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In this work, we consider the low rank decomposition (SDPR) of general convex semidefinite programming problems (SDP) that contain both a positive semidefinite matrix and a nonnegative vector as variables. We develop a rank-support-adaptive…
Conventional algorithms in autonomous exploration face challenges due to their inability to accurately and efficiently identify the spatial distribution of convex regions in the real-time map. These methods often prioritize navigation…
Blind source separation (BSS) is a natural framework for studying how latent causes may be recovered from sensory mixtures, but deriving online and biologically plausible algorithms for structured (i.e., constrained to known domains) and…
A large number of problems in optimization, machine learning, signal processing can be effectively addressed by suitable semidefinite programming (SDP) relaxations. Unfortunately, generic SDP solvers hardly scale beyond instances with a few…
We obtain the patch-repetition entropy Sigma within the Random First Order Transition theory (RFOT) and for the square plaquette system, a model related to the dynamical facilitation theory of glassy dynamics. We find that in both cases the…
We extend the scale-dependent Gaussian Streaming Model (GSM) to produce analytical predictions for the anisotropic redshift-space correlation function for biased tracers in modified gravity models. Employing the Convolution Lagrangian…
In this paper, we introduce the concept of spatially coupled turbo codes (SC-TCs), as the turbo codes counterpart of spatially coupled low-density parity-check codes. We describe spatial coupling for both Berrou et al. and Benedetto et al.…
The use of high-dimensional features has become a normal practice in many computer vision applications. The large dimension of these features is a limiting factor upon the number of data points which may be effectively stored and processed,…
The properties of flat minima in the empirical risk landscape of neural networks have been debated for some time. Increasing evidence suggests they possess better generalization capabilities with respect to sharp ones. First, we discuss…
Stochastic gradient descent (SGD) has been studied extensively over the past decades due to its simplicity and broad applicability in machine learning. In this work, we analyze the local behavior of gradient descent and stochastic gradient…
The radial overlap correction, $\delta_{RO}$ is re-examined for 30 superallowed $\beta$ decays using the shell model with Hartree-Fock (HF) radial wave functions. Our calculation is based on the Skyrme interaction including Coulomb,…
This thesis contributes to the theoretical understanding of local update algorithms, especially Local SGD, in distributed and federated optimization under realistic models of data heterogeneity. A central focus is on the bounded…
For noisy compressive sensing systems, the asymptotic distortion with respect to an arbitrary distortion function is determined when a general class of least-square based reconstruction schemes is employed. The sampling matrix is considered…
In this paper, we study the phenomenon of Hopf or more specifically quantum double symmetry breaking. We devise a criterion for this type of symmetry breaking which is more general than the one existing in the literature, and therefore…
We consider the evolution of a network of neurons, focusing on the asymptotic behavior of spikes dynamics instead of membrane potential dynamics. The spike response is not sought as a deterministic response in this context, but as a…
The ability to efficiently match the frequency of the brain's response to repetitive visual stimuli in real time is the basis for reliable SSVEP-based Brain-Computer-Interfacing (BCI). The detection of different stimuli is posed as a…
This study develops an algorithm for distributed computing of linear programming problems of huge-scales. Global consensus with single common variable, multiblocks, and augmented Lagrangian are adopted. The consensus is used to partition…
Approximate counting via correlation decay is the core algorithmic technique used in the sharp delineation of the computational phase transition that arises in the approximation of the partition function of anti-ferromagnetic two-spin…
Low-rank plus diagonal (LRPD) decompositions provide a powerful structural model for large covariance matrices, simultaneously capturing global shared factors and localized corrections that arise in covariance estimation, factor analysis,…
We investigate the combinatorial discrepancy of geometric set systems having bounded shallow cell complexity in the \emph{Beck-Fiala} setting, where each point belongs to at most $t$ ranges. For set systems with shallow cell complexity…