Chain varieties of monoids

A variety of universal algebras is called a chain variety if its subvariety lattice is a chain. Non-group chain varieties of semigroups were completely classified by Sukhanov in 1982. Here we completely determine non-group chain varieties of monoids as algebras of tyoe (2,0).Comment: 76 pages, 3 figures, 3 tables. In comparison with the previous version, we made a number of linguistic corrections onl

Minimal monoids generating varieties with complex subvariety lattices

A variety is finitely universal if its lattice of subvarieties contains an isomorphic copy of every finite lattice. We show that the 6-element Brandt monoid generates a finitely universal variety of monoids and, by the previous results, it is the smallest generator for a monoid variety with this property. It is also deduced that the join of two Cross varieties of monoids can be finitely universal. In particular, we exhibit a finitely universal variety of monoids with uncountably many subvarieties which is the join of two Cross varieties of monoids whose lattices of subvarieties are the 6-element and the 7-element chains, respectively.Comment: 22 pages. In version 3, Remark 4 is update

Varieties of aperiodic monoids with commuting idempotents whose subvariety lattice is distributive

We completely classify all varieties of aperiodic monoids with commuting idempotents whose subvariety lattice is distributive.Comment: 75 page

Semiring and involution identities of powers of inverse semigroups

The set of all subsets of any inverse semigroup forms an involution semiring under set-theoretical union and element-wise multiplication and inversion. We find structural conditions on a finite inverse semigroup guaranteeing that neither semiring nor involution identities of the involution semiring of its subsets admit a finite identity basis.Comment: 9 page

Varieties of Monoids with Complex Lattices of Subvarieties

A variety is finitely universal if its lattice of subvarieties contains an isomorphic copy of every finite lattice. Examples of finitely universal varieties of semigroups have been available since the early 1970s, but it is unknown if there exists a finitely universal variety of monoids. The main objective of the present article is to exhibit the first examples of finitely universal varieties of monoids. The finite universality of these varieties is established by showing that the lattice of equivalence relations on every sufficiently large finite set is anti-isomorphic to some subinterval of the lattice of subvarieties

Cancellable Elements of the Lattice of Monoid Varieties

The set of all cancellable elements of the lattice of semigroup varieties has recently been shown to be countably infinite. But the description of all cancellable elements of the lattice MON of monoid varieties remains unknown. This problem is addressed in the present article. The first example of a monoid variety with modular but non-distributive subvariety lattice is first exhibited. Then a necessary condition of the modularity of an element in MON is established. These results play a crucial role in the complete description of all cancellable elements of the lattice MON. It turns out that there are precisely five such elements

The lattice of varieties of monoids

We survey results devoted to the lattice of varieties of monoids. Along with known results, some unpublished results are given with proofs. A number of open questions and problems are also formulated

Forecasting stock market returns over multiple time horizons

In this paper we seek to demonstrate the predictability of stock market returns and explain the nature of this return predictability. To this end, we introduce investors with different investment horizons into the news-driven, analytic, agent-based market model developed in Gusev et al. (2015). This heterogeneous framework enables us to capture dynamics at multiple timescales, expanding the model's applications and improving precision. We study the heterogeneous model theoretically and empirically to highlight essential mechanisms underlying certain market behaviors, such as transitions between bull- and bear markets and the self-similar behavior of price changes. Most importantly, we apply this model to show that the stock market is nearly efficient on intraday timescales, adjusting quickly to incoming news, but becomes inefficient on longer timescales, where news may have a long-lasting nonlinear impact on dynamics, attributable to a feedback mechanism acting over these horizons. Then, using the model, we design algorithmic strategies that utilize news flow, quantified and measured, as the only input to trade on market return forecasts over multiple horizons, from days to months. The backtested results suggest that the return is predictable to the extent that successful trading strategies can be constructed to harness this predictability.Comment: This is the version accepted for publication in a journal Quantitative Finance. A draft was posted here on 18 August 2015. 50 page