A Birkhoff connection between quantum circuits and linear classical reversible circuits

Birkhoff's theorem tells how any doubly stochastic matrix can be decomposed as a weighted sum of permutation matrices. Similar theorems on unitary matrices reveal a connection between quantum circuits and linear classical reversible circuits. It triggers the question whether a quantum computer can be regarded as a superposition of classical reversible computers

Gene-culture coevolution of a linguistic system in two modalities

Complex communication can take place in a range of modalities such as auditory, visual, and tactile modalities. In a very general way, the modality that individuals use is constrained by their biological biases (humans cannot use magnetic fields directly to communicate to each other). The majority of natural languages have a large audible component. However, since humans can learn sign languages just as easily, it’s not clear to what extent the prevalence of spoken languages is due to biological biases, the social environment or cultural inheritance. This paper suggests that we can explore the relative contribution of these factors by modelling the spontaneous emergence of sign languages that are shared by the deaf and hearing members of relatively isolated communities. Such shared signing communities have arisen in enclaves around the world and may provide useful insights by demonstrating how languages evolve as the deaf proportion of its members has strong biases towards the visual language modality. In this paper we describe a model of cultural evolution in two modalities, combining aspects that are thought to impact the emergence of sign languages in a more general evolutionary framework. The model can be used to explore hypotheses about how sign languages emerge

On two subgroups of U(n), useful for quantum computing

As two basic building blocks for any quantum circuit, we consider the 1-qubit PHASOR circuit Phi(theta) and the 1-qubit NEGATOR circuit N(theta). Both are roots of the IDENTITY circuit. Indeed: both (NO) and N(0) equal the 2 x 2 unit matrix. Additionally, the NEGATOR is a root of the classical NOT gate. Quantum circuits (acting on w qubits) consisting of controlled PHASORs are represented by matrices from ZU(2(w)); quantum circuits consisting of controlled NEGATORs are represented by matrices from XU(2(w)). Here, ZU(n) and XU(n) are subgroups of the unitary group U(n): the group XU(n) consists of all n x n unitary matrices with all 2n line sums (i.e. all n row sums and all n column sums) equal to 1 and the group ZU(n) consists of all n x n unitary diagonal matrices with first entry equal to 1. Any U(n) matrix can be decomposed into four parts: U = exp(i alpha) Z(1)XZ(2), where both Z(1) and Z(2) are ZU(n) matrices and X is an XU(n) matrix. We give an algorithm to find the decomposition. For n = 2(w) it leads to a four-block synthesis of an arbitrary quantum computer

Isolation and mapping of a C3'H gene (CYP98A49) from globe artichoke, and its expression upon UV-C stress

Globe artichoke represents a natural source of phenolic compounds with dicaffeoylquinic acids along with their biosynthetic precursor chlorogenic acid (5-caffeoylquinic acid) as the predominant molecules. We report the isolation and characterization of a full-length cDNA and promoter of a globe artichoke p-coumaroyl ester 3¿-hydroxylase (CYP98A49), which is involved in both chlorogenic acid and lignin biosynthesis. Phylogenetic analyses demonstrated that this gene belongs to the CYP98 family. CYP98A49 was also heterologously expressed in yeast, in order to perform an enzymatic assay with p-coumaroylshikimate and p-coumaroylquinate as substrates. Real Time quantitative PCR analysis revealed that CYP98A49 expression is induced upon exposure to UV-C radiation. A single nucleotide polymorphism in the CYP98A49 gene sequence of two globe artichoke varieties used for genetic mapping allowed the localization of this gene to linkage group 10 within the previously developed map

Structure, Organization, and Expression of the lct Gene for Lacticin 481, a Novel Lantibiotic Produced by Lactococcus lactis

The structural gene for the lactococcal lantibiotic lacticin 481 (lct) has been identified and cloned using a degenerated 20-mer DNA oligonucleotide based on the amino-terminal 7 amino acid residues of the purified protein. The transcription of the lct gene was analyzed, and its promoter was mapped. DNA sequence analysis of the lct gene revealed an open reading frame encoding a peptide of 51 amino acids. Comparison of its deduced amino acid sequence with the amino-terminal sequence and the amino acid composition of lacticin 481 indicates that the 61-residue peptide is prelacticin 481, containing a 27-residue carboxyl-terminal propeptide and a 24-residue amino-terminal leader peptide which lacks the properties of a typical signal sequence and which is significantly different from the leaders of other lantibiotics. The predicted amino acid sequence of prolacticin 481 contains 3 cysteines, 2 serines, and 2 threonines which were not detectable in amino acid analyses of mature lacticin 481. Based on these results and on characterization by two-dimensional NMR techniques, a structural model is proposed in which 2 cysteine residues are involved in lanthionine and one in β-methyllanthionine formation, and a 4th threonine residue is dehydrated. This model predicts a molecular mass for lacticin 481 of 2,901, which is in excellent agreement with that obtained from mass spectrometry.