77,985 research outputs found
On the Limits of Depth Reduction at Depth 3 Over Small Finite Fields
Recently, Gupta et.al. [GKKS2013] proved that over Q any -variate
and -degree polynomial in VP can also be computed by a depth three
circuit of size . Over fixed-size
finite fields, Grigoriev and Karpinski proved that any
circuit that computes (or ) must be of size
[GK1998]. In this paper, we prove that over fixed-size finite fields, any
circuit for computing the iterated matrix multiplication
polynomial of generic matrices of size , must be of size
. The importance of this result is that over fixed-size
fields there is no depth reduction technique that can be used to compute all
the -variate and -degree polynomials in VP by depth 3 circuits of
size . The result [GK1998] can only rule out such a possibility
for depth 3 circuits of size .
We also give an example of an explicit polynomial () in
VNP (not known to be in VP), for which any circuit computing
it (over fixed-size fields) must be of size . The
polynomial we consider is constructed from the combinatorial design. An
interesting feature of this result is that we get the first examples of two
polynomials (one in VP and one in VNP) such that they have provably stronger
circuit size lower bounds than Permanent in a reasonably strong model of
computation.
Next, we prove that any depth 4
circuit computing
(over any field) must be of size . To the best of our knowledge, the polynomial is the
first example of an explicit polynomial in VNP such that it requires
size depth four circuits, but no known matching
upper bound
Statistics of Mesoscopic Fluctuations of Quantum Capacitance
The Thouless formula for the two-probe dc
conductance of a d-dimensional mesoscopic cube is re-analysed to relate its
quantum capacitance to the reciprocal of the level spacing . To
this end, the escape time-scale occurring in the Thouless correlation
energy is interpreted as the {\em time constant} with 1, giving at once . Thus,
the statistics of the quantum capacitance is directly related to that of the
level spacing, which is well known from the Random Matrix Theory for all the
three universality classes of statistical ensembles. The basic questions of how
intrinsic this quantum capacitance can arise purely quantum-resistively, and of
its observability {\em vis-a-vis} the external geometric capacitance that
combines with it in series, are discussed
A performance model of speculative prefetching in distributed information systems
Previous studies in speculative prefetching focus on building and evaluating access models for the purpose of access prediction. This paper investigates a complementary area which has been largely ignored, that of performance modelling. We use improvement in access time as the performance metric, for which we derive a formula in terms of resource parameters (time available and time required for prefetching) and speculative parameters (probabilities for next access). The performance maximization problem is expressed as a stretch knapsack problem. We develop an algorithm to maximize the improvement in access time by solving the stretch knapsack problem, using theoretically proven apparatus to reduce the search space. Integration between speculative prefetching and caching is also investigated, albeit under the assumption of equal item sizes
Landau diamagnetism revisited
The problem of diamagnetism, solved by Landau, continues to pose fascinating
issues which have relevance even today. These issues relate to inherent quantum
nature of the problem, the role of boundary and dissipation, the meaning of
thermodynamic limits, and above all, the quantum-classical crossover occasioned
by environment-induced decoherence. The Landau Diamagnetism provides a unique
paradigm for discussing these issues, the significance of which are
far-reaching. Our central result is a remarkable one as it connects the mean
orbital magnetic moment, a thermodynamic property, with the electrical
resistivity, which characterizes transport properties of materials.Comment: 4 pages, 1 figur
Statistical separability and classification of land use classes using image-100
The author has identified the following significant results. The statistical separability of land use classes in the subsets of one to four spectral channels was investigated. Using ground observations and aerial photography, the MSS data of LANDSAT were analyzed with the Image-100. In the subsets of one to three spectral channels, channel 4, channel 4 & 7, and channels 4, 5, & 7 were found to be the best choices (ch.4 - 0.5 to 0.6 microns, ch. 5 - 0.6 to 0.7 microns, ch. 6 - 0.7 to 0.8 microns, and ch. 7 - 0.8 to 1.1 microns). For the single cell option of the Image-100, the errors of omission varied from 5% for the industrial class to 46% for the institutional class. The errors of commission varied from 11% for the commercial class to 39% for the industrial class. On the whole, the sample classifier gave considerably more accurate results compared to the single cell or multicell option
Can re-entrance be observed in force induced transitions?
A large conformational change in the reaction co-ordinate and the role of the
solvent in the formation of base-pairing are combined to settle a long standing
issue {\it i.e.} prediction of re-entrance in the force induced transition of
DNA. A direct way to observe the re-entrance, i.e a strand goes to the closed
state from the open state and again to the open state with temperature, appears
difficult to be achieved in the laboratory. An experimental protocol (in direct
way) in the constant force ensemble is being proposed for the first time that
will enable the observation of the re-entrance behavior in the
force-temperature plane. Our exact results for small oligonucleotide that forms
a hairpin structure provide the evidence that re-entrance can be observed.Comment: 12 pages and 5 figures (RevTex4). Accepted in Europhys Lett. (2009
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