Related papers: Algebraic Experimental Design: Theory and Computat…
A promising approach to study condensed-matter systems is to simulate them on an engineered quantum platform. However, achieving the accuracy needed to outperform classical methods has been an outstanding challenge. Here, using eighteen…
Simulation and modeling are essential in product development, integrated into the design and manufacturing process to enhance efficiency and quality. They are typically represented as complex nonlinear differential algebraic equations. The…
Many inference problems in structured prediction can be modeled as maximizing a score function on a space of labels, where graphs are a natural representation to decompose the total score into a sum of unary (nodes) and pairwise (edges)…
Fractional polynomial models are potentially useful for response surfaces investigations. With the availability of routines for fitting nonlinear models in statistical packages they are increasingly being used. However, as in all…
Considering the worst-case scenario, junction tree algorithm remains the most general solution for exact MAP inference with polynomial run-time guarantees. Unfortunately, its main tractability assumption requires the treewidth of a…
We propose a novel methodology for discovering the presence of relationships realized as binary time series between variables in high dimension. To make it visually intuitive, we regard the existence of a relationship as an edge connection,…
A useful approach to the mathematical analysis of large-scale biological networks is based upon their decompositions into monotone dynamical systems. This paper deals with two computational problems associated to finding decompositions…
The quality of numerical reconstructions for unknown parameters in inverse problems depends fundamentally on the selection of experimental data. To ensure a robust reconstruction, it is crucial to select data that are sensitive to the…
We study the problem of learning a latent tree graphical model where samples are available only from a subset of variables. We propose two consistent and computationally efficient algorithms for learning minimal latent trees, that is, trees…
A challenge of molecular self-assembly is to understand how to design particles that self-assemble into a desired structure and not any of a potentially large number of undesired structures. Here we use simulation to show that a strategy of…
Reconstructing continuous signals from a small number of discrete samples is a fundamental problem across science and engineering. In practice, we are often interested in signals with 'simple' Fourier structure, such as bandlimited,…
Variability has always been a challenge to mitigate in electronics. This especially holds true for organic semiconductors, where reproducibility and long-term stability concerns hinder industrialization. By relying on a bio-inspired…
This paper aims to maximize algebraic connectivity of networks via topology design under the presence of constraints and an adversary. We are concerned with three problems. First, we formulate the concave maximization topology design…
The language of graph theory, or network science, has proven to be an exceptional tool for addressing myriad problems in neuroscience. Yet, the use of networks is predicated on a critical simplifying assumption: that the quintessential unit…
We consider ordered pairs $(X,\mathcal{B})$ where $X$ is a finite set of size $v$ and $\mathcal{B}$ is some collection of $k$-element subsets of $X$ such that every $t$-element subset of $X$ is contained in exactly $\lambda$ "blocks" $B\in…
Autonomous reconfiguration of agent-based systems is a key challenge in the study of programmable matter, distributed robotics, and molecular self-assembly. While substantial prior work has focused on size-preserving transformations, much…
Minimum storage regenerating codes have minimum storage of data in each node and therefore are maximal distance separable (MDS for short) codes. Thus, the number of nodes is upper bounded by $2^{\fb}$, where $\fb$ is the bits of data stored…
We study the generalized minimum Manhattan network (GMMN) problem: given a set $P$ of pairs of two points in the Euclidean plane $\mathbb{R}^2$, we are required to find a minimum-length geometric network which consists of axis-aligned…
This paper presents the novel `uniqueness tree' algorithm, as one possible method for determining whether two finite, undirected graphs are isomorphic. We prove that the algorithm has polynomial time complexity in the worst case, and that…
We study experiment design for unique identification of the causal graph of a simple SCM, where the graph may contain cycles. The presence of cycles in the structure introduces major challenges for experiment design as, unlike acyclic…