Cutting the traintracks: Cauchy, Schubert and Calabi-Yau

In this note we revisit the maximal-codimension residues, or leading singularities, of four-dimensional $L$-loop traintrack integrals with massive legs, both in Feynman parameter space and in momentum (twistor) space. We identify a class of "half traintracks" as the most general degenerations of traintracks with conventional (0-form) leading singularities, although the integrals themselves still have rigidity $\lfloor\frac{L-1}2\rfloor$ due to lower-loop "full traintrack'' subtopologies. As a warm-up exercise, we derive closed-form expressions for their leading singularities both via (Cauchy's) residues in Feynman parameters, and more geometrically using the so-called Schubert problems in momentum twistor space. For $L$-loop full traintracks, we compute their leading singularities as integrals of $(L{-}1)$-forms, which proves that the rigidity is $L{-}1$ as expected; the form is given by an inverse square root of an irreducible polynomial quartic with respect to each variable, which characterizes an $(L{-}1)$-dim Calabi-Yau manifold (elliptic curve, K3 surface, etc.) for any $L$. We also briefly comment on the implications for the "symbology" of these traintrack integrals.Comment: refs updated; 36 pages, 12 figure

Bootstrapping octagons in reduced kinematics from A2A_2 cluster algebras

Multi-loop scattering amplitudes/null polygonal Wilson loops in ${\mathcal N}=4$ super-Yang-Mills are known to simplify significantly in reduced kinematics, where external legs/edges lie in an $1+1$ dimensional subspace of Minkowski spacetime (or boundary of the $\rm AdS_3$ subspace). Since the edges of a $2n$-gon with even and odd labels go along two different null directions, the kinematics is reduced to two copies of $G(2,n)/T \sim A_{n{-}3}$. In the simplest octagon case, we conjecture that all loop amplitudes and Feynman integrals are given in terms of two overlapping $A_2$ functions (a special case of two-dimensional harmonic polylogarithms): in addition to the letters $v, 1+v, w, 1+w$ of $A_1 \times A_1$, there are two letters $v-w, 1- v w$ mixing the two sectors but they never appear together in the same term; these are the reduced version of four-mass-box algebraic letters. Evidence supporting our conjecture includes all known octagon amplitudes as well as new computations of multi-loop integrals in reduced kinematics. By leveraging this alphabet and conditions on first and last entries, we initiate a bootstrap program in reduced kinematics: within the remarkably simple space of overlapping $A_2$ functions, we easily obtain octagon amplitudes up to two-loop NMHV and three-loop MHV. We also briefly comment on the generalization to $2n$-gons in terms of $A_2$ functions and beyond.Comment: 26 pages, several figures and tables, an ancilary fil

Synergy between CSST galaxy survey and gravitational-wave observation: Inferring the Hubble constant from dark standard sirens

Gravitational waves (GWs) from compact binary coalescences encode the absolute luminosity distances of GW sources. Once the redshifts of GW sources are known, one can use the distance-redshift relation to constrain cosmological parameters. One way to obtain the redshifts is to localize GW sources by GW observations and then use galaxy catalogs to determine redshifts from a statistical analysis of redshift information of the potential host galaxies, commonly referred to as the dark siren method. The third-generation (3G) GW detectors are planned to work in the 2030s and will observe numerous compact binary coalescences. Using these GW events as dark sirens requires high-quality galaxy catalogs from future sky survey projects. The China Space Station Telescope (CSST) will be launched in 2024 and will observe billions of galaxies within a 17500 deg$^2$ survey area with redshift up to $z\sim 4$, providing photometric and spectroscopic galaxy catalogs. In this work, we simulate the CSST galaxy catalogs and the 5-year GW data from the 3G GW detectors and combine them to infer the Hubble constant ($H_0$). Our results show that the measurement precision of $H_0$ could reach the sub-percent level, meeting the standard of precision cosmology. We conclude that the synergy between CSST and the 3G GW detectors is of great significance in measuring the Hubble constant.Comment: 13 pages, 5 figure

Deterministic weighted scale-free small-world networks

We propose a deterministic weighted scale-free small-world model for considering pseudofractal web with the coevolution of topology and weight. In the model, we have the degree distribution exponent $\gamma$ restricted to a range between 2 and 3, simultaneously tunable with two parameters. At the same time, we provide a relatively complete view of topological structure and weight dynamics characteristics of the networks: weight and strength distribution; degree correlations; average clustering coefficient and degree-cluster correlations; as well as the diameter. We show that our model is particularly effective at mimicing weighted scale-free small-world networks with a high and relatively stable clustering coefficient, which rapidly decline with the network size in most previous models.Comment: a paper with 15 pages and 5 figure

A new approach to enhancing the CO2 capture performance of defective UiO-66 via post-synthetic defect exchange

Zirconium-based metal-organic frameworks (Zr-MOFs) are a subclass of MOFs known for their remarkable stability, especially in the presence of water. This makes them extremely attractive for practical applications, including CO2 capture from industrial emission sources; however, the CO2 adsorption capacity of Zr-MOFs is moderate compared to that of the best performing MOFs reported to date. Functionalization of Zr-MOFs with amino groups has been demonstrated to increase their affinity for CO2. In this work, we assessed the potential of post-synthetic defect exchange (PSDE) as an alternative approach to introduce amino functionalities at missing-cluster defective sites in formic acid modulated UiO-66. Both pyridine-containing (picolinic acid and nicotinic acid) and aniline-containing (3-aminobenzoic acid and anthranilic acid) monocarboxylates were integrated within defective UiO-66 with this method. Non-defective UiO-66 modified with linkers bearing the same amino groups (2,5-pyridinedicarboxylic acid and 2-aminoterephthalic acid) were prepared by classical post-synthetic ligand exchange (PSE), in order to compare the effect of introducing functionalities at defective sites versus installing them on the backbone. PSDE reduces the porosity of defective UiO-66, but improves both the CO2 uptake and the CO2/N2 selectivity, whereas PSE has no effect on the porosity of non-defective UiO-66, improving the CO2 uptake but leaving selectivity unchanged. Modification of defective UiO-66 with benzoic acid reveals that pore size reduction is the main factor responsible for the observed uptake improvement, whereas the presence of nitrogen atoms in the pores seems to be beneficial for increasing selectivity

miR-200 Enhances Mouse Breast Cancer Cell Colonization to Form Distant Metastases

BACKGROUND: The development of metastases involves the dissociation of cells from the primary tumor to penetrate the basement membrane, invade and then exit the vasculature to seed, and colonize distant tissues. The last step, establishment of macroscopic tumors at distant sites, is the least well understood. Four isogenic mouse breast cancer cell lines (67NR, 168FARN, 4TO7, and 4T1) that differ in their ability to metastasize when implanted into the mammary fat pad are used to model the steps of metastasis. Only 4T1 forms macroscopic lung and liver metastases. Because some miRNAs are dysregulated in cancer and affect cellular transformation, tumor formation, and metastasis, we examined whether changes in miRNA expression might explain the differences in metastasis of these cells. METHODOLOGY/PRINCIPAL FINDINGS: miRNA expression was analyzed by miRNA microarray and quantitative RT-PCR in isogenic mouse breast cancer cells with distinct metastatic capabilities. 4T1 cells that form macroscopic metastases had elevated expression of miR-200 family miRNAs compared to related cells that invade distant tissues, but are unable to colonize. Moreover, over-expressing miR-200 in 4TO7 cells enabled them to metastasize to lung and liver. These findings are surprising since the miR-200 family was previously shown to promote epithelial characteristics by inhibiting the transcriptional repressor Zeb2 and thereby enhancing E-cadherin expression. We confirmed these findings in these cells. The most metastatic 4T1 cells acquired epithelial properties (high expression of E-cadherin and cytokeratin-18) compared to the less metastatic cells. CONCLUSIONS/SIGNIFICANCE: Expression of miR-200, which promotes a mesenchymal to epithelial cell transition (MET) by inhibiting Zeb2 expression, unexpectedly enhances macroscopic metastases in mouse breast cancer cell lines. These results suggest that for some tumors, tumor colonization at metastatic sites might be enhanced by MET. Therefore the epithelial nature of a tumor does not predict metastatic outcome

Inferring causal molecular networks: empirical assessment through a community-based effort

Inferring molecular networks is a central challenge in computational biology. However, it has remained unclear whether causal, rather than merely correlational, relationships can be effectively inferred in complex biological settings. Here we describe the HPN-DREAM network inference challenge that focused on learning causal influences in signaling networks. We used phosphoprotein data from cancer cell lines as well as in silico data from a nonlinear dynamical model. Using the phosphoprotein data, we scored more than 2,000 networks submitted by challenge participants. The networks spanned 32 biological contexts and were scored in terms of causal validity with respect to unseen interventional data. A number of approaches were effective and incorporating known biology was generally advantageous. Additional sub-challenges considered time-course prediction and visualization. Our results constitute the most comprehensive assessment of causal network inference in a mammalian setting carried out to date and suggest that learning causal relationships may be feasible in complex settings such as disease states. Furthermore, our scoring approach provides a practical way to empirically assess the causal validity of inferred molecular networks

Inferring causal molecular networks: empirical assessment through a community-based effort

It remains unclear whether causal, rather than merely correlational, relationships in molecular networks can be inferred in complex biological settings. Here we describe the HPN-DREAM network inference challenge, which focused on learning causal influences in signaling networks. We used phosphoprotein data from cancer cell lines as well as in silico data from a nonlinear dynamical model. Using the phosphoprotein data, we scored more than 2,000 networks submitted by challenge participants. The networks spanned 32 biological contexts and were scored in terms of causal validity with respect to unseen interventional data. A number of approaches were effective, and incorporating known biology was generally advantageous. Additional sub-challenges considered time-course prediction and visualization. Our results suggest that learning causal relationships may be feasible in complex settings such as disease states. Furthermore, our scoring approach provides a practical way to empirically assess inferred molecular networks in a causal sense

The Tianlai Cylinder Pathfinder array: System functions and basic performance analysis

The Tianlai Cylinder Pathfinder is a radio interferometer array designed to test techniques for 21 cm intensity mapping in the post-reionization Universe, with the ultimate aim of mapping the large scale structure and measuring cosmological parameters such as the dark energy equation of state. Each of its three parallel cylinder reflectors is oriented in the north-south direction, and the array has a large field of view. As the Earth rotates, the northern sky is observed by drift scanning. The array is located in Hongliuxia, a radio-quiet site in Xinjiang, and saw its first light in September 2016. In this first data analysis paper for the Tianlai cylinder array, we discuss the sub-system qualification tests, and present basic system performance obtained from preliminary analysis of the commissioning observations during 2016-2018. We show typical interferometric visibility data, from which we derive the actual beam profile in the east-west direction and the frequency band-pass response. We describe also the calibration process to determine the complex gains for the array elements, either using bright astronomical point sources, or an artificial on site calibrator source, and discuss the instrument response stability, crucial for transit interferometry. Based on this analysis, we find a system temperature of about 90 K, and we also estimate the sensitivity of the array