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

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

High Performance Interference Suppression in Multi-User Massive MIMO Detector

In this paper, we propose a new nonlinear detector with improved interference suppression in Multi-User Multiple Input, Multiple Output (MU-MIMO) system. The proposed detector is a combination of the following parts: QR decomposition (QRD), low complexity users sorting before QRD, sorting-reduced (SR) K-best method and minimum mean square error (MMSE) pre-processing. Our method outperforms a linear interference rejection combining (IRC, i.e. MMSE naturally) method significantly in both strong interference and additive white noise scenarios with both ideal and real channel estimations. This result has wide application importance for scenarios with strong interference, i.e. when co-located users utilize the internet in stadium, highway, shopping center, etc. Simulation results are presented for the non-line of sight 3D-UMa model of 5G QuaDRiGa 2.0 channel for 16 highly correlated single-antenna users with QAM16 modulation in 64 antennas of Massive MIMO system. The performance was compared with MMSE and other detection approaches.Comment: Accepted for presentation at the VTC2020-Spring conferenc

Randomised Prior Feedback Modulates Neural Signals of Outcome Monitoring

Substantial evidence indicates that decision outcomes are typically evaluated relative to expectations learned from relatively long sequences of previous outcomes. This mechanism is thought to play a key role in general learning and adaptation processes but relatively little is known about the determinants of outcome evaluation when the capacity to learn from series of prior events is difficult or impossible. To investigate this issue, we examined how the feedback-related negativity (FRN) is modulated by information briefly presented before outcome evaluation. The FRN is a brain potential time-locked to the delivery of decision feedback and it is widely thought to be sensitive to prior expectations. We conducted a multi-trial gambling task in which outcomes at each trial were fully randomised to minimise the capacity to learn from long sequences of prior outcomes. Event-related potentials for outcomes (Win/Loss) in the current trial (Outcomet) were separated according to the type of outcomes that occurred in the preceding two trials (Outcomet-1 and Outcomet-2). We found that FRN voltage was more positive during the processing of win feedback when it was preceded by wins at Outcomet-1 compared to win feedback preceded by losses at Outcomet-1. However, no influence of preceding outcomes was found on FRN activity relative to the processing of loss feedback. We also found no effects of Outcomet-2 on FRN amplitude relative to current feedback. Additional analyses indicated that this effect was largest for trials in which participants selected a decision different to the gamble chosen in the previous trial. These findings are inconsistent with models that solely relate the FRN to prediction error computation. Instead, our results suggest that if stable predictions about future events are weak or non-existent, then outcome processing can be determined by affective systems. More specifically, our results indicate that the FRN is likely to reflect the activity of positive affective systems in these contexts. Importantly, our findings indicate that a multifactorial explanation of the nature of the FRN is necessary and such an account must incorporate affective and motivational factors in outcome processing