Capacity-achieving ensembles for the binary erasure channel with bounded complexity

We present two sequences of ensembles of non-systematic irregular repeat-accumulate codes which asymptotically (as their block length tends to infinity) achieve capacity on the binary erasure channel (BEC) with bounded complexity per information bit. This is in contrast to all previous constructions of capacity-achieving sequences of ensembles whose complexity grows at least like the log of the inverse of the gap (in rate) to capacity. The new bounded complexity result is achieved by puncturing bits, and allowing in this way a sufficient number of state nodes in the Tanner graph representing the codes. We also derive an information-theoretic lower bound on the decoding complexity of randomly punctured codes on graphs. The bound holds for every memoryless binary-input output-symmetric channel and is refined for the BEC.Comment: 47 pages, 9 figures. Submitted to IEEE Transactions on Information Theor

Phase Dynamics of Two Entangled Qubits

We make a geometric study of the phases acquired by a general pure bipartite two level system after a cyclic unitary evolution. The geometric representation of the two particle Hilbert space makes use of Hopf fibrations. It allows for a simple description of the dynamics of the entangled state's phase during the whole evolution. The global phase after a cyclic evolution is always an entire multiple of $\pi$ for all bipartite states, a result that does not depend on the degree of entanglement. There are three different types of phases combining themselves so as to result in the $n \pi$ global phase. They can be identified as dynamical, geometrical and topological. Each one of them can be easily identified using the presented geometric description. The interplay between them depends on the initial state and on its trajectory and the results obtained are shown to be in connection to those on mixed states phases.Comment: 9 figures, slightly different version from the accepted on

Geometry of entangled states, Bloch spheres and Hopf fibrations

We discuss a generalization to 2 qubits of the standard Bloch sphere representation for a single qubit, in the framework of Hopf fibrations of high dimensional spheres by lower dimensional spheres. The single qubit Hilbert space is the 3-dimensional sphere S3. The S2 base space of a suitably oriented S3 Hopf fibration is nothing but the Bloch sphere, while the circular fibres represent the qubit overall phase degree of freedom. For the two qubits case, the Hilbert space is a 7-dimensional sphere S7, which also allows for a Hopf fibration, with S3 fibres and a S4 base. A main striking result is that suitably oriented S7 Hopf fibrations are entanglement sensitive. The relation with the standard Schmidt decomposition is also discussedComment: submitted to J. Phys.

Geometrical organization of solutions to random linear Boolean equations

The random XORSAT problem deals with large random linear systems of Boolean variables. The difficulty of such problems is controlled by the ratio of number of equations to number of variables. It is known that in some range of values of this parameter, the space of solutions breaks into many disconnected clusters. Here we study precisely the corresponding geometrical organization. In particular, the distribution of distances between these clusters is computed by the cavity method. This allows to study the `x-satisfiability' threshold, the critical density of equations where there exist two solutions at a given distance.Comment: 20 page

Achievable rates for the Gaussian quantum channel

We study the properties of quantum stabilizer codes that embed a finite-dimensional protected code space in an infinite-dimensional Hilbert space. The stabilizer group of such a code is associated with a symplectically integral lattice in the phase space of 2N canonical variables. From the existence of symplectically integral lattices with suitable properties, we infer a lower bound on the quantum capacity of the Gaussian quantum channel that matches the one-shot coherent information optimized over Gaussian input states.Comment: 12 pages, 4 eps figures, REVTe

HDAC inhibitor-dependent transcriptome and memory reinstatement in cognitive decline models.

Aging and increased amyloid burden are major risk factors for cognitive diseases such as Alzheimer's disease (AD). Effective therapies for these diseases are lacking. Here, we evaluated mouse models of age-associated memory impairment and amyloid deposition to study transcriptome and cell type-specific epigenome plasticity in the brain and peripheral organs. We determined that aging and amyloid pathology are associated with inflammation and impaired synaptic function in the hippocampal CA1 region as the result of epigenetic-dependent alterations in gene expression. In both amyloid and aging models, inflammation was associated with increased gene expression linked to a subset of transcription factors, while plasticity gene deregulation was differentially mediated. Amyloid pathology impaired histone acetylation and decreased expression of plasticity genes, while aging altered H4K12 acetylation-linked differential splicing at the intron-exon junction in neurons, but not nonneuronal cells. Furthermore, oral administration of the clinically approved histone deacetylase inhibitor vorinostat not only restored spatial memory, but also exerted antiinflammatory action and reinstated epigenetic balance and transcriptional homeostasis at the level of gene expression and exon usage. This study provides a systems-level investigation of transcriptome plasticity in the hippocampal CA1 region in aging and AD models and suggests that histone deacetylase inhibitors should be further explored as a cost-effective therapeutic strategy against age-associated cognitive decline

Probabilistic Reconstruction in Compressed Sensing: Algorithms, Phase Diagrams, and Threshold Achieving Matrices

Compressed sensing is a signal processing method that acquires data directly in a compressed form. This allows one to make less measurements than what was considered necessary to record a signal, enabling faster or more precise measurement protocols in a wide range of applications. Using an interdisciplinary approach, we have recently proposed in [arXiv:1109.4424] a strategy that allows compressed sensing to be performed at acquisition rates approaching to the theoretical optimal limits. In this paper, we give a more thorough presentation of our approach, and introduce many new results. We present the probabilistic approach to reconstruction and discuss its optimality and robustness. We detail the derivation of the message passing algorithm for reconstruction and expectation max- imization learning of signal-model parameters. We further develop the asymptotic analysis of the corresponding phase diagrams with and without measurement noise, for different distribution of signals, and discuss the best possible reconstruction performances regardless of the algorithm. We also present new efficient seeding matrices, test them on synthetic data and analyze their performance asymptotically.Comment: 42 pages, 37 figures, 3 appendixe

Restriction endonuclease MvaI is a monomer that recognizes its target sequence asymmetrically

Restriction endonuclease MvaI recognizes the sequence CC/WGG (W stands for A or T, ‘/’ designates the cleavage site) and generates products with single nucleotide 5′-overhangs. The enzyme has been noted for its tolerance towards DNA modifications. Here, we report a biochemical characterization and crystal structures of MvaI in an apo-form and in a complex with target DNA at 1.5 Å resolution. Our results show that MvaI is a monomer and recognizes its pseudosymmetric target sequence asymmetrically. The enzyme consists of two lobes. The catalytic lobe anchors the active site residues Glu36, Asp50, Glu55 and Lys57 and contacts the bases from the minor grove side. The recognition lobe mediates all major grove interactions with the bases. The enzyme in the crystal is bound to the strand with T at the center of the recognition sequence. The crystal structure with calcium ions and DNA mimics the prereactive state. MvaI shows structural similarities to BcnI, which cleaves the related sequence CC/SGG and to MutH enzyme, which is a component of the DNA repair machinery, and nicks one DNA strand instead of making a double-strand break