Vacuum spacetimes of embedding class two

Doubt is cast on the much quoted results of Yakupov that the torsion vector in embedding class two vacuum space-times is necessarily a gradient vector and that class 2 vacua of Petrov type III do not exist. The rst result is equivalent to the fact that the two second fundamental forms associated with the embedding necessarily commute and has been assumed in most later investigations of class 2 vacuum space-times. Yakupov stated the result without proof, but hinted that it followed purely algebraically from his identity: Rijkl Ckl = 0 where Cij is the commutator of the two second fundamental forms of the embedding.From Yakupov's identity, it is shown that the only class two vacua with non-zero commutator Cij must necessarily be of Petrov type III or N. Several examples are presented of non-commuting second fundamental forms that satisfy Yakupovs identity and the vacuum condition following from the Gauss equation; both Petrov type N and type III examples occur. Thus it appears unlikely that his results could follow purely algebraically. The results obtained so far do not constitute denite counter-examples to Yakupov's results as the non-commuting examples could turn out to be incompatible with the Codazzi and Ricci embedding equations. This question is currently being investigated

The algorithm of the expert system of APCS (automated process control systems) tests

description of a general algorithm of the expert system of APCS tests is presented

Perceived and mentally rotated contents are differentially represented in cortical depth of V1

Primary visual cortex (V1) in humans is known to represent both veridically perceived external input and internally-generated contents underlying imagery and mental rotation. However, it is unknown how the brain keeps these contents separate thus avoiding a mixture of the perceived and the imagined which could lead to potentially detrimental consequences. Inspired by neuroanatomical studies showing that feedforward and feedback connections in V1 terminate in different cortical layers, we hypothesized that this anatomical compartmentalization underlies functional segregation of external and internally-generated visual contents, respectively. We used high-resolution layer-specific fMRI to test this hypothesis in a mental rotation task. We found that rotated contents were predominant at outer cortical depth bins (i.e. superficial and deep). At the same time perceived contents were represented stronger at the middle cortical bin. These results identify how through cortical depth compartmentalization V1 functionally segregates rather than confuses external from internally-generated visual contents. These results indicate that feedforward and feedback manifest in distinct subdivisions of the early visual cortex, thereby reflecting a general strategy for implementing multiple cognitive functions within a single brain region

Перспективы применения искусственных нейронных сетей для прогнозирования объемов грузоперевозок в транспортных системах

The purpose of research – to identify the prospects for the use of neural network approach in relation to the tasks of economic forecasting of logistics performance, in particular of volume freight traffic in the transport system promiscuous regional freight traffic, as well as to substantiate the effectiveness of the use of artificial neural networks (ANN), as compared with the efficiency of traditional extrapolative methods of forecasting. The authors consider the possibility of forecasting to use ANN for these economic indicators not as an alternative to the traditional methods of statistical forecasting, but as one of the available simple means for solving complex problems.Materials and methods. When predicting the ANN, three methods of learning were used: 1) the Levenberg-Marquardt algorithm-network training stops when the generalization ceases to improve, which is shown by the increase in the mean square error of the output value; 2) Bayes regularization method - network training is stopped in accordance with the minimization of adaptive weights; 3) the method of scaled conjugate gradients, which is used to find the local extremum of a function on the basis of information about its values and gradient. The Neural Network Toolbox package is used for forecasting. The neural network model consists of a hidden layer of neurons with a sigmoidal activation function and an output neuron with a linear activation function, the input values of the dynamic time series, and the predicted value is removed from the output. For a more objective assessment of the prospects of the ANN application, the results of the forecast are presented in comparison with the results obtained in predicting the method of exponential smoothing.Results. When predicting the volumes of freight transportation by rail, satisfactory indicators of the verification of forecasting by both the method of exponential smoothing and ANN had been obtained, although the neural network showed the best result (the average relative forecast error was 8.97% for ANN and 11.21% for the method of exponential smoothing, respectively). This can explained by the fact that the temporal dynamic range of the values of the volumes of cargo transportation by this type of transport, for the period under review, has a nonlinear but uniformly changing character. In the case of forecasting the volumes of cargo transportation by road, the time series of initial values for the reporting period is simultaneously non-linear and unevenly changing. This explains the large values of forecasting errors by the method of exponential smoothing (the average relative forecast error of 47.47% for methods of exponential smoothing ); the forecast error with ANN was 13.97%, therefore the results of the prediction obtained by the method of exponential smoothing are considered unsatisfactory, and for ANN – satisfactory.The conclusion. The results of the study confirm the feasibility of using trained artificial neural networks in forecasting the volumes of freight traffic with different cargo flows that have the initial statistical data of which have an uneven nonlinearly changing character in the time dynamic series. A sufficiently high verification in the application of ANN for difficult-to-forecast indicators of the transport process confirms the practical significance of the application of this method in the modeling of the logistics network. Цель исследования – выявить перспективы применения нейросетевого подхода применительно к задачам экономического прогнозирования транспортно-логистических показателей, в частности объемов грузовых перевозок в транспортной системе разноструктурных региональных грузопотоков, а также обосновать эффективность применения искусственных нейронных сетей (ИНС) в сравнении с эффективностью традиционных экстраполятивных методов прогнозирования. Возможность прогноза с использованием ИНС для данных экономических показателей рассматривается авторами не как альтернатива традиционным методам статистического прогнозирования, а как одно из доступных простых средств для решения сложных задач.Материалы и методы. При прогнозировании ИНС использовались три метода обучения: 1) алгоритм Левенберга-Марквардта – обучение сети останавливается, когда обобщение перестает улучшается, что показывает увеличение средней квадратичной ошибки выходного значения; 2) метод регуляризации Байеса – обучение сети останавливается в соответствии с минимизацией адаптивных весовых коэффициентов; 3) метод масштабированных сопряженных градиентов, который используется для нахождения локального экстремума функции на основе информации о её значениях и градиенте. При прогнозировании использован пакет Neural Network Toolbox – нейросетевая модель состоит из скрытого слоя нейронов с сигмоидальной функцией активации и выходного нейрона с линейной функцией активации, на вход подаются значения временных динамических рядов, с выхода снимается прогнозируемое значение. Для более объективной оценки эффективности и перспектив применения ИНС результаты прогноза представлены в сравнении с результатами, полученными при прогнозировании методом экспоненциального сглаживания.Результаты. При прогнозировании объемов грузовых перевозок железнодорожным транспортом получены удовлетворительные показатели верификации прогнозирования как методом экспоненциального сглаживания, так и ИНС, хотя нейронная сеть показала лучший результат (средняя относительная ошибка прогноза – 8,97% для ИНС и 11,21% для МЭС соответственно). Это объясняется тем, что временной динамический ряд значений объемов грузоперевозок данным видом транспорта, за исследуемый отчетный период, имеет пусть и нелинейный, но равномерно меняющийся характер. В случае прогнозирования объемов грузоперевозок автомобильным транспортом временной динамический ряд исходных значений за отчетный период имеет одновременно и нелинейный, и неравномерный меняющийся характер. Этим объясняется большие значения ошибок прогнозирования методом экспоненциального сглаживания (средняя относительная ошибка прогноза 47,47% для МЭС); ошибка прогноза с применением ИНС составила – 13,97%, следовательно результаты прогнозирования, полученные методом экспоненциального сглаживания, признаем неудовлетворительными, а для ИНС – удовлетворительными.Заключение. Результаты исследования подтверждают целесообразность применения обучаемых искусственных нейронных сетей при прогнозировании объемов грузовых перевозок с разноструктурными грузопотоками, исходные статистические данные которых имеют неравномерный нелинейно меняющийся характер во временном динамическом ряду. Достаточно высокая верификация при применении ИНС для сложнопрогнозируемых показателей транспортного процесса подтверждает практическое значения применения данного метода при моделировании транспортно-логистической сети.

Triple visual hemifield maps in a case of optic chiasm hypoplasia

In humans, each hemisphere comprises an overlay of two visuotopic maps of the contralateral visual field, one from each eye. Is the capacity of the visual cortex limited to these two maps or are plastic mechanisms available to host more maps? We determined the cortical organization of the visual field maps in a rare individual with chiasma hypoplasia, where visual cortex plasticity is challenged to accommodate three hemifield maps. Using high-resolution fMRI at 7T and diffusion-weighted MRI at 3T, we found three hemiretinal inputs, instead of the normal two, to converge onto the left hemisphere. fMRI-based population receptive field mapping of the left V1-V3 at 3T revealed three superimposed hemifield representations in the left visual cortex, i.e. two representations of opposing visual hemifields from the left eye and one right hemifield representation from the right eye. We conclude that developmental plasticity including the re-wiring of local intra- and cortico-cortical connections is pivotal to support the coexistence and functioning of three hemifield maps within one hemisphere

Gaussian Process-based prediction of memory performance and biomarker status in ageing and Alzheimer's disease-A systematic model evaluation

Neuroimaging markers based on Magnetic Resonance Imaging (MRI) combined with various other measures (such as genetic covariates, biomarkers, vascular risk factors, neuropsychological tests etc.) might provide useful predictions of clinical outcomes during the progression towards Alzheimer's disease (AD). The use of multiple features in predictive frameworks for clinical outcomes has become increasingly prevalent in AD research. However, many studies do not focus on systematically and accurately evaluating combinations of multiple input features. Hence, the aim of the present work is to explore and assess optimal combinations of various features for MR-based prediction of (1) cognitive status and (2) biomarker positivity with a multi kernel learning Gaussian process framework. The explored features and parameters included (A) combinations of brain tissues, modulation, smoothing, and image resolution;(B) incorporating demographics & clinical covariates;(C) the impact of the size of the training data set;(D) the influence of dimensionality reduction and the choice of kernel types. The approach was tested in a large German cohort including 959 subjects from the multicentric longitudinal study of cognitive impairment and dementia (DELCODE). Our evaluation suggests the best prediction of memory performance was obtained for a combination of neuroimaging markers, demographics, genetic information (ApoE4) and CSF biomarkers explaining 57% of outcome variance in out-of sample predictions. The highest performance for A 42/40 status classification was achieved for a combination of demographics, ApoE4, and a memory score while usage of structural MRI further improved the classification of individual patient's pTau status

Gaussian Process-based prediction of memory performance and biomarker status in ageing and Alzheimer's disease-A systematic model evaluation

Neuroimaging markers based on Magnetic Resonance Imaging (MRI) combined with various other measures (such as genetic covariates, biomarkers, vascular risk factors, neuropsychological tests etc.) might provide useful predictions of clinical outcomes during the progression towards Alzheimer's disease (AD). The use of multiple features in predictive frameworks for clinical outcomes has become increasingly prevalent in AD research. However, many studies do not focus on systematically and accurately evaluating combinations of multiple input features. Hence, the aim of the present work is to explore and assess optimal combinations of various features for MR-based prediction of (1) cognitive status and (2) biomarker positivity with a multi kernel learning Gaussian process framework. The explored features and parameters included (A) combinations of brain tissues, modulation, smoothing, and image resolution;(B) incorporating demographics & clinical covariates;(C) the impact of the size of the training data set;(D) the influence of dimensionality reduction and the choice of kernel types. The approach was tested in a large German cohort including 959 subjects from the multicentric longitudinal study of cognitive impairment and dementia (DELCODE). Our evaluation suggests the best prediction of memory performance was obtained for a combination of neuroimaging markers, demographics, genetic information (ApoE4) and CSF biomarkers explaining 57% of outcome variance in out-of sample predictions. The highest performance for A 42/40 status classification was achieved for a combination of demographics, ApoE4, and a memory score while usage of structural MRI further improved the classification of individual patient's pTau status

Resting-State Network Alterations Differ between Alzheimer's Disease Atrophy Subtypes

Several Alzheimer's disease (AD) atrophy subtypes were identified, but their brain network properties are unclear. We analyzed data from two independent datasets, including 166 participants (103 AD/63 controls) from the DZNE-longitudinal cognitive impairment and dementia study and 151 participants (121 AD/30 controls) from the AD neuroimaging initiative cohorts, aiming to identify differences between AD atrophy subtypes in resting-state functional magnetic resonance imaging intra-network connectivity (INC) and global and nodal network properties. Using a data-driven clustering approach, we identified four AD atrophy subtypes with differences in functional connectivity, accompanied by clinical and biomarker alterations, including a medio-temporal-predominant (S-MT), a limbic-predominant (S-L), a diffuse (S-D), and a mild-atrophy (S-MA) subtype. S-MT and S-D showed INC reduction in the default mode, dorsal attention, visual and limbic network, and a pronounced reduction of "global efficiency" and decrease of the "clustering coefficient" in parietal and temporal lobes. Despite severe atrophy in limbic areas, the S-L exhibited only marginal global network but substantial nodal network failure. S-MA, in contrast, showed limited impairment in clinical and cognitive scores but pronounced global network failure. Our results contribute toward a better understanding of heterogeneity in AD with the detection of distinct differences in functional connectivity networks accompanied by CSF biomarker and cognitive differences in AD subtypes

Effect of natalizumab on disease progression in secondary progressive multiple sclerosis (ASCEND). a phase 3, randomised, double-blind, placebo-controlled trial with an open-label extension

Background: Although several disease-modifying treatments are available for relapsing multiple sclerosis, treatment effects have been more modest in progressive multiple sclerosis and have been observed particularly in actively relapsing subgroups or those with lesion activity on imaging. We sought to assess whether natalizumab slows disease progression in secondary progressive multiple sclerosis, independent of relapses. Methods: ASCEND was a phase 3, randomised, double-blind, placebo-controlled trial (part 1) with an optional 2 year open-label extension (part 2). Enrolled patients aged 18–58 years were natalizumab-naive and had secondary progressive multiple sclerosis for 2 years or more, disability progression unrelated to relapses in the previous year, and Expanded Disability Status Scale (EDSS) scores of 3·0–6·5. In part 1, patients from 163 sites in 17 countries were randomly assigned (1:1) to receive 300 mg intravenous natalizumab or placebo every 4 weeks for 2 years. Patients were stratified by site and by EDSS score (3·0–5·5 vs 6·0–6·5). Patients completing part 1 could enrol in part 2, in which all patients received natalizumab every 4 weeks until the end of the study. Throughout both parts, patients and staff were masked to the treatment received in part 1. The primary outcome in part 1 was the proportion of patients with sustained disability progression, assessed by one or more of three measures: the EDSS, Timed 25-Foot Walk (T25FW), and 9-Hole Peg Test (9HPT). The primary outcome in part 2 was the incidence of adverse events and serious adverse events. Efficacy and safety analyses were done in the intention-to-treat population. This trial is registered with ClinicalTrials.gov, number NCT01416181. Findings: Between Sept 13, 2011, and July 16, 2015, 889 patients were randomly assigned (n=440 to the natalizumab group, n=449 to the placebo group). In part 1, 195 (44%) of 439 natalizumab-treated patients and 214 (48%) of 448 placebo-treated patients had confirmed disability progression (odds ratio [OR] 0·86; 95% CI 0·66–1·13; p=0·287). No treatment effect was observed on the EDSS (OR 1·06, 95% CI 0·74–1·53; nominal p=0·753) or the T25FW (0·98, 0·74–1·30; nominal p=0·914) components of the primary outcome. However, natalizumab treatment reduced 9HPT progression (OR 0·56, 95% CI 0·40–0·80; nominal p=0·001). In part 1, 100 (22%) placebo-treated and 90 (20%) natalizumab-treated patients had serious adverse events. In part 2, 291 natalizumab-continuing patients and 274 natalizumab-naive patients received natalizumab (median follow-up 160 weeks [range 108–221]). Serious adverse events occurred in 39 (13%) patients continuing natalizumab and in 24 (9%) patients initiating natalizumab. Two deaths occurred in part 1, neither of which was considered related to study treatment. No progressive multifocal leukoencephalopathy occurred. Interpretation: Natalizumab treatment for secondary progressive multiple sclerosis did not reduce progression on the primary multicomponent disability endpoint in part 1, but it did reduce progression on its upper-limb component. Longer-term trials are needed to assess whether treatment of secondary progressive multiple sclerosis might produce benefits on additional disability components. Funding: Biogen

Arterial hypertension and β-amyloid accumulation have spatially overlapping effects on posterior white matter hyperintensity volume: a cross-sectional study

Background: White matter hyperintensities (WMH) in subjects across the Alzheimer’s disease (AD) spectrum with minimal vascular pathology suggests that amyloid pathology—not just arterial hypertension—impacts WMH, which in turn adversely influences cognition. Here we seek to determine the effect of both hypertension and Aβ positivity on WMH, and their impact on cognition. Methods: We analysed data from subjects with a low vascular profile and normal cognition (NC), subjective cognitive decline (SCD), and amnestic mild cognitive impairment (MCI) enrolled in the ongoing observational multicentre DZNE Longitudinal Cognitive Impairment and Dementia Study (n = 375, median age 70.0 [IQR 66.0, 74.4] years; 178 female; NC/SCD/MCI 127/162/86). All subjects underwent a rich neuropsychological assessment. We focused on baseline memory and executive function—derived from multiple neuropsychological tests using confirmatory factor analysis—, baseline preclinical Alzheimer’s cognitive composite 5 (PACC5) scores, and changes in PACC5 scores over the course of three years (ΔPACC5). Results: Subjects with hypertension or Aβ positivity presented the largest WMH volumes (pFDR < 0.05), with spatial overlap in the frontal (hypertension: 0.42 ± 0.17; Aβ: 0.46 ± 0.18), occipital (hypertension: 0.50 ± 0.16; Aβ: 0.50 ± 0.16), parietal lobes (hypertension: 0.57 ± 0.18; Aβ: 0.56 ± 0.20), corona radiata (hypertension: 0.45 ± 0.17; Aβ: 0.40 ± 0.13), optic radiation (hypertension: 0.39 ± 0.18; Aβ: 0.74 ± 0.19), and splenium of the corpus callosum (hypertension: 0.36 ± 0.12; Aβ: 0.28 ± 0.12). Elevated global and regional WMH volumes coincided with worse cognitive performance at baseline and over 3 years (pFDR < 0.05). Aβ positivity was negatively associated with cognitive performance (direct effect—memory: − 0.33 ± 0.08, pFDR < 0.001; executive: − 0.21 ± 0.08, pFDR < 0.001; PACC5: − 0.29 ± 0.09, pFDR = 0.006; ΔPACC5: − 0.34 ± 0.04, pFDR < 0.05). Splenial WMH mediated the relationship between hypertension and cognitive performance (indirect-only effect—memory: − 0.05 ± 0.02, pFDR = 0.029; executive: − 0.04 ± 0.02, pFDR = 0.067; PACC5: − 0.05 ± 0.02, pFDR = 0.030; ΔPACC5: − 0.09 ± 0.03, pFDR = 0.043) and WMH in the optic radiation partially mediated that between Aβ positivity and memory (indirect effect—memory: − 0.05 ± 0.02, pFDR = 0.029). Conclusions: Posterior white matter is susceptible to hypertension and Aβ accumulation. Posterior WMH mediate the association between these pathologies and cognitive dysfunction, making them a promising target to tackle the downstream damage related to the potentially interacting and potentiating effects of the two pathologies. Trial registration: German Clinical Trials Register (DRKS00007966, 04/05/2015)