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A functional theory based on single-particle occupation numbers is developed for pairing. This functional, that generalizes the BCS approach, directly incorporates corrections due to particle number conservation. The functional is…
In this paper, the target controllability of multiagent systems under directed weighted topology is studied. A graph partition is constructed, in which part of the nodes are divided into different cells, which are selected as leaders. The…
A novel matching based heuristic algorithm designed to detect specially formulated infeasible zero-one IPs is presented. The algorithm input is a set of nested doubly stochastic subsystems and a set E of instance defining variables set at…
Pearl's Causal Hierarchy (PCH) is a central framework for reasoning about probabilistic, interventional, and counterfactual statements, yet the satisfiability problem for PCH formulas is computationally intractable in almost all classical…
Causal discovery aims to learn causal relationships between variables from targeted data, making it a fundamental task in machine learning. However, causal discovery algorithms often rely on unverifiable causal assumptions, which are…
This thesis develops exact analytical tools to study strongly correlated stochastic systems, with a focus on extreme value statistics, gap statistics, and full counting statistics in multi-particle processes. A central contribution is the…
Generalizing the notion of matched pair of groups, we define and study matched pairs of locally compact groupoids endowed with Haar systems, in order to give new examples of measured quantum groupoids.
Dynamical signatures are known to precede jamming in hard-particle systems, but static structural signatures have proven more elusive. The observation that compressing hard-particle packings towards jamming causes growing hyperuniformity…
We outline ideas on desired properties for a new generation of effective core potentials (ECPs) that will allow valence-only calculations to reach the full potential offered by recent advances in many-body wave function methods. The key…
Modern experimental methods enable the creation of self-assembly building blocks with tunable interactions, but optimally exploiting this tunability for the self-assembly of desired structures remains an important challenge. Many studies of…
Coarse-grained (CG) models are often parametrized to reproduce one-dimensional structural correlation functions of an atomically-detailed model along the degrees of freedom governing each interaction potential. While cross correlations…
Conformal mapping, a classical topic in complex analysis and differential geometry, has become a subject of great interest in the area of surface parameterization in recent decades with various applications in science and engineering.…
Physically unclonable functions (PUFs) identify integrated circuits using nonlinearly-related challenge-response pairs (CRPs). Ideally, the relationship between challenges and corresponding responses is unpredictable, even if a subset of…
We examine the structure and dynamics of small isolated $N$-particle clusters interacting via short-ranged Morse potentials. "Ideally preprared ensembles" obtained via exact enumeration studies of sticky hard sphere packings serve as…
We present a non-standard Hubbard model applicable to arbitrary single-particle potential profiles and inter-particle interactions. Our approach involves a novel treatment of Wannier functions, free from the ambiguities of conventional…
Learning-based approaches for controlling safety-critical systems are rapidly growing in popularity; thus, it is important to assure their performance and safety. Hamilton-Jacobi (HJ) reachability analysis is a popular formal verification…
We present a new approach to derive the connectivity properties of pairwise interacting n-body systems in thermal equilibrium. We formulate an integral equation that relates the pair connectedness to the distribution of nearest neighbors.…
The Unitary Correlation Operator Method (UCOM) provides a means for nuclear structure calculations starting from realistic NN potentials. The dominant short-range central and tensor correlations are described explicitly by a unitary…
The local arrangement of atoms is one of the most important predictors of mechanical and functional properties of materials. However, algorithms for identifying the geometrical arrangements of atoms in complex materials systems are lacking.…
It has been suggested that a certain class of UV-incomplete quantum field theories can avoid unitarity violation above the cut-off energy scale by forming classical configurations at a length scale much larger than the cut-off length. This…