Abstract:
Double fertilization is one of the predominant features of sexual reproduction in flowering plants but, because of the physical inaccessibility of gametes, the essential molecular mechanisms in these processes are largely unknown. Based on the techniques for isolating highly purified gametes from several species and well-developed methods for manipulating RNA from limited quantities of gametes, genome-wide investigations of gamete transcription profiles were recently conducted in flowering plants. In this review, we survey the accumulated knowledge on gamete collection and purification, cDNA library construction, and transcript profile analysis to assess our understanding of the molecular mechanisms of gamete specialization and fertilization.

Abstract:
In the title dioxidovanadium complex, [V(C13H17N2O)O2], the VV atom is in a square-based pyramidal coordination: the basal plane is defined by the phenolate O, imine N and amine N atoms of the tridentate Schiff base ligand, and by one oxide O atom. The apical position is occupied by the other oxide O atom. In the crystal, molecules are connected by N—H...O and N—H...(O,O) hydrogen bonds, forming a tetramer.

Abstract:
A checklist of Chinese Oligaphorurini is given. Two new Chinese species, Micraphorura changbaiensis sp. n. and Oligaphorura pseudomontana sp. n., are described from Changbai Mountain Range. M. changbaiensis sp. n. has the same dorsal pseudocelli formula and number of papillae in Ant. III sensory organ as M. uralica, but they can be easily distinguished by number of chaetae in Ant. III sensory organ, ventral pseudocelli formula, ventral parapseudocelli formula, number of pseudocelli on subcoxa 1 of legs I–III, dorsal axial chaeta on Abd. V and number of chaetae on tibiotarsi. O. pseudomontana sp. n. is very similar to the species O. montanaan increased number of pseudocelli on body dorsally, well marked base of antenna with 1 pseudocellus and 3 pseudocelli outside, subcoxa 1 of legs I–III with 1 pseudocellus each, dorsally S-chaetae formula as 11/011/22211 from head to Abd. V, S-microchaeta present on Th. II–III, claw without inner teeth and with 1+1 lateral teeth, and unguiculus with basal lamella; but they can be separated easily by the number of pseudocelli on Abd. V and VI terga, parapseudocelli on the body, number of chaetae on Th. I tergum, and number of chaetae on tibiotarsi. A key to Chinese species of Oligaphorurini is provided in the present paper.

Abstract:
The static current operator leads to definitional zero frequency divergence and unphysical results in studying nonlinear optical susceptibilities of polymers. A well-defined dipole-dipole correlation is superior to the complicated current-current correlation to solve this problem. As illustrative examples, optical susceptibilities under both SSH and TLM models of trans-(CH)_x are studied. New analytical results are obtained. The reasons of previous improper results are analyzed.

Abstract:
The analytical solutions for the third-harmonic generation (THG) on infinite chains in both Su-Shrieffer-Heeger (SSH) and Takayama-Lin-Liu-Maki (TLM) models of trans-polyacetylene are obtained through the scheme of dipole-dipole ($DD$) correlation. They are not equivalent to the results obtained through static current-current ($J_0J_0$) correlation or under polarization operator $\hat{P}$. The van Hove singularity disappears exactly in the analytical forms, showing that the experimentally observed two-photon absorption peak (TPA) in THG may not be directly explained by the single electron models.

Abstract:
The static current-current correlation leads to the definitional zero frequency divergence (ZFD) in the optical susceptibilities. Previous computations have shown nonequivalent results between two gauges (${\bf p\cdot A}$ and ${\bf E \cdot r}$) under the exact same unperturbed wave functions. We reveal that those problems are caused by the improper treatment of the time-dependent gauge phase factor in the optical response theory. The gauge phase factor, which is conventionally ignored by the theory, is important in solving ZFD and obtaining the equivalent results between these two gauges. The Hamiltonians with these two gauges are not necessary equivalent unless the gauge phase factor is properly considered in the wavefunctions. Both Su-Shrieffer-Heeger (SSH) and Takayama-Lin-Liu-Maki (TLM) models of trans-polyacetylene serve as our illustrative examples to study the linear susceptibility $\chi^{(1)}$ through both current-current and dipole-dipole correlations. Previous improper results of the $\chi^{(1)}$ calculations and distribution functions with both gauges are discussed. The importance of gauge phase factor to solve the ZFD problem is emphasized based on SSH and TLM models. As a conclusion, the reason why dipole-dipole correlation favors over current-current correlation in the practical computations is explained.

Abstract:
Rapid and reliable detection and identification of unknown chemical substances is critical to homeland security. It is challenging to identify chemical components from a wide range of explosives. There are two key steps involved. One is a nondestructive and informative spectroscopic technique for data acquisition. The other is an associated library of reference features along with a computational method for feature matching and meaningful detection within or beyond the library. Recently several experimental techniques based on Raman scattering have been developed to perform standoff detection and identification of explosives, and they prove to be successful under certain idealized conditions. However data analysis is limited to standard least squares method assuming the complete knowledge of the chemical components. In this paper, we develop a new iterative method to identify unknown substances from mixture samples of Raman spectroscopy. In the first step, a constrained least squares method decomposes the data into a sum of linear combination of the known components and a non-negative residual. In the second step, a sparse and convex blind source separation method extracts components geometrically from the residuals. Verification based on the library templates or expert knowledge helps to confirm these components. If necessary, the confirmed meaningful components are fed back into step one to refine the residual and then step two extracts possibly more hidden components. The two steps may be iterated until no more components can be identified. We illustrate the proposed method in processing a set of the so called swept wavelength optical resonant Raman spectroscopy experimental data by a satisfactory blind extraction of a priori unknown chemical explosives from mixture samples.

Abstract:
In this paper, we develop a novel blind source separation (BSS) method for nonnegative and correlated data, particularly for the nearly degenerate data. The motivation lies in nuclear magnetic resonance (NMR) spectroscopy, where a multiple mixture NMR spectra are recorded to identify chemical compounds with similar structures (degeneracy). There have been a number of successful approaches for solving BSS problems by exploiting the nature of source signals. For instance, independent component analysis (ICA) is used to separate statistically independent (orthogonal) source signals. However, signal orthogonality is not guaranteed in many real-world problems. This new BSS method developed here deals with nonorthogonal signals. The independence assumption is replaced by a condition which requires dominant interval(s) (DI) from each of source signals over others. Additionally, the mixing matrix is assumed to be nearly singular. The method first estimates the mixing matrix by exploiting geometry in data clustering. Due to the degeneracy of the data, a small deviation in the estimation may introduce errors (spurious peaks of negative values in most cases) in the output. To resolve this challenging problem and improve robustness of the separation, methods are developed in two aspects. One technique is to find a better estimation of the mixing matrix by allowing a constrained perturbation to the clustering output, and it can be achieved by a quadratic programming. The other is to seek sparse source signals by exploiting the DI condition, and it solves an $\ell_1$ optimization. We present numerical results of NMR data to show the performance and reliability of the method in the applications arising in NMR spectroscopy.

Abstract:
We construct a natural discrete random field on $\mathbb{Z}^{d}$, $d\geq 5$ that converges weakly to the bi-Laplacian Gaussian field in the scaling limit. The construction is based on assigning i.i.d. Bernoulli random variables on each component of the uniform spanning forest, thus defines an associated random function. To our knowledge, this is the first natural discrete model (besides the discrete bi-Laplacian Gaussian field) that converges to the bi-Laplacian Gaussian field.

Abstract:
We prove scaling limit results for the finite-volume version of the inventory accumulation model of Sheffield (2011), which encodes a random planar map decorated by a collection of loops sampled from the critical Fortuin-Kasteleyn (FK) model. In particular, we prove that the random walk associated with the finite-volume version of this model converges in the scaling limit to a correlated Brownian motion $\dot Z$ conditioned to stay in the first quadrant for two units of time and satisfy $\dot Z(2) = 0$. We also show that the times which describe complementary connected components of FK loops in the discrete model converge to the $\pi/2$-cone times of $\dot Z$. Combined with recent results of Duplantier, Miller, and Sheffield, our results imply that many interesting functionals of the FK loops on a finite-volume FK planar map (e.g. their boundary lengths and areas) converge in the scaling limit to the corresponding "quantum" functionals of the CLE$_\kappa$ loops on a $4/\sqrt\kappa$-Liouville quantum gravity sphere for $\kappa \in (4,8)$. Our results are finite-volume analogues of the scaling limit theorems for the infinite-volume version of the inventory accumulation model proven by Sheffield (2011) and Gwynne, Mao, and Sun (2015).