相关论文: Additive Separability, Optimization, and Trivial W…
Structural controllability has been proposed as an analytical framework for making predictions regarding the control of complex networks across myriad disciplines in the physical and life sciences (Liu et al., Nature:473(7346):167-173,…
This paper proposes a theory of encapsulation, establishing a relationship between encapsulation and information hiding through the concept of potential structural complexity (P.S.C.), the maximum possible number of source code dependencies…
We examine the relationship between learnability and robust (or agnostic) learnability for the problem of distribution learning. We show that, contrary to other learning settings (e.g., PAC learning of function classes), realizable…
Derivation-based differential calculi are of great importance in noncommutative geometry, noncommutative gauge theory and integrable systems. In this paper, we propose the connection and curvature from a class of deformed derivation-based…
Extending the well-known star-comb lemma for infinite graphs, we characterise the graphs that do not contain an infinite comb or an infinite star, respectively, attached to a given set of vertices. We offer several characterisations: in…
We present a simple combinatorial model for quasipositive surfaces and positive braids, based on embedded bipartite graphs. As a first application, we extend the well-known duality on standard diagrams of torus links to twisted torus links.…
We state some elementary problems concerning the relation between difference calculus and differential calculus, and we try to convince the reader that, in spite of the simplicity of the statements, a solution of these problems would be a…
This monograph, written for educational purposes, serves as an introduction to the concept of integrability as it applies to systems of differential equations (both ordinary and partial) as well as to vector-valued fields. The general cases…
Understanding how singularities behave under small perturbations is a central theme in singularity theory. In this paper we establish sufficient conditions for families of analytic function-germs on a germ of a complex analytic space to…
Under a slightly stronger hypothesis, one improves a connectedness result of Debarre [D] for a product of two projective spaces in terms of the extension problem of formal-rational functions (see Theorems 1.3 and 1.4 of the introduction)
The parallel computational complexity or depth of growing network models is investigated. The networks considered are generated by preferential attachment rules where the probability of attaching a new node to an existing node is given by a…
We investigate the isomorphism problem in the setting of definable sets (equivalent to sets with atoms): given two definable relational structures, are they related by a definable isomorphism? Under mild assumptions on the underlying…
Existing methods for differentiable structure learning in discrete data typically assume that the data are generated from specific structural equation models. However, these assumptions may not align with the true data-generating process,…
Entity-linking is a natural-language-processing task that consists in identifying the entities mentioned in a piece of text, linking each to an appropriate item in some knowledge base; when the knowledge base is Wikipedia, the problem comes…
We give a new, elementary proof of what we believe is the simplest known example of a ``natural'' problem in computational 3-dimensional topology that is $\mathsf{NP}$-hard -- namely, the \emph{Trivial Sublink Problem}: given a diagram $L$…
Consider a simple finite graph and its nodes to represent identical water barrels (containing different amounts of water) on a level plane. Each edge corresponds to a (locked, water-filled) pipe connecting two barrels below the plane. We…
An input-output model for networks with link uncertainty is developed. The main result presents a set of integral quadratic constraints (IQCs) that collectively imply robust stability of the uncertain network dynamics. The model dependency…
We analyze the mixing properties of growing networks and find that, in some cases, the assortativity patterns are reversed once links' direction is considered: the disassortative behavior observed in such networks is a spurious effect, and…
Connectivity is a central notion of graph theory and plays an important role in graph algorithm design and applications. With emerging new applications in networks, a new type of graph connectivity problem has been getting more…
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…