Path Gain Algebraic Formulation for the Scalar Linear Network Coding Problem

In the algebraic view, the solution to a network coding problem is seen as a variety specified by a system of polynomial equations typically derived by using edge-to-edge gains as variables. The output from each sink is equated to its demand to obtain polynomial equations. In this work, we propose a method to derive the polynomial equations using source-to-sink path gains as the variables. In the path gain formulation, we show that linear and quadratic equations suffice; therefore, network coding becomes equivalent to a system of polynomial equations of maximum degree 2. We present algorithms for generating the equations in the path gains and for converting path gain solutions to edge-to-edge gain solutions. Because of the low degree, simplification is readily possible for the system of equations obtained using path gains. Using small-sized network coding problems, we show that the path gain approach results in simpler equations and determines solvability of the problem in certain cases. On a larger network (with 87 nodes and 161 edges), we show how the path gain approach continues to provide deterministic solutions to some network coding problems.Comment: 12 pages, 6 figures. Accepted for publication in IEEE Transactions on Information Theory (May 2010

Problems of diseases on marine fish and prawn farming in India

The problems of diseases are of great concern to the fish cultivators and research workers. The disease in severe cases inflicts heavy losses on the fish crop by reducing the yield. Information regarding its identification nature, extent of damage and controi measures etc, is being briefly summarised in this article

Strong Secrecy for Erasure Wiretap Channels

We show that duals of certain low-density parity-check (LDPC) codes, when used in a standard coset coding scheme, provide strong secrecy over the binary erasure wiretap channel (BEWC). This result hinges on a stopping set analysis of ensembles of LDPC codes with block length $n$ and girth $\geq 2k$, for some $k \geq 2$. We show that if the minimum left degree of the ensemble is $l_\mathrm{min}$, the expected probability of block error is \calO(\frac{1}{n^{\lceil l_\mathrm{min} k /2 \rceil - k}}) when the erasure probability $\epsilon < \epsilon_\mathrm{ef}$, where $\epsilon_\mathrm{ef}$ depends on the degree distribution of the ensemble. As long as $l_\mathrm{min} > 2$ and $k > 2$, the dual of this LDPC code provides strong secrecy over a BEWC of erasure probability greater than $1 - \epsilon_\mathrm{ef}$.Comment: Submitted to the Information Theory Workship (ITW) 2010, Dubli

Formation and Acceleration of Uniformly-Filled Ellipsoidal Electron Bunches Obtained via Space-Charge-Driven Expansion from a Cesium-Telluride Photocathode

We report the experimental generation, acceleration and characterization of a uniformly-filled electron bunch obtained via space-charge-driven expansion (often referred to as "blow-out regime") in an L-band (1.3-GHz) radiofrequency photoinjector. The beam is photoemitted from a Cesium-Telluride semiconductor photocathode using a short ($<200$ fs) ultraviolet laser pulse. The produced electron bunches are characterized with conventional diagnostics and the signatures of their ellipsoidal character is observed. We especially demonstrate the production of ellipsoidal bunches with charges up to $\sim0.5$ nC corresponding to a $\sim20$-fold increase compared to previous experiments with metallic photocathodes.Comment: 9, pages, 13 figure

Design of a high-power compact SRF linac for industrial applications of e-beam irradiation

Fermilab has developed a novel concept for an industrial electron linac using Nb3Sn coating technology and conduction cooling. These conduction-cooled linacs can generate electron beam energies up to 10 MeV in continuous-wave operation and reach higher power (>=1 MW) by combing several modules. Compact and light enough to mount on mobile platforms, our machine is anticipated to enable new in-situ environmental remediation applications such as waste-water treatment for urban areas, X-ray medical device sterilization, and innovative pavement applications. We highlight a few aspects of a 1 MW design of such a machine in this paper. A detailed plan is in Dhuley et al. (2022) Phys. Rev. Accel. Beams 25, 041601.Comment: arXiv admin note: substantial text overlap with arXiv:2112.0923

Amp\`ere-Class Pulsed Field Emission from Carbon-Nanotube Cathodes in a Radiofrequency Resonator

Pulsed field emission from cold carbon-nanotube cathodes placed in a radiofrequency resonant cavity was observed. The cathodes were located on the backplate of a conventional $1+\frac{1}{2}$-cell resonant cavity operating at 1.3-GHz and resulted in the production of bunch train with maximum average current close to 0.7 Amp\`ere. The measured Fowler-Nordheim characteristic, transverse emittance, and pulse duration are presented and, when possible, compared to numerical simulations. The implications of our results to high-average-current electron sources are briefly discussed.Comment: 5 pages, 6 figures; submitted to Applied Physics Letter