2,205 research outputs found
Localization and Pattern Formation in Quantum Physics. II. Waveletons in Quantum Ensembles
In this second part we present a set of methods, analytical and numerical,
which can describe behaviour in (non) equilibrium ensembles, both classical and
quantum, especially in the complex systems, where the standard approaches
cannot be applied. The key points demonstrating advantages of this approach
are: (i) effects of localization of possible quantum states; (ii) effects of
non-perturbative multiscales which cannot be calculated by means of
perturbation approaches; (iii) effects of formation of complex/collective
quantum patterns from localized modes and classification and possible control
of the full zoo of quantum states, including (meta) stable localized patterns
(waveletons). We demonstrate the appearance of nontrivial localized (meta)
stable states/patterns in a number of collective models covered by the
(quantum)/(master) hierarchy of Wigner-von Neumann-Moyal-Lindblad equations,
which are the result of ``wignerization'' procedure (Weyl-Wigner-Moyal
quantization) of classical BBGKY kinetic hierarchy, and present the explicit
constructions for exact analytical/numerical computations (fast convergent
variational-wavelet representation). Numerical modeling shows the creation of
different internal structures from localized modes, which are related to the
localized (meta) stable patterns (waveletons), entangled ensembles (with
subsequent decoherence) and/or chaotic-like type of behaviour.Comment: LaTeX2e, spie.cls, 13 pages, 6 figures, submitted to Proc. of SPIE
Meeting, The Nature of Light: What is a Photon? Optics & Photonics, SP200,
San Diego, CA, July-August, 200
Complexity Analysis Of Next-Generation VVC Encoding and Decoding
While the next generation video compression standard, Versatile Video Coding
(VVC), provides a superior compression efficiency, its computational complexity
dramatically increases. This paper thoroughly analyzes this complexity for both
encoder and decoder of VVC Test Model 6, by quantifying the complexity
break-down for each coding tool and measuring the complexity and memory
requirements for VVC encoding/decoding. These extensive analyses are performed
for six video sequences of 720p, 1080p, and 2160p, under Low-Delay (LD),
Random-Access (RA), and All-Intra (AI) conditions (a total of 320
encoding/decoding). Results indicate that the VVC encoder and decoder are 5x
and 1.5x more complex compared to HEVC in LD, and 31x and 1.8x in AI,
respectively. Detailed analysis of coding tools reveals that in LD on average,
motion estimation tools with 53%, transformation and quantization with 22%, and
entropy coding with 7% dominate the encoding complexity. In decoding, loop
filters with 30%, motion compensation with 20%, and entropy decoding with 16%,
are the most complex modules. Moreover, the required memory bandwidth for VVC
encoding/decoding are measured through memory profiling, which are 30x and 3x
of HEVC. The reported results and insights are a guide for future research and
implementations of energy-efficient VVC encoder/decoder.Comment: IEEE ICIP 202
Quantum phase space trajectories with application to quantum cosmology
We develop an approach to quantum dynamics based on quantum phase space
trajectories. The latter are built from a unitary irreducible representation of
the symmetry group of the respective classical phase space. We use a quantum
action functional to derive the basic equations. In principle, our formulation
is equivalent to the Hilbert space formulation. However, the former allows for
consistent truncations to reduced phase spaces in which approximate quantum
dynamics can be derived. We believe that our approach can be very useful in the
domain of quantum cosmology and therefore, we use the cosmological phase space
example to establish the basic equations of this formalism.Comment: 11 pages, 4 figures, the new version contains improved discussion
Modeling M-Theory Vacua via Gauged S-Duality
We construct a model of M-theory vacua using gauged S-duality and the
Chan-Paton symmetries by introducing an infinite number of open string charges.
In the Bechi-Rouet-Stora-Tyutin formalism, the local description of the gauged
S-duality on its moduli space of vacua is fully determined by one physical
state condition on the vacua. We introduce the string probe of the spatial
degrees of freedom and define the increment of the cosmic time. The
dimensionality of space-time and the gauge group of the low energy effective
theory originate in the symmetries (with or without their breakdown) in our
model. This modeling leads to the derived category formulation of the quantum
mechanical world including gravity and to the concept of a non-linear potential
of gauged and affinized S-duality which specifies the morphism structure of
this derived category.Comment: 31 pages, version reflecting the erratum. arXiv admin note:
substantial text overlap with arXiv:1102.460
Optimal quantization for the pricing of swing options
In this paper, we investigate a numerical algorithm for the pricing of swing
options, relying on the so-called optimal quantization method. The numerical
procedure is described in details and numerous simulations are provided to
assert its efficiency. In particular, we carry out a comparison with the
Longstaff-Schwartz algorithm.Comment: 27
Option Pricing with Orthogonal Polynomial Expansions
We derive analytic series representations for European option prices in
polynomial stochastic volatility models. This includes the Jacobi, Heston,
Stein-Stein, and Hull-White models, for which we provide numerical case
studies. We find that our polynomial option price series expansion performs as
efficiently and accurately as the Fourier transform based method in the nested
affine cases. We also derive and numerically validate series representations
for option Greeks. We depict an extension of our approach to exotic options
whose payoffs depend on a finite number of prices.Comment: forthcoming in Mathematical Finance, 38 pages, 3 tables, 7 figure
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