Traversing the FFT Computation Tree for Dimension-Independent Sparse Fourier Transforms

We consider the well-studied Sparse Fourier transform problem, where one aims to quickly recover an approximately Fourier $k$-sparse vector $\widehat{x} \in \mathbb{C}^{n^d}$ from observing its time domain representation $x$. In the exact $k$-sparse case the best known dimension-independent algorithm runs in near cubic time in $k$ and it is unclear whether a faster algorithm like in low dimensions is possible. Beyond that, all known approaches either suffer from an exponential dependence on the dimension $d$ or can only tolerate a trivial amount of noise. This is in sharp contrast with the classical FFT of Cooley and Tukey, which is stable and completely insensitive to the dimension of the input vector: its runtime is $O(N\log N)$ in any dimension $d$ for $N=n^d$. Our work aims to address the above issues. First, we provide a translation/reduction of the exactly $k$-sparse FT problem to a concrete tree exploration task which asks to recover $k$ leaves in a full binary tree under certain exploration rules. Subsequently, we provide (a) an almost quadratic in $k$ time algorithm for this task, and (b) evidence that a strongly subquadratic time for Sparse FT via this approach is likely impossible. We achieve the latter by proving a conditional quadratic time lower bound on sparse polynomial multipoint evaluation (the classical non-equispaced sparse FT) which is a core routine in the aforementioned translation. Thus, our results combined can be viewed as an almost complete understanding of this approach, which is the only known approach that yields sublinear time dimension-independent Sparse FT algorithms. Subsequently, we provide a robustification of our algorithm, yielding a robust cubic time algorithm under bounded $\ell_2$ noise. This requires proving new structural properties of the recently introduced adaptive aliasing filters combined with a variety of new techniques and ideas

Oblivious Sketching of High-Degree Polynomial Kernels

Kernel methods are fundamental tools in machine learning that allow detection of non-linear dependencies between data without explicitly constructing feature vectors in high dimensional spaces. A major disadvantage of kernel methods is their poor scalability: primitives such as kernel PCA or kernel ridge regression generally take prohibitively large quadratic space and (at least) quadratic time, as kernel matrices are usually dense. Some methods for speeding up kernel linear algebra are known, but they all invariably take time exponential in either the dimension of the input point set (e.g., fast multipole methods suffer from the curse of dimensionality) or in the degree of the kernel function. Oblivious sketching has emerged as a powerful approach to speeding up numerical linear algebra over the past decade, but our understanding of oblivious sketching solutions for kernel matrices has remained quite limited, suffering from the aforementioned exponential dependence on input parameters. Our main contribution is a general method for applying sketching solutions developed in numerical linear algebra over the past decade to a tensoring of data points without forming the tensoring explicitly. This leads to the first oblivious sketch for the polynomial kernel with a target dimension that is only polynomially dependent on the degree of the kernel function, as well as the first oblivious sketch for the Gaussian kernel on bounded datasets that does not suffer from an exponential dependence on the dimensionality of input data points

How accessibility influences citation counts: The case of citations to the full text articles available from ResearchGate

It is generally believed that the number of citations to an article can positively be correlated to its free online availability. In the present study, we investigated the possible impact of academic social networks on the number of citations. We chose the social web service “ResearchGate” as a case. This website acts both as a social network to connect researchers, and at the same time, as an open access repository to publish post-print version of the accepted manuscripts and final versions of open access articles. We collected the data of 1823 articles published by the authors from four different universities. By analyzing these data, we showed that although different levels of full text availability are observed for the four universities, there is always a significant positive correlation between full text availability and the citation count. Moreover, we showed that both post-print version and publisher’s version (i.e., final published version) of the archived manuscripts receive more citations than non-OA articles, and the difference in the citation counts of post-print manuscripts and publisher’s version articles is nonsignificant

Global, regional, and national burden of disorders affecting the nervous system, 1990–2021: a systematic analysis for the Global Burden of Disease Study 2021

BackgroundDisorders affecting the nervous system are diverse and include neurodevelopmental disorders, late-life neurodegeneration, and newly emergent conditions, such as cognitive impairment following COVID-19. Previous publications from the Global Burden of Disease, Injuries, and Risk Factor Study estimated the burden of 15 neurological conditions in 2015 and 2016, but these analyses did not include neurodevelopmental disorders, as defined by the International Classification of Diseases (ICD)-11, or a subset of cases of congenital, neonatal, and infectious conditions that cause neurological damage. Here, we estimate nervous system health loss caused by 37 unique conditions and their associated risk factors globally, regionally, and nationally from 1990 to 2021.MethodsWe estimated mortality, prevalence, years lived with disability (YLDs), years of life lost (YLLs), and disability-adjusted life-years (DALYs), with corresponding 95% uncertainty intervals (UIs), by age and sex in 204 countries and territories, from 1990 to 2021. We included morbidity and deaths due to neurological conditions, for which health loss is directly due to damage to the CNS or peripheral nervous system. We also isolated neurological health loss from conditions for which nervous system morbidity is a consequence, but not the primary feature, including a subset of congenital conditions (ie, chromosomal anomalies and congenital birth defects), neonatal conditions (ie, jaundice, preterm birth, and sepsis), infectious diseases (ie, COVID-19, cystic echinococcosis, malaria, syphilis, and Zika virus disease), and diabetic neuropathy. By conducting a sequela-level analysis of the health outcomes for these conditions, only cases where nervous system damage occurred were included, and YLDs were recalculated to isolate the non-fatal burden directly attributable to nervous system health loss. A comorbidity correction was used to calculate total prevalence of all conditions that affect the nervous system combined.FindingsGlobally, the 37 conditions affecting the nervous system were collectively ranked as the leading group cause of DALYs in 2021 (443 million, 95% UI 378–521), affecting 3·40 billion (3·20–3·62) individuals (43·1%, 40·5–45·9 of the global population); global DALY counts attributed to these conditions increased by 18·2% (8·7–26·7) between 1990 and 2021. Age-standardised rates of deaths per 100 000 people attributed to these conditions decreased from 1990 to 2021 by 33·6% (27·6–38·8), and age-standardised rates of DALYs attributed to these conditions decreased by 27·0% (21·5–32·4). Age-standardised prevalence was almost stable, with a change of 1·5% (0·7–2·4). The ten conditions with the highest age-standardised DALYs in 2021 were stroke, neonatal encephalopathy, migraine, Alzheimer's disease and other dementias, diabetic neuropathy, meningitis, epilepsy, neurological complications due to preterm birth, autism spectrum disorder, and nervous system cancer.InterpretationAs the leading cause of overall disease burden in the world, with increasing global DALY counts, effective prevention, treatment, and rehabilitation strategies for disorders affecting the nervous system are needed