Relaxed Local Correctability from Local Testing

We cement the intuitive connection between relaxed local correctability and local testing by presenting a concrete framework for building a relaxed locally correctable code from any family of linear locally testable codes with sufficiently high rate. When instantiated using the locally testable codes of Dinur et al. (STOC 2022), this framework yields the first asymptotically good relaxed locally correctable and decodable codes with polylogarithmic query complexity, which finally closes the superpolynomial gap between query lower and upper bounds. Our construction combines high-rate locally testable codes of various sizes to produce a code that is locally testable at every scale: we can gradually "zoom in" to any desired codeword index, and a local tester at each step certifies that the next, smaller restriction of the input has low error. Our codes asymptotically inherit the rate and distance of any locally testable code used in the final step of the construction. Therefore, our technique also yields nonexplicit relaxed locally correctable codes with polylogarithmic query complexity that have rate and distance approaching the Gilbert-Varshamov bound.Comment: 18 page

Genome Halving and Aliquoting Under the Copy Number Distance

Large-scale genome rearrangements occur frequently in species evolution and cancer evolution. While the computation of evolutionary distances is tractable for balanced rearrangements, such as inversions and translocations, computing distances involving duplications and deletions is much more difficult. In the recently proposed Copy Number Distance (CND) model, a genome is represented as a Copy Number Profile (CNP), a sequence of integers, and the CND between two CNPs is the length of a shortest sequence of deletions and amplifications of contiguous segments that transforms one CNP into the other. In addition to these segmental events, genomes also undergo global events such as Whole Genome Duplication (WGD) or polyploidization that multiply the entire genome content. These global events are common and important in both species and cancer evolution. In this paper, we formulate the genome halving problem of finding a closest preduplication CNP that has undergone a WGD and evolved into a given CNP under the CND model. We also formulate the analogous genome aliquoting problem of finding the closest prepolyploidzation CNP under the CND distance. We give a linear time algorithm for the halving distance and a quadratic time dynamic programming algorithm for the aliquoting distance. We implement these algorithms and show that they produce reasonable solutions on simulated CNPs

Robot guided 'pen skill' training in children with motor difficulties

Motor deficits are linked to a range of negative physical, social and academic consequences. Haptic robotic interventions, based on the principles of sensorimotor learning, have been shown previously to help children with motor problems learn new movements. We therefore examined whether the training benefits of a robotic system would generalise to a standardised test of 'pen-skills', assessed using objective kinematic measures [via the Clinical Kinematic Assessment Tool, CKAT]. A counterbalanced, cross-over design was used in a group of 51 children (37 male, aged 5-11 years) with manual control difficulties. Improved performance on a novel task using the robotic device could be attributed to the intervention but there was no evidence of generalisation to any of the CKAT tasks. The robotic system appears to have the potential to support motor learning, with the technology affording numerous advantages. However, the training regime may need to target particular manual skills (e.g. letter formation) in order to obtain clinically significant improvements in specific skills such as handwriting.</p

Predicting the Effect of Surface Texture on the Qualitative Form of Prehension

Reach-to-grasp movements change quantitatively in a lawful (i.e. predictable) manner with changes in object properties. We explored whether altering object texture would produce qualitative changes in the form of the precontact movement patterns. Twelve participants reached to lift objects from a tabletop. Nine objects were produced, each with one of three grip surface textures (high-friction, medium-friction and low-friction) and one of three widths (50 mm, 70 mm and 90 mm). Each object was placed at three distances (100 mm, 300 mm and 500 mm), representing a total of 27 trial conditions. We observed two distinct movement patterns across all trials—participants either: (i) brought their arm to a stop, secured the object and lifted it from the tabletop; or (ii) grasped the object ‘on-the-fly’, so it was secured in the hand while the arm was moving. A majority of grasps were on-the-fly when the texture was high-friction and none when the object was low-friction, with medium-friction producing an intermediate proportion. Previous research has shown that the probability of on-the-fly behaviour is a function of grasp surface accuracy constraints. A finger friction rig was used to calculate the coefficients of friction for the objects and these calculations showed that the area available for a stable grasp (the ‘functional grasp surface size’) increased with surface friction coefficient. Thus, knowledge of functional grasp surface size is required to predict the probability of observing a given qualitative form of grasping in human prehensile behaviour

Chandra Spectral and Timing Analysis of Sgr A*'s Brightest X-ray Flares

We analyze the two brightest Chandra X-ray flares detected from Sagittarius A*, with peak luminosities more than 600 x and 245 x greater than the quiescent X-ray emission. The brightest flare has a distinctive double-peaked morphology --- it lasts 5.7 ksec ($\sim 2$ hours), with a rapid rise time of 1500 sec and a decay time of 2500 sec. The second flare lasts 3.4 ksec, with rise and decay times of 1700 sec and 1400 sec. These luminous flares are significantly harder than quiescence: the first has a power law spectral index $\Gamma = 2.06\pm 0.14$ and the second has $\Gamma = 2.03\pm 0.27$, compared to $\Gamma = 3.0\pm0.2$ for the quiescent accretion flow. These spectral indices (as well as the flare hardness ratios) are consistent with previously-detected Sgr A* flares, suggesting that bright and faint flares arise from similar physical processes. Leveraging the brightest flare's long duration and high signal-to-noise, we search for intraflare variability and detect excess X-ray power at a frequency of $\nu \approx 3$ mHz, but show that it is an instrumental artifact and not of astrophysical origin. We find no other evidence (at the 95% confidence level) for periodic or quasi-periodic variability in either flares' time series. We also search for non-periodic excess power but do not find compelling evidence in the power spectrum. Bright flares like these remain our most promising avenue for identifying Sgr A*'s short timescale variability in the X-ray, which may probe the characteristic size scale for the X-ray emission region.Comment: Updated to match published version; 19 pages, 7 figures, 3 table

Training compliance control yields improvements in drawing as a function of beery scores

Many children have difficulty producing movements well enough to improve in sensori-motor learning. Previously, we developed a training method that supports active movement generation to allow improvement at a 3D tracing task requiring good compliance control. Here, we tested 7–8 year old children from several 2nd grade classrooms to determine whether 3D tracing performance could be predicted using the Beery VMI. We also examined whether 3D tracing training lead to improvements in drawing. Baseline testing included Beery, a drawing task on a tablet computer, and 3D tracing. We found that baseline performance in 3D tracing and drawing co-varied with the visual perception (VP) component of the Beery. Differences in 3D tracing between children scoring low versus high on the Beery VP replicated differences previously found between children with and without motor impairments, as did post-training performance that eliminated these differences. Drawing improved as a result of training in the 3D tracing task. The training method improved drawing and reduced differences predicted by Beery scores

Robot Guided ‘Pen Skill’ Training in Children with Motor Difficulties

Motor deficits are linked to a range of negative physical, social and academic consequences. Haptic robotic interventions, based on the principles of sensorimotor learning, have been shown previously to help children with motor problems learn new movements. We therefore examined whether the training benefits of a robotic system would generalise to a standardised test of ‘pen-skills’, assessed using objective kinematic measures [via the Clinical Kinematic Assessment Tool, CKAT]. A counterbalanced, cross-over design was used in a group of 51 children (37 male, aged 5-11 years) with manual control difficulties. Improved performance on a novel task using the robotic device could be attributed to the intervention but there was no evidence of generalisation to any of the CKAT tasks. The robotic system appears to have the potential to support motor learning, with the technology affording numerous advantages. However, the training regime may need to target particular manual skills (e.g. letter formation) in order to obtain clinically significant improvements in specific skills such as handwriting

Finishing the euchromatic sequence of the human genome

The sequence of the human genome encodes the genetic instructions for human physiology, as well as rich information about human evolution. In 2001, the International Human Genome Sequencing Consortium reported a draft sequence of the euchromatic portion of the human genome. Since then, the international collaboration has worked to convert this draft into a genome sequence with high accuracy and nearly complete coverage. Here, we report the result of this finishing process. The current genome sequence (Build 35) contains 2.85 billion nucleotides interrupted by only 341 gaps. It covers ∼99% of the euchromatic genome and is accurate to an error rate of ∼1 event per 100,000 bases. Many of the remaining euchromatic gaps are associated with segmental duplications and will require focused work with new methods. The near-complete sequence, the first for a vertebrate, greatly improves the precision of biological analyses of the human genome including studies of gene number, birth and death. Notably, the human enome seems to encode only 20,000-25,000 protein-coding genes. The genome sequence reported here should serve as a firm foundation for biomedical research in the decades ahead

Query Complexity of Graph Problems in a Directed Cut Oracle Model

Inspired by the work of Rubinstein, Schramm, and Weinberg on the undirected cut oracle model, we explore the directed cut oracle model. In this model, the only way to learn any information about a hidden directed graph is to query its directed cut function. We cannot learn the directions of directed cycles in the graph in this model, but we prove that this is the only information that we cannot learn. We use our result to build a new algorithm that learns the directed cut function with near-optimal cut query complexity. Next, can we learn only part of the directed graph efficiently, to solve problems without learning the entire cut function? We prove that the existence of one such subroutine (one that finds outneighbors of vertices) yields near-optimal algorithms for topological sort and acyclicity testing. While searching for query lower bounds that would disprove the existence of this subroutine, we determine that the deterministic communication complexity of acyclicity is $\Theta(n \log n)$. Finally, we focus on the directed mincut problem, with the goal of adapting some techniques used by Rubinstein, Schramm, and Weinberg to show that undirected mincut can be solved with $\tilde O(n)$ undirected cut queries. We show that balanced directed graphs can be sparsified with $\tilde O(n)$ directed cut queries, and that we can bound the number of arcs that cross approximate mincuts in balanced graphs. For general graphs, we show a weaker bound that only considers minimal mincuts and counts arcs crossing in a single direction

SCARLET: Single-cell tumor phylogeny inference with copy-number constrained mutation losses.

A small number of somatic mutations drive the development of cancer, but all somatic mutations are markers of the evolutionary history of a tumor. Prominent methods to construct phylogenies from single-cell sequencing data use single-nucleotide variants (SNVs) as markers but fail to adequately account for copy-number aberrations (CNAs), which can overlap SNVs and result in SNV losses. Here, we introduce SCARLET, an algorithm that infers tumor phylogenies from single-cell DNA sequencing data while accounting for both CNA-driven loss of SNVs and sequencing errors. SCARLET outperforms existing methods on simulated data, with more accurate inference of the order in which mutations were acquired and the mutations present in individual cells. Using a single-cell dataset from a patient with colorectal cancer, SCARLET constructs a tumor phylogeny that is consistent with the observed CNAs and suggests an alternate origin for the patient's metastases. SCARLET is available at: github.com/raphael-group/scarlet