## We present a direct manipulation technique that allows material scientists to interactively highlight relevant parameterized simulation instances located in dimensionally reduced spaces, enabling a user-defined understanding of a continuous parameter space.

Drag and Track: A Direct Manipulation Interface for Contextualizing Data Instances within a Continuous Parameter Space

## Overall, a dimensionally reduced space does not significantly affect the prediction performance of the SDP models.

ELM and KELM based software defect prediction using feature selection techniques

## The reduced space harmonic balance method is demonstrated to find the maximum vibration responses of rotor systems.

The application of reduced space harmonic balance method for the nonlinear vibration problem in rotor dynamics

## In the current signal reconstruction, the introduced PLL topology has the advantage of reduced space harmonics.

Sensorless Control Applying Signal Injection Methodology on Modified Model of Permanent Magnet Synchronous Machine

## This is especially applicable for urban areas and bottlenecks, since the compact design of the high-temperature superconductor cables (HTS cables) and the reduced space requirement leads to a significant reduction in the civil engineering expenditure and to a reduction in installation costs.

Investigation of the Electromagnetic Fields of a HTS-Three Core Cable Arrangement at Mains Frequency for the Determination of Electrical Properties by Using FEM

## The d-MTMDs are also convenient to install owing to the reduced space requirements, being placed at various floors.

Distributed Tuned Mass Dampers for Multi-Mode Control of Benchmark Building under Seismic Excitations

10.1016/j.jmva.2018.09.011

## Rather than estimating the full quadratic discriminant rule, we propose to perform simultaneous variable selection and linear dimension reduction on the original data, with the subsequent application of quadratic discriminant analysis on the reduced space.

Sparse quadratic classification rules via linear dimension reduction

## The method for full conformational analysis includes Cartesian coordinates sampling through quantum chemical molecular dynamics simulations, reduction of dimensionality by principal component analysis, determination of probability distributions in a reduced space of Cartesian coordinates and search for all the strict extrema points in probability distribution functions.

Conformational Analysis of Cinhonine and Cinhonidine by Tensor Decomposition of Molecular Dynamics Trajectories

10.1007/978-3-030-16181-1_82

## Adequate prediction results were achieved in a reduced space of characteristics.

Study of the Number Recognition Algorithms Efficiency After a Reduction of the Characteristic Space Using Typical Testors

10.3389/fphy.2019.00194

## The second method uses the popular IsoMap nonlinear dimensionality reduction algorithm, and assigns an outlier score by comparing the geodesic distances with the distances in the reduced space.

Outlier Mining Methods Based on Graph Structure Analysis

10.1504/ijbm.2019.10023701

## Then QPSO is applied to fetch the optimal features set over the reduced space that contains the best vectors only.

Feature selection for face authentication systems: feature space reductionism and QPSO

10.1073/pnas.1906995116

## In this work, we design a custom deep autoencoder network to discover a coordinate transformation into a reduced space where the dynamics may be sparsely represented.

Data-driven discovery of coordinates and governing equations

10.1007/s40314-020-1092-1

## Afterwards, we derive efficiently computable and rigorous a posteriori error bounds for various quantities of interest which is a tool to generate the reduced space.

A solution for fractional PDE constrained optimization problems using reduced basis method

10.1007/s10957-018-1396-0

## The proposed method is based on relaxations of algorithms using McCormick relaxations in a reduced space (Mitsos et al.

Deterministic Global Optimization with Artificial Neural Networks Embedded

10.1016/j.physd.2020.132368

## Our formulation is devised in a non-intrusive manner with an equation-free evolution of dynamics in a reduced space with the latter being obtained through a proper orthogonal decomposition.

Time-series learning of latent-space dynamics for reduced-order model closure.

10.1103/PhysRevB.100.125161

## The reduced space group symmetry of the crystal allows for several channels for spin-operator bilinears to couple to the electric field.

Optical excitation of magnons in an easy-plane antiferromagnet: Application to Sr$_2$IrO$_4$.

10.1016/j.jcp.2018.10.001

## In order to retrieve accuracy, we first project every such coarse solution into the reduced space, and then further improve them via a rectification technique.

A non-intrusive reduced basis approach for parametrized heat transfer problems

10.1080/15397734.2018.1519634

## The reduced space harmonic balance method is demonstrated to find the maximum vibration responses of rotor systems.

The application of reduced space harmonic balance method for the nonlinear vibration problem in rotor dynamics

10.1109/SYSOSE.2019.8753840

## Successful collaboration and interaction between component systems in (increasingly) reduced spaces is contingent to precise and accurate perception, interpretation and management of various spatial representations of self and teaming systems.

Spatial Functions for Modeling and Analysis of Safety-Critical Systems of Systems

10.1038/s41433-019-0627-4

## Conclusions A marked retardation of displacement was demonstrated for all IRL within the immature fovea of preterms with decreased areal and volume magnification and reduced space available for synaptic communication coupled to the degree of immaturity.

Structural consequences of arrested foveal development in preterms with persisting signs of immaturity

10.1007/978-3-030-18305-9_53

## We found that the SCCA provides reasonable correlation scores in the reduced space, enables interpretability, and also provides the best classification performance among the three methods.

Genome-Wide Canonical Correlation Analysis-Based Computational Methods for Mining Information from Microbiome and Gene Expression Data

## Biological samples are a complex and heterogeneous matrix where different macromolecules with different physicochemical parameters cohabit in reduced spaces.

Synthesis, Photophysics, and Solvatochromic Studies of an Aggregated-Induced-Emission Luminogen Useful in Bioimaging

10.1504/ijmms.2019.10025066

## The main drawback is that machine tools generally offer reduced spaces for the actuator location close to the cutting point and, hence, a reduced volume design is required for this external device.

Comparison of model free control strategies for chatter suppression by an inertial actuator

10.1016/J.ATMOSENV.2018.11.051

## Furthermore a set of hyper-surface functions associated with each POD basis function is constructed for representing the fluid dynamics over the reduced space.

Machine learning-based rapid response tools for regional air pollution modelling

10.1007/978-3-030-01641-8_11

## In this research, a heuristic optimisation paradigm Reduced Space Searching Algorithm, combined with soft-computing-based modelling and data analysis techniques, is employed to solve the problem.

Optimisation in Friction Stir Welding: Modelling, Monitoring and Design

10.1109/EMBC.2019.8857879

## Existing methods rely on either the probabilistic distribution of training data or the discriminant power of the reduced space, disregarding the impact of repeatability and uncertainty in features.

Selection of Radiomics Features based on their Reproducibility

10.1007/s00027-019-0634-3

## In aquatic systems, increasing density of aquatic vegetation creates more habitat structural complexity for fishes, but only up to a certain threshold, beyond which fish abundance and diversity are restricted by reduced space.

α and β diversity of fishes in relation to a gradient of habitat structural complexity supports the role of environmental filtering in community assembly

10.1007/s10444-019-09716-7

## In the second approach, we derive an inf-sup stable velocity-pressure reduced-order model by enriching the velocity reduced space with supremizers computed on a velocity reference space.

POD model order reduction with space-adapted snapshots for incompressible flows

10.1016/J.ENGAPPAI.2019.04.013

## However, because these monitoring methods use Hotelling’s T 2 statistics in the reduced space, a normality assumption underlies the construction of these tools.

Process monitoring using variational autoencoder for high-dimensional nonlinear processes

10.1109/TIMES-iCON47539.2019.9024501

## An enterprise that has implemented virtualization can consolidate multiple servers into fewer host servers and get the benefits of reduced space, power, and administrative requirements.

Server Scalability Using Kubernetes

10.1016/J.INS.2019.04.005

## Besides, an explicit nonlinear mapping relationship from data to the reduced space can be obtained as the regression of a nonlinear function.

A manifold learning approach to dimensionality reduction for modeling data

10.1007/978-3-030-41057-5_146

## A Rayleigh-Ritz approach, based on a suitable number of modal shapes of the uniform shear-torsional beam models, allows to discretize the analysis and to evaluate the response in the generalized reduced space.

A Simplified Beam-Like Model for the Dynamic Analysis of Multi-storey Buildings

10.1007/s13258-019-00896-6

## Results The characteristics of the dimensionality reduction methods are observed on the nine groups of three different tissues in the reduced space with dimensionality of two, three, and four.

Performance comparison of dimensionality reduction methods on RNA-Seq data from the GTEx project

10.1016/j.anihpc.2020.05.003

## By making use of symmetries and suitable first integrals of the system, we explicitly define a global 2-form for which the gauge transformed nonholonomic bracket gives rise to a new bracket on the reduced space codifying the nonholonomic dynamics and carrying an almost symplectic foliation (determined by the common level sets of the first integrals).

Conserved quantities and Hamiltonization of nonholonomic systems

10.20944/preprints201910.0139.v1

## Biological samples are a complex and heterogeneous matrix where different macromolecules with different physicochemical parameters cohabit in reduced spaces.

Synthesis, Photophysics, and Solvatochromic Studies of an Aggregated-Induced-Emission Luminogen Useful in Bioimaging

## We provide a data‐driven approach to generating nonlinear reduced spaces for deformation dynamics.

Latent‐space Dynamics for Reduced Deformable Simulation

10.1109/TVCG.2018.2865051

## We present a direct manipulation technique that allows material scientists to interactively highlight relevant parameterized simulation instances located in dimensionally reduced spaces, enabling a user-defined understanding of a continuous parameter space.

Drag and Track: A Direct Manipulation Interface for Contextualizing Data Instances within a Continuous Parameter Space

10.1007/s11063-019-10039-3

## This paper combines the nonnegativity and graph constraints to find the original geometrical information intrinsic to high dimensional data, keeping it in a dimensionality reduced space.

Graph Regularized Sparse Autoencoders with Nonnegativity Constraints

10.1088/1361-6544/ab28aa

## Specifically, we combine symplectic reduction by stages with a dual pair associated with the reduction by rotations to show that the -reduced space with non-zero angular impulse is a coadjoint orbit.

Symplectic reduction and the Lie–Poisson shape dynamics of N point vortices on the plane

## For the iterative diagonalization, pairs of Hermitian and anti-Hermitian trial vectors are used which facilitate, on the one hand, an efficient solution of the pair-structured generalized eigenvalue problem in the reduced space, and on the other hand, make the full multiconfigurational random phase approximation as efficient as the corresponding Tamm-Dancoff approximation.

CASSCF linear response calculations for large open-shell molecules.

10.1007/978-3-030-31680-8_26

## This is especially applicable for urban areas and bottlenecks, since the compact design of the high-temperature superconductor cables (HTS cables) and the reduced space requirement leads to a significant reduction in the civil engineering expenditure and to a reduction in installation costs.

Investigation of the Electromagnetic Fields of a HTS-Three Core Cable Arrangement at Mains Frequency for the Determination of Electrical Properties by Using FEM

10.1016/J.ASR.2019.06.033

## This model defines a Poisson flow endowed with invariants defining a S M 2 × S M 2 reduced space.

Relative equilibria of an intermediary model for the roto-orbital dynamics. The low rotation regime

10.1016/J.CMA.2018.10.013

## The adjoint of the tangent linear model is replaced by the adjoint of linear reduced model and the minimization problem is then solved in the reduced space at very low computational cost.

A variational approach for parameter estimation based on balanced proper orthogonal decomposition

10.1007/s12530-017-9207-7

## These methods transform the time series from the original space into a reduced space, where they can be managed more efficiently.

Applying nature-inspired optimization algorithms for selecting important timestamps to reduce time series dimensionality

10.1109/ICECCT.2019.8869493

## Our algorithm consists of two steps: in the first step we decompose the output label space into lower dimensions using simple matrix factorization method; subsequently we employ feature selection process in the decoupled reduced space.

A Simple Method of Solution For Multi-label Feature Selection

10.1007/s10898-019-00791-0

## We see that the presented algorithm provides a significant improvement in tightness and decrease in computational time, especially in the case studies using the reduced space formulation presented in (Bongartz and Mitsos in J Glob Optim 69:761–796, 2017).

Tighter McCormick relaxations through subgradient propagation

10.1007/978-3-030-31574-0_6

## Model reduction be used to approach the solution of the problem in a reduced space dimension.

Reduced Order Methods

10.1016/J.JCP.2019.01.031

## As a regression model of the RB method for unsteady flows, the neural network approximates the map between the time/parameter value and the projection coefficients of the high-fidelity solution onto the reduced space.

Non-intrusive reduced order modeling of unsteady flows using artificial neural networks with application to a combustion problem

10.1109/CoDIT.2019.8820700

## In the current signal reconstruction, the introduced PLL topology has the advantage of reduced space harmonics.

Sensorless Control Applying Signal Injection Methodology on Modified Model of Permanent Magnet Synchronous Machine

## The proposed configuration aids in capturing more data in a reduced space as well as tunable frequency operation.

A high capacity tunable retransmission type frequency coded chipless radio frequency identification system

10.1134/S1560354719040026

## The intermediate reduced spaces obtained by left or right reduction are shown to be coadjoint orbits of the special Euclidean group $SE(4)$.

Singular Reduction of the 2-Body Problem on the 3-Sphere and the 4-Dimensional Spinning Top.

## We show that the reduced space for this Hamiltonian action for 3 vortices is generically a 2-sphere, and proceed to describe the reduced dynamics under simple hypotheses on the type of Hamiltonian interaction.

Generalized point vortex dynamics on \begin{document}$\mathbb{CP} ^2$\end{document}

## This relies upon applying Seiberg-Witten theory to the resolution of symplectic $4$-orbifolds occurring as the reduced spaces of $M$.

S1‐invariant symplectic hypersurfaces in dimension 6 and the Fano condition

10.1080/13632469.2017.1351407

## The d-MTMDs are also convenient to install owing to the reduced space requirements, being placed at various floors.

Distributed Tuned Mass Dampers for Multi-Mode Control of Benchmark Building under Seismic Excitations

## These reduced spaces are chosen based on the independent mode displaced harmonic oscillator model.

Vibrationally resolved emission spectra of luminescent conjugated oligothiophenes from anharmonic calculations.

10.29327/24816.4.3-11

## Case Report: Male patient, 13 years old, Angle Class I in the mixed dentition stage, with the tooth 21 impacted and reduced space for its eruption due to the migration of adjacent teeth.

INTEGRATED TREATMENT BETWEEN ORTHODONTICS AND PEDIATRIC DENTISTRY USING THE ULECTOMY TECHNIQUE: CASE REPORT

10.1007/S11071-019-04940-8

## Therefore, the exact linear eigensolution is employed to formulate a nonlinearly coupled two-degrees-of-freedom model, defined in the reduced space of the modal amplitudes corresponding to a global and a local mode.

Modal interactions in the nonlinear dynamics of a beam–cable–beam

10.23919/ELINFOCOM.2019.8706479

## For radar detection of range-spread targets with unknown Doppler shift, we derive a detector, called the maximization in the reduced space (MRS) detector, based on simplification of the generalized likelihood ratio test.

Performance and Computational Efficiency of a Radar Detection Scheme for Range-Spread Targets

10.1007/978-981-13-1280-9_44

## Our proposed algorithms works by combining Principal Component Analysis (PCA) with Random Projection (RP) to project the data into feature space, then performs K-means clustering on that reduced space (feature space).

Clustering High-Dimensional Data: A Reduction-Level Fusion of PCA and Random Projection

10.1021/acs.jctc.9b00032

## By constructing a bias potential in this reduced space, one is then able to sample efficiently and reconstruct the free energy landscape.

Making the Best of a Bad Situation: A Multiscale Approach to Free Energy Calculation.

10.26714/medart.1.2.2019.45-56

## Patients usually come to a health care provider with nonspecific complaints and with symptoms such as pain in the ankles, swelling and reduced space for movement.

Patofisiologi dan Tatalaksana Osteochondral Lesion of the Talus

10.1080/02522667.2019.1637999

## Overall, a dimensionally reduced space does not significantly affect the prediction performance of the SDP models.

ELM and KELM based software defect prediction using feature selection techniques

10.1007/978-3-030-23756-1_46

## In this study, a completely different reduced space method based on Learning Vector Quantization is suggested for positioning analysis.

Competitive Positioning Analysis with Learning Vector Quantization

10.1109/ISPA-BDCloud-SustainCom-SocialCom48970.2019.00110

## Experimental results confirm that the PLS method is faster than Nauty, and has reduced space requirements.

Towards a Latin-Square Search Engine

10.1016/J.FLOWMEASINST.2019.05.002

## Finally, a support vector machine (SVM) is deployed to develop an objective classifier in the reduced space.

Identification of gas-liquid flow regimes using a non-intrusive Doppler ultrasonic sensor and virtual flow regime maps

10.1109/TFUZZ.2018.2879465

## In this study, a minimum spanning tree based reduced space FJP algorithm is proposed.

A Space Efficient Minimum Spanning Tree Approach to the Fuzzy Joint Points Clustering Algorithm

10.15199/48.2019.10.43

## The PCA model built from historical measurements of 12 selected process variables, mapped to the reduced space of three Principal Components (PC) of the highest magnitude, was used to establish the confidence ellipsoid, i.

Application of PCA for early leak detection in a pipeline system of a steam boiler

10.1109/ICHVET.2019.8724361

## Gas Insulated Substations (GIS) offer significant advantages over conventional Air Insulated Substations (AIS) on account of reduced space and operational efficiency.

Ultra-High Frequency (UHF) Based Partial Discharge Measurement in Gas Insulated Switchgear (GIS)

10.1007/s12530-017-9207-7

## These methods transform the time series from the original space into a reduced space, where they can be managed more efficiently.

Applying Nature-Inspired Optimization Algorithms for Selecting Important Timestamps to Reduce Time Series Dimensionality

10.1109/TAES.2018.2847980

## Employing the generalized likelihood ratio test and semidefinite programming (SDP), we derive two detectors, called the SDP and maximization in the reduced space (MRS) detectors for range-spread targets with unknown Doppler shift.

Detection Schemes for Range-Spread Targets Based on the Semidefinite Problem

10.36453/2318-5104.2019.V17.N1.P273

## In the formations the principles of the educational sport, criteria for choosing a good game, variations and activities for reduced spaces were approached.

Interfaces entre pesquisa e extensão: uma proposta de ressignificação da formação em educação física escolar

10.1016/J.COMPSTRUC.2019.03.012

## The second-level reduction then solves the complex, nonlinear eigenmode solutions in the tier-one reduced space about a fixed temperature to further reduce the equations-of-motion.

Two-tier model reduction of viscoelastically damped finite element models

## Our solver is based on a globalized, preconditioned, inexact reduced space Gauss--Newton--Krylov scheme.

CLAIRE: A distributed-memory solver for constrained large deformation diffeomorphic image registration

10.1007/S00158-018-2079-Z

## Moreover, the whole optimization algorithm is carried out alternately in the global space and a reduced space.

Multi-surrogate-based global optimization using a score-based infill criterion

10.1007/s10915-018-0894-4