Chain Integral Solutions to Tautological Systems

We give a new geometrical interpretation of the local analytic solutions to a differential system, which we call a tautological system $\tau$, arising from the universal family of Calabi-Yau hypersurfaces $Y_a$ in a $G$-variety $X$ of dimension $n$. First, we construct a natural topological correspondence between relative cycles in $H_n(X-Y_a,\cup D-Y_a)$ bounded by the union of $G$-invariant divisors $\cup D$ in $X$ to the solution sheaf of $\tau$, in the form of chain integrals. Applying this to a toric variety with torus action, we show that in addition to the period integrals over cycles in $Y_a$, the new chain integrals generate the full solution sheaf of a GKZ system. This extends an earlier result for hypersurfaces in a projective homogeneous variety, whereby the chains are cycles. In light of this result, the mixed Hodge structure of the solution sheaf is now seen as the MHS of $H_n(X-Y_a,\cup D-Y_a)$. In addition, we generalize the result on chain integral solutions to the case of general type hypersurfaces. This chain integral correspondence can also be seen as the Riemann-Hilbert correspondence in one homological degree. Finally, we consider interesting cases in which the chain integral correspondence possibly fails to be bijective.Comment: Revision made and references adde

Low-Dimensional Gradient Helps Out-of-Distribution Detection

Detecting out-of-distribution (OOD) samples is essential for ensuring the reliability of deep neural networks (DNNs) in real-world scenarios. While previous research has predominantly investigated the disparity between in-distribution (ID) and OOD data through forward information analysis, the discrepancy in parameter gradients during the backward process of DNNs has received insufficient attention. Existing studies on gradient disparities mainly focus on the utilization of gradient norms, neglecting the wealth of information embedded in gradient directions. To bridge this gap, in this paper, we conduct a comprehensive investigation into leveraging the entirety of gradient information for OOD detection. The primary challenge arises from the high dimensionality of gradients due to the large number of network parameters. To solve this problem, we propose performing linear dimension reduction on the gradient using a designated subspace that comprises principal components. This innovative technique enables us to obtain a low-dimensional representation of the gradient with minimal information loss. Subsequently, by integrating the reduced gradient with various existing detection score functions, our approach demonstrates superior performance across a wide range of detection tasks. For instance, on the ImageNet benchmark, our method achieves an average reduction of 11.15% in the false positive rate at 95% recall (FPR95) compared to the current state-of-the-art approach. The code would be released

Period Integrals and the Riemann-Hilbert Correspondence

A tautological system, introduced in [20][21], arises as a regular holonomic system of partial differential equations that governs the period integrals of a family of complete intersections in a complex manifold X, equipped with a suitable Lie group action. A geometric formula for the holonomic rank of such a system was conjectured in [5], and was verified for the case of projective homogeneous space under an assumption. In this paper, we prove this conjecture in full generality. By means of the Riemann–Hilbert correspondence and Fourier transforms, we also generalize the rank formula to an arbitrary projective manifold with a group action

Self-Ensemble Protection: Training Checkpoints Are Good Data Protectors

As data become increasingly vital for deep learning, a company would be very cautious about releasing data, because the competitors could use the released data to train high-performance models, thereby posing a tremendous threat to the company's commercial competence. To prevent training good models on the data, imperceptible perturbations could be added to it. Since such perturbations aim at hurting the entire training process, they should reflect the vulnerability of DNN training, rather than that of a single model. Based on this new idea, we seek adversarial examples that are always unrecognized (never correctly classified) in training. In this paper, we uncover them by modeling checkpoints' gradients, forming the proposed self-ensemble protection (SEP), which is very effective because (1) learning on examples ignored during normal training tends to yield DNNs ignoring normal examples; (2) checkpoints' cross-model gradients are close to orthogonal, meaning that they are as diverse as DNNs with different architectures in conventional ensemble. That is, our amazing performance of ensemble only requires the computation of training one model. By extensive experiments with 9 baselines on 3 datasets and 5 architectures, SEP is verified to be a new state-of-the-art, e.g., our small $\ell_\infty=2/255$ perturbations reduce the accuracy of a CIFAR-10 ResNet18 from 94.56\% to 14.68\%, compared to 41.35\% by the best-known method.Code is available at https://github.com/Sizhe-Chen/SEP

A Geometrically Supported z∼10z\sim10 Candidate Multiply-Imaged by the Hubble Frontier Fields Cluster Abell 2744

The deflection angles of lensed sources increase with their distance behind a given lens. We utilize this geometric effect to corroborate the $z_{phot}\simeq9.8$ photometric redshift estimate of a faint near-IR dropout, triply-imaged by the massive galaxy cluster Abell 2744 in deep Hubble Frontier Fields images. The multiple images of this source follow the same symmetry as other nearby sets of multiple images which bracket the critical curves and have well defined redshifts (up to $z_{spec}\simeq3.6$), but with larger deflection angles, indicating that this source must lie at a higher redshift. Similarly, our different parametric and non-parametric lens models all require this object be at $z\gtrsim4$, with at least 95\% confidence, thoroughly excluding the possibility of lower-redshift interlopers. To study the properties of this source we correct the two brighter images for their magnifications, leading to a SFR of $\sim0.3 M_{\odot}$/yr, a stellar mass of $\sim4\times10^{7} M_{\odot}$, and an age of $\lesssim220$ Myr (95\% confidence). The intrinsic apparent magnitude is 29.9 AB (F160W), and the rest-frame UV ($\sim1500 \AA$) absolute magnitude is $M_{UV,AB}=-17.6$. This corresponds to $\sim0.1 L^{*}_{z=8}$ ($\sim0.2 L^{*}_{z=10}$, adopting $dM^{*}/dz\sim0.45$), making this candidate one of the least luminous galaxies discovered at $z\sim10$.Comment: 7 pages, 4 figures, 1 table; V2: very minor changes, ApJ Letters Accepte

Mid-late Holocene temperature and precipitation variations in the Guanting Basin, upper reaches of the Yellow River

The reconstruction of prehistoric temperature and precipitation variations in the upper reaches of the Yellow River is essential for understanding the cultural evolution of the region, but related information is sparse due to the limitations of the available proxies. Recent studies have shown that microbial glycerol dialkyl glycerol tetraethers (GDGTs) are promising tools for reconstructing mean annual temperature (MAT) and mean annual precipitation (MAP) in terrestrial deposits. In this study, we reconstructed mid-late Holocene climatic changes using GDGT distributions in a loess-paleosol sequence in the Lajia Ruins of the Neolithic Qijia Culture, Guanting Basin, in the southwestern end of the Chinese Loess Plateau. Our GDGT records show that MAP decreased from ca. 600 mm to 430 mm, while MAT decreased from 11.9 degrees C to 8.0 degrees C, during the past ca. 7000 yr, and a drastic decline in MAP (70 mm), accompanied by a 0.8 degrees C decline in MAT, occurred at 3800-3400 yr BP. Our results provide direct evidence supporting a hypothesis that the flourishing (4200-4000 yr BP) and decline (4000-3600 yr BP) of the Qijia culture (mainly based on millets cultivation) and subsequent rise of the Xindian/Kayue culture (3600-2600 yr BP), based on mixed agriculture of sheep husbandry and millets cultivation were triggered by climate change

CLASH: Extreme Emission Line Galaxies and Their Implication on Selection of High-Redshift Galaxies

We utilize the CLASH (Cluster Lensing And Supernova survey with Hubble) observations of 25 clusters to search for extreme emission-line galaxies (EELGs). The selections are carried out in two central bands: F105W (Y105) and F125W (J125), as the flux of the central bands could be enhanced by the presence of [O III] 4959, 5007 at redshift of about 0.93-1.14 and 1.57-1.79, respectively. The multi-band observations help to constrain the equivalent widths of emission lines. Thanks to cluster lensing, we are able to identify 52 candidates down to an intrinsic limiting magnitude of 28.5 and to a rest-frame [O III] 4959,5007 equivalent width of about 3737 angstrom. Our samples include a number of EELGs at lower luminosities that are missed in other surveys, and the extremely high equivalent width can be only found in such faint galaxies. These EELGs can mimic the dropout feature similar to that of high redshift galaxies and contaminate the color-color selection of high redshift galaxies when the S/N ratio is limited or the band coverage is incomplete. We predict that the fraction of EELGs in the future high redshift galaxy selections cannot be neglected.Comment: 17 pages, 9 figures, 2 tables, Accepted for publication in AP

Preparation of a nano emodin transfersome and study on its anti-obesity mechanism in adipose tissue of diet-induced obese rats

OBJECTIVE: To describe the preparation of nano emodin transfersome (NET) and investigate its effect on mRNA expression of adipose triglyceride lipase (ATGL) and G0/G1 switch gene 2 (G0S2) in adipose tissue of diet-induced obese rats. METHODS: NET was prepared by film-ultrasonic dispersion method. The effects of emodin components at different ratios on encapsulation efficiency were investigated.The NET envelopment rate was determined by ultraviolet spectrophotometry. The particle size and Zeta potential of NET were evaluated by Zetasizer analyzer. Sixty male SD rats were assigned to groups randomly. After 8-week treatment, body weight, wet weight of visceral fat and the percentage of body fat (PBF) were measured. Fasting blood glucose and serum lipid levels were determined. The adipose tissue section was HE stained, and the cellular diameter and quantity of adipocytes were evaluated by light microscopy. The mRNA expression of ATGL and G0S2 from the peri-renal fat tissue was assayed by RT-PCR. RESULTS: The appropriate formulation was deoxycholic acid sodium salt vs. phospholipids 1:8, cholesterol vs. phospholipids 1:3, vitamin Evs. phospholipids 1:20, and emodin vs. phospholipid 1:6. Zeta potential was −15.11 mV, and the particle size was 292.2 nm. The mean encapsulation efficiency was (69.35 ± 0.25)%. Compared with the obese model group, body weight, wet weight of visceral fat, PBF and mRNA expression of G0S2 from peri-renal fat tissue were decreased significantly after NET treatment (all P < 0.05), while high-density lipoprotein cholesterol (HDL-C), the diameter of adipocytes and mRNA expression of ATGL from peri-renal fat tissue were increased significantly (all P < 0.05). CONCLUSION: The preparation method is simple and reasonable. NET with negative electricity was small and uniform in particle size, with high encapsulation efficiency and stability. NET could reduce body weight and adipocyte size, and this effect was associated with the up-regulation of ATGL, down-regulation of G0S2 expression in the adipose tissue, and improved insulin sensitivity

The synthesis of higher alcohols from CO2 hydrogenation over Mn-Cu-K modified Fe5C2 and CuZnAlZr tandem catalysts

The catalytic production of higher alcohols (HAs) is a promising path for converting CO2 into value-added chemical products. The application is still limited by the low selectivity of HAs (less than 10%) on most catalysts. Here, we report a tandem catalyst consisting of Mn-Cu-K modified iron carbide and CuZnAlZr catalyst. The modification of iron carbide with Mn, Cu and K promoters improves the formation of HAs (13.5% Sel.), and the construction of tandem catalysts with CuZnAlZr can further enhance the catalytic performance. By examining different catalyst filling methods and the filling ratio of the tandem catalyst, it was found that the powder mixing resulted in a higher selectivity of HAs with a mass ratio of the two components of 1:1, and a synergistic effect leads to a higher selectivity of HAs (15.5%) with about 40% of propanol and butanol among HAs