2,016 research outputs found
Kodaira-Saito vanishing and applications
The first part of the paper contains a detailed proof of M. Saito's
generalization of the Kodaira vanishing theorem, following the original
argument and with ample background, based on a lecture given at a Clay workshop
on mixed Hodge modules. The second part contains some recent applications, and
a Kawamata-Viehweg-type statement in the setting of mixed Hodge modules.Comment: 33 pages; final version, with expository improvements, updates, and
substantial additions in the background section
Optimisation of multiplier-less FIR filter design techniques
This thesis is concerned with the design of multiplier-less (ML) finite impulse response (FIR) digital filters. The use of multiplier-less digital filters results in simplified filtering structures, better throughput rates and higher speed. These characteristics are very desirable in many DSP systems. This thesis concentrates on the design of digital filters with power-of-two coefficients that result in simplified filtering structures. Two distinct classesof ML FIR filter design algorithms are developed and compared
with traditional techniques. The first class is based on the sensitivity of filter coefficients to rounding to power-of-two. Novel elements include extending of the algorithm for multiple-bands filters and introducing mean square error as the sensitivity criterion. This improves the performance of the algorithm and reduces the complexity of resulting filtering structures. The second class of filter design algorithms is based on evolutionary techniques, primarily genetic algorithms. Three different algorithms based on genetic algorithm kernel are developed. They include simple genetic algorithm, knowledge-based genetic algorithm and hybrid of genetic algorithm and simulated annealing. Inclusion of the additional knowledge has been found very useful when re-designing filters or refining previous designs. Hybrid techniques are useful when exploring large, N-dimensional searching spaces. Here, the genetic algorithm is used to explore searching space rapidly, followed by fine search using simulated annealing. This approach has been found beneficial for design of high-order filters. Finally, a formula for estimation of the filter length from its specification and complementing both
classes of design algorithms, has been evolved using techniques of symbolic regression and genetic programming. Although the evolved formula is very complex and not easily understandable, statistical analysis has shown that it produces
more
accurate results than traditional Kaiser's formula.
In summary, several novel algorithms for the design of multiplier-less digital filters
have been developed. They outperform traditional techniques that are used for the
design of ML FIR filters and hence contributed to the knowledge in the field of ML
FIR filter design
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Kommutative Algebra
The workshop brought together researchers on various areas of Commutative Algebra. New results in combinatorial commutative algebra, homological methods and invariants, characteristic p-methods, and in general commutative algebra and algebraic geometry were presented in the lectures of the workshop
Gauge Theories as String Theories: the First Results
The brief review of the duality between gauge theories and closed strings
propagating in the curved space is based on the lectures given at ITEP Winter
School - 2005Comment: Latex, 35 pages, Lectures given at ITEP Winter School, March 200
On solvable models of type IIB superstring in NS-NS and R-R plane wave backgrounds
We consider type IIB string in the two plane-wave backgrounds which may be
interpreted as special limits of the AdS_3 x S^3 metric supported by either the
NS-NS or R-R 3-form field. The NS-NS plane-wave string model is equivalent to a
direct generalization of the Nappi-Witten model, with its spectrum being
similar to that of strings in constant magnetic field. The R-R model can be
solved in the light-cone gauge, where the Green-Schwarz action describes 4
massive and 4 massless copies of free bosons and fermions. We find the spectra
of the two string models and study the asymptotic density of states. We also
discuss a more general class of exactly solvable plane-wave models with reduced
supersymmetry which is obtained by adding twists in two spatial 2-planes.Comment: 36 pages, harvmac. v2: discussion of equivalence of the supergravity
parts of the spectra of the NS-NS and R-R models added in sect.5.3; v3: added
remark on periodicity of the NS-NS spectrum; v4: minor correction in sect.6.
F-singularities in families
We study the behavior of test ideals and F-singularities in families. In
particular, we obtain generic (and non-generic) restriction theorems for test
ideals and non-F-pure ideals. Additionally, we study the global behavior of
certain canonical linear systems (induced by Frobenius) associated to adjoint
line bundles, in families. As a consequence, we obtain some positivity results
for pushforwards of some adjoint line bundles and for certain subsheaves of
these.Comment: 60 pages, typos corrected throughout and improved exposition, to
appear in Algebraic Geometr
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