The Wonderful Lemma, that was first proved by Roussel and Rubio, is one of the most important tools in the proof of the Strong Perfect Graph Theorem. Here we give a short proof of this lemma.

The aim of this article is to simplify Pfanzagl’s proof of consistency for asymptotic maximum likelihood estimators, and to extend it to more general asymptotic M -estimators. The method relies on the existence of a sort of contraction of the parameter space which admits the true parameter as a fixed point. The proofs are short and elementary.

We show a model construction for a system of higher-order illative combinatory logic Iω, thus establishing its strong consistency. We also use a variant of this construction to provide a complete embedding of first-order intuitionistic predicate logic with second-order propositional quantifiers into the system I0 of Barendregt, Bunder and Dekkers, which gives a partial answer to a question pose...

We explore the notion of a pseudo-free group, first introduced by Hohenberger [Hoh03], and provide an alternative stronger definition. We show that if Zn is a pseudo-free abelian group (as we conjecture), then Zn also satisfies the Strong RSA Assumption [FO97,CS00,BP97]. Being a “pseudo-free abelian group” may be the strongest natural cryptographic assumption one can make about a group such as ...

Poor households worldwide rely on savings groups (SGs) to satisfy their financial needs, yet very little is known about these groups’ ability to meet them. In this paper we develop a theoretical model illustrating the basic trade-offs in the functioning of SGs, and present stylized facts derived from the financial accounts of a sample of Ugandan SGs. The main conclusion from the theoretical mod...

We establish several results regarding dividing and forking in NTP2 theories. We show that dividing is the same as array-dividing. Combining it with existence of strictly invariant sequences we deduce that forking satisfies the chain condition over extension bases (namely, the forking ideal is S1, in Hrushovski’s terminology). Using it we prove an independence theorem over extension bases (whic...

In this paper, a setup-driving verifiably committed signature based on the strong RSA assumption within the standard complexity model is presented. The idea behind our construction is that given any valid partial signature of a message m, if an arbitrator with its auxiliary input is able to generate variables called the resolution of messagem such that the distribution of the resulting variable...

In this paper, regression function estimation from independent and identically distributed data is considered. We establish strong pointwise consistency of the famous Nadaraya-Watson estimator under weaker conditions which permit to apply kernels with unbounded support and even not integrable ones and provide a general approach for constructing strongly consistent kernel estimates of regression...

We give a number of characterizations of structural entailment. In particular, we show that an alter ego M∼ structurally entails an algebraic relation s on a finite algebra M if and only if s can be obtained via a local construct from M∼ . We show, via a range of applications, that, whereas entailment is important in the study of dualisability, structural entailment is important in the study of...