1,087 research outputs found
New Finite Rogers-Ramanujan Identities
We present two general finite extensions for each of the two Rogers-Ramanujan
identities. Of these one can be derived directly from Watson's transformation
formula by specialization or through Bailey's method, the second similar
formula can be proved either by using the first formula and the q-Gosper
algorithm, or through the so-called Bailey lattice.Comment: 19 pages. to appear in Ramanujan
Partitions with Prescribed Hook Differences
We investigate partition identities related to off-diagonal hook differences. Our results generalize previous extensions of the RogersâRamanujan identities. The identity of the related polynomials with constructs in statistical mechanics is discussed
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Fewer epistemological challenges for connectionism
Seventeen years ago, John McCarthy wrote the note Epistemological challenges for connectionism as a response to Paul Smolenskyâs paper 'On the proper treatment of connectionism'. I will discuss the extent to which the four key challenges put forward by McCarthy have been solved, and what are the new challenges ahead. I argue that there are fewer epistemological challenges for connectionism, but progress has been slow. Nevertheless, there is now strong indication that neural-symbolic integration can provide effective systems of expressive reasoning and robust learning due to the recent developments in the field
Measurement-induced Squeezing of a Bose-Einstein Condensate
We discuss the dynamics of a Bose-Einstein condensate during its
nondestructive imaging. A generalized Lindblad superoperator in the condensate
master equation is used to include the effect of the measurement. A continuous
imaging with a sufficiently high laser intensity progressively drives the
quantum state of the condensate into number squeezed states. Observable
consequences of such a measurement-induced squeezing are discussed.Comment: 4 pages, 2 figures, submitted to PR
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Symbolic knowledge extraction from trained neural networks: A sound approach
Although neural networks have shown very good performance in many application domains, one of their main drawbacks lies in the incapacity to provide an explanation for the underlying reasoning mechanisms.
The âexplanation capabilityâ of neural networks can be achieved by the extraction of symbolic knowledge. In this paper, we present a new method of extraction that captures nonmonotonic rules encoded in the network, and prove that such a method is sound.
We start by discussing some of the main problems of knowledge extraction methods. We then discuss how these problems may be ameliorated. To this end, a partial ordering on the set of input vectors of a network is defined, as well as a number of pruning and simplification rules. The pruning rules are then used to reduce the search space of the extraction algorithm during a pedagogical extraction, whereas the simplification rules are used to reduce the size of the extracted set of rules. We show that, in the case of regular networks, the extraction algorithm is sound and complete.
We proceed to extend the extraction algorithm to the class of non-regular networks, the general case. We show that non-regular networks always contain regularities in their subnetworks. As a result, the underlying extraction method for regular networks can be applied, but now in a decompositional fashion. In order to combine the sets of rules extracted from each subnetwork into the final set of rules, we use a method whereby we are able to keep the soundness of the extraction algorithm.
Finally, we present the results of an empirical analysis of the extraction system, using traditional examples and real-world application problems. The results have shown that a very high fidelity between the extracted set of rules and the network can be achieved
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Influence of soil physicochemical properties on hydrology and restoration response in Carolina Bay wetlands.
Carolina Bays are shallow depression wetlands found in the southeast US that have been severely altered by human activity. The need to restore these complex and diverse systems is well established, but our understanding of basic wetland hydrological processes is limited, hence our ability to predict the need for and/or assess the effectiveness of bay restorations is hindered. Differing physicochemical properties of soils within bay interiors may control bay hydrology. However, previous efforts to establish relationships between soil characteristics and bay hydrology have been inconclusive and the question still remains as to why some bays are ponded throughout the year while others, within a similar landscape unit, are predominantly dry. An assessment of soil and hydrologic characteristics was initiated in restored and unrestored control bays to determine if a relationship exists. Soil morphology was described and permanent monitoring wells were installed at each site. Soil samples were collected by horizon to a depth of 2 meters at the topographic center of each site, and then analyzed. After three years, multiple regression analysis (stepwise backward and forward) was used to establish relationships between the soil physicochemical characteristics and bay hydroperiod in the undisturbed sites. Results from surface soils indicated that exchangeable acidity (EA) was the best single predictor of hydrology. The best double predictor was EA and total N and EA, total N and total C as the best triple predictor. A significant relationship (r2 = 0.96) between hydroperiod and clay content in the argillic horizon (Bt) was also observed. Subsequently, this relationship was utilized to predict hydrologic response using pre-restoration hydroperiod data. The model accurately identified sites that did not need hydrologic restoration (too wet), and effectively showed sites that responded well to restoration activities
In-situ velocity imaging of ultracold atoms using slow--light
The optical response of a moving medium suitably driven into a slow-light
propagation regime strongly depends on its velocity. This effect can be used to
devise a novel scheme for imaging ultraslow velocity fields. The scheme turns
out to be particularly amenable to study in-situ the dynamics of collective and
topological excitations of a trapped Bose-Einstein condensate. We illustrate
the advantages of using slow-light imaging specifically for sloshing
oscillations and bent vortices in a stirred condensate
Nonlocal appearance of a macroscopic angular momentum
We discuss a type of measurement in which a macroscopically large angular
momentum (spin) is "created" nonlocally by the measurement of just a few atoms
from a double Fock state. This procedure apparently leads to a blatant
nonconservation of a macroscopic variable - the local angular momentum. We
argue that while this gedankenexperiment provides a striking illustration of
several counter-intuitive features of quantum mechanics, it does not imply a
non-local violation of the conservation of angular momentum.Comment: 10 pages, 1 figur
Dynamics of spin-2 Bose condensate driven by external magnetic fields
Dynamic response of the F=2 spinor Bose-Einstein condensate (BEC) under the
influence of external magnetic fields is studied. A general formula is given
for the oscillation period to describe population transfer from the initial
polar state to other spin states. We show that when the frequency and the
reduced amplitude of the longitudinal magnetic field are related in a specific
manner, the population of the initial spin-0 state will be dynamically
localized during time evolution. The effects of external noise and nonlinear
spin exchange interaction on the dynamics of the spinor BEC are studied. We
show that while the external noise may eventually destroy the Rabi oscillations
and dynamic spin localization, these coherent phenomena are robust against the
nonlinear atomic interaction.Comment: 16 pages, 7 figures. accepted by Phys. Rev.
A new multivariable 6-psi-6 summation formula
By multidimensional matrix inversion, combined with an A_r extension of
Jackson's 8-phi-7 summation formula by Milne, a new multivariable 8-phi-7
summation is derived. By a polynomial argument this 8-phi-7 summation is
transformed to another multivariable 8-phi-7 summation which, by taking a
suitable limit, is reduced to a new multivariable extension of the
nonterminating 6-phi-5 summation. The latter is then extended, by analytic
continuation, to a new multivariable extension of Bailey's very-well-poised
6-psi-6 summation formula.Comment: 16 page
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