Online Linear Extractors for Independent Sources

In this work, we characterize online linear extractors. In other words, given a matrix $A \in \mathbb{F}_2^{n \times n}$, we study the convergence of the iterated process $\mathbf{S} \leftarrow A\mathbf{S} \oplus \mathbf{X}$, where $\mathbf{X} \sim D$ is repeatedly sampled independently from some fixed (but unknown) distribution $D$ with (min)-entropy at least $k$. Here, we think of $\mathbf{S} \in \{0,1\}^n$ as the state of an online extractor, and $\mathbf{X} \in \{0,1\}^n$ as its input. As our main result, we show that the state $\mathbf{S}$ converges to the uniform distribution for all input distributions $D$ with entropy $k > 0$ if and only if the matrix $A$ has no non-trivial invariant subspace (i.e., a non-zero subspace $V \subsetneq \mathbb{F}_2^n$ such that $AV \subseteq V$). In other words, a matrix $A$ yields an online linear extractor if and only if $A$ has no non-trivial invariant subspace. For example, the linear transformation corresponding to multiplication by a generator of the field $\mathbb{F}_{2^n}$ yields a good online linear extractor. Furthermore, for any such matrix convergence takes at most $\widetilde{O}(n^2(k+1)/k^2)$ steps. We also study the more general notion of condensing---that is, we ask when this process converges to a distribution with entropy at least $\ell$, when the input distribution has entropy greater than $k$. (Extractors corresponding to the special case when $\ell = n$.) We show that a matrix gives a good condenser if there are relatively few vectors $\mathbf{w} \in \mathbb{F}_2^n$ such that $\mathbf{w}, A^T\mathbf{w}, \ldots, (A^T)^{n-k-1} \mathbf{w}$ are linearly dependent. As an application, we show that the very simple cyclic rotation transformation $A(x_1,\ldots, x_n) = (x_n,x_1,\ldots, x_{n-1})$ condenses to $\ell = n-1$ bits for any $k > 1$ if $n$ is a prime satisfying a certain simple number-theoretic condition. Our proofs are Fourier-analytic and rely on a novel lemma, which gives a tight bound on the product of certain Fourier coefficients of any entropic distribution

Enhanced Quadratic Video Interpolation

With the prosperity of digital video industry, video frame interpolation has arisen continuous attention in computer vision community and become a new upsurge in industry. Many learning-based methods have been proposed and achieved progressive results. Among them, a recent algorithm named quadratic video interpolation (QVI) achieves appealing performance. It exploits higher-order motion information (e.g. acceleration) and successfully models the estimation of interpolated flow. However, its produced intermediate frames still contain some unsatisfactory ghosting, artifacts and inaccurate motion, especially when large and complex motion occurs. In this work, we further improve the performance of QVI from three facets and propose an enhanced quadratic video interpolation (EQVI) model. In particular, we adopt a rectified quadratic flow prediction (RQFP) formulation with least squares method to estimate the motion more accurately. Complementary with image pixel-level blending, we introduce a residual contextual synthesis network (RCSN) to employ contextual information in high-dimensional feature space, which could help the model handle more complicated scenes and motion patterns. Moreover, to further boost the performance, we devise a novel multi-scale fusion network (MS-Fusion) which can be regarded as a learnable augmentation process. The proposed EQVI model won the first place in the AIM2020 Video Temporal Super-Resolution Challenge.Comment: Winning solution of AIM2020 VTSR Challenge (in conjunction with ECCV 2020

No Time to Hash: On Super Efficient Entropy Accumulation

Real-world random number generators (RNGs) cannot afford to use (slow) cryptographic hashing every time they refresh their state $R$ with a new entropic input $X$. Instead, they use ``superefficient\u27\u27 simple entropy-accumulation procedures, such as $$R \leftarrow \mathsf{rot}_{\alpha, n}(R) \oplus X,$$ where $\mathsf{rot}_{\alpha,n}$ rotates an $n$-bit state $R$ by some fixed number $\alpha$. For example, Microsoft\u27s RNG uses $\alpha=5$ for $n=32$ and $\alpha=19$ for $n=64$. Where do these numbers come from? Are they good choices? Should rotation be replaced by a better permutation $\pi$ of the input bits? In this work we initiate a rigorous study of these pragmatic questions, by modeling the sequence of successive entropic inputs $X_1,X_2,\ldots$ as independent (but otherwise adversarial) samples from some natural distribution family ${\mathcal D}$. Our contribution is as follows. * We define $2$-monotone distributions as a rich family ${\mathcal D}$ that includes relevant real-world distributions (Gaussian, exponential, etc.), but avoids trivial impossibility results. * For any $\alpha$ with $\gcd(\alpha,n)=1$, we show that rotation accumulates $\Omega(n)$ bits of entropy from $n$ independent samples $X_1,\ldots,X_n$ from any (unknown) $2$-monotone distribution with entropy $k > 1$. * However, we also show that some choices of $\alpha$ perform much better than others for a given $n$. E.g., we show $\alpha=19$ is one of the best choices for $n=64$; in contrast, $\alpha=5$ is good, but generally worse than $\alpha=7$, for $n=32$. * More generally, given a permutation $\pi$ and $k\ge 1$, we define a simple parameter, the covering number $C_{\pi,k}$, and show that it characterizes the number of steps before the rule $$(R_1,\ldots,R_n)\leftarrow (R_{\pi(1)},\ldots, R_{\pi(n)})\oplus X$$ accumulates nearly $n$ bits of entropy from independent, $2$-monotone samples of min-entropy $k$ each. * We build a simple permutation $\pi^*$, which achieves nearly optimal $C_{\pi^*,k}\approx n/k$ for all values of $k$ simultaneously, and experimentally validate that it compares favorably with all rotations $\mathsf{rot}_{\alpha,n}$

Self-Compassion and Symptoms of Depression and Anxiety in Chinese Cancer Patients:the Mediating Role of Illness Perceptions

Objectives An adaptive role of self-compassion for psychological functioning in cancer patients has been highlighted, yet less is known about the underlying mechanisms. This study aimed to examine the mediating role of cancer patients' illness perceptions in the relations between self-compassion and psychological symptoms. Methods This cross-sectional study focused on 301 people with heterogeneous types of cancer. A self-reported questionnaire was used to collect participants' levels of self-compassion, illness perceptions, and symptoms of depression and anxiety. Parallel mediation analyses were performed to examine the research questions. Results The relation between self-compassion and depressive symptoms was mediated by perceived consequences and a timeline cyclical of cancer. Perceived consequences also mediated the relation between self-compassion and symptoms of anxiety, with an additional mediating role of personal control. Conclusions These findings suggest that both self-compassion and illness perceptions were closely linked with cancer patients' psychological symptoms. Particularly, cancer patients who feel more self-compassionate perceive fewer negative consequences of cancer, a less timeline cyclical, and more personal control over their life and report fewer psychological symptoms

Decision tool of medical endoscope maintenance service in Chinese hospitals: a conjoint analysis

Medical devices are instruments, apparatus, appliances, software, implants, reagents, materials or other articles that are intended for use in the treatment or diagnosis of disease or injury in humans. Concerning medical endoscope devices, which enable doctors to observe and manipulate the area under examination through a puncture hole in the body cavity or organ, hospitals predominantly consider the quality and cost of maintenance services when making their selection. The effective and efficient provision of maintenance services plays a crucial role in ensuring cost-effective and high-quality management of medical devices. In this study, we have developed an innovative decision tool that analyzed key factors impacting the choice of medical devices’ maintenance service. This tool assists hospitals in evaluating and selecting appropriate maintenance services for medical device, specifically endoscopy devices. Moreover, it also serves as a valuable resource for manufacturers and suppliers to enhance their after-sales service offerings

Mass testing of the JUNO experiment 20-inch PMTs readout electronics

The Jiangmen Underground Neutrino Observatory (JUNO) is a multi-purpose, large size, liquid scintillator experiment under construction in China. JUNO will perform leading measurements detecting neutrinos from different sources (reactor, terrestrial and astrophysical neutrinos) covering a wide energy range (from 200 keV to several GeV). This paper focuses on the design and development of a test protocol for the 20-inch PMT underwater readout electronics, performed in parallel to the mass production line. In a time period of about ten months, a total number of 6950 electronic boards were tested with an acceptance yield of 99.1%

Implementation and performances of the IPbus protocol for the JUNO Large-PMT readout electronics

The Jiangmen Underground Neutrino Observatory (JUNO) is a large neutrino detector currently under construction in China. Thanks to the tight requirements on its optical and radio-purity properties, it will be able to perform leading measurements detecting terrestrial and astrophysical neutrinos in a wide energy range from tens of keV to hundreds of MeV. A key requirement for the success of the experiment is an unprecedented 3% energy resolution, guaranteed by its large active mass (20 kton) and the use of more than 20,000 20-inch photo-multiplier tubes (PMTs) acquired by high-speed, high-resolution sampling electronics located very close to the PMTs. As the Front-End and Read-Out electronics is expected to continuously run underwater for 30 years, a reliable readout acquisition system capable of handling the timestamped data stream coming from the Large-PMTs and permitting to simultaneously monitor and operate remotely the inaccessible electronics had to be developed. In this contribution, the firmware and hardware implementation of the IPbus based readout protocol will be presented, together with the performances measured on final modules during the mass production of the electronics

Validation and integration tests of the JUNO 20-inch PMTs readout electronics

The Jiangmen Underground Neutrino Observatory (JUNO) is a large neutrino detector currently under construction in China. JUNO will be able to study the neutrino mass ordering and to perform leading measurements detecting terrestrial and astrophysical neutrinos in a wide energy range, spanning from 200 keV to several GeV. Given the ambitious physics goals of JUNO, the electronic system has to meet specific tight requirements, and a thorough characterization is required. The present paper describes the tests performed on the readout modules to measure their performances.Comment: 20 pages, 13 figure