Pseudorandom Self-Reductions for NP-Complete Problems

A language L is random-self-reducible if deciding membership in L can be reduced (in polynomial time) to deciding membership in L for uniformly random instances. It is known that several "number theoretic" languages (such as computing the permanent of a matrix) admit random self-reductions. Feigenbaum and Fortnow showed that NP-complete languages are not non-adaptively random-self-reducible unless the polynomial-time hierarchy collapses, giving suggestive evidence that NP may not admit random self-reductions. Hirahara and Santhanam introduced a weakening of random self-reductions that they called pseudorandom self-reductions, in which a language L is reduced to a distribution that is computationally indistinguishable from the uniform distribution. They then showed that the Minimum Circuit Size Problem (MCSP) admits a non-adaptive pseudorandom self-reduction, and suggested that this gave further evidence that distinguished MCSP from standard NP-Complete problems. We show that, in fact, the Clique problem admits a non-adaptive pseudorandom self-reduction, assuming the planted clique conjecture. More generally we show the following. Call a property of graphs ? hereditary if G ? ? implies H ? ? for every induced subgraph of G. We show that for any infinite hereditary property ?, the problem of finding a maximum induced subgraph H ? ? of a given graph G admits a non-adaptive pseudorandom self-reduction

Probabilistic Invariant Learning with Randomized Linear Classifiers

Designing models that are both expressive and preserve known invariances of tasks is an increasingly hard problem. Existing solutions tradeoff invariance for computational or memory resources. In this work, we show how to leverage randomness and design models that are both expressive and invariant but use less resources. Inspired by randomized algorithms, our key insight is that accepting probabilistic notions of universal approximation and invariance can reduce our resource requirements. More specifically, we propose a class of binary classification models called Randomized Linear Classifiers (RLCs). We give parameter and sample size conditions in which RLCs can, with high probability, approximate any (smooth) function while preserving invariance to compact group transformations. Leveraging this result, we design three RLCs that are provably probabilistic invariant for classification tasks over sets, graphs, and spherical data. We show how these models can achieve probabilistic invariance and universality using less resources than (deterministic) neural networks and their invariant counterparts. Finally, we empirically demonstrate the benefits of this new class of models on invariant tasks where deterministic invariant neural networks are known to struggle

Postoperative complications of combined phacoemulsification and pars plana vitrectomy in diabetic retinopathy patients

PurposeTo compare intra- and postoperative complications in combined phacoemulsification and pars plana vitrectomy surgeries performed in patients with non-proliferative diabetic retinopathy (NPDR) vs. proliferative diabetic retinopathy (PDR). MethodsRetrospective, case series of patients with diabetic retinopathy who underwent combined phacovitrectomy surgery between 2008 and 2017. We compared intraoperative complications including posterior capsular rupture and retinal tear, and postoperative complications including corneal edema, macular edema (ME), epiretinal membrane (ERM), neovascular glaucoma and persistent inflammation. ResultsA total of 104 eyes of 104 patients were included in this study. Twenty-four eyes (23.1%) were categorized as NPDR and 80 eyes (76.9%) as PDR. The most common indications for surgery in the NPDR group were ERM (67%) and rhegmatogenous retinal detachment (12.5%), while in the PDR group, indications were vitreous hemorrhage (56%) and tractional retinal detachment (19%). The most common intraoperative complication was retinal tear (8% in NPDR and 19% in PDR, p = 0.195) and postoperative complication was ME (29% in NPDR and 26% in PDR, p = 0.778). There were no statistically significant differences in intra- and postoperative complication rates between the NPDR and PDR groups, even after adjusting for confounders; patient age at surgery and indication for surgery. ConclusionAfter combined phacovitrectomy in NPDR and PDR patients, new-onset ME was found in about a quarter of eyes in both groups. Intraoperative anti-VEGF or steroid administration, and intense postoperative anti-inflammatory medication and follow-up should be regarded after phacovitrectomy regardless of the DR level.Peer reviewe

Brain volumetric changes in the general population following the COVID-19 outbreak and lockdown

The coronavirus disease 2019 (COVID-19) outbreak introduced unprecedented health-risks, as well as pressure on the economy, society, and psychological well-being due to the response to the outbreak. In a preregistered study, we hypothesized that the intense experience of the outbreak potentially induced stress-related brain modifications in the healthy population, not infected with the virus. We examined volumetric changes in 50 participants who underwent MRI scans before and after the COVID-19 outbreak and lockdown in Israel. Their scans were compared with those of 50 control participants who were scanned twice prior to the pandemic. Following COVID-19 outbreak and lockdown, the test group participants uniquely showed volumetric increases in bilateral amygdalae, putamen, and the anterior temporal cortices. Changes in the amygdalae diminished as time elapsed from lockdown relief, suggesting that the intense experience associated with the pandemic induced transient volumetric changes in brain regions commonly associated with stress and anxiety. The current work utilizes a rare opportunity for real-life natural experiment, showing evidence for brain plasticity following the COVID-19 global pandemic. These findings have broad implications, relevant both for the scientific community as well as the general public

Efficient gene replacement by CRISPR/Cas-mediated homologous recombination in the model diatom Thalassiosira pseudonana

CRISPR/Cas enables targeted genome editing in many different plant and algal species including the model diatom Thalassiosira pseudonana. However, efficient gene targeting by homologous recombination (HR) to date is only reported for photosynthetic organisms in their haploid life-cycle phase. Here, a CRISPR/Cas construct, assembled using Golden Gate cloning, enabled highly efficient HR in a diploid photosynthetic organism. Homologous recombination was induced in T. pseudonana using sequence-specific CRISPR/Cas, paired with a dsDNA donor matrix, generating substitution of the silacidin, nitrate reductase and urease genes by a resistance cassette (FCP:NAT). Up to c. 85% of NAT-resistant T. pseudonana colonies screened positive for HR by nested PCR. Precise integration of FCP:NAT at each locus was confirmed using an inverse PCR approach. The knockout of the nitrate reductase and urease genes impacted growth on nitrate and urea, respectively, while the knockout of the silacidin gene in T. pseudonana caused a significant increase in cell size, confirming the role of this gene for cell-size regulation in centric diatoms. Highly efficient gene targeting by HR makes T. pseudonana as genetically tractable as Nannochloropsis and Physcomitrella, hence rapidly advancing functional diatom biology, bionanotechnology and biotechnological applications targeted on harnessing the metabolic potential of diatoms

Environmental Stresses Disrupt Telomere Length Homeostasis

Telomeres protect the chromosome ends from degradation and play crucial roles in cellular aging and disease. Recent studies have additionally found a correlation between psychological stress, telomere length, and health outcome in humans. However, studies have not yet explored the causal relationship between stress and telomere length, or the molecular mechanisms underlying that relationship. Using yeast as a model organism, we show that stresses may have very different outcomes: alcohol and acetic acid elongate telomeres, whereas caffeine and high temperatures shorten telomeres. Additional treatments, such as oxidative stress, show no effect. By combining genome-wide expression measurements with a systematic genetic screen, we identify the Rap1/Rif1 pathway as the central mediator of the telomeric response to environmental signals. These results demonstrate that telomere length can be manipulated, and that a carefully regulated homeostasis may become markedly deregulated in opposing directions in response to different environmental cues

SN2010jp (PTF10aaxi): A Jet-Driven Type II Supernova

We present photometry and spectroscopy of the peculiar TypeII supernova (SN) 2010jp, also named PTF10aaxi. The light curve exhibits a linear decline with a relatively low peak absolute magnitude of only -15.9, and a low radioactive decay luminosity at late times that suggests a nickel mass below 0.003 $M_{\odot}$. Spectra of SN2010jp display an unprecedented triple-peaked H$\alpha$ line profile, showing: (1) a narrow (800 km/s) central component that suggests shock interaction with dense CSM; (2) high-velocity blue and red emission features centered at -12600 and +15400 km/s; and (3) broad wings extending from -22000 to +25000 km/s. These features persist during 100 days after explosion. We propose that this line profile indicates a bipolar jet-driven explosion, with the central component produced by normal SN ejecta and CSM interaction at mid latitudes, while the high-velocity bumps and broad line wings arise in a nonrelativistic bipolar jet. Two variations of the jet interpretation seem plausible: (1) A fast jet mixes 56Ni to high velocities in polar zones of the H-rich envelope, or (2) the reverse shock in the jet produces blue and red bumps in Balmer lines when a jet interacts with dense CSM. Jet-driven SNeII are predicted for collapsars resulting from a wide range of initial masses above 25 $M_{\odot}$ at sub-solar metallicity. This seems consistent with the SN host environment, which is either an extremely low-luminosity dwarf galaxy or very remote parts of an interacting pair of star-forming galaxies. It also seems consistent with the low 56Ni mass that may accompany black hole formation. We speculate that the jet survives to produce observable signatures because the star's H envelope was mostly stripped away by previous eruptive mass loss.Comment: 11 pages, 9 figures, submitted to MNRA

Multi-epoch high-spectral-resolution observations of neutral sodium in 14 Type Ia supernovae

One of the main questions concerning Type Ia supernovae is the nature of the binary companion of the exploding white dwarf. A major discriminant between different suggested models is the presence and physical properties of circumstellar material at the time of explosion. If present, this material will be ionized by the ultraviolet radiation of the explosion and later recombine. This ionization-recombination should manifest itself as time-variable absorption features that can be detected via multi-epoch high-spectral-resolution observations. Previous studies have shown that the strongest effect is seen in the neutral sodium D lines. We report on observations of neutral sodium absorption features observed in multi-epoch high-resolution spectra of 14 Type Ia supernova events. This is the first multi-epoch high-resolution study to include multiple SNe. No variability in line strength that can be associated with circumstellar material is detected in the events presented in this paper. If we include previously published events, we find that ~18 per cent of the events in the extended sample exhibit time-variable sodium features associated with circumstellar material. We explore the implication of this study on our understanding of the progenitor systems of Type Ia supernovae via the current Type Ia supernova multi-epoch high-spectral-resolution sample