246 research outputs found
Matrix bandwidth and profile reduction
This program, REDUCE, reduces the bandwidth and profile of sparse symmetric matrices, using row and corresponding column permutations. It is a realization of the algorithm described by the authors elsewhere. It was extensively tested and compared with several other programs and was found to be considerably faster than the others, superior for bandwidth reduction and as satisfactory as any other for profile reduction
Spin-injection Hall effect in a planar photovoltaic cell
Successful incorporation of the spin degree of freedom in semiconductor
technology requires the development of a new paradigm allowing for a scalable,
non-destructive electrical detection of the spin-polarization of injected
charge carriers as they propagate along the semiconducting channel. In this
paper we report the observation of a spin-injection Hall effect (SIHE) which
exploits the quantum-relativistic nature of spin-charge transport and which
meets all these key requirements on the spin detection. The two-dimensional
electron-hole gas photo-voltaic cell we designed to observe the SIHE allows us
to develop a quantitative microscopic theory of the phenomenon and to
demonstrate its direct application in optoelectronics. We report an
experimental realization of a non-magnetic spin-photovoltaic effect via the
SIHE, rendering our device an electrical polarimeter which directly converts
the degree of circular polarization of light to a voltage signal.Comment: 14 pages, 4 figure
Probabilistic Model Counting with Short XORs
The idea of counting the number of satisfying truth assignments (models) of a
formula by adding random parity constraints can be traced back to the seminal
work of Valiant and Vazirani, showing that NP is as easy as detecting unique
solutions. While theoretically sound, the random parity constraints in that
construction have the following drawback: each constraint, on average, involves
half of all variables. As a result, the branching factor associated with
searching for models that also satisfy the parity constraints quickly gets out
of hand. In this work we prove that one can work with much shorter parity
constraints and still get rigorous mathematical guarantees, especially when the
number of models is large so that many constraints need to be added. Our work
is based on the realization that the essential feature for random systems of
parity constraints to be useful in probabilistic model counting is that the
geometry of their set of solutions resembles an error-correcting code.Comment: To appear in SAT 1
Descriptive Complexity of Deterministic Polylogarithmic Time and Space
We propose logical characterizations of problems solvable in deterministic
polylogarithmic time (PolylogTime) and polylogarithmic space (PolylogSpace). We
introduce a novel two-sorted logic that separates the elements of the input
domain from the bit positions needed to address these elements. We prove that
the inflationary and partial fixed point vartiants of this logic capture
PolylogTime and PolylogSpace, respectively. In the course of proving that our
logic indeed captures PolylogTime on finite ordered structures, we introduce a
variant of random-access Turing machines that can access the relations and
functions of a structure directly. We investigate whether an explicit predicate
for the ordering of the domain is needed in our PolylogTime logic. Finally, we
present the open problem of finding an exact characterization of
order-invariant queries in PolylogTime.Comment: Submitted to the Journal of Computer and System Science
Logics for Unranked Trees: An Overview
Labeled unranked trees are used as a model of XML documents, and logical
languages for them have been studied actively over the past several years. Such
logics have different purposes: some are better suited for extracting data,
some for expressing navigational properties, and some make it easy to relate
complex properties of trees to the existence of tree automata for those
properties. Furthermore, logics differ significantly in their model-checking
properties, their automata models, and their behavior on ordered and unordered
trees. In this paper we present a survey of logics for unranked trees
Randomisation and Derandomisation in Descriptive Complexity Theory
We study probabilistic complexity classes and questions of derandomisation
from a logical point of view. For each logic L we introduce a new logic BPL,
bounded error probabilistic L, which is defined from L in a similar way as the
complexity class BPP, bounded error probabilistic polynomial time, is defined
from PTIME. Our main focus lies on questions of derandomisation, and we prove
that there is a query which is definable in BPFO, the probabilistic version of
first-order logic, but not in Cinf, finite variable infinitary logic with
counting. This implies that many of the standard logics of finite model theory,
like transitive closure logic and fixed-point logic, both with and without
counting, cannot be derandomised. Similarly, we present a query on ordered
structures which is definable in BPFO but not in monadic second-order logic,
and a query on additive structures which is definable in BPFO but not in FO.
The latter of these queries shows that certain uniform variants of AC0
(bounded-depth polynomial sized circuits) cannot be derandomised. These results
are in contrast to the general belief that most standard complexity classes can
be derandomised. Finally, we note that BPIFP+C, the probabilistic version of
fixed-point logic with counting, captures the complexity class BPP, even on
unordered structures
Evaluating QBF Solvers: Quantifier Alternations Matter
We present an experimental study of the effects of quantifier alternations on
the evaluation of quantified Boolean formula (QBF) solvers. The number of
quantifier alternations in a QBF in prenex conjunctive normal form (PCNF) is
directly related to the theoretical hardness of the respective QBF
satisfiability problem in the polynomial hierarchy. We show empirically that
the performance of solvers based on different solving paradigms substantially
varies depending on the numbers of alternations in PCNFs. In related
theoretical work, quantifier alternations have become the focus of
understanding the strengths and weaknesses of various QBF proof systems
implemented in solvers. Our results motivate the development of methods to
evaluate orthogonal solving paradigms by taking quantifier alternations into
account. This is necessary to showcase the broad range of existing QBF solving
paradigms for practical QBF applications. Moreover, we highlight the potential
of combining different approaches and QBF proof systems in solvers.Comment: preprint of a paper to be published at CP 2018, LNCS, Springer,
including appendi
Composition with Target Constraints
It is known that the composition of schema mappings, each specified by
source-to-target tgds (st-tgds), can be specified by a second-order tgd (SO
tgd). We consider the question of what happens when target constraints are
allowed. Specifically, we consider the question of specifying the composition
of standard schema mappings (those specified by st-tgds, target egds, and a
weakly acyclic set of target tgds). We show that SO tgds, even with the
assistance of arbitrary source constraints and target constraints, cannot
specify in general the composition of two standard schema mappings. Therefore,
we introduce source-to-target second-order dependencies (st-SO dependencies),
which are similar to SO tgds, but allow equations in the conclusion. We show
that st-SO dependencies (along with target egds and target tgds) are sufficient
to express the composition of every finite sequence of standard schema
mappings, and further, every st-SO dependency specifies such a composition. In
addition to this expressive power, we show that st-SO dependencies enjoy other
desirable properties. In particular, they have a polynomial-time chase that
generates a universal solution. This universal solution can be used to find the
certain answers to unions of conjunctive queries in polynomial time. It is easy
to show that the composition of an arbitrary number of standard schema mappings
is equivalent to the composition of only two standard schema mappings. We show
that surprisingly, the analogous result holds also for schema mappings
specified by just st-tgds (no target constraints). This is proven by showing
that every SO tgd is equivalent to an unnested SO tgd (one where there is no
nesting of function symbols). Similarly, we prove unnesting results for st-SO
dependencies, with the same types of consequences.Comment: This paper is an extended version of: M. Arenas, R. Fagin, and A.
Nash. Composition with Target Constraints. In 13th International Conference
on Database Theory (ICDT), pages 129-142, 201
Multiparticle equations for interacting Dirac fermions in magnetically confined graphene quantum dots
We study the energy of quasi-particles in graphene within the Hartree-Fock approximation. The quasi-particles are confined via an inhomogeneous magnetic field and interact via the Coulomb potential. We show that the associated functional has a minimizer and determines the stability conditions for the N-particle problem in such a graphene quantum dot
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