Path ideals of rooted trees and their graded Betti numbers

Let $\Gamma$ be a rooted tree and let $t$ be a positive integer. We study algebraic invariants and properties of the path ideal generated by monomial corresponding to paths of length $(t-1)$ in $\Gamma$. In particular, we give a recursive formula to compute the graded Betti numbers, a general bound for the regularity, an explicit computation of the linear strand, and we characterize when this path ideal has a linear resolution.Comment: 18 page

Van der Waals Coefficients of Atoms and Molecules from a Simple Approximation for the Polarizability

A simple and computationally efficient scheme to calculate approximate imaginary-frequency dependent polarizability, hence asymptotic van der Waals coefficient, within density functional theory is proposed. The dynamical dipolar polarizabilities of atoms and molecules are calculated starting from the Thomas-Fermi-von Weizs\"acker (TFvW) approximation for the independent-electron kinetic energy functional. The van der Waals coefficients for a number of closed-shell ions and a few molecules are hence calculated and compared with available values obtained by fully first-principles calculations. The success in these test cases shows the potential of the proposed TFvW approximate response function in capturing the essence of long range correlations and may give useful information for constructing a functional which naturally includes van der Waals interactions.Comment: 6 pages, 4 figures. To appear in Phys. Rev.

Exploring Tourist Dining Preferences Based on Restaurant Reviews

Dining is an essential tourism component that attracts significant expenditure from tourists. Tourism practitioners need insights into the dining behaviors of tourists to support their strategic planning and decision making. Traditional surveys and questionnaires are time consuming and inefficient in capturing the complex dining behaviors of tourists at a large scale. Thus far, the understanding about the dining preferences and opinions of different tourist groups is limited. This article aims to fill the void by presenting a method that utilizes online restaurant reviews and text processing techniques in analyzing the dining behaviors of tourists. The effectiveness of the proposed method is demonstrated in a case study on international tourists visiting Australia using a large-scale data set of more than 40,000 restaurant reviews made by tourists on 2,265 restaurants. The proposed method can help researchers gain comprehensive insights into the dining preferences of tourists. </jats:p

Birationality of \'etale morphisms via surgery

We use a counting argument and surgery theory to show that if $D$ is a sufficiently general algebraic hypersurface in $\Bbb C^n$, then any local diffeomorphism $F:X \to \Bbb C^n$ of simply connected manifolds which is a $d$-sheeted cover away from $D$ has degree $d=1$ or $d=\infty$ (however all degrees $d > 1$ are possible if $F$ fails to be a local diffeomorphism at even a single point). In particular, any \'etale morphism $F:X \to \Bbb C^n$ of algebraic varieties which covers away from such a hypersurface $D$ must be birational.Comment: 17 pages. Replaced to add further references and make language more consistent with the literatur

Metabolic syndrome does not affect sustained virologic response of direct-acting antivirals while hepatitis C clearance improves hemoglobin A1c.

AimTo determine whether successful treatment with directacting antivirals (DAA) is associated with improvements in hemoglobin A1c (HbA1c) and if type 2 diabetes mellitus (T2DM) or metabolic syndrome affects sustained virologic response (SVR).MethodsWe performed a retrospective analysis of all hepatitis C virus (HCV) patients at the VA Greater Los Angeles Healthcare System treated with varying DAA therapy between 2014-2016. Separate multivariable logistic regression was performed to determine predictors of HbA1c decrease ≥ 0.5 after DAA treatment and predictors of SVR 12-wk post treatment (SVR12).ResultsA total of 1068 patients were treated with DAA therapy between 2014-2016. The presence of T2DM or metabolic syndrome did not adversely affect SVR12. 106 patients had both HCV and T2DM. Within that cohort, patients who achieved SVR12 had lower mean HbA1c pre treatment (7.35 vs 8.60, P = 0.02), and lower mean HbA1c post-treatment compared to non-responders (6.55 vs 8.61, P = 0.01). The mean reduction in HbA1c after treatment was greater for those who achieved SVR12 than for non-responders (0.79 vs 0.01, P = 0.03). In adjusted models, patients that achieved SVR12 were more likely to have a HbA1c decrease of ≥ 0.5 than those that did not achieve SVR12 (adjusted OR = 7.24, 95%CI: 1.22-42.94).ConclusionIn HCV patients with T2DM, successful treatment with DAA was associated with a significant reduction in HbA1c suggesting that DAA may have a role in improving insulin sensitivity. Furthermore, the presence of T2DM or metabolic syndrome does not adversely affect SVR12 rates in patients treated with DAA

Extremely Large and Anisotropic Upper Critical Field and the Ferromagnetic Instability in UCoGe

Magnetoresistivity measurements with fine tuning of the field direction on high quality single crystals of the ferromagnetic superconductor UCoGe show anomalous anisotropy of the upper critical field H_c2. H_c2 for H // b-axis (H_c2^b) in the orthorhombic crystal structure is strongly enhanced with decreasing temperature with an S-shape and reaches nearly 20 T at 0 K. The temperature dependence of H_c2^a shows upward curvature with a low temperature value exceeding 30 T, while H_c2^c at 0 K is very small (~ 0.6 T). Contrary to conventional ferromagnets, the decrease of the Curie temperature with increasing field for H // b-axis marked by an enhancement of the effective mass of the conduction electrons appears to be the origin of the S-shaped H_c2^b curve. These results indicate that the field-induced ferromagnetic instability or magnetic quantum criticality reinforces superconductivity.Comment: 5 pages, 4 figures, accepted for publication in J. Phys. Soc. Jp

Improved Worst-Group Robustness via Classifier Retraining on Independent Splits

High-capacity deep neural networks (DNNs) trained with Empirical Risk Minimization (ERM) often suffer from poor worst-group accuracy despite good on-average performance, where worst-group accuracy measures a model's robustness towards certain subpopulations of the input space. Spurious correlations and memorization behaviors of ERM trained DNNs are typically attributed to this degradation in performance. We develop a method, called CRIS, that address these issues by performing robust classifier retraining on independent splits of the dataset. This results in a simple method that improves upon state-of-the-art methods, such as Group DRO, on standard datasets while relying on much fewer group labels and little additional hyperparameter tuning

Upper critical field in superconductors near ferromagnetic quantum critical points; UCoGe

We study the strong-coupling superconductivity near ferromagnetic quantum critical points, mainly focusing on the upper critical fields $H_{c2}$. Based on our simple model calculations, we discuss experimentally observed unusual behaviors of $H_{c2}$ in a recently discovered ferromagnetic superconductor UCoGe. Especially, the large anisotropy between $H_{c2}\parallel a$-axis and $H_{c2}\parallel c$-axis, and the strong-coupling behaviors in $H_{c2}^{\parallel a}$ are investigated. We also examine effects of non-analytic corrections in the spin susceptibility on the superconductivity, which can arise from effective long range interactions due to particle-hole excitations.Comment: Proceedings of ICHE2010, Toky

Refsum's Disease—Use of the Intestinal Lipase Inhibitor, Orlistat, as a Novel Therapeutic Approach to a Complex Disorder

Refsum's Disease is an inherited metabolic disorder in which a metabolite of branched chain fatty acids accumulates due to lack of appropriate oxidative enzymes. Patients have elevated plasma phytanic acid levels and high concentrations of phytanic acid in a variety of tissues leading to progressive tissue damage. Besides retinal degeneration or retinal dystrophy associated with adult onset retinitis pigmentosa, additional symptoms include chronic polyneuropathy, cerebellar ataxia, sensorineural hearing loss, anosmia, ichthyosis, as well as skeletal, cardiac, hepatic, and renal abnormalities. Current management includes avoidance of dietary sources of branched chain fatty acids and regular plasmapheresis to prevent accumulation of these compounds to ameliorate progressive neurological deficits. Two brothers with Refsum's disease who experienced progressive symptoms despite optimal diet and plasmapheresis were commenced on a novel therapy. We report the effect of the intestinal lipase inhibitor, Orlistat, which led to significant reduction (P-value <0.001 on 2-sample unpaired t-test) of mean preplasmapheresis phytanic acid levels with retardation of the progression of most of their dermatological and neurological symptoms