Coupled cluster theory: Towards an algebraic geometry formulation

Coupled cluster theory produced arguably the most widely used high-accuracy computational quantum chemistry methods. Despite the approach's overall great computational success, its mathematical understanding is so far limited to results within the realm of functional analysis. The coupled cluster amplitudes, which are the targeted objects in coupled cluster theory, correspond to solutions to the coupled cluster equations, which is a system of polynomial equations of at most degree four. The high dimensionality of the electronic Schr\"odinger equation and the non-linearity of the coupled cluster ansatz have so far stalled a formal analysis of this polynomial system. In this article, we present algebraic investigations that shed light on the coupled cluster equations and the root structure of this ansatz. This is of importance for the a posteriori evaluation of coupled cluster calculations. To that end, we investigate the root structure by means of Newton polytopes. We derive a general v-description, which is subsequently turned into an h-description for explicit examples. This perspective reveals an apparent connection between Pauli's exclusion principle and the geometrical structure of the Newton polytopes. We also propose an alternative characterization of the coupled cluster equations projected onto singles and doubles as cubic polynomials on an algebraic variety with certain sparsity patterns. Moreover, we provide numerical simulations of two computationally tractable systems, namely, the two electrons in four spin-orbitals system and the three electrons in six spin-orbitals system. These simulations provide novel insight into the root structure of the coupled cluster solutions when the coupled cluster ansatz is truncated

Large expert-curated database for benchmarking document similarity detection in biomedical literature search

Document recommendation systems for locating relevant literature have mostly relied on methods developed a decade ago. This is largely due to the lack of a large offline gold-standard benchmark of relevant documents that cover a variety of research fields such that newly developed literature search techniques can be compared, improved and translated into practice. To overcome this bottleneck, we have established the RElevant LIterature SearcH consortium consisting of more than 1500 scientists from 84 countries, who have collectively annotated the relevance of over 180 000 PubMed-listed articles with regard to their respective seed (input) article/s. The majority of annotations were contributed by highly experienced, original authors of the seed articles. The collected data cover 76% of all unique PubMed Medical Subject Headings descriptors. No systematic biases were observed across different experience levels, research fields or time spent on annotations. More importantly, annotations of the same document pairs contributed by different scientists were highly concordant. We further show that the three representative baseline methods used to generate recommended articles for evaluation (Okapi Best Matching 25, Term Frequency-Inverse Document Frequency and PubMed Related Articles) had similar overall performances. Additionally, we found that these methods each tend to produce distinct collections of recommended articles, suggesting that a hybrid method may be required to completely capture all relevant articles. The established database server located at https://relishdb.ict.griffith.edu.au is freely available for the downloading of annotation data and the blind testing of new methods. We expect that this benchmark will be useful for stimulating the development of new powerful techniques for title and title/abstract-based search engines for relevant articles in biomedical research.Peer reviewe

The Fight-Or-Flight Response Is Associated with PBMC Expression Profiles Related to Immune Defence and Recovery in Swine

Defining phenotypes according to molecular features would promote the knowledge of functional traits like behaviour in both human and animal research. Beside physiological states or environmental factors, an innate predisposition of individual coping strategies was discussed, including the proactive and reactive pattern. According to backtest reactivity, animals assigned as high-resisting (proactive) and low-resisting (reactive) were immune challenged with tetanus toxoid in a time course experiment. Using the Affymetrix platform and qPCR, individual coping characteristics were reflected as gene expression signatures in porcine peripheral blood mononuclear cells (PBMC) at naïve state (day 0) and in response to the model antigen (day 14, day 28, and day 140). Further, the blood cell count was analysed at all stages. On the transcriptional level, processes acting on cell communication, vasculogenesis, and blood coagulation were highlighted in high-resisting animals at naïve state (day 0), temporarily blurred due to immune challenge (day 14) but subsequently restored and intensified (day 28). Notably, similar amounts of white and red blood cells, platelets and haematocrit between high-resisting and low-resisting samples suggest coping-specific expression patterns rather than alterations in blood cell distribution. Taken together, the gene expression patterns indicate that proactive pigs might favour molecular pathways enabling an effective strategy for defence and recovery. This corroborates the previously suggested belief, that proactive animals are prone to an increased number of injuries as an evolutionary inherited mechanism. In contrast to previous assumptions, coping-specific immunity in pigs lacks inherited shifts between cellular and humoral immune responses

Development of a Multidirectional Wire Arc Additive Manufacturing (WAAM) Process with Pure Object Manipulation: Process Introduction and First Prototypes

Wire Arc Additive Manufacturing (WAAM) with eccentric wire feed requires defined operating conditions due to the possibility of varying shapes of the deposited and solidified material depending on the welding torch orientation. In consequence, the produced component can contain significant errors because single bead geometrical errors are cumulatively added to the next layer during a building process. In order to minimise such inaccuracies caused by torch manipulation, this article illustrates the concept and testing of object-manipulated WAAM by incorporating robotic and welding technologies. As the first step towards this target, robotic hardware and software interfaces were developed to control the robot. Alongside, a fixture for holding the substrate plate was designed and fabricated. After establishing the robotic setup, in order to complete the whole WAAM process setup, a Gas Metal Arc Welding (GMAW) process was built and integrated into the system. Later, an experimental plan was prepared to perform single and multilayer welding experiments as well as for different trajectories. According to this plan, several welding experiments were performed to decide the parametric working range for the further WAAM experiments. In the end, the results of the first multilayer depositions over intricate trajectories are shown. Further performance and quality optimization strategies are also discussed at the end of this article

Development of a Multidirectional Wire Arc Additive Manufacturing (WAAM) Process with Pure Object Manipulation: Process Introduction and First Prototypes

Wire Arc Additive Manufacturing (WAAM) with eccentric wire feed requires defined operating conditions due to the possibility of varying shapes of the deposited and solidified material depending on the welding torch orientation. In consequence, the produced component can contain significant errors because single bead geometrical errors are cumulatively added to the next layer during a building process. In order to minimise such inaccuracies caused by torch manipulation, this article illustrates the concept and testing of object-manipulated WAAM by incorporating robotic and welding technologies. As the first step towards this target, robotic hardware and software interfaces were developed to control the robot. Alongside, a fixture for holding the substrate plate was designed and fabricated. After establishing the robotic setup, in order to complete the whole WAAM process setup, a Gas Metal Arc Welding (GMAW) process was built and integrated into the system. Later, an experimental plan was prepared to perform single and multilayer welding experiments as well as for different trajectories. According to this plan, several welding experiments were performed to decide the parametric working range for the further WAAM experiments. In the end, the results of the first multilayer depositions over intricate trajectories are shown. Further performance and quality optimization strategies are also discussed at the end of this article

Comparison of microarray and quantitative PCR (qPCR) results for selected transcripts (<i>CD69</i>, <i>GNAZ</i>, <i>ITGA2B</i>) to verify microarray data.

<p>Values were calculated by factorial normalisation on <i>IQGAP1</i> and <i>TSC22D2</i> expression values. Fold-changes displayed in red circles indicate significant differences in mRNA abundances between HR and LR at either microarray (solid lined circles) or qPCR data (dashed lined circles). Positive values display increased mRNA abundances in HR (HR > LR). Correlation of normalized expression values was calculated by Spearman (n = 176). * p = 0.06.</p

Heatmap displaying probe-sets with significantly altered mRNA abundances.

<p>Effects mediated by coping group appeared to dominate early sampling points (day 0, day 14, day 28). Later, age-specific effects were more pronounced as visualized by young adult subgroups (day 140). Columns = variance component coping group x time; Rows = transcripts showing altered mRNA abundances between HR and LR on at least one time point; HR—High resisting; LR—Low resisting.</p