pinecone/core-2020-05-10-deduplication huggingface dataset:
Chondroitin sulphate proteoglycan is involved in lens vesicle morphogenesis in chick embryos

Producción CientíficaProteoglycans have been implicated in the invagination and formation of various embryonal cavitied
primordia. In this paper the expression of chondroitin sulphate proteoglycan is analysed (CSPG) in the lens
primordium during lens vesicle formation, and demonstrate that this proteoglycan has a speci®c
distribution pattern with regard to invagination and fusion processes in the transformation of placode into
lens vesicle. More speci®cally, CSPG was detached in: (1) the apical surface of lens epithelial cells, where
early CSPG expression was observed in the whole of the lens placode whilst in the vesicle phase it was
restricted to the posterior epithelium; (2) intense CSPG expression in the basal lamina, which remained
constant for the entire period under study; (3) CSPG expression in the intercellular spaces of the lens
primordium epithelium, which increased during the invagination of the primordium and which at the
vesicle stage was more evident in the posterior epithelium; and (4) CSPG expression on the edges of the
lens placode both prior to and during fusion. Treatment with b-D-xyloside causes signi®cant CSPG
depletion in the lens primordium together with severe alterations in the invagination and fusion of the
lens vesicle; this leads to the formation of lens primordia which in some cases remain practically ¯at or
show partial invagination defects or fusion disruption. Similar results were obtained by enzyme digestion
with chondroitinase AC but not with type II heparinase, which indicates that alterations induced by b-Dxyloside
were due to interference in CSPG synthesis. The ®ndings demonstrate that CSPG is a common
component of the lens primordium at the earliest developmental stages during which it undergoes speci®c
modi®cations. It also includes experimental evidence to show that `in vivo' CSPG plays an important role
in the invagination and fusion processes of the lens primordium. # 2001 Academic Press
Key words: lens development; CSPG; b-D-xyloside; extracellular matrix; epithelial invaginatio
Manganese-induced hydroxyl radical formation in rat striatum is not attenuated by dopamine depletion or iron chelation in vivo

The present studies were aimed at investigating the possible roles of dopamine (DA) and iron in production of hydroxyl radicals (.OH) in rat striatum after Mn2+ intoxication. For this purpose, DA depletions were assessed concomitant with in vivo 2,3- and 2,5-dihydroxybenzoic acid (DHBA) formation from the reaction of salicylate with .OH, of which 2,3-DHBA is a nonenzymatic adduct. Following intrastriatal Mn2+ injection, marked 2,3-DHBA increases were observed in a time- and dose-dependent fashion reaching maximum levels at 6-18 h and a plateau beyond 0.4 μmol (fourfold increase). The delayed increase of 2,3-DHBA levels suggests that Mn2+ induces OH formation in the living brain by an indirect process. The early DA depletion (2 h) and relatively late .OH formation (6 h) indicate independent processes by Mn2+. In addition, depletion of DA (about 90%) by reserpine pretreatment did not significantly alter Mn2+-induced 2,3-DHBA formation or the extent of DA depletion, suggesting that DA or DA autoxidation are not participating in Mn2+-induced .OH formation in vivo. Furthermore, Mn2+ injection did not significantly alter the low molecular weight iron pool in striatum, and co-injections of the iron-chelator deferoxamine with Mn2+ into striatum did not significantly attenuate Mn2+-induced 2,3-DHBA formation. These findings suggest no role of chelatable iron in generation of Mn2+-induced .OH, but do not exclude a role for mitochondrial heme-iron or peroxynitrite (Fe-independent) in Mn2+-induced .OH formation
Explicit Iterative Constructions of Normal Bases and Completely Free Elements in Finite Fields

AbstractA characterization of normal bases and complete normal bases in GF(qrn) over GF(q), whereq> 1 is any prime power,ris any prime number different from the characteristic of GF(q), andn≥ 1 is any integer, leads to a general construction scheme of series (vn)n≥0in GF(qr∞) ≔ ∪ni≥0GF(≔qrn) having the property that the partial sumswn≔ Σni≔0viare free or completely free in GF(qrn) over GF(q), depending on the choice ofvn.In the case whereris an odd prime divisor ofq− 1 or wherer= 2 andq≡ 1 mod 4, for any integern≥ 1, all free and completely free elements in GF(qrn) over GF(q) are explicitly determined in terms of certain roots of unity.In the case wherer= 2 andq≡ 3 mod 4, for anyn≥ 1, in terms of certain roots of unity, an explicit recursive construction for free and completely free elements in GF(q2n) over GF(q) is given.As an example, for a particular series of completely free elements the corresponding minimal polynomials are given explicitly
Normal Bases and Completely Free Elements in Prime Power Extensions over Finite Fields

AbstractWe continue the work of the previous paper (Hachenberger,Finite Fields Appl., in press), and, generalizing some of the results obtained there, we give explicit constructions of free and completely free elements in GF(qrn) over GF(q), wherenis any nonnegative integer and whereris any odd prime number which does not divide the characteristic of GF(q) or wherer= 2 andq≡ 1 mod 4. Together with results on the case wherer= 2 andq≡ 3 mod 4 obtained in the previous paper and results on the well-known case whereris equal to the characteristic of GF(q), we are able to explicitly determine free and completely free elements in GF(qm) over GF(q) for every nonnegative integermand every prime powerq
Finite Upper Half Planes over Finite Fields

AbstractFinite upper half planes have been studied by Terras, Poulos, Celniker, Trimble, and Velasquez. Motivated by Stark'sp-adic upper half plane as ap-adic analog of the Poincaré upper half plane, a finite field of odd characteristic was used as the finite analog of the real line. The analog of the upper half plane was constructed by adjoining the square root of a non-square to the finite field. Since this is not possible with a finite field of even characteristic, this paper will introduce a modification which will enable all finite fields to be considered. After constructing the finite upper half planes, graphs on these planes will be considered. We are interested in the spectrum, girth, diameter, and other combinatorial properties of these graphs
Description of Minimum Weight Codewords of Cyclic Codes by Algebraic Systems

AbstractWe consider cyclic codes of lengthnover Fq,nbeing prime toq. For such a cyclic codeC, we describe a system of algebraic equations, denoted by SC(w), wherewis a positive integer. The system is constructed from Newton's identities, which are satisfied by the elementary symmetric functions and the (generalized) power sum symmetric functions of the locators of codewords of weightw. The main result is that, in a certain sense, thealgebraicsolutions of SC(w) are in one-to-one correspondence with all the codewords ofChaving weight lower thanw. In the particular case wherewis the minimum distance ofC, all minimum weight codewords are described by SC(w). Because the system SC(w) is very large, with many indeterminates, no great insight can be directly obtained, and specific tools are required in order to manipulate the algebraic systems. For this purpose, the theory ofGröbner basescan be used. A Gröbner basis of SC(w) gives information about the minimum weight codewords
Classification of Algebraic Function Fields with Divisor Class Number Two

AbstractIn a previous paper we proved that there are 11 quadratic algebraic function fields with divisor class number two. Here we complete the classification of algebraic function fields with divisor class number two giving all non-quadratic solutions. Our result is the following. Let us denote bykthe finite field withqelements. Up to isomorphism, there are exactly 8 non-quadratic algebraic function fields of one variableK/khavingkfor full constant field and with a divisor class number equal to two
Weight Behavior of Irreducible Cyclic BWD-Codes

AbstractIn Langevin and Zanotti (1995), we introduced a new class of codes called balanced weight distribution (BWD)-codes, with the remarkable property that their weight distribution is balanced, i.e., there are the same number of codewords for each non-zero weight. The aim of this paper is to study the weights of such codes in the irreducible cyclic case. First we recall the fundamental property of BWD-codes, and we start this study from a deep link between weights and Gauss sums. We see that this particular situation is, roughly speaking, in opposition to those studied by McEliece (1974). We give the weights for the two-weight case, and we show that the weights ofanyN-weight BWD-code defined over Fqis completely determined by theNweights of a BWD-code of dimensionNdefined over the prime field Fp. The main result is on the asymptotic behavior of Gauss sums over Fp, by means of a nice technique introduced by Rodier (1993)
The Incongruence of Consecutive Values of Polynomials

AbstractSuppose thatf∈ Z|x|. PutDf(n) = min{k> 0|f(1), ... ,f(n) are pairwise incongruent modulok}. Special cases of this function were previously considered, using methods from elementary number theory. Results from the theory of finite fields are used to prove a theorem that for allfin a large subset of Z|x| provides a characterization ofDf(n) for allnsufficiently large. This theorem partially encompasses results due to Bremser, Schumer and Washington and to Moree and Mullen, who characterizedDf(n) for cyclic, respectively, Dickson polynomials
Binary Representations of Finite Fields and Their Application to Complexity Theory

AbstractBinary representations of finite fields are defined as an injective mapping from a finite field tol-tuples with components in {0, 1} where 0 and 1 are elements of the field itself. This permits one to study the algebraic complexity of a particular binary representation, i.e., the minimum number of additions and multiplications in the field needed to compute the binary representation. The two-way complexity of a binary representation is defined as the sum of the algebraic complexities of the binary representation and of its inverse mapping. Two particular binary representations are studied: the standard representation and the logarithmic representation. A method of surrogate computation is developed and used to deduce relationships between the algebraic complexities of certain functions. The standard representation of a finite field is shown to be among the two-way easiest representations of this field. In particular, the standard representation of a finite field with characteristicpis two-way easy wheneverp− 1 has only small prime factors. For any finite field having a two-way easy binary representation, the algebraic complexity in this field is shown to be essentially equivalent to Boolean circuit complexity. For any finite field, the Boolean circuit complexity of Zech's (or Jacobi's) logarithm is shown to be closely related to the Boolean circuit complexity of the discrete logarithm problem that is used in public-key cryptography
Vanishing Sums ofmth Roots of Unity in Finite Fields

AbstractIn an earlier work, the authors determined all possible weightsnfor which there exists a vanishing sum ζ1+ ··· + ζn= 0 ofmth roots of unity ζiin characteristic 0. In this paper, the same problem is studied in finite fields of characteristicp. For givenmandp, results are obtained on integersn0such that all integersn≥n0are in the “weight set”Wp(m). The main result in this paper guarantees, under suitable conditions, the existence of solutions ofxd1 + ··· +xdn= 0with all coordinates not equal to zeroover a finite field
A Weil-Bound Free Proof of Schur's Conjecture

AbstractLetfbe a polynomial with coefficients in the ring OKof integers of a number field. Suppose thatfinduces a permutation on the residue fields OK/p for infinitely many nonzero prime ideals p of OK. Then Schur's conjecture, namely thatfis a composition of linear and Dickson polynomials, has been proved by M. Fried. All the present versions of the proof use Weil's bound on the number of points of absolutely irreducible curves over finite fields in order to get a Galois theoretic translation and to finish the proof by means of finite group theory. This note replaces the use of this deep result by elementary arguments
Cyclic Self-DualZ4-Codes

AbstractFornodd, theZ4cyclic code generated by 2 is self-dual. We call this a trivial cyclic self-dual code. When do there exist nontrivial cyclic self-dual codes of odd lengthn? We give an answer in this paper by characterizing thesenand describing generators of such codes; this yields an existence test for cyclic difference sets. We also give all examples of nontrivial cyclic self-dual codes up to length 39. From these nontrivial cyclic, self-dual codes, construction A yields unimodular lattices of Type I, some of which are extremal; extension and augmentation yields three new extremal Type II codes of length 32, and an extremal self-dual code of Type II of length 40
Blocking Sets in Desarguesian Affine and Projective Planes

AbstractIn this paper we show that blocking sets of cardinality less than 3(q+ 1)/2 (q=pn) in Desarguesian projective planes intersect every line in 1 moduloppoints. It is also shown that the cardinality of a blocking set must lie in a few relatively short intervals. This is similar to previous results of Rédei, which were proved for a special class of blocking sets. In the particular caseq=p2, the above result implies that a nontrivial blocking set either contains a Baer-subplane or has size at least 3(q+ 1)/2; and this result is sharp. As a by-product, new proofs are given for the Jamison, Brouwer-Schrijver theorem on blocking sets in Desarguesian affine planes, and for Blokhuis' theorem on blocking sets in Desarguesian projective planes
Density of Normal Elements

AbstractLetf∈ Fq[x] be a monic polynomial of degreen, and let Φ(f) denote the number of polynomials in Fq[x] of degree <nthat are relatively prime tof. Let κ(f) = Φ(f)/qn. We slightly improve the previous known lower bounds of κ(f). The density of normal elements in Fqnover Fqis κ(xn− 1) = Φ(xn− 1)/qn. We prove that κ(xn− 1) ≥C> 0 forn=pe11pe22···pett, wherepiare any fixed primes,eivary, andCis a constant independent ofei's. Unfortunately, this is not true for generaln. Indeed, we show an upper bound on κ(xn− 1) for infinitely many values ofnthat goes to 0 asnapproaches infinity. This upper bound is almost tight with our lower bound for a general polynomialf
Average Discrepancy, Hyperplanes, and Compound Pseudorandom Numbers

AbstractThis paper deals with compound nonlinear congruential methods for generating uniform pseudorandom numbers. The average equidistribution and statistical independence behavior of the generated sequences over arbitrary parts of the period is studied, based on the average value of the discrepancy of certain point sets. General upper bounds for these average values are established, which depend on the number of points on certain hyperplanes over finite fields. These bounds are applied to the compound explicit inversive congruential method, which has been introduced recently
Parallel Streams of Nonlinear Congruential Pseudorandom Numbers

AbstractThis paper deals with the general nonlinear congruential method for generating uniform pseudorandom numbers, in which permutation polynomials over finite prime fields play an important role. It is known that these pseudorandom numbers exhibit an attractive equidistribution and statistical independence behavior. In the context of parallelized simulation methods, a large number of parallel streams of pseudorandom numbers with strong mutual statistical independence properties are required. In the present paper, such properties of parallelized nonlinear congruential generators are studied based on the discrepancy of certain point sets. Upper and lower bounds for the discrepancy both over the full period and over (sufficiently large) parts of the period are established. The method of proof rests on the classical Weil bound for exponential sums
On the Existence of Abelian Hadamard Difference Sets and a New Family of Difference Sets

AbstractWe present a construction of Hadamard difference sets in abelian groups of order 4p4n, whose Sylowp-subgroups are elementary. By a standard composition procedure, we can now conclude that (4h2, 2h2−h,h2−h)-Hadamard difference sets exist forh= 2ϵ13ϵ2u2, where ϵ1, ϵ2= 0 or 1 anduis a positive integer. We then generalize the construction of Hadamard difference sets to construct a family of (4q2n(q2n− 1)/(q2−1),q2n−1[2(q2n− 1)/(q+ 1) + 1], (q2n−q2n−1)(q2n−1 + 1)/(q+ 1)-difference sets, whereqis an even power of an odd prime or any power of 3
On Towers and Composita of Towers of Function Fields over Finite Fields

AbstractFor a towerF1⊆F2⊆ ··· of algebraic function fieldsFi/Fq, define λ = limi→∞N(Fi)/g(Fi), whereN(Fi) is the number of rational places andg(Fi) is the genus ofFi/Fq. The tower is said to be asymptotically good if λ > 0. We give a very simple explicit example of an asymptotically good tower for all non-prime fields Fq. In this example, all stepsFi+1/Fiare tamely ramified Kummer extensions. We then show that any function fieldF/Fqhaving at least one rational place can be embedded into an asymptotically good tower, and we study the behaviour of λ in the compositum of a towerF1⊆F2⊆ ··· with an extensionE/F1
On the Number of Solutions of Polynomial Systems

AbstractWe consider systems of homogenous polynomial equations of degreedin a projective space Pmover a finite field Fq. We attempt to determine the maximum possible number of solutions of such systems. The complete answer for the caser= 2,d<q− 1 is given, as well as new conjectures about the general case. We also prove a bound on the number of points of an algebraic set of given codimension and degree. We also discuss an application of our results to coding theory, namely to the problem of computing generalized Hamming weights forq-ary projective Reed–Muller codes
Cyclic Codes over the Integers Modulopm

AbstractThe purpose of this paper is twofold. First, we generalize the results of Pless and Qian and those of Pless, Solé, and Qian for cyclic Z4-codes to cyclic Zpm-codes. Second, we establish connections between this new development and the results on cyclic Zpm-codes obtained by Calderbank and Sloane. We produce generators for the cyclic Zpm-codes which are analogs to those for cyclic Z4-codes. We show that these may be used to produce a single generator for such codes. In particular, this proves that the ringRn= Zpm[x]/(xn− 1) is principal, a result that had been previously announced with an incorrect proof. Generators for dual codes of cyclic Zpm-codes are produced from the generators of the corresponding cyclic Zpm-codes. In addition, we also obtain generators for the cyclicpm-ary codes induced from the idempotent generators for cyclicp-ary codes
α-Flocks with Oval Herds and Monomial Hyperovals

AbstractInPG(3,q),qeven, Cherowitzo made a detailed study of flocks of a cone with a translation oval as base; also calledα-flocks [4]. To a flock of a quadratic cone inPG(3,q),qeven, there always corresponds a set ofq+1 ovals inPG(2,q), called anoval herd. To anα-flock of a cone with an arbitrary translation oval as base, there corresponds a herd ofq+1 permutation polynomials. For some, but not for all, known examples ofα-flocks, theseq+1 permutation polynomials define an oval herd. This leads to the fundamental problem of determining whichα-flocks correspond to an oval herd. This article studies a class ofα-flocks and explicitly describes which members of this class have an associated oval herd. To achieve this goal, all monomial hyperovals {(1,t,tk)∥t∈Fq}∪{(0, 1, 0), (0, 0, 1)} withk=2i+2j,i≠j, are determined
Similarity to Symmetric Matrices over Finite Fields

AbstractIt has been known for some time that every polynomial with coefficients from a finite field is the minimum polynomial of a symmetric matrix with entries from the same field. What have remained unknown, however, are the possible sizes for the symmetric matrices with a specified minimum polynomial and, in particular, the least possible size. In this paper we answer these questions using only the prime factorization of the given polynomial. Closely related is the question of whether or not a given matrix over a finite field is similar to a symmetric matrix over that field. Although partial results on that question have been published before, this paper contains a complete characterization
Polynomial Factorisation and an Application to Regular Directed Graphs

AbstractThe main theme is the distribution of polynomials of given degree which split into a product of linear factors over a finite field. The work was motivated by the following problem on regular directed graphs. Extending a notion of Chung, Katz has defined a regular directed graph based on thek-algebrak[X]/(f), wherekis the finite field of orderqandfa monic polynomial of degreenoverk. It is shown that the diameter of this graph is at mostn+2 wheneverq≥B(n)=[n(n+2)!]2. This improves on the work of Katz who gave a similar result for square-free polynomialsfwithout specifyingB(n)
Subregular Spreads ofPG(2n+1,q)

AbstractIn this paper, we develop some of the theory of spreads of projective spaces with an eye towards generalizing the results of R. H. Bruck (1969,in“Combinatorial Mathematics and Its Applications,” Chap. 27, pp. 426–514, Univ. of North Carolina Press, Chapel Hill). In particular, we wish to generalize the notion of asubregularspread to the higher dimensional case. Most of the theory here was anticipated by Bruck in later papers; however, he never provided a detailed formulation. We fill this gap here by developing the connections between a regular spread of (2n+1)-dimensional projective space and ann-dimensional circle geometry, which is the appropriate generalization of the Miquelian inversive plane. After developing this theory, we provide a fairly general method for constructing subregular spreads ofPG(5,q). Finally, we explore a special case of this construction, which yields several examples of three-dimensional subregular translation planes which are not André planes
On Value Sets of Polynomials over a Finite Field

AbstractWe study value sets of polynomials over a finite field, and value sets associated to pairs of such polynomials. For example, we show that the value sets (counting multiplicities) of two polynomials of degree at mostdare identical or have at mostq−(q−1)/dvalues in common whereqis the number of elements in the finite field. This generalizes a theorem of D. Wan concerning the size of a single value set. We generalize our result to pairs of value sets obtained by restricting the domain to certain subsets of the field. These results are preceded by results concerning symmetric expressions (of low degree) of the value set of a polynomial. K. S. Williams, D. Wan, and others have considered such expressions in the context of symmetric polynomials, but we consider (multivariable) polynomials invariant under certain important subgroups of the full symmetry group