Differential Harnack Estimates for Parabolic Equations

Let $(M,g(t))$ be a solution to the Ricci flow on a closed Riemannian manifold. In this paper, we prove differential Harnack inequalities for positive solutions of nonlinear parabolic equations of the type \ppt f=\Delta f-f \ln f +Rf. We also comment on an earlier result of the first author on positive solutions of the conjugate heat equation under the Ricci flow.Comment: 10 page

Robust Image Segmentation Quality Assessment

Deep learning based image segmentation methods have achieved great success, even having human-level accuracy in some applications. However, due to the black box nature of deep learning, the best method may fail in some situations. Thus predicting segmentation quality without ground truth would be very crucial especially in clinical practice. Recently, people proposed to train neural networks to estimate the quality score by regression. Although it can achieve promising prediction accuracy, the network suffers robustness problem, e.g. it is vulnerable to adversarial attacks. In this paper, we propose to alleviate this problem by utilizing the difference between the input image and the reconstructed image, which is conditioned on the segmentation to be assessed, to lower the chance to overfit to the undesired image features from the original input image, and thus to increase the robustness. Results on ACDC17 dataset demonstrated our method is promising

On Locally Conformally Flat Gradient Shrinking Ricci Solitons

In this paper, we first apply an integral identity on Ricci solitons to prove that closed locally conformally flat gradient Ricci solitons are of constant sectional curvature. We then generalize this integral identity to complete noncompact gradient shrinking Ricci solitons, under the conditions that the Ricci curvature is bounded from below and the Riemannian curvature tensor has at most exponential growth. As a consequence of this identity, we classify complete locally conformally flat gradient shrinking Ricci solitons with Ricci curvature bounded from below.Comment: 13 pages, revised version, third author adde

Unsupervised anomaly localization using VAE and beta-VAE

Variational Auto-Encoders (VAEs) have shown great potential in the unsupervised learning of data distributions. An VAE trained on normal images is expected to only be able to reconstruct normal images, allowing the localization of anomalous pixels in an image via manipulating information within the VAE ELBO loss. The ELBO consists of KL divergence loss (image-wise) and reconstruction loss (pixel-wise). It is natural and straightforward to use the later as the predictor. However, usually local anomaly added to a normal image can deteriorate the whole reconstructed image, causing segmentation using only naive pixel errors not accurate. Energy based projection was proposed to increase the reconstruction accuracy of normal regions/pixels, which achieved the state-of-the-art localization accuracy on simple natural images. Another possible predictors are ELBO and its components gradients with respect to each pixels. Previous work claimed that KL gradient is a robust predictor. In this paper, we argue that the energy based projection in medical imaging is not as useful as on natural images. Moreover, we observe that the robustness of KL gradient predictor totally depends on the setting of the VAE and dataset. We also explored the effect of the weight of KL loss within beta-VAE and predictor ensemble in anomaly localization.Comment: arXiv admin note: substantial text overlap with arXiv:2002.03734 by other author

Estrogen status alters tissue distribution and metabolism of oral dose of 75Se-selenite

An association between male and female sex hormones and selenium (Se) status has been reported in animals and humans. These relationships may be important relative to the use of selenium in hormone related diseases such as breast cancer. The purpose of this study is to examine the effect of estrogen status on the absorption, tissue distribution and metabolism of Se. 60 µCi of 75Se as selenite was orally administered to bilaterally ovariectomized rats 5 weeks after implantation of either placebo pellet (-E) or pellet with estradiol (+E). Blood and tissues were collected 1, 3, 6, and 24 h after dosing. Although absorption of 75Se was independent of E status, 75Se activity differed (P<0.05) in blood, liver, heart, kidney, spleen, brain, and thymus at certain times. For example, total 75Se activity in liver was greater in -E than in +E rats after 1 hour (13.1% vs. 3.9% of total dose). However, +E group had greater 75Se in liver after 6 h than -E group (18.0% vs. 10.9%). The relative distribution of 75Se between cytosol and membrane fractions in tissues was independent of E status. Nor it affected the relative distribution of 75Se among the selenoproteins in cytosol of the above tissues and plasma. However, larger percent of 75Se was incorporated into selenoprotein P (SeP) and glutathione peroxidase (GPx) in plasma in +E group at 3, 6 and 24 h compared to -E group (P<0.05). These results suggest that the effects of estrogen status on selenium distribution among tissues are tissue specific and time-dependent.Supported by the OARDC Grant OHO0020

Estrogen status alters tissue distribution of oral dose of 75Se-selenite and enhances hepatic levels of SelP mRNA, GPx mRNA, GPx activity, and Se

An association between male and female sex hormones and selenium (Se) status has been reported in animals and humans. These relationships may be important relative to the use of selenium in hormone related diseases such as breast cancer. The purpose of this study was to examine the effect of estrogen status on the tissue distribution of Se and mRNA levels of selenoprotein P (SelP) and glutathione peroxidase (GPx) in liver. 60 µCi of 75Se as selenite was orally administered to each bilaterally ovariectomized rat 5 weeks after implantation with either placebo pellet (OVX) or pellet with estradiol (OVX+E2). Blood and tissues were collected 1, 3, 6, and 24 h after dosing. Differences (P<0.05) in 75Se in blood, liver, heart, kidney, spleen, brain, and thymus were noted at certain times. Plasma SelP in OVX+E2 group contained a greater percentage of 75Se at 3, 6 and 24 h compared to OVX group (P<0.05); 75Se in plasma GPx also was greater in OVX+E2 compared to OVX group at 24 h (P<0.05). Real-time RT-PCR analysis showed that both hepatic SelP mRNA (0.93 vs. 0.50) and GPx mRNA (2.81 vs. 2.24) were significantly greater in OVX+E2 group than in OVX group. These results suggest that estrogen status affects distribution of ingested Se in tissue- and time-dependent manners, as well as the expression of hepatic SelP and GPx at both protein and mRNA level. (Supported by the OARDC Grant OHO00201).OARD

Non-smooth model and numerical analysis of a friction driven structure for piezoelectric motors

In this contribution, typical friction driven structures are summarized and presented considering the mechanical structures and operation principles of different types of piezoelectric motors. A two degree-of-freedom dynamic model with one unilateral frictional contact is built for one of the friction driven structures. Different contact regimes and the transitions between them are identified and analyzed. Numerical simulations are conducted to find out different operation modes of the system concerning the sequence of contact regimes in one steady state period. The influences of parameters on the operation modes and corresponding steady state characteristics are also explored. Some advice are then given in terms of the design of friction driven structures and piezoelectric motors

Concurrency Protocol Aiming at High Performance of Execution and Replay for Smart Contracts

Although the emergence of the programmable smart contract makes blockchain systems easily embrace a wider range of industrial areas, how to execute smart contracts efficiently becomes a big challenge nowadays. Due to the existence of Byzantine nodes, the mechanism of executing smart contracts is quite different from that in database systems, so that existing successful concurrency control protocols in database systems cannot be employed directly. Moreover, even though smart contract execution follows a two-phase style, i.e, the miner node executes a batch of smart contracts in the first phase and the validators replay them in the second phase, existing parallel solutions only focus on the optimization in the first phase, but not including the second phase. In this paper, we propose a novel efficient concurrency control scheme which is the first one to do optimization in both phases. Specifically, (i) in the first phase, we give a variant of OCC (Optimistic Concurrency Control) protocol based on {\em batching} feature to improve the concurrent execution efficiency for the miner and produce a schedule log with high parallelism for validators. Also, a graph partition algorithm is devised to divide the original schedule log into small pieces and further reduce the communication cost; and (ii) in the second phase, we give a deterministic OCC protocol to replay all smart contracts efficiently on multi-core validators where all cores can replay smart contracts independently. Theoretical analysis and extensive experimental results illustrate that the proposed scheme outperforms state-of-art solutions significantly

Nash Equilibrium in the Quantum Battle of Sexes Game

We investigate Nash Equilibrium in the quantum Battle of Sexes Game. We find the game has infinite Nash Equilibria and all of them leads to the asymmetry result. We also show that there is no unique but infinite Nash Equilibrium in it if we use the quantizing scheme proposed by Eisert et al and the two players are allowed to adopt any unitary operator as his/her strategies

On the Discrimination-Generalization Tradeoff in GANs

Generative adversarial training can be generally understood as minimizing certain moment matching loss defined by a set of discriminator functions, typically neural networks. The discriminator set should be large enough to be able to uniquely identify the true distribution (discriminative), and also be small enough to go beyond memorizing samples (generalizable). In this paper, we show that a discriminator set is guaranteed to be discriminative whenever its linear span is dense in the set of bounded continuous functions. This is a very mild condition satisfied even by neural networks with a single neuron. Further, we develop generalization bounds between the learned distribution and true distribution under different evaluation metrics. When evaluated with neural distance, our bounds show that generalization is guaranteed as long as the discriminator set is small enough, regardless of the size of the generator or hypothesis set. When evaluated with KL divergence, our bound provides an explanation on the counter-intuitive behaviors of testing likelihood in GAN training. Our analysis sheds lights on understanding the practical performance of GANs.Comment: ICLR 201