253 research outputs found
The Power of Non-Determinism in Higher-Order Implicit Complexity
We investigate the power of non-determinism in purely functional programming
languages with higher-order types. Specifically, we consider cons-free programs
of varying data orders, equipped with explicit non-deterministic choice.
Cons-freeness roughly means that data constructors cannot occur in function
bodies and all manipulation of storage space thus has to happen indirectly
using the call stack.
While cons-free programs have previously been used by several authors to
characterise complexity classes, the work on non-deterministic programs has
almost exclusively considered programs of data order 0. Previous work has shown
that adding explicit non-determinism to cons-free programs taking data of order
0 does not increase expressivity; we prove that this - dramatically - is not
the case for higher data orders: adding non-determinism to programs with data
order at least 1 allows for a characterisation of the entire class of
elementary-time decidable sets.
Finally we show how, even with non-deterministic choice, the original
hierarchy of characterisations is restored by imposing different restrictions.Comment: pre-edition version of a paper accepted for publication at ESOP'1
An analysis of students\u27 perceptions of online multimedia tutorials to assist classroom instruction
Multimedia has become the new learning environment. As technology advances and becomes more prominent, traditional education needs to adapt and utilize all the benefits that can be achieved with computer-assisted instruction. Awareness of students\u27 attitudes toward multimedia-based education is critical in the evaluation of multimedia courses and development of multimedia-based curriculum. The purpose of this study was to examine students\u27 perceptions of multimedia-based instruction. Educational institutions are faced with the challenges of delivering valuable training options to meet the varying needs of students and staff; computer technology has become and will continually be integrated into the classroom to make learning easier, more successful and efficient. For this reason, the promotion and monitoring of positive attitudes towards multimedia-based instruction is critical.
Four courses were selected by the researcher for analysis because of their use of a multimedia learning environment. A29-item questionnaire was administered to 123 students to measure their attitudes towards online learning with multimedia tutorials. Students were segregated into groups based on their prior experience and analyzed using descriptive statistics (mean, median, mode, standard deviation and frequency) and an independent t test. The data collected from the survey answered questions pertaining to the benefit of additional online tutorials, learner independence, classroom autonomy, effect on their learning, and anxiety.
Based on the results of this study, the statistical analysis indicated there were significant differences at the \u3c.05 level between the two groups of students for each of the five hypotheses. Additionally, students\u27 attitudes on average were nearly half a point higher (M = 0.46) for those who had prior experience with multimedia in the classroom than students with no experience based on a Likert five-point scale. However, students\u27 attitudes were lower for students with prior experience (M = 2. 76, SD = 0. 77) over students without experience (M = 2.81, SD = 1.00) for the research question about whether students prefer online multimedia learning tutorials over traditional class handouts
Gravity-driven Lyα blobs from cold streams into galaxies
We use high-resolution cosmological hydrodynamical adaptive mesh refinement (AMR) simulations to predict the characteristics of Lyα emission from the cold gas streams that fed galaxies in massive haloes at high redshift. The Lyα luminosity in our simulations is powered by the release of gravitational energy as gas flows from the intergalactic medium into the halo potential wells. The ultraviolet UV background contributes only <20 per cent to the gas heating. The Lyα emissivity is due primarily to electron-impact excitation cooling radiation in gas at âŒ2 Ă 104 K. We calculate the Lyα emissivities assuming collisional ionization equilibrium at all gas temperatures. The simulated streams are self-shielded against the UV background, so photoionization and recombination contribute negligibly to the Lyα line formation. We produce theoretical maps of the Lyα surface brightnesses, assuming that âŒ85 per cent of the Lyα photons are directly observable. We do not consider transfer of the Lyα radiation, nor do we include the possible effects of internal sources of photoionization such as star-forming regions. Dust absorption is expected to obscure a small fraction of the luminosity in the streams. We find that typical haloes of mass Mv⌠1012-1013 Mâ at z⌠3 emit as Lyα blobs (LABs) with luminosities 1043-1044 erg sâ1. Most of the Lyα comes from the extended (50-100 kpc) narrow, partly clumpy, inflowing, cold streams of (1-5) Ă 104 K that feed the growing galaxies. The predicted LAB morphology is therefore irregular, with dense clumps and elongated extensions. The integrated area contained within surface brightness isophotes of 2 Ă 10â18 erg sâ1 cmâ2 arcsecâ2 is âŒ2-100 arcsec2, consistent with observations. The linewidth is expected to range from 102 to more than 103 km sâ1 with a large variance. The typical Lyα surface brightness profile is ârâ1.2 where r is the distance from the halo centre. Our simulated LABs are similar in luminosity, morphology and extent to the observed LABs, with distinct kinematic features. The predicted Lyα luminosity function is consistent with observations, and the predicted areas and linewidths roughly recover the observed scaling relations. This mechanism for producing LABs appears inevitable in many high-z galaxies, though it may work in parallel with other mechanisms. Some of the LABs may thus be regarded as direct detections of the cold streams that drove galaxy evolution at high
Tricritical Points in Random Combinatorics: the (2+p)-SAT case
The (2+p)-Satisfiability (SAT) problem interpolates between different classes
of complexity theory and is believed to be of basic interest in understanding
the onset of typical case complexity in random combinatorics. In this paper, a
tricritical point in the phase diagram of the random -SAT problem is
analytically computed using the replica approach and found to lie in the range
. These bounds on are in agreement with previous
numerical simulations and rigorous results.Comment: 7 pages, 1 figure, RevTeX, to appear in J.Phys.
Dynamical friction in constant density cores: a failure of the Chandrasekhar formula
Using analytic calculations and N-body simulations we show that in constant density (harmonic) cores, sinking satellites undergo an initial phase of very rapid (super-Chandrasekhar) dynamical friction, after which they experience no dynamical friction at all. For density profiles with a central power law profile, Ïârâα, the infalling satellite heats the background and causes α to decrease. For α < 0.5 initially, the satellite generates a small central constant density core and stalls as in the α= 0 case. We discuss some astrophysical applications of our results to decaying satellite orbits, galactic bars and mergers of supermassive black hole binaries. In a companion paper we show that a central constant density core can provide a natural solution to the timing problem for Fornax's globular cluster
Fast Scalable Construction of (Minimal Perfect Hash) Functions
Recent advances in random linear systems on finite fields have paved the way
for the construction of constant-time data structures representing static
functions and minimal perfect hash functions using less space with respect to
existing techniques. The main obstruction for any practical application of
these results is the cubic-time Gaussian elimination required to solve these
linear systems: despite they can be made very small, the computation is still
too slow to be feasible.
In this paper we describe in detail a number of heuristics and programming
techniques to speed up the resolution of these systems by several orders of
magnitude, making the overall construction competitive with the standard and
widely used MWHC technique, which is based on hypergraph peeling. In
particular, we introduce broadword programming techniques for fast equation
manipulation and a lazy Gaussian elimination algorithm. We also describe a
number of technical improvements to the data structure which further reduce
space usage and improve lookup speed.
Our implementation of these techniques yields a minimal perfect hash function
data structure occupying 2.24 bits per element, compared to 2.68 for MWHC-based
ones, and a static function data structure which reduces the multiplicative
overhead from 1.23 to 1.03
Resolving the timing problem of the globular clusters orbiting the Fornax dwarf galaxy
We re-investigate the old problem of the survival of the five globular
clusters orbiting the Fornax dwarf galaxy in both standard and modified
Newtonian dynamics. For the first time in the history of the topic, we use
accurate mass models for the Fornax dwarf, obtained through Jeans modelling of
the recently published line of sight velocity dispersion data, and we are also
not resigned to circular orbits for the globular clusters. Previously conceived
problems stem from fixing the starting distances of the globulars to be less
than half the tidal radius. We relax this constraint since there is absolutely
no evidence for it and show that the dark matter paradigm, with either cusped
or cored dark matter profiles, has no trouble sustaining the orbits of the two
least massive globular clusters for a Hubble time almost regardless of their
initial distance from Fornax. The three most massive globulars can remain in
orbit as long as their starting distances are marginally outside the tidal
radius. The outlook for modified Newtonian dynamics is also not nearly as bleak
as previously reported. Although dynamical friction inside the tidal radius is
far stronger in MOND, outside dynamical friction is negligible due to the
absence of stars. This allows highly radial orbits to survive, but more
importantly circular orbits at distances more than 85% of Fornax's tidal radius
to survive indefinitely. The probability of the globular clusters being on
circular orbits at this distance compared with their current projected
distances is discussed and shown to be plausible. Finally, if we ignore the
presence of the most massive globular (giving it a large line of sight
distance) we demonstrate that the remaining four globulars can survive within
the tidal radius for the Hubble time with perfectly sensible orbits.Comment: 8 pages, 10 figures, 1 table, MNRAS in pres
Phase coexistence and finite-size scaling in random combinatorial problems
We study an exactly solvable version of the famous random Boolean
satisfiability problem, the so called random XOR-SAT problem. Rare events are
shown to affect the combinatorial ``phase diagram'' leading to a coexistence of
solvable and unsolvable instances of the combinatorial problem in a certain
region of the parameters characterizing the model. Such instances differ by a
non-extensive quantity in the ground state energy of the associated diluted
spin-glass model. We also show that the critical exponent , controlling
the size of the critical window where the probability of having solutions
vanishes, depends on the model parameters, shedding light on the link between
random hyper-graph topology and universality classes. In the case of random
satisfiability, a similar behavior was conjectured to be connected to the onset
of computational intractability.Comment: 10 pages, 5 figures, to appear in J. Phys. A. v2: link to the XOR-SAT
probelm adde
Cluster expansions in dilute systems: applications to satisfiability problems and spin glasses
We develop a systematic cluster expansion for dilute systems in the highly
dilute phase. We first apply it to the calculation of the entropy of the
K-satisfiability problem in the satisfiable phase. We derive a series expansion
in the control parameter, the average connectivity, that is identical to the
one obtained by using the replica approach with a replica symmetric ({\sc rs})
{\it Ansatz}, when the order parameter is calculated via a perturbative
expansion in the control parameter. As a second application we compute the
free-energy of the Viana-Bray model in the paramagnetic phase. The cluster
expansion allows one to compute finite-size corrections in a simple manner and
these are particularly important in optimization problems. Importantly enough,
these calculations prove the exactness of the {\sc rs} {\it Ansatz} below the
percolation threshold and might require its revision between this and the
easy-to-hard transition.Comment: 21 pages, 7 figs, to appear in Phys. Rev.
Simplest random K-satisfiability problem
We study a simple and exactly solvable model for the generation of random
satisfiability problems. These consist of random boolean constraints
which are to be satisfied simultaneously by logical variables. In
statistical-mechanics language, the considered model can be seen as a diluted
p-spin model at zero temperature. While such problems become extraordinarily
hard to solve by local search methods in a large region of the parameter space,
still at least one solution may be superimposed by construction. The
statistical properties of the model can be studied exactly by the replica
method and each single instance can be analyzed in polynomial time by a simple
global solution method. The geometrical/topological structures responsible for
dynamic and static phase transitions as well as for the onset of computational
complexity in local search method are thoroughly analyzed. Numerical analysis
on very large samples allows for a precise characterization of the critical
scaling behaviour.Comment: 14 pages, 5 figures, to appear in Phys. Rev. E (Feb 2001). v2: minor
errors and references correcte
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