Elliptic logarithms, diophantine approximation and the Birch and Swinnerton-Dyer conjecture

Most, if not all, unconditional results towards the abc-conjecture rely ultimately on classical Baker's method. In this article, we turn our attention to its elliptic analogue. Using the elliptic Baker's method, we have recently obtained a new upper bound for the height of the S-integral points on an elliptic curve. This bound depends on some parameters related to the Mordell-Weil group of the curve. We deduce here a bound relying on the conjecture of Birch and Swinnerton-Dyer, involving classical, more manageable quantities. We then study which abc-type inequality over number fields could be derived from this elliptic approach.Comment: 20 pages. Some changes, the most important being on Conjecture 3.2, three references added ([Mas75], [MB90] and [Yu94]) and one reference updated [BS12]. Accepted in Bull. Brazil. Mat. So

Homozygosity for a missense mutation in the 67 kDa isoform of glutamate decarboxylase in a family with autosomal recessive spastic cerebral palsy: parallels with Stiff-Person Syndrome and other movement disorders

Background Cerebral palsy (CP) is an heterogeneous group of neurological disorders of movement and/or posture, with an estimated incidence of 1 in 1000 live births. Non-progressive forms of symmetrical, spastic CP have been identified, which show a Mendelian autosomal recessive pattern of inheritance. We recently described the mapping of a recessive spastic CP locus to a 5 cM chromosomal region located at 2q24-31.1, in rare consanguineous families. Methods Here we present data that refine this locus to a 0.5 cM region, flanked by the microsatellite markers D2S2345 and D2S326. The minimal region contains the candidate gene GAD1, which encodes a glutamate decarboxylase isoform (GAD67), involved in conversion of the amino acid and excitatory neurotransmitter glutamate to the inhibitory neurotransmitter γ-aminobutyric acid (GABA). Results A novel amino acid mis-sense mutation in GAD67 was detected, which segregated with CP in affected individuals. Conclusions This result is interesting because auto-antibodies to GAD67 and the more widely studied GAD65 homologue encoded by the GAD2 gene, are described in patients with Stiff-Person Syndrome (SPS), epilepsy, cerebellar ataxia and Batten disease. Further investigation seems merited of the possibility that variation in the GAD1 sequence, potentially affecting glutamate/GABA ratios, may underlie this form of spastic CP, given the presence of anti-GAD antibodies in SPS and the recognised excitotoxicity of glutamate in various contexts

Using Strategic Movement to Calibrate a Neural Compass: A Spiking Network for Tracking Head Direction in Rats and Robots

The head direction (HD) system in mammals contains neurons that fire to represent the direction the animal is facing in its environment. The ability of these cells to reliably track head direction even after the removal of external sensory cues implies that the HD system is calibrated to function effectively using just internal (proprioceptive and vestibular) inputs. Rat pups and other infant mammals display stereotypical warm-up movements prior to locomotion in novel environments, and similar warm-up movements are seen in adult mammals with certain brain lesion-induced motor impairments. In this study we propose that synaptic learning mechanisms, in conjunction with appropriate movement strategies based on warm-up movements, can calibrate the HD system so that it functions effectively even in darkness. To examine the link between physical embodiment and neural control, and to determine that the system is robust to real-world phenomena, we implemented the synaptic mechanisms in a spiking neural network and tested it on a mobile robot platform. Results show that the combination of the synaptic learning mechanisms and warm-up movements are able to reliably calibrate the HD system so that it accurately tracks real-world head direction, and that calibration breaks down in systematic ways if certain movements are omitted. This work confirms that targeted, embodied behaviour can be used to calibrate neural systems, demonstrates that ‘grounding’ of modelled biological processes in the real world can reveal underlying functional principles (supporting the importance of robotics to biology), and proposes a functional role for stereotypical behaviours seen in infant mammals and those animals with certain motor deficits. We conjecture that these calibration principles may extend to the calibration of other neural systems involved in motion tracking and the representation of space, such as grid cells in entorhinal cortex

Repair of the TGFBI gene in human corneal keratocytes derived from a granular corneal dystrophy patient via CRISPR/Cas9-induced homology-directed repair

Abstract Granular corneal dystrophy (GCD) is an autosomal dominant hereditary disease in which multiple discrete and irregularly shaped granular opacities are deposited in the corneal stroma. GCD is caused by a point mutation in the transforming growth factor-β-induced (TGFBI) gene, located on chromosome 5q31. Here, we report the first successful application of CRISPR-Cas9-mediated genome editing for the correction of a TGFBI mutation in GCD patient-derived primary corneal keratocytes via homology-directed repair (HDR). To correct genetic defects in GCD patient cells, we designed a disease-specific guide RNA (gRNA) targeting the R124H mutation of TGFBI, which causes GCD type 2 (GCD2). An R124H mutation in primary human corneal keratocytes derived from a GCD2 patient was corrected by delivering a CRISPR plasmid expressing Cas9/gRNA and a single-stranded oligodeoxynucleotide HDR donor template in vitro. The gene correction efficiency was 20.6% in heterozygous cells and 41.3% in homozygous cells. No off-target effects were detected. These results reveal a new therapeutic strategy for GCD2; this method may also be applicable to other heredity corneal diseases

Grounding Word Learning in Space

Humans and objects, and thus social interactions about objects, exist within space. Words direct listeners' attention to specific regions of space. Thus, a strong correspondence exists between where one looks, one's bodily orientation, and what one sees. This leads to further correspondence with what one remembers. Here, we present data suggesting that children use associations between space and objects and space and words to link words and objects—space binds labels to their referents. We tested this claim in four experiments, showing that the spatial consistency of where objects are presented affects children's word learning. Next, we demonstrate that a process model that grounds word learning in the known neural dynamics of spatial attention, spatial memory, and associative learning can capture the suite of results reported here. This model also predicts that space is special, a prediction supported in a fifth experiment that shows children do not use color as a cue to bind words and objects. In a final experiment, we ask whether spatial consistency affects word learning in naturalistic word learning contexts. Children of parents who spontaneously keep objects in a consistent spatial location during naming interactions learn words more effectively. Together, the model and data show that space is a powerful tool that can effectively ground word learning in social contexts

Solving Navigational Uncertainty Using Grid Cells on Robots

To successfully navigate their habitats, many mammals use a combination of two mechanisms, path integration and calibration using landmarks, which together enable them to estimate their location and orientation, or pose. In large natural environments, both these mechanisms are characterized by uncertainty: the path integration process is subject to the accumulation of error, while landmark calibration is limited by perceptual ambiguity. It remains unclear how animals form coherent spatial representations in the presence of such uncertainty. Navigation research using robots has determined that uncertainty can be effectively addressed by maintaining multiple probabilistic estimates of a robot's pose. Here we show how conjunctive grid cells in dorsocaudal medial entorhinal cortex (dMEC) may maintain multiple estimates of pose using a brain-based robot navigation system known as RatSLAM. Based both on rodent spatially-responsive cells and functional engineering principles, the cells at the core of the RatSLAM computational model have similar characteristics to rodent grid cells, which we demonstrate by replicating the seminal Moser experiments. We apply the RatSLAM model to a new experimental paradigm designed to examine the responses of a robot or animal in the presence of perceptual ambiguity. Our computational approach enables us to observe short-term population coding of multiple location hypotheses, a phenomenon which would not be easily observable in rodent recordings. We present behavioral and neural evidence demonstrating that the conjunctive grid cells maintain and propagate multiple estimates of pose, enabling the correct pose estimate to be resolved over time even without uniquely identifying cues. While recent research has focused on the grid-like firing characteristics, accuracy and representational capacity of grid cells, our results identify a possible critical and unique role for conjunctive grid cells in filtering sensory uncertainty. We anticipate our study to be a starting point for animal experiments that test navigation in perceptually ambiguous environments

Modelling a response as a function of high frequency count data: the association between physical activity and fat mass

We present a new statistical modelling approach where the response is a function of high frequency count data. Our application is about investigating the relationship between the health outcome fat mass and physical activity (PA) measured by accelerometer. The accelerometer quantifies the intensity of physical activity as counts per epoch over a given period of time. We use data from the Avon longitudinal study of parents and children (ALSPAC) where accelerometer data is available as a time series of accelerometer counts per minute over seven days for a subset of children. In order to compare accelerometer profiles between individuals and to reduce the high dimension a functional summary of the profiles is used. We use the histogram as a functional summary due to its simplicity, suitability and ease of interpretation. Our model is an extension of generalised regression of scalars on functions or signal regression. It allows also multi-dimensional functional predictors and additive non-linear predictors for metric covariates. The additive multidimensional functional predictors allow investigating specific questions about whether the effect of PA varies over its intensity, by gender, by time of day or by day of the week. The key feature of the model is that it utilises the full profile of measured PA without requiring cut-points defining intensity levels for light, moderate and vigorous activity. We show that the (not necessarily causal) effect of PA is not linear and not constant over the activity intensity. Also, there is little evidence to suggest that the effect of PA intensity varies by gender or whether it happens on weekdays or on weekends

A Modified Sagittal Spine Postural Classification and Its Relationship to Deformities and Spinal Mobility in a Chinese Osteoporotic Population

BACKGROUND: Abnormal posture and spinal mobility have been demonstrated to cause functional impairment in the quality of life, especially in the postmenopausal osteoporotic population. Most of the literature studies focus on either thoracic kyphosis or lumbar lordosis, but not on the change of the entire spinal alignment. Very few articles reported the spinal alignment of Chinese people. The purpose of this study was threefold: to classify the spinal curvature based on the classification system defined by Satoh consisting of the entire spine alignment; to identify the change of trunk mobility; and to relate spinal curvature to balance disorder in a Chinese population. METHODOLOGY/PRINCIPAL FINDINGS: 450 osteoporotic volunteers were recruited for this study. Spinal range of motion and global curvature were evaluated noninvasively using the Spinal-Mouse® system and sagittal postural deformities were characterized. RESULTS: We found a new spine postural alignment consisting of an increased thoracic kyphosis and decreased lumbar lordosis which we classified as our modified round back. We did not find any of Satoh's type 5 classification in our population. Type 2 sagittal alignment was the most common spinal deformity (38.44%). In standing, thoracic kyphosis angles in types 2 (58.34°) and 3 (58.03°) were the largest and lumbar lordosis angles in types 4 (13.95°) and 5 (-8.61°) were the smallest. The range of flexion (ROF) and range of flexion-extension (ROFE) of types 2 and 3 were usually greater than types 4 and 5, with type 1 being the largest. CONCLUSIONS/SIGNIFICANCE: The present study classified and compared for the first time the mobility, curvature and balance in a Chinese population based on the entire spine alignment and found types 4 and 5 to present the worst balance and mobility. This study included a new spine postural alignment classification that should be considered in future population studies