Combinatorial proofs on the joint distribution of descents and inverse descents

Let $A_{n,i,j}$ be the number of permutations on $[n]$ with $i-1$ descents and $j-1$ inverse descents. Carlitz, Roselle and Scoville in 1966 first revealed some combinatorial and arithmetic properties of $A_{n,i,j}$, which contain a recurrence of $A_{n,i,j}$. Using the idea of balls in boxes, Petersen gave a combinatorial interpretation for the generating function of $A_{n,i,j}$, and obtained the same recurrence of $A_{n,i,j}$ from its generating function. Subsequently, Petersen asked whether there is a visual way to understand this recurrence. In this paper, after observing the internal structures of permutation grids, we present a combinatorial proof of the recurrence of $A_{n,i,j}$. Let $I_{n,k}$ and $J_{n,k}$ count the number of involutions and fixed-point free involutions on $[n]$ with $k$ descents, respectively. With the help of generating functions, Guo and Zeng derived two recurrences of $I_{n,k}$ and $J_{2n,k}$ that play an essential role in the proof of their unimodal properties. Unexpectedly, the constructive approach to the recurrence of $A_{n,i,j}$ is found to fuel the combinatorial interpretations of these two recurrences of $I_{n,k}$ and $J_{2n,k}$

A CRISPR/Cas9-based genome-editing system for yam (Dioscorea spp.)

Open Access Journal; Published online: 22 Nov 202

C-MYC Targeting by Degradation: Novel Dual c-Myc/GSPT1 Degrader GT19715 Exerts Profound Cell Kill in vitro and in vivo in Acute Myeloid Leukemia and Lymphomas

View full abstracthttps://openworks.mdanderson.org/leading-edge/1020/thumbnail.jp

Spatial Guilds in the Serengeti Food Web Revealed by a Bayesian Group Model

Food webs, networks of feeding relationships among organisms, provide fundamental insights into mechanisms that determine ecosystem stability and persistence. Despite long-standing interest in the compartmental structure of food webs, past network analyses of food webs have been constrained by a standard definition of compartments, or modules, that requires many links within compartments and few links between them. Empirical analyses have been further limited by low-resolution data for primary producers. In this paper, we present a Bayesian computational method for identifying group structure in food webs using a flexible definition of a group that can describe both functional roles and standard compartments. The Serengeti ecosystem provides an opportunity to examine structure in a newly compiled food web that includes species-level resolution among plants, allowing us to address whether groups in the food web correspond to tightly-connected compartments or functional groups, and whether network structure reflects spatial or trophic organization, or a combination of the two. We have compiled the major mammalian and plant components of the Serengeti food web from published literature, and we infer its group structure using our method. We find that network structure corresponds to spatially distinct plant groups coupled at higher trophic levels by groups of herbivores, which are in turn coupled by carnivore groups. Thus the group structure of the Serengeti web represents a mixture of trophic guild structure and spatial patterns, in contrast to the standard compartments typically identified in ecological networks. From data consisting only of nodes and links, the group structure that emerges supports recent ideas on spatial coupling and energy channels in ecosystems that have been proposed as important for persistence.Comment: 28 pages, 6 figures (+ 3 supporting), 2 tables (+ 4 supporting

Evolutionary Patterning: A Novel Approach to the Identification of Potential Drug Target Sites in Plasmodium falciparum

Malaria continues to be the most lethal protozoan disease of humans. Drug development programs exhibit a high attrition rate and parasite resistance to chemotherapeutic drugs exacerbates the problem. Strategies that limit the development of resistance and minimize host side-effects are therefore of major importance. In this study, a novel approach, termed evolutionary patterning (EP), was used to identify suitable drug target sites that would minimize the emergence of parasite resistance. EP uses the ratio of non-synonymous to synonymous substitutions (ω) to assess the patterns of evolutionary change at individual codons in a gene and to identify codons under the most intense purifying selection (ω≤0.1). The extreme evolutionary pressure to maintain these residues implies that resistance mutations are highly unlikely to develop, which makes them attractive chemotherapeutic targets. Method validation included a demonstration that none of the residues providing pyrimethamine resistance in the Plasmodium falciparum dihydrofolate reductase enzyme were under extreme purifying selection. To illustrate the EP approach, the putative P. falciparum glycerol kinase (PfGK) was used as an example. The gene was cloned and the recombinant protein was active in vitro, verifying the database annotation. Parasite and human GK gene sequences were analyzed separately as part of protozoan and metazoan clades, respectively, and key differences in the evolutionary patterns of the two molecules were identified. Potential drug target sites containing residues under extreme evolutionary constraints were selected. Structural modeling was used to evaluate the functional importance and drug accessibility of these sites, which narrowed down the number of candidates. The strategy of evolutionary patterning and refinement with structural modeling addresses the problem of targeting sites to minimize the development of drug resistance. This represents a significant advance for drug discovery programs in malaria and other infectious diseases

Transcriptional Activation of OsDERF1 in OsERF3 and OsAP2-39 Negatively Modulates Ethylene Synthesis and Drought Tolerance in Rice

The phytohormone ethylene is a key signaling molecule that regulates a variety of developmental processes and stress responses in plants. Transcriptional modulation is a pivotal process controlling ethylene synthesis, which further triggers the expression of stress-related genes and plant adaptation to stresses; however, it is unclear how this process is transcriptionally modulated in rice. In the present research, we report the transcriptional regulation of a novel rice ethylene response factor (ERF) in ethylene synthesis and drought tolerance. Through analysis of transcriptional data, one of the drought-responsive ERF genes, OsDERF1, was identified for its activation in response to drought, ethylene and abscisic acid. Transgenic plants overexpressing OsDERF1 (OE) led to reduced tolerance to drought stress in rice at seedling stage, while knockdown of OsDERF1 (RI) expression conferred enhanced tolerance at seedling and tillering stages. This regulation was supported by negative modulation in osmotic adjustment response. To elucidate the molecular basis of drought tolerance, we identified the target genes of OsDERF1 using the Affymetrix GeneChip, including the activation of cluster stress-related negative regulators such as ERF repressors. Biochemical and molecular approaches showed that OsDERF1 at least directly interacted with the GCC box in the promoters of ERF repressors OsERF3 and OsAP2-39. Further investigations showed that OE seedlings had reduced expression (while RI lines showed enhanced expression) of ethylene synthesis genes, thereby resulting in changes in ethylene production. Moreover, overexpression of OsERF3/OsAP2-39 suppressed ethylene synthesis. In addition, application of ACC recovered the drought-sensitive phenotype in the lines overexpressing OsERF3, showing that ethylene production contributed to drought response in rice. Thus our data reveal that a novel ERF transcriptional cascade modulates drought response through controlling the ethylene synthesis, deepening our understanding of the regulation of ERF proteins in ethylene related drought response

Heavy Quarks and Heavy Quarkonia as Tests of Thermalization

We present here a brief summary of new results on heavy quarks and heavy quarkonia from the PHENIX experiment as presented at the "Quark Gluon Plasma Thermalization" Workshop in Vienna, Austria in August 2005, directly following the International Quark Matter Conference in Hungary.Comment: 8 pages, 5 figures, Quark Gluon Plasma Thermalization Workshop (Vienna August 2005) Proceeding

Reconfigurable self-assembly through chiral control of interfacial tension

Author Posting. © The Author(s), 2011. This is the author's version of the work. It is posted here by permission of Nature Publishing Group for personal use, not for redistribution. The definitive version was published in Nature 481 (2012): 348–351, doi:10.1038/nature10769.From determining optical properties of simple molecular crystals to establishing preferred handedness in highly complex vertebrates, molecular chirality profoundly influences the structural, mechanical, and optical properties of both synthetic and biological matter at macroscopic lengthscales1,2. In soft materials such as amphiphilic lipids and liquid crystals, the competition between local chiral interactions and global constraints imposed by the geometry of the self-assembled structures leads to frustration and the assembly of unique materials3-6. An example of particular interest is smectic liquid crystals, where the 2D layered geometry cannot support twist, expelling chirality to the edges in a manner analogous to the expulsion of a magnetic field from superconductors7-10. Here, we demonstrate a previously unexplored consequence of this geometric frustration which leads to a new design principle for the assembly of chiral molecules. Using a model system of colloidal membranes11, we show that molecular chirality can control the interfacial tension, an important property of multi-component mixtures. This finding suggests an analogy between chiral twist which is expelled to the edge of 2D membranes, and amphiphilic surfactants which are expelled to oil-water interfaces12. Similar to surfactants, chiral control of interfacial tension drives the assembly of myriad polymorphic assemblages such as twisted ribbons with linear and circular topologies, starfish membranes, and double and triple helices. Tuning molecular chirality in situ enables dynamical control of line tension that powers polymorphic transitions between various chiral structures. These findings outline a general strategy for the assembly of reconfigurable chiral materials which can easily be moved, stretched, attached to one another, and transformed between multiple conformational states, thus enabling precise assembly and nano-sculpting of highly dynamical and designable materials with complex topologies.This work was supported by the National Science Foundation (NSF-MRSEC-0820492, NSF-DMR-0955776, NSF-MRI 0923057) and Petroleum Research Fund (ACS-PRF 50558-DNI7).2012-07-0