Search results for " Closed"

Wellfounded Trees and Dependent Polynomial Functors

2004

We set out to study the consequences of the assumption of types of wellfounded trees in dependent type theories. We do so by in- vestigating the categorical notion of wellfounded tree introduced in [16]. Our main result shows that wellfounded trees allow us to define initial algebras for a wide class of endofunctors on locally cartesian closed cat- egories.

Maximal Closed Substrings

2022

A string is closed if it has length 1 or has a nonempty border without internal occurrences. In this paper we introduce the definition of a maximal closed substring (MCS), which is an occurrence of a closed substring that cannot be extended to the left nor to the right into a longer closed substring. MCSs with exponent at least 2 are commonly called runs; those with exponent smaller than 2, instead, are particular cases of maximal gapped repeats. We show that a string of length n contains O(n1.5) MCSs. We also provide an output-sensitive algorithm that, given a string of length n over a constant-size alphabet, locates all m MCSs the string contains in O(nlog n+ m) time.

Varieties of algebras with pseudoinvolution: Codimensions, cocharacters and colengths

2022

Abstract Let A be a finitely generated superalgebra with pseudoinvolution ⁎ over an algebraically closed field F of characteristic zero. In this paper we develop a theory of polynomial identities for this kind of algebras . In particular, we shall consider three sequences that can be attached to Id ⁎ ( A ) , the T 2 ⁎ -ideal of identities of A: the sequence of ⁎-codimensions c n ⁎ ( A ) , the sequence of ⁎-cocharacter χ 〈 n 〉 ⁎ ( A ) and the ⁎-colength sequence l n ⁎ ( A ) . Our purpose is threefold. First we shall prove that the ⁎-codimension sequence is eventually non-decreasing, i.e., c n ⁎ ( A ) ≤ c n + 1 ⁎ ( A ) , for n large enough. Secondly, we study superalgebras with pseudoinvoluti…

Open and Closed Words

2017

Combinatorics on words aims at finding deep connections between properties of sequences. The resulting theoretical findings are often used in the design of efficient combinatorial algorithms for string processing, but may also have independent interest, especially in connection with other areas of discrete mathematics. The property we discuss here is, for a given finite word, that of being closed. A finite word is called closed if it has length ≤ 1 or it contains a proper factor (substring) that occurs both as a prefix and as a suffix but does not have internal occurrences. Otherwise the word is called open. We illustrate several aspects of open and closed words and factors, and propose som…

On the Quadratic Type of Some Simple Self-Dual Modules over Fields of Characteristic Two

1997

Let G be a finite group and let K be an algebraically closed field of Ž characteristic 2. Let V be a non-trivial simple self-dual KG-module we . say that V is self-dual if it is isomorphic to its dual V * . It is a theorem of w x Fong 4, Lemma 1 that in this case there is a non-degenerate G-invariant alternating bilinear form, F, say, defined on V = V. We say that V is a KG-module of quadratic type if F is the polarization of a non-degenerate w x G-invariant quadratic form defined on V. In a previous paper 6 , the present authors described some methods to decide if such a module V is of w x quadratic type. One of the main results of 6 is the following. Suppose that Ž . G is a group with a s…

An Intracortical Implantable Brain-Computer Interface for Telemetric Real-Time Recording and Manipulation of Neuronal Circuits for Closed-Loop Interv…

2021

Recording and manipulating neuronal ensemble activity is a key requirement in advanced neuromodulatory and behavior studies. Devices capable of both recording and manipulating neuronal activity brain-computer interfaces (BCIs) should ideally operate un-tethered and allow chronic longitudinal manipulations in the freely moving animal. In this study, we designed a new intracortical BCI feasible of telemetric recording and stimulating local gray and white matter of visual neural circuit after irradiation exposure. To increase the translational reliance, we put forward a Göttingen minipig model. The animal was stereotactically irradiated at the level of the visual cortex upon defining the targe…

Existentially closed central extensions of locally finite p-groups

1986

Throughout, p will be a fixed prime, and will denote the class of all locally finite p-groups. For a fixed Abelian p-group A, we letwhere ζ(P) denotes the centre of P. Notice that A is not a class in the usual group-theoretic sense, since it is not closed under isomorphisms.

Graded Involutions on Upper-triangular Matrix Algebras

2009

Let UTn be the algebra of n × n upper-triangular matrices over an algebraically closed field of characteristic zero. We describe all G-gradings on UTn by a finite abelian group G commuting with an involution (involution gradings).

Finite Groups with Only One NonLinear Irreducible Representation

2012

Let 𝕂 be an algebraically closed field. We classify the finite groups having exactly one irreducible 𝕂-representation of degree bigger than one. The case where the characteristic of 𝕂 is zero, was done by G. Seitz in 1968.

A Uniform Way to Control Chief Series in Finite p -Groups and to Construct the Countable Algebraically Closed Locally Finite p -Groups

1986