Related papers: Multiplicative error set system sparsification: A …
Spectral clustering is a fundamental method for graph partitioning, but its reliance on eigenvector computation limits scalability to massive graphs. Classical sparsification methods preserve spectral properties by sampling edges…
The constraint satisfaction problem (CSP) involves deciding, given a set of variables and a set of constraints on the variables, whether or not there is an assignment to the variables satisfying all of the constraints. One formulation of…
Can we use sparse tokens for dense prediction, e.g., segmentation? Although token sparsification has been applied to Vision Transformers (ViT) to accelerate classification, it is still unknown how to perform segmentation from sparse tokens.…
We present the derivation, implementation, and analysis of a multiresolution adaptive grid framework for numerical simulations on octree-based 3D block-structured collocated grids with distributed computational architectures. Our approach…
Motivated by the grid search method and Bayesian optimization, we introduce the concept of contractibility and its applications in model-based optimization. First, a basic framework of contraction methods is established to construct a…
A $\mu$-constrained Boolean Max-CSP$(\psi)$ instance is a Boolean Max-CSP instance on predicate $\psi:\{0,1\}^r \to \{0,1\}$ where the objective is to find a labeling of relative weight exactly $\mu$ that maximizes the fraction of satisfied…
A $\left(n,\ell,\gamma\right)$-sharing set family of size $m$ is a family of sets $S_1,\ldots,S_m\subseteq [n]$ s.t. each set has size $\ell$ and each pair of sets shares at most $\gamma$ elements. We let $m\left(n,\ell,\gamma\right)$…
We study the compressed sensing (CS) signal estimation problem where an input signal is measured via a linear matrix multiplication under additive noise. While this setup usually assumes sparsity or compressibility in the input signal…
We prove that approximating the size of stopping and trapping sets in Tanner graphs of linear block codes, and more restrictively, the class of low-density parity-check (LDPC) codes, is NP-hard. The ramifications of our findings are that…
In this short note we give a new upper bound for the size of a set family with a single Hamming distance. Our proof is an application of the linear algebra bound method.
We analyse how the standard reductions between constraint satisfaction problems affect their proof complexity. We show that, for the most studied propositional, algebraic, and semi-algebraic proof systems, the classical constructions of…
In this paper, we study the strength of convex relaxations obtained by convexification of aggregation of constraints for a set $S$ described by two bilinear bipartite equalities. Aggregation is the process of rescaling the original…
We study the structure of the solution space and behavior of local search methods on random 3-SAT problems close to the SAT/UNSAT transition. Using the overlap measure of similarity between different solutions found on the same problem…
The recent work of \cite{CRT,DonohoPol} rigorously proved (in a large dimensional and statistical context) that if the number of equations (measurements in the compressed sensing terminology) in the system is proportional to the length of…
The explosion in the volumes of data being stored online has resulted in distributed storage systems transitioning to erasure coding based schemes. Yet, the codes being deployed in practice are fairly short. In this work, we address what we…
Reducing the conditions under which a given set satisfies the stipulations of the subset sum proposition to a set of linear relationships, the question of whether a set satisfies subset sum may be answered in a polynomial number of steps by…
The Boolean lattice $2^{[n]}$ is the family of all subsets of $[n]=\{1,\dots,n\}$ ordered by inclusion, and a chain is a family of pairwise comparable elements of $2^{[n]}$. Let $s=2^{n}/\binom{n}{\lfloor n/2\rfloor}$, which is the average…
Single domain proteins are thought to be tightly packed. The introduction of voids by mutations is often regarded as destabilizing. In this study we show that packing density for single domain proteins decreases with chain length. We find…
We show that a generalised sparse grid combination technique which combines multi-variate extrapolation of finite difference solutions with the standard combination formula lifts a second order accurate scheme on regular meshes to a fourth…
We study a generalized framework for structured sparsity. It extends the well-known methods of Lasso and Group Lasso by incorporating additional constraints on the variables as part of a convex optimization problem. This framework provides…