Sparser Johnson-Lindenstrauss Transforms

We give two different and simple constructions for dimensionality reduction in $\ell_2$ via linear mappings that are sparse: only an $O(\varepsilon)$-fraction of entries in each column of our embedding matrices are non-zero to achieve distortion $1+\varepsilon$ with high probability, while still achieving the asymptotically optimal number of rows. These are the first constructions to provide subconstant sparsity for all values of parameters, improving upon previous works of Achlioptas (JCSS 2003) and Dasgupta, Kumar, and Sarl\'{o}s (STOC 2010). Such distributions can be used to speed up applications where $\ell_2$ dimensionality reduction is used.Comment: v6: journal version, minor changes, added Remark 23; v5: modified abstract, fixed typos, added open problem section; v4: simplified section 4 by giving 1 analysis that covers both constructions; v3: proof of Theorem 25 in v2 was written incorrectly, now fixed; v2: Added another construction achieving same upper bound, and added proof of near-tight lower bound for DKS schem

Outcomes of patients with advanced cancer and KRAS mutations in phase I clinical trials.

BackgroundKRAS mutation is common in human cancer. We assessed the clinical factors, including type of KRAS mutation and treatment, of patients with advanced cancer and tumor KRAS mutations and their association with treatment outcomes.MethodsPatients referred to the Phase I Clinic for treatment who underwent testing for KRAS mutations were analyzed.ResultsOf 1,781 patients, 365 (21%) had a KRAS mutation. The G12D mutation was the most common mutation (29%). PIK3CA mutations were found in 24% and 10% of patients with and without KRAS mutations (p<0.0001). Of 223 patients with a KRAS mutation who were evaluable for response, 56 were treated with a MEK inhibitor-containing therapy and 167 with other therapies. The clinical benefit (partial response and stable disease lasting ≥6 months) rates were 23% and 9%, respectively, for the MEK inhibitor versus other therapies (p=0.005). The median progression-free survival (PFS) was 3.3 and 2.2 months, respectively (p=0.09). The respective median overall survival was 8.4 and 7.0 months (p=0.38). Of 66 patients with a KRAS mutation and additional alterations, higher rates of clinical benefit (p=0.04), PFS (p=0.045), and overall survival (p=0.02) were noted in patients treated with MEK inhibitor-containing therapy (n=9) compared to those treated with targeted therapy matched to the additional alterations (n=24) or other therapy (n=33).ConclusionsMEK inhibitors in patients with KRAS-mutated advanced cancer were associated with higher clinical benefit rates compared to other therapies. Therapeutic strategies that include MEK inhibitors or novel agents combined with other targeted therapies or chemotherapy need further investigation

Origin of the anapole condition as revealed by a simple expansion beyond the toroidal multipole

Toroidal multipoles are a topic of increasing interest in the nanophotonics and metamaterials communities. In this paper, we separate out the toroidal multipole components of multipole expansions in polar coordinates (two- and three-dimensional) by expanding the Bessel or spherical Bessel functions. We discuss the formation of the lowest order of magnetic anapoles from the interaction between the magnetic toroidal dipole and the magnetic dipole. Our method also reveals that there are higher order current configurations other than the electric toroidal multipole that have the same radiation characteristics as the pure electric dipole. Furthermore, we find that the anapole condition requires that there is a perfect cancellation of all higher order current configurations

The Effect of a Refractory Period on the Power Spectrum of Neuronal Discharge

The interspike intervals in steady-state neuron firing are assumed to be independently and identically distributed random variables. In the simplest model discussed, each interval is assumed to be the sum of a random neuron refractory period and a statistically independent interval due to a stationary external process, whose statistics are assumed known. The power spectral density (hence the autocorrelation) of the composite neuron-firing renewal process is derived from the known spectrum of the external process and from the unknown spectrum of the neuron-refraction process. The results are applied to spike trains recorded in a previous study [2] of single neurons in the visual cortex of an awake monkey. Two models are demonstrated that may produce peaks in the power spectrum near 40 Hz

Bounding right-arm rotation distances

Rotation distance measures the difference in shape between binary trees of the same size by counting the minimum number of rotations needed to transform one tree to the other. We describe several types of rotation distance where restrictions are put on the locations where rotations are permitted, and provide upper bounds on distances between trees with a fixed number of nodes with respect to several families of these restrictions. These bounds are sharp in a certain asymptotic sense and are obtained by relating each restricted rotation distance to the word length of elements of Thompson's group F with respect to different generating sets, including both finite and infinite generating sets.Comment: 30 pages, 11 figures. This revised version corrects some typos and has some clearer proofs of the results for the lower bounds and better figure

Characterization of wild and captive baboon gut microbiota and their antibiotic resistomes

Antibiotic exposure results in acute and persistent shifts in the composition and function of microbial communities associated with vertebrate hosts. However, little is known about the state of these communities in the era before the widespread introduction of antibiotics into clinical and agricultural practice. We characterized the fecal microbiota and antibiotic resistomes of wild and captive baboon populations to understand the effect of human exposure and to understand how the primate microbiota may have been altered during the antibiotic era. We used culture-independent and bioinformatics methods to identify functional resistance genes in the guts of wild and captive baboons and show that exposure to humans is associated with changes in microbiota composition and resistome expansion compared to wild baboon groups. Our results suggest that captivity and lifestyle changes associated with human contact can lead to marked changes in the ecology of primate gut communities.Environmental microbes have harbored the capacity for antibiotic production for millions of years, spanning the evolution of humans and other vertebrates. However, the industrial-scale use of antibiotics in clinical and agricultural practice over the past century has led to a substantial increase in exposure of these agents to human and environmental microbiota. This perturbation is predicted to alter the ecology of microbial communities and to promote the evolution and transfer of antibiotic resistance (AR) genes. We studied wild and captive baboon populations to understand the effects of exposure to humans and human activities (e.g., antibiotic therapy) on the composition of the primate fecal microbiota and the antibiotic-resistant genes that it collectively harbors (the “resistome”). Using a culture-independent metagenomic approach, we identified functional antibiotic resistance genes in the gut microbiota of wild and captive baboon groups and saw marked variation in microbiota architecture and resistomes across habitats and lifeways. Our results support the view that antibiotic resistance is an ancient feature of gut microbial communities and that sharing habitats with humans may have important effects on the structure and function of the primate microbiota