Canonical Products Research Articles

Tailored fatty acid synthesis via dynamic control of fatty acid elongation

Medium-chain fatty acids (MCFAs, 4-12 carbons) are valuable as precursors to industrial chemicals and biofuels, but are not canonical products of microbial fatty acid synthesis. We engineered microbial production of the full range of even- and odd-chain-length MCFAs and found that MCFA production is limited by rapid, irreversible elongation of their acyl-ACP precursors. To address this limitation, we programmed an essential ketoacyl synthase to degrade in response to a chemical inducer, thereby slowing acyl-ACP elongation and redirecting flux from phospholipid synthesis to MCFA production. Our results show that induced protein degradation can be used to dynamically alter metabolic flux, and thereby increase the yield of a desired compound. The strategy reported herein should be widely useful in a range of metabolic engineering applications in which essential enzymes divert flux away from a desired product, as well as in the production of polyketides, bioplastics, and other recursively synthesized hydrocarbons for which chain-length control is desired.

Zero distribution and factorization of analytic functions of slow growth in the unit disc

For a meromorphic function f f in the unit disc, let the ρ ∞ \rho _\infty -order of the growth be the limit of the orders of L p L_p -norms of log ⁡ | f ( r e i θ ) | \log |f(re^{i\theta })| over the circle. In the case when the order of the maximum modulus function is smaller than 1, we describe zero distribution of canonical products and derive a new factorization theorem and logarithmic derivative estimates.

Tensor products for non-unital operator systems

In this short article, we study tensor products of not necessarily unital operator systems (for short, NUOS). We will define canonical functorial NUOS tensor products (in a similar fashion to Kavruk et al. (2011) [4]) as well as a subclass of them consisting of reduced functorial NUOS tensor products (that are defined through a unitalization process). We show that if a NUOS X is (Min,Max)-nuclear (in the sense that there is only one NUOS tensor product of X with any NUOS Y), then X is trivial. However, if V is a unital operator system, then V is (min0,max0)-nuclear (in the sense that there is only one reduced NUOS tensor product of V with any NUOS Y) if and only if V is (min,max)-nuclear in the sense of Han and Paulsen (2011) [2] (i.e. there is only one unital operator system tensor product of V with any unital operator system W). On the other hand, a C∗-algebra A is (min0,max0)-nuclear if and only if A is a nuclear C∗-algebra.

Canonical products generated by perturbations of the sequence of integers, and their asymptotic estimation

We obtain asymptotic estimates for canonical products with complex zeros of the form . A formula is found for the excess of the system of exponentials in the space . We consider some particular cases of sequences .

Asymptotic estimates for the canonical products with zeros of a particular form

We obtain sharp asymptotic estimates on the whole complex plane for the canonical products with zeros of the form λn = s-nαl(n), where α > 0 and l(t) is a slowly varying function.

A Large Fraction of Extragenic RNA Pol II Transcription Sites Overlap Enhancers

Author SummaryMammalian genomes contain vast intergenic regions that are extensively transcribed and generate various types of short and long non-coding RNAs (ncRNAs). Although in some cases specific functions have been assigned to intergenic transcripts, the functional significance of this transcriptional output remains largely unknown, and the possibility exists that part of this transcription reflects noise generated by random collisions of the transcriptional machinery with the genome to generate meaningless transcription. In this study we used chromatin signatures to characterize extragenic transcription sites targeted by RNA Polymerase II (RNA Pol II) in a highly regulated response—endotoxin activation of macrophages. We found that a significant portion of extragenic transcription sites are associated with the chromatin signature characteristic of enhancers. Consistent with their chromatin signature, we found that these extragenic transcription sites are under purifying selection and contain binding sites for inflammatory transcription factors, as well as for PU.1, a hematopoietic transcription factor that marks enhancers in macrophages. Moreover, much of this extragenic transcription is regulated by stimulation. We also identified hundreds of transcribed regions with a signature of canonical RNA genes. Our data indicate that extragenic transcription sites can be efficiently classified using chromatin signatures, which will be relevant for functional annotation of mammalian genomes.

Canonical Tensor Products as a Generalization of Gaussian-type Orbitals

Abstract We propose a possible generalization of Gaussian-type orbital (GTO) bases by means of canonical tensor products. The present work focus on the application of tensor products as an alternative to conventional GTO based density fitting schemes. Tensor product approximation leads to highly nonlinear optimization problems which require sophisticated algorithms. We give a brief description of the optimization problem and algorithm. The present work extends our previous paper [S. R. Chinnamsetty, M. Espig, B. N. Khoromskij, W. Hackbusch and H.-J. Flad, J. Chem. Phys. 127 (2007), 084110], where we discussed tensor product approximations of the electron density and the Hartree potential, to orbital products which are required for the exchange part of Hartree-Fock and in post Hartree-Fock methods. We provide a detailed error analysis for the Coulomb and exchange terms in Hartree-Fock calculations. Furthermore, a comparison is given between all-electron and pseudopotential calculations.

Lower and upper bounds for canonical products

New upper and lower bounds for the canonical products of finite order entire functions are established.

On the regularity of growth of canonical products with real zeros

We obtain a criterion for totally regular growth of canonical products with real symmetric zeros, which involves a generalization of the notion of condensation index of a sequence of positive numbers of a finite upper density.

Hzf, a p53-Responsive Gene, Regulates Maintenance of the G2 Phase Checkpoint Induced by DNA Damage

The hematopoietic zinc finger protein, Hzf, is induced in response to genotoxic and oncogenic stress. The Hzf protein is encoded by a p53-responsive gene, and its overexpression, either in cells retaining or lacking functional 53, halts their proliferation. Enforced expression of Hzf led to the appearance of tetraploid cells with supernumerary centrosomes and, ultimately, to cell death. Eliminating Hzf mRNA expression by use of short hairpin (sh) RNAs had no overt effect on unstressed cells but inhibited the maintenance of G2 phase arrest following ionizing radiation (IR), thereby sensitizing cells to DNA damage. Canonical p53-responsive gene products such as p21Cip1 and Mdm2 were induced by IR in cells treated with Hzf shRNA. However, the reduction in the level of Hzf protein was accompanied by increased polyubiquitination and turnover of p21Cip1, an inhibitor of cyclin-dependent kinases whose expression contributes to maintaining the duration of the G2 checkpoint in cells that have sustained DNA damage. Thus, two p53-inducible gene products, Hzf and p21Cip1, act concomitantly to enforce the G(2) checkpoint.

Canonical products of small order and related Pick functions

We show that various functions related to the logarithms of the canonical products P ρ ( z ) = ∏ n = 1 ∞ ( 1 + z / n ρ ) , ρ > 1 and Q ( z ) = ∏ n = 0 ∞ ( 1 + zq n ) , q ∈ ( 0 , 1 ) are Pick functions. As a consequence we find an integral expansion of a function involving the logarithm of Jacksons q-gamma function.

Berezin-Toeplitz Operators, a Semi-Classical Approach

This article is devoted to the Toeplitz Operators [4] in the context of the geometric quantization [11, 15]. We propose an ansatz for their Schwartz kernel. From this, we deduce the main known properties of the principal symbol of these operators and obtain new results : we define their covariant and contravariant symbols, which are full symbols, and compute the product of these symbols in terms of the Kahler metric. This gives canonical star products on the Kahlerian manifolds. This ansatz is also useful to introduce the notion of microsupport.

Variations on the theme of Marcinkiewicz’ inequality

We present a new approach to the Marcinkiewicz interpolation inequality for the distribution function of the Hilbert transform, and prove an abstract version of this inequality. The approach uses logarithmic determinants and new estimates of canonical products of genus one.

Language Teaching at University: A Clash of Cultures

Language teaching at university may seem to be flourishing - many students take up the option of an extra module in a foreign language, to add to their skill-base. The thriving of language courses is largely due to the increased implementation of instrumental values in higher education, which regards language learning as a skill rather than as a creative medium to inform students' understanding of society. In this paper I trace the roots of these two dominant educational philosophies and I examine the place that language teaching occupies within them, relating this to the methodologies employed within these contexts. I argue that the opposing views both have a limited view on language teaching - one as a tool for providing access to esteemed canonical products and the other to provide a pragmatic application. Whilst the liberal humanist paradigm still influences language teaching at some institutions, the language debate in other institutions has been dominated by instrumental values. I argue that neither of these approaches to language teaching alone allow for a critical and deep understanding of how language functions within society now. I also argue for recognising language as a means of expressing individuality. Finally, I touch on the possibilities of an integrated approach within these two opposing paradigms.

A Direct Interpolation Method for Irregular Sampling

In this paper, band-limited functions are reconstructed from their values taken at a sequence of irregularly spaced sample points. We use a modified Lagrange formula, which is attributed to Boas and Bernstein. The formula used in this paper differs from the classical Boas–Bernstein formula in the following way. Instead of using infinite canonical products with respect to the whole sequence of sample points, we use canonical products with respect to sequences of sample points which are irregularly spaced only on finite intervals. Estimates for the truncation error of this reconstruction method are given.

Enforcing the Wheeler-DeWitt constraint the easy way

The author proves that the Wheeler-DeWitt symmetry must be gauge-fixed in canonical inner products. When this is done every functional integral represents the expectation value of an invariant operator in the presence of an invariant state. A corollary is that certain minisuperspace models are devoid of quantum phenomena.

Canonical products of infinite order.

Canonical products of infinite order.

Local boundary conditions for the Dirac operator and one-loop quantum cosmology.

This paper studies local boundary conditions for fermionic fields in quantum cosmology, originally introduced by Breitenlohner, Freedman, and Hawking for gauged supergravity theories in anti-de Sitter space. For a spin-\textonehalf{} field, the conditions involve the normal to the boundary and the undifferentiated field. A first-order differential operator for this Euclidean boundary-value problem exists which is symmetric and has self-adjoint extensions. The resulting eigenvalue equation in the case of a flat Euclidean background with a three-sphere boundary of radius $a$ is found to be $F(E)={[{J}_{n+1}(\mathrm{Ea})]}^{2}\ensuremath{-}{[{J}_{n+2}(\mathrm{Ea})]}^{2}=0$, $\ensuremath{\forall}n\ensuremath{\ge}0$. Using the theory of canonical products, this function $F$ may be expanded in terms of squared eigenvalues, in a way which has been used in other recent one-loop calculations involving eigenvalues of second-order operators. One can then study the generalized Riemann $\ensuremath{\zeta}$ function formed from these squared eigenvalues. The value of $\ensuremath{\zeta}(0)$ determines the scaling of the one-loop prefactor in the Hartle-Hawking amplitude in quantum cosmology. Suitable contour formulas, and the uniform asymptotic expansions of the Bessel functions ${J}_{m}$ and their derivatives ${J}_{m}^{\ensuremath{'}}$, yield, for a massless Majorana field, $\ensuremath{\zeta}(0)=\frac{11}{360}$. Combining this with $\ensuremath{\zeta}(0)$ values for other spins, one can then check whether the one-loop divergences in quantum cosmology cancel in a supersymmetric theory.

Interpolation in the semiplane by generalized canonical products

The problem of the interpolation of functions, analytic in the upper semiplane, of type not greater than normal, and of given order, is considered. Necessary and sufficient conditions for its solvability are obtained.

Canonical products and the weights [formula omitted], with applications

Let α > 1. For each positive integer n, a polynomial S n ( x) of degree ⩽ n is constructed such that S n(x) ~ exp(−¦x¦ α), ¦x¦ ⩽ Cn 1 α , where C > 0 is independent of n. These polynomials enable one to estimate Christoffel functions and prove L p Markov-Bernstein inequalities for all 0 < p ⩽ ∞, and for all the weights exp(− ¦x¦ α), α > 1 . In particular, the gap 1 < α < 2 in Feud's approximation theory can be filled, and one can prove L p Markov-Bernstein inequalities for 0 < p < 1.