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Background: Efforts to profile atopic dermatitis (AD) tissues have intensified, yet comprehensive analysis of systemic immune landscapes in severe AD remains crucial. Methods: Employing single‐cell RNA sequencing, we analyzed over 300,000 peripheral blood mononuclear cells from 12 severe AD patients (Eczema area and severity index (EASI) > 21) and six healthy controls. Results: Results revealed significant immune cell shifts in AD patients, including increased Th2 cell abundance, reduced NK cell clusters with compromised cytotoxicity, and correlated Type 2 innate lymphoid cell proportions with disease severity. Moreover, unique monocyte clusters reflecting activated innate immunity emerged in very severe AD (EASI > 30). While overall dendritic cells (DCs) counts decreased, a distinct Th2‐priming subset termed "Th2_DC" correlated strongly with disease severity, validated across skin tissue data, and flow cytometry with additional independent severe AD samples. Beyond the recognized role of Th2 adaptive immunity, our findings highlight significant innate immune cell alterations in severe AD, implicating their roles in disease pathogenesis and therapeutic potentials. Conclusion: Apart from the widely recognized role of Th2 adaptive immunity in AD pathogenesis, alterations in innate immune cells and impaired cytotoxic cells have also been observed in severe AD. The impact of these alterations on disease pathogenesis and the effectiveness of potential therapeutic targets requires further investigation. [ABSTRACT FROM AUTHOR]

This paper considers intelligent reflecting surface (IRS)-aided single-user (SU) massive multiple-input multiple-output (mMIMO) millimeter wave (mmWave) downlink communication system. We aim to maximize the achievable spectral efficiency by separately designing the passive beamforming and active precoding (combining) through a decoupling strategy to reduce computational complexity. We propose two algorithms for passive beamforming design, which are followed by singular value decomposition (SVD) of the effective channel matrix to generate the active precoding and combining matrices at the bases station (BS) and user equipment (UE), respectively. The first algorithm employs the SVD of the BS-IRS and the IRS-UE channel matrices to generate the unitary matrices. These matrices are used to develop the optimization problem, which is solved via a Riemannian conjugate gradient (RCG)-based algorithm, yielding a passive beamforming vector. In the second algorithm, we propose a greedy-search (GS)-based method to select the array response vectors and their corresponding path gains of the mmWave channels between the BS (IRS) and IRS (UE) required to formulate the optimization problem, which is also solved via the RCG-based algorithm, resulting in a passive beamforming vector. The simulation results show that the proposed schemes achieve an improved trade-off between the spectral efficiency and computational complexity. [ABSTRACT FROM AUTHOR]

In this work, we investigate hybrid analog–digital beamforming (HBF) architectures for uplink cell-free (CF) millimeter-wave (mmWave) massive multiple-input multiple-output (MIMO) systems. We first propose two HBF schemes, namely, decentralized HBF (D-HBF) and semi-centralized HBF (SC-HBF). In the former, both the digital and analog beamformers are generated independently at each AP based on the local channel state information (CSI). In contrast, in the latter, only the digital beamformer is obtained locally at the access point (AP), whereas the analog beamforming matrix is generated at the central processing unit (CPU) based on the global CSI received from all APs. We show that the analog beamformers generated in these two HBF schemes provide approximately the same achievable rates despite the lower complexity of D-HBF and its lack of CSI requirement. Furthermore, to reduce the power consumption, we propose a novel adaptive radio frequency (RF) chain-activation (ARFA) scheme, which dynamically activates/deactivates RF chains and their connected analog-to-digital converters (ADCs) and phase shifters (PSs) at the APs based on the CSI. For the activation of RF chains, low-complexity algorithms are proposed, which can achieve significant improvement in energy efficiency (EE) with only a marginal loss in the total achievable rate. [ABSTRACT FROM AUTHOR]

This work investigates the multiple-input multiple-output system in the context of the selective decode-and-forward multihop relay network under short-packet communications to facilitate not only ultra-reliability, but also low-latency communications. For the transmit and receive diversity techniques, we analyze the transmit antenna selection (TAS) and maximum-ratio transmission (MRT) schemes at the transmit side, whereas the selection-combining (SC) and maximum-ratio combining (MRC) schemes are leveraged at the receive side. For quasi-static Rayleigh fading channels and the finite-blocklength regime, we derive the approximate closed-form expressions of the end-to-end (e2e) block error rate (BLER) for the TAS/MRC, TAS/SC, and MRT/MRC schemes. The asymptotic performance in the high signal-to-noise ratio regime is derived, from which the comparison among diversity schemes in terms of the diversity order, e2e BLER loss, and SNR gap is provided. Furthermore, based on the asymptotic results, we develop power-allocation, relay-location, and joint simplified optimizations to minimize the asymptotic e2e BLER under the system constraints. The e2e latency and throughputs are also analyzed for the considered schemes. The correctness of our analysis is confirmed via Monte Carlo simulations. [ABSTRACT FROM AUTHOR]

Reconfigurable intelligentsurface (RIS) has emerged as a cost- and energy-efficient solution to enhance the wireless communications capacity. However, recent studies show that a very large surface is required for a RIS-assisted communications system; otherwise, they may be outperformed by the conventional relay. Furthermore, the performance gain of a RIS can be considerably degraded by hardware impairments such as limited-resolution phase shifters. To overcome those challenges, we propose a hybrid relay-reflecting intelligent surface (HR-RIS) architecture, in which a single or few elements serve as active relays, while the remaining only reflect the incident signals. We propose two HR-RIS architectures, namely, the fixed and dynamic HR-RIS. The joint transmit beamforming at the base station and hybrid relay-reflecting at the HR-RIS are designed based on alternating optimization and successive convex approximation methods. The simulation results for a $4 \times 2$ multiple-input multiple-output system show that the proposed HR-RIS with only a single active element can achieve about 40% and 25% improvement in spectral efficiency and energy efficiency, respectively, with respect to the conventional RIS-aided system. The results also show that the HR-RIS can outperform the conventional relaying scheme in most of the considered scenarios. [ABSTRACT FROM AUTHOR]

In this paper, we investigate a realistic code-acquisition-assisted cooperative noncoherent (NC) multiple-input--multiple-output (MIMO) direct-sequence code-division multiple-access (DS-CDMA) downlink scenario, when communicating over uncorrelated single- and multipath Rayleigh channels. The probabilities of correct detection and false alarm have analytically been derived. Furthermore, a mean acquisition time (MAT) formula is provided for the cooperative transmission scenario considered. The associated MAT performance trends are characterized as a function of both the number of relay stations (RSs) and the number of receive antennas and link imbalance. As opposed to the classic scenario of having colocated MIMO elements, our findings suggest that employing distributed MIMO elements acting as RSs combined with multiple receive antennas leads to an improved MAT performance. Index Terms--Code acquisition, cooperative, direct-sequence code-division multiple-access (DS-CDMA), noncoherent (NC) MIMO system, relay station (RS).

In this work, we apply deep learning to estimate the direction-of-arrival (DoA) of multiple narrowband signals with a uniform linear array in a coherent environment. First, the logarithmic eigenvalue-based classification network (LogECNet) is introduced to enhance signal number detection accuracy in challenging scenarios, such as the low signal-to-noise (SNR) regime and limited snapshots. Next, a multi-label classification model called the root-spectrum network (RSNet) is devised to estimate the DoAs using the signal number inferred by LogECNet. In the proposed architecture, the full-row Toeplitz matrices reconstruction (FTMR), which exploits all rows of the signal covariance matrix (SCM), is combined with LogECNet and RSNet to inversely map the SCM to the numerical DoAs in the coherent scenario. It is shown that the eigenvalues factorized from the FTMR output matrix become more robust sources for signal enumeration than those of the forward/backward spatial smoothing (FBSS) algorithm. Furthermore, the logarithmic scaling of the eigenvalues of the FTMR results in LogECNet outperforming other detectors. The simulation results show our proposed method not only improves the signal number detection and angular estimation performance, but also achieves the complexity reduction with respect to the prior schemes. [ABSTRACT FROM AUTHOR]

Link adaptation (LA) is an adaptive transmission technique that determines the modulation and coding scheme (MCS) based on channel-state information. In LA, an accurate estimation of the link performance is required to optimally determine the MCS level. In this correspondence, a high-accuracy machine-learning (ML)-aided link-level performance-prediction method for coded multiple-input–multiple-output (MIMO) systems is proposed. The basic concept of this scheme is to apply the ML model to train the relation between the inputs, such as the channel matrix and signal-to-noise ratio, and the output of the block-error rate (BLER). Specifically, we predict the index of the quantized BLER value using a random forest classifier. The simulation results show that the proposed scheme is able to accurately predict the link performance of MIMO systems and outperforms the conventional link performance-prediction schemes. [ABSTRACT FROM AUTHOR]

We propose a training-sequence-based frequency-offset estimator for a multiple transmit-and-receive antenna system in frequency-flat fading channels. The estimator is based on the maximum likelihood (ML) criterion and does not require channel information. To reduce the computational load, they propose to use special training sequences--the periodic orthogonal codes. Using these codes, we get a dosed form estimator which requires much lower computational load (some additions and multiplications). For the high signal-to-noise ratio and small frequency offset, the proposed estimator achieves the performance of the optimal ML estimator, which locates the peak of the likelihood function. We also apply the proposed estimator to a multiple antenna system in frequency-selective channels and an orthogonal-frequency-division-multiplexing system. With theoretical analysis and simulations, we evaluate the performance of the proposed estimator. Index Terms--Frequency offset, multiple-input multiple-output (MIMO), multiple antennas, orthogonal frequency division multiplexing (OFDM).

Although the sphere decoder (SD) is a powerful detector for multiple-input multiple-output (MIMO) systems, it has become computationally prohibitive in massive MIMO systems, where a large number of antennas are employed. To overcome this challenge, we propose fast deep learning (DL)-aided SD (FDL-SD) and fast DL-aided $K$ -best SD (KSD, FDL-KSD) algorithms. Therein, the major application of DL is to generate a highly reliable initial candidate to accelerate the search in SD and KSD in conjunction with candidate/layer ordering and early rejection. Compared to existing DL-aided SD schemes, our proposed schemes are more advantageous in both offline training and online application phases. Specifically, unlike existing DL-aided SD schemes, they do not require performing the conventional SD in the training phase. For a $24 \times 24$ MIMO system with QPSK, the proposed FDL-SD achieves a complexity reduction of more than 90% without any performance loss compared to conventional SD schemes. For a $32 \times 32$ MIMO system with QPSK, the proposed FDL-KSD only requires $K = 32$ to attain the performance of the conventional KSD with $K=256$ , where $K$ is the number of survival paths in KSD. This implies a dramatic improvement in the performance–complexity tradeoff of the proposed FDL-KSD scheme. [ABSTRACT FROM AUTHOR]

In this work, we propose a novel dynamic unequal sub-array (DUESA) architecture for massive multiple-input multiple-output (MIMO) systems with partially connected hybrid beamforming (PC-HBF) that relaxes the antenna-allocation constraint in the conventional unequal sub-array (UESA) architecture. The proposed DUESA architecture dynamically allocates antennas to sub-arrays based on channel state information, which leads to a combinatorial problem to optimize the sum rate. The exact solution to this problem requires an exhaustive search; however, the total number of candidates to search through can be extremely large in massive MIMO systems. To address this challenge, we propose three sub-optimal algorithms. The first is a tabu search-based algorithm, which examines the neighbors of the current solution to antenna-to-sub-array allocation and moves to the best one in each iteration. The second is a sequential antenna-reallocation algorithm with reduced complexity, which updates an antenna-to-sub-array assignment in each iteration. The third algorithm, that is, greedy antenna allocation, is composed of two sub-optimal algorithms. In its first part, only a single antenna is allocated to each sub-array based on a conventional algorithm. Then, in the second part, the antennas are added sequentially to each sub-array to optimize the system sum rate. The numerical results demonstrate that the DUESA architecture achieves substantially higher total achievable rates than conventional PC-HBF schemes. Furthermore, it has approximately 10%–20% higher energy efficiency than the conventional UESA architecture. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new hybrid analog and digital combining architecture for millimeter wave (mmWave) multi-user multiple-input multiple-output (MU-MIMO) systems. The proposed structure employs antenna subset selection per radio frequency (RF) chain based on active/inactive switches and uses constant phase shifters (CPS) to control the phases of signals in the RF circuit. In this scheme, for each RF chain, a subset of receive antennas that contribute more to the desired signal power than the interference power is chosen for signal combining in the analog domain, whereas other receive antennas are excluded from signal combining, thereby enhancing sum-rates. Simultaneously, the proposed structure reduces power consumption in the RF circuit by exclusively activating switches that correspond to the antennas selected for each RF chain. We also develop three low-complexity algorithms for per-RF chain antenna subset selection. Finally, through numerical simulation, we show that the proposed structure provides higher spectral efficiency and higher energy efficiency than conventional hybrid analog and digital combining schemes for mmWave MU-MIMO systems. [ABSTRACT FROM AUTHOR]

A variety of hybrid analog-digital beamforming architectures have recently been proposed for massive multiple-input multiple-output (MIMO) systems to reduce energy consumption and the cost of implementation. In the analog processing network of these architectures, the practical sub-connected structure requires lower power consumption and hardware complexity than the fully connected structure but cannot fully exploit the beamforming gains, which leads to a loss in overall performance. In this work, we propose a novel unequal sub-connected architecture for hybrid combining at the receiver of a massive MIMO system that employs unequal numbers of antennas in sub-antenna arrays. The optimal design of the proposed architecture is analytically derived, and includes antenna allocation and channel ordering schemes. Simulation results show that an enhancement of up to 10% can be attained in the total achievable rate by unequally assigning antennas to sub-arrays in the sub-connected system at the cost of a marginal increase in power consumption. Furthermore, in order to reduce the computational complexity involved in finding the optimal number of antennas connected to each radio frequency (RF) chain, we propose three low-complexity antenna allocation algorithms. The simulation results show that they can yield a significant reduction in complexity while achieving near-optimal performance. [ABSTRACT FROM AUTHOR]

In the conventional tabu search (TS) detection algorithm for multiple-input multiple-output (MIMO) systems, the metrics of all neighboring vectors are computed to determine the best one to move to. This strategy requires high computational complexity, especially in large MIMO systems with high-order modulation schemes such as 16- and 64-QAM signaling. This paper proposes a novel reduced-complexity TS detection algorithm called neighbor-grouped TS (NG-TS), which divides the neighbors into groups and finds the best neighbor by using a simplified cost function. Furthermore, based on the complexity analysis of NG-TS, we propose a channel ordering scheme that further reduces its complexity. Simulation results show that the proposed NG-TS with channel ordering can achieve up to 85% complexity reduction with respect to the conventional TS algorithm with no performance loss in both low- and higher-order modulation schemes. [ABSTRACT FROM AUTHOR]

This paper proposes an adaptive threshold-aided K-best sphere decoding (AKSD) algorithm for large multiple-input multiple-output systems. In the proposed scheme, to reduce the average number of visited nodes compared to the conventional K-best sphere decoding (KSD), the threshold for retaining the nodes is adaptively determined at each layer of the tree. Specifically, we calculate the adaptive threshold based on the signal-to-noise ratio and index of the layer. The ratio between the first and second smallest accumulated path metrics at each layer is also exploited to determine the threshold value. In each layer, in addition to the K paths associated with the smallest path metrics, we also retain the paths whose path metrics are within the threshold from the Kth smallest path metric. The simulation results show that the proposed AKSD provides nearly the same bit error rate performance as the conventional KSD scheme while achieving a significant reduction in the average number of visited nodes, especially at high signal-to-noise ratios. [ABSTRACT FROM AUTHOR]

In this paper, the authors propose a novel partially connected hybrid beamforming (PC-HBF) architecture, which employs variable phase shifters (VPSs) and constant phase shifters (CPSs) for analog beamforming to harness the potential of these two types of phase shifters. In the proposed architecture, the system sum rate optimization to determine the analog precoders can be formulated as a combinatorial problem. However, its exact solution is intractable, and in massive multiple-input multiple-output systems, exhaustive search to solve the corresponding combinatorial problem is practically infeasible. To resolve this problem, we employ a greedy algorithm that provides a near-optimal solution with reduced complexity. The simulation results obtained herein show that by optimally combining VPSs and CPSs, the proposed architecture achieves performance close to that of the VPS-based PC-HBF architecture. Furthermore, its energy efficiency is up to 27.3 % higher than that of the CPS-based fully connected HBF scheme. [ABSTRACT FROM AUTHOR]

In the conventional tabu search (TS) detection algorithm for multiple-input multiple-output (MIMO) systems, the cost metrics of all neighboring vectors are computed to determine the best neighbor. This can require an excessively high computational complexity, especially in large MIMO systems because the number of neighboring vectors and the dimension per vector are large. In this study, we propose an improved TS algorithm based on the QR decomposition of the channel matrix (QR-TS), which allows for finding the best neighbor with a significantly lower complexity compared with the conventional TS algorithm. Specifically, QR-TS does not compute all metrics by early rejecting unpromising neighbors, which reduces the computational load of TS without causing any performance loss. To further optimize the QR-TS algorithm, we investigate novel ordering schemes, namely the transmit-ordering (Tx-ordering) and receive-ordering (Rx-ordering), which can considerably reduce the complexity of QR-TS. Simulation results show that QR-TS reduces the complexity approximately by a factor of two compared with the conventional TS. Furthermore, when both Tx-ordering and Rx-ordering are applied, QR-TS requires approximately $60\%\text{ -- }90\%$ less complexity compared with the conventional TS scheme. The proposed algorithms are suitable for both low-order and high-order modulation, and can achieve a significant complexity reduction compared to the Schnorr–Euchner and $K\text{-}$ best sphere decoders in large MIMO systems. [ABSTRACT FROM AUTHOR]

In this study, we consider the downlink of millimeter-wave massive multiple-input multiple-output systems that employ orthogonal random precoding (ORP) and minimum-mean-square-error (MMSE) receivers. In the ORP scheme, a precoding matrix consisting of orthogonal vectors is utilized at the transmitter, which provides beamforming gains to enhance the maximum signal-to-interference-plus-noise ratio (SINR) at the receivers. In this study, the ability of the ORP scheme with MMSE receivers to extend the cell coverage and its sum-rate performance for cell-edge users are investigated. In particular, we first derive the approximate distribution of the maximum SINR at the output of the MMSE receiver. Then, to analyze and optimize the ORP scheme with MMSE receivers in terms of coverage and sum-rate performance, the analytical expressions for the downlink coverage probability and sum rate are derived. It is shown that there is a tradeoff between coverage and sum-rate performance in the ORP scheme. In particular, a smaller number of precoding vectors provides larger coverage; however, it leads to a lower sum rate. To achieve optimal tradeoff between coverage and sum rate for the ORP scheme, we propose using multiple random precoder groups over multiple time slots. It is shown that the proposed scheme is capable of significantly enhancing coverage performance while preserving an acceptable sum rate for cell-edge users. The simulation results validate the analytical findings. [ABSTRACT FROM AUTHOR]

In this study, low-complexity sphere decoding (SD) algorithms for generalized spatial modulation (GSM) are proposed. To reduce the computational complexity of the SD algorithm for GSM, layer ordering and transmit antenna combination (TAC) partitioning are employed. The layer ordering scheme determines the detection order of layers based on their reliabilities, which are measured by their minimum mean-square errors (MMSEs). In TAC partitioning, which is combined with the early termination technique, the likely TACs are selected by exploiting an MMSE-based weighting metric to reduce the search space. Simulation results demonstrate that the proposed ordering and partitioning aided SD schemes achieve nearly the same performance as the conventional SD scheme; however, they require significantly low complexity, especially in large GSM multiple-input-multiple-output systems and in the low SNR region. [ABSTRACT FROM AUTHOR]

This letter proposes a novel opportunistic beamforming algorithm, called adaptive perturbation-aided opportunistic beamforming. In each time slot, the proposed algorithm makes a random adjustment to the beamforming vector. Then, for data transmission, it adopts the successful perturbation, which yields performance improvements. By contrast, the failed perturbation is discarded. In addition to random perturbation, an adaptive component, which depends on the feedback information, is added to generate the next beamforming vector. Simulation results show that the proposed scheme provides significant improvement in terms of system throughput, especially, when there is a small number of mobile stations. [ABSTRACT FROM AUTHOR]

This correspondence paper proposes a low-complexity adaptive spatial modulation (ASM) scheme, which is based on sphere search (SS). To find the optimal ASM mode, the existing ASM schemes examine each error vector in the search space. By contrast, in the proposed SS-aided strategy, the search space is reduced to the error vectors inside a sphere, which results in significant complexity reduction. By exploiting a similar structure between the error vectors in ASM and symbol vectors in generalized spatial modulation (GSM), we modify the sphere decoder for GSM to develop an efficient two-step SS scheme for ASM. In addition, an early termination scheme is employed to further reduce the computational load of the SS process for each ASM mode. Simulation results show that SS-aided ASM provides a significant reduction in computational complexity compared to the existing ASM schemes. [ABSTRACT FROM AUTHOR]

This paper proposes a linear interference alignment (IA) scheme, which can be used for uplink channels in a general multicell multiuser multiple-input-multiple-output (MIMO) cellular network. The proposed scheme aims to align interference caused by signals from a set of transmitters into a subspace that is established by the signals from only a subset of those transmitters, thereby effectively reducing the number of interfering transmitters. The total degrees of freedom (DoF) achievable by the proposed scheme is given in closed-form expression, and a numerical analysis shows that the proposed scheme can achieve the optimal DoF in certain scenarios and provides a higher total DoF than other related schemes in most cases. [ABSTRACT FROM AUTHOR]

In this study, novel ordering algorithms of sphere decoding (SD) for spatial modulation (SM) are proposed to reduce the computational complexity. In the receive-ordering (Rx-ordering) scheme, the signals encountered at receive antennas are ordered to increase the probability of early termination during the search process. In contrast, the transmit-antenna indices and the constellation points in the transmit-ordering (Tx-ordering) scheme are ordered on the basis of a suboptimal solution, which is obtained from a subset of the received signals. To further reduce the computational complexity, the combined scheme of Rx-ordering and Tx-ordering is also presented. Simulation results show that SD aided by the proposed ordering schemes provides a substantial reduction in the computational complexity compared to existing SD algorithms in various environments while achieving near-optimal decoding performance. [ABSTRACT FROM PUBLISHER]

In this paper, we present uplink interference alignment (IA) schemes for two-cell multiple-input–multiple-output (MIMO) channels. Assuming that each cell has K interfering users, we propose an IA scheme for the full interference channel (FIC) and derive the achievable degrees of freedom (DOFs). The proposed scheme is extended to a two-cell Z-interference channel (ZIC), where only one of the two cells is subject to interference. The achievable DOF for the two-cell ZIC channel is also derived, and it is compared with that of the FIC with the IA and that of the conventional orthogonal scheme based on numerical results. [ABSTRACT FROM PUBLISHER]

An initial solution based on lattice reduction (LR) and a novel stopping criterion for the tabu search (TS) detection algorithm are proposed for use in multiple input multiple output (MIMO) antenna systems. LR aided‐detection is performed and its result is utilised as an initial solution to the TS algorithm, while a measure of the condition of the lattice‐reduced channel is used as a criterion for early termination of the algorithm. On the basis of the simulation results, this approach outperforms other initial solutions by about 3.5 dB at a BER of 10−3 for the 16‐QAM 16 × 16 MIMO with only a slight increment in computational cost. The proposed stopping criterion reduces the complexity further with virtually no loss in BER performance. [ABSTRACT FROM AUTHOR]

Summary: We present a new on-line internal calibration algorithm for a CDMA (code division multiple access) antenna array. The proposed calibration algorithm gives an accurate calibration vector, and as byproducts, the vector-channel parameters of an arbitrarily selected reference user. [Copyright &y& Elsevier]

The development of stress in metallic thin films, monitored by in-situ curvature measurements during deposition, is analyzed. Three distinct stress regions including initial compressive, broad tensile, and incremental compressive stress were reported in terms of the film thickness (deposition time) by F. Spaepen. An experimental set-up was assembled for the in-situ curvature measurements utilizing vacuum thermal evaporation and multi-beam laser reflection points arrayed in x- and y-axis. The change in the spacing of laser reflected points was converted to the curvature of specimen, in turn, to instantaneous stress levels in the growing films using Stoney's formula. To investigate the effect on the distinct stress regions, the flux of the depositing metallic atoms was used as an experimental variable in this study. For the lowest flux cases for Cu and Ag, an additional second compressive stress stages after tensile maximum stress was observed in this study. Initial compressive part and tensile maximum stress regions appeared in shorter period of time for the thin films deposited at higher flux of atoms. Thus the flux of depositing atoms may affect the mechanisms of each stage. The initial compressive stress is conjectured to stem from the state of thin film surfaces; dynamic and relaxed surface. A broad tensile region is reported from the fact that the reduction of excess volume associated with grain boundaries and/or the coalescence of grains for high mobility materials. The incremental compressive stress region may be related to surface state and atomic mobilities.