Deleterious variants in TRAK1 disrupt mitochondrial movement and cause fatal encephalopathy

This is the author accepted manuscript. The final version is available from Oxford University Press via the DOI in this record.The corrigendum to this article is in ORE: http://hdl.handle.net/10871/33588Cellular distribution and dynamics of mitochondria are regulated by several motor proteins and a microtubule network. In neurons, mitochondrial trafficking is crucial because of high energy needs and calcium ion buffering along axons to synapses during neurotransmission. The trafficking kinesin proteins (TRAKs) are well characterized for their role in lysosomal and mitochondrial trafficking in cells, especially neurons. Using whole exome sequencing, we identified homozygous truncating variants in TRAK1 (NM_001042646:c.287-2A > C), in six lethal encephalopathic patients from three unrelated families. The pathogenic variant results in aberrant splicing and significantly reduced gene expression at the RNA and protein levels. In comparison with normal cells, TRAK1-deficient fibroblasts showed irregular mitochondrial distribution, altered mitochondrial motility, reduced mitochondrial membrane potential, and diminished mitochondrial respiration. This study confirms the role of TRAK1 in mitochondrial dynamics and constitutes the first report of this gene in association with a severe neurodevelopmental disorder.D.M.E. and J.K. are supported by the Office of Naval Research (ONR) Grant N000141410538. M.S. is supported by the BBSRC (BB/K006231/1), a Wellcome Trust Institutional Strategic Support Award (WT097835MF, WT105618MA), and a Marie Curie Initial Training Network (ITN) action PerFuMe (316723). M.C.V.M., J.S., H.P., C.F., T.V. and W.A.G. are supported by the NGHRI Intramural Research Program. G.R. is supported by the Kahn Family Foundation and the Israeli Centers of Excellence (I-CORE) Program (ISF grant no. 41/11)

Geometric rank of tensors and subrank of matrix multiplication

Motivated by problems in algebraic complexity theory (e.g., matrix multiplication) and extremal combinatorics (e.g., the cap set problem and the sunflower problem), we introduce the geometric rank as a new tool in the study of tensors and hypergraphs. We prove that the geometric rank is an upper bound on the subrank of tensors and the independence number of hypergraphs. We prove that the geometric rank is smaller than the slice rank of Tao, and relate geometric rank to the analytic rank of Gowers and Wolf in an asymptotic fashion. As a first application, we use geometric rank to prove a tight upper bound on the (border) subrank of the matrix multiplication tensors, matching Strassen's well-known lower bound from 1987

Evolution of the diatoms: insights from fossil, biological and molecular data

Molecular sequence analyses have yielded many important insights into diatom evolution, but there have been few attempts to relate these to the extensive fossil record of diatoms, probably because of unfamiliarity with the data available, which are scattered widely through the geological literature. We review the main features of molecular phylogenies and concentrate on the correspondence between these and the fossil record; we also review the evolution of major morphological, cytological and life cycle characteristics, and possible diatom origins. The first physical remains of diatoms are from the Jurassic, and well-preserved, diverse floras are available from the Lower Cretaceous. Though these are unequivocally identifiable as centric diatoms, none except a possible Stephanopyxis can be unequivocally linked to lineages of extant diatoms, although it is almost certain that members of the Coscinodiscophyceae (radial centrics) and Mediophyceae (polar centrics) were present; some display curious morphological features that hint at an unorthodox cell division mechanism and life cycle. It seems most likely that the earliest diatoms were marine, but recently discovered fossil deposits hint that episodes of terrestrial colonization may have occurred in the Mesozoic, though the main invasion of freshwaters appears to have been delayed until the Cenozoic. By the Upper Cretaceous, many lineages are present that can be convincingly related to extant diatom taxa. Pennate diatoms appear in the late Cretaceous and raphid diatoms in the Palaeocene, though molecular phylogenies imply that raphid diatoms did in fact evolve considerably earlier. Recent evidence shows that diatoms are substantially underclassified at the species level, with many semicryptic or cryptic species to be recognized; however, there is little prospect of being able to discriminate between such taxa in fossil material

Towards a combinatorial characterization of bounded-memory learning

Combinatorial dimensions play an important role in the theory of machine learning. For example, VC dimension characterizes PAC learning, SQ dimension characterizes weak learning with statistical queries, and Littlestone dimension characterizes online learning. In this paper we aim to develop combinatorial dimensions that characterize bounded memory learning. We propose a candidate solution for the case of realizable strong learning under a known distribution, based on the SQ dimension of neighboring distributions. We prove both upper and lower bounds for our candidate solution, that match in some regime of parameters. This is the first characterization of strong learning under space constraints in any regime. In this parameter regime there is an equivalence between bounded memory and SQ learning. We conjecture that our characterization holds in a much wider regime of parameters

Geometric Rank of Tensors and Subrank of Matrix Multiplication

Motivated by problems in algebraic complexity theory (e.g., matrix multiplication) and extremal combinatorics (e.g., the cap set problem and the sunflower problem), we introduce the geometric rank as a new tool in the study of tensors and hypergraphs. We prove that the geometric rank is an upper bound on the subrank of tensors and the independence number of hypergraphs. We prove that the geometric rank is smaller than the slice rank of Tao, and relate geometric rank to the analytic rank of Gowers and Wolf in an asymptotic fashion. As a first application, we use geometric rank to prove a tight upper bound on the (border) subrank of the matrix multiplication tensors, matching Strassen’s well-known lower bound from 1987

Bounded Memory Active Learning through Enriched Queries

The explosive growth of easily-accessible unlabeled data has lead to growing interest in active learning, a paradigm in which data-hungry learning algorithms adaptively select informative examples in order to lower prohibitively expensive labeling costs. Unfortunately, in standard worst-case models of learning, the active setting often provides no improvement over non-adaptive algorithms. To combat this, a series of recent works have considered a model in which the learner may ask enriched queries beyond labels. While such models have seen success in drastically lowering label costs, they tend to come at the expense of requiring large amounts of memory. In this work, we study what families of classifiers can be learned in bounded memory. To this end, we introduce a novel streaming-variant of enriched-query active learning along with a natural combinatorial strategy called lossless sample compression that is sufficient for learning not only with bounded memory, but in a query-optimal and computationally efficient manner as well. Finally, we give three fundamental examples of classifier families with small, easy to compute lossless compression schemes when given access to basic enriched queries: axis-aligned rectangles, decision trees, and halfspaces in two dimensions

An improved lower bound for arithmetic regularity

The arithmetic regularity lemma due to Green [GAFA 2005] is an analogue of the famous Szemerédi regularity lemma in graph theory. It shows that for any abelian group G and any bounded function f : G → [0, 1], there exists a subgroup H ≤ G of bounded index such that, when restricted to most cosets of H, the function f is pseudorandom in the sense that all its nontrivial Fourier coefficients are small. Quantitatively, if one wishes to obtain that for 1 - ϵ fraction of the cosets, the nontrivial Fourier coefficients are bounded by ϵ, then Green shows that |G/H| is bounded by a tower of twos of height 1/ϵ3. He also gives an example showing that a tower of height Ω(log 1/ϵ) is necessary. Here, we give an improved example, showing that a tower of height Ω(1/ϵ) is necessary