Related papers: Characteristic-Dependent Linear Rank Inequalities …
We classify all finite linear spaces on at most 15 points admitting a blocking set. There are no such spaces on 11 or fewer points, one on 12 points, one on 13 points, two on 14 points, and five on 15 points. The proof makes extensive use…
We investigate the two unicast flow problem over layered linear deterministic networks with arbitrary number of nodes. When the minimum cut value between each source-destination pair is constrained to be 1, it is obvious that the triangular…
Identifying and explaining the structure of complex networks at different scales has become an important problem across disciplines. At the mesoscale, modular architecture has attracted most of the attention. At the macroscale, other…
Ranking problems, also known as preference learning problems, define a widely spread class of statistical learning problems with many applications, including fraud detection, document ranking, medicine, credit risk screening, image ranking…
A key property of neural networks is their capacity of adapting to data during training. Yet, our current mathematical understanding of feature learning and its relationship to generalization remain limited. In this work, we provide a…
We use techniques from (tracial noncommutative) polynomial optimization to formulate hierarchies of semidefinite programming lower bounds on matrix factorization ranks. In particular, we consider the nonnegative rank, the positive…
In this paper, we study network coding capacity for random wireless networks. Previous work on network coding capacity for wired and wireless networks have focused on the case where the capacities of links in the network are independent. In…
It is well-known that coupling constraints in linear bilevel optimization can lead to disconnected feasible sets, which is not possible without coupling constraints. However, there is no difference between linear bilevel problems with and…
Neural networks are known to give better performance with increased depth due to their ability to learn more abstract features. Although the deepening of networks has been well established, there is still room for efficient feature…
The sum-rank metric naturally extends both the Hamming and rank metrics in coding theory over fields. It measures the error-correcting capability of codes in multishot matrix-multiplicative channels (e.g. linear network coding or the…
Low Rank Parity Check (LRPC) codes form a class of rank-metric error-correcting codes that was purposely introduced to design public-key encryption schemes. An LRPC code is defined from a parity check matrix whose entries belong to a…
We consider the link prediction problem in a partially observed network, where the objective is to make predictions in the unobserved portion of the network. Many existing methods reduce link prediction to binary classification problem.…
Link prediction, a foundational task in complex network analysis, has extensive applications in critical scenarios such as social recommendation, drug target discovery, and knowledge graph completion. However, existing evaluations of…
An important issue in neural network research is how to choose the number of nodes and layers such as to solve a classification problem. We provide new intuitions based on earlier results by An et al. (2015) by deriving an upper bound on…
In the real world, the stable operation of a network is usually inseparable from the mutual support of other networks. In such an interdependent network, a node in one layer may depend on multiple nodes in another layer, forming a complex…
The principal permanent rank characteristic sequence is a binary sequence $r_0 r_1 \ldots r_n$ where $r_k = 1$ if there exists a principal square submatrix of size $k$ with nonzero permanent and $r_k = 0$ otherwise, and $r_0 = 1$ if there…
In network design problems capacity constraints are modeled in three different ways depending on the application and the underlying technology for installing capacity: directed, bidirected, and undirected. In the literature, polyhedral…
Quadratic constraints (QCs) are widely used to characterize nonlinearities and uncertainties, but generic analytical characterizations can be conservative on bounded domains. This paper develops a framework for constructing verified…
Cycles, which can be found in many different kinds of networks, make the problems more intractable, especially when dealing with dynamical processes on networks. On the contrary, tree networks in which no cycle exists, are simplifications…
We define the notion of characteristic rank, $\mathrm{charrank}_X(\xi)$, of a real vector bundle $\xi$ over a connected finite $CW$-complex $X$. This is a bundle-dependent version of the notion of characteristic rank introduced by…