A new algorithm for fast generalized DFTs

We give an new arithmetic algorithm to compute the generalized Discrete Fourier Transform (DFT) over finite groups $G$. The new algorithm uses $O(|G|^{\omega/2 + o(1)})$ operations to compute the generalized DFT over finite groups of Lie type, including the linear, orthogonal, and symplectic families and their variants, as well as all finite simple groups of Lie type. Here $\omega$ is the exponent of matrix multiplication, so the exponent $\omega/2$ is optimal if $\omega = 2$. Previously, "exponent one" algorithms were known for supersolvable groups and the symmetric and alternating groups. No exponent one algorithms were known (even under the assumption $\omega = 2$) for families of linear groups of fixed dimension, and indeed the previous best-known algorithm for $SL_2(F_q)$ had exponent $4/3$ despite being the focus of significant effort. We unconditionally achieve exponent at most $1.19$ for this group, and exponent one if $\omega = 2$. Our algorithm also yields an improved exponent for computing the generalized DFT over general finite groups $G$, which beats the longstanding previous best upper bound, for any $\omega$. In particular, assuming $\omega = 2$, we achieve exponent $\sqrt{2}$, while the previous best was $3/2$

On Multidimensional and Monotone k-SUM

The well-known k-SUM conjecture is that integer k-SUM requires time Omega(n^{ceil{k/2}-o(1)}). Recent work has studied multidimensional k-SUM in F_p^d, where the best known algorithm takes time tilde O(n^{ceil{k/2}}). Bhattacharyya et al. [ICS 2011] proved a min(2^{Omega(d)},n^{Omega(k)}) lower bound for k-SUM in F_p^d under the Exponential Time Hypothesis. We give a more refined lower bound under the standard k-SUM conjecture: for sufficiently large p, k-SUM in F_p^d requires time Omega(n^{k/2-o(1)}) if k is even, and Omega(n^{ceil{k/2}-2k(log k)/(log p)-o(1)}) if k is odd. For a special case of the multidimensional problem, bounded monotone d-dimensional 3SUM, Chan and Lewenstein [STOC 2015] gave a surprising tilde O(n^{2-2/(d+13)}) algorithm using additive combinatorics. We show this algorithm is essentially optimal. To be more precise, bounded monotone d-dimensional 3SUM requires time Omega(n^{2-frac{4}{d}-o(1)}) under the standard 3SUM conjecture, and time Omega(n^{2-frac{2}{d}-o(1)}) under the so-called strong 3SUM conjecture. Thus, even though one might hope to further exploit the structural advantage of monotonicity, no substantial improvements beyond those obtained by Chan and Lewenstein are possible for bounded monotone d-dimensional 3SUM

The prism manifold realization problem

The spherical manifold realization problem asks which spherical three-manifolds arise from surgeries on knots in S³. In recent years, the realization problem for C–, T–, O– and I–type spherical manifolds has been solved, leaving the D–type manifolds (also known as the prism manifolds) as the only remaining case. Every prism manifold can be parametrized as P(p,q) for a pair of relatively prime integers p>1 and q. We determine a list of prism manifolds P(p,q) that can possibly be realized by positive integral surgeries on knots in S³ when q<0. Based on the forthcoming work of Berge and Kang, we are confident that this list is complete. The methodology undertaken to obtain the classification is similar to that of Greene for lens spaces

Stroke genetics informs drug discovery and risk prediction across ancestries

Previous genome-wide association studies (GWASs) of stroke — the second leading cause of death worldwide — were conducted predominantly in populations of European ancestry1,2. Here, in cross-ancestry GWAS meta-analyses of 110,182 patients who have had a stroke (five ancestries, 33% non-European) and 1,503,898 control individuals, we identify association signals for stroke and its subtypes at 89 (61 new) independent loci: 60 in primary inverse-variance-weighted analyses and 29 in secondary meta-regression and multitrait analyses. On the basis of internal cross-ancestry validation and an independent follow-up in 89,084 additional cases of stroke (30% non-European) and 1,013,843 control individuals, 87% of the primary stroke risk loci and 60% of the secondary stroke risk loci were replicated (P < 0.05). Effect sizes were highly correlated across ancestries. Cross-ancestry fine-mapping, in silico mutagenesis analysis3, and transcriptome-wide and proteome-wide association analyses revealed putative causal genes (such as SH3PXD2A and FURIN) and variants (such as at GRK5 and NOS3). Using a three-pronged approach4, we provide genetic evidence for putative drug effects, highlighting F11, KLKB1, PROC, GP1BA, LAMC2 and VCAM1 as possible targets, with drugs already under investigation for stroke for F11 and PROC. A polygenic score integrating cross-ancestry and ancestry-specific stroke GWASs with vascular-risk factor GWASs (integrative polygenic scores) strongly predicted ischaemic stroke in populations of European, East Asian and African ancestry5. Stroke genetic risk scores were predictive of ischaemic stroke independent of clinical risk factors in 52,600 clinical-trial participants with cardiometabolic disease. Our results provide insights to inform biology, reveal potential drug targets and derive genetic risk prediction tools across ancestries

Comparação de eficiência computacional entre as transformadas rápidas de Fourier e de Hartley

TCC (graduação) - Universidade Federal de Santa Catarina. Centro Tecnológico. Curso de Ciências da Computação.Será analisada essa transformada de maneira teórica e prática a transformada de Hartley sempre a comparando com a transformada de Fourier. Primeiramente serão estudados os fundamentos teóricos que tornaram possível a criação da transformada de Hartley e em que esses conceitos se assemelham e diferem dos equivalentes à transformada de Fourier. Ainda sob o aspecto teórico, utilizando as ferramentas da análise numérica as duas transformadas serão comparadas em complexidade e demanda de recursos computacionais, levando-se em conta número de operações necessárias e memória consumida. Na prática serão implementadas as duas transformadas e serão testadas em condições iguais para a comprovação dos resultados teóricos obtidos. Também será proposta a aplicação da transformada de Hartley em substituição à transformada de Fourier em algum laboratório, onde esta última seja largamente utilizada para processamento de sinais eletromagnéticos, de forma a verificar a diferença de desempenho obtida em uma área onde a transformada de Fourier é fundamental

The value of open-source clinical science in pandemic response: lessons from ISARIC

International audienc

Association of Country Income Level With the Characteristics and Outcomes of Critically Ill Patients Hospitalized With Acute Kidney Injury and COVID-19

Introduction: Acute kidney injury (AKI) has been identified as one of the most common and significant problems in hospitalized patients with COVID-19. However, studies examining the relationship between COVID-19 and AKI in low- and low-middle income countries (LLMIC) are lacking. Given that AKI is known to carry a higher mortality rate in these countries, it is important to understand differences in this population. Methods: This prospective, observational study examines the AKI incidence and characteristics of 32,210 patients with COVID-19 from 49 countries across all income levels who were admitted to an intensive care unit during their hospital stay. Results: Among patients with COVID-19 admitted to the intensive care unit, AKI incidence was highest in patients in LLMIC, followed by patients in upper-middle income countries (UMIC) and high-income countries (HIC) (53%, 38%, and 30%, respectively), whereas dialysis rates were lowest among patients with AKI from LLMIC and highest among those from HIC (27% vs. 45%). Patients with AKI in LLMIC had the largest proportion of community-acquired AKI (CA-AKI) and highest rate of in-hospital death (79% vs. 54% in HIC and 66% in UMIC). The association between AKI, being from LLMIC and in-hospital death persisted even after adjusting for disease severity. Conclusions: AKI is a particularly devastating complication of COVID-19 among patients from poorer nations where the gaps in accessibility and quality of healthcare delivery have a major impact on patient outcomes