On minima of sum of theta functions and Mueller-Ho Conjecture

Let $z=x+iy \in \mathbb{H}:=\{z= x+ i y\in\mathbb{C}: y>0\}$ and $\theta (s;z)=\sum_{(m,n)\in\mathbb{Z}^2 } e^{-s \frac{\pi }{y }|mz+n|^2}$ be the theta function associated with the lattice $\Lambda ={\mathbb Z}\oplus z{\mathbb Z}$. In this paper we consider the following pair of minimization problems $$\min_{ \mathbb{H} } \theta (2;\frac{z+1}{2})+\rho\theta (1;z),\;\;\rho\in[0,\infty),$$ $$\min_{ \mathbb{H} } \theta (1; \frac{z+1}{2})+\rho\theta (2; z),\;\;\rho\in[0,\infty),$$ where the parameter $\rho\in[0,\infty)$ represents the competition of two intertwining lattices. We find that as $\rho$ varies the optimal lattices admit a novel pattern: they move from rectangular (the ratio of long and short side changes from $\sqrt3$ to 1), square, rhombus (the angle changes from $\pi/2$ to $\pi/3$) to hexagonal; furthermore, there exists a closed interval of $\rho$ such that the optimal lattices is always square lattice. This is in sharp contrast to optimal lattice shapes for single theta function ($\rho=\infty$ case), for which the hexagonal lattice prevails. As a consequence, we give a partial answer to optimal lattice arrangements of vortices in competing systems of Bose-Einstein condensates as conjectured (and numerically and experimentally verified) by Mueller-Ho \cite{Mue2002}.Comment: 42 pages; comments welcom

A Fusion-Denoising Attack on InstaHide with Data Augmentation

InstaHide is a state-of-the-art mechanism for protecting private training images, by mixing multiple private images and modifying them such that their visual features are indistinguishable to the naked eye. In recent work, however, Carlini et al. show that it is possible to reconstruct private images from the encrypted dataset generated by InstaHide. Nevertheless, we demonstrate that Carlini et al.'s attack can be easily defeated by incorporating data augmentation into InstaHide. This leads to a natural question: is InstaHide with data augmentation secure? In this paper, we provide a negative answer to this question, by devising an attack for recovering private images from the outputs of InstaHide even when data augmentation is present. The basic idea is to use a comparative network to identify encrypted images that are likely to correspond to the same private image, and then employ a fusion-denoising network for restoring the private image from the encrypted ones, taking into account the effects of data augmentation. Extensive experiments demonstrate the effectiveness of the proposed attack in comparison to Carlini et al.'s attack.Comment: 15 page

A novel electrochemical system with adiabatic pre-charging and pre-discharging processes for efficient refrigeration

[EN]The extraordinary thermal-to-electricity conversion efficiency of thermally regenerative electrochemical cycle triggers interest in its reverse counterpart, namely thermally regenerative electrochemical refrigerator (TRER), a promising alternative to conventional cooling devices. Nevertheless, due to three fundamental obstacles, the practically feasible TRER model is still absent, which hinders the development of follow-up research. To break this bottleneck, heating by discharging and cooling by charging effects are innovatively utilized to construct TRER models where the electrochemical counterparts of traditional adiabatic compression and expansion processes, namely adiabatic pre-charging and pre-discharging processes, are proposed and introduced. Significantly, the maximum coefficient of performance (COP) and the COP at maximum cooling power are predicted to achieve up to 40% and 5% of Carnot COP, respectively for the given values of parameters. Moreover, the great potential for efficient refrigeration is highlighted by comparing the obtained results with various refrigeration systems. This work lays the foundation for further experimental investigations and opens a new avenue for constructing other novel electrochemical cycles

Role of CTSC in Glioblastoma Based on Oncomine and TCGA Database

Background and objective Glioblastoma (GBM) is one of the malignant tumors causing death worldwide. Most patients were found in the middle and late stages and had poor prognosis. The purpose of this study was to investigate the expression and significance of CTSC in GBM. Methods The information about CTSC in Oncomine database was collected and analyzed twice. The role of CTSC in GBM was meta-analyzed. The expression of CTSC in glioma cell lines was retrieved by CCLE database, and the survival of patients was analyzed by TCGA database. Results A total of 1,459 different types of CTSC were collected in Oncomine database, 134 of which had statistical differences in CTSC expression, 89 of which had increased CTSC expression and 45 of which had decreased CTSC expression. A total of 50 studies involving the expression of CTSC in GBM cancer and normal tissues included 1,189 samples. Compared with the control group, CTSC was highly expressed in GBM (P < 0.05). Moreover, CTSC was highly expressed in glioma cell lines. There was a correlation between the expression of CTSC and the overall survival rate of GBM. The overall survival rate of patients with high expression of CTSC was worse, while the prognosis of patients with low expression of SPC24 was better (P < 0.05). Conclusion Through the in-depth mining of oncomine gene chip database, we propose that CTSC is highly expressed in GBM tissues and is related to the prognosis of GBM, which may provide an important theoretical basis for the treatment of glioma

GWAS Identifies Novel Susceptibility Loci on 6p21.32 and 21q21.3 for Hepatocellular Carcinoma in Chronic Hepatitis B Virus Carriers

Genome-wide association studies (GWAS) have recently identified KIF1B as susceptibility locus for hepatitis B virus (HBV)–related hepatocellular carcinoma (HCC). To further identify novel susceptibility loci associated with HBV–related HCC and replicate the previously reported association, we performed a large three-stage GWAS in the Han Chinese population. 523,663 autosomal SNPs in 1,538 HBV–positive HCC patients and 1,465 chronic HBV carriers were genotyped for the discovery stage. Top candidate SNPs were genotyped in the initial validation samples of 2,112 HBV–positive HCC cases and 2,208 HBV carriers and then in the second validation samples of 1,021 cases and 1,491 HBV carriers. We discovered two novel associations at rs9272105 (HLA-DQA1/DRB1) on 6p21.32 (OR = 1.30, P = 1.13×$10^{−19}$) and rs455804 (GRIK1) on 21q21.3 (OR = 0.84, P = 1.86×$10^{−8}$), which were further replicated in the fourth independent sample of 1,298 cases and 1,026 controls (rs9272105: OR = 1.25, P = 1.71×$10^{−4}$; rs455804: OR = 0.84, P = 6.92×$10^{−3}$). We also revealed the associations of HLA-DRB1*0405 and 0901*0602, which could partially account for the association at rs9272105. The association at rs455804 implicates GRIK1 as a novel susceptibility gene for HBV–related HCC, suggesting the involvement of glutamate signaling in the development of HBV–related HCC

First report of bicolour FISH of Berberis diaphana and B. soulieana reveals interspecific differences and co-localization of (AGGGTTT)3 and rDNA 5S in B. diaphana

Abstract Background Berberis consists of approximately 500 species and is the largest genus in Berberidaceae. Most Berberis species lack cytological data, and bicolour fluorescence in situ hybridization (FISH) has never been performed on Berberis. In this work, a karyotype of Berberis diaphana, an alpine Berberis species obtained from an altitude of 3600 m in Wolong National Nature Reserve, China, was analysed and compared with Berberis soulieana Schneid. via FISH using oligonucleotide telomere probes for (AGGGTTT)3 and 5S rDNA (41 bp) for the first time. Results Berberis diaphana belonged to cytotype 2A and had the karyotype formula 2n = 2x = 28 = 26 m + 2 sm (2SAT). The mitotic metaphase chromosome lengths ranged from 1.82 ± 0.04 μm to 2.75 ± 0.00 μm. Clear (AGGGTTT)3 signals were detected at two telomeres in every chromosome and were co–localized with 5S rDNA at the terminal regions of the long arms in the 6th pair of chromosomes. One pair of (AGGGTTT)3 sites was localized in the satellites of the 7th pair of chromosomes, which are the only submetacentric chromosomes in this species. Totally 28 chromosomes with one pair of satellited chromosomes were observed in B. soulieana. This species had four 5S rDNA signals with two weak signals at the end of long arms in the 5th pair of chromosomes and another two strong signals detected in the interstitial region close to the end of short arms in the 6th pair of chromosomes. Each large signal consisted of two smaller signals with secondary constrictions around them. Conclusions FISH physical mapping of B. diaphana suggested that (AGGGTTT)3 and rDNA 5S co-localize at the 6th pair of chromosomes. The density, location and number difference of 5S rDNA loci indicated structural differences among the chromosomes between B. diaphana and B. soulieana. Our results provide information that may contribute to future studies on the physical assembly of the Berberis genome and the evolution of rDNA and telomere FISH patterns in Berberis