In compressed sensing, one takes n < N samples of an N-dimensional vector x 0 using an n × N matrix A, obtaining undersampled measurements y = Ax 0 . For random matrices with independent standard Gaussian entries, it is known that, when x 0 is k-sparse, there is a precisely determined phase transition: for a certain region in the (k/n,n/N)-phase diagram, convex optimization min || x || 1 subject to y = Ax, x ∈ X N typically finds the sparsest solution, whereas outside that region, it typically fails. It has been shown empirically that the same property-with the same phase transition location-holds for a wide range of non-Gaussian random matrix ensembles. We report extensive experiments showing that the Gaussian phase transition also describes numerous deterministic matrices, including Spikes and Sines, Spikes and Noiselets, Paley Frames, Delsarte-Goethals Frames, Chirp Sensing Matrices, and Grassmannian Frames. Namely, for each of these deterministic matrices in turn, for a typical k-sparse object, we observe that convex optimization is successful over a region of the phase diagram that coincides with the region known for Gaussian random matrices. Our experiments considered coefficients constrained to X N for four different sets X ∈ {[0, 1], R + , R, C}, and the results establish our finding for each of the four associated phase transitions.sparse recovery | universality in random matrix theory equiangular tight frames | restricted isometry property | coherence C ompressed sensing aims to recover a sparse vector x 0 ∈ X N from indirect measurements y = Ax 0 ∈ X n with n < N, and therefore, the system of equations y = Ax 0 is underdetermined. Nevertheless, it has been shown that, under conditions on the sparsity of x 0 , by using a random measurement matrix A with Gaussian i.i.d entries and a nonlinear reconstruction technique based on convex optimization, one can, with high probability, exactly recover x 0 (1, 2). The cleanest expression of this phenomenon is visible in the large n; N asymptotic regime. We suppose that the object x 0 is k-sparse-has, at most, k nonzero entries-and consider the situation where k ∼ ρn and n ∼ δN. Fig. 1A depicts the phase diagram ðρ; δ; Þ ∈ ð0; 1Þ 2 and a curve ρ*ðδÞ separating a success phase from a failure phase. Namely, if ρ < ρ*ðδÞ, then with overwhelming probability for large N, convex optimization will recover x 0 exactly; however, if ρ > ρ*ðδÞ, then with overwhelming probability for large N convex optimization will fail. [Indeed, Fig. 1 depicts four curves ρ*ðδjXÞ of this kind for X ∈ f½0; 1; R + ; R; Cg-one for each of the different types of assumptions that we can make about the entries of x 0 ∈ X N (details below).]How special are Gaussian matrices to the above results? It was shown, first empirically in ref. 3 and recently, theoretically in ref. 4, that a wide range of random matrix ensembles exhibits precisely the same behavior, by which we mean the same phenomenon of separation into success and failure phases with the same phase boundary. Such universality, if exhib...

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Nine new 2-D OOCs are presented here, all sharing the common feature of a code size that is much larger in relation to the number of time slots than those of constructions appearing previously in the literature. Each of these constructions is either optimal or asymptotically optimal with respect to either the original Johnson bound or else a non-binary version of the Johnson bound introduced in this paper.The first 5 codes are constructed using polynomials over finite fields -the first construction is optimal while the remaining 4 are asymptotically optimal. The next two codes are constructed using rational functions in place of polynomials and these are asymptotically optimal. The last two codes, also asymptotically optimal, are constructed by composing two of the above codes with a constant weight binary code.Also presented, is a three-dimensional OOC that exploits the polarization dimension.Finally, phase-encoded optical CDMA is considered and construction of two efficient codes are provided.

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SUMMARY In this paper, the effect of operating temperature on optimal purge interval for maximum energy efficiency in a proton exchange membrane fuel cell (PEMFC) with dead‐ended anode (DEA) was experimentally investigated. The study was conducted with a focus on challenges associated with operation at temperatures lower than the recommended designed temperature. With DEA, gradual voltage drop happens due to the accumulation of water and impurities such as nitrogen. Hence, periodic purging of the anode side is required to remove excess water and impurities that are accumulated at the anode side over time. Short purge intervals increase hydrogen loss that translates into low fuel utilisation, whereas long purge intervals result in voltage drop due to high water and impurity accumulations. Therefore, an optimal purge strategy should be implemented to maximise the stack energy efficiency. Depending on the operating conditions and loads, there are instances that a fuel cell stack operates at temperatures lower than its recommended designed temperature. Considering the temperature effect on the cell water management, operating temperature is an important factor to consider for optimising the purge strategy in PEMFCs. At lower operating temperatures (ie, below 50°C), more water is formed in liquid form, which makes the optimisation of purge strategy more challenging. For a stack temperature of 40°C, it was observed that with an increase in stack current from 0.25 to 0.45 A cm−2, the optimal purge interval decreases from 90 seconds to around 45 seconds, respectively. Increasing the stack temperature from 40°C to 50°C resulted in an increase in the optimal purge interval to 120 seconds and 90 seconds for stack currents of 0.25 (ie, low current density) and 0.45 A cm−2, respectively. At lower operating temperatures, more frequent purging schedules are needed accordingly to remove the liquid water from the cell. These results indicated that at lower operating temperatures, water accumulation at the anode side becomes more dominant compared with higher operating temperatures.