The finite element method is a well-established method for the numerical solution of partial differential equations (PDEs), both linear and nonlinear. However, the repeated re -assemblage of finite element matrices for nonlinear PDEs is frequently pointed ...
In this paper, we study the problem of learning Graph Neural Networks (GNNs) with Differential Privacy (DP). We propose a novel differentially private GNN based on Aggregation Perturbation (GAP), which adds stochastic noise to the GNN's aggregation functio ...
Modern data management systems aim to provide both cutting-edge functionality and hardware efficiency. With the advent of AI-driven data processing and the post-Moore Law era, traditional memory-bound scale-up data management operations face scalability ch ...
In this thesis we study how physical principles imposed on the S-matrix, such as Lorentz invariance, unitarity, crossing symmetry and analyticity constrain quantum field theories at the nonperturbative level. We start with a pedagogical introduction to the ...
The set of finite binary matrices of a given size is known to carry a finite type AA bicrystal structure. We first review this classical construction, explain how it yields a short proof of the equality between Kostka polynomials and one-dimensional sums t ...
State-of-the-art Artificial Intelligence (AI) algorithms, such as graph neural networks and recommendation systems, require floating-point computation of very large matrix multiplications over sparse data. Their execution in resource-constrained scenarios, ...
The boundary correlation functions for a quantum field theory (QFT) in a fixed anti-de Sitter (AdS) background should reduce to S-matrix elements in the flat-space limit. We consider this procedure in detail for four-point functions. With minimal assumptio ...
Federated learning is a semi-distributed algorithm, where a server communicates with multiple dispersed clients to learn a global model. The federated architecture is not robust and is sensitive to communication and computational overloads due to its one-m ...
We expand Hilbert series technologies in effective field theory for the inclusion of massive particles, enabling, among other things, the enumeration of operator bases for non-linearly realized gauge theories. We find that the Higgs mechanism is manifest a ...
The thesis develops a planning framework for ADNs to achieve their dispatchability by means of ESS allocation while ensuring a reliable and secure operation of ADNs. Second, the framework is extended to include grid reinforcements and ESSs planning. Finall ...
