Idempotent permutations

Together with a characteristic function, idempotent permutations uniquely determine idempotent maps, as well as their linearly ordered arrangement simultaneously. Furthermore, in-place linear time transformations are possible between them. Hence, they may be important for succinct data structures, information storing, sorting and searching. In this study, their combinatorial interpretation is given and their application on sorting is examined. Given an array of n integer keys each in [1,n], if it is allowed to modify the keys in the range [-n,n], idempotent permutations make it possible to obtain linearly ordered arrangement of the keys in O(n) time using only 4log(n) bits, setting the theoretical lower bound of time and space complexity of sorting. If it is not allowed to modify the keys out of the range [1,n], then n+4log(n) bits are required where n of them is used to tag some of the keys.Comment: 32 page

Cosine Similarity Measure According to a Convex Cost Function

In this paper, we describe a new vector similarity measure associated with a convex cost function. Given two vectors, we determine the surface normals of the convex function at the vectors. The angle between the two surface normals is the similarity measure. Convex cost function can be the negative entropy function, total variation (TV) function and filtered variation function. The convex cost function need not be differentiable everywhere. In general, we need to compute the gradient of the cost function to compute the surface normals. If the gradient does not exist at a given vector, it is possible to use the subgradients and the normal producing the smallest angle between the two vectors is used to compute the similarity measure

Pulse shape design using iterative projections

In this paper, the pulse shape design for various communication systems including PAM, FSK, and PSK is considered. The pulse is designed by imposing constraints on the time and frequency domains constraints on the autocorrelation function of the pulse shape. Intersymbol interference, finite duration and spectral mask restrictions are a few examples leading to convex sets in L 2. The autocorrelation function of the pulse is obtained by performing iterative projections onto convex sets. After this step, the minimum phase or maximum phase pulse producing the autocorrelation function is obtained by cepstral deconvolution

LAVA Simulations for the AIAA Sonic Boom Prediction Workshop

Computational simulations using the Launch Ascent and Vehicle Aerodynamics (LAVA) framework are presented for the First AIAA Sonic Boom Prediction Workshop test cases. The framework is utilized with both structured overset and unstructured meshing approaches. The three workshop test cases include an axisymmetric body, a Delta Wing-Body model, and a complete low-boom supersonic transport concept. Solution sensitivity to mesh type and sizing, and several numerical convective flux discretization choices are presented and discussed. Favorable comparison between the computational simulations and experimental data of nearand mid-field pressure signatures were obtained