Why Does a Kronecker Model Result in Misleading Capacity Estimates?

Many recent works that study the performance of multi-input multi-output (MIMO) systems in practice assume a Kronecker model where the variances of the channel entries, upon decomposition on to the transmit and the receive eigen-bases, admit a separable form. Measurement campaigns, however, show that the Kronecker model results in poor estimates for capacity. Motivated by these observations, a channel model that does not impose a separable structure has been recently proposed and shown to fit the capacity of measured channels better. In this work, we show that this recently proposed modeling framework can be viewed as a natural consequence of channel decomposition on to its canonical coordinates, the transmit and/or the receive eigen-bases. Using tools from random matrix theory, we then establish the theoretical basis behind the Kronecker mismatch at the low- and the high-SNR extremes: 1) Sparsity of the dominant statistical degrees of freedom (DoF) in the true channel at the low-SNR extreme, and 2) Non-regularity of the sparsity structure (disparities in the distribution of the DoF across the rows and the columns) at the high-SNR extreme.Comment: 39 pages, 5 figures, under review with IEEE Trans. Inform. Theor

Design of High Speed Comparator

A new CMOS dynamic comparator using dual input single output differential amplifier as latch stage suitable for high speed analog - to - digital converters with High Spee d, low power dissipation and immune to. Back - to - back inverter in the latch stage is replaced with dual - input single output differential amplifier. This topology completely removes the noise that is present in the input. The stru cture shows lower power dissipation and higher speed than the conventional comparators. The circuit is simulated with 1V DC supply voltage and 250 MHz clock frequency. The proposed topology is based on two cross coupled differential pairs positive feedback and switchable current source ces, has a lower power dissipation, higher speed, less area, and it is shown to be very robust against transistor mismatch, n oise immunity

The solution structure of the heavy chain–only C5-Fc nanobody reveals exposed variable regions that are optimal for COVID-19 antigen interactions

Heavy chain–only antibodies can offer advantages of higher binding affinities, reduced sizes, and higher stabilities than conventional antibodies. To address the challenge of SARS-CoV-2 coronavirus, a llama-derived single-domain nanobody C5 was developed previously that has high COVID-19 virus neutralization potency. The fusion protein C5-Fc comprises two C5 domains attached to a glycosylated Fc region of a human IgG1 antibody and shows therapeutic efficacy in vivo. Here, we have characterized the solution arrangement of the molecule. Two 1443 Da N-linked glycans seen in the mass spectra of C5-Fc were removed and the glycosylated and deglycosylated structures were evaluated. Reduction of C5-Fc with 2-mercaptoethylamine indicated three interchain Cys–Cys disulfide bridges within the hinge. The X-ray and neutron Guinier RG values, which provide information about structural elongation, were similar at 4.1 to 4.2 nm for glycosylated and deglycosylated C5-Fc. To explain these RG values, atomistic scattering modeling based on Monte Carlo simulations resulted in 72,737 and 56,749 physically realistic trial X-ray and neutron structures, respectively. From these, the top 100 best-fit X-ray and neutron models were identified as representative asymmetric solution structures, similar to that of human IgG1, with good R-factors below 2.00%. Both C5 domains were solvent exposed, consistent with the functional effectiveness of C5-Fc. Greater disorder occurred in the Fc region after deglycosylation. Our results clarify the importance of variable and exposed C5 conformations in the therapeutic function of C5-Fc, while the glycans in the Fc region are key for conformational stability in C5-Fc.</p

Synthesis, characterization and biological screening of various pharmacophoric derivatives of 4-alkylpyrimidine-5-carbonitrile

81-874-Isobutyl-1,6-dihydro-1-methyl-2-(methylthio)-6-oxopyrimidine-5-carbonitrile has been used as a starting material. Reaction of 4-isobutyl-1,6-dihydro-1-methyl-2-(methylthio)-6-oxopyrimidine-5-carbonitrile with hydrazine hydrate and amine gives 2-hydrazino and 2-(alkyl/ substituted aryl amino)-4-isobutyl-1,6-dihydro-1-methyl-6-oxopyrimidine-5- carbonitrile compounds respectively. The hydrazino compounds react with different aromatic aldehydes, substituted benzene sulphonyl chloride and s-triazine derivative to form Schiff base, sulphonamide and s-triazine derivatives respectively. Reaction of Schiff base with mercapto lactic acid and chloroacetyl chloride yield 4-thiazolidinones and 2-azetidinones respectively

Characteristic distributions of finite-time Lyapunov exponents

We study the probability densities of finite-time or \local Lyapunov exponents (LLEs) in low-dimensional chaotic systems. While the multifractal formalism describes how these densities behave in the asymptotic or long-time limit, there are significant finite-size corrections which are coordinate dependent. Depending on the nature of the dynamical state, the distribution of local Lyapunov exponents has a characteristic shape. For intermittent dynamics, and at crises, dynamical correlations lead to distributions with stretched exponential tails, while for fully-developed chaos the probability density has a cusp. Exact results are presented for the logistic map, $x \to 4x(1-x)$. At intermittency the density is markedly asymmetric, while for `typical' chaos, it is known that the central limit theorem obtains and a Gaussian density results. Local analysis provides information on the variation of predictability on dynamical attractors. These densities, which are used to characterize the {\sl nonuniform} spatial organization on chaotic attractors are robust to noise and can therefore be measured from experimental data.Comment: To be appear in Phys. Rev