Size Scaling Research Articles

SGSI – A Scalable GPU-Friendly Subgraph Isomorphism Algorithm

Due to the inherent hardness of subgraph isomorphism, the performance is often a bottleneck in various real-world applications. We address this by designing an efficient subgraph isomorphism algorithm leveraging features of GPU architecture. Existing GPU-based solutions adopt two-step output scheme, performing the same join twice in order to write intermediate results concurrently. They also lack GPU architecture-aware optimizations that allow scaling to large graphs. In this paper, we propose a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S</i> calable <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">G</i> PU-friendly <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</i> ubgraph <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</i> somorphism algorithm, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">SGSI</i> . SGSI incorporates a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Prealloc-Combine</i> strategy based on the vertex-oriented framework, which avoids joining-twice in existing solutions. It uses a GPU-friendly data structure (called <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">PCSR</i> ) to represent an edge-labeled graph. We also study fine-grained load balance strategies and discuss how to handle enormous graphs that cannot be resident in GPU memory. A partition-based pipeline framework is proposed. Extensive experiments on both synthetic and real graphs show that SGSI outperforms the state-of-the-art algorithms by up to several orders of magnitude and has a good scalability with graph size scaling to billions of edges.

Evolutionary scaling and cognitive correlates of primate frontal cortex microstructure.

Investigating evolutionary changes in frontal cortex microstructure is crucial to understanding how modifications of neuron and axon distributions contribute to phylogenetic variation in cognition. In the present study, we characterized microstructural components of dorsolateral prefrontal cortex, orbitofrontal cortex, and primary motor cortex from 14 primate species using measurements of neuropil fraction and immunohistochemical markers for fast-spiking inhibitory interneurons, large pyramidal projection neuron subtypes, serotonergic innervation, and dopaminergic innervation. Results revealed that the rate of evolutionary change was similar across these microstructural variables, except for neuropil fraction, which evolves more slowly and displays the strongest correlation with brain size. We also found that neuropil fraction in orbitofrontal cortex layers V-VI was associated with cross-species variation in performance on experimental tasks that measure self-control. These findings provide insight into the evolutionary reorganization of the primate frontal cortex in relation to brain size scaling and its association with cognitive processes.

Stochastic analysis of chemical reactions in multi-component interacting systems at criticality

We numerically and analytically investigate the behavior of a non-equilibrium phase transition in the second Schlögl autocatalytic reaction scheme. Our model incorporates both an interaction-induced phase separation and a bifurcation in the reaction kinetics, with these critical lines coalescing at a bicritical point in the macroscopic limit. We construct a stochastic master equation for the reaction processes to account for the presence of mutual particle interactions in a thermodynamically consistent manner by imposing a generalized detailed balance condition, which leads to exponential corrections for the transition rates. In a non-spatially extended (zero-dimensional) setting, we treat the interactions in a mean-field approximation, and introduce a minimal model that encodes the physical behavior of the bicritical point and permits the exact evaluation of the anomalous scaling for the particle number fluctuations in the thermodynamic limit. We obtain that the system size scaling exponent for the particle number variance changes from at the standard non-interacting bifurcation to at the interacting bicritical point. The methodology developed here provides a generic route for the quantitative analysis of fluctuation effects in chemical reactions occurring in multi-component interacting systems.

Physical properties of a generalized model of multilayer adsorption of dimers.

We investigate the transport properties of a complex porous structure with branched fractal architectures formed due to the gradual deposition of dimers in a model of multilayer adsorption. We thoroughly study the interplay between the orientational anisotropy parameter p_{0} of deposited dimers and the formation of porous structures, as well as its impact on the conductivity of the system, through extensive numerical simulations. By systematically varying the value of p_{0}, several critical and off-critical scaling relations characterizing the behavior of the system are examined. The results demonstrate that the degree of orientational anisotropy of dimers plays a significant role in determining the structural and physical characteristics of the system. We find that the Einstein relation relating to the size scaling of the electrical conductance holds true only in the limiting case of p_{0}→1. Monitoring the fractal dimension of the interface of the multilayer formation for various p_{0} values, we reveal that in a wide range of p_{0}>0.2 interface shows the characteristic of a self-avoiding random walk, compared to the limiting case of p_{0}→0 where it is characterized by the fractal dimension of the backbone of ordinary percolation cluster at criticality. Our results thus can provide useful information about the fundamental mechanisms underlying the formation and behavior of wide varieties of amorphous and disordered systems that are of paramount importance both in science and technology as well as in environmental studies.

A three-dimensional musculoskeletal model of the pelvis and lower limb of Australopithecus afarensis.

Musculoskeletal modeling is a powerful approach for studying the biomechanics and energetics of locomotion. Australopithecus (A.) afarensis is among the best represented fossil hominins and provides critical information about the evolution of musculoskeletal design and locomotion in the hominin lineage. Here, we develop and evaluate a three-dimensional (3-D) musculoskeletal model of the pelvis and lower limb of A. afarensis for predicting muscle-tendon moment arms and moment-generating capacities across lower limb joint positions encompassing a range of locomotor behaviors. A 3-D musculoskeletal model of an adult A. afarensis pelvis and lower limb was developed based primarily on the A.L. 288-1 partial skeleton. The model includes geometric representations of bones, joints and 35 muscle-tendon units represented using 43 Hill-type muscle models. Two muscle parameter datasets were created from human and chimpanzee sources. 3-D muscle-tendon moment arms and isometric joint moments were predicted over a wide range of joint positions. Predicted muscle-tendon moment arms generally agreed with skeletal metrics, and corresponded with human and chimpanzee models. Human and chimpanzee-based muscle parameterizations were similar, with some differences in maximum isometric force-producing capabilities. The model is amenable to size scaling from A.L. 288-1 to the larger KSD-VP-1/1, which subsumes a wide range of size variation in A. afarensis. This model represents an important tool for studying the integrated function of the neuromusculoskeletal systems in A. afarensis. It is similar to current human and chimpanzee models in musculoskeletal detail, and will permit direct, comparative 3-D simulation studies.

Scale effect on unnotched and open-hole cross-ply glass fiber/epoxy non-crimp fabric (NCF) composites under quasi-static tensile loading

This study explores the effect of size scaling and stacking sequence on the quasi-static tensile behavior of sublaminate-level and ply-level scaled glass/epoxy laminates. Test results showed that the unnotched tensile strengths of both scaled specimens were comparable for a given scaling factor, even though ply-level scaled specimens suffered extensive delamination between and ply blocks. In contrast, the open hole tensile (OHT) strength was reduced with increased scale in sublaminate-level and was marginally increased in ply-level scaled specimens. Similar to unnotched specimens, ply-level scaled OHT specimens exhibited extensive delamination.

Probing the jet size of two black hole X-ray binaries in the hard state

ABSTRACT Using multifrequency very long baseline interferometry (VLBI) observations, we probe the jet size in the optically thick hard state jets of two black hole X-ray binary (BHXRB) systems, MAXI J1820+070 and V404 Cygni. Because of optical depth effects, the phase-referenced VLBI core positions move along the jet axis of the BHXRB in a frequency-dependent manner. We use this ‘core shift’ to constrain the physical size of the hard state jet. We place an upper limit of 0.3 au on the jet size measured between the 15 and 5 GHz emission regions of the jet in MAXI J1820+070, and an upper limit of 1.0 au between the 8.4 and 4.8 GHz emission regions of V404 Cygni. Our limit on the jet size in MAXI J1820+070 observed in the low-hard state is a factor of 5 smaller than the values previously observed in the high-luminosity hard state (using time lags between multifrequency light curves), thus showing evidence of the BHXRB jet scaling in size with jet luminosity. We also investigate whether motion of the radio-emitting region along the jet axis could affect the measured VLBI parallaxes for the two systems, leading to a mild tension with the parallax measurements of Gaia. Having mitigated the impact of any motion along the jet axis in the measured astrometry, we find the previous VLBI parallax measurements of MAXI J1820+070 and V404 Cygni to be unaffected by jet motion. With a total time baseline of 8 yr, due to having incorporated 14 new epochs in addition to the previously published ones, our updated parallax measurement of V404 Cygni is 0.450 ± 0.018 mas (2.226 ± 0.091 kpc).

When is a disparity not a disparity? Toward an old theory of three-dimensional vision.

The aims of this paper are twofold: first, to discuss and analyze the concept of binocular disparity and second, to contrast the traditional "air theory" of three-dimensional vision with the much older "ground theory," first suggested by Ibn al-Haytham more than a thousand years ago. The origins of an "air theory" of perception can be traced back to Descartes and subsequently to the philosopher George Berkeley, who claimed that distance "could not be seen" because points lying along the same line of sight (in an empty space) would all project to the same location on the retina. However, Descartes was also aware that the angle of convergence of the two eyes could solve the problem of the "missing" information for the monocular observer and, since then, most visual scientists have assumed that eye vergence plays an important role both in judging absolute distance and for scaling retinal size and binocular disparities. In contrast, al-Haytham's and Gibson's "ground theories," which are based on the geometry of the textured ground plane surface that has surrounded us throughout evolution and during our lifetimes, are not just more ecologically based but they also obviate the need for disparity scaling.

Channelling electric current during the field-assisted sintering technique (FAST) to control microstructural evolution in Ti-6Al-4V

Perhaps the most defining feature of field-assisted sintering technology (FAST) is the application of an electric current, in addition to the uniaxial pressure, to create resistive heating in and around the sample region. However, with a few exceptions, most research takes this as an unchangeable part of the process. Here, this current flow has been directed to specific regions within the toolset, using boron nitride as electrically insulating material. This caused the heating to occur in differing regions within the Ti-6Al-4V sample and mould over four insulating configurations, with the shift in current density resulting in an extreme disparity in the final microstructures. The samples were imaged and analysed with deep learning in MIPAR, alongside comparisons with finite element analysis (FEA) models for 20 s and 5 min dwell times, to provide the technique with predictive capabilities for grain size and microstructure. The results gathered imply significant potential for this concept to improve the flexibility of FAST, and reduce negative effects such as undesirable temperature profiles in size scaling sintering for industry.

Origami Chomper‐Based Flexible Gripper with Superior Gripping Performances

Flexible grippers with superior gripping capabilities are essential for carrying objects. Herein, an origami chomper‐based flexible gripper is designed using a combination of the origami technique and a newly developed nonlinear topology optimization method. This novel origami chomper‐based flexible gripper exhibits superior gripping performance, as revealed by a series of experiments, including gripping range capability under an identical input load, maximum gripping ratio, gripping adaptability, and achieving richer gripping characteristics by size scaling. The origami chomper‐based flexible gripper can handle a wide range of object irregularities in textures and uneven shapes and can enable effective gripping of objects across scales from millimeters to centimeters to decimeters through size scaling. This study paves the way for innovative high‐performance designs of flexible grippers.

Evolutionary divergence of body size and wing and leg structure in relation to foraging mode in Darwin’s Galapagos finches

Abstract The wings, legs, and tail in Darwin’s finches show many clear adaptations to different types of locomotion used during foraging. We use size scaling to analyse how various characters vary with body mass to clarify dimensional relationships. The selective advantage of a character is judged in terms of energy savings. The wing aspect ratio (4.6–4.9) is very low, so the energy costs for flight are high. Low body mass, low wing loading, and short arm wings in the warbler finch, small tree finch, and small ground finch promote agility and manoeuvrability among vegetation, along with short wings in the warbler finch. Evolution towards a shorter arm wing seems to be favoured in the smaller finch species. Long legs, long toes, and long curved claws are adaptations for climbing/clinging locomotion without tail support (woodpecker finch, small and large tree finches, cactus finch but having short legs). Selection for longer legs seems to act towards a lengthening of the tarsometatarsus. The climbing technique in the woodpecker finch is described. We discuss how the diversification in the beaks relates to the locomotion organs.

Universality in Anderson localization on random graphs with varying connectivity

We perform a thorough and complete analysis of the Anderson localization transition on several models of random graphs with regular and random connectivity. The unprecedented precision and abundance of our exact diagonalization data (both spectra and eigenstates), together with new finite size scaling and statistical analysis of the graph ensembles, unveils a universal behavior which is described by two simple, integer, scaling exponents. A by-product of such analysis is a reconciliation of the tension between the results of perturbation theory coming from strong disorder and earlier numerical works, which seemed to suggest that there should be a non-ergodic region above a given value of disorder W_{E}WE which is strictly less than the Anderson localization critical disorder W_CWC, and that of other works which suggest that there is no such region. We find that, although no separate W_{E}WE exists from W_CWC, the length scale at which fully developed ergodicity is found diverges like |W-W_C|^{-1}|W−WC|−1, while the critical length over which delocalization develops is \sim |W-W_C|^{-1/2}∼|W−WC|−1/2. The separation of these two scales at the critical point allows for a true non-ergodic, delocalized region. In addition, by looking at eigenstates and studying leading and sub-leading terms in system size-dependence of participation entropies, we show that the former contain information about the non-ergodicity volume which becomes non-trivial already deep in the delocalized regime. We also discuss the quantitative similarities between the Anderson transition on random graphs and many-body localization transition.

Super-diffusion and crossover from diffusive to anomalous transport in a one-dimensional system

We study transport in a one-dimensional lattice system with two conserved quantities - “volume” and energy. Considering a slowly evolving local equilibrium state that is slightly deviated from an underlying global equilibrium, we estimate the correction to the local equilibrium distribution. This correction arises mainly through the space-time correlations of some local currents. In the continuum limit, we show that the local equilibrium distribution along with the correction yields drift-diffusion equation for the “volume” and super-diffusion equation for the energy in the linear response regime as macroscopic hydrodynamics as one would obtain from non-linear fluctuating hydrodynamic theory. We find explicit expression of the super-diffusion equation. Further, we find diffusive correction to the super-diffusive evolution. Such a correction allows us to study a crossover from diffusive to anomalous transport. We demonstrate this crossover numerically through the spreading of an initially localized heat pulse in equilibrium as well as through the system size scaling of the stationary current in non-equilibrium steady state.

Reversing A Decades‐Long Scaling Law of Dielectric Breakdown using Hydrogen‐Plasma‐Treated HfO2 ReRAM Devices

AbstractDielectric breakdown (BD) is known to cause component failure in electronic devices and high‐voltage power lines over many decades. In recent years, this failure mechanism has been exploited to intentionally form nanoscale filaments in resistive random‐access‐memory (ReRAM) devices for artificial intelligence (AI). The statistical nature of this failure mechanism, known as the inverse size scaling law based on the weakest‐link theory, dictates the ever‐higher forming voltages for ReRAM devices, in turn, requiring additional peripheral transistors. This law also causes diminishing lifetimes of electronic components for future generations of very‐large‐integrated circuits (VLSI) technology. Currently, the semiconductor industry faces these scaling barriers limiting the miniaturization of both VLSI and AI hardware technology. Here, experimental evidence of a reverse area dependence is presented by introducing an innovative fabrication process with a hydrogen‐plasma‐treated layer in a bilayer HfO2 structure. Using joint order statistics rather than traditional extreme‐value statistics, a physics‐based statistical model is developed in agreement with the experimental data, thus demonstrating that there is no fundamental reason preventing this law from being reversed or altered. These findings will have a significant impact on both technology scaling and fabrication innovation for electronic and/or bioinspired nanomaterials; moreover, stimulate much research in physics, statistics, and reliability.

On a Population Sizing Model for Evolution Strategies Optimizing the Highly Multimodal Rastrigin Function.

A model is presented that allows for the calculation of the success probability by which a vanilla Evolution Strategy converges to the global optimizer of the Rastrigin test function. As a result a population size scaling formula will be derived that allows for an estimation of the population size needed to ensure a high convergence security depending on the search space dimensionality.

2D Short‐Channel Tunneling Transistor Relying on Dual‐Gate Modulation for Integrated Circuits Application

AbstractWith continuous size scaling, the surface dangling bonds and short‐channel effects will degrade silicon based transistor performance. Thus, it is of great importance to seek new channel materials and transistor architectures to further continue Moore's law. Herein, a new ultra‐thin short‐channel tunneling transistor is developed comprising all 2D‐ components. Distinct from usual 2D planar transistor, this device is configured with vertical MoS2/WSe2 junction and in‐plane WSe2 channel, the switch states are realized by the gate‐regulated barrier height of heterojunction, enabling the transition of transport mechanism between thermionic‐emission and tunneling. Under dual‐gate configuration, the transistor exhibits high performance with drive current of 4.58 µA, on/off ratio of 4 × 107, subthreshold swing (SS) of 97 mV decade−1 and drain‐induced barrier lowering (DIBL) of 12 mV V−1, that can meet the requirement of logical applications in integrated circuits (IC). Taking advantage of the high‐speed tunneling current and unique short‐channel architecture, the device overcomes the issues of voltage spikes and long reverse recovery time that exist in usual electric components, and thus gains an access to the IC interface. This work provides a proof‐of‐concept transistor architecture relying on dual‐gate modulation, opening up a promising perspective for next generation low‐power, high‐density, and large‐scale IC technologies.

Size scaling of failure strength at high disorder

We investigate how the macroscopic response and the size scaling of the ultimate strength of materials change when their local strength is sampled from a fat-tailed distribution and the degree of disorder is varied in a broad range. Using equal and localized load sharing in a fiber bundle model, we demonstrate that a transition occurs from a perfectly brittle to a quasi-brittle behavior as the amount of disorder is gradually increased. When the load sharing is localized the high load concentration around failed regions make the system more prone to failure so that a higher degree of disorder is required for stabilization. Increasing the system size at a fixed degree of disorder an astonishing size effect is obtained: at small sizes the ultimate strength of the system increases with its size, the usual decreasing behavior sets on only beyond a characteristic system size. The increasing regime of the size effect prevails even for localized load sharing, however, above the characteristic system size the load concentration results in a substantial strength reduction compared to equal load sharing. We show that an adequate explanation of the results can be obtained based on the extreme order statistics of fibers’ strength.

The activated scaling behavior of quantum Griffiths singularity in two-dimensional superconductors

Quantum Griffiths singularity (QGS) is characterized by the divergence of the dynamical critical exponent with the activated scaling law and has been widely observed in various two-dimensional superconductors. Recently, the direct activated scaling analysis with the irrelevant correction was proposed and successfully used to analyze the experimental data of crystalline PdTe2 and polycrystalline -W films, which provides new evidence of QGS. Here we show that the direct activated scaling analysis is applicable to the experimental data in different superconducting films, including tri-layer Ga films and LaAlO3/SrTiO3 interface superconductors. When taking the irrelevant correction into account, we calculate the corrected sheet resistance at ultralow temperatures. The scaling behavior of the corrected resistance in a comparably large temperature regime and the theoretical fitting of the phase boundary give unambiguous evidence of QGS. Compared to previous methods based on finite size scaling, the direct activated scaling analysis represents a more direct and precise way to analyze the experimental data of QGS in diverse two-dimensional superconductors.

A high-speed quadruple-node-upset-tolerant latch in 22 nm CMOS technology

With the scaling of CMOS feature size, the multi-node upset caused by radiation has become an important reliability issue of storage devices. In order to improve the robustness of the storage devices, this paper proposes a High-Speed Quadruple-Node-Upset tolerant latch (HS-QNU). The proposed HS-QNU latch consists of two single-node-upset-resilient RFCs, two single-node-upset-resilient DICEs and a clocked quadruple-input C-element. Based on the single-node-upset-resilient ability of DICE and RFC and the blocking ability of C-element, the proposed HS-QNU latch can effectively tolerate soft errors when any four internal nodes upset by transient faults at the same time. Meanwhile, the latch effectively reduces delay and power consumption by using high-speed path and clock-gating technique. Extensive SPICE simulation in 22 nm CMOS technology shows that compared with QNUTL, the proposed latch reduces delay by 30.68 %, reduces power consumption by 30.86 %, reduces power-delay-product by 52.07 %, reduces area-power-delay-product by 49.08 %, and only increases area overhead by 6.25 %. The proposed HS-QNU latch achieves good tradeoff among delay, power consumption and area. Compared with the previous hardened latches, the proposed HS-QNU latch has the best hardening ability, the highest speed and the smallest power-delay-product. The variation analysis shows that the proposed HS-QNU latch is insensitive to temperature and voltage variations.

The developmental basis for scaling of mammalian tooth size

When evolution leads to differences in body size, organs generally scale along. A well-known example of the tight relationship between organ and body size is the scaling of mammalian molar teeth. To investigate how teeth scale during development and evolution, we compared molar development from initiation through final size in the mouse and the rat. Whereas the linear dimensions of the rat molars are twice that of the mouse molars, their shapes are largely the same. Here, we focus on the first lower molars that are considered the most reliable dental proxy for size-related patterns due to their low within-species variability. We found that scaling of the molars starts early, and that the rat molar is patterned equally as fast but in a larger size than the mouse molar. Using transcriptomics, we discovered that a known regulator of body size, insulin-like growth factor 1 (Igf1), is more highly expressed in the rat molars compared to the mouse molars. Ex vivo and in vivo mouse models demonstrated that modulation of the IGF pathway reproduces several aspects of the observed scaling process. Furthermore, analysis of IGF1-treated mouse molars and computational modeling indicate that IGF signaling scales teeth by simultaneously enhancing growth and by inhibiting the cusp-patterning program, thereby providing a relatively simple mechanism for scaling teeth during development and evolution. Finally, comparative data from shrews to elephants suggest that this scaling mechanism regulates the minimum tooth size possible, as well as the patterning potential of large teeth.