Orthogonal Gradient Research Articles

Massive-MIMO Sparse Uplink Channel Estimation Using Implicit Training and Compressed Sensing

Massive multiple-input multiple-output (massive-MIMO) is foreseen as a potential technology for future 5G cellular communication networks due to its substantial benefits in terms of increased spectral and energy efficiency. These advantages of massive-MIMO are a consequence of equipping the base station (BS) with quite a large number of antenna elements, thus resulting in an aggressive spatial multiplexing. In order to effectively reap the benefits of massive-MIMO, an adequate estimate of the channel impulse response (CIR) between each transmit–receive link is of utmost importance. It has been established in the literature that certain specific multipath propagation environments lead to a sparse structured CIR in spatial and/or delay domains. In this paper, implicit training and compressed sensing based CIR estimation techniques are proposed for the case of massive-MIMO sparse uplink channels. In the proposed superimposed training (SiT) based techniques, a periodic and low power training sequence is superimposed (arithmetically added) over the information sequence, thus avoiding any dedicated time/frequency slots for the training sequence. For the estimation of such massive-MIMO sparse uplink channels, two greedy pursuits based compressed sensing approaches are proposed, viz: SiT based stage-wise orthogonal matching pursuit (SiT-StOMP) and gradient pursuit (SiT-GP). In order to demonstrate the validity of proposed techniques, a performance comparison in terms of normalized mean square error (NCMSE) and bit error rate (BER) is performed with a notable SiT based least squares (SiT-LS) channel estimation technique. The effect of channels’ sparsity, training-to-information power ratio (TIR) and signal-to-noise ratio (SNR) on BER and NCMSE performance of proposed schemes is thoroughly studied. For a simulation scenario of: 4 × 64 massive-MIMO with a channel sparsity level of 80 % and signal-to-noise ratio (SNR) of 10 dB , a performance gain of 18 dB and 13 dB in terms of NCMSE over SiT-LS is observed for the proposed SiT-StOMP and SiT-GP techniques, respectively. Moreover, a performance gain of about 3 dB and 2.5 dB in SNR is achieved by the proposed SiT-StOMP and SiT-GP, respectively, for a BER of 10 − 2 , as compared to SiT-LS. This performance gain NCME and BER is observed to further increase with an increase in channels’ sparsity.

A Novel Measurement Matrix Optimization Approach for Hyperspectral Unmixing

Each pixel in the hyperspectral unmixing process is modeled as a linear combination of endmembers, which can be expressed in the form of linear combinations of a number of pure spectral signatures that are known in advance. However, the limitation of Gaussian random variables on its computational complexity or sparsity affects the efficiency and accuracy. This paper proposes a novel approach for the optimization of measurement matrix in compressive sensing (CS) theory for hyperspectral unmixing. Firstly, a new Toeplitz-structured chaotic measurement matrix (TSCMM) is formed by pseudo-random chaotic elements, which can be implemented by a simple hardware; secondly, rank revealing QR factorization with eigenvalue decomposition is presented to speed up the measurement time; finally, orthogonal gradient descent method for measurement matrix optimization is used to achieve optimal incoherence. Experimental results demonstrate that the proposed approach can lead to better CS reconstruction performance with low extra computational cost in hyperspectral unmixing.

Comparison Between 3-Scan Trace and Diagonal Body Diffusion-Weighted Imaging Acquisitions: A Phantom and Volunteer Study.

Diagonal diffusion-weighted imaging (dDWI) uses simultaneous maximized application of 3 orthogonal gradient systems as opposed to sequential acquisition in 3 directions in conventional 3-scan trace DWI (tDWI). Several theoretical advantages of dDWI vs. tDWI include reduced artifacts and increased sharpness. We compared apparent diffusion coefficient (ADC) quantification and image quality between monopolar dDWI and tDWI in a dedicated diffusion phantom (b = 0/500/900/2000 s/mm2) and in the abdomen (b = 50/400/800 s/mm2) and pelvis (b = 50/1000/1600 s/mm2) of 2 male volunteers at 1.5 T and 3.0 T. Phantom estimated signal-to-noise ratio (eSNR) was also measured. Two independent observers assessed the image quality on a 5-point scale. In the phantom, image quality was similar between tDWI and dDWI, with equivalent ADC quantification (mean coefficient of variation [CV] between sequences: 1.4% ± 1.2% at 1.5 T and 0.7% ± 0.7% at 3.0 T). Phantom eSNR was similar for both tDWI and dDWI, except for a significantly lower eSNR for b900 of dDWI at 3.0 T (P = .006). In the volunteers, the CV values between tDWI and dDWI were higher than those in the phantom (CV range: abdominal organs, 1.3%–13.3%; pelvic organs, 0.6%–5.7%). A trend toward significant better image quality for dDWI compared with tDWI was observed for b800 (abdomen) at 3.0 T and for b1000 and b1600 (pelvis) at 1.5 T (P = .063 to .066). Our data suggest that dDWI may provide better image quality than tDWI without affecting ADC quantification, needing confirmation in a future clinical study.

The temporal–spatial dynamics of feature maps during monocular deprivation revealed by chronic imaging and self-organization model simulation

Experiments on the adult visual cortex of cats, ferrets and monkeys have revealed organized spatial relationships between multiple feature maps which can also be reproduced by the Kohonen and elastic net self-organization models. However, attempts to apply these models to simulate the temporal kinetics of monocular deprivation (MD) during the critical period, and their effects on the spatial arrangement of feature maps, have led to conflicting results. In this study, we performed MD and chronic imaging in the ferret visual cortex during the critical period of ocular dominance (OD) plasticity. We also used the Kohonen model to simulate the effects of MD on OD and orientation map development. Both the experiments and simulations demonstrated two general parameter-insensitive findings. Specifically, our first finding demonstrated that the OD index shift resulting from MD, and its subsequent recovery during binocular vision (BV), were both nonlinear, with a significantly stronger shift occurring during the initial period. Meanwhile, spatial reorganization of feature maps led to globally unchanged but locally shifted map patterns. In detail, we found that the periodicity of OD and orientation maps remained unchanged during, and after, deprivation. Relationships between OD and orientation maps remained similar but were significantly weakened due to OD border shifts. These results indicate that orthogonal gradient relationships between maps may be preset and are only mildly modifiable during the critical period. The Kohonen model was able to reproduce these experimental results, hence its role is further extended to the description of cortical feature map dynamics during development.

Experimental comparison between speckle and grating-based imaging technique using synchrotron radiation X-rays.

X-ray phase contrast and dark-field imaging techniques provide important and complementary information that is inaccessible to the conventional absorption contrast imaging. Both grating-based imaging (GBI) and speckle-based imaging (SBI) are able to retrieve multi-modal images using synchrotron as well as lab-based sources. However, no systematic comparison has been made between the two techniques so far. We present an experimental comparison between GBI and SBI techniques with synchrotron radiation X-ray source. Apart from the simple experimental setup, we find SBI does not suffer from the issue of phase unwrapping, which can often be problematic for GBI. In addition, SBI is also superior to GBI since two orthogonal differential phase gradients can be simultaneously extracted by one dimensional scan. The GBI has less stringent requirements for detector pixel size and transverse coherence length when a second or third grating can be used. This study provides the reference for choosing the most suitable technique for diverse imaging applications at synchrotron facility.

Directing the spatial patterning of motor neuron differentiation in engineered microenvironments.

Embryonic development of the spinal cord proceeds through a carefully orchestrated temporal and spatial sequence of chemical cues to provide precise patterning of adult cell types. Recreating this complex microenvironment in a standard cell culture dish is difficult, if not impossible. In this paper, a microfluidic device is used to recapitulate, in vitro, the graded patterning events which occur during early spinal cord development. The microdevice design is developed using COMSOL modeling, with which the spatiotemporal profiles of multiple, diffusible morphogens are simulated. Four independently addressed source/sinks are employed to generate two overlapping orthogonal gradients within a cell culture chamber, mimicking the dorsoventral and anteroposterior axes of the developing embryo. Mouse embryonic stem cells are directed therein to differentiate into motor neurons in a spatially organized manner, reminiscent of a neural tube.

Direct Measurement of the Fluid Phase Diagram.

The thermodynamic phase of a fluid (liquid, vapor or supercritical) is fundamental to all chemical processes, and the critical point is particularly important for supercritical chemical extraction. Conventional phase measurement methods require hours to obtain a single datum on the pressure and temperature diagram. Here, we present the direct measurement of the full pressure-temperature phase diagram, with 10 000 microwells. Orthogonal, linear, pressure and temperature gradients are obtained with 100 parallel microchannels (spanning the pressure range), each with 100 microwells (spanning the temperature range). The phase-mapping approach is demonstrated with both a pure substance (CO2) and a mixture (95% CO2 + 5% N2). Liquid, vapor, and supercritical regions are clearly differentiated, and the critical pressure is measured at 1.2% error with respect to the NIST standard. This approach provides over 100-fold improvement in measurement speed over conventional methods.

Two-dimensional single-shot diffusion-weighted stimulated EPI with reduced FOV for ultrahigh-b radial diffusion-weighted imaging of spinal cord.

High-resolution diffusion-weighted imaging (DWI) of the spinal cord (SC) is problematic because of the small cross-section of the SC and the large field inhomogeneity. Obtaining the ultrahigh-b DWI poses a further challenge. The purpose of the study was to design and validate two-dimensional (2D) single-shot diffusion-weighted stimulated echo planar imaging with reduced field of view (2D ss-DWSTEPI-rFOV) for ultrahigh-b radial DWI (UHB-rDWI) of the SC. A novel time-efficient 2D ss-DWSTEPI-rFOV sequence was developed based on the stimulated echo sequence. Reduced-phase field of view was obtained by using two slice-selective 90 ° radiofrequency pulses in the presence of the orthogonal slice selection gradients. The sequence was validated on a cylindrical phantom and demonstrated on SC imaging. Ultrahigh-b radial diffusion-weighted ( bmax = 7300 s/mm2) images of the SC with greatly reduced distortion were obtained. The exponential plus constant fitting of the diffusion-decay curve estimated the constant fraction (restricted water fraction) as 0.36 ± 0.05 in the SC white matter. A novel 2D ss-DWSTEPI-rFOV sequence has been designed and demonstrated for high-resolution UHB-rDWI of localized anatomic structures with significantly reduced distortion induced by nonlinear static field inhomogeneity. Magn Reson Med 77:2167-2173, 2017. © 2016 International Society for Magnetic Resonance in Medicine.

Adaptively weighted orthogonal gradient binary pattern for single sample face recognition under varying illumination

To overcome the limitation of traditional illumination invariant methods for single sample face recognition, a modified version of gradientface named adaptively weighted orthogonal gradient binary pattern (AWOGBP), which is proved robust to illumination variation, is proposed in this study. First, the Tetrolet transform is performed on the images to obtain low frequency and high frequency components and the retina model processing is applied to low frequency component to make the image more robust to illumination, in the meantime, the authors multiply each element in high frequency components with a scale factor to accentuate details. Then the proposed AWOGBP is used to get the feature vectors of each direction and all the feature vectors are concatenated into the general feature vector for face recognition with the weights of the sub-graph based on their information entropy which is defined as the contribution to describe the whole face images. Finally the principle component analysis method is used to reduce dimensions and the nearest neighbour classifier is used for face image classification and recognition. Experimental results on CMU PIE and Extended Yale B face databases indicate that the proposed method is significantly better as compared with related state-of-the-art methods.

Development-on-chip: in vitro neural tube patterning with a microfluidic device.

Embryogenesis is a highly regulated process in which the precise spatial and temporal release of soluble cues directs differentiation of multipotent stem cells into discrete populations of specialized adult cell types. In the spinal cord, neural progenitor cells are directed to differentiate into adult neurons through the action of mediators released from nearby organizing centers, such as the floor plate and paraxial mesoderm. These signals combine to create spatiotemporal diffusional landscapes that precisely regulate the development of the central nervous system (CNS). Currently, in vivo and ex vivo studies of these signaling factors present some inherent ambiguity. In vitro methods are preferred for their enhanced experimental clarity but often lack the technical sophistication required for biological realism. In this article, we present a versatile microfluidic platform capable of mimicking the spatial and temporal chemical environments found in vivo during neural tube development. Simultaneous opposing and/or orthogonal gradients of developmental morphogens can be maintained, resulting in neural tube patterning analogous to that observed in vivo.

A numerical study of iterative substructuring method for finite element analysis of high frequency electromagnetic fields

This paper describes iterative methods for the high frequency electromagnetic analysis using the finite element method of Maxwell equations including displacement current. The conjugate orthogonal conjugate gradient method has been widely used to solve a complex symmetric system. However, the conventional method suffers from oscillating convergence histories in large-scale analysis. In this paper, to solve large-scale complex symmetric systems arising from the formulation of the E method, an iterative substructuring method like the minimal residual method is presented, and the performance of the convergence of the method is evaluated by numerical results. As the result, the proposed method shows a stable convergence behavior and a fast convergence rate compared to other iterative methods.

Maps of the Auditory Cortex.

One of the fundamental properties of the mammalian brain is that sensory regions of cortex are formed of multiple, functionally specialized cortical field maps (CFMs). Each CFM comprises two orthogonal topographical representations, reflecting two essential aspects of sensory space. In auditory cortex, auditory field maps (AFMs) are defined by the combination of tonotopic gradients, representing the spectral aspects of sound (i.e., tones), with orthogonal periodotopic gradients, representing the temporal aspects of sound (i.e., period or temporal envelope). Converging evidence from cytoarchitectural and neuroimaging measurements underlies the definition of 11 AFMs across core and belt regions of human auditory cortex, with likely homology to those of macaque. On a macrostructural level, AFMs are grouped into cloverleaf clusters, an organizational structure also seen in visual cortex. Future research can now use these AFMs to investigate specific stages of auditory processing, key for understanding behaviors such as speech perception and multimodal sensory integration.

The Effect of Microcirculatory Flow on Oscillating Gradient Diffusion MRI and Diffusion Encoding with Dual-Frequency Orthogonal Gradients (DEFOG).

We investigated the effect of microcirculatory flow on oscillating gradient spin echo (OGSE) diffusion MRI at low b-values and developed a diffusion preparation method called diffusion encoding with dual-frequency orthogonal gradients (DEFOG) to suppress the effect. Compared to conventional OGSE sequences, DEFOG adds a pulsed gradient that is orthogonal to the oscillating gradient and has a moderate diffusion weighting (e.g., 300 s/mm2 ). In vivo MRI data were acquired from adult mouse brains (n = 5) on an 11.7 Tesla scanner, with diffusion times from 23.2 to 0.83 ms and b-values from 50 to 700 s/mm2 . Apparent diffusion coefficients (ADCs) measured using a conventional OGSE sequence at low b-values (< 200 mm2 /s) were significantly higher than those measured at moderate b-values (> 300 mm2 /s), potentially due to contributions from microcirculatory flow. In comparison, OGSE ADCs measured using the DEFOG method at low b-values were comparable to those measured at moderate b-values. The effect of microcirculatory flow on diffusion signals was diffusion time-dependent, and this dependency may reflect the capillary geometry and blood flow velocity in the mouse cortex. Microcirculatory flow affects OGSE diffusion MRI measurements at low b-values, and this effect can be suppressed using the DEFOG method. Magn Reson Med 77:1583-1592, 2017. © 2016 International Society for Magnetic Resonance in Medicine.

New version of hex-ecs, the B-spline implementation of exterior complex scaling method for solution of electron–hydrogen scattering

We provide an updated version of the program hex-ecs originally presented in Comput. Phys. Commun. 185 (2014) 2903–2912. The original version used an iterative method preconditioned by the incomplete LU factorization (ILU), which–though very stable and predictable–requires a large amount of working memory. In the new version we implemented a “separated electrons” (or “Kronecker product approximation”, KPA) preconditioner as suggested by Bar-On et al., Appl. Num. Math. 33 (2000) 95–104. This preconditioner has much lower memory requirements, though in return it requires more iterations to reach converged results. By careful choice between ILU and KPA preconditioners one is able to extend the computational feasibility to larger calculations.Secondly, we added the option to run the KPA preconditioner on an OpenCL device (e.g. GPU). GPUs have generally better memory access times, which speeds up particularly the sparse matrix multiplication. New version program summaryProgram title: hex-ecsCatalogue identifier: AETI_v2_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AETI_v2_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: MIT LicenseNo. of lines in distributed program, including test data, etc.: 73693No. of bytes in distributed program, including test data, etc.: 520475Distribution format: tar.gzProgramming language: C++11.Computer: Any recent CPU, preferably 64-bit. Computationally intensive parts can be run on GPU (tested on AMD Tahiti and NVidia TitanX models).Operating system: Tested on Windows 10 and various Linux distributions.RAM: Depends on the problem solved and particular setup; KPA test run uses apx. 300 MiB.Classification: 2.4.Catalogue identifier of previous version: AETI_v2_0Journal reference of previous version: Comput. Phys. Comm. 185 (2014) 2903External routines: GSL [1], UMFPACK [2], BLAS and LAPACK (ideally threaded OpenBLAS [3]).Does the new version supersede the previous version?: YesNature of problem: Solution of the two-particle Schrödinger equation in central field.Solution method: The two-electron states are expanded into angular momentum eigenstates, which gives rise to the coupled bi-radial equations. The bi-radially dependent solution is then represented in a B-spline product basis, which transforms the set of equations into a large matrix equation in this basis. The boundary condition is of Dirichlet type, thanks to the use of the exterior complex scaling method, which extends the coordinates into the complex plane. The matrix equation is then solved by preconditioned conjugated orthogonal conjugate gradient method (PCOCG) [4].Reasons for new version: The original program has been updated to achieve better performance. Also, some external dependencies have been removed (HDF5, FFTW3), which simplifies deployment.Summary of revisions: We implemented a new preconditioner introduced in [5], both for general CPU and also for an arbitrary OpenCL device (e.g. GPU) conforming to the OpenCL 2.0 specification. Furthermore, many other minor improvements have been made, particularly with the intention of reducing the memory requirements. With appropriate switches the program now does not precompute the used matrices and only calculates their elements on the fly. This is aided also by the vectorized B-spline evaluation function, which can now make use of AVX instructions when a single B-spline is being evaluated at several points. The accompanying tools hex-db and hex-dwba [6] have been also updated to use the shared code base.Running time: KPA test run — apx. 2 minutes on Intel i7-4790K (4 threads)

Tree diversity reduces pest damage in mature forests across Europe.

Forest pest damage is expected to increase with global change. Tree diversity could mitigate this impact, but unambiguous demonstration of the diversity–resistance relationship is lacking in semi-natural mature forests. We used a network of 208 forest plots sampled along two orthogonal gradients of increasing tree species richness and latitudes to assess total tree defoliation in Europe. We found a positive relationship between tree species richness and resistance to insect herbivores: overall damage to broadleaved species significantly decreased with the number of tree species in mature forests. This pattern of associational resistance was frequently observed across tree species and countries, irrespective of their climate. These findings confirm the greater potential of mixed forests to face future biotic disturbances in a changing world.

Inverse source problem based on two dimensionless dispersion-current functions in 2D evolution transport equations

Abstract The paper deals with the nonlinear inverse source problem of identifying an unknown time-dependent point source occurring in a two-dimensional evolution advection-dispersion-reaction equation with spatially varying velocity field and dispersion tensor. The originality of this study consists in establishing a constructive identifiability theorem that leads to develop an identification method using only significant boundary observations and operating other than the classic optimization approach. To this end, we derive two dispersion-current functions that have the main property to be of orthogonal gradients which yield identifiability of the elements defining the involved unknown source from some boundary observations related to the associated state. Provided the velocity field fulfills the so-called no-slipping condition, the required boundary observations are reduced to only recording the state on the outflow boundary and its flux on the inflow boundary of the monitored domain. We establish an identification method that uses those boundary records (1) to localize the sought source position as the unique solution of a nonlinear system defined by the two dispersion-current functions, (2) to give lower and upper bounds of the total amount loaded by the unknown time-dependent source intensity function, (3) to transform the identification of this latest into solving a deconvolution problem. Some numerical experiments on a variant of the surface water BOD pollution model are presented.

Concentration-Dependent hMSC Differentiation on Orthogonal Concentration Gradients of GRGDS and BMP-2 Peptides.

Self-assembled monolayer substrates containing tethered orthogonal concentration profiles of GRGDS (glycine/arginine/glycine/aspartic acid/serine) and BMP-2 (bone morphogenetic protein) peptides are shown to accelerate or decelerate, depending on the concentrations, the proliferation and osteoblastic differentiation of human mesenchymal stem cell (hMSC) populations in vitro without the use of osteogenic additives in culture medium. Concurrently, the single peptide gradient controls (GRGDS or BMP-2 only) induce significantly different proliferation and differentiation behavior from the orthogonal substrates. Bone sialoprotein (BSP) and Runt-related transcription factor 2 (Runx2) PCR data acquired from hMSC populations isolated by laser capture microdissection correspond spatially and temporally to protein marker data obtained from immunofluorescent imaging tracking of the differentiation process. Although genomic and protein data at high concentrations area GRGDS (71-83 pmol/cm(2)):BMP-2 (25 pmol/cm(2)) reveal an implicit acceleration on the hMSC differentiation timeline relative to the individual peptide concentrations, most of the GRGDS and BMP-2 combinations displayed significant antagonistic behavior during the hMSC differentiation. These data highlight the utility of the orthogonal gradient approach to aid in identifying optimal concentration ranges of translationally relevant peptides and growth factors for targeting cell lineage commitment.

Single-scan MRI with exceptional resilience to field heterogeneities.

Single-scan two-dimensional MRI has been generally constrained to acquisitions in high quality magnets. This study introduces a methodology, cross-term spatiotemporal encoding (xSPEN), that delivers such images under much poorer external field conditions. xSPEN departs from conventional k-space scanning, by relying on spatiotemporally encoding the image being sought. Unlike hitherto proposed SPEN methods, however, xSPEN's image readout does not take place using a field gradient along the direction being probed, but rather with the aid of an ancillary source of inhomogeneous frequency broadening. This ancillary dimension was here imposed by an orthogonal field gradient; for example, images along the "y" axis were read out by application of a "z" gradient. The principles and characteristics of this new approach, compatible with existing scanners and free from the need to collect auxiliary information such as field maps, are presented and discussed. Single- and multi-slice in vitro, ex vivo, and in vivo MRI experiments, confirmed the unusual resilience of this new single-shot MRI method to multiple chemical sites on phantoms, animals and humans. xSPEN can deliver single-scan MRI with good sensitivity and exceptional resilience to field inhomogeneities. This could enable investigations that have hitherto escaped from MRI's scope. Magn Reson Med 77:623-634, 2017. © 2016 International Society for Magnetic Resonance in Medicine.

Intra-coil interactions in split gradient coils in a hybrid MRI–LINAC system

An MRI–LINAC system combines a magnetic resonance imaging (MRI) system with a medical linear accelerator (LINAC) to provide image-guided radiotherapy for targeting tumors in real-time. In an MRI–LINAC system, a set of split gradient coils is employed to produce orthogonal gradient fields for spatial signal encoding. Owing to this unconventional gradient configuration, eddy currents induced by switching gradient coils on and off may be of particular concern. It is expected that strong intra-coil interactions in the set will be present due to the constrained return paths, leading to potential degradation of the gradient field linearity and image distortion. In this study, a series of gradient coils with different track widths have been designed and analyzed to investigate the electromagnetic interactions between coils in a split gradient set. A driving current, with frequencies from 100Hz to 10kHz, was applied to study the inductive coupling effects with respect to conductor geometry and operating frequency. It was found that the eddy currents induced in the un-energized coils (hereby-referred to as passive coils) positively correlated with track width and frequency. The magnetic field induced by the eddy currents in the passive coils with wide tracks was several times larger than that induced by eddy currents in the cold shield of cryostat. The power loss in the passive coils increased with the track width. Therefore, intra-coil interactions should be included in the coil design and analysis process.

Biomass partitioning in grassland plants along independent gradients in temperature and precipitation

How plants allocate biomass to different parts strongly affects vegetation dynamics and ecosystem processes and services such as productivity and carbon storage. We tested the hypothesis that plant size explains the majority of variation in the size of plant parts (as predicted by allometric partitioning theory, APT) and that additional variation is explained by optimal responses for a given individual reproductive state and environment (as predicted by optimal partitioning theory, OPT) for alpine-lowland species pairs from three genera of grassland plants (Veronica, Viola and Carex) sampled along orthogonal gradients in temperature and precipitation. We found general patterns of allometric scaling (allometric exponents) of roots, stems, leaves and flowers, more or less as predicted by APT, and these patterns remained fairly constant across temperature and precipitation gradients. In contrast, basic allocation (allometric coefficients) was clearly related to climate, such as less allocation to leaves but more to roots, stems and flowers with increasing temperatures, in accordance with OPT. Furthermore, our results show that basic allocation is related to habitat affinity (alpine, lowland) and individual life-history states (reproductive or not) and that there is greater variability in small plants, which suggests that biomass partitioning theory should consider both the life-history and ecology of small plants to accurately predict climate-related grassland plant allocation and its implications.