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Marc D Riedel - One of the best experts on this subject based on the ideXlab platform.
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a reconfigurable architecture with sequential logic based stochastic computing
ACM Journal on Emerging Technologies in Computing Systems, 2017Co-Authors: Hassan M Najafi, David J Lilja, Kia Bazargan, Peng Li, Weikang Qian, Marc D RiedelAbstract:Computations based on stochastic bit streams have several advantages compared to deterministic binary radix computations, including low power consumption, low hardware cost, high fault tolerance, and skew tolerance. To take advantage of this computing technique, previous work proposed a combinational logic-based reconfigurable architecture to perform Complex Arithmetic operations on stochastic streams of bits. The long execution time and the cost of converting between binary and stochastic representations, however, make the stochastic architectures less energy efficient than the deterministic binary implementations. This article introduces a methodology for synthesizing a given target function stochastically using finite-state machines (FSMs), and enhances and extends the reconfigurable architecture using sequential logic. Compared to the previous approach, the proposed reconfigurable architecture can save hardware area and energy consumption by up to 30% and 40%, respectively, while achieving a higher processing speed. Both stochastic reconfigurable architectures are much more tolerant of soft errors (bit flips) than the deterministic binary radix implementations, and their fault tolerance scales gracefully to very large numbers of errors.
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a deterministic approach to stochastic computation
International Conference on Computer Aided Design, 2016Co-Authors: Devon Jenson, Marc D RiedelAbstract:Stochastic logic performs computation on data represented by random bit streams. The representation allows Complex Arithmetic to be performed with very simple logic, but it suffers from high latency and poor precision. Furthermore, the results are always somewhat inaccurate due to random fluctuations. The random or pseudorandom sources required to generate the representation are costly, consuming a majority of the circuit area (and diminishing the overall gains in area). In this paper, we show that randomness is not a requirement for this computational paradigm. If properly structured, the same Arithmetical constructs can operate on deterministic bit streams, with the data represented uniformly by the fraction of 1's versus 0's. This paper presents three approaches for the computation: relatively prime stream lengths, rotation, and clock division. The three methods are evaluated on a collection of Arithmetical functions. Unlike stochastic methods, all three of our deterministic methods produce completely accurate results. The cost of generating the deterministic streams is a small fraction of the cost of generating streams from random/pseudorandom sources. Most importantly, the latency is reduced by a factor of 1/2n, where n is the equivalent number of bits of precision.
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an efficient implementation of numerical integration using logical computation on stochastic bit streams
International Conference on Computer Aided Design, 2012Co-Authors: Weikang Qian, Chen Wang, David J Lilja, Kia Bazargan, Marc D RiedelAbstract:Numerical integration is a widely used approach for computing an approximate result of a definite integral. Conventional digital implementations of numerical integration using binary radix encoding are costly in terms of hardware and have long computational delay. This work proposes a novel method for performing numerical integration based on the paradigm of logical computation on stochastic bit streams. In this paradigm, ordinary digital circuits are employed but they operate on stochastic bit streams instead of deterministic values; the signal value is encoded by the probability of obtaining a one versus a zero in the streams. With this type of computation, Complex Arithmetic operations can be implemented with very simple circuitry. However, typically, such stochastic implementations have long computational delay, since long bit streams are required to encode precise values. This paper proposes a stochastic design for numerical integration characterized by both small area and short delay -- so, in contrast to previous applications, a win on both metrics. The design is based on mathematical analysis that demonstrates that the summation of a large number of terms in the numerical integration could lead to a significant delay reduction. An architecture is proposed for this task. Experiments confirm that the stochastic implementation has smaller area and shorter delay than conventional implementations.
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the synthesis of Complex Arithmetic computation on stochastic bit streams using sequential logic
International Conference on Computer Aided Design, 2012Co-Authors: Peng Li, David J Lilja, Kia Bazargan, Weikang Qian, Marc D RiedelAbstract:The paradigm of logical computation on stochastic bit streams has several key advantages compared to deterministic computation based on binary radix, including error-tolerance and low hardware area cost. Prior research has shown that sequential logic operating on stochastic bit streams can compute non-polynomial functions, such as the tanh function, with less energy than conventional implementations. However, the functions that can be computed in this way are quite limited. For example, high order polynomials and non-polynomial functions cannot be computed using prior approaches. This paper proposes a new finite-state machine (FSM) topology for Complex Arithmetic computation on stochastic bit streams. It describes a general methodology for synthesizing such FSMs. Experimental results show that these FSM-based implementations are more tolerant of soft errors and less costly in terms of the area-time product that conventional implementations.
Jens Saak - One of the best experts on this subject based on the ideXlab platform.
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RADI: a low-rank ADI-type algorithm for large scale algebraic Riccati equations
Numerische Mathematik, 2018Co-Authors: Peter Benner, Patrick Kürschner, Zvonimir Bujanović, Jens SaakAbstract:This paper introduces a new algorithm for solving large-scale continuous-time algebraic Riccati equations (CARE). The advantage of the new algorithm is in its immediate and efficient low-rank formulation, which is a generalization of the Cholesky-factored variant of the Lyapunov ADI method. We discuss important implementation aspects of the algorithm, such as reducing the use of Complex Arithmetic and shift selection strategies. We show that there is a very tight relation between the new algorithm and three other algorithms for CARE previously known in the literature—all of these seemingly different methods in fact produce exactly the same iterates when used with the same parameters: they are algorithmically different descriptions of the same approximation sequence to the Riccati solution.
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on the benefits of the ldlt factorization for large scale differential matrix equation solvers
Linear Algebra and its Applications, 2015Co-Authors: Norman Lang, Jens Saak, Hermann MenaAbstract:Abstract We propose efficient algorithms for solving large-scale matrix differential equations. In particular, we deal with the differential Riccati equations (DRE) and state the applicability to the differential Lyapunov equations (DLE). We focus on methods, based on standard versions of ordinary differential equations, in the matrix setting. The application of these methods yields algebraic Lyapunov equations (ALEs) with a certain structure to be solved in every step. The alternating direction implicit (ADI) algorithm and Krylov subspace based methods allow to exploit this special structure. However, a direct application of classic low-rank formulations requires the use of Complex Arithmetic. Using an L D L T -type decomposition of both, the right hand side and the solution of the equation, we avoid this problem. Thus, the proposed methods are a more practical alternative for large-scale problems arising in applications. Also, they make the application of higher order methods feasible. The numerical results show the better performance of the proposed methods compared to earlier formulations.
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an ldlt factorization based adi algorithm for solving large scale differential matrix equations
Pamm, 2014Co-Authors: Norman Lang, Jens Saak, Hermann MenaAbstract:Large-scale differential matrix equations appear in many applications like optimal control of partial differential equations, balanced truncation model order reduction of linear time varying systems etc. Here, we will focus on matrix Riccati differential equations (RDE). Solving such matrix valued ordinary differential equations (ODE) is a highly storage and time consuming process. Therefore, it is necessary to develop efficient solution strategies minimizing both. We present an LDLT factorization based ADI method for solving algebraic Lyapunov equations (ALE) arising in the innermost iteration during the application of Rosenbrock ODE solvers to RDEs. We show that the LDLT-type decomposition avoids Complex Arithmetic, as well as cancellation effects arising from indefinite right hand sides of the ALEs appearing in the classic ZZT based approach. Additionally, a certain number of linear system solves can be saved within the ADI algorithm by reducing the number of column blocks in the right hand sides while the full accuracy of the standard low-rank ADI is preserved. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
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Efficient handling of Complex shift parameters in the low-rank Cholesky factor ADI method
Numerical Algorithms, 2013Co-Authors: Peter Benner, Patrick Kürschner, Jens SaakAbstract:The solution of large-scale Lyapunov equations is a crucial problem for several fields of modern applied mathematics. The low-rank Cholesky factor version of the alternating directions implicit method (LRCF-ADI) is one iterative algorithm that computes approximate low-rank factors of the solution. In order to achieve fast convergence it requires adequate shift parameters, which can be Complex if the matrices defining the Lyapunov equation are unsymmetric. This will require Complex Arithmetic computations as well as storage of Complex data and thus, increase the overall Complexity and memory requirements of the method. In this article we propose a novel reformulation of LRCF-ADI which generates real low-rank factors by carefully exploiting the dependencies of the iterates with respect to pairs of Complex conjugate shift parameters. It significantly reduces the amount of Complex Arithmetic calculations and requirements for Complex storage. It is hence often superior in terms of efficiency compared to other real formulations.
Ernest C D M Van Lieshout - One of the best experts on this subject based on the ideXlab platform.
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Arithmetic difficulties in children with cerebral palsy are related to executive function and working memory
Journal of Child Psychology and Psychiatry, 2009Co-Authors: K M Jenks, Jan De Moor, Ernest C D M Van LieshoutAbstract:Background: Although it is believed that children with cerebral palsy are at high risk for learning difficulties and Arithmetic difficulties in particular, few studies have investigated this issue. Methods: Arithmetic ability was longitudinally assessed in children with cerebral palsy in special (n = 41) and mainstream education (n = 16) and controls in mainstream education (n = 16). Second grade executive function and working memory scores were used to predict third grade Arithmetic accuracy and response time. Results: Children with cerebral palsy in special education were less accurate and slower than their peers on all Arithmetic tests, even after controlling for IQ, whereas children with cerebral palsy in mainstream education performed as well as controls. Although the performance gap became smaller over time, it did not disappear. Children with cerebral palsy in special education showed evidence of executive function and working memory deficits in shifting, updating, visuospatial sketchpad and phonological loop (for digits, not words) whereas children with cerebral palsy in mainstream education only had a deficit in visuospatial sketchpad. Hierarchical regression revealed that, after controlling for intelligence, components of executive function and working memory explained large proportions of unique variance in Arithmetic accuracy and response time and these variables were sufficient to explain group differences in simple, but not Complex, Arithmetic. Conclusions: Children with cerebral palsy are at risk for specific executive function and working memory deficits that, when present, increase the risk for Arithmetic difficulties in these children.
Hikaru Takeuchi - One of the best experts on this subject based on the ideXlab platform.
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Association of copper levels in the hair with gray matter volume, mean diffusivity, and cognitive functions
Brain Structure and Function, 2019Co-Authors: Hikaru Takeuchi, Yasuyuki Taki, Rui Nouchi, Ryoichi Yokoyama, Yuka Kotozaki, Seishu Nakagawa, Atsushi Sekiguchi, Kunio Iizuka, Yuki Yamamoto, Sugiko HanawaAbstract:Although copper plays a critical role in normal brain functions and development, it is known that excess copper causes toxicity. Here we investigated the associations of copper levels in the hair with regional gray matter volume (rGMV), mean diffusivity (MD), and cognitive differences in a study cohort of 924 healthy young adults. Our findings showed that high copper levels were associated mostly with low cognitive abilities (low scores on the intelligence test consisting of Complex speed tasks, involving reasoning task, a Complex Arithmetic task, and a reading comprehension task) as well as lower reverse Stroop interference, high rGMV over widespread areas of the brain [mainly including the bilateral lateral and medial parietal cortices, medial temporal structures (amygdala, hippocampus, and parahippocampal gyrus), middle cingulate cortex, orbitofrontal cortex, insula, perisylvian areas, inferior temporal lobe, temporal pole, occipital lobes, and supplementary motor area], as well as high MD of the right substantia nigra and bilateral hippocampus, which are indicative of low density in brain tissues. These results suggest that copper levels are associated with mostly aberrant cognitive functions, greater rGMV in extensive areas, greater MD (which are indicative of low density in brain tissues) in subcortical structures in the healthy young adults, possibly reflecting copper’s Complex roles in neural mechanisms.
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working memory training using mental calculation impacts regional gray matter of the frontal and parietal regions
PLOS ONE, 2011Co-Authors: Hikaru Takeuchi, Yasuyuki Taki, Atsushi Sekiguchi, Yuko Sassa, Hiroshi Hashizume, Ai Fukushima, Ryuta KawashimaAbstract:Training working memory (WM) improves performance on untrained cognitive tasks and alters functional activity. However, WM training's effects on gray matter morphology and a wide range of cognitive tasks are still unknown. We investigated this issue using voxel-based morphometry (VBM), various psychological measures, such as non-trained WM tasks and a creativity task, and intensive adaptive training of WM using mental calculations (IATWMMC), all of which are typical WM tasks. IATWMMC was associated with reduced regional gray matter volume in the bilateral fronto-parietal regions and the left superior temporal gyrus. It improved verbal letter span and Complex Arithmetic ability, but deteriorated creativity. These results confirm the training-induced plasticity in psychological mechanisms and the plasticity of gray matter structures in regions that have been assumed to be under strong genetic control.
Seda Cavdaroglu - One of the best experts on this subject based on the ideXlab platform.
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Fact learning in Complex Arithmetic-the role of the angular gyrus revisited.
Human brain mapping, 2016Co-Authors: Johannes Bloechle, Julia Bahnmueller, Klaus Willmes, Stefan Huber, Johannes Rennig, Seda CavdarogluAbstract:In recent theoretical considerations as well as in neuroimaging findings the left angular gyrus (AG) has been associated with the retrieval of Arithmetic facts. This interpretation was corroborated by higher AG activity when processing trained as compared with untrained multiplication problems. However, so far neural correlates of processing trained versus untrained problems were only compared after training. We employed an established learning paradigm (i.e., extensive training of multiplication problems) but measured brain activation before and afte training to evaluate neural correlates of Arithmetic fact acquisition more specifically. When comparing activation patterns for trained and untrained problems of the post-training session, higher AG activation for trained problems was replicated. However, when activation for trained problems was compared to activation for the same problems in the pre-training session, no signal change in the AG was observed. Instead, our results point toward a central role of hippocampal, para-hippocampal, and retrosplenial structures in Arithmetic fact retrieval. We suggest that the AG might not be associated with the actual retrieval of Arithmetic facts, and outline an attentional account of the role of the AG in Arithmetic fact retrieval that is compatible with recent attention to memory hypotheses. Hum Brain Mapp 37:3061-3079, 2016. © 2016 Wiley Periodicals, Inc.