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The use of deep learning techniques has achieved significant progress for program synthesis from input-output examples. However, when the program semantics become more complex, it still remains a challenge to synthesize programs that are…
This thesis includes analysis of disordered spin ensembles corresponding to Exact Cover, a multi-access channel problem, and composite models combining sparse and dense interactions. The satisfiability problem in Exact Cover is addressed…
We analyse supersymmetric models that show supersymmetry breaking in one and two dimensions using lattice methods. Starting from supersymmetric quantum mechanics we explain the fundamental principles and problems that arise in putting…
Error-tolerant graph matching gathers an important family of problems. These problems aim at finding correspondences between two graphs while integrating an error model. In the Graph Edit Distance (GED) problem, the insertion/deletion of…
In this article, we focus on extending the notion of lattice linearity to self-stabilizing programs. Lattice linearity allows a node to execute its actions with old information about the state of other nodes and still preserve correctness.…
Currently, industrial anomaly detection suffers from two bottlenecks: (i) the rarity of real-world defect images and (ii) the opacity of sample quality when synthetic data are used. Existing synthetic strategies (e.g., cut-and-paste)…
Early detection of newly emerging diseases, lesion severity assessment, differentiation of medical conditions and automated screening are examples for the wide applicability and importance of anomaly detection (AD) and unsupervised…
In this paper, we propose new coupled codes constructed by overlapping circular spatially-coupled low-density parity-check (SC-LDPC) codes, which show better asymptotic and finite-length decoding performance compared to the conventional…
A majority logic decoder made of unreliable logic gates, whose failures are transient and datadependent, is analyzed. Based on a combinatorial representation of fault configurations a closed-form expression for the average bit error rate…
Decoding algorithms are essential to fault-tolerant quantum-computing architectures. In this perspective we explore decoding algorithms for the surface code; a prototypical quantum low-density parity-check code that underlies many of the…
This paper introduces a federated learning framework that enables over-the-air computation via digital communications, using a new joint source-channel coding scheme. Without relying on channel state information at devices, this scheme…
This paper attempts to derive a mathematical formulation for real-practice clinical laboratory schedul-ing, and to present a syntactic adaptive problem solver by leveraging landscape structures. After formulating scheduling of medical tests…
Demonstrating subthreshold scaling of a surface-code quantum memory on hardware whose native connectivity does not match the code remains a central challenge. We address this on IBM heavy-hex superconducting processors by co-designing the…
This paper proposes an efficient algorithm for solving the Hartree--Fock equation combining a multilevel correction scheme with an adaptive refinement technique to improve computational efficiency. The algorithm integrates a multilevel…
We propose a multiscale method for mixed-dimensional elliptic problems with highly heterogeneous coefficients arising, for example, in the modeling of fractured porous media. The method is based on the Localized Orthogonal Decomposition…
Generalized code surgery is a versatile and low-overhead technique for performing fault-tolerant computation on quantum low-density parity-check (qLDPC) codes. In many settings, surgery exhibits practical space overheads, while its time…
We propose, analyze, and numerically validate a correction adaptive two-grid finite element method (CAT-GFEM) for nonselfadjoint or indefinite elliptic problems. In contrast to the adaptive two-grid finite element method (ATGFEM) of Li and…
In this work we explore the fidelity of numerical approximations to the analytic spectra of hyperbolic partial differential equation systems with variable coefficients. We are particularly interested in the ability of discrete methods to…
Recent experimental progress in realizing surface code on hardware, including demonstrations of break-even logical memory on devices with up to hundreds of physical qubits, has materially advanced the prospects for fault-tolerant quantum…
Since its inception, Benders Decomposition (BD) has been successfully applied to a wide range of large-scale mixed-integer (linear) problems. The key element of BD is the derivation of Benders cuts, which are often not unique. In this…