Block-diagonal reduction of matrices over commutative rings I. (Decomposition of modules vs decomposition of their support)

Consider rectangular matrices over a commutative ring R. Assume the ideal of maximal minors factorizes, I_m(A)=J_1*J_2. When is A left-right equivalent to a block-diagonal matrix? (When does the module/sheaf Coker(A) decompose as the corresponding direct sum?) If R is not a principal ideal ring (or a close relative of a PIR) one needs additional assumptions on A. No necessary and sufficient criterion for such block-diagonal reduction is known. In this part we establish the following: * The persistence of (in)decomposability under the change of rings. For example, the passage to Noetherian/local/complete rings, the decomposability of A over a graded ring R vs the decomposability of Coker(A) locally at the points of Proj(R), the restriction to a subscheme in Spec(R). * The necessary and sufficient condition for decomposability of square matrices in the case: det(A)=f_1*f_2 is not a zero divisor and f_1,f_2 are co-prime. As an immediate application we give criteria of simultaneous (block-)diagonal reduction for tuples of matrices over a field, i.e. linear determinantal representations

Comparing Multidimensional Poverty between Egypt and Tunisia

It is common to argue that poverty is a multidimensional issue. Yet few studies have included the various dimensions of deprivation to yield a broader and fuller picture of poverty. The present paper considers the multidimensional aspects of deprivation by specifying a poverty line for each aspect and combines their associated one-dimensional poverty-gaps into multidimensional poverty measures. An application of these measures to compare poverty between Egypt and Tunisia is illustrated using robustness analysis and household data from each country.Multidimensional poverty indices, Robustness analysis, Egypt, Tunisia

On tree decomposability of Henneberg graphs

In this work we describe an algorithm that generates well constrained geometric constraint graphs which are solvable by the tree-decomposition constructive technique. The algorithm is based on Henneberg constructions and would be of help in transforming underconstrained problems into well constrained problems as well as in exploring alternative constructions over a given set of geometric elements.Postprint (published version

Higher-order interference and single-system postulates characterizing quantum theory

We present a new characterization of quantum theory in terms of simple physical principles that is different from previous ones in two important respects: first, it only refers to properties of single systems without any assumptions on the composition of many systems; and second, it is closer to experiment by having absence of higher-order interference as a postulate, which is currently the subject of experimental investigation. We give three postulates -- no higher-order interference, classical decomposability of states, and strong symmetry -- and prove that the only non-classical operational probabilistic theories satisfying them are real, complex, and quaternionic quantum theory, together with 3-level octonionic quantum theory and ball state spaces of arbitrary dimension. Then we show that adding observability of energy as a fourth postulate yields complex quantum theory as the unique solution, relating the emergence of the complex numbers to the possibility of Hamiltonian dynamics. We also show that there may be interesting non-quantum theories satisfying only the first two of our postulates, which would allow for higher-order interference in experiments while still respecting the contextuality analogue of the local orthogonality principle.Comment: 21 + 6 pages, 1 figure. v4: published version (includes several minor corrections

Competing through business models

In this article a business model is defined as the firm choices on policies, assets and governance structure of those policies and assets, together with their consequences, be them flexible or rigid. We also provide a way to represent such business models to highlight the dynamic loops and to facilitate understanding interaction with other business models. Furthermore, we develop some tests to evaluate the goodness of a business model both in isolation as well as in interaction with other business models of different organizations, be those competitors, complements, suppliers, partners, etc.Business model; Interaction; Competitive Strategy; Competitive Dynamics;