Sketched Ridgeless Linear Regression: The Role of Downsampling

Overparametrization often helps improve the generalization performance. This paper presents a dual view of overparametrization suggesting that downsampling may also help generalize. Focusing on the proportional regime $m\asymp n \asymp p$, where $m$ represents the sketching size, $n$ is the sample size, and $p$ is the feature dimensionality, we investigate two out-of-sample prediction risks of the sketched ridgeless least square estimator. Our findings challenge conventional beliefs by showing that downsampling does not always harm generalization but can actually improve it in certain cases. We identify the optimal sketching size that minimizes out-of-sample prediction risks and demonstrate that the optimally sketched estimator exhibits stabler risk curves, eliminating the peaks of those for the full-sample estimator. To facilitate practical implementation, we propose an empirical procedure to determine the optimal sketching size. Finally, we extend our analysis to cover central limit theorems and misspecified models. Numerical studies strongly support our theory.Comment: Add more numerical experiments and some discussions, relax the Gaussian assumption of coefficient vector to moment condition

Experimental Evaluations of the Impact of an Additive Oxidizing Electronic Air Cleaner on Particles and Gases

Electronic air cleaning (EAC) technologies have garnered significant attention for use in buildings. Many EAC technologies rely on the addition of reactive constituents to indoor air to react with gas-phase compounds, enhance particle deposition, and/or inactivate microorganisms. However, limited data are available on the efficacy of many EAC technologies and their potential to form chemical byproducts during operation. Here we experimentally evaluate the indoor air quality impacts, specifically targeting particles and gases but not microbial constituents, of a commercially available additive oxidizing EAC that generates positive and negative ions and hydrogen peroxide (H2O2). Tests were conducted in a large unoccupied test chamber in Chicago, IL and an unoccupied laboratory in Portland, OR under a combination of natural conditions (i.e., without pollutant injection) and perturbation conditions (i.e., with pollutant injection and decay). A combination of integrated and time-resolved measurements was used across both test locations. Chamber tests at lower airflow rates demonstrated that operation of the EAC: (i) had no discernible impact on particle concentrations or particle loss rates, with estimated clean air delivery rates (CADRs) for various particle measures less than ±10 m3/h, (ii) was associated with apparent decreases in some volatile organic compounds (VOCs) and increases in other VOCs and aldehydes, especially acetaldehyde, although a combination of high propagated uncertainty, limitations in test methods (e.g., lack of replicates), and variability between repeated tests limit what quantitative conclusions can be drawn regarding gas-phase organics; (iii) did generate H2O2, assessed using a crude measure, and (iv) did not generate ozone (O3). Laboratory tests at higher airflow rates, which involved injection and decay of particles and a single VOC (limonene), both simultaneously and separately, demonstrated that: (i) pollutant loss rates for both particles and limonene were slightly lower with the EAC on compared to off, yielding slightly negative pollutant removal efficiencies (albeit largely within propagated uncertainty) and (ii) there was a change in observed concentrations of one potential limonene degradation product, m/z 59 (putatively identified as acetone), with steady-state levels increasing from 10 ppb (air cleaner off) to 15 ppb (air cleaner on). No increases or decreases beyond measurement uncertainty were observed for other analyzed gaseous limonene degradation products. Overall, both chamber and laboratory tests demonstrated negligible effectiveness of this device at the test conditions described herein for removing particles and mixed results for VOCs, including decreases in some VOCs, no discernible differences in other VOCs, and apparent increases in other compounds, especially lower molecular weight aldehydes including acetaldehyde

Segment Together: A Versatile Paradigm for Semi-Supervised Medical Image Segmentation

Annotation scarcity has become a major obstacle for training powerful deep-learning models for medical image segmentation, restricting their deployment in clinical scenarios. To address it, semi-supervised learning by exploiting abundant unlabeled data is highly desirable to boost the model training. However, most existing works still focus on limited medical tasks and underestimate the potential of learning across diverse tasks and multiple datasets. Therefore, in this paper, we introduce a \textbf{Ver}satile \textbf{Semi}-supervised framework (VerSemi) to point out a new perspective that integrates various tasks into a unified model with a broad label space, to exploit more unlabeled data for semi-supervised medical image segmentation. Specifically, we introduce a dynamic task-prompted design to segment various targets from different datasets. Next, this unified model is used to identify the foreground regions from all labeled data, to capture cross-dataset semantics. Particularly, we create a synthetic task with a cutmix strategy to augment foreground targets within the expanded label space. To effectively utilize unlabeled data, we introduce a consistency constraint. This involves aligning aggregated predictions from various tasks with those from the synthetic task, further guiding the model in accurately segmenting foreground regions during training. We evaluated our VerSemi model on four public benchmarking datasets. Extensive experiments demonstrated that VerSemi can consistently outperform the second-best method by a large margin (e.g., an average 2.69\% Dice gain on four datasets), setting new SOTA performance for semi-supervised medical image segmentation. The code will be released

A new two-scroll chaotic system with two nonlinearities: dynamical analysis and circuit simulation

Chaos theory has several applications in science and engineering. In this work, we announce a new two-scroll chaotic system with two nonlinearities. The dynamical properties of the system such as dissipativity, equilibrium points, Lyapunov exponents, Kaplan-Yorke dimension and bifurcation diagram are explored in detail. The presence of coexisting chaotic attractors, coexisting chaotic and periodic attractors in the system is also investigated. In addition, the offset boosting of a variable in the new chaotic system is achieved by adding a single controlled constant. It is shown that the new chaotic system has rotation symmetry about the z-axis. An electronic circuit simulation of the new two-scroll chaotic system is built using Multisim to check the feasibility of the theoretical model.

Multicarrier Modulation-Based Digital Radio-over-Fibre System Achieving Unequal Bit Protection with Over 10 dB SNR Gain

We propose a multicarrier modulation-based digital radio-over-fibre system achieving unequal bit protection by bit and power allocation for subcarriers. A theoretical SNR gain of 16.1 dB is obtained in the AWGN channel and the simulation results show a 13.5 dB gain in the bandwidth-limited case

Rheumatoid meningitis: a rare neurological complication of rheumatoid arthritis

ObjectiveTo describe the clinical and neuroimaging characteristics of rheumatoid meningitis (RM) in Chinese patients. MethodsThe patients admitted to our hospital with the diagnosis of RM in the past 8 years were retrospectively analyzed. ResultsSix patients with RM were identified among 933 patients admitted with rheumatoid arthritis (RA). The symptoms of meningitis occurred after onset of arthritis in five patients and before onset in one. Headache (n=6), hyperacute focal neurological deficits (n=4) and seizures (n=3) were the most prevalent symptoms. The nadir modified Rankin Scale score was ≥3 in five patients. Rheumatoid factor was elevated in all patients, and interleukin-6 levels in cerebrospinal fluid were dramatically elevated in three of four tested patients. Magnetic resonance imaging of the brain revealed that the meninges were affected in all patients and the cerebral parenchyma was affected in one patient. The lesions were generally located in the frontoparietal region and showed restricted diffusion along the adjacent subarachnoid space. RM occurred during disease-modifying therapy in four patients. In the acute episode, three patients improved on tocilizumab and the other three improved on pulse corticosteroids. For maintenance therapy, two patients received combined therapy of tocilizumab and other immunosuppressive agents, one received adalimumab and methotrexate, and two received low-dose oral corticosteroids with an immunosuppressive agent. Five patients had a good outcome, and one died of Pneumocystis jirovecii pneumonia after stabilization of his neurologic conditions. No relapse of RM occurred on immunotherapy during follow-up. ConclusionsChinese patients with RM share some remarkable clinical and neuroimaging features and respond well to appropriate immunotherapy. Tocilizumab could be a treatment option for this severe complication of RA

Search for dark matter produced in association with bottom or top quarks in √s = 13 TeV pp collisions with the ATLAS detector

A search for weakly interacting massive particle dark matter produced in association with bottom or top quarks is presented. Final states containing third-generation quarks and miss- ing transverse momentum are considered. The analysis uses 36.1 fb−1 of proton–proton collision data recorded by the ATLAS experiment at √s = 13 TeV in 2015 and 2016. No significant excess of events above the estimated backgrounds is observed. The results are in- terpreted in the framework of simplified models of spin-0 dark-matter mediators. For colour- neutral spin-0 mediators produced in association with top quarks and decaying into a pair of dark-matter particles, mediator masses below 50 GeV are excluded assuming a dark-matter candidate mass of 1 GeV and unitary couplings. For scalar and pseudoscalar mediators produced in association with bottom quarks, the search sets limits on the production cross- section of 300 times the predicted rate for mediators with masses between 10 and 50 GeV and assuming a dark-matter mass of 1 GeV and unitary coupling. Constraints on colour- charged scalar simplified models are also presented. Assuming a dark-matter particle mass of 35 GeV, mediator particles with mass below 1.1 TeV are excluded for couplings yielding a dark-matter relic density consistent with measurements