Related papers: A Note on Ordinal Submodularity
Multimodular functions, primarily used in the literature of queueing theory, discrete-event systems, and operations research, constitute a fundamental function class in discrete convex analysis. The objective of this paper is to clarify the…
Local terms in the Operator Product Expansion in Superconformal Theories with extended supersymmetry are identified. Assuming a factorized structure for these terms their contributions are discussed.
In this exposition, we get examples of what is called a "linear hyperdoctrine", based on categories of comodules indexed by coalgebras. This structures can model first order linear logic.
We define a family of functionals, called p-oscillation functionals, that can be interpreted as discrete versions of the classical total variation functional for p=1 and of the p-Dirichlet functionals for p>1. We introduce the notion of…
The similar sublattices of a planar lattice can be classified via its multiplier ring. The latter is the ring of rational integers in the generic case, and an order in an imaginary quadratic field otherwise. Several classes of examples are…
A complete classification of unimodular valuations on the set of lattice polygons with values in the spaces of polynomials and formal power series, respectively, is established. The valuations are classified in terms of their behaviour with…
We consider the problem of maximizing a monotone submodular function under noise. There has been a great deal of work on optimization of submodular functions under various constraints, resulting in algorithms that provide desirable…
In this paper, we define finitely additive, probability and modular functions over semiring-like structures. We investigate finitely additive functions with the help of complemented elements of a semiring. We also generalize some classical…
Normal and composition series of modules enumerated by ordinal numbers are studied. The Jordan-Holder theorem for them is discussed.
Several results in functional analysis are extended to the setting of $L^0$-modules, where $L^0$ denotes the ring of all measurable functions $x\colon \Omega\to \mathbb{R}$. The focus is on results involving compactness. To this end, a…
We completely determine all lower-modular elements of the lattice of all semigroup varieties. As a corollary, we show that a lower-modular element of this lattice is modular.
Submodular optimization generalizes many classic problems in combinatorial optimization and has recently found a wide range of applications in machine learning (e.g., feature engineering and active learning). For many large-scale…
We present a definition of a (super)-modular functor which includes certain interesting cases that previous definitions do not allow. We also introduce a notion of topological twisting of a modular functor, and construct formally a…
We give several characterizations of discrete Sugeno integrals over bounded distributive lattices, as particular cases of lattice polynomial functions, that is, functions which can be represented in the language of bounded lattices using…
In this note, we establish some new results on some special types of function algebras and also give new proofs to some existing ones
The quantification of controllability and observability has recently received new interest in the context of large, complex networks of dynamical systems. A fundamental but computationally difficult problem is the placement or selection of…
We introduce a new class of functions that can be minimized in polynomial time in the value oracle model. These are functions $f$ satisfying $f(x)+f(y)\ge f(x \sqcap y)+f(x \sqcup y)$ where the domain of each variable $x_i$ corresponds to…
We extend the work of Narasimhan and Bilmes [30] for minimizing set functions representable as a dierence between submodular functions. Similar to [30], our new algorithms are guaranteed to monotonically reduce the objective function at…
We study functional clones, which are sets of non-negative pseudo-Boolean functions (functions $\{0,1\}^k\to\mathbb{R}_{\geq 0}$) closed under (essentially) multiplication, summation and limits. Functional clones naturally form a lattice…
We introduce a new covering property, defined in terms of order types of sequences of open sets, rather than in terms of cardinalities of families. The most general form of this compactness notion depends on two ordinal parameters. In the…