A unary error correction code for the near-capacity joint source and channel coding of symbol values from an infinite set

A novel Joint Source and Channel Code (JSCC) is proposed, which we refer to as the Unary Error Correction (UEC) code. Unlike existing JSCCs, our UEC facilitates the practical encoding of symbol values that are selected from a set having an infinite cardinality. Conventionally, these symbols are conveyed using Separate Source and Channel Codes (SSCCs), but we demonstrate that the residual redundancy that is retained following source coding results in a capacity loss, which is found to have a value of 1.11 dB in a particular practical scenario. By contrast, the proposed UEC code can eliminate this capacity loss, or reduce it to an infinitesimally small value. Furthermore, the UEC code has only a moderate complexity, facilitating its employment in practical low-complexity applications

On q-ary codes correcting all unidirectional errors of a limited magnitude

We consider codes over the alphabet Q={0,1,..,q-1}intended for the control of unidirectional errors of level l. That is, the transmission channel is such that the received word cannot contain both a component larger than the transmitted one and a component smaller than the transmitted one. Moreover, the absolute value of the difference between a transmitted component and its received version is at most l. We introduce and study q-ary codes capable of correcting all unidirectional errors of level l. Lower and upper bounds for the maximal size of those codes are presented. We also study codes for this aim that are defined by a single equation on the codeword coordinates(similar to the Varshamov-Tenengolts codes for correcting binary asymmetric errors). We finally consider the problem of detecting all unidirectional errors of level l.Comment: 22 pages,no figures. Accepted for publication of Journal of Armenian Academy of Sciences, special issue dedicated to Rom Varshamo

4D ultrafast electron diffraction, crystallography, and microscopy

In this review, we highlight the progress made in the development of 4D ultrafast electron diffraction (UED), crystallography (UEC), and microscopy (UEM) with a focus on concepts, methodologies, and prototypical applications. The joint atomic-scale resolutions in space and time, and sensitivity reached, make it possible to determine complex transient structures and assemblies in different phases. These applications include studies of isolated chemical reactions (molecular beams), interfaces, surfaces and nanocrystals, self-assembly, and 2D crystalline fatty-acid bilayers. In 4D UEM, we are now able, using timed, single-electron packets, to image nano-to-micro scale structures of materials and biological cells. Future applications of these methods are foreseen across areas of physics, chemistry, and biology

One-dimensional quantum random walks with two entangled coins

We offer theoretical explanations for some recent observations in numerical simulations of quantum random walks (QRW). Specifically, in the case of a QRW on the line with one particle (walker) and two entangled coins, we explain the phenomenon, called "localization", whereby the probability distribution of the walker's position is seen to exhibit a persistent major "spike" (or "peak") at the initial position and two other minor spikes which drift to infinity in either direction. Another interesting finding in connection with QRW's of this sort pertains to the limiting behavior of the position probability distribution. It is seen that the probability of finding the walker at any given location becomes eventually stationary and non-vanishing. We explain these observations in terms of the degeneration of some eigenvalue of the time evolution operator $U(k)$. An explicit general formula is derived for the limiting probability, from which we deduce the limiting value of the height of the observed spike at the origin. We show that the limiting probability decreases {\em quadratically} for large values of the position $x$. We locate the two minor spikes and demonstrate that their positions are determined by the phases of non-degenerated eigenvalues of $U(k)$. Finally, for fixed time $t$ sufficiently large, we examine the dependence on $t$ of the probability of finding a particle at a given location $x$.Comment: 11 page

Red blood cells and other non-spherical capsules in shear flow: oscillatory dynamics and the tank-treading-to-tumbling transition

We consider the motion of red blood cells and other non-spherical microcapsules dilutely suspended in a simple shear flow. Our analysis indicates that depending on the viscosity, membrane elasticity, geometry and shear rate, the particle exhibits either tumbling, tank-treading of the membrane about the viscous interior with periodic oscillations of the orientation angle, or intermittent behavior in which the two modes occur alternately. For red blood cells, we compute the complete phase diagram and identify a novel tank-treading-to-tumbling transition at low shear rates. Observations of such motions coupled with our theoretical framework may provide a sensitive means of assessing capsule properties.Comment: 11 pages, 4 figure