Truncation Level Research Articles

General Value Function Networks

State construction is important for learning in partially observable environments. A general purpose strategy for state construction is to learn the state update using a Recurrent Neural Network (RNN), which updates the internal state using the current internal state and the most recent observation. This internal state provides a summary of the observed sequence, to facilitate accurate predictions and decision-making. At the same time, specifying and training RNNs is notoriously tricky, particularly as the common strategy to approximate gradients back in time, called truncated Back-prop Through Time (BPTT), can be sensitive to the truncation window. Further, domain-expertise—which can usually help constrain the function class and so improve trainability—can be difficult to incorporate into complex recurrent units used within RNNs. In this work, we explore how to use multi-step predictions to constrain the RNN and incorporate prior knowledge. In particular, we revisit the idea of using predictions to construct state and ask: does constraining (parts of) the state to consist of predictions about the future improve RNN trainability? We formulate a novel RNN architecture, called a General Value Function Network (GVFN), where each internal state component corresponds to a prediction about the future represented as a value function. We first provide an objective for optimizing GVFNs, and derive several algorithms to optimize this objective. We then show that GVFNs are more robust to the truncation level, in many cases only requiring one-step gradient updates.

An experimental study on the control of plug nozzle jets

Experimental studies are performed for the near- and far-field characteristics of a plug nozzle jet with the objective to see the effect of truncation of the plug on mean flow characteristics of the jet and its control using vortex generators (VGs). To this end, the plug is truncated at 50%, 40%, and 30% of the axial length from the throat, and mean flow characteristics are studied by the schlieren technique and a pitot pressure survey. Nozzle pressure ratio (NPR) is varied from 2 to 8 for a Mach 1.8 nozzle designed to give correctly expanded flow at NPR 5.74. During over-expansion mode, all the truncation levels are observed to increase core length and strengthen shock cells of the jet, whereas, during under-expansion, truncation up to 50% of the plug is not found to alter the core length. To promote mixing, two rectangular VGs of different aspect ratios but same blockage area of 2% are attached to the base of the truncated plugs. The influence of pressure ratio on the flow structure of controlled and uncontrolled jets is discussed in detail. Results have shown VGs to be effective in mixing enhancement and weakening of shock cells over the nozzle pressure ratios studied.

Spectrally-truncated kernel ridge regression and its free lunch

Kernel ridge regression (KRR) is a well-known and popular nonparametric regression approach with many desirable properties, including minimax rate-optimality in estimating functions that belong to common reproducing kernel Hilbert spaces (RKHS). The approach, however, is computationally intensive for large data sets, due to the need to operate on a dense n×n kernel matrix, where n is the sample size. Recently, various approximation schemes for solving KRR have been considered, and some analyzed. Some approaches such as Nyström approximation and sketching have been shown to preserve the rate optimality of KRR. In this paper, we consider the simplest approximation, namely, spectrally truncating the kernel matrix to its largest r<n eigenvalues. We derive an exact expression for the maximum risk of this truncated KRR, over the unit ball of the RKHS. This result can be used to study the exact trade-off between the level of spectral truncation and the regularization parameter. We show that, as long as the RKHS is infinite-dimensional, there is a threshold on r, above which, the spectrally-truncated KRR surprisingly outperforms the full KRR in terms of the minimax risk, where the minimum is taken over the regularization parameter. This strengthens the existing results on approximation schemes, by showing that not only one does not lose in terms of the rates, truncation can in fact improve the performance, for all finite samples (above the threshold). Moreover, we show that the implicit regularization achieved by spectral truncation is not a substitute for Hilbert norm regularization. Both are needed to achieve the best performance.

Truncated simulation and inference in edge-exchangeable networks

Edge-exchangeable probabilistic network models generate edges as an i.i.d.~sequence from a discrete measure, providing a simple means for statistical inference of latent network properties. The measure is often constructed using the self-product of a realization from a Bayesian nonparametric (BNP) discrete prior; but unlike in standard BNP models, the self-product measure prior is not conjugate the likelihood, hindering the development of exact simulation and inference algorithms. Approximation via finite truncation of the discrete measure is a straightforward alternative, but incurs an unknown approximation error. In this paper, we develop methods for forward simulation and posterior inference in random self-product-measure models based on truncation, and provide theoretical guarantees on the quality of the results as a function of the truncation level. The techniques we present are general and extend to the broader class of discrete Bayesian nonparametric models.

Basis set extrapolation in pair natural orbital theories.

We present the results of a benchmark study of the effect of Pair Natural Orbital (PNO) truncation errors on the performance of basis set extrapolation. We find that reliable conclusions from the application of Helgaker's extrapolation method are only obtained when using tight PNO thresholds of at least 10-7. The use of looser thresholds introduces a significant risk of observing a false basis set convergence and underestimating the residual basis set errors. We propose an alternative extrapolation approach based on the PNO truncation level that only requires a single basis set and show that it is a viable alternative to hierarchical basis set extrapolation methods.

Analysis of dry and wet climate characteristics at Uttarakhand (India) using effective drought index

Drought is a complex natural disaster that adversely affects human life and the ecosystem. A variety of drought indexes are available for monitoring meteorological drought events. In the present study, Effective Drought Index (EDI) was utilized to quantify the drought and wet conditions with their probability at 13 districts of Uttarakhand State (India). The EDI was calculated for all study locations by using monthly rainfall data. The drought and wet incidents (i.e., moderate, severe, extreme) were categorized by setting a truncation level to the respective EDI value by using the runs theory concept. The results of the EDI examination explore that the probability of occurrence (PO) of normal events (conditions) was found to be 68% at Almora and Dehradun; 72% at Bageshwar; 71% at Chamoli and Pauri Garhwal; 69% at Champawat; Haridwar, Nainital, and Rudraprayag; 77% at Pithoragarh; 74% at Tehri Garhwal; and 44% at Pantnagar. Similarly, the PO of moderate drought and wet (MD and MW) events was found to be relatively more than the severe and extreme drought and wet events, except the Pantnagar station (extreme wet = 0.54). Thus, the outcomes of this study can be utilized to formulate the mitigation strategy in that way to store the surplus water in wet eras and utilized the same during drought for domestic and agricultural drives in the study districts.

Theory and implementation of a novel stochastic approach to coupled cluster.

We present a detailed discussion of our novel diagrammatic coupled cluster Monte Carlo (diagCCMC) [Scott et al. J. Phys. Chem. Lett. 10, 925 (2019)]. The diagCCMC algorithm performs an imaginary-time propagation of the similarity-transformed coupled cluster Schrödinger equation. Imaginary-time updates are computed by the stochastic sampling of the coupled cluster vector function: each term is evaluated as a randomly realized diagram in the connected expansion of the similarity-transformed Hamiltonian. We highlight similarities and differences between deterministic and stochastic linked coupled cluster theory when the latter is re-expressed as a sampling of the diagrammatic expansion and discuss details of our implementation that allow for a walker-less realization of the stochastic sampling. Finally, we demonstrate that in the presence of locality, our algorithm can obtain a fixed errorbar per electron while only requiring an asymptotic computational effort that scales quartically with system size, independent of the truncation level in coupled cluster theory. The algorithm only requires an asymptotic memory cost scaling linearly, as demonstrated previously. These scaling reductions require no ad hoc modifications to the approach.

Testing for stationarity of functional time series in the frequency domain

Interest in functional time series has spiked in the recent past with papers covering both methodology and applications being published at a much increased pace. This article contributes to the research in this area by proposing a new stationarity test for functional time series based on frequency domain methods. The proposed test statistics is based on joint dimension reduction via functional principal components analysis across the spectral density operators at all Fourier frequencies, explicitly allowing for frequency-dependent levels of truncation to adapt to the dynamics of the underlying functional time series. The properties of the test are derived both under the null hypothesis of stationary functional time series and under the smooth alternative of locally stationary functional time series. The methodology is theoretically justified through asymptotic results. Evidence from simulation studies and an application to annual temperature curves suggests that the test works well in finite samples.

A mimetic method for polygons

A new method for mimetic interpolation on polygonal meshes is described. This new method is based on harmonic function interpolation. Explicit formulas for harmonic functions on general polygons do not exist, so truncated harmonic polynomial expansions are used for computational efficiency. We show that the naive harmonic polynomial expansion, is not stable for arbitrary polygons. However, higher level truncations of harmonic interpolations are stable and accurate. This new method is shown to be a direct extension of the lowest order Raviart-Thomas finite elements to polygons. This method is also a direct extension of the finite volume MAC method to polygons. The accuracy of the interpolation is shown to be first-order irrespective of the polynomial truncation level. However the accuracy of vector Laplace equation solutions using this inner product is shown to be second-order accurate, in keeping with other lowest order Mimetic methods. The versatility of this numerical method is demonstrated on a multiphase incompressible flow problem with a density jump of 1000, on a moving polygonal mesh.

Low Concentrating Photovoltaics (LCPV) for buildings and their performance analyses

Low concentrating photovoltaic technologies (LCPV) for building application offer viable solutions in improving the conversion efficiency of solar cells leading to an improved electrical output per unit cell area required when compared to conventional solar photovoltaic modules. The current study explores the feasibility of different geometrically equivalent LCPVs designed for building application through indoor experimental characterisation and analytical investigations. LCPV concentrator geometries were designed and simulated to predict optical efficiency at various truncation levels and range of angles of incidence using ray trace module in COMSOL Multiphysics version 5.3. The geometric concentration ratios of LCPVs investigated Compound Parabolic Concentrator (CPC), V-Trough and Asymmetric Compound Parabolic Concentrator (ACPC) with geometric concentration ratios of 1.46, 1.40, and 1.53 respectively. These prototypes were manufactured and their electrical conversion efficiency in conjunction with crystalline silicon (c-Si) solar photovoltaic cells were measured using OAI Trisol Class AAA solar simulator. Analytical model developed in the present study predicts the annual energy output generated and payback period for the LCPVs compared to an equivalent area of conventional flat module. Theoretical modeling results have showed that Asymmetric Compound Parabolic Concentrator (ACPC) with mono-crystalline silicon cells (m-Si) have generated highest energy output per unit area of 177 kWh/m2 as compared to the other configurations which make it economically viable for building retrofit with a predicted payback period of 9.7 years.

Numerical Simulation and Contour Design of Aerospike Nozzle: a Behavioural Study on Truncation Effects of Nozzle

The objective of this paper is to present a design and an analysis procedure for a highly efficient aerospike nozzle that uses Liquid Oxygen and Liquid Hydrogen (LOX/LH2) as fuel for a Single Stage to Orbit (SSTO) spacecraft. This paper provides a simple method to design an aerospike nozzle contour in addition to the results of the Computational Fluid Dynamics (CFD) analysis carried out for this nozzle with and without truncation. The results have been compared with the theoretical values, and the changes in specific thrust with different level of truncation have been shown. The geometry of the nozzle has been created using the method of characteristics and python codes, and flow analysis have been carried out using ANSYS FLUENT for the optimum working condition of the nozzle. The nozzles have been able to achieve excellent altitude compensation, and the nozzle with 40% truncation has come out to be the most efficient.

Relativistic and correlation effects in the photoionization dynamics of oganesson (Z=118) : Spin-orbit-interaction-activated interchannel coupling effects

High-$Z$ atoms are excellent laboratories to study the combination of relativistic and many-electron correlation effects in electronic structure and dynamics. In the present work, the relativistic-random-phase approximation at different levels of truncation is employed to explore the final-state correlation effects in the photoelectron dynamics of the heaviest known element in the Periodic Table: oganesson (Og) with $Z=118$. The focus of this work is to illustrate the relativistic effects resulting from coupling different photoionization channels arising from spin-orbit split subshells, termed the spin-orbit-interaction-activated interchannel coupling effect. Comparison with the photoelectron dynamics of Rn on a qualitative level is also carried out, since Og is a homologue of Rn. The photoelectron dynamics of $7p,7s$, and $6d$ subshells are investigated and differences between Og and Rn, due to enhanced relativistic effects, are investigated.

Aspects of entropy generation for the non-similar three-dimensional bioconvection flow of nanofluids

This research work presents the entropy analysis of the three-dimensional bioconvection flow of nanofluid over a linearly moving plate in the presence of magnetic effects. Nanoparticles and microorganisms have been considered in the fluid, with the magnetic field acting in the transverse direction to the plate. The viscous dissipation term is also considered in the energy equation. The partial differential equations (PDEs) of the boundary layer region of this problem are transformed with suitable non-similarity transformations into a system of nonlinear PDEs. Afterward, the local non-similarity method via the BVP4c MATLAB algorithm with a second level of truncation delivers a solution of the problem. The effect of important parameters such as magnetic field, Eckert number, thermophoresis, Prandtl number, Peclet number, Brownian motion, Schmidt number, Brinkman number, Lewis number, slip factor on temperature distribution, concentration of nanofluid, density of motile microorganisms, and entropy generation are shown in the graphical profiles.

Characterization of flow through random media via Karhunen–Loève expansion: an information theory perspective

We leverage on information theory to assess the fidelity of approximated numerical stochastic groundwater flow simulations. We consider flow in saturated heterogeneous porous media, where the Karhunen–Loeve (KL) expansion is used to express the hydraulic conductivity as a spatially correlated random field. We quantify the impact of the KL expansion truncation on the uncertainty associated with punctual values of hydraulic conductivity and flow velocity. In particular, we compare the statistical dependence between variables by considering (a) linear correlation metrics (Pearson coefficient of correlation) and (b) metrics capable of accounting for nonlinear dependence (coefficient of uncertainty based on mutual information). We test the selected metrics by analyzing the relationship between hydraulic conductivity fields generated via Monte Carlo sampling with different levels of truncation of the KL expansion and the corresponding fluid velocity fields, obtained through the numerical solution of Darcy’s flow. Our analysis shows that employing linear correlation metrics leads to a general overestimation of the correlation level and information theory based indicators are valuable tools to assess the impact of the KL truncation on the output velocity values. We then analyze the impact of the number of retained modes on the spatial organization of the velocity field. Results indicates that (i) as the number of modes decrease the spatial correlations of the velocity field increases; (ii) linear indicators of spatial correlation are again larger than their nonlinear counterparts.

Approximate Compressor-Based Multiplier Design Methodology for Error-Resilient Digital Signal Processing

As many digital signal processing (DSP) applications such as digital filtering are inherently error-tolerant, approximate computing has attracted significant attention. A multiplier is the fundamental component for DSP applications and takes up the most part of the resource utilization, namely power and area. A multiplier consists of partial product arrays (PPAs) and compressors are often used to reduce partial products (PPs) to generate the final product. Approximate computing has been studied as an innovative paradigm for reducing resource utilization for the DSP systems. In this paper, a 4:2 approximate compressor-based multiplier is studied. Approximate 4:2 compressors are designed with a practical design criterion, and an approximate multiplier that uses both truncation and the proposed compressors for PP reduction is subsequently designed. Different levels of truncation and approximate compression combination are studied for accuracy and electrical performance. A practical selection algorithm is then leveraged to identify the optimal combinations for multiplier designs with better performance in terms of both accuracy and electrical performance measurements. Two real case studies are performed, i.e., image processing and a finite impulse response (FIR) filter. The design proposed in this paper has achieved up to 16.96% and 20.81% savings on power and area with an average signal-to-noise ratio (SNR) larger than 25[Formula: see text]dB for image processing; similarly, with a decrease of 0.3[Formula: see text]dB in the output SNR, 12.22% and 30.05% savings on power and area have been achieved for an FIR filter compared to conventional multiplier designs.

Optimal unbiased estimation for expected cumulative discounted cost

We consider estimating an expected infinite-horizon cumulative discounted cost/reward contingent on an underlying stochastic process by Monte Carlo simulation. An unbiased estimator based on truncating the cumulative cost at a random horizon is proposed. Explicit forms for the optimal distributions of the random horizon are given, and explicit expressions for the optimal random truncation level are obtained, leading to a full analysis of the bias-variance tradeoff when comparing this new class of randomized estimators with traditional fixed truncation estimators. Moreover, we characterize when the optimal randomized estimator is preferred over a fixed truncation estimator by considering the tradeoff between bias and variance. This comparison provides guidance on when to choose randomized estimators over fixed truncation estimators in practice. Numerical experiments substantiate the theoretical results.

Relativistic Two-Component Multireference Configuration Interaction Method with Tunable Correlation Space.

The multiconfiguration nature of late-row (≥4th) elements and their molecular complexes, combined with significant relativistic effects, present large challenges for the accurate description of their electronic structure. To address these challenges and incorporate both relativistic and electron correlation effects, we present a two-component Kramers-unrestricted multireference configuration interaction method where relativistic effects are included variationally at the molecular orbital level via use of the "exact two-component" transformation of the solution of the one-electron modified Dirac equation. This method is developed within the restricted active space framework, allowing flexibility in both the choice of correlation space and the level of truncation of the excitation operator, as well as promoting the efficiency of generating and book-keeping unique electronic configurations. This method is applied to the study of fine structure splitting in selected p-block and d-block elements and is further applied to the study of the open-shell heavy-element uranium(V) ion.

Analysis of the caustics of partially coherently combined truncated Gaussian beams.

A theoretical model of the caustics of partially coherently combined beams (CBCs) was derived to model CBCs in the case of truncated Gaussian beams. The model enables the analysis of different lattice structures and partial coherence effects, including incoherent beam combining. The impacts of the coherence state, geometry of the array and truncation losses were analyzed. An optimal truncation level of about 6% was found and a maximum CBC efficiency of 62% was determined for this CBC system. With an increase in the beam numbers in the lattice, the relative caustics length decreases, which is consistent with the general rules of diffraction theory.

Prevention of complications depending on the level of amputation (exarticulation) of the lower limb

In the mid-end of the last century, unification was carried out to select the level of limb trimming, based on the principle of achieving the maximum possible functionality in the stump-prosthesis system. Over time, due to the development of surgical techniques and the level of prosthetic and orthopedic products, previously developed schemes for choosing the level of amputation have lost their relevance. However, the most typical complications and the associated decrease in prosthetics functionality continue to occur in the current time period. The article provides an analysis of the possible variants of complications in relation to the level of limb truncation, options for their prevention and elimination, and how the general assessment of the effect on the stat-dynamic function of the stump length at various levels is presented.

Adenosine Protects Zebrafish Photoreceptors from Apoptosis and Damage in a Dose‐Dependent Manner in a Light‐Induced Retinal Degeneration Model of Age‐Related Macular Degeneration

PurposeAdenosine has been shown to be neuroprotective in the CNS and in retinal ganglion cells in the inner retina. However, the neuroprotective effects of adenosine on outer retinal neurons, in particular photoreceptors, is not known. Age‐related macular degeneration (AMD) is a multifactorial disease characterized by the impairment or loss of central vision due to macular dropout and loss of photoreceptors. Adenosine has been shown to inhibit photoreceptor excitability by suppressing Ca2+ influx through voltage‐gated Ca2+ channels, which could lead to cell death. The purpose of this study was to see if adenosine would reduce photoreceptor damage and death in a light‐induced retinal degeneration (LIRD) model in pigmented zebrafish.MethodsAdult wild‐type and Tg(nrd:GFP) zebrafish (used to GFP label rod photoreceptors) were dark‐adapted for 24 hours, followed by intravitreal injections of ~ 0.5 ml of 0.1 mM, 1 mM, or 5 mM (final conc: 1.67 to 167 mM) of adenosine in both eyes. Controls were injected with saline in both eyes. All zebrafish were exposed to full spectrum high‐intensity light (≥ 20,000 lux) for four days and collected at 0 and 96 hours post dark‐adaptation. Immunohistochemical analysis was performed on vertical retinal sections in order to visualize cones, rods, and the outer nuclear layer of the retina. Retinal damage was assessed using confocal microscopy with a TUNEL assay and cell specific markers.ResultsPhotoreceptors in control retinas collected at 96 hours exhibited severe truncation or loss of the outer segments, and swelling of the cell body. Additionally, there was an increase in TUNEL‐positive cells and a significant decrease in rod and cone photoreceptors in the control retinas. Photoreceptors from retinas treated with higher concentrations of adenosine (1 mM and 5 mM) lacked swelling, exhibited less cell death, reduced truncation of the outer segments, and had cell morphology similar to retinas collected prior to light exposure. Photoreceptors from retinas treated with 0.1 mM adenosine exhibited no significant differences in cell death in comparison to control retinas at 96 hours, and had similar levels of outer segment truncation and cell body morphology. However, there was a significant reduction in the number of cones and rods lost in the 0.1 mM adenosine‐treated retinas at 96 hours in comparison to control retinas at 96 hours.ConclusionThese findings show that adenosine can prevent light‐induced structural damage to rod and cone photoreceptors, prevent photoreceptor death and loss, and provide evidence of a potential novel therapeutic target for the treatment of the “dry” form of AMD.Support or Funding InformationHMC CURE Zebrafish Pilot Grant from Penn State University College of Medicine, Pennsylvania Department of Health Tobacco CURE Fund