The girth of a matrix is the least number of linearly dependent columns, in contrast to the rank which is the largest number of linearly independent columns. This paper considers the construction of high-girth matrice...
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(纸本)9781467377058
The girth of a matrix is the least number of linearly dependent columns, in contrast to the rank which is the largest number of linearly independent columns. This paper considers the construction of high-girth matrices, whose probabilistic girth is close to their rank. Random matrices can be used to show the existence of high-girth matrices. This paper uses a recursive construction based on conditional ranks (inspired by polar codes) to obtain a deterministic and efficient construction of high-girth matrices for arbitrary relative ranks. Interestingly, the construction is agnostic to the underlying field and applies to both finite and continuous fields with the same binary matrix. The construction gives in particular the following: (i) over the binary field, high-girth matrices are equivalent to capacity-achieving codes, and our construction turns out to match exactly the BEC polar codes (even at finite block length). It hence gives a different interpretation of BEC polar codes, using the parity-check matrix instead of the generator matrix, and basic linear algebra instead of the mutual information, and generalizes to larger fields; (ii) for the BSC, our construction gives an operational meaning to the Bhattacharyya upper-bound process used in polar codes; (iii) for the reals, it gives an explicit candidate matrix for sparse recovery.
In this paper, the authors study the long time behavior of solutions to stochastic non-Newtonian fluids in a two-dimensional bounded domain, and prove the existence of H2-regularity random attractor.
In this paper, the authors study the long time behavior of solutions to stochastic non-Newtonian fluids in a two-dimensional bounded domain, and prove the existence of H2-regularity random attractor.
In parallel shear flows, the lower branch solution follows simple streamwise dynamics. A decomposition of this solution into Fourier modes in this direction yields modes whose amplitudes scale with inverse powers of t...
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In this paper, we compared the performance profile of the classical conjugate gradient coefficients FR, PRP with two new βk. These two new βk possess global convergence properties using the exact line search. Prelim...
In this paper, we compared the performance profile of the classical conjugate gradient coefficients FR, PRP with two new βk. These two new βk possess global convergence properties using the exact line search. Preliminary numerical results show that, the two new βk is very promising and efficient when compared to CG coefficients FR, PRP.
We present a concept for an ultra-wide band, high-sensitivity and low-resolution radio telescope array operating at 200 MHz-1100 MHz, which is optimized for cosmology with 21 cm intensity mapping in the post-reionizat...
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Betatron radiation from direct-laser-accelerated electrons is characterized analytically and numerically. It is shown here that the electron dynamics is strongly dependent on a self-similar parameter S(≡nenca0). Both...
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Betatron radiation from direct-laser-accelerated electrons is characterized analytically and numerically. It is shown here that the electron dynamics is strongly dependent on a self-similar parameter S(≡nenca0). Both the electron transverse momentum and energy are proportional to the normalized amplitude of laser field (a0) for a fixed value of S. As a result, the total number of radiated photons scales as a02/S and the energy conversion efficiency of photons from the accelerated electrons scales as a03/S. The particle-in-cell simulations agree well with the analytical scalings. It is suggested that a tunable high-energy and high-flux radiation source can be achieved by exploiting this regime.
The following coupled Schrodinger system with a small perturbationis considered, where β and ε are small parameters. The whole system has a periodic solution with the aid of a Fourier series expansion technique, and...
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The following coupled Schrodinger system with a small perturbation
is considered, where β and ε are small parameters. The whole system has a periodic solution with the aid of a Fourier series expansion technique, and its dominant system has a heteroclinic solution. Then adjusting some appropriate constants and applying the fixed point theorem and the perturbation method yield that this heteroclinic solution deforms to a heteroclinic solution exponentially approaching the obtained periodic solution （called the generalized heteroclinic solution thereafter）.
The Winter Colloquium on the Physics of Quantum Electronics (PQE) has been a seminal force in quantum optics and related areas since 1971. It is rather mindboggling to recognize how the concepts presented at these con...
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By performing large-scale density-matrix renormalization group simulations, we investigate a one-dimensional correlated bosonic lattice model with a synthetic spin-orbit coupling realized in recent experiments. In the...
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By performing large-scale density-matrix renormalization group simulations, we investigate a one-dimensional correlated bosonic lattice model with a synthetic spin-orbit coupling realized in recent experiments. In the insulating regime, this model exhibits a symmetry-protected topological phase. This symmetry-protected topological phase is stabilized by time-reversal symmetry and it is identified as a Haldane phase. We confirm our conclusions further by analyzing the entanglement spectrum. In addition, we find four conventional phases: a Mott insulating phase with no long range order, a ferromagnetic superfluid phase, a ferromagnetic insulating phase, and a density-wave phase.
In this paper, the notion of m -preinvex and ( α , m ) -preinvex functions is introduced and then several inequalities of Hermite–Hadamard type for differentiable m -preinvex and ( α , m ) -preinvex functions are e...
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In this paper, the notion of m -preinvex and ( α , m ) -preinvex functions is introduced and then several inequalities of Hermite–Hadamard type for differentiable m -preinvex and ( α , m ) -preinvex functions are established.
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