Minimum Step Research Articles

An Adaptive Method for Numerical Differentiation of Difficult-to-Compute Functions

An adaptive approach to the numerical differentiation of difficult-to-compute functions is considered. Complex dependencies, which are the result of multiple superpositions of functions or the product of various algorithmic processes, are knowingly difficult to study directly. To establish the nature of the behavior of such dependencies, one has to resort to numerical analysis. One of the important characteristics of functions is a derivative, which indicates the direction and rate of change of a dependence. However, with difficult-to-compute functions, the available a priori information is not always sufficient to achieve the appropriate accuracy of the solution by known means. The loss of accuracy occurs due to the accumulation of round-off errors that grow in proportion to the number of calculated values of a function. In this case, it is necessary to pass on to the posterior approach in order to determine the behavior of the function and move away from the scheme of equidistant nodes, relying on an adaptive way of studying the local situation in the domain of the function. This paper implements an adaptive method for finding derivatives of a function with a minimum of restrictive requirements for the class of functions and the form of their assignment. Due to this, the costs of calculating the function have been significantly reduced with the result that their number has been brought to almost the optimal level. At the same time, the amount of RAM used has sharply decreased. There is no need for a preliminary analysis of the problem of establishing the class of the function under study, in the involvement of special functions or transformation of initial conditions for using standard tables of weight coefficients, etc. For research, it is enough to assign a continuous and bounded function on a fixed segment and a minimum step, which is indirectly responsible for ensuring the required accuracy of differentiation. The effectiveness of the proposed method is demonstrated on a number of test examples. The developed method can be used in more complex problems, for example, in solving some types of differential and integral equations, as well as for a wide range of optimization problems in a wide variety of areas of applied analysis and synthesis.

Bioremediation of Chromium by Microorganisms and Its Mechanisms Related to Functional Groups

Heavy metals generated mainly through many anthropogenic processes, and some natural processes have been a great environmental challenge and continued to be the concern of many researchers and environmental scientists. This is mainly due to their highest toxicity even at a minimum concentration as they are nonbiodegradable and can persist in the aquatic and terrestrial environments for long periods. Chromium ions, especially hexavalent ions (Cr(VI)) generated through the different industrial process such as tanneries, metallurgical, petroleum, refractory, oil well drilling, electroplating, mining, textile, pulp and paper industries, are among toxic heavy metal ions, which pose toxic effects to human, plants, microorganisms, and aquatic lives. This review work is aimed at biosorption of hexavalent chromium (Cr(VI)) through microbial biomass, mainly bacteria, fungi, and microalgae, factors influencing the biosorption of chromium by microorganisms and the mechanism involved in the remediation process and the functional groups participated in the uptake of toxic Cr(VI) from contaminated environments by biosorbents. The biosorption process is relatively more advantageous over conventional remediation technique as it is rapid, economical, requires minimal preparatory steps, efficient, needs no toxic chemicals, and allows regeneration of biosorbent at the end of the process. Also, the presence of multiple functional groups in microbial cell surfaces and more active binding sites allow easy uptake and binding of a greater number of toxic heavy metal ions from polluted samples. This could be useful in creating new insights into the development and advancement of future technologies for future research on the bioremediation of toxic heavy metals at the industrial scale.

Controlled Synthesis of Metal-Organic Frameworks in Scalable Open-Porous Contactor for Maximizing Carbon Capture Efficiency.

Metal–organic frameworks (MOFs) are a class of microporous materials that have been highlighted with fast and selective sorption of gas molecules; however, they are at least partially unstable in the scale-up process. Here, we report a rational shaping of MOFs in a scalable architecture of fiber sorbent. The long-standing stability challenge of MOFs was resolved by using stable metal oxide precursors that are subject to controlled surface oxide dissolution-growth chemistry during the Mg-based MOF synthesis. Highly uniform MOF crystals are synthesized along with the open-porous fiber sorbents networks, showing unprecedented cyclic CO2 capacities in both flue gas and direct air capture (DAC) conditions. The same chemistry enables an in situ flow synthesis of Mg-MOF fiber sorbents, providing a scalable pathway for MOF synthesis in an inert condition with minimal handling steps. This modular approach can serve both as a reaction stage for enhanced MOF fiber sorbent synthesis and as a “process-ready” separation device.

Standard Validation Protocol for Selected Ion Flow Tube Mass Spectrometry Methods Applied to Direct Headspace Analysis of Aqueous Volatile Organic Compounds.

Analysis of volatile organic compounds (VOCs) in water is conventionally conducted using gas chromatography (GC)-based methods, for which sample preparation demands are relatively high and throughput is relatively low due to the time taken to achieve chromatographic separation. Direct mass spectrometry (DMS) techniques such as selected ion flow tube mass spectrometry (SIFT-MS) have potential to analyze water headspace (HS) at high sensitivity with minimal sample preparation, eliminating preconcentration/purging and/or water management steps. However, the dearth of guidance for validation of DMS methods is an impediment to their adoption in routine analysis. This study applies and adapts an internationally recognized pharmaceutical industry guidance document for method validation to a prototypical SIFT-MS headspace analysis method for 17 toxic VOCs in water. The approach to validation is, however, applicable to any routine analysis conducted using SIFT-MS, and very likely to any methods developed using other DMS techniques. For the method developed and validated here, linearities (as measured by the linear regression coefficient, R2) were better than 0.990 for all compounds. Repeatability (measured using relative standard deviation, RSD) was less than 10% for all compounds. Similar method performance was observed for accuracy and recovery. The performance criteria achieved by this HS-SIFT-MS method suggest it has potential application in environmental and pharmaceutical routine analyses, perhaps as a rapid screening tool.

One-to-one innervation of vocal muscles allows precise control of birdsong

The motor control resolution of any animal behavior is limited to the minimal force step available when activating muscles, which is set by the number and size distribution of motor units (MUs) and muscle-specific force. Birdsong is an excellent model system for understanding acquisition and maintenance of complex fine motor skills, but we know surprisingly little about how the motor pool controlling the syrinx is organized and how MU recruitment drives changes in vocal output. Here we developed an experimental paradigm to measure MU size distribution using spatiotemporal imaging of intracellular calcium concentration in cross-sections of living intact syrinx muscles. We combined these measurements with muscle stress and an invitro syrinx preparation to determine the control resolution of fundamental frequency (fo), a key vocal parameter, in zebra finches. We show that syringeal muscles have extremely small MUs, with 40%-50% innervating ≤3 and 13%-17% innervating a single muscle fiber. Combined with the lowest specific stress (5mN/mm2) known to skeletal vertebrate muscle, small force steps by the major fo controlling muscle provide control of 50-mHz to 7.3-Hz steps per MU. We show that the song system has the highest motor control resolution possible in the vertebrate nervous system and suggest this evolved due to strong selection on fine gradation of vocal output. Furthermore, we propose that high-resolution motor control was a key feature contributing to the radiation of songbirds that allowed diversification of song and speciation by vocal space expansion.

Comparative study of novel green UV-spectrophotometric platforms for simultaneous rapid analysis of flumethasone pivalate and clioquinol in their combined formulation

Flumethasone pivalate (FP) and clioquinol (CL) formulation was developed as a prodigious remedy to cure the external ear inflammatory disorders. So, the current research introduces five smart and novel UV-spectrophotometric platforms relying on minimal mathematical manipulation steps for simultaneous green analysis of FP and CL with no preliminary separation in their formulation that suffered from the high difference of their ratio and severe spectral overlapping. These platforms involved dual-wavelength, first derivative ratio, Fourier self-deconvolution, area under the curve, and bivariate methods. The suggested platform’ linearity was observed over the concentration range of 3–42 µg/ml for FP and 1.5–8 µg/ml for CL. All suggested platforms were validated according to ICH recommendations regarding accuracy, precision, repeatability, and selectivity producing satisfactory results within the accepted limits. These platforms were represented as rapid, green, and cheap alternatives to the reported chromatographic method due to lower solvent consumption and waste generation. Furthermore, they improved the determination sensitivity of the studied drugs and enhanced the recorded data signals or its spectral resolution by the newly introduced Fourier self-deconvoluted method. The statistical comparison between the results of the suggested platforms with each other and with those of the reported method showed no significant differences between them.

A Numerical Implementation of the Finite-Difference Algorithm for solving Conserved Cahn–Hilliard Equation

Phase field modelling technique is critical to contextualizing material microstructures and to represent the composition of microstructural evolution. This work utilizes the periodic boundary condition to numerically solve the Cahn-Hilliard equation. To enhance computation and improve flexibility, Python programming language is introduced to develop and implement the proposed approach. The numerical implementation considered a hypothetical binary system of element A and B using the finite difference method on the conserved order parameter. The work also validates the concentration dependent gradient of the system and the energy coefficient which serves as the first step to show spinodal decomposition in a system. The implementation involves solving the Cahn Hillard equation in multi-dimensions capturing minimal time steps evolution, thus serving as an esplanade, an approach into crystallization. The system shows that the element A and B can be used to describe evolution phases alpha (α) and beta (β) through a persisting thermodynamic variable to form a single phase. The time-dependent phase morphology of the studied system, and the concentration and mobility effects are discussed in this paper.

(Invited) Layer Transfer Technology for Stacked Multi-Channel Semiconductor-on-Insulator Platform

Continuous scaling of device dimension pushed Si channel to its physical limit, alternative high mobility channels such as (Si)Ge and (In)GaAs have been considered to replace Si to further enhance CMOS performance. In the meantime, ultrathin body (UTB) semiconductor-on-insulator is compulsory structure for improved gate control and immunity against short channel effects in the ultimately scaled high performance and low power dissipation CMOS. To realize stacked multi- channel semiconductor-on-insulator platform on current mainstream Si wafers, layer transfer technology [1-3] utilizing direct bonding and selective etching was developed to integrate (Si)Ge or (In)GaAs channels on Si, showing great potential for ultimate device structures with heterogeneous integration.Figure 1(a) is the process flow for integrating InGaAs channel onto SiGe-on-insulator (SGOI) structure utilizing layer transfer technology [4]. It started with bottom SGOI pMOSFET fabrication. The SGOI structure was realized by 2-step Ge condensation technique, resulting in Ge content of 70%. After high k metal gate process, self-aligned Ni-SiGe alloy was formed as S/D metal. Subsequently, SiO2 interlayer was deposited by CVD, followed by CMP planarization. Then, InGaAs grown on InP was directly bonded onto SiO2 and InP substrates were selectively etched away. Finally, the top InGaAsOI nMOSFET fabrication and metal interconnection completed the CMOS fabrication. Fig. 1(b) shows the cross-sectional TEM images of fabricated InGaAs/SiGe channel stacked CMOS. Well aligned top and bottom devices are seen without any distinct defects.Figures 2 is a schematic flow for fabricating Ge/Si double channel-on-insulator structure by low temperature hetero-layer bonding technology (LT-HBT). The technology starts with the preparation of donor wafers (Fig. 2(a)) for the top Ge channel layer and host wafers (Fig. 2(b)) for the bottom Si channel layer. For donor wafers, a 200-nm-thick Ge was epitaxially grown on SOI wafer by reduced pressure CVD. After CMP planarization, ALD SiO2 is deposited onto Ge. For host wafers, implantation and dopant activation were carried out, followed by chemical treatment for Si oxidation. After surface activation by room temperature chemical treatment (Fig. 2(c)), the direct wafer bonding of both SiO2 surface was performed at 200 °C in a press machine (Fig. 2(d)). Then, the Si substrate of the donor wafer was removed with deep RIE. At this time, the BOX layer of the donor wafer serves as an etch-stop layer. Subsequently, the BOX layer and thin Si layer of the donor wafer were removed selectively in HF and TMAH solution, respectively (Fig. 2(f)). To precise control the top Ge channel thickness, a series of low damage etching process was adapted to thin down Ge (Fig. 2(g)). The realized double channel structure is fully isolated with an insulating insertion layer,[5] which is very promising for realizing novel complementary FET (CFET) with minimum process steps. The cross-sectional TEM image of Ge/Si stacked channel of CFET after high k metal gate process is demonstrated in Fig. 2(h). Even more multiple stacks can be realized by using LT-HBT. A vertically stacked three-layer structure with 2 bottom Si layers and 1 top Ge layers is also demonstrated using SOI-based donor wafers in Fig. 3, indicating the highly integrated density channel structure is possible. The feasibility of layer transfer technology has been proved for multi-channel structure with high mobility channels for N2 node and beyond. Acknowledgement This work was supported by JST Japan-Taiwan Collaborative Research Program, Grant Number JPMJKB1902, Japan and the Ministry of Science and Technology under Grant Number MOST-109-2628-E-492-001-MY3, 109-2923-E-492-001-MY3, 107-2221-E-492-016-MY3.

Fast Current Control Without Computational Delay by Minimizing Update Latency

This letter proposes a fast current control scheme for ac drives by minimizing the latency from current sampling to the updation of a pulsewidth-modulation (PWM) command. By reconstructing the architecture of a linear controller, the minimal necessary steps to obtain the output voltage are deduced as the <i>primary calculation</i>, and the other computation work of the current loop is done in the <i>postcalculation</i> after updating the PWM command. With the proposed method, the computational delay is reduced with negligible loss in the available modulation index, and a higher stability margin or system bandwidth is realized. Also, the developed controller structure exhibits inherited antiwindup characteristics. The technique has been validated by experimental investigations on a permanent magnet synchronous motor.

Direct oligonucleotide sequencing with nanopores

Third-generation DNA sequencing has enabled sequencing of long, unamplified DNA fragments with minimal steps. Direct sequencing of ssDNA or RNA gives valuable insights like base-level modifications, phosphoramidite synthesis yield estimates and strand quality analysis, without the need to add the complimentary strand. Direct sequencing of single-stranded nucleic acid species is challenging as they are non-compatible to the double-stranded sequencing adapters used by manufacturers. The MinION platform from Oxford Nanopore Technologies performs sequencing by passing single-strands of DNA through a layer of biological nanopore sensors; although sequencing is performed on single-strands, the recommended template by the manufacturer is double-stranded. We have identified that the MinION platform can perform sequencing of short, single-strand oligonucleotides directly without amplification or second-strand synthesis by performing a single annealing step before library preparation. Short 5’ phosphorylated oligos when annealed to an adapter sequence can be directly sequenced in the 5' to 3' direction via nanopores. Adapter sequences were designed to bind to the 5’ end of the oligos and to leave a 3’ adenosine overhang after binding to their target. The 3’ adenosine overhang of the adapter and the terminal phosphate makes the 5’ end of the oligo analogous to an end-prepared dsDNA, rendering it compatible with ligation-based library preparation for sequencing. An oligo-pool containing 42,000, 120 nt orthogonal sequences was phosphorylated and sequenced using this method and ~90% of these sequences were recovered with high accuracy using BLAST. In the nanopore raw data, we have identified that empty signals can be wrongly identified as a valid read by the MinION platform and sometimes multiple signals containing several strands can be fused into a single raw sequence file due to segmentation faults in the software. This direct oligonucleotide sequencing method enables novel applications in DNA data storage systems where short oligonucleotides are the primary information carriers.

Real-time Likelihood-free Inference of Roman Binary Microlensing Events with Amortized Neural Posterior Estimation

Abstract Fast and automated inference of binary-lens, single-source (2L1S) microlensing events with sampling-based Bayesian algorithms (e.g., Markov Chain Monte Carlo, MCMC) is challenged on two fronts: the high computational cost of likelihood evaluations with microlensing simulation codes, and a pathological parameter space where the negative-log-likelihood surface can contain a multitude of local minima that are narrow and deep. Analysis of 2L1S events usually involves grid searches over some parameters to locate approximate solutions as a prerequisite to posterior sampling, an expensive process that often requires human-in-the-loop domain expertise. As the next-generation, space-based microlensing survey with the Roman Space Telescope is expected to yield thousands of binary microlensing events, a new fast and automated method is desirable. Here, we present a likelihood-free inference approach named amortized neural posterior estimation, where a neural density estimator (NDE) learns a surrogate posterior as an observation-parameterized conditional probability distribution, from pre-computed simulations over the full prior space. Trained on 291,012 simulated Roman-like 2L1S simulations, the NDE produces accurate and precise posteriors within seconds for any observation within the prior support without requiring a domain expert in the loop, thus allowing for real-time and automated inference. We show that the NDE also captures expected posterior degeneracies. The NDE posterior could then be refined into the exact posterior with a downstream MCMC sampler with minimal burn-in steps.

Rapid Access to N-Protected Sulfonimidoyl Fluorides: Divergent Synthesis of Sulfonamides and Sulfonimidamides.

Herein we report a practical and efficient copper-catalyzed approach for the conversion of various arenediazonium salts to the corresponding N-protected sulfonimidoyl fluorides. This operationally simple protocol tolerates a wide range of functional groups and can be applied to the late-stage modification of complex bioactive molecules. Furthermore, pharmaceutically important primary sulfonamides and sulfonimidamides derived from these valuable N-protected sulfonimidoyl fluoride units were prepared in minimal synthetic steps.

Modeling Group II Chaperonin “Heat Shock” Protein Structure: pH and temperature dependency Piyasi Ghosh1,2 Vivek Govind Kumar1,3 Mahmoud Moradi3 Ruben Michael Ceballos1,2,4 University of Arkansas, Cell and Molecular Biology Program University of Arkansas, Department of Biological Sciences University of Arkansas, Department of Chemistry and Biochemistry Arkansas Center for Space and Planetary Sciences Program

Group II chaperonins or “heat shock proteins” (HSPs) are expressed in hyperthermophilic archaea of the family Sulfolobaceae. Three chaperonins designated as HSPα, HSPβ, and HSPγ have been reported and serve as subunits in the formation of nonameric double-ring (18-mer) complexes. HSP complexes in nature function to protect cellular proteins (e.g., enzymes) during thermal shock and, perhaps, other stressors such as pH flux. HSPα and HSPβ are stoichiometrically favored in HSP complex formation, whereas the HSPγ subunit is more rarely found as a constituent subunit. In vitro, HSPα homomers, HSPβ homomers, and HSPα/HSPβ heteromers will form in the presence of ATP and divalent cations (e.g., Mg++). HSP complexes feature a central pore that leads to an internal cavity. Pore openings are found at both apical and basal extremities of the 18-mer complex. It has been suggested that HSPs have “opened” and “closed” states. Whether the pore is “opened” or “closed” is a function of conformational changes in the individual HSP subunits that lead to subunit rearrangements in the complex. Since the thermotolerant nature and protective function of HSP complexes is likely based on the ability of the system to open and close, it is of interest to understand the changes in subunit ultra-structure that mediate switching between to these two conformational states. In this study, molecular dynamics simulations were conducted test the relative stability of HSPα versus HSPβ and to determine how HSPα and HSPβ tertiary structure may be impacted by temperature and pH. SWISS-MODEL and PyMOL were used to generate the 3-D HSP structures. CHARMM-GUI solution builder was used to solvate the modeled structures in a “water box” as an energy minimization step prior to running simulations, which were performed in Nanoscale Molecular Dynamics (NAMD). Output was later visualized using Visual Molecular Dynamics (VMD). We demonstrate that HSP a-helical structures change conformation as pH drops from neutral to acidic. Our data suggest that changes in subunit structure under thermal shock lead to changes in pore diameter; however, it is unclear if pH flux influences opening and closing of the HSP complex pore. These results demonstrate a plausible biophysical mechanism by which group II chaperonin complexes change conformation while serving client proteins.

A novel synthesis of sulfurized magnetic biochar for aqueous Hg(II) capture as a potential method for environmental remediation in water

Due to public health threats resulting from mercury (Hg) and its distribution in the food chain, global restrictions have been placed on Hg use and emissions. Biochar is a porous, carbonaceous adsorbent typically derived from waste biomass or organic matter, making it an eco-friendly material for aqueous mercury (Hg(II)) control. Functionalization of biochar can improve performance in pollution control applications. In this work, carbonization, magnetization, and sulfurization of biochar were combined into a single heating step to prepare sulfurized magnetic biochar (SMBC) for Hg(II) removal from water. Results indicate that SMBC prepared at 600 °C adsorbed 8.93 mg/g Hg(II), more than materials prepared at 400, 500, 700, 800, and 900 °C. Additionally, Hg(II) adsorption onto SMBC was 53.0% and 11.5% greater than onto magnetic biochar (MBC) and biochar (BC), respectively. Hg(II) adsorption is shown to be favorable in acidic conditions (pH 3.5–5), thermodynamically spontaneous, and endothermic. Adsorption results fit the pseudo-second-order (R2 = 0.990 and the sum of squared error (SSE) = 5.382) and external mass transfer (R2 = 0.971 and SSE = 9.422) models. The partitioning coefficients were 4.964 mg/g/μM in freshwater, 0.176 mg/g/μM in estuary water, and 0.275 mg/g/μM in seawater, highlighting the importance of salinity in environmental remediation applications. In summary, SMBC can be readily prepared with minimal processing steps. The product is a robust adsorbent for Hg(II), and it can potentially be applied to remediate contaminated water/sediment/soil in the future.

Electrosynthesis of HKUST-1 with Flow-Reactor Post-Processing

Electrochemical synthesis has been proposed as an efficient method for cost-effective and large-scale production of metal-organic frameworks (MOFs). This work investigates the combined electrochemical synthesis with flow synthesis post-treatment for the production of high surface area HKUST-1. The electrochemical synthesis process used in the experimental work did not require additional electrolytes or washing of the synthesis product. Batch electrosynthesis and electrosynthesis with flow synthesis were compared for the quality of the product using Brunauer–Emmett–Teller (BET) surface area, X-ray diffraction (XRD), and scanning electron microscopy (EIS). Batch electrosynthesis in 0.01 M benzene-1,3,5-tricarboxylic acid (H3BTC) solution produced HKUST-1 with BET surface area of 1550 m2/g which was increased further to 1716 m2/g with post-flow-synthesis treatment. The greatest change in surface area after flow processing was observed when using 0.78 M H3BTC, with corresponding surface areas of 481 m2/g and 1531 m2/g. According to SEM and BET results, the product purity improved during the post-flow-synthesis treatment. The proposed method enables continuous flow synthesis of high-quality MOFs with minimal purification steps.

Wars, Pandemics and Emergencies: What Can History Tell Us about Executive Power and Surveillance in Times of Crisis?

In the fight against coronavirus, the Australian government has enacted a series of measures that represent an expansion of executive powers. These include the use of smartphone contact-tracing technology, mandatory isolation arrangements, and the closure of businesses. Critics have expressed concerns about the long-term implications of these measures upon individual rights.?This article will analyse the validity of such concerns in the context of other historical uses of executive power in Australia in times of crisis: during the Spanish Flu pandemic of 1918, the First and Second World Wars, and the ‘War on Terror’ post-September 2001. Drawing its conclusions from these historical precedents, the article argues that clear legislative safeguards are a minimum necessary step both to prevent police and governmental abuse of privacy, and to foster and maintain trust in the government’s ability to manage their ‘emergency’ powers in a manner consistent with human rights.

A flexible shaft based travelling wave ultrasonic motor with high-precision positioning characteristics

To improve positioning precision of the traveling wave ultrasonic motor (USM), a flexible shaft was used, and the structure was redesigned to reduce the fluctuations of step angles and speed. The start and stop response performances of the motor were analyzed theoretically and tested by a high-resolution test rig. The step characteristics were calculated, which showed the minimum step angle is below 0.20″ under different torques. The positioning process included two modes: continuous mode and step mode. In continuous mode, the speed of the motor was controlled by PID control based on the tests of frequency-speed characteristic of the motor. In step mode, the step characteristics of the motor was tested under different load torques and applied different lengths of driving voltage to find the minimum of step angle. From the tests, the step angle increases rapidly with the periods of driving voltage and the single-step angle fluctuations of the motor with flexible shaft is much less than that of motor with normal shaft. Finally, the positioning performances of USM were tested. The results showed that the minimum positioning error of the motor with flexible shaft could achieve 0.37″ (1.79 μrad) and the time costed was below 1 s.

Determining the Minimum Scan Step of an Electronically Scanned Antenna

Introduction. Electronically scanned antennas (ESA) appeared about a century ago. Although the methods of their design and production have been sufficiently studied, some individual parameters are yet to be revealed. One of such parameters is the minimum step of movement, along with a related parameter – the accuracy of beam alignment in a given direction. From the electrodynamic problem of radiation, it is obvious that the step is associated with the number of radiators and the accuracy of phase adjustment in analogue phase shifters, or with the quantization step in the case of using phase shifters with a discrete step.Aim. To discover a connection between the design parameters of ESA and the step of beam steering; to investigate the dependence between the step and the parameters of the phase shifter and types of beam forming phased array circuits; to create a mathematical apparatus for calculating the minimum step of beam movement for the sum and difference radiation patterns.Materials and methods. Analytical relations were determined for calculating the step depending on the geometric dimensions and location of the radiators. A software application was developed for calculating radiation patterns. A software and hardware complex was designed for beam control of an experimental C-band ESA.Results. A method was developed for calculating the minimum step of ESA scanning. Mathematical relations for calculating the minimum step and accuracy of the ESA beam setting were obtained. A comparison of the experimental and theoretical data on the minimum step of movement of the sum and difference beams of a C-band ESA with the ratio D/λ=10 in the X coordinate and D/λ=5 in the Y coordinate showed good agreement.Conclusion. The created mathematical apparatus makes it possible to calculate the minimum step of electron beam scanning with sufficient accuracy. The experimentally measured steps of the beam movement for an array of 144 elements confirmed the obtained analytical relationships. In an ESA with a small number of elements (N &lt; 10), the minimum step of movement can be variable. The theoretically achievable minimum step of beam movement is determined by the phase shift of the least significant bit of the phase shifter and the electrical length of the antenna aperture.

A fast saddle-point dynamical system approach to robust deep learning

Recent focus on robustness to adversarial attacks for deep neural networks produced a large variety of algorithms for training robust models. Most of the effective algorithms involve solving the min–max optimization problem for training robust models (min step) under worst-case attacks (max step). However, they often suffer from high computational cost from running several inner maximization iterations (to find an optimal attack) inside every outer minimization iteration. Therefore, it becomes difficult to readily apply such algorithms for moderate to large size real world data sets. To alleviate this, we explore the effectiveness of iterative descent–ascent algorithms where the maximization and minimization steps are executed in an alternate fashion to simultaneously obtain the worst-case attack and the corresponding robust model. Specifically, we propose a novel discrete-time dynamical system-based algorithm that aims to find the saddle point of a min–max optimization problem in the presence of uncertainties. Under the assumptions that the cost function is convex and uncertainties enter concavely in the robust learning problem, we analytically show that our algorithm converges asymptotically to the robust optimal solution under a general adversarial budget constraints as induced by ℓp norm, for 1≤p≤∞. Based on our proposed analysis, we devise a fast robust training algorithm for deep neural networks. Although such training involves highly non-convex robust optimization problems, empirical results show that the algorithm can achieve significant robustness compared to other state-of-the-art robust models on benchmark data sets.

Acheulian shortcuts: Cumulative culture and the use of handaxes as cores for the production of predetermined blanks

Handaxes, the hallmark of the Acheulian cultural complex, were occasionally recycled at the end of the Lower Paleolithic period as cores for the production of predetermined blanks. It appears that Late Acheulian flint knappers were well acquainted with both handaxe manufacture and the application of prepared core technologies. Following previous suggestions, we propose here that Late Acheulian knappers took advantage of handaxes convexities as a “shortcut” in the reduction sequence, enabling the detachment of predetermined blanks with minimal preparatory steps. The two phases of use of late Acheulian handaxes, first as handaxes and later as cores, were documented at several late Acheulian sites in the Old World and seem to be integral to late Acheulian lithic technologies and core reduction systems.The multi-layered late Acheulian site of Revadim and the newly discovered late Acheulian site of Jaljulia (both in Israel) yielded rich lithic assemblages typical of the late Acheulian Levant. The assemblages include handaxes but are mostly dominated by flake-production technologies and flake tools. Both sites provide late Acheulian evidence for what is termed here “proto-Levallois” core technology that later, in fully fledged form, characterized the Middle Paleolithic Levallois method. Here we consider handaxes transformed into cores for the production of predetermined blanks from these two sites and discuss this phenomenon in the framework of human cultural evolution. We further propose that these two key cultural markers, the Lower Paleolithic handaxes and the Middle Paleolithic Levallois method, which are linked by means of this special late Acheulian reduction strategy, can be seen as an early archaeological example of cumulative culture.