Probabilistic estimation of the rank 1 cross approximation accuracy

In the construction of low-rank matrix approximation and maximum element search it is effective to use maxvol algorithm. Nevertheless, even in the case of rank 1 approximation the algorithm does not always converge to the maximum matrix element, and it is unclear how often close to the maximum element can be found. In this article it is shown that with a certain degree of randomness in the matrix and proper selection of the starting column, the algorithm with high probability in a few steps converges to an element, which module differs little from the maximum. It is also shown that with more severe restrictions on the error matrix no restrictions on the starting column need to be introduced

Close to optimal column approximations with a single SVD

The best column approximation in the Frobenius norm with $r$ columns has an error at most $\sqrt{r+1}$ times larger than the truncated singular value decomposition. Reaching this bound in practice involves either expensive random volume sampling or at least $r$ executions of singular value decomposition. In this paper it will be shown that the same column approximation bound can be reached with only a single SVD (which can also be replaced with approximate SVD). As a corollary, it will be shown how to find a highly nondegenerate submatrix in $r$ rows of size $N$ in just $O(Nr^2)$ operations, which mostly has the same properties as the maximum volume submatrix

Exact solutions of temperature-dependent Smoluchowski equations

We report a number of exact solutions for temperature-dependent Smoluchowski equations. These equations quantify the ballistic agglomeration, where the evolution of densities of agglomerates of different size is entangled with the evolution of the mean kinetic energy (partial temperatures) of such clusters. The obtained exact solutions may be used as a benchmark to assess the accuracy and computational efficiency of the numerical approaches, developed to solve the temperature-dependent Smoluchowski equations. Moreover, they may also illustrate the possible evolution regimes in these systems. The exact solutions have been obtained for a series of model rate coefficients, and we demonstrate that there may be an infinite number of such model coefficient which allow exact analysis. We compare our exact solutions with the numerical solutions for various evolution regimes; an excellent agreement between numerical and exact results proves the accuracy of the exploited numerical method

Collision fragmentation of aggregates. The role of the interaction potential between comprising particles

We investigate disruptive collisions of aggregates comprised of particles with different interaction potentials. We study Lennard-Jones (L-J), Tersoff, modified L-J potential and the one associated with Johnson-Kendall-Roberts (JKR) model. These refer to short, middle and long-ranged inter-particle potentials and describe both inter-atomic interactions and interactions of macroscopic adhesive bodies. We perform comprehensive molecular dynamics simulations and observe for all four potentials power-law dependencies for the size distribution of collision fragments and for their size-velocity correlation. We introduce a new fragmentation characteristic -- the shattering degree $S$, quantifying the fraction of monomers in debris and reveal its universal behavior. Namely, we demonstrate that for all potentials, $1-S$ is described by a universal function of the impact velocity. Using the above results, we perform the impact classification and construct the respective collision phase diagram. Finally, we present a qualitative theory that explains the observed scaling behavior.Comment: Submitted to Physica

Dynamics of ligand substitution in labile cobalt complexes resolved by ultrafast T-jump

Ligand exchange of hydrated metal complexes is common in chemical and biological systems. Using the ultrafast T-jump, we examined this process, specifically the transformation of aqua cobalt (II) complexes to their fully halogenated species. The results reveal a stepwise mechanism with time scales varying from hundreds of picoseconds to nanoseconds. The dynamics are significantly faster when the structure is retained but becomes rate-limited when the octahedral-to-tetrahedral structural change bottlenecks the transformation. Evidence is presented, from bimolecular kinetics and energetics (enthalpic and entropic), for a reaction in which the ligand assists the displacement of water molecules, with the retention of the entering ligand in the activated state. The reaction time scale deviates by one to two orders of magnitude from that of ionic diffusion, suggesting the involvement of a collisional barrier between the ion and the much larger complex

Theoretical Performance Bound of Uplink Channel Estimation Accuracy in Massive MIMO

In this paper, we present a new performance bound for uplink channel estimation (CE) accuracy in the Massive Multiple Input Multiple Output (MIMO) system. The proposed approach is based on noise power prediction after the CE unit. Our method outperforms the accuracy of a well-known Cramer-Rao lower bound (CRLB) due to considering more statistics since performance strongly depends on a number of channel taps and power ratio between them. Simulation results are presented for the non-line of sight (NLOS) 3D-UMa model of 5G QuaDRiGa 2.0 channel and compared with CRLB and state-of-the-art CE algorithms.Comment: accepted for presentation in a poster session at the ICASSP 2020 conferenc

Study of temperature dependence for the electron injection-induced effects in GaN

Electron-beam injection-induced increase of minority carrier diffusion length in p-type GaN was studied as a function of sample temperature ranging from 25 degreesC to 130 degreesC. It was found that the rate for diffusion length increase exponentially decays with increasing temperature. This decay was attributed to a temperature-activated release of electron-beam injected electrons trapped on Mg levels. The activation energy of these levels was found to be similar to178 meV. This is in good agreement with the previously reported position for Mg levels in the GaN band gap