Approximate Rules Research Articles

Hebbian priming of human motor learning

Motor learning relies on experience-dependent plasticity in relevant neural circuits. In four experiments, we provide initial evidence and a double-blinded, sham-controlled replication (Experiment I-II) demonstrating that motor learning involving ballistic index finger movements is improved by preceding paired corticospinal-motoneuronal stimulation (PCMS), a human model for exogenous induction of spike-timing-dependent plasticity. Behavioral effects of PCMS targeting corticomotoneuronal (CM) synapses are order- and timing-specific and partially bidirectional (Experiment III). PCMS with a 2 ms inter-arrival interval at CM-synapses enhances learning and increases corticospinal excitability compared to control protocols. Unpaired stimulations did not increase corticospinal excitability (Experiment IV). Our findings demonstrate that non-invasively induced plasticity interacts positively with experience-dependent plasticity to promote motor learning. The effects of PCMS on motor learning approximate Hebbian learning rules, while the effects on corticospinal excitability demonstrate timing-specificity but not bidirectionality. These findings offer a mechanistic rationale to enhance motor practice effects by priming sensorimotor training with individualized PCMS.

Laser site-selective spectroscopy and magnetic hyperfine splittings of Ho3+ doped Y2SiO5

Laser site-selective spectroscopy and high-resolution absorption measurements have been used to determine 51 crystal-field energy levels for one of the Ho3+ centres in Y2SiO5. This centre is denoted as Site 2 and has been tentatively assigned as the seven-fold coordinated centre. High resolution absorption measurements reveal complex hyperfine patterns that obey an approximate selection rule. The application of a magnetic field along the three optical axes reveals the presence of avoided crossings below 0.5 Tesla, in both the ground and excited states.

The strain demand of reinforced concrete bridge columns under seismic loading

The steel in reinforced concrete (RC) members that form plastic hinges must possess sufficient strain capacity to dissipate seismic deformation demands. Unfortunately, there is limited information on the seismic strain demands of bridge column plastic hinges. Instead, designers rely on a perception of cyclic strain capacity that is an approximate rule of thumb. A standard methodology needs to be established for quantifying the strain demand on these structural members as a function of the expected seismic hazard. To develop this methodology, 1944 columns were analyzed with nonlinear time-history analyses (NLTHAs) using ground motions from a range of earthquakes. This study evaluates the strain demand on RC bridge columns by defining the relationship between the strain demand and earthquake intensity. The results of the model are defined in terms of the peak tensile strain of the reinforcing bar, [Formula: see text]. The earthquake intensity with the highest correlation to the [Formula: see text] was determined to be the elastic spectral displacement at the optimal period ([Formula: see text]), which is defined as 75% of the effective period. The relationship between [Formula: see text] and [Formula: see text] can be used to predict the strain demand for an RC bridge column at a given geographic location. Results are presented as a probability density function (PDF), representing strain demand, compared to a PDF of the column capacity. The intersection of the capacity curve and demand curve represents the maximum acceptable strain given as a function of [Formula: see text]. This methodology can help understand the demand placed on a structural system given a region’s seismicity.

Robust approximation rules for critical electric field of dielectric gas mixtures

A semi-analytic method for quickly approximating the density-reduced critical electric field for arbitrary mixtures of gases is proposed and validated. Determination of this critical electric field is crucial for designing and testing alternatives to SF6 for insulating high voltage electrical equipment. We outline the theoretical basis of the approximation formula from electron fluid conservation equations, and demonstrate how for binary mixtures the critical electric field can be computed from the transport data of electrons in the pure gases. We demonstrate validity of the method in mixtures of N2 and O2, and SF6 and O2. We conclude with an application of the method to approximate the critical electric field for mixtures of SF6 and HFO1234ze(E), which is a high interest mixture being actively studied for high voltage insulation applications.

A new health state assessment method for complex systems based on approximate belief rule base with attribute reliability

A new health state assessment method for complex systems based on approximate belief rule base with attribute reliability

Coronary artery calcium score percentiles: data from a single center in Turkey.

The coronary artery calcium (CAC) score is used in decision-making for preventive medications in patients with borderline clinical risk scores. Both absolute and percentile CAC scores can be used; however, a percentile CAC score is especially useful in young patients and women. The aim of this study is to present CAC score percentiles across age categories in women and men using a large database. Bilkent City Hospital database was screened for patients who underwent CAC score measurements between January 2021 and March 2022. Of the 4,487 patients, 546 were excluded due to 1) a history of coronary stent implantation or bypass surgery or 2) missing information regarding a history of revascularization or calcium scores. Therefore, the final study population included 3,941 participants. The percentiles for age categories within each sex were tabulated, and percentile plots were created for each sex using locally weighted scatterplot smoothing regression. The proportion of men included in the study was higher compared with that of women (57.09% vs. 42.91%). The mean age was 52.20 ± 11.11 years, and it was higher in women than in men (54.07 ± 10.47 vs. 50.80 ± 11.37, respectively; P < 0.001). A zero CAC score was observed in 2,381 (60.42%) patients; the percentage was higher in women than in men (68.60% vs. 54.27%; P < 0.001). When the cut-off value for the high-risk category was taken as the 75th percentile, a non-zero CAC score directly assigned a patient into the high-risk category in women aged <55 years and men aged <45 years. Percentile plots were also provided for each sex. In this large-scale study, including patients referred for CAC scoring and/or coronary computed tomography angiography, CAC score percentiles were provided for women and men across the selected age categories which may be in therapeutic decision-making. As an approximate rule of thumb, a non-zero CAC score corresponds to the high-risk category in women aged <55 years and in men aged <45 years.

From Maternal Preference to Shared Parenting: Child’s Well-Being. Lessons from the USA

The article concerns parenting after divorce or separation within the context of social changes. Special attention is paid to the principle of the welfare of the child, which is the most important criterion for deciding child custody. The child’s welfare is an open concept that grants a wide discretion to courts in choosing the best custodial arrangement for a child in a particular case. In this context, reference was made to the American experience on parenting after family break-up, separation or divorce. In the USA different theories were developed to explain which parenting model best fulfils the principle of the child’s welfare. This article discusses the tender years doctrine, primary care-taker preference, psychological parent doctrine and approximation rule. After a divorce, a mother was usually granted custody and a father paid child-support. He was placed in the background and excluded from the daily activities of his child. Currently, the theory of mother-nurturer and father-breadwinner is coming to an end; the father is no longer the only breadwinner responsible for providing the family an adequate standard for living, and the mother is no longer primarily responsible for the duties of childrearing and household chores. The changes taking place are reflected in struggling for equal treatment in the award of custody and abandoning the stereotypical approaches based on awarding custody automatically to mothers. A significant rise in the number of parents entering into joint custody arrangements is observed.

An abstract approach to Marcinkiewicz-Zygmund inequalities for approximation and quadrature in modulation spaces

We study the approximation and quadrature error of points that satisfy Marcinkiewicz-Zygmund inequalities. First, we investigate the use of Marcinkiewicz-Zygmund inequalities in an abstract Hilbert space for an abstract approximation and quadrature rule. The setting is then specified to Sobolev spaces induced by Freud weights e − 2 σ | x | α e^{-2\sigma |x|^\alpha } with α &gt; 1 \alpha &gt;1 and σ &gt; 0 \sigma &gt;0 , and we derive specific bounds for the approximation and quadrature error. For the Gaussian weight e − 2 π x 2 e^{-2\pi x^2} , we verify that the Sobolev spaces essentially coincide with a specific class of modulation spaces that are well known in (time-frequency) analysis.

Experimental and numerical investigations towards the lateral torsional buckling of cellular steel beams

This paper deals with the response of so-called “cellular members” against lateral torsional buckling. These beams comprising regularly-spaced circular web openings are especially used for their high resistance-to-weight ratio, the possibility to integrate service pipes within their height, and for aesthetics. Such profiles usually exhibit a complex behaviour and many potential failure modes, including interactional local/global instability modes. Regarding global instability, the members are usually designed by means of approximate design rules, which often lead to an unduly conservative solution, with beams sometimes showing up to 150 % resistance reserves.The present research works aim at improving this situation, through the development of adequate design formulae. In this respect, the present paper reports on investigations led towards improved solutions for cellular members at the experimental and numerical levels. This first paper focuses on experimental activities and on the development and validation of dedicated shell F.E. models. The results of three bending tests on members spanning from 7.5 m to 11 m are reported. Cross-sectional dimensions, material properties and accurate initial geometrical imperfections were measured for each specimen and further introduced in the corresponding F.E. models, which are shown to provide predictions in close agreement with the experimental results. The companion paper [1] further makes use of the F.E. models within extensive parametric studies and proposes a new set of design rules that could be proposed for integration in Eurocode 3.

Microsolvation of Hot Ions: Spectroscopy and Statistical Mechanics of Phenide-Water Interactions.

Thermal excitation alters the spectroscopic signatures of solvated ions and affects their interactions with neighboring molecules. By analyzing the photoelectron spectra of microhydrated phenide (Ph-), the temperatures of the Ph-·H2O and Ph-·(H2O)2 clusters from a hot ion source were determined to be 560 and 520 K, respectively, vs 700 K for unsolvated Ph-. Compared to theory predictions for cold clusters, the high temperature of the environment significantly reduces the average hydration stabilization of the ions and the corresponding band shifts in their spectra. The results are discussed in terms of a statistical model that describes the energy content of the intermolecular (IM) degrees of freedom of the cluster, ⟨EIM⟩. We show that over the entire solvation energy range, the density of states associated with the IM modes of Ph-·H2O, of which there are only 6, is more than an order of magnitude greater than that associated with the 27 internal vibrations of the core anion. The results suggest that the observed cluster temperatures are not determined by the ion source but represent the intrinsic properties of the clusters. The energetics and statistical mechanics of microsolvation limit the excitation that the IM degrees of freedom can sustain without significant solvent evaporation on the timescale of the experiment. The limit is expressed as a characteristic solvation temperature (CST), which is the maximum canonical temperature of a stable cluster ensemble. Driven by evaporative cooling, the terminal cluster temperature from a hot ion source will always be close to the cluster's CST. Only if the source temperature is lower than CST will the observed cluster temperature be determined by the source conditions. An approximate rule is proposed for estimating the characteristic temperature of any cluster using the inflection point on the ⟨EIM⟩ vs T curve.

Approximately optimal forest rotation in a nonstationary environment

AbstractThe problem of optimal forest rotation in a nonstationary environment can, in general, not be solved analytically. Even qualitatively characterizing how the solution changes over time is only possible in some special cases. In this paper, we consider an approximation of the true solution to the nonstationary problem. We derive an approximate harvesting rule by solving a sequence of stationary problems that assume the growth conditions at that point in time will prevail indefinitely. Each such problem can be solved using the classic Faustmann rule. We numerically compare this approximate solution to the true solution, both in terms of the harvesting rule and the resulting expected profits, for a wide range of scenarios. We find that the harvesting rules are very similar (mostly % difference) and the profit losses associated with following the approximate rule are very small (less than 0.3%).

Premium control with reinforcement learning

AbstractWe consider a premium control problem in discrete time, formulated in terms of a Markov decision process. In a simplified setting, the optimal premium rule can be derived with dynamic programming methods. However, these classical methods are not feasible in a more realistic setting due to the dimension of the state space and lack of explicit expressions for transition probabilities. We explore reinforcement learning techniques, using function approximation, to solve the premium control problem for realistic stochastic models. We illustrate the appropriateness of the approximate optimal premium rule compared with the true optimal premium rule in a simplified setting and further demonstrate that the approximate optimal premium rule outperforms benchmark rules in more realistic settings where classical approaches fail.

Energy Correlations of Non-Integrable Ising Models: The Scaling Limit in the Cylinder

We consider a class of non-integrable 2D Ising models whose Hamiltonian, in addition to the standard nearest neighbor couplings, includes additional weak multi-spin interactions which are even under spin flip. We study the model in cylindrical domains of arbitrary aspect ratio and compute the multipoint energy correlations at the critical temperature via a multiscale expansion, uniformly convergent in the domain size and in the lattice spacing. We prove that, in the scaling limit, the multipoint energy correlations converge to the same limiting correlations as those of the nearest neighbor Ising model in a finite cylinder with renormalized horizontal and vertical couplings, up to an overall multiplicative constant independent of the shape of the domain. The proof is based on a representation of the generating function of correlations in terms of a non-Gaussian Grassmann integral, and a constructive Renormalization Group (RG) analysis thereof. A key technical novelty compared with previous works is a systematic analysis of the effect of the boundary corrections to the RG flow, in particular a proof that the scaling dimension of boundary operators is better by one dimension than their bulk counterparts. In addition, a cancellation mechanism based on an approximate image rule for the fermionic Green’s function is of crucial importance for controlling the flow of the (superficially) marginal boundary terms under RG iterations.

Towards a Unified Quadrature Framework for Large-Scale Kernel Machines.

In this paper, we develop a quadrature framework for large-scale kernel machines via a numerical integration representation. Considering that the integration domain and measure of typical kernels, e.g., Gaussian kernels, arc-cosine kernels, are fully symmetric, we leverage a numerical integration technique, deterministic fully symmetric interpolatory rules, to efficiently compute quadrature nodes and associated weights for kernel approximation. Thanks to the full symmetric property, the applied interpolatory rules are able to reduce the number of needed nodes while retaining a high approximation accuracy. Further, we randomize the above deterministic rules by the classical Monte-Carlo sampling and control variates techniques with two merits: 1) The proposed stochastic rules make the dimension of the feature mapping flexibly varying, such that we can control the discrepancy between the original and approximate kernels by tuning the dimnension. 2) Our stochastic rules have nice statistical properties of unbiasedness and variance reduction. In addition, we elucidate the relationship between our deterministic/stochastic interpolatory rules and current typical quadrature based rules for kernel approximation, thereby unifying these methods under our framework. Experimental results on several benchmark datasets show that our methods compare favorably with other representative kernel approximation based methods.

Hydrodynamics Simulations and Analyses of a Fluid Lubricated Screw-Nut Pair

A new method is proposed to solve the hydrodynamics performances of a fluid lubricated screw-nut pair using FLUENT. Before the simulations, the Computational Fluid Dynamics (CFD) model of the gap flow field is built, based on some approximation rules. During the simulations, the dynamic mesh technology is employed to realize the real-time update of the grids of the computational domain. For a given velocity perturbation, the stiffness and damping coefficients of the system are solved using the finite difference method, and the influences of the perturbations on the system are compared among different ranges. With the fluid–solid interaction and the real-time restriction of the restrictors considered, the system is solved under different loading conditions. A more accurate solution method for the dynamic stiffness and damping coefficients is provided, and the dynamics characteristics of the system after loading are analyzed. On this basis, a qualitative and quantitative comparison is carried out between the method based on the simplified Reynolds equation and the proposed method in this paper, showing the latter superiorities in illustrating the field. A general understanding of the dynamics properties under different loading conditions of the system is obtained through this research, providing a basis for the precision control of the system in the future research.

Meta-learning spiking neural networks with surrogate gradient descent

Adaptive ‘life-long’ learning at the edge and during online task performance is an aspirational goal of artificial intelligence research. Neuromorphic hardware implementing spiking neural networks (SNNs) are particularly attractive in this regard, as their real-time, event-based, local computing paradigm makes them suitable for edge implementations and fast learning. However, the long and iterative learning that characterizes state-of-the-art SNN training is incompatible with the physical nature and real-time operation of neuromorphic hardware. Bi-level learning, such as meta-learning is increasingly used in deep learning to overcome these limitations. In this work, we demonstrate gradient-based meta-learning in SNNs using the surrogate gradient method that approximates the spiking threshold function for gradient estimations. Because surrogate gradients can be made twice differentiable, well-established, and effective second-order gradient meta-learning methods such as model agnostic meta learning (MAML) can be used. We show that SNNs meta-trained using MAML perform comparably to conventional artificial neural networks meta-trained with MAML on event-based meta-datasets. Furthermore, we demonstrate the specific advantages that accrue from meta-learning: fast learning without the requirement of high precision weights or gradients, training-to-learn with quantization and mitigating the effects of approximate synaptic plasticity rules. Our results emphasize how meta-learning techniques can become instrumental for deploying neuromorphic learning technologies on real-world problems.

Numerical evaluation and analysis of highly oscillatory singular Bessel transforms with a particular oscillator

This paper proposes and analyzes two affordable and efficient quadrature rules for the numerical approximation of the oscillatory Bessel transform ∫0bxα(b−x)βf(x)Jν(ωxγ)dx with algebraic singularities, where b,α,β,ν,ω,γ denote the given constants. Firstly, we derive the explicit formula and asymptotic estimation of the generalized moments ∫0bxα′(b−x)β′Jν(ωxγ)dx with α′,β′>−1 by means of the Meijer G function. Furthermore, we design a modified Filon-type method based on a two-endpoint Taylor interpolation polynomial. In particular, we also give a more efficient Clenshaw–Curtis–Filon-type method in view of a special Hermite interpolation polynomial at the Clenshaw–Curtis points. Moreover, this method is easily implemented by the fast Fourier transform and fast computation of the modified moments. The useful homogeneous recurrence relation of the required modified moments is derived by the Bessel equation and the properties of the Chebyshev polynomial. Importantly, the rigorous error analyses in inverse powers of ω for the proposed numerical methods are carried out in details. Some primary numerical experiments can confirm our theoretical analysis, and verify the accuracy and efficiency of the proposed numerical methods.

A δ

Over the last decade, automatic differentiation (AD) has profoundly impacted graphics and vision applications --- both broadly via deep learning and specifically for inverse rendering. Traditional AD methods ignore gradients at discontinuities, instead treating functions as continuous. Rendering algorithms intrinsically rely on discontinuities, crucial at object silhouettes and in general for any branching operation. Researchers have proposed fully- automatic differentiation approaches for handling discontinuities by restricting to affine functions, or semi- automatic processes restricted either to invertible functions or to specialized applications like vector graphics. This paper describes a compiler-based approach to extend reverse mode AD so as to accept arbitrary programs involving discontinuities. Our novel gradient rules generalize differentiation to work correctly, assuming there is a single discontinuity in a local neighborhood, by approximating the prefiltered gradient over a box kernel oriented along a 1D sampling axis. We describe when such approximation rules are first-order correct, and show that this correctness criterion applies to a relatively broad class of functions. Moreover, we show that the method is effective in practice for arbitrary programs, including features for which we cannot prove correctness. We evaluate this approach on procedural shader programs, where the task is to optimize unknown parameters in order to match a target image, and our method outperforms baselines in terms of both convergence and efficiency. Our compiler outputs gradient programs in TensorFlow, PyTorch (for quick prototypes) and Halide with an optional auto-scheduler (for efficiency). The compiler also outputs GLSL that renders the target image, allowing users to interactively modify and animate the shader, which would otherwise be cumbersome in other representations such as triangle meshes or vector art.

Response of Structures to Bidirectional Seismic Loading: Research Progress and Future Directions

Rigorous assessment of structural response to seismic excitation poses challenges for researchers in their bid to account for the effects of (1) biaxial interaction; and (2) incidence angles of a ground motion relative to the structure. Keeping these two major issues in view, this paper presents a comprehensive review of the progress of research in the related areas. Studies since the 1970s clearly bring out the significance of interaction effect especially for stiff systems, and also the sensitivity of response to incidence angles. Further, a scrutiny of the design guidelines embodied in modern codes shows that, to account for the interaction effect, the codes primarily rely on the approximate combination rules evolved in the mid-1970s. In addition, both research findings and codified guidelines clearly reveal an apparent lack of consensus on the choice of appropriate incidence angle. With reference to bidirectional analysis, modern views of researchers on important aspects including quantification of damage and selection of ground motions are also discussed. Based on a critical review of the recent works and the codes, the paper recommends the use of an improved yet simple methodology for practical design. Directions for future research are also brought out.

Online estimation of satellite lithium-ion battery capacity based on approximate belief rule base and hidden Markov model

To ensure safety of satellite operation in orbit, it is important to estimate the capacity of lithium-ion battery in time. However, the battery capacity cannot be measured directly in space, and it is continually changing due to the usage that changes with the space environment. Because of the complex electrochemical side reactions inside battery, it is difficult to establish an accurate model. To solve the above problems, eight features from battery usage of three processes are selected to comprehensively depict the change of battery capacity. Taking the battery capacity as hidden state, an online estimation model is proposed based on approximate belief rule base and hidden Markov model by using historical data and expert knowledge. Based on the performance test data of a certain type of satellite battery, the effectiveness of the proposed model is verified. The capacity of an in-orbit satellite battery is estimated and analyzed by using the telemetry data.