Search results for "Theoretical Computer Science"
showing 10 items of 1151 documents
Laplacian versus Adjacency Matrix in Quantum Walk Search
2015
A quantum particle evolving by Schr\"odinger's equation contains, from the kinetic energy of the particle, a term in its Hamiltonian proportional to Laplace's operator. In discrete space, this is replaced by the discrete or graph Laplacian, which gives rise to a continuous-time quantum walk. Besides this natural definition, some quantum walk algorithms instead use the adjacency matrix to effect the walk. While this is equivalent to the Laplacian for regular graphs, it is different for non-regular graphs, and is thus an inequivalent quantum walk. We algorithmically explore this distinction by analyzing search on the complete bipartite graph with multiple marked vertices, using both the Lapla…
Free boundary methods and non-scattering phenomena
2021
We study a question arising in inverse scattering theory: given a penetrable obstacle, does there exist an incident wave that does not scatter? We show that every penetrable obstacle with real-analytic boundary admits such an incident wave. At zero frequency, we use quadrature domains to show that there are also obstacles with inward cusps having this property. In the converse direction, under a nonvanishing condition for the incident wave, we show that there is a dichotomy for boundary points of any penetrable obstacle having this property: either the boundary is regular, or the complement of the obstacle has to be very thin near the point. These facts are proved by invoking results from t…
Nonlocality threshold for entanglement under general dephasing evolutions: A case study
2015
Determining relationships between different types of quantum correlations in open composite quantum systems is important since it enables the exploitation of a type by knowing the amount of another type. We here review, by giving a formal demonstration, a closed formula of the Bell function, witnessing nonlocality, as a function of the concurrence, quantifying entanglement, valid for a system of two noninteracting qubits initially prepared in extended Werner-like states undergoing any local pure-dephasing evolution. This formula allows for finding nonlocality thresholds for the concurrence depending only on the purity of the initial state. We then utilize these thresholds in a paradigmatic …
Unique continuation of the normal operator of the x-ray transform and applications in geophysics
2020
We show that the normal operator of the X-ray transform in $\mathbb{R}^d$, $d\geq 2$, has a unique continuation property in the class of compactly supported distributions. This immediately implies uniqueness for the X-ray tomography problem with partial data and generalizes some earlier results to higher dimensions. Our proof also gives a unique continuation property for certain Riesz potentials in the space of rapidly decreasing distributions. We present applications to local and global seismology. These include linearized travel time tomography with half-local data and global tomography based on shear wave splitting in a weakly anisotropic elastic medium.
Automatic landmark detection and 3D Face data extraction
2017
Abstract This paper contributes to 3D facial synthesis by presenting a novel method for parameterization using Landmark Point detection. The approach presented aims at improving facial recognition even in varying facial expressions, and missing data in 3D facial models. As such, the prime objective was to develop an automatically embedded process that can detect any frontal face in 3D face recognition systems, with face segmentation and surface curvature information. Using the hybrid interpolation method, experiments on facial landmarks were performed on 4950 images from Face Recognition Grand Challenge database (FRGC). Distinctive facial landmarks from the nose–tips, Limits mouth and two e…
Quotients of Fermat curves and a Hecke character
2005
AbstractWe explicitly identify infinitely many curves which are quotients of Fermat curves. We show that some of these have simple Jacobians with complex multiplication by a non-cyclotomic field. For a particular case we determine the local zeta functions with two independent methods. The first uses Jacobi sums and the second applies the general theory of complex multiplication, we verify that both methods give the same result.
More restrictive Gray codes for some classes of pattern avoiding permutations
2009
In a recent article [W.M.B. Dukes, M.F. Flanagan, T. Mansour, V. Vajnovszki, Combinatorial Gray codes for classes of pattern avoiding permutations, Theoret. Comput. Sci. 396 (2008) 35-49], Dukes, Flanagan, Mansour and Vajnovszki present Gray codes for several families of pattern avoiding permutations. In their Gray codes two consecutive objects differ in at most four or five positions, which is not optimal. In this paper, we present a unified construction in order to refine their results (or to find other Gray codes). In particular, we obtain more restrictive Gray codes for the two Wilf classes of Catalan permutations of length n; two consecutive objects differ in at most two or three posit…
Minimal change list for Lucas strings and some graph theoretic consequences
2005
AbstractWe give a minimal change list for the set of order p length-n Lucas strings, i.e., the set of length-n binary strings with no p consecutive 1's nor a 1ℓ prefix and a 1m suffix with ℓ+m⩾p. The construction of this list proves also that the order p n-dimensional Lucas cube has a Hamiltonian path if and only if n is not a multiple of p+1, and its second power always has a Hamiltonian path.
Multi-frequency orthogonality sampling for inverse obstacle scattering problems
2011
We discuss a simple non-iterative method to reconstruct the support of a collection of obstacles from the measurements of far-field patterns of acoustic or electromagnetic waves corresponding to plane-wave incident fields with one or few incident directions at several frequencies. The method is a variant of the orthogonality sampling algorithm recently studied by Potthast (2010 Inverse Problems 26 074015). Our theoretical analysis of the algorithm relies on an asymptotic expansion of the far-field pattern of the scattered field as the size of the scatterers tends to zero with respect to the wavelength of the incident field that holds not only at a single frequency, but also across appropria…