Full diversity product codes for block erasure and block fading channels

We show how to build full-diversity product codes under both iterative encoding and decoding over non-ergodic channels, in presence of block erasure and block fading. The concept of a rootcheck or a root subcode is introduced by generalizing the same principle recently invented for low-density parity-check codes. We also describe some channel related graphical properties of the new family of product codes, a familyreferred to as root product codes.

Experiencing simulated outcomes

Whereas much literature has documented difficulties in making probabilistic inferences, it hasalso emphasized the importance of task characteristics in determining judgmental accuracy.Noting that people exhibit remarkable efficiency in encoding frequency information sequentially,we construct tasks that exploit this ability by requiring people to experience the outcomes ofsequentially simulated data. We report two experiments. The first involved seven well-knownprobabilistic inference tasks. Participants differed in statistical sophistication and answered withand without experience obtained through sequentially simulated outcomes in a design thatpermitted both between- and within-subject analyses. The second experiment involvedinterpreting the outcomes of a regression analysis when making inferences for investmentdecisions. In both experiments, even the statistically naïve make accurate probabilistic inferencesafter experiencing sequentially simulated outcomes and many prefer this presentation format. Weconclude by discussing theoretical and practical implications.

Homotopy Batalin-Vilkovisky algebras

This paper provides an explicit cofibrant resolution of the operad encoding Batalin-Vilkovisky algebras. Thus it defines the notion of homotopy Batalin-Vilkovisky algebras with the required homotopy properties. To define this resolution we extend the theory of Koszul duality to operads and properads that are defind by quadratic and linear relations. The operad encoding Batalin-Vilkovisky algebras is shown to be Koszul in this sense. This allows us to prove a Poincare-Birkhoff-Witt Theorem for such an operad and to give an explicit small quasi-free resolution for it. This particular resolution enables us to describe the deformation theory and homotopy theory of BV-algebras and of homotopy BV-algebras. We show that any topological conformal field theory carries a homotopy BV-algebra structure which lifts the BV-algebra structure on homology. The same result is proved for the singular chain complex of the double loop space of a topological space endowed with an action of the circle. We also prove the cyclic Deligne conjecture with this cofibrant resolution of the operad BV. We develop the general obstruction theory for algebras over the Koszul resolution of a properad and apply it to extend a conjecture of Lian-Zuckerman, showing that certain vertex algebras have an explicit homotopy BV-algebra structure.