where |x| = max0≤i≤m |xi| and ν < q−2m. Form = 1, it follows from Roth’s approximation theorem (cf. [Sch 2], p. 120) that if the linear factors of F are pairwise non-proportional, then (1.1) has only finitely many solutions. Using his subspace theorem, W.M. Schmidt ([Sch 1], [Sch 2]) generalized this for arbitrary m, under the assumptions that (i) any m+1 of the linear factors of F are linearly...

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...

We propose a strategy for disclosure risk evaluation and disclosure control of a microdata set based on fitting decomposable models of a multiway contingency table corresponding to the microdata set. By fitting decomposable models, we can evaluate per-record identification (or re-identification) risk of a microdata set. Furthermore we can easily determine swappability of risky records which doe...

Given a random vector X, we address the question of linear separability of X, that is, the task of finding a linear operator W such that we have (S1, . . . ,SM ) = (WX) with statistically independent random vectors Si. As this requirement alone is already fulfilled trivially by X being independent of the empty rest, we require that the components be not further decomposable. We show that if X h...

A VLSI architecture is proposed for the realization of real-time two-dimensional (2-D) image filtering in an addressevent-representation (AER) vision system. The architecture is capable of implementing any convolutional kernel F (x; y) as long as it is decomposable into x-axis and y-axis components, i.e., F (x; y) = H(x)V (y), for some rotated coordinate system fx; yg and if this product can be...

We propose a strategy for disclosure risk evaluation and disclosure control of a microdata set based on fitting decomposable models of a multiway contingency table corresponding to the microdata set. By fitting decomposable models, we can evaluate per-record identification (or re-identification) risk of a microdata set. Furthermore we can easily determine swappability of risky records which doe...

To understand the behavior of a complex system, you must understand the tangled web of interactions between the system’s many parts. The web is tractable in systems that are somewhat decomposable, meaning that the interactions influence only weakly the short-term behavior of the parts. But how to handle complexity in systems that are nowhere near decomposable? Science’s principal tool for deali...