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Neural networks are widely used for image-related tasks but typically demand considerable computing power. Once a network has been trained, however, its memory- and compute-footprint can be reduced by compression. In this work, we focus on…
As the vast majority of network measures are defined for one-mode networks, two-mode networks often have to be projected onto one-mode networks to be analyzed. A number of issues arise in this transformation process, especially when…
Random walks are the simplest way to explore or search a graph, and have revealed a very useful tool to investigate and characterize the structural properties of complex networks from the real world, e.g. they have been used to identify the…
Weighted reciprocity between two agents can be defined as the minimum of sending and receiving value in their bilateral relationship. In financial networks, such reciprocity characterizes the importance of individual banks as both liquidity…
In this paper we introduce TWIG (Topologically-Weighted Intelligence Generation), a novel, embedding-free paradigm for simulating the output of KGEs that uses a tiny fraction of the parameters. TWIG learns weights from inputs that consist…
Neural operators have emerged as a powerful tool for solving partial differential equations (PDEs) and other complex scientific computing tasks. However, the performance of single operator block is often limited, thus often requiring…
A three-path-configuration is a graph consisting of three pairwise internally-disjoint paths the union of every two of which is an induced cycle of length at least four. A graph is 3PC-free if no induced subgraph of it is a…
Grokking -- the abrupt transition from memorization to generalization long after near-zero training loss -- has been studied mainly in single-task settings. We extend geometric analysis to multi-task modular arithmetic, training…
Over the last two decades, network theory has shown to be a fruitful paradigm in understanding the organization and functioning of real-world complex systems. One technique helpful to this endeavor is identifying functionally influential…
A fundamental problem in mathematics and network analysis is to find conditions under which a graph can be partitioned into smaller pieces. The most important tool for this partitioning is the Fiedler vector or discrete Cheeger inequality.…
Several modern applications involve huge graphs and require fast answers to reachability queries. In more than two decades since first proposals, several approaches have been presented adopting on-line searches, hop labelling or transitive…
Let $G$ be a directed graph with $n$ vertices and $m$ edges, embedded on a surface $S$, possibly with boundary, with first Betti number $\beta$. We consider the complexity of finding closed directed walks in $G$ that are either contractible…
We investigate the conductance of a quantum wire with two embedded quantum dots using a T-matrix approach based on the Lippmann-Schwinger formalism. The quantum dots are represented by a quantum well with Gaussian shape and the wire is…
We study the corrections to adiabatic dynamics of two coupled quantum dot spin-qubits, each dot singly occupied with an electron, in the context of a quantum computing operation. Tunneling causes double occupancy at the conclusion of an…
We report measurements of multi-path transport through a triple quantum dot (TQD) in the few-electron regime using a GaAs three-terminal device with a separate lead attached to each dot. When two paths reside inside the transport window and…
Nonlocal two-qubit quantum gates are represented by canonical decomposition or equivalently by operator-Schmidt decomposition. The former decomposition results in geometrical representation such that all the two-qubit gates form tetrahedron…
A double pants decomposition of a 2-dimensional surface is a collection of two pants decomposition of this surface introduced in arXiv:1005.0073v2. There are two natural operations acting on double pants decompositions: flips and handle…
Let $G$ be an undirected network with a distinguished set of terminals $T \subseteq V(G)$ and edge capacities $cap: E(G) \rightarrow \mathbb{R}_+$. By an odd $T$-walk we mean a walk in $G$ (with possible vertex and edge self-intersections)…
We study finite-dimensional integrals in a way that elucidates the mathematical meaning behind the formal manipulations of path integrals occurring in quantum field theory. This involves a proper understanding of how Wick's theorem allows…
In this paper we revisit the classical Edge Disjoint Paths (EDP) problem, where one is given an undirected graph G and a set of terminal pairs P and asks whether G contains a set of pairwise edge-disjoint paths connecting every terminal…