Information preserving structures: A general framework for quantum zero-error information

Quantum systems carry information. Quantum theory supports at least two distinct kinds of information (classical and quantum), and a variety of different ways to encode and preserve information in physical systems. A system's ability to carry information is constrained and defined by the noise in its dynamics. This paper introduces an operational framework, using information-preserving structures to classify all the kinds of information that can be perfectly (i.e., with zero error) preserved by quantum dynamics. We prove that every perfectly preserved code has the same structure as a matrix algebra, and that preserved information can always be corrected. We also classify distinct operational criteria for preservation (e.g., "noiseless", "unitarily correctible", etc.) and introduce two new and natural criteria for measurement-stabilized and unconditionally preserved codes. Finally, for several of these operational critera, we present efficient (polynomial in the state-space dimension) algorithms to find all of a channel's information-preserving structures.Comment: 29 pages, 19 examples. Contains complete proofs for all the theorems in arXiv:0705.428

Synthetic and genomic regulatory elements reveal aspects of cis-regulatory grammar in mouse embryonic stem cells

In embryonic stem cells (ESCs), a core transcription factor (TF) network establishes the gene expression program necessary for pluripotency. To address how interactions between four key TFs contribute t

On the computation of zone and double zone diagrams

Classical objects in computational geometry are defined by explicit relations. Several years ago the pioneering works of T. Asano, J. Matousek and T. Tokuyama introduced "implicit computational geometry", in which the geometric objects are defined by implicit relations involving sets. An important member in this family is called "a zone diagram". The implicit nature of zone diagrams implies, as already observed in the original works, that their computation is a challenging task. In a continuous setting this task has been addressed (briefly) only by these authors in the Euclidean plane with point sites. We discuss the possibility to compute zone diagrams in a wide class of spaces and also shed new light on their computation in the original setting. The class of spaces, which is introduced here, includes, in particular, Euclidean spheres and finite dimensional strictly convex normed spaces. Sites of a general form are allowed and it is shown that a generalization of the iterative method suggested by Asano, Matousek and Tokuyama converges to a double zone diagram, another implicit geometric object whose existence is known in general. Occasionally a zone diagram can be obtained from this procedure. The actual (approximate) computation of the iterations is based on a simple algorithm which enables the approximate computation of Voronoi diagrams in a general setting. Our analysis also yields a few byproducts of independent interest, such as certain topological properties of Voronoi cells (e.g., that in the considered setting their boundaries cannot be "fat").Comment: Very slight improvements (mainly correction of a few typos); add DOI; Ref [51] points to a freely available computer application which implements the algorithms; to appear in Discrete & Computational Geometry (available online

Global entrainment of transcriptional systems to periodic inputs

This paper addresses the problem of giving conditions for transcriptional systems to be globally entrained to external periodic inputs. By using contraction theory, a powerful tool from dynamical systems theory, it is shown that certain systems driven by external periodic signals have the property that all solutions converge to a fixed limit cycle. General results are proved, and the properties are verified in the specific case of some models of transcriptional systems. The basic mathematical results needed from contraction theory are proved in the paper, making it self-contained

A proof of the Mazur-Orlicz theorem via the Markov-Kakutani common fixed point theorem, and vice versa

In this paper, we present a new proof of the Mazur-Orlicz theorem, which uses the Markov-Kakutani common fixed point theorem, and a new proof of the Markov-Kakutani common fixed point theorem, which uses the Mazur-Orlicz theorem

Interpolating orientation fields : an axiomatic approach

International audienc

N-Terminal Phosphorylation of the Dopamine Transporter Is Required for Amphetamine-Induced Efflux

Amphetamine (AMPH) elicits its behavioral effects by acting on the dopamine (DA) transporter (DAT) to induce DA efflux into the synaptic cleft. We previously demonstrated that a human DAT construct in which the first 22 amino acids were truncated was not phosphorylated by activation of protein kinase C, in contrast to wild-type (WT) DAT, which was phosphorylated. Nonetheless, in all functions tested to date, which include uptake, inhibitor binding, oligomerization, and redistribution away from the cell surface in response to protein kinase C activation, the truncated DAT was indistinguishable from the full-length WT DAT. Here, however, we show that in HEK-293 cells stably expressing an N-terminal-truncated DAT (del-22 DAT), AMPH-induced DA efflux is reduced by approximately 80%, whether measured by superfusion of a population of cells or by amperometry combined with the patch-clamp technique in the whole cell configuration. We further demonstrate in a full-length DAT construct that simultaneous mutation of the five N-terminal serine residues to alanine (S/A) produces the same phenotype as del-22—normal uptake but dramatically impaired efflux. In contrast, simultaneous mutation of these same five serines to aspartate (S/D) to simulate phosphorylation results in normal AMPH-induced DA efflux and uptake. In the S/A background, the single mutation to Asp of residue 7 or residue 12 restored a significant fraction of WT efflux, whereas mutation to Asp of residues 2, 4, or 13 was without significant effect on efflux. We propose that phosphorylation of one or more serines in the N-terminus of human DAT, most likely Ser7 or Ser12, is essential for AMPH-induced DAT-mediated DA efflux. Quite surprisingly, N-terminal phosphorylation shifts DAT from a “reluctant” state to a “willing” state for AMPH-induced DA efflux, without affecting inward transport. These data raise the therapeutic possibility of interfering selectively with AMPH-induced DA efflux without altering physiological DA uptake