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This article reviews and evaluates models of network evolution based on the notion of structural diversity. We show that diversity is an underlying theme of three principles of network evolution: the preferential attachment model,…
Convolutional Neural Networks (CNNs) are build specifically for computer vision tasks for which it is known that the input data is a hierarchical structure based on locally correlated elements. The question that naturally arises is what…
Explicit characterization of the capacity region of communication networks is a long standing problem. While it is known that network coding can outperform routing and replication, the set of feasible rates is not known in general.…
Shared randomness is a valuable resource in distributed computing, allowing some form of coordination between processors without explicit communication. But what happens when the shared random string can affect the inputs to the system?…
There has been a large amount of interest, both in the past and particularly recently, into the power of different families of universal approximators, e.g. ReLU networks, polynomials, rational functions. However, current research has…
As the discipline has evolved, research in machine learning has been focused more and more on creating more powerful neural networks, without regard for the interpretability of these networks. Such "black-box models" yield state-of-the-art…
A correspondence is established between the elements of logic reasoning systems (knowledge bases, rules, inference and queries) and the hardware and dynamical operations of neural networks. The correspondence is framed as a general…
Reed-Muller (RM) codes are among the oldest, simplest and perhaps most ubiquitous family of codes. They are used in many areas of coding theory in both electrical engineering and computer science. Yet, many of their important properties are…
In one of their seminal articles on allowable sequences, Goodman and Pollack gave combinatorial generalizations for three problems in discrete geometry, one of which being the Dirac conjecture. According to this conjecture, any set of $n$…
As data-driven methods rise in popularity in materials science applications, a key question is how these machine learning models can be used to understand microstructure. Given the importance of process-structure-property relations…
As demonstrated in many areas of real-life applications, neural networks have the capability of dealing with high dimensional data. In the fields of optimal control and dynamical systems, the same capability was studied and verified in many…
We study complexity measures on subsets of the boolean hypercube and exhibit connections between algebra (the Hilbert function) and combinatorics (VC theory). These connections yield results in both directions. Our main complexity-theoretic…
The problem of statistical inference in its various forms has been the subject of decades-long extensive research. Most of the effort has been focused on characterizing the behavior as a function of the number of available samples, with far…
Sorting extremely large datasets is a frequently occuring task in practice. These datasets are usually much larger than the computer's main memory; thus external memory sorting algorithms, first introduced by Aggarwal and Vitter (1988), are…
In upcoming papers by Conrey, Farmer and Zirnbauer there appear conjectural formulas for averages, over a family, of ratios of products of shifted L-functions. In this paper we will present various applications of these ratios conjectures…
Possibility theory offers a framework where both Lehmann's "preferential inference" and the more productive (but less cautious) "rational closure inference" can be represented. However, there are situations where the second inference does…
Different techniques have been used to prove several transference theorems of the form "nontrivial algorithms for a circuit class C yield circuit lower bounds against C". In this survey we revisit many of these results. We discuss how…
Researchers currently use a number of approaches to predict and substantiate information-computation gaps in high-dimensional statistical estimation problems. A prominent approach is to characterize the limits of restricted models of…
Designing large coupling memory quasi-cyclic spatially-coupled LDPC (QC-SC-LDPC) codes with low error floors requires eliminating specific harmful substructures (e.g., short cycles) induced by edge spreading and lifting. Building on our…
The log-rank conjecture is one of the fundamental open problems in communication complexity. It speculates that the deterministic communication complexity of any two-party function is equal to the log of the rank of its associated matrix,…