A class of infinite convex geometries

Various characterizations of finite convex geometries are well known. This note provides similar characterizations for possibly infinite convex geometries whose lattice of closed sets is strongly coatomic and lower continuous. Some classes of examples of such convex geometries are given.Comment: 10 page

Ergodicity probes: using time-fluctuations to measure the Hilbert space dimension

Quantum devices, such as quantum simulators, quantum annealers, and quantum computers, may be exploited to solve problems beyond what is tractable with classical computers. This may be achieved as the Hilbert space available to perform such `calculations' is far larger than that which may be classically simulated. In practice, however, quantum devices have imperfections, which may limit the accessibility to the whole Hilbert space. We thus determine that the dimension of the space of quantum states that are available to a quantum device is a meaningful measure of its functionality, though unfortunately this quantity cannot be directly experimentally determined. Here we outline an experimentally realisable approach to obtaining the required Hilbert space dimension of such a device to compute its time evolution, by exploiting the thermalization dynamics of a probe qubit. This is achieved by obtaining a fluctuation-dissipation theorem for high-temperature chaotic quantum systems, which facilitates the extraction of information on the Hilbert space dimension via measurements of the decay rate, and time-fluctuations

How Vocabulary is Learned

Vocabulary learning requires two basic conditions – repetition (quantity of meetings with words) and good quality mental processing of the meetings. Other factors also affect vocabulary learning. For example, learners may differ greatly in their motivation to engage in learning, and words may differ greatly in their learning burden. However, without quantity and quality of processing, learning cannot occur. The greater the number of repetitions, the more likely learning is to occur. The deeper and more thoughtful the quality of processing, the more likely learning is to occur. This paper explains quantity and quality, and shows how teachers and learners can increase the quantity and quality of their processing of vocabulary, thus increasing their vocabulary size

Comparing generalisation in children and adults learning an artificial language

Successful language acquisition involves generalization, but learners must balance this against the acquisition of lexical constraints. Examples occur throughout language. For example, English native speakers know that certain noun-adjective combinations are impermissible (e.g., strong winds, high winds, strong breezes, *high breezes). Another example is the restrictions imposed by verb sub-categorization (e.g., I gave/sent/threw the ball to him; I gave/sent/threw him the ball; I donated/carried/pushed the ball to him; * I donated/carried/pushed him the ball; Baker, 1979). A central debate has been the extent to which learning such patterns depends on semantic cues (Pinker, 1989) and/or distributional statistics (Braine et al., 1990). The current experiments extend previous work which used Artificial Language learning to demonstrate that adults (Wonnacott et al., 2008) and 6 year olds (Wonnacott, 2011) are able to learn lexically based restrictions on generalization using distributional statistics. Here we directly compare the two age groups learning the same artificial language, with a view to exploring maturational differences in language learning. In addition to manipulating frequency (across high and low frequency items) and quantity of exposure (across days), languages were constructed such that a word’s semantic class was helpful for learning the restrictions for some types of lexical items, but potentially misleading for others

Congruence lattices of semilattices

The main result of this paper is that the class of congruence lattices of semilattices satisfies no nontrivial lattice identities. It is also shown that the class of subalgebra lattices of semilattices satisfies no nontrivial lattice identities. As a consequence it is shown that if V is a semigroup variety all of whose congruence lattices satisfy some fixed nontrivial lattice identity, then all the members of V are groups with exponent dividing a fixed finite number

Ultra-Strong Optomechanics Incorporating the Dynamical Casimir Effect

We propose a superconducting circuit comprising a dc-SQUID with mechanically compliant arm embedded in a coplanar microwave cavity that realizes an optomechanical system with a degenerate or non-degenerate parametric interaction generated via the dynamical Casimir effect. For experimentally feasible parameters, this setup is capable of reaching the single-photon, ultra-strong coupling regime, while simultaneously possessing a parametric coupling strength approaching the renormalized cavity frequency. This opens up the possibility of observing the interplay between these two fundamental nonlinearities at the single-photon level.Comment: 7 pages, 1 figure, 1 tabl

Discovery of the D-basis in binary tables based on hypergraph dualization

Discovery of (strong) association rules, or implications, is an important task in data management, and it nds application in arti cial intelligence, data mining and the semantic web. We introduce a novel approach for the discovery of a speci c set of implications, called the D-basis, that provides a representation for a reduced binary table, based on the structure of its Galois lattice. At the core of the method are the D-relation de ned in the lattice theory framework, and the hypergraph dualization algorithm that allows us to e ectively produce the set of transversals for a given Sperner hypergraph. The latter algorithm, rst developed by specialists from Rutgers Center for Operations Research, has already found numerous applications in solving optimization problems in data base theory, arti cial intelligence and game theory. One application of the method is for analysis of gene expression data related to a particular phenotypic variable, and some initial testing is done for the data provided by the University of Hawaii Cancer Cente