Evaluation of binomial double sums involving absolute values

We show that double sums of the form $$\sum_{i,j=-n} ^{n} |i^sj^t(i^k-j^k)^\beta| \binom {2n} {n+i} \binom {2n} {n+j}$$ can always be expressed in terms of a linear combination of just four functions, namely $\binom {4n}{2n}$, ${\binom {2n}n}^2$, $4^n\binom {2n}n$, and $16^n$, with coefficients that are rational in $n$. We provide two different proofs: one is algorithmic and uses the second author's computer algebra package Sigma; the second is based on complex contour integrals. In many instances, these results are extended to double sums of the above form where $\binom {2n}{n+j}$ is replaced by $\binom {2m}{m+j}$ with independent parameter $m$.Comment: AmS-LaTeX, 42 pages; substantial revision: several additional and more general results, see Proposition 11 and Theorems 15-1

Indirect and direct impacts of typhoon In-Fa (2021) on heavy precipitation in inland and coastal areas of China: synoptic-scale environments and return period analysis

In July 2021, Typhoon In-Fa (TIF) triggered a significant indirect heavy precipitation event (HPE) in central China and a direct HPE in eastern China. Both these events led to severe disasters. However, the synoptic-scale conditions and the impacts of these HPEs on future estimations of return periods remain poorly understood. Here, we find that the remote HPE that occurred̰2200 km ahead of TIF over central China was a predecessor rain event (PRE). The PRE unfolded under the equatorward entrance of the upper-level westerly jet. This event, which encouraged divergent and adiabatic outflow in the upper level, subsequently intensified the strength of the upper-level westerly jet. In contrast, the direct HPE in eastern China was due primarily to the long duration and slow movement of TIF. The direct HPE occurred in areas situated less than 200 km from TIF’s center and to the left of TIF’s propagation trajectory. Anomaly analyses reveal favorable thermodynamic and dynamic conditions and abundant atmospheric moisture that sustained TIF’s intensity. A saddle-shaped pressure field in the north of eastern China and peripheral weak steering flow impeded TIF’s movement northward. Hydrologically, the inclusion of these two HPEs in the historical record leads to a decrease in the estimated return periods of similar HPEs. Our findings highlight the potential difficulties that HPEs could introduce for the design of hydraulic engineering infrastructure as well as for the disaster mitigation measures required to alleviate future risk, particularly in central China

Process-informed subsampling improves subseasonal rainfall forecasts in Central America

Subseasonal rainfall forecast skill is critical to support preparedness for hydrometeorological extremes. We assess how a process-informed evaluation, which subsamples forecasting model members based on their ability to represent potential predictors of rainfall, can improve monthly rainfall forecasts within Central America in the following month, using Costa Rica and Guatemala as test cases. We generate a constrained ensemble mean by subsampling 130 members from five dynamic forecasting models in the C3S multimodel ensemble based on their representation of both (a) zonal wind direction and (b) Pacific and Atlantic sea surface temperatures (SSTs), at the time of initialization. Our results show in multiple months and locations increased mean squared error skill by 0.4 and improved detection rates of rainfall extremes. This method is transferrable to other regions driven by slowly-changing processes. Process-informed subsampling is successful because it identifies members that fail to represent the entire rainfall distribution when wind/SST error increases

On the exponential transform of lemniscates

It is known that the exponential transform of a quadrature domain is a rational function for which the denominator has a certain separable form. In the present paper we show that the exponential transform of lemniscate domains in general are not rational functions, of any form. Several examples are given to illustrate the general picture. The main tool used is that of polynomial and meromorphic resultants.Comment: 19 pages, to appear in the Julius Borcea Memorial Volume, (eds. Petter Branden, Mikael Passare and Mihai Putinar), Trends in Mathematics, Birkhauser Verla

A generalization of the q-Saalschutz sum and the Burge transform

A generalization of the q-(Pfaff)-Saalschutz summation formula is proved. This implies a generalization of the Burge transform, resulting in an additional dimension of the ``Burge tree''. Limiting cases of our summation formula imply the (higher-level) Bailey lemma, provide a new decomposition of the q-multinomial coefficients, and can be used to prove the Lepowsky and Primc formula for the A_1^{(1)} string functions.Comment: 18 pages, AMSLaTe

Soil Moisture to Runoff (SM2R): A Data-Driven Model for Runoff Estimation Across Poorly Gauged Asian Water Towers Based on Soil Moisture Dynamics

Data Availability Statement: RA5L reanalysis data (Muñoz Sabater, 2019) are available at https://cds.climate.copernicus.eu/cdsapp#!/dataset/10.24381/cds.68d2bb30 . Data sets from the HWSD (Fischer et al., 2008) are accessed at https://www.fao.org/soils-portal/data-hub/soil-maps-and-databases/harmonized-world-soil-database-v12/en/ . Glacier elevation changes (Berthier et al., 2021) are provided at https://doi.org/10.6096/13 , and the RGI 6.0 glacier mask (RGI Consortium, 2017) can be accessed at https://doi.org/10.7265/4m1f-gd79 . Percentages of persistent snow cover in each water tower (Immerzeel et al., 2019) are provided at https://doi.org/10.5281/zenodo.3521933 . Soil moisture estimated from GLDAS NOAH [Beaudoing and Rodell, 2020; Rodell et al., 2004] and CLSM [B. Li et al., 2019; B. Li et al., 2020] land surface models can be accessed at https://disc.gsfc.nasa.gov/datasets/GLDAS_NOAH025_M_2.1/summary and https://disc.gsfc.nasa.gov/datasets/GLDAS_CLSM025_DA1_D_2.2/summary , respectively. Precipitation estimated from the IMERG product (Huffman et al., 2019) can be accessed at https://disc.gsfc.nasa.gov/datasets/GPM_3IMERGDF_06/summary . Runoff estimation results of this study (Li & Long, 2023) are available at https://doi.org/10.5281/zenodo.7505876 .Supporting Information is available online at https://doi.org/10.1029/2022WR033597 .Copyright © 2022 The Author(s) and American Geophysical Union. Almost 2 billion people depend on freshwater provided by the Asian water towers, yet long-term runoff estimation is challenging in this high-mountain region with a harsh environment and scarce observations. Most hydrologic models rely on observed runoff for calibration, and have limited applicability in the poorly gauged Asian water towers. To overcome such limitations, here we propose a novel data-driven model, SM2R (Soil Moisture to Runoff), to simulate monthly runoff based on soil moisture dynamics using reanalysis forcing data. The SM2R model was applied and examined in 20 drainage basins across seven Asian water towers during the past four decades of 1981–2020. Without invoking any observations for calibration, the overall good performance of SM2R-derived runoff (correlation coefficient ≥0.74 and normalized root mean square error ≤0.22 compared to observed runoff at 20 gauges) suggests considerable potential for runoff simulation in poorly gauged basins. Even though the SM2R model is forced by ERA5-Land (ERA5L) reanalysis data, it largely outperforms the ERA5L-estimated runoff across the seven Asian water towers, particularly in basins with widely distributed glaciers and frozen soil. The SM2R approach is highly promising for constraining hydrologic variables from soil moisture information. Our results provide valuable insights for not only long-term runoff estimation over key Asian basins, but also understanding hydrologic processes across poorly gauged regions globally.Second Tibetan Plateau Scientific Expedition and Research program. Grant Number: 2019QZKK0105 National Natural Science Foundation of China. Grant Number: 92047301,92047203 UK Research and Innovation. Grant Number: MR/V022008/

The Dimensional Recurrence and Analyticity Method for Multicomponent Master Integrals: Using Unitarity Cuts to Construct Homogeneous Solutions

We consider the application of the DRA method to the case of several master integrals in a given sector. We establish a connection between the homogeneous part of dimensional recurrence and maximal unitarity cuts of the corresponding integrals: a maximally cut master integral appears to be a solution of the homogeneous part of the dimensional recurrence relation. This observation allows us to make a necessary step of the DRA method, the construction of the general solution of the homogeneous equation, which, in this case, is a coupled system of difference equations.Comment: 17 pages, 2 figure

Fasting before evening exercise reduces net energy intake and increases fat oxidation, but impairs performance in healthy males and females

Acute morning fasted exercise may create a greater negative 24-hr energy balance than the same exercise performed after a meal, but research exploring fasted evening exercise is limited. This study assessed the effects of 7-hr fasting before evening exercise on energy intake, metabolism, and performance. Sixteen healthy males and females (n = 8 each) completed two randomized, counterbalanced trials. Participants consumed a standardized breakfast (08:30) and lunch (11:30). Two hours before exercise (16:30), participants consumed a meal (543 ± 86 kcal; FED) or remained fasted (FAST). Exercise involved 30-min cycling (∼60% VO2peak) and a 15-min performance test (∼85% VO2peak; 18:30). Ad libitum energy intake was assessed 15 min postexercise. Subjective appetite was measured throughout. Energy intake was 99 ± 162 kcal greater postexercise (p < .05), but 443 ± 128 kcal lower over the day (p < .001) in FAST. Appetite was elevated between the preexercise meal and ad libitum meal in FAST (p < .001), with no further differences (p ≥ .458). Fat oxidation was greater (+3.25 ± 1.99 g), and carbohydrate oxidation was lower (−9.16 ± 5.80 g) during exercise in FAST (p < .001). Exercise performance was 3.8% lower in FAST (153 ± 57 kJ vs. 159 ± 58 kJ, p < .05), with preexercise motivation, energy, readiness, and postexercise enjoyment also lower in FAST (p < .01). Fasted evening exercise reduced net energy intake and increased fat oxidation compared to exercise performed 2 hr after a meal. However, fasting also reduced voluntary performance, motivation, and exercise enjoyment. Future studies are needed to examine the long-term effects of this intervention as a weight management strategy

Convergence and divergence in the evolution of cat skulls: temporal and spatial patterns of morphological diversity

Background: Studies of biological shape evolution are greatly enhanced when framed in a phylogenetic perspective. Inclusion of fossils amplifies the scope of macroevolutionary research, offers a deep-time perspective on tempo and mode of radiations, and elucidates life-trait changes. We explore the evolution of skull shape in felids (cats) through morphometric analyses of linear variables, phylogenetic comparative methods, and a new cladistic study of saber-toothed cats. Methodology/Principal Findings: A new phylogenetic analysis supports the monophyly of saber-toothed cats (Machairodontinae) exclusive of Felinae and some basal felids, but does not support the monophyly of various sabertoothed tribes and genera. We quantified skull shape variation in 34 extant and 18 extinct species using size-adjusted linear variables. These distinguish taxonomic group membership with high accuracy. Patterns of morphospace occupation are consistent with previous analyses, for example, in showing a size gradient along the primary axis of shape variation and a separation between large and small-medium cats. By combining the new phylogeny with a molecular tree of extant Felinae, we built a chronophylomorphospace (a phylogeny superimposed onto a two-dimensional morphospace through time). The evolutionary history of cats was characterized by two major episodes of morphological divergence, one marking the separation between saber-toothed and modern cats, the other marking the split between large and small-medium cats. Conclusions/Significance: Ancestors of large cats in the ‘Panthera’ lineage tend to occupy, at a much later stage, morphospace regions previously occupied by saber-toothed cats. The latter radiated out into new morphospace regions peripheral to those of extant large cats. The separation between large and small-medium cats was marked by considerable morphologically divergent trajectories early in feline evolution. A chronophylomorphospace has wider applications in reconstructing temporal transitions across two-dimensional trait spaces, can be used in ecophenotypical and functional diversity studies, and may reveal novel patterns of morphospace occupation

CT colonography: optimisation, diagnostic performance and patient acceptability of reduced-laxative regimens using barium-based faecal tagging

To establish the optimum barium-based reduced-laxative tagging regimen prior to CT colonography (CTC). Ninety-five subjects underwent reduced-laxative (13 g senna/18 g magnesium citrate) CTC prior to same-day colonoscopy and were randomised to one of four tagging regimens using 20 ml 40%w/v barium sulphate: regimen A: four doses, B: three doses, C: three doses plus 220 ml 2.1% barium sulphate, or D: three doses plus 15 ml diatriazoate megluamine. Patient experience was assessed immediately after CTC and 1 week later. Two radiologists graded residual stool (1: none/scattered to 4: >50% circumference) and tagging efficacy for stool (1: untagged to 5: 100% tagged) and fluid (1: untagged, 2: layered, 3: tagged), noting the HU of tagged fluid. Preparation was good (76–94% segments graded 1), although best for regimen D (P = 0.02). Across all regimens, stool tagging quality was high (mean 3.7–4.5) and not significantly different among regimens. The HU of layered tagged fluid was higher for regimens C/D than A/B (P = 0.002). Detection of cancer (n = 2), polyps ≥6 mm (n = 21), and ≤5 mm (n = 72) was 100, 81 and 32% respectively, with only four false positives ≥6 mm. Reduced preparation was tolerated better than full endoscopic preparation by 61%. Reduced-laxative CTC with three doses of 20 ml 40% barium sulphate is as effective as more complex regimens, retaining adequate diagnostic accuracy