Network reconstruction, i.e., obtaining network structure from data, is a central theme in systems biology, economics and engineering. In some previous work, we introduced dynamical structure functions as a tool for posing and solving the problem of network reconstruction between measured states. While recovering the network structure between hidden states is not possible since they are not mea...

An order bounded disjointness preserving operator T on an Archimedean vector lattice is algebraic if and only if the restriction of Tn! to the vector sublattice generated by the range of Tm is strongly diagonal, where n is the degree of the minimal polynomial of T and m is its ‘valuation’.

We present the results of an experiment on learning with minimal information. Particularly, subjects are only provided with feedback about their own payoff from the last period of the game being played, but not with information about the structure of the game. We compare the empirical structure of the decision algorithm for this setting with the empirical structure of algorithms for subjects wh...

@0-categorical o-minimal structures were completely described in 4], and are essentially built up from copies of the rationals as an ordered set by`cutting and copying'. Here we investigate the possible structures which an @0-categorical weakly o-minimal set may carry, and nd that there are some rather more interesting (and not o-minimal) examples. We show that even here the possibilities are l...

Let L/K be a separable field extension of degree 6. An 1867 theorem of P. Joubert asserts that if char(K) 6= 2 then L is generated over K by an element whose minimal polynomial is of the form t + at + bt + ct+ d for some a, b, c, d ∈ K. We show that this theorem fails in

A linearly ordered structure is weakly o-minimal if all of its definable sets in one variable are the union of finitely many convex sets in the structure. Weakly o-minimal structures were introduced by Dickmann, and they arise in several contexts. We here prove several fundamental results about weakly o-minimal structures. Foremost among these, we show that every weakly o-minimal ordered field ...