Induced subgraphs in sparse random graphs with given degree sequence

For any $S\subset [n]$, we compute the probability that the subgraph of $\mathcal{G}_{n,d}$ induced by $S$ is a given graph $H$ on the vertex set $S$. The result holds for any $d=o(n^{1/3})$ and is further extended to $\mathcal{G}_{{\bf d}}$, the probability space of random graphs with a given degree sequence $\bf d$.Comment: 31 pages, 11 figure

Novel vortex structures in dipolar condensates

We investigate the properties of single vortices and of vortex lattice in a rotating dipolar condensate. We show that vortices in this system possess many novel features induced by the long-range anisotropic dipolar interaction between particles. For example, when the dipoles are polarized along the rotation axis, vortices may display a crater-like structure; when dipoles are polarized orthogonal to the rotation axis, vortex cores takes an elliptical shape and the vortex lattice no longer possesses hexagonal symmetry.Comment: 4 pages, 5 figure

Applications of ion mobility spectrometry, collision-induced dissociation and electron activated dissociation tandem mass spectrometry to structural analysis of proteins, glycoproteins and glycans

This dissertation mainly focuses on analytical method development for characterization of proteins, glycoproteins and glycans using the recently developed ion mobility spectrometry (IMS) techniques and various electron activated dissociation (ExD) tandem mass spectrometry methods. IMS and ExD have become important techniques in structure analysis of biomolecules. IMS is a gas-phase separation method orthogonal to liquid chromatography (LC) fractionation. ExD is capable of producing a large number of structurally informative fragment ions for elucidation of structural details, complementary to collision-induced dissociation (CID). We first applied the selected accumulation-trapped IMS (SA-TIMS)-electronic excitation dissociation (EED) method to analyze various mixtures of glycan isomers. Glycan linkage isomers with linear or branched structure were successfully separated and subsequently identified. Theoretical modeling was also performed to gain a better understanding of isomer separation. The calculated collisional cross section (CCS) values match well with the experimentally measured ones, and suggested that the choice of metal charge carrier and charge state is critical for successful IMS separation of isomeric glycans. In addition, a SA-TIMS-electron capture dissociation (ECD) approach was employed to study gas-phase protein conformation, as the ECD fragmentation pattern is influenced by both the charge distribution and the presence of various non-covalent interactions. We demonstrated that different conformations of protein ions in a single charge state could produce distinct fragmentation pattern, presumably because of their differences in tertiary structures and/or proton locations. The second part describes characterization of glycoproteins using LC-hot ECD. To improve the cleavage coverage of glycopeptides, hot ECD, a fragmentation method utilizing the irradiation of high-energy electrons, was optimized for both middle-down and bottom-up analyses of glycopeptides, including peptides with multiple glycosylation sites. Hot ECD was shown to be an effective fragmentation technique for sequencing of glycopeptides, even for ions in lower charge states. In addition, the online LC-hot ECD approach was applied to characterize extensively modified glycoproteins from biological sources in which all glycosylation sites could be unambiguously determined. This study expands the applications of IMS, CID and ExD to structural analysis of various biomolecules, and explores the analytical potential of combining them for investigation of complex biological systems, in particular, enzyme mechanisms

Abnormal enhancement of electric field inside a thin permittivity-near-zero object in free space

It is found that the electric field can be enhanced strongly inside a permittivity-near-zero object in free space, when the transverse cross section of the object is small and the length along the propagation direction of the incident wave is large enough as compared with the wavelength. The physical mechanism is explained in details. The incident electromagnetic energy can only flow almost normally through the outer surface into or out of the permittivity-near-zero object, which leads to large energy stream density and then strong electric field inside the object. Meanwhile, the magnetic field inside the permittivity-near-zero object may be smaller than that of the incident wave, which is also helpful for enhancing the electric field. Two permittivity-near-zero objects of simple shapes, namely, a thin cylindrical shell and a long thin rectangular bar, are chosen for numerical illustration. The enhancement of the electric field becomes stronger when the permittivity-near-zero object becomes thinner. The physical mechanism of the field enhancement is completely different from the plasmonic resonance enhancement at a metal surface