In the largest, longitudinal study of young, deaf children before and three years after cochlear implantation, we compared symbolic play and novel noun learning to age-matched hearing peers. Participants were 180 children from six cochlear implant centers and 96 hearing children. Symbolic play was measured during five minutes of videotaped, structured solitary play. Play was coded as "symbolic"...

In 2020, the educational systems of several countries have been affected by Covid-19 pandemic. Brazil, Education Ministry allowed substitution in person classes for digital environments. We report our experience an academic internship project psychology based on sociodramatic methodology and a focus permanence success as symbolic conditions linked to development role university student times Em...

This mini-workshop brought together researchers with diverse backgrounds and a common interest in facets of the Pisot conjecture, which relates certain properties of a substitution to dynamical properties of the associated subshift. Mathematics Subject Classification (2000): 37B10, 28A80, 37B50, 52C23. Introduction by the Organisers A substitution is a non-erasing morphism of the free monoid. S...

Recent work investigates the combination of Computer Algebra Systems and Automated Theorem Provers We elaborate a concrete example the generic construction of complex numbers quaternions Cayley numbers on top of real numbers The implementation is done by a functor in the programming language SML which can be instantiated to perform the algebraic computations Another instantiation of the same fu...

We consider S-adic expansions associated with continued fraction algorithms, where an S-adic expansion corresponds to an infinite composition of substitutions. Recall that a substitution is a morphism of the free monoid. We focus in particular on the substitutions associated with regular continued fractions (Sturmian substitutions), and with Arnoux–Rauzy, Brun, and Jacobi–Perron (multidimension...

Suppose a, b, c are algebraic indeterminates. The mapping (a, b, c) → (bc, ca, ab) is an example of a second-degree involutory symbolic substitution (SISS) which maps the transfigured plane of a triangle to itself. The main result is a classification of SISSs as four individual mappings and two families of mappings. The SISS (a, b, c) → (bc, ca, ab) maps the circumcircle onto the Steiner ellips...

1. S.L. Bloom, The hyperprojective hierarchy, Notices of the AMS, Vol. 15(1968), 343. 2. S.L. Bloom, Theories of kind W, Notices of the AMS, 16(1969), 507. 3. S.L. Bloom, D. Brown, Classical abstract logics I, Notices of the AMS, 18(1971), 827. 4. S.L. Bloom, D. Brown, Classical abstract logics II, Notices of the AMS, 18(1971), 968. 5. S.L. Bloom, R. Suszko, D. Brown, Structurality, substitutio...

For general-purpose quantum computing, the addition rules must be imposed and implemented first. An examination of this condition shows that the use of qubits is fundamentally flawed. The reasons are elaborated here. When two qubits are used for an addition operation of two bits, it is not the four states in superposition that are relevant for the addition. Rather it is the four symbolic substi...

This paper presents a novel method for loop optimization that exploits symbolic evaluation of chains of recurrences (CRs). The method generalizes loop induction expression recognition, loop parallelization by induction variable substitution, loop strength reduction , and loop invariant expression elimination (code motion). Symbolic diierencing of loops has been extensively studied by Haghighat ...