On arithmetic and asymptotic properties of up-down numbers

Let $\sigma=(\sigma_1,..., \sigma_N)$, where $\sigma_i =\pm 1$, and let $C(\sigma)$ denote the number of permutations $\pi$ of $1,2,..., N+1,$ whose up-down signature $\mathrm{sign}(\pi(i+1)-\pi(i))=\sigma_i$, for $i=1,...,N$. We prove that the set of all up-down numbers $C(\sigma)$ can be expressed by a single universal polynomial $\Phi$, whose coefficients are products of numbers from the Taylor series of the hyperbolic tangent function. We prove that $\Phi$ is a modified exponential, and deduce some remarkable congruence properties for the set of all numbers $C(\sigma)$, for fixed $N$. We prove a concise upper-bound for $C(\sigma)$, which describes the asymptotic behaviour of the up-down function $C(\sigma)$ in the limit $C(\sigma) \ll (N+1)!$.Comment: Recommended for publication in Discrete Mathematics subject to revision

First Report of African Fig Fly, Zaprionus indianus Gupta (Diptera: Drosophilidae), on the Island of Maui, Hawaii, USA, in 2017 and Potential Impacts to the Hawaiian Entomofauna

This report confirms the first reported observation of Zaprionus indianus Gupta (Diptera: Drosophilidae), commonly known as African fig fly, on Maui (new island record). Adult specimens were collected in October and November 2017 while surveying for populations of Drosophila suzukii (Matsumura) (Diptera: Drosophilidae). Specimens were retrieved from four localities in Haiku and Kula among traps positioned at fruiting height in six host plant environments (orange, lemon, starfruit, banana, strawberry, and cherimoya). Historically, the earliest records of Z. indianus in the state were recorded on Oahu in 2013 (new state record, new island record), on Kauai in 2015 (new island record), and on the Big Island (Hawaii) in 2017 (new island record). Including this report, there are currently at least 33 introduced Drosophilidae species established in the state of Hawaii. Furthermore, it is the second member belonging to genus Zaprionus that has been identified on the Hawaiian Islands. Specimens were not only retrieved from farms and subdivisions but also within mountain ranges and state forest reserves, suggesting that further research is needed to evaluate potential impacts to endemic entomofauna

The XFEM with an Explicit-Implicit Crack Description for Hydraulic Fracture Problems

The Extended Finite Element Method (XFEM) approach is applied to the coupled problem of fluid flow, solid deformation, and fracture propagation. The XFEM model description of hydraulic fracture propagation is part of a joint project in which the developed numerical model will be verified against large-scale laboratory experiments. XFEM forms an important basis towards future combination with heat and mass transport simulators and extension to more complex fracture systems. The crack is described implicitly using three level-sets to evaluate enrichment functions. Additionally, an explicit crack representation is used to update the crack during propagation. The level-set functions are computed exactly from the explicit representation. This explicit/implicit representation is applied to a fluid-filled crack in an impermeable, elastic solid and compared to the early-time solution of a plane-strain hydraulic fracture problem with a fluid lag

A human relevent rat model of breast cancer

Abstract only availableBecause women experience a bewildering array of chemicals, foods and lifestyles, only profound effects on preventing or promoting breast cancer are detectible in human studies. Subtle or delayed effects can be detected in animal models. Mammary tumors in ACI rats share important similarities with the majority of human breast cancers. The link between life time estrogen exposure and breast cancer risk in humans is well established. A high percentage of human breast cancers express ER, are stimulated to grow by the addition of exogenous estrogen, and respond to the antiestrogen tamoxifen. The ACI rat is the only rodent model in which estrogen-sensitive tumors are induced by estrogen. The ACI.COP-Ept2 substrain, derived from the ACI rat, develops mammary tumors similar to those of the ACI rat, but with reduced pituitary hyperplasia. We show that estrogen-induced mammary tumors in ACI.COP-Ept2 express ERα and respond to tamoxifen. Furthermore, tumors express ERβ, progesterone receptor and Her2/neu. The average latency was 183±6 days (n=24) and average tumor burden 1,107±415 mm3. The similarities of ACI.COP-Ept2 tumors to human breast cancers make this a valuable model for determining which of the myriad of lifestyle and diet choices reportedly protecting women from breast cancer actually reduce cancer incidence.Food for the 21st Century Undergraduate Research Program in Nutritional Science

On Growth, Disorder, and Field Theory

This article reviews recent developments in statistical field theory far from equilibrium. It focuses on the Kardar-Parisi-Zhang equation of stochastic surface growth and its mathematical relatives, namely the stochastic Burgers equation in fluid mechanics and directed polymers in a medium with quenched disorder. At strong stochastic driving -- or at strong disorder, respectively -- these systems develop nonperturbative scale-invariance. Presumably exact values of the scaling exponents follow from a self-consistent asymptotic theory. This theory is based on the concept of an operator product expansion formed by the local scaling fields. The key difference to standard Lagrangian field theory is the appearance of a dangerous irrelevant coupling constant generating dynamical anomalies in the continuum limit.Comment: review article, 50 pages (latex), 10 figures (eps), minor modification of original versio

Predicting Cell Cycle Regulated Genes by Causal Interactions

The fundamental difference between classic and modern biology is that technological innovations allow to generate high-throughput data to get insights into molecular interactions on a genomic scale. These high-throughput data can be used to infer gene networks, e.g., the transcriptional regulatory or signaling network, representing a blue print of the current dynamical state of the cellular system. However, gene networks do not provide direct answers to biological questions, instead, they need to be analyzed to reveal functional information of molecular working mechanisms. In this paper we propose a new approach to analyze the transcriptional regulatory network of yeast to predict cell cycle regulated genes. The novelty of our approach is that, in contrast to all other approaches aiming to predict cell cycle regulated genes, we do not use time series data but base our analysis on the prior information of causal interactions among genes. The major purpose of the present paper is to predict cell cycle regulated genes in S. cerevisiae. Our analysis is based on the transcriptional regulatory network, representing causal interactions between genes, and a list of known periodic genes. No further data are used. Our approach utilizes the causal membership of genes and the hierarchical organization of the transcriptional regulatory network leading to two groups of periodic genes with a well defined direction of information flow. We predict genes as periodic if they appear on unique shortest paths connecting two periodic genes from different hierarchy levels. Our results demonstrate that a classical problem as the prediction of cell cycle regulated genes can be seen in a new light if the concept of a causal membership of a gene is applied consequently. This also shows that there is a wealth of information buried in the transcriptional regulatory network whose unraveling may require more elaborate concepts than it might seem at first

Hierarchical coordination of periodic genes in the cell cycle of Saccharomyces cerevisiae

<p>Abstract</p> <p>Background</p> <p>Gene networks are a representation of molecular interactions among genes or products thereof and, hence, are forming causal networks. Despite intense studies during the last years most investigations focus so far on inferential methods to reconstruct gene networks from experimental data or on their structural properties, e.g., degree distributions. Their structural analysis to gain functional insights into organizational principles of, e.g., pathways remains so far under appreciated.</p> <p>Results</p> <p>In the present paper we analyze cell cycle regulated genes in <it>S. cerevisiae</it>. Our analysis is based on the transcriptional regulatory network, representing causal interactions and not just associations or correlations between genes, and a list of known periodic genes. No further data are used. Partitioning the transcriptional regulatory network according to a graph theoretical property leads to a hierarchy in the network and, hence, in the information flow allowing to identify two groups of periodic genes. This reveals a novel conceptual interpretation of the working mechanism of the cell cycle and the genes regulated by this pathway.</p> <p>Conclusion</p> <p>Aside from the obtained results for the cell cycle of yeast our approach could be exemplary for the analysis of general pathways by exploiting the rich causal structure of inferred and/or curated gene networks including protein or signaling networks.</p