Sharp Information-Theoretic Thresholds for Shuffled Linear Regression

This paper studies the problem of shuffled linear regression, where the correspondence between predictors and responses in a linear model is obfuscated by a latent permutation. Specifically, we consider the model $y = \Pi_* X \beta_* + w$, where $X$ is an $n \times d$ standard Gaussian design matrix, $w$ is Gaussian noise with entrywise variance $\sigma^2$, $\Pi_*$ is an unknown $n \times n$ permutation matrix, and $\beta_*$ is the regression coefficient, also unknown. Previous work has shown that, in the large $n$-limit, the minimal signal-to-noise ratio ($\mathsf{SNR}$), $\lVert \beta_* \rVert^2/\sigma^2$, for recovering the unknown permutation exactly with high probability is between $n^2$ and $n^C$ for some absolute constant $C$ and the sharp threshold is unknown even for $d=1$. We show that this threshold is precisely $\mathsf{SNR} = n^4$ for exact recovery throughout the sublinear regime $d=o(n)$. As a by-product of our analysis, we also determine the sharp threshold of almost exact recovery to be $\mathsf{SNR} = n^2$, where all but a vanishing fraction of the permutation is reconstructed.Comment: 18 pages (9 main, 1 references, 8 appendix

Quantum Cognitive Modeling: New Applications and Systems Research Directions

Expanding the benefits of quantum computing to new domains remains a challenging task. Quantum applications are concentrated in only a few domains, and driven by these few, the quantum stack is limited in supporting the development or execution demands of new applications. In this work, we address this problem by identifying both a new application domain, and new directions to shape the quantum stack. We introduce computational cognitive models as a new class of quantum applications. Such models have been crucial in understanding and replicating human intelligence, and our work connects them with quantum computing for the first time. Next, we analyze these applications to make the case for redesigning the quantum stack for programmability and better performance. Among the research opportunities we uncover, we study two simple ideas of quantum cloud scheduling using data from gate-based and annealing-based quantum computers. On the respective systems, these ideas can enable parallel execution, and improve throughput. Our work is a contribution towards realizing versatile quantum systems that can broaden the impact of quantum computing on science and society

Emergent organization of receptive fields in networks of excitatory and inhibitory neurons

Local patterns of excitation and inhibition that can generate neural waves are studied as a computational mechanism underlying the organization of neuronal tunings. Sparse coding algorithms based on networks of excitatory and inhibitory neurons are proposed that exhibit topographic maps as the receptive fields are adapted to input stimuli. Motivated by a leaky integrate-and-fire model of neural waves, we propose an activation model that is more typical of artificial neural networks. Computational experiments with the activation model using both natural images and natural language text are presented. In the case of images, familiar "pinwheel" patterns of oriented edge detectors emerge; in the case of text, the resulting topographic maps exhibit a 2-dimensional representation of granular word semantics. Experiments with a synthetic model of somatosensory input are used to investigate how the network dynamics may affect plasticity of neuronal maps under changes to the inputs

A stronger association of depression with rheumatoid arthritis in presence of obesity and hypertriglyceridemia

Background: Rheumatoid arthritis (RA) is an autoimmune disorder characterized by chronic and systemic inflammation. Recent research underscores the role of chronic inflammation in multiple common RA comorbidities such as depression, obesity, and cardiovascular diseases (CVDs), suggesting a potential overlap of the pathogenic mechanisms for RA. However, it is not well understood how the coexistence of these comorbid conditions impacts the risk of RA and whether any such association relates to body\u27s inflammatory state. Methods: We used data from the 2007-2010 United States National Health and Nutrition Examination Survey (NHANES) database and compared RA prevalence between subsamples with the presence of any two conditions among depression, obesity, and hypertriglyceridemia (HTG). Each subsample was further divided into three categories based on the serum level of the inflammatory marker C-reactive protein (CRP) and analyzed for statistically significant differences using three-way χ2 tests of independence. Results: The study was conducted on 4,136 patients who fulfilled the inclusion criteria (representing 163,540,241 individuals after adjustment for sampling weights). Rates of depression, obesity, and HTG were found to be significantly higher (P \u3c 0.001) among the subjects with RA compared with the control population with no arthritis. The presence of depression along with obesity or HTG showed a noticeably higher RA prevalence but such an association was not observed for the combination of obesity and HTG. The synergistic effect of HTG with depression was found to be most prominent at a medium CRP level (1-3 mg/L), while for obesity, the effect was observed across all CRP levels examined. These findings were further confirmed by the three-way χ2 test for independence. Conclusions: The presence of obesity or HTG in subjects suffering from depression might pose an increased risk of RA. Inflammatory mechanisms potentially play an important underlying role as suggested by the strong dependency of the association to CRP level. Identification of synergistic associations between RA risk conditions could provide useful information to predict the development and progress of RA

Vitamin A regulation of BMP4 expression in the male germ line

The molecular mechanisms leading to male infertility in vitamin A deficient (VAD) rodents have never been fully elucidated. Here, we report an interaction between BMP4 and retinoid signaling pathways in germ cells that may help clarify the biochemical basis of VAD. Adult germ cells, in particular spermatogonia, expressed BMP4 at both the mRNA and protein levels. BMP4 expression was significantly up-regulated in the testes of VAD mice and was down-regulated in freshly isolated germ cells and VAD testes by retinol, but not retinoic acid. The retinoid-responsive gene, RAR[beta], was not induced in germ cells following retinoid treatment. Examination of BMP4 promoter usage in spermatogonia and the VAD testis revealed that germ cells utilize the recently characterized BMP4 intron 2 promoter, in addition to the classical 1A and 1B promoters. The observed decrease in BMP4 in response to retinol was mediated by the 1A and intron 2 promoters of the BMP4 gene. Our results reflect a direct requirement for retinoids by germ cells for the resumption of spermatogenesis in VAD animals via mechanisms that involve the suppression of BMP4 expression

Vitamin A in Reproduction and Development

The requirement for vitamin A in reproduction was first recognized in the early 1900’s, and its importance in the eyes of developing embryos was realized shortly after. A greater understanding of the large number of developmental processes that require vitamin A emerged first from nutritional deficiency studies in rat embryos, and later from genetic studies in mice. It is now generally believed that all-trans retinoic acid (RA) is the form of vitamin A that supports both male and female reproduction as well as embryonic development. This conclusion is based on the ability to reverse most reproductive and developmental blocks found in vitamin A deficiency induced either by nutritional or genetic means with RA, and the ability to recapitulate the majority of embryonic defects in retinoic acid receptor compound null mutants. The activity of the catabolic CYP26 enzymes in determining what tissues have access to RA has emerged as a key regulatory mechanism, and helps to explain why exogenous RA can rescue many vitamin A deficiency defects. In severely vitamin A-deficient (VAD) female rats, reproduction fails prior to implantation, whereas in VAD pregnant rats given small amounts of carotene or supported on limiting quantities of RA early in organogenesis, embryos form but show a collection of defects called the vitamin A deficiency syndrome or late vitamin A deficiency. Vitamin A is also essential for the maintenance of the male genital tract and spermatogenesis. Recent studies show that vitamin A participates in a signaling mechanism to initiate meiosis in the female gonad during embryogenesis, and in the male gonad postnatally. Both nutritional and genetic approaches are being used to elucidate the vitamin A-dependent pathways upon which these processes depend