Matthew Welborn

System considerations for ultra-wideband wireless networks

This paper describes some general properties of ultra-wideband (UWB) communications systems and identify characteristics of UWB technology that make it an attractive solution for indoor wireless networks. This paper describes a number of different modulation and coding schemes that are possible for UWB communication systems. Based on results in the literature and additional analysis here, approaches likely to provide the best performance for wireless network applications are identified.

π-Clamp-mediated cysteine conjugation

Site-selective functionalization of complex molecules is one of the most significant challenges in chemistry. Typically, protecting groups or catalysts must be used to enable the selective modification of one site among many that are similarly reactive, and general strategies that selectively tune the local chemical environment around a target site are rare. Here, we show a four-amino-acid sequence (Phe-Cys-Pro-Phe), which we call the ‘π-clamp’, that tunes the reactivity of its cysteine thiol for site-selective conjugation with perfluoroaromatic reagents. We use the π-clamp to selectively modify one cysteine site in proteins containing multiple endogenous cysteine residues. These examples include antibodies and cysteine-based enzymes that would be difficult to modify selectively using standard cysteine-based methods. Antibodies modified using the π-clamp retained binding affinity to their targets, enabling the synthesis of site-specific antibody–drug conjugates for selective killing of HER2-positive breast cancer cells. The π-clamp is an unexpected approach to mediate site-selective chemistry and provides new avenues to modify biomolecules for research and therapeutics. Incorporation of a π-clamp—a four-residue sequence (Phe-Cys-Pro-Phe)—into a protein enables the site-specific modification of the π-clamp cysteine side-chain. The π-clamp can be genetically encoded and does not require protecting-groups or catalysts to provide selective conjugation.

Direct waveform synthesis for software radios

This work presents results that show how direct digital synthesis (DDS) techniques can be extended to produce frequency modulated (FM) waveforms as well as many types of digitally modulated waveforms, such as PSK or QAM. We show how digitally modulated waveforms can be efficiently synthesized from tables of pre-computed samples. This work also reports on the implementation of these algorithms in a software radio system.

Density matrix embedding in an antisymmetrized geminal power bath

Density matrix embedding theory (DMET) has emerged as a powerful tool for performing wave function-in-wave function embedding for strongly correlated systems. In traditional DMET, an accurate calculation is performed on a small impurity embedded in a mean field bath. Here, we extend the original DMET equations to account for correlation in the bath via an antisymmetrized geminal power (AGP) wave function. The resulting formalism has a number of advantages. First, it allows one to properly treat the weak correlation limit of independent pairs, which DMET is unable to do with a mean-field bath. Second, it associates a size extensive correlation energy with a given density matrix (for the models tested), which AGP by itself is incapable of providing. Third, it provides a reasonable description of charge redistribution in strongly correlated but non-periodic systems. Thus, AGP-DMET appears to be a good starting point for describing electron correlation in molecules, which are aperiodic and possess both strong and weak electron correlation.

Narrowband channel extraction for wideband receivers

One of the most computationally intensive processing stages of a wideband digital receiver is the extraction of a narrowband channel from a wideband input signal. In implementations that compute the convolutional sum, the computation is proportional to the bandwidth of the input signal. This paper shows how to break this dependence, reducing the limiting factor to the requirement to maintain a sufficient output signal-to-noise ratio (SNR). This paper describes two complementary algorithms for efficient channel extraction in wideband receivers. The first allows the required frequency translation to be performed at the lower sample rate of the channel filter output. The second algorithm decouples the effect of interference rejection from the SNR improvement and improves the computational efficiency of filtering by using only a subset of the input samples. Additionally, we present a simple model to quantify the effects of this technique and experimental verification using a wideband software radio receiver.

Error Analysis of Free Probability Approximations to the Density of States of Disordered Systems

Theoretical studies of localization, anomalous diffusion and ergodicity breaking require solving the electronic structure of disordered systems. We use free probability to approximate the ensemble-averaged density of states without exact diagonalization. We present an error analysis that quantifies the accuracy using a generalized moment expansion, allowing us to distinguish between different approximations. We identify an approximation that is accurate to the eighth moment across all noise strengths, and contrast this with perturbation theory and isotropic entanglement theory.

Waveform synthesis for transmission of complex waveforms

A new transmit architecture for digital radios is proposed that emphasizes the use of pre-computed waveforms stored in memory instead of real-time computation. We present results that show how direct synthesis techniques can be extended to directly generate many types of digitally modulated waveforms such as PSK or QAM. These techniques are especially appropriate for software radios implemented on systems with general purpose processors and large memory systems.

Why many semiempirical molecular orbital theories fail for liquid water and how to fix them

Water is an extremely important liquid for chemistry and the search for more accurate force fields for liquid water continues unabated. Neglect of diatomic differential overlap (NDDO) molecular orbital methods provide and intriguing generalization of classical force fields in this regard because they can account both for bond breaking and electronic polarization of molecules. However, we show that most standard NDDO methods fail for water because they give an incorrect description of hydrogen bonding, waters key structural feature. Using force matching, we design a reparameterized NDDO model and find that it qualitatively reproduces the experimental radial distribution function of water, as well as various monomer, dimer, and bulk properties that PM6 does not. This suggests that the apparent limitations of NDDO models are primarily due to poor parameterization and not to the NDDO approximations themselves. Finally, we identify the physical parameters that most influence the condensed phase properties. These results help to elucidate the chemistry that a semiempirical molecular orbital picture of water must capture. We conclude that properly parameterized NDDO models could be useful for simulations that require electronically detailed explicit solvent, including the calculation of redox potentials and simulation of charge transfer and photochemistry.

Densities of states for disordered systems from free probability

We investigate how free probability allows us to approximate the density of states in tight binding models of disordered electronic systems. Extending our previous studies of the Anderson model in one dimension with nearest-neighbor interactions [J. Chen et al., Phys. Rev. Lett. 109, 036403 (2012)], we find that free probability continues to provide accurate approximations for systems with constant interactions on twoand three-dimensional lattices or with next-nearest-neighbor interactions, with the results being visually indistinguishable from the numerically exact solution. For systems with disordered interactions, we observe a small but visible degradation of the approximation. To explain this behavior of the free approximation, we develop and apply an asymptotic error analysis scheme to show that the approximation is accurate to the eighth moment in the density of states for systems with constant interactions, but is only accurate to sixth order for systems with disordered interactions. The error analysis also allows us to calculate asymptotic corrections to the density of states, allowing for systematically improvable approximations as well as insight into the sources of error without requiring a direct comparison to an exact solution.

A structural and mechanistic study of π-clamp-mediated cysteine perfluoroarylation

Natural enzymes use local environments to tune the reactivity of amino acid side chains. In searching for small peptides with similar properties, we discovered a four-residue π-clamp motif (Phe-Cys-Pro-Phe) for regio- and chemoselective arylation of cysteine in ribosomally produced proteins. Here we report mutational, computational, and structural findings directed toward elucidating the molecular factors that drive π-clamp-mediated arylation. We show the significance of a trans conformation prolyl amide bond for the π-clamp reactivity. The π-clamp cysteine arylation reaction enthalpy of activation (ΔH‡) is significantly lower than a non-π-clamp cysteine. Solid-state NMR chemical shifts indicate the prolyl amide bond in the π-clamp motif adopts a 1:1 ratio of the cis and trans conformation, while in the reaction product Pro3 was exclusively in trans. In two structural models of the perfluoroarylated product, distinct interactions at 4.7 Å between Phe1 side chain and perfluoroaryl electrophile moiety are observed. Further, solution 19F NMR and isothermal titration calorimetry measurements suggest interactions between hydrophobic side chains in a π-clamp mutant and the perfluoroaryl probe. These studies led us to design a π-clamp mutant with an 85-fold rate enhancement. These findings will guide us toward the discovery of small reactive peptides to facilitate abiotic chemistry in water.