Pseudodeterminants and perfect square spanning tree counts

The pseudodeterminant $\textrm{pdet}(M)$ of a square matrix is the last nonzero coefficient in its characteristic polynomial; for a nonsingular matrix, this is just the determinant. If $\partial$ is a symmetric or skew-symmetric matrix then $\textrm{pdet}(\partial\partial^t)=\textrm{pdet}(\partial)^2$. Whenever $\partial$ is the $k^{th}$ boundary map of a self-dual CW-complex $X$, this linear-algebraic identity implies that the torsion-weighted generating function for cellular $k$-trees in $X$ is a perfect square. In the case that $X$ is an \emph{antipodally} self-dual CW-sphere of odd dimension, the pseudodeterminant of its $k$th cellular boundary map can be interpreted directly as a torsion-weighted generating function both for $k$-trees and for $(k-1)$-trees, complementing the analogous result for even-dimensional spheres given by the second author. The argument relies on the topological fact that any self-dual even-dimensional CW-ball can be oriented so that its middle boundary map is skew-symmetric.Comment: Final version; minor revisions. To appear in Journal of Combinatoric

Morphological regions and oblique incidence dot formation in a model of surface sputtering

We study solid surface morphology created by off-normal ion-beam sputtering with an atomistic, solid-on-solid model of sputter erosion. With respect to an earlier version of the model, we extend this model with the inclusion of lateral erosion. Using the 2-dimensional structure factor, we found an upper bound $\mu\simeq 2$, in the lateral straggle $\mu$, for clear ripple formation. Above this upper bound, for longitudinal straggle $\sigma\gtrsim 1.7$, we found the possibility of dot formation (without sample rotation). Moreover, a temporal crossover from a hole topography to ripple topography with the same value of collision cascade parameters was found. Finally, a scaling analysis of the roughness, using the consecutive gradient approach, yields the growth exponents $\beta=0.33$ and 0.67 for two different topographic regimes.Comment: 8 pages, 14 figure

The effects of grape seed extract on glycemic control, serum lipoproteins, inflammation, and body weight: A systematic review and meta-analysis of randomized controlled trials

The aim of this systematic review and meta-analysis was to analyze the effects of grape seed extract (GSE) on glycemic control and serum lipoproteins, inflammation and body weight. Two independent authors systematically searched online databases including EMBASE, Scopus, PubMed, Cochrane Library, and Web of Science from inception until May 30, 2019. Cochrane Collaboration risk of bias tool was applied to assess the methodological quality of included trials. The heterogeneity among the included studies was assessed using Cochrane's Q test and I-square (I2) statistic. Data were pooled using a random-effects model and weighted mean difference (WMD) was considered as the overall effect size. Fifty trials were included in this meta-analysis. Pooling effect sizes from studies demonstrated a significant decrease in fasting plasma glucose (FPG) (WMD): �2.01; 95 confidence interval (CI): �3.14, �0.86), total cholesterol (TC; WMD: �6.03; 95 CI: �9.71, �2.35), low-density lipoprotein (LDL) cholesterol (WMD: �4.97; 95 CI: �8.37, �1.57), triglycerides (WMD: �6.55; 95 CI: �9.28, �3.83), and C-reactive protein (CRP) concentrations (WMD: �0.81; 95 CI: �1.25, �0.38) following GSE therapy. Grape seed did not influence HbA1c, HDL cholesterol levels, and anthropometric measurements. This meta-analysis demonstrated that GSE intake significantly reduced FPG, TC, LDL cholesterol, triglycerides, and CRP levels. © 2019 John Wiley & Sons, Ltd

The effect of berberine supplementation on obesity parameters, inflammation and liver function enzymes: A systematic review and meta-analysis of randomized controlled trials

Introduction: So far, no study has summarized the findings on the effects of berberine intake on anthropometric parameters, C-reactive protein (CRP) and liver enzymes. This systematic review and meta-analysis were done based upon randomized controlled trials (RCTs) to analyze the effects of berberine on anthropometric parameters, CRP and liver enzymes. Method: Following databases were searched for eligible studies published from inception to 30 July 2019: MEDLINE, EMBASE, Web of Science, Cochrane Library, PubMed and Google scholar. Necessary data were extracted. Data were pooled by the inverse variance method and expressed as mean difference with 95 Confidence Intervals (95 CI). Result: 12 studies were included. Berberine treatment moderately but significantly decreased body weight (WMD = �2.07 kg, 95 CI -3.09, �1.05, P < 0.001), body mass index (BMI) (WMD = �0.47 kg/m2, 95 CI -0.70, �0.23, P < 0.001), waist circumference (WC) (WMD = �1.08 cm, 95 CI -1.97, �0.19, P = 0.018) and C-reactive protein (CRP) concentrations (WMD = �0.42 mg/L, 95 CI -0.82, �0.03, P = 0.034). However, berberine intake did not affect liver enzymes, including alanine aminotransferase (ALT) (WMD = �1.66 I/U, 95 CI -3.98, 0.65, P = 0.160) and aspartate aminotransferase (AST) (WMD = �0.87 I/U, 95 CI -2.56, 0.82, P = 0.311). Conclusion: This meta-analysis found a significant reduction of body weight, BMI, WC and CRP levels associated with berberine intake which may have played an indirect role in improved clinical symptoms in diseases with metabolic disorders. Berberine administration had no significant effect on ALT and AST levels. © 2020 European Society for Clinical Nutrition and Metabolis

Effect of green cardamom on lipoproteins, glycemic control and anthropometric parameters: A meta-analysis of randomized clinical trials

Introduction: The aim of this systematic review and meta-analysis was to summarize all the existing randomized controlled trials (RCTs) evidence and to evaluate the effects of green cardamom on lipoproteins, glycemic control and anthropometric parameters in healthy and/or with disease types compared with the control. Method: Two independent authors systematically searched online databases including EMBASE, Scopus, PubMed, Cochrane Library, and Web of Science from inception until 30th July 2019. RCTs complying with the following criteria were included in this meta-analysis: human trials with either cross-over design or parallel design, trials with data on the effects of green cardamom on serum lipoproteins and glycemic control and anthropometric parameters with standard deviation and related 95 confidence interval for the both intervention and placebo groups. The heterogeneity among the included studies was assessed using Cochrane's Q test and I-square (I2) statistic. Data were pooled using a random-effects model and weighted mean difference (WMD) was considered as the overall effect size. Result: Seven trials were included in this meta-analysis. Triglycerides were significantly reduced after cardamom supplementation when compared with the control group. Cardamom intake from 3 small studies resulted in a significant increase in BMI when compared with the control group. However, cardamom supplementation did not have any significant effect on total cholesterol, LDL-cholesterol, HDL-cholesterol, fasting plasma glucose and body weight when compared with the control group. Conclusion: This meta-analysis demonstrated that green cardamom intake significantly reduced triglycerides levels which may have played an indirect role in improved clinical symptoms in diseases with metabolic disorders. © 2020 European Society for Clinical Nutrition and Metabolis

Polymers pushing Polymers: Polymer Mixtures in Thermodynamic Equilibrium with a Pore

We investigate polymer partitioning from polymer mixtures into nanometer size cavities by formulating an equation of state for a binary polymer mixture assuming that only one (smaller) of the two polymer components can penetrate the cavity. Deriving the partitioning equilibrium equations and solving them numerically allows us to introduce the concept of "polymers-pushing-polymers" for the action of non-penetrating polymers on the partitioning of the penetrating polymers. Polymer partitioning into a pore even within a very simple model of a binary polymer mixture is shown to depend in a complicated way on the composition of the polymer mixture and/or the pore-penetration penalty. This can lead to enhanced as well as diminished partitioning, due to two separate energy scales that we analyse in detail.Comment: 10 pages, 6 figure

Determination of Electromagnetic Source Direction as an Eigenvalue Problem

Low-frequency solar and interplanetary radio bursts are generated at frequencies below the ionospheric plasma cutoff and must therefore be measured in space, with deployable antenna systems. The problem of measuring both the general direction and polarization of an electromagnetic source is commonly solved by iterative fitting methods such as linear regression that deal simultaneously with both directional and polarization parameters. We have developed a scheme that separates the problem of deriving the source direction from that of determining the polarization, avoiding iteration in a multi-dimensional manifold. The crux of the method is to first determine the source direction independently of concerns as to its polarization. Once the source direction is known, its direct characterization in terms of Stokes vectors in a single iteration if desired, is relatively simple. This study applies the source-direction determination to radio signatures of flares received by STEREO. We studied two previously analyzed radio type III bursts and found that the results of the eigenvalue decomposition technique are consistent with those obtained previously by Reiner et al. (Solar Phys. 259, 255, 2009). For the type III burst observed on 7 December 2007, the difference in travel times from the derived source location to STEREO A and B is the same as the difference in the onset times of the burst profiles measured by the two spacecraft. This is consistent with emission originating from a single, relatively compact source. For the second event of 29 January 2008, the relative timing does not agree, suggesting emission from two sources separated by 0.1 AU, or perhaps from an elongated region encompassing the apparent source locations.Comment: 22 pages, 7 figures, Accepted in Solar Physic

C–H-Bond Activation and Isoprene Polymerization Studies Applying Pentamethylcyclopentadienyl-Supported Rare-Earth-Metal Bis(Tetramethylaluminate) and Dimethyl Complexes

As previously shown for lutetium and yttrium, 1,2,3,4,5-pentamethylcyclopentadienyl (C5Me5 = Cp*)-bearing rare-earth metal dimethyl half-sandwich complexes [Cp*LnMe2]3 are now also accessible for holmium, dysprosium, and terbium via tetramethylaluminato cleavage of [Cp*Ln(AlMe4)2] with diethyl ether (Ho, Dy) and tert-butyl methyl ether (TBME) (Tb). C–H-bond activation and ligand redistribution reactions are observed in case of terbium and are dominant for the next larger-sized gadolinium, as evidenced by the formation of mixed methyl/methylidene clusters [(Cp*Ln)5(CH2)(Me)8] and metallocene dimers [Cp*2Ln(AlMe4)]2 (Ln = Tb, Gd). Applying TBME as a “cleaving” reagent can result in both TBME deprotonation and ether cleavage, as shown for the formation of the 24-membered macrocycle [(Cp*Gd)2(Me)(CH2OtBu)2(AlMe4)]4 or monolanthanum complex [Cp*La(AlMe4){Me3Al(CH2)OtBu}] and monoyttrium complex [Cp*Y(AlMe4)(Me3AlOtBu)], respectively. Complexes [Cp*Ln(AlMe4)2] (Ln = Ho, Dy, Tb, Gd) and [Cp*LnMe2]3 (Ln = Ho, Dy) are applied in isoprene and 1,3-butadiene polymerization, upon activation with borates [Ph3C][B(C6F5)4] and [PhNHMe2][B(C6F5)4], as well as borane B(C6F5)3. The trans-directing effect of AlMe3 in the binary systems [Cp*Ln(AlMe4)2]/borate is revealed and further corroborated by the fabrication of high-cis-1,4 polybutadiene (97%) with “aluminum-free” [Cp*DyMe2]3/[Ph3C][B(C6F5)4]. The formation of multimetallic active species is supported by the polymerization activity of pre-isolated cluster [(Cp*Ho)3Me4(CH2)(thf)2].publishedVersio