Complex Convolution Research Articles

Transient Electromagnetic-Thermal Simulation of Dispersive Media Using DGTD Method

In this paper, the transient electromagnetic–thermal simulation is performed for dispersive media using the discontinuous Galerkin time-domain (DGTD) method. Both the frequency-dependent and temperature-dependent properties of dispersive media are considered in the modeling. Instead of executing the complex convolution in the time domain, an auxiliary differential equation (ADE) method is employed to manipulate dispersive media, where the polarization current density is introduced as an auxiliary variable. While dealing with the thermal issue by the DGTD, the heat flux is utilized to construct the ADE for solving the thermal conduction equation. As the heat source in electromagnetic–thermal simulation, the transient power loss density for three typical dispersive media (Debye, Lorentz, and Drude) is derived by the electrodynamic approach and also explained with equivalent circuit models. The validity and accuracy of the proposed electromagnetic–thermal co-simulation method are demonstrated by the numerical examples.

Energy-Efficient Convolution Architecture Based on Rescheduled Dataflow

This paper presents a rescheduled dataflow of convolution and its hardware architecture that can enhance energy efficiency. For convolution involving a large amount of computations and memory accesses, previous accelerators employed parallel processing elements to meet real-time constraints. Though the previous approaches made a success in implementing complex convolution models, they load the same input features and filter weights from on-chip memories multiple times due to the iterative property of convolution operations, suffering from high energy consumption. To mitigate redundant memory accesses, a novel dataflow is proposed that computes convolution operations incrementally so as to reuse the loaded data as maximally as possible. In addition, several convolution accelerators supporting the rescheduled dataflow are investigated, and qualitative and quantitative analyses are performed to suggest a promising candidate for various convolution models. Simulation results show that the energy efficiency of the proposed accelerator outperforms that of the previous accelerator significantly.

Quantifying the contribution of the Megha‐Tropiques mission to the estimation of daily accumulated rainfall in the Tropics

Satellite estimation of accumulated precipitation is an important facet of the study of the tropical water cycle. An advanced data merging approach using infrared geostationary imagery and microwave constellation based instantaneous rain rate estimates has been implemented in the framework of the Megha‐Tropiques and Global Precipitation Measurements missions. The Tropical Amount of Rainfall with Estimation of ERors (TAPEER) algorithm has been tailored to account for the loss of the MADRAS conical scanning radiometer by using the SAPHIR sounder rainfall detection capability, thanks to a novel two‐constellation implementation of the algorithm. A new bias correction module based on the TRMM PR observations is also presented. The performances of this new version of the product are reviewed with emphasis on West Africa. In particular, using data‐denial experiments, the contribution of SAPHIR data to the rainfall daily accumulation is quantified for various configurations of the microwave constellation and various algorithmic parameter selections. The results show that the daily accumulation statistics are well improved when SAPHIR is taken into the constellation. The improvements can be quantified using bulk statistics but are more evident following a frequency analysis. The pattern of the impact is a complex convolution of rainfall occurrence and of the Megha‐Tropiques mission original sampling. Over the 20°N–20°S belt, in zonal mean, the inclusion of SAPHIR data alters the daily accumulation substantially (more than 50% of the daily accumulation) more than 10% of the time and more than 20% when conditioned upon rainfall. Under both metrics, the improvement is majored in the 12°–17° latitude band where the Megha‐Tropiques mission sampling is at its maximum.

Exact errors of best approximation for complex-valued periodic functions

We extend Nagy's theorem on best approximation by trigonometric polynomials in the metric to certain complex-valued periodic functions. We use this result to find exact constants of best approximation in and on some complex convolution classes. For classes of real-valued convolutions these constants were found by Nikol'skii. As an example, we apply these results to the Schwarz kernel and to the corresponding convolution classes. Bibliography: 20 titles.

Exact errors of best approximation for complex-valued nonperiodic functions

We extend Markov’s and Nagy’s theorems on best approximation by entire functions of exponential type in the L1(R) metric to some complex-valued integrable and locally integrable functions. We use these results for finding sharp constants of best approximation in L1(R) and L∞(R) on some complex convolution classes. For classes of real-valued convolutions those constants were found by Akhiezer. As an example, we apply these results to the Schwarz-type kernel and to the corresponding convolution classes.

Flying IoT: Toward Low-Power Vision in the Sky

The Internet of Things (IoT) is rapidly enabling applications in many different fields by embedding itself into the physical world. Many potential IoT devices require some level of machine learning or cognitive capability to be truly effective, but the high computational complexity of cognitive algorithms makes them unsuitable for low-power IoT processors. To understand the design challenges of cognitive IoT devices, the authors study a cognitive drone application in a design space called Flying IoT. They find that the computing capability provided by typical drone processors falls far short of satisfying the real-time performance requirements of their application. To improve their processor’s performance on the edge while maintaining its low power consumption and small form factor, the authors propose a sensor-cloud architecture in which data collection is done at the edge and data processing is offloaded to the cloud. Their sensor-cloud architecture can process complex convolution neural network models nearly in real time with software optimizations such as downsampling and compression, while consuming less power than state-of-the art embedded processors such as the Jetson TX1.

A Resource-Limited Hardware Accelerator for Convolutional Neural Networks in Embedded Vision Applications

In this brief, we introduce an architecture for accelerating convolution stages in convolutional neural networks (CNNs) implemented in embedded vision systems. The purpose of the architecture is to exploit the inherent parallelism in CNNs to reduce the required bandwidth, resource usage, and power consumption of highly computationally complex convolution operations as required by real-time embedded applications. We also implement the proposed architecture using fixed-point arithmetic on a ZC706 evaluation board that features a Xilinx Zynq-7000 system on-chip, where the embedded ARM processor with high clocking speed is used as the main controller to increase the flexibility and speed. The proposed architecture runs under a frequency of 150 MHz, which leads to 19.2 Giga multiply accumulation operations per second while consuming less than 10 W in power. This is done using only 391 DSP48 modules, which shows significant utilization improvement compared to the state-of-the-art architectures.

Tuning of Silver Catalyst Mesostructure Promotes Selective Carbon Dioxide Conversion into Fuels.

An electrode's performance for catalytic CO2 conversion to fuels is a complex convolution of surface structure and transport effects. Using well-defined mesostructured silver inverse opal (Ag-IO) electrodes, it is demonstrated that mesostructure-induced transport limitations alone serve to increase the turnover frequency for CO2 activation per unit area, while simultaneously improving reaction selectivity. The specific activity for catalyzed CO evolution systematically rises by three-fold and the specific activity for catalyzed H2 evolution systematically declines by ten-fold with increasing mesostructural roughness of Ag-IOs. By exploiting the compounding influence of both of these effects, we demonstrate that mesostructure, rather than surface structure, can be used to tune CO evolution selectivity from less than 5 % to more than 80 %. These results establish electrode mesostructuring as a powerful complementary tool for tuning both catalyst selectivity and efficiency for CO2 conversion into fuels.

Tuning of Silver Catalyst Mesostructure Promotes Selective Carbon Dioxide Conversion into Fuels

AbstractAn electrode's performance for catalytic CO2 conversion to fuels is a complex convolution of surface structure and transport effects. Using well‐defined mesostructured silver inverse opal (Ag‐IO) electrodes, it is demonstrated that mesostructure‐induced transport limitations alone serve to increase the turnover frequency for CO2 activation per unit area, while simultaneously improving reaction selectivity. The specific activity for catalyzed CO evolution systematically rises by three‐fold and the specific activity for catalyzed H2 evolution systematically declines by ten‐fold with increasing mesostructural roughness of Ag‐IOs. By exploiting the compounding influence of both of these effects, we demonstrate that mesostructure, rather than surface structure, can be used to tune CO evolution selectivity from less than 5 % to more than 80 %. These results establish electrode mesostructuring as a powerful complementary tool for tuning both catalyst selectivity and efficiency for CO2 conversion into fuels.

Pre‐image sample algorithm with irregular Gaussian distribution and construction of identity‐based signature

SummaryLattice has become an attractive cryptographic tool due to its potential resistance to quantum attacks, worst‐case hardness, simple computation kind, and flexibility. The pre‐image sample algorithm is the most fundamental algorithm in lattice‐based cryptography for its comprehensive applications in various primitives. Currently, due to Micciancio and Peikert (MP) sample algorithm is the most efficient pre‐image sample algorithm. However, this algorithm also needs massive computations. On the one hand, it expenses the cube of the lattice dimension multiplications over reals to set matrices as Gaussian parameters. On the other hand, it needs complex discrete convolution computations.First, this paper proposes an efficient pre‐image sample algorithm with outputs obeying irregular Gaussian distribution. Two measures are adopted to prevent the leakage of the geometrical property of trapdoor caused by irregular Gaussian outputs. A variant of MP trapdoor is proposed, and a new trapdoor is randomly assembled from a big enough space in each sample. Although still using a matrix as the Guassian parameter, in the proposed algorithm, the computational cost to set Gaussian parameters is zero. Meanwhile, the computational overhead for every sample is far less than that of MP sample algorithm. Second, to demonstrate the security and efficiency of the proposed sample algorithm, a hierarchical identity‐based signature scheme is put forward. This scheme is proved existentially unforgeable against selective identity adaptively chosen‐message attacks. Furthermore, the theoretical analysis shows that the proposed identity‐based signature is more efficient than the existing schemes. Copyright © 2016 John Wiley & Sons, Ltd.

Cortical Folding Pattern and its Consistency Induced by Biological Growth.

Cortical folding, characterized by convex gyri and concave sulci, has an intrinsic relationship to the brain’s functional organization. Understanding the mechanism of the brain’s convoluted patterns can provide useful clues into normal and pathological brain function. In this paper, the cortical folding phenomenon is interpreted both analytically and computationally, and, in some cases, the findings are validated with experimental observations. The living human brain is modeled as a soft structure with a growing outer cortex and inner core to investigate its developmental mechanism. Analytical interpretations of differential growth of the brain model provide preliminary insight into critical growth ratios for instability and crease formation of the developing brain. Since the analytical approach cannot predict the evolution of cortical complex convolution after instability, non-linear finite element models are employed to study the crease formation and secondary morphological folds of the developing brain. Results demonstrate that the growth ratio of the cortex to core of the brain, the initial thickness, and material properties of both cortex and core have great impacts on the morphological patterns of the developing brain. Lastly, we discuss why cortical folding is highly correlated and consistent by presenting an intriguing gyri-sulci formation comparison.

A unifying framework to quantify the effects of substrate interactions, stiffness, and roughness on the dynamics of thin supported polymer films.

Changes in the dynamics of supported polymer films in comparison to bulk materials involve a complex convolution of effects, such as substrate interactions, roughness, and compliance, in addition to film thickness. We consider molecular dynamics simulations of substrate-supported, coarse-grained polymer films where these parameters are tuned separately to determine how each of these variables influence the molecular dynamics of thin polymer films. We find that all these variables significantly influence the film dynamics, leading to a seemingly intractable degree of complexity in describing these changes. However, by considering how these constraining variables influence string-like collective motion within the film, we show that all our observations can be understood in a unified and quantitative way. More specifically, the string model for glass-forming liquids implies that the changes in the structural relaxation of these films are governed by the changes in the average length of string-like cooperative motions and this model is confirmed under all conditions considered in our simulations. Ultimately, these changes are parameterized in terms of just the activation enthalpy and entropy for molecular organization, which have predictable dependences on substrate properties and film thickness, offering a promising approach for the rational design of film properties.

Interrogating Micro-Scale Spatial Variation in the Performance and Properties of Photoelectrodes with in Situ Scanning Probe Techniques

Photoelectrochemical (PEC) water splitting is a promising route to solar-driven H2 production, but the efficiency and stability of semiconducting photoelectrodes must be improved for commercialization of this technology. Among the many challenges of developing and optimizing durable and efficient photoelectrode materials are the inherent complexities that arise from the heterogeneous nature of many real-world materials. For example, the surface of a given photoelectrode can possess substantially different crystal phases and orientations, composition, morphology, dopant distribution, defect structures, and more. Different structures and compositions can have vastly different optical, electronic, and catalytic properties, resulting in a photoelectrode whose macro-scale properties and performance is often a complex convolution of the properties and performance of the micro- and/or nano-scale regimes that comprise it. Being able to establish the structure-property relations that exist on these heterogeneous surfaces is therefore of great importance for optimizing photoelectrode performance. Fortunately, there are several complementary experimental techniques that can be used to analyze the spatial variation in performance and properties of photoelectrodes at the micro- or nano-scale. In this work, we have used two scanning probe techniques to investigate spatial variation in the optical, electronic, and catalytic properties of p-Si-based photocathodes (Fig. 1). The first technique is scanning photocurrent microscopy (SPCM), a technique in which a laser beam is focused onto the photoelectrode surface, resulting in a “local” photocurrent that is measured by a potentiostat. Using a nano- or micro-positioning stage, the position of the laser beam is scanned across the sample surface while recording change in local photocurrent. The second technique employed in this work is scanning electrochemical microscopy (SECM), in which an ultramicroelectrode (UME) is used to monitor spatial variation in the concentration of product species evolved from the photoelectrode surface. For our work on p-Si photocathodes, a positive potential is applied to the UME such that the H2 evolved from the photoelectrode surface is oxidized, resulting in an electrical current in the UME (JUME). This current is proportional to the amount of H2 evolved from the photoelectrode surface in the vicinity of the UME and therefore strongly reflects the catalytic activity of the surface positioned beneath it. As a platform for these SPCM and SECM investigations, our work has focused on the study of p-Si-based photocathodes for H2 evolution based upon the metal-insulator-semiconductor (MIS) architecture that have demonstrated great potential for highly efficient and stable solar water splitting.(1,2,3,4) Our studies have involved both planar (Fig. 2c) and 3D-structured MIS photoelectrodes (Fig. 2a). SPCM and SECM have been used to investigate spatial variation in performance relating to 3D structuring (Fig. 2b), intentionally introduced defects (Fig. 2d), and more. Knowledge gained from these micro-scale measurements is shown to be invaluable for i.) engineering more efficient photoelectrodes, and ii.) developing a deeper understanding of fundamental optical, electronic, and catalytic phenomena in MIS photoelectrodes. In addition to presenting results from the application of SPCM and SECM to the study of p-Si MIS photocathodes, this talk will also highlight the challenges and opportunities for applying these techniques more broadly to the field of photoelectrochemistry. Figure 1

Fundamental edge broadening effects during focused electron beam induced nanosynthesis.

The present study explores lateral broadening effects of 3D structures fabricated through focused electron beam induced deposition using MeCpPt(IV)Me3 precursor. In particular, the scaling behavior of proximity effects as a function of the primary electron energy and the deposit height is investigated through experiments and validated through simulations. Correlated Kelvin force microscopy and conductive atomic force microscopy measurements identified conductive and non-conductive proximity regions. It was determined that the highest primary electron energies enable the highest edge sharpness while lower energies contain a complex convolution of broadening effects. Moreover, it is demonstrated that intermediate energies lead to even more complex proximity effects that significantly reduce lateral edge sharpness and thus should be avoided if desiring high lateral resolution.

О представлении операторов обобщённого дифференцирования Гельфонда — Леонтьева в односвязной области

Some new properties of the multiplier are determined. A class of simply connected regions whose multiplier is a connected set is described. This class is characterized by the availability of spirals in a multiplier. Let the Gelfond — Leontiev generalized differentiation operator be continuous in the space of the analytic functions in simply connected region G of a complex plane. It is known to be presented as an operator of general complex convolution. The convolution kernel is generated by the many-valued function of one variable. The set M(G) with the property M(G)·G ⊆ G is called multiplier G. Let the region multiplier be connected, and it does not align with identity. It is proved in the paper that the functions under consideration will be univalent under these conditions. If multiplier G is unconnected, then there is always a generalized differentiation Gelfond—Leontiev operator with a many-valued generating function.

ON PRESENTATION OF LINEAR OPERATORS COMMUTING WITH DIFFERENTIATION IN SIMPLY-CONNECTED DOMAIN

Let   H G be a space of analytic functions of one variable in simply - connected domain G of the complex plane. It is known that a linear complex convolution operator is generated by a one - variable analytic function, a multivalued one in general. A known problem when all such functions are single - valued is solved. As it turned out, the solution to the problem is connected with the geometry of G domain. Set   s G with property   s G G G   is termed re sidue of G domain. A class of simply connected regions whose residue is a connected set is described. Let the linear operator be continuous in function space, analytical in simply - connected domain G, and let it commute with diffe rentiation. Then it can be reduced to a complex convoluti on operator. It is proved that the function generating such an operator will always be single - valued for regions with a connected residue. When the residue of region G is not connected, there is always a complex convolution operator with a multivalued func tion generating a kernel.

Measurements of the neutron spectrum on the Martian surface with MSL/RAD

The Radiation Assessment Detector (RAD), onboard the Mars Science Laboratory (MSL) rover Curiosity, measures the energetic charged and neutral particles and the radiation dose rate on the surface of Mars. An important factor for determining the biological impact of the Martian surface radiation is the specific contribution of neutrons, with their deeper penetration depth and ensuing high biological effectiveness. This is very difficult to measure quantitatively, resulting in considerable uncertainties in the total radiation dose. In contrast to charged particles, neutral particles (neutrons and gamma rays) are generally only measured indirectly. Measured spectra are a complex convolution of the incident particle spectrum with the detector response function and must be unfolded. We apply an inversion method (based on a maximum likelihood estimation) to calculate the neutron and gamma spectra from the RAD neutral particle measurements. Here we show the first spectra on the surface of Mars and compare them to theoretical predictions. The measured neutron spectrum (ranging from 8 to 740 MeV) translates into a radiation dose rate of 14±4μGy/d and a dose equivalent rate of 61±15μSv/d. This corresponds to 7% of the measured total surface dose rate and 10% of the biologically relevant surface dose equivalent rate on Mars. Measuring the Martian neutron and gamma spectra is an essential step for determining the mutagenic influences to past or present life at or beneath the Martian surface as well as the radiation hazard for future human exploration, including the shielding design of a potential habitat.

Maxwell stress-induced flow control of a free surface electro-osmotic flow in a rectangular microchannel

Multiphase flow control is a challenging task in microfluidic systems. Application of such ideas in electro-osmotic actuation of multiphase flows, which involves a complex convolution of phenomena ranging from electro-chemistry to hydrodynamics, is even more tricky. Most of the existing studies in the field have limited their scope to the thin electric double layer (EDL) limit, where the role of ionic space charge distribution in the EDL is simplified to provide a slip velocity boundary condition at the substrate, and the role of the fluid–fluid interface is limited to continuity of velocity and hydrodynamic shear stress. In this study, electro-osmotic flow of two immiscible fluids, an electrolytic solution and an inert gas, are studied in a rectangular microchannel and the role of interfacial potential and Maxwell stress-generated dynamics is explored in a wide range of EDL thicknesses. A net stress term is used in the transport equations which includes the electric effects by Maxwell stress as well as the hydrodynamic stress. It is observed that the free surface, depending upon its potential may enhance the fluid velocity or act as a rigid wall. With the help of two-dimensional velocity contour plots, the role of various flow parameters on flow profile is discussed. Further, a parametric analysis of flow rate gives interesting insights into the flow rate reversal and control in such microfluidic devices.

The role of drift, diffusion, and recombination in time‐resolved photoluminescence of CdTe solar cells determined through numerical simulation

AbstractTime‐resolved photoluminescence (TRPL) measurements are one of the key metrics available to determine the minority‐carrier lifetime in the absorber layer of direct band gap photovoltaic devices. Direct measurement of the minority‐carrier lifetime is essential to understanding the impact of changes in deposition and processing on material quality. Unfortunately, the TRPL signal is determined by a complex convolution of multiple physical factors including bulk carrier lifetime, interface recombination velocity, electric field, doping density, photo‐excited carrier density, and carrier mobility. To gain clarity, we have used numerical simulations to analyze the carrier dynamics after a CdTe device is illuminated with a short light pulse. After the light pulse, the photo‐generated carriers undergo complex dynamics including drift, diffusion, interface, and bulk recombination. In this work, we develop a new formalism that enables much greater insight into which factors dominate the TRPL decay dynamics. By breaking down the carrier dynamics into drift, diffusion, and recombination terms, we have developed six‐factor, four‐factor, and two‐factor analyses that provide clear understanding of which physical factors dominate the decay dynamics under various conditions and at different times during the decay. We show that in a typical CdTe device under the typical experimental conditions used in our laboratories, the faster part of the decay is dominated by charge separation, whereas the slower part is dominated by carrier recombination. Therefore, under the conditions investigated in this study, the slower part of the decay is a better parameter to explain the defect density in the CdTe layer. Copyright © 2013 John Wiley & Sons, Ltd.

Approximation properties of bivariate complex q-Bernstein polynomials in the case q > 1

In the paper, we discuss convergence properties and Voronovskaja type theorem for bivariate q-Bernstein polynomials for a function analytic in the polydisc \({D_{{R_1}}} \times {D_{{R_2}}} = \{ z \in C:\left| z \right| < {R_1}\} \times \{ z \in C:\left| z \right| < {R_1}\} \) for arbitrary fixed q > 1. We give quantitative Voronovskaja type estimates for the bivariate q-Bernstein polynomials for q > 1. In the univariate case the similar results were obtained by S.Ostrovska: q-Bernstein polynomials and their iterates. J. Approximation Theory 123 (2003), 232–255, and S.G.Gal: Approximation by Complex Bernstein and Convolution Type Operators. Series on Concrete and Applicable Mathematics 8. World Scientific, New York, 2009.