The literature on sparse recovery often adopts the “norm” ( ) as the penalty to induce sparsity of the signal satisfying an underdetermined linear system. The performance of the corresponding minimization problem can be characterized by its null space constant. In spite of the NP-hardness of computing the constant, its properties can still help in illustrating the performance of minimization. I...

We quantify the asymptotic vanishing of the ground-state overlap of two noninteracting Fermi gases in d -dimensional Euclidean space in the thermodynamic limit. Given two one-particle Schrödinger operators in nite-volume which di er by a compactly supported bounded potential, we prove a power-law upper bound on the ground-state overlap of the corresponding non-interacting N -Fermion systems. We...

A continuum theory for non-Newtonian flow of a two-phase composite containing rigid inclusions is presented. I t predicts flow suppression by a factor of (1 V)p, where V is the volume fraction of the rigid inclusion and q depends on the stress exponent and the inclusion shape. Stress concentrations in the rigid inclusion have also been evaluated. As the stress exponent increases, flow suppressi...

We consider concentric circular defects in the two-dimensional Ising model, which are distributed according to a generalized Fredholm sequence, i. e. at exponentially increasing radii. This type of aperiodicity does not change the bulk critical behaviour but introduces a marginal extended perturbation. The critical exponent of the local magnetization is obtained through finite-size scaling, usi...

This paper presents a new multiplicative algorithm for nonnegative matrix factorization with β-divergence. The derived update rules have a similar form to those of the conventional multiplicative algorithm, only differing through the presence of an exponent term depending on β. The convergence is theoretically proven for any real-valued β based on the auxiliary function method. The convergence ...

Finite-dimensional nonrelativistic conformal Lie algebras spanned by polynomial vector fields of Galilei spacetime arise if the dynamical exponent is z = 2/N with N = 1, 2, . . . . Their underlying group structure and matrix representation are constructed (up to a covering) by means of the Veronese map of degree N . Suitable quotients of the conformal Galilei groups provide us with Newton-Hooke...

We provide sharp exponential moment bounds for (Stratonovich) iterated stochastic integrals under conditioning by certain small balls, including balls in certain HH older-like norms of exponent greater than 1=3. The proof uses a control of the variation of the L evy area, under conditioning. The results are applied to the computation of the Onsager-Machlup functional of diiusion processes with ...

For a connected graph G, we derive tight inequalities relating the smallest signless Laplacian eigenvalue to the largest normalised Laplacian eigenvalue. We investigate how vectors yielding small values of the Rayleigh quotient for the signless Laplacian matrix can be used to identify bipartite subgraphs. Our results are applied to some graphs with degree sequences approximately following a pow...

The Rubinstein-Duke model for polymer reptation is analyzed by means of density matrix renormalization techniques. It is found that the crossover in the scaling behavior of polymer renewal time (or viscosity) arises from the competing effect of the contribution due to tube length fluctuations and higher-order corrections, which are of opposite sign. Experiments which ought to emphasize both con...

We investigate numerically the power-law random matrix ensembles. Wave functions are fractal up to a characteristic length whose logarithm diverges asymmetrically with different exponents, 1 in the localized phase and 0.5 in the extended phase. The characteristic length is so anomalously large that for macroscopic samples there exists a finite critical region, in which this length is larger tha...