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We consider several classes of highly important semidefinite optimization problems that involve both a convex objective function (smooth or nonsmooth) and additional linear or nonlinear smooth and convex constraints, which are ubiquitous in…
Sparse principal component analysis (sparse PCA) is a widely used technique for dimensionality reduction in multivariate analysis, addressing two key limitations of standard PCA. First, sparse PCA can be implemented in high-dimensional low…
Indicator functions of taking values of zero or one are essential to numerous applications in machine learning and statistics. The corresponding primal optimization model has been researched in several recent works. However, its dual…
This paper studies stochastic optimization for a sum of compositional functions, where the inner-level function of each summand is coupled with the corresponding summation index. We refer to this family of problems as finite-sum coupled…
Micro-Doppler signatures are a proven modality for discriminating between drones and birds, but their reliability degrades in low-SNR, data-constrained settings where deep learning models often fail. This paper presents a systematic study…
Low-rank modeling has a lot of important applications in machine learning, computer vision and social network analysis. While the matrix rank is often approximated by the convex nuclear norm, the use of nonconvex low-rank regularizers has…
Relationship between the superconducting gap and the pseudogap has been the subject of controversies. In order to clarify this issue, we have studied the superconducting gap and pseudogap of the high-Tc superconductor La2-xSrxCuO4 (x=0.10,…
The statistical property of the weak lensing fields is studied quantitatively using the ray-tracing simulations. Motivated by the empirical lognormal model that characterizes the probability distribution function(PDF) of the…
A central issue on high-Tc superconductivity is the nature of the normal-state gap (pseudogap) in the underdoped regime and its relationship with superconductivity. Despite persistent efforts, theoretical ideas for the pseudogap evolve…
Principal component analysis (PCA) requires the computation of a low-rank approximation to a matrix containing the data being analyzed. In many applications of PCA, the best possible accuracy of any rank-deficient approximation is at most a…
Singular value decomposition (SVD) based principal component analysis (PCA) breaks down in the high-dimensional and limited sample size regime below a certain critical eigen-SNR that depends on the dimensionality of the system and the…
In 2010, Gordan \v{Z}itkovi\'{c} introduced the notion of convex compactness for a convex subset of a linear topological space and gave some important applications to both nonlinear analysis and mathematical economics in [ Gordan…
Although more than twenty years have passed since the discovery of high temperature cuprate superconductivity, the identification of the superconducting order parameter is still under debate. Here, we show that the nodal gap component is…
We establish that the cuprate pseudogap plays a crucial role in the $ab$-plane optical conductivity $\sigma(\omega,T)$ for temperatures $T \le T_c$. The pseudogap signatures in $\sigma(\omega,T)$ associated with competing proposals of a…
The (delta-) normal cone to an arbitrary intersection of sublevel sets of proper, lower semicontinuous, and convex functions is characterized, using either epsilon-subdifferentials at the nominal point or exact subdifferentials at nearby…
The pseudogap stands out in the phase diagram of the cuprate high-temperature superconductors because its origin and relationship to superconductivity remain elusive. The origin of the pseudogap has been debated, with competing hypotheses…
A graph is chordal if every cycle of length at least four contains a chord, that is, an edge connecting two nonconsecutive vertices of the cycle. Several classical applications in sparse linear systems, database management, computer vision,…
We present a novel representation of rank constraints for non-square real matrices. We establish relationships with some existing results, which are particular cases of our representation. One of these particular cases, is a representation…
Ultrafast broadband transient reflectivity experiments are performed to study the interplay between the non-equilibrium dynamics of the pseudogap and the superconducting phases in Bi$_{2}$Sr$_{2}$Ca$_{0.92}$Y$_{0.08}$Cu$_{2}$O$_{8+\delta}$.…
In a random ray method of neutral particle transport simulation, each iteration begins by sampling a set of rays before proceeding to solve the characteristic transport equation along the linear paths the rays follow. Historically,…