Sandpiles, spanning trees, and plane duality

Let G be a connected, loopless multigraph. The sandpile group of G is a finite abelian group associated to G whose order is equal to the number of spanning trees in G. Holroyd et al. used a dynamical process on graphs called rotor-routing to define a simply transitive action of the sandpile group of G on its set of spanning trees. Their definition depends on two pieces of auxiliary data: a choice of a ribbon graph structure on G, and a choice of a root vertex. Chan, Church, and Grochow showed that if G is a planar ribbon graph, it has a canonical rotor-routing action associated to it, i.e., the rotor-routing action is actually independent of the choice of root vertex. It is well-known that the spanning trees of a planar graph G are in canonical bijection with those of its planar dual G*, and furthermore that the sandpile groups of G and G* are isomorphic. Thus, one can ask: are the two rotor-routing actions, of the sandpile group of G on its spanning trees, and of the sandpile group of G* on its spanning trees, compatible under plane duality? In this paper, we give an affirmative answer to this question, which had been conjectured by Baker.Comment: 13 pages, 9 figure

Morphology, photosynthetic physiology and biochemistry of nine herbaceous plants under water stress

Global climate warming and shifts in rainfall patterns are expected to trigger increases in the frequency and magnitude of drought and/or waterlogging stress in plants. To cope with water stress, plants develop diverse tactics. However, the adoption capability and mechanism vary depending upon the plant species identity as well as stress duration and intensity. The objectives of this study were to evaluate the species-dependent responses of alpine herbaceous species to water stress. Nine herbaceous species were subjected to different water stresses (including moderate drought and moderate waterlogging) in pot culture using a randomized complete block design with three replications for each treatment. We hypothesized that water stress would negatively impact plant growth and metabolism. We found considerable interspecies differences in morphological, physiological, and biochemical responses when plants were exposed to the same water regime. In addition, we observed pronounced interactive effects of water regime and plant species identity on plant height, root length, root/shoot ratio, biomass, and contents of chlorophyll a, chlorophyll b, chlorophyll (a+b), carotenoids, malondialdehyde, soluble sugar, betaine, soluble protein and proline, implying that plants respond to water regime differently. Our findings may cast new light on the ecological restoration of grasslands and wetlands in the Qinghai-Tibetan Plateau by helping to select stress-tolerant plant species

Effect of Amorphization Methods on the Properties and Structures of Potato Starch-Monoglyceride Complex

Recently, starch-based fat replacers (FRs) have emerged as unique ingredients, possessing few calories and high vascular scavenger function without adverse organoleptic changes. Here, a two-step modification method for the development of a starch-based FRs is reported. First, native potato starch is amorphized by grinding, alkali and ethanol treatment. Then, the amorphized starch is complexed with monoglyceride. The results show that alkaline amorphous potato starch (AAPS) has the best emulsifying activity; ethanol amorphous potato starch complex (EAPSC) has the highest content of resistant starch (RS) (21.49%), while grinding amorphous potato starch (GAPS) retains the granular structure of the original starch best. The amorphization reduces the amylose content of starch, leading to reduced swelling power and increased digestibility. Complexation, on the other hand, is more like attaching a layer of the hydrophobic membrane. Combined with DSC and XRD, amorphization reduces the value of enthalpy and crystallinity, while the complexation process does the opposite. Overall, EAPSC is the best candidate for novel FRs, due to its greater emulsion stability and enzyme resistance. The experimental results provide a theoretical basis for the application of a novel potato starch-monoglyceride complex in foods such as cakes and snack fillings

Growth of millimeter-sized high-quality CuFeSe2_2 single crystals by the molten salt method and study of their semiconducting behavior

An eutectic AlCl$_3$/KCl molten salt method in a horizontal configuration was employed to grow millimeter-sized and composition homogeneous CuFeSe$_2$ single crystals due to the continuous growth process in a temperature gradient induced solution convection. The typical as-grown CuFeSe$_2$ single crystals in cubic forms are nearly 1.6$\times$1.2$\times$1.0 mm3 in size. The chemical composition and homogeneity of the crystals was examined by both inductively coupled plasma atomic emission spectroscopy and energy dispersive spectrometer with Cu:Fe:Se = 0.96:1.00:1.99 consistent with the stoichiometric composition of CuFeSe$_2$. The magnetic measurements suggest a ferrimagnetic or weak ferromagnetic transition below T$_C$ = 146 K and the resistivity reveals a semiconducting behavior and an abrupt increase below T$_C$

Evolution of vegetation and climate variability on the Tibetan Plateau over the past 1.74 million years

The Tibetan Plateau exerts a major influence on Asian climate, but its long-term environmental history remains largely unknown. We present a detailed record of vegetation and climate changes over the past 1.74 million years in a lake sediment core from the Zoige Basin, eastern Tibetan Plateau. Results show three intervals with different orbital- and millennial-scale features superimposed on a stepwise long-term cooling trend. The interval of 1.74–1.54 million years ago is characterized by an insolation-dominated mode with strong ~20,000-year cyclicity and quasi-absent millennial-scale signal. The interval of 1.54–0.62 million years ago represents a transitional insolation-ice mode marked by ~20,000- and ~40,000-year cycles, with superimposed millennial-scale oscillations. The past 620,000 years are characterized by an ice-driven mode with 100,000-year cyclicity and less frequent millennial-scale variability. A pronounced transition occurred 620,000 years ago, as glacial cycles intensified. These new findings reveal how the interaction of low-latitude insolation and high-latitude ice-volume forcing shaped the evolution of the Tibetan Plateau climate.publishedVersio

Genome-wide identification and expression analysis of AUX/LAX family genes in Chinese hickory (Carya cathayensis Sarg.) Under various abiotic stresses and grafting

Auxin is essential for regulating plant growth and development as well as the response of plants to abiotic stresses. AUX/LAX proteins are auxin influx transporters belonging to the amino acid permease family of proton-driven transporters, and are involved in the transport of indole-3-acetic acid (IAA). However, how AUX/LAX genes respond to abiotic stresses in Chinese hickory is less studied. For the first time identification, structural characteristics as well as gene expression analysis of the AUX/LAX gene family in Chinese hickory were conducted by using techniques of gene cloning and real-time fluorescent quantitative PCR. Eight CcAUX/LAXs were identified in Chinese hickory, all of which had the conserved structural characteristics of AUX/LAXs. CcAUX/LAXs were most closely related to their homologous proteins in Populus trichocarpa , which was in consistence with their common taxonomic character of woody trees. CcAUX/LAXs exhibited different expression profiles in different tissues, indicating their varying roles during growth and development. A number of light-, hormone-, and abiotic stress responsive cis-acting regulatory elements were detected on the promoters of CcAUX/LAX genes. CcAUX/LAX genes responded differently to drought and salt stress treatments to varying degrees. Furthermore, CcAUX/LAX genes exhibited complex expression changes during Chinese hickory grafting. These findings not only provide a valuable resource for further functional validation of CcAUX/LAXs, but also contribute to a better understanding of their potential regulatory functions during grafting and abiotic stress treatments in Chinese hickory

Optimal Allocation Algorithm for Sequential Resource Allocation in the Context of Food Banks Operations

This thesis studies a Sequential Resource Allocation (SRA) problem that is faced by food distribution of a nonprofit organization (e.g. food banks). Different from commercial operations’ objective aimed at maximizing profit, the primary objective arising in nonprofit organizations is to fairly satisfy the demand of recipients. Rising demand and limited resource increase the importance of effective food allocation operations that maximize equity and resource utilization at the same time. In the context of food bank operations, we consider the problem of collecting an uncertain quantities of donation and allocating them sequentially to meet customers’ demands that are uncertain until arriving at the customer’s location. A SRA model is formulated that can be used to design an optimal visiting route; it focus on equity maximization and waste reduction. Without considering travel cost/time restriction, our work solves the problem by developing a new objective function to minimize the filling rate (i.e., the ratio of the allocation quantity to observed demand) gap among agencies. An experimentation is designed to evaluate and analyze the performance of the algorithm, and the proposed method yield better solutions in terms of waste reduction. Furthermore, by using adaptive large neighborhood search (ALNS), we extend the model to include travel cost into consideration to find a near-optimal visiting route. A case study with larger scale is also performed that shows the algorithm obtains high-quality solutions in terms of equity and efficiency (travel costs)