In this thesis, we investigate the inverse problem of trees and barcodes from a combinatorial, geometric, probabilistic and statistical point of view.Computing the persistent homology of a merge tree yields a barcode B. Reconstructing a tree from B invol ...
In this thesis we propose and analyze algorithms for some numerical linear algebra tasks: finding low-rank approximations of matrices, computing matrix functions, and estimating the trace of matrices.In the first part, we consider algorithms for building ...
Methods of topological data analysis have been successfully applied in a wide range of fields to provide useful summaries of the structure of complex data sets in terms of topological descriptors, such as persistence diagrams. While there are many powerful ...
This paper theoretically proposes a multichannel nonlocal metasurface computer characterized by generalized sheet transition conditions (GSTCs) and surface susceptibility tensors. The study explores polarization- and angle-multiplexed metasurfaces enabling ...
Analog optical signal processing has dramatically transcended the speed and energy limitations accompanied with its digital microelectronic counterparts. Motivated by recent metasurface?s evolution, the angular scattering diversity of a reciprocal passive ...
This thesis looks at efficient information processing for two network applications: content delivery with caching and collecting summary statistics in wireless sensor networks. Both applications are studied under the same paradigm: function computation ove ...
Let be a symmetric space of noncompact type. A result of Gelander provides exponential upper bounds in terms of the volume for the torsion homology of the noncompact arithmetic locally symmetric spaces . We show that under suitable assumptions on this resu ...
Let W be a vector space over an algebraically closed field k. Let H be a quasisimple group of Lie type of characteristic p not equal char(k) acting irreducibly on W. Suppose also that G is a classical group with natural module W, chosen minimally with resp ...
Following the work of B. Kulshammer, J. B. Olsson and G. R. Robinson on generalized blocks of the symmetric groups, we give a definition for the l-defect of characters of the symmetric group G(n), where l > 1 is an arbitrary integer. We prove that the l-de ...
In a paper of 2003, Kulshammer, Olsson and Robinson defined l-blocks for the symmetric groups, where l > 1 is an arbitrary integer. In this paper, we give a definition for the defect group of the principal l-block. We then check that, in the Abelian case, ...
In an article of 2003, Kulshammer, Olsson, and Robinson defined l-blocks for the symmetric groups, where l is an arbitrary integer, and proved that they satisfy an analogue of the Nakayama Conjecture. Inspired by this work and the definitions of generalize ...
We propose a design oriented charge-based model for undoped DG MOSFETs under symmetrical operation that aims at giving a comprehensive understanding of the device from the design strategy. In particular, we introduce useful normalizations for current and c ...
