The planar Ising model in an external magnetic field and with multi-spin interactions is shown to be equivalent to a vertex problem. The equivalence can be extended to higher spins and higher dimensions. In a recent paper Malakis (1979) reported the proof of an equivalence between a certain staggered vertex model and a zero-field Ising model. The equivalence has since been extended (Malakis 198...

In multi-label classification, where the evaluation of predictions is less straightforward than in single-label various meaningful, though different, loss functions have been proposed. Ideally, learning algorithm should be customizable towards a specific choice performance measure. Modern implementations boosting, most prominently gradient boosted decision trees, appear to appealing from this p...

Abstract: Decomposable graphs are known for their tedious and complicated Markov update steps. Instead of modelling them directly, this work introduces a class of tree-dependent bipartite graphs that span the projective space of decomposable graphs. This is achieved through dimensionality expansion that causes the graph nodes to be conditionally independent given a latent tree. The Markov updat...

The k-dimensional assignment problem with decomposable costs is formulated as follows. Given is a complete k-partite graph G = (X0 u ... u X,_ I, E), with lXil = p for each i, and a nonnegative length function defined on the edges of G. A clique of G is a subset of vertices meeting each Xi in exactly one vertex. The cost of a clique is a function of the lengths of the edges induced by the cliqu...

In this paper some types of decomposable signed fuzzy measures have been presented. We discuss properties of 6-and ⊕decomposable signed fuzzy measures. We consider their relationship with bi-capacities.

Decomposable Negation Normal Form formulae (DNNFs) form an interesting propositional fragment, both for efficiency and succinctness reasons. A famous subclass of the DNNF fragment is the OBDD fragment which offers many polytime queries and transformations, including quantifier eliminations (under some ordering restrictions). Nevertheless, the decomposable AND nodes at work in OBDDs enable only ...

An additive hereditary graph property is a class of simple graphs which is closed under unions, subgraphs and isomorphisms. If P1, . . . ,Pn are graph properties, then a (P1, . . . ,Pn)-decomposition of a graph G is a partition E1, . . . , En of E(G) such that G[Ei], the subgraph of G induced by Ei, is in Pi, for i = 1, . . . , n. The sum of the properties P1, . . . ,Pn is the property P1 ⊕ · ·...

Sequential composition of voting rules, by making use of structural properties of the voters’ preferences, provide computationally economical ways for making a common decision over a Cartesian product of finite local domains. A sequential composition is usually defined on a set of legal profiles following a fixed order. In this paper, we generalize this by order-independent sequential compositi...

The algebraic stability theorem for pointwise finite dimensional (p.f.d.) R-persistence modules is a central result in the theory of stability for persistence modules. We present a stability theorem for n-dimensional rectangle decomposable p.f.d. persistence modules up to a constant (2n− 1) that is a generalization of the algebraic stability theorem. We give an example to show that the bound ca...