purely topological result of Witten, we find a non-trivial curvature
correction to the modular weights of the partition function. But S-duality can
be restored by adding gravitational counter terms to the Lagrangian in the
usual way. In the ALF case however we encounter non-trivial difficulties
stemming from original non-compact ALF phenomena. Fortunately our careful
definition of the partition function makes it possible to circumnavigate them
and conclude that the partition function has the same modular properties as in
the compact case.Comment: LaTeX; 22 pages, no figure
Hierarchic Superposition Revisited
Many applications of automated deduction require reasoning in first-order
logic modulo background theories, in particular some form of integer
arithmetic. A major unsolved research challenge is to design theorem provers
that are "reasonably complete" even in the presence of free function symbols
ranging into a background theory sort. The hierarchic superposition calculus of
Bachmair, Ganzinger, and Waldmann already supports such symbols, but, as we
demonstrate, not optimally. This paper aims to rectify the situation by
introducing a novel form of clause abstraction, a core component in the
hierarchic superposition calculus for transforming clauses into a form needed
for internal operation. We argue for the benefits of the resulting calculus and
provide two new completeness results: one for the fragment where all
background-sorted terms are ground and another one for a special case of linear
(integer or rational) arithmetic as a background theory
Hierarchic Superposition Revisited
Many applications of automated deduction require reasoning in first-order logic modulo background theories, in particular some form of integer arithmetic. A major unsolved research challenge is to design theorem provers that are "reasonably complete" even in the presence of free function symbols ranging into a background theory sort. The hierarchic superposition calculus of Bachmair, Ganzinger, and Waldmann already supports such symbols, but, as we demonstrate, not optimally. This paper aims to rectify the situation by introducing a novel form of clause abstraction, a core component in the hierarchic superposition calculus for transforming clauses into a form needed for internal operation. We argue for the benefits of the resulting calculus and provide two new completeness results: one for the fragment where all background-sorted terms are ground and another one for a special case of linear (integer or rational) arithmetic as a background theory
The phase transition of the diffusive pair contact process revisited
The restricted diffusive pair contact process 2A->3A, 2A->0 (PCPD) and the
classification of its critical behavior continues to be a challenging open
problem of non-equilibrium statistical mechanics. Recently Kockelkoren and
Chate [Phys. Rev. Lett. 90, 125701 (2003)] suggested that the PCPD in one
spatial dimension represents a genuine universality class of non-equilibrium
phase transitions which differs from previously known classes. To this end they
introduced an efficient lattice model in which the number of particles per site
is unrestricted. In numerical simulations this model displayed clean power
laws, indicating ordinary critical behavior associated with certain non-trivial
critical exponents. In the present work, however, we arrive at a different
conclusion. Increasing the numerical effort, we find a slow drift of the
effective exponents which is of the same type as observed in previously studied
fermionic realizations. Analyzing this drift we discuss the possibility that
the asymptotic critical behavior of the PCPD may be governed by an ordinary
directed percolation fixed point.Comment: 6 pages, 1 figur
Improved polynomial chaos discretization schemes to integrate interconnects into design environments
Recently, an efficient stochastic modeling method for interconnects with inherent variability in their physical parameters was proposed, based on applying the so-called polynomial chaos (PC) approach in conjunction with a Stochastic Galerkin Method (SGM) onto telegrapher's equations. Although this approach was already very successful from a numerical point of view, the novel technique could not be conveniently integrated into SPICE-like solvers, limiting the applicability of the method. In this letter, the PC-SGM scheme for telegrapher's equations is revisited, pinpointing the origin of this inconvenience and immediately allowing to mitigate the issue. By adapting the traditional discretization of the stochastic telegrapher's equations approach, an augmented, yet deterministic, set of ordinary differential equations is obtained that turns out to be of the same type as the telegrapher's equations, and hence, the physical property of reciprocity is preserved. Consequently, it can be directly and more efficiently handled using SPICE-like solvers, which usually assume matrix symmetries. As an application example, the variability analysis of a state-of-the-art on-chip line for millimeter-wave applications is performed in a SPICE solver
Generalised Mersenne Numbers Revisited
Generalised Mersenne Numbers (GMNs) were defined by Solinas in 1999 and
feature in the NIST (FIPS 186-2) and SECG standards for use in elliptic curve
cryptography. Their form is such that modular reduction is extremely efficient,
thus making them an attractive choice for modular multiplication
implementation. However, the issue of residue multiplication efficiency seems
to have been overlooked. Asymptotically, using a cyclic rather than a linear
convolution, residue multiplication modulo a Mersenne number is twice as fast
as integer multiplication; this property does not hold for prime GMNs, unless
they are of Mersenne's form. In this work we exploit an alternative
generalisation of Mersenne numbers for which an analogue of the above property
--- and hence the same efficiency ratio --- holds, even at bitlengths for which
schoolbook multiplication is optimal, while also maintaining very efficient
reduction. Moreover, our proposed primes are abundant at any bitlength, whereas
GMNs are extremely rare. Our multiplication and reduction algorithms can also
be easily parallelised, making our arithmetic particularly suitable for
hardware implementation. Furthermore, the field representation we propose also
naturally protects against side-channel attacks, including timing attacks,
simple power analysis and differential power analysis, which is essential in
many cryptographic scenarios, in constrast to GMNs.Comment: 32 pages. Accepted to Mathematics of Computatio
In the Age of Web: Typed Functional-First Programming Revisited
Most programming languages were designed before the age of web. This matters
because the web changes many assumptions that typed functional language
designers take for granted. For example, programs do not run in a closed world,
but must instead interact with (changing and likely unreliable) services and
data sources, communication is often asynchronous or event-driven, and programs
need to interoperate with untyped environments.
In this paper, we present how the F# language and libraries face the
challenges posed by the web. Technically, this comprises using type providers
for integration with external information sources and for integration with
untyped programming environments, using lightweight meta-programming for
targeting JavaScript and computation expressions for writing asynchronous code.
In this inquiry, the holistic perspective is more important than each of the
features in isolation. We use a practical case study as a starting point and
look at how F# language and libraries approach the challenges posed by the web.
The specific lessons learned are perhaps less interesting than our attempt to
uncover hidden assumptions that no longer hold in the age of web.Comment: In Proceedings ML/OCaml 2014, arXiv:1512.0143
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