High Entropy Regions Research Articles

Reusing the steel slag to design a gradient-doped high-entropy oxide for high-performance sodium ion batteries

Herein, a high-entropy layered oxide (HEO) is proposed as an outstanding cathode material for long-life sodium-ion batteries. Based on the self-segregation of elements from surface to bulk phase, a multi-element gradient doped high-entropy cathode material is prepared by doping steel slag with available elements (Mg, Al, Si, Fe, Ca). The surface high-entropy region vastly improves the air stability of materials and reduces surface impurities and side reactions. The Na-O-Mg configuration of near-surface high-entropy region continuously stimulates the anionic redox activity, and the DEMS shows the high-strength Al-O bonding achieves zero oxygen release. Therefore, the LNSM-0.01 reveals a stable capacity of ∼24 mA h g−1 in the range of 4.0–4.5 V. The Ca2+ in bulk phase high-entropy region disrupts the Na+/vacancy ordering transition and enhances the kinetic performance (90 mA h g−1 at 1000 mA g−1), while Fe2+/3+ provides a large amount number of charge compensation. Further, DFT calculations prove that the entropy stability based on synergistic effect immeasurably reinforce the layered oxide configuration, building a more robust structural framework during cycling. This work deepens the understanding on multi-element gradient doping to prepare HEOs, and provides a novel pathway for resource utilization of solid waste.

Optimization of Guide Vane Centrifugal Pumps Based on Response Surface Methodology and Study of Internal Flow Characteristics

The methodologies of computational fluid dynamics (CFD) and response surface method (RSM) were integrated to uncover the optimal correlational framework for intricate hydraulic geometric parameters of guide vane centrifugal pumps. Parameters such as blade number, blade wrap angle, blade outlet angle, and relative axial distance between the guide vane and impeller, as well as radial distance, are embraced as optimization design variables. Meanwhile, pump head and efficiency were chosen as responsive variables. An analysis of 46 sets of hydraulic performance data was carried out by using the Box–Behnken experimental design method. Subsequently, response surface approximation models were established between hydraulic parameters and the efficiency, as well as the head. The optimal design point was predicted and a simulation of the hydraulic characteristics for the optimal scheme was conducted; the errors were 0.846% for head and 0.256% for efficiency between the simulation results with predicted results from RSM. The optimized model demonstrates noteworthy enhancements in hydraulic performance in comparison to the original model. By analyzing the internal flow of the optimized model under transient conditions, it was found that, as the internal flow of the flow passage components is relatively disordered at small flow rates, the amplitude of pressure pulsation is affected a lot. At other flow rates, the inside pressure pulsation waveform exhibits pronounced periodicity, and the primary causes of pressure pulsation in various flow components are not the same. Wall dissipation and turbulent dissipation emerge as significant contributors to the entropy generation in this centrifugal pump. The magnitude of entropy generation is correlated with the flow rate and the structural configuration of the pump’s components. High-entropy regions concentrate around the leading and trailing edges of the blades.

Characteristics of inlet guide vane adjustment of multi-stage axial compressor in compressed air energy storage system

The compressor in compressed air energy storage (CAES) system needs to balance continuous variable conditions and high-efficiency operation. The adjustment of inlet guide vanes (IGV) can effectively expand the stable working range of the compressor and improve the variable condition performance. The purpose of this study is to provide a reference for the efficient and variable condition operation of axial compressors in CAES system. This study takes a five-stage axial compressor in a specific CAES system as the research object, and uses numerical method to investigate the IGV adjustment characteristics of the compressor. Firstly, the overall performance variation of the compressor is analyzed. It is found that the IGV adjustment has a significant effect on expanding the stability range of the compressor, increasing it from 11.6 % to 33.4 %. The optimal adjustment curve of the IGV serves as a reference for achieving high-efficiency operation of the energy storage compressor. Secondly, the variations of the stage static pressure ratio, stage degree of reaction, rotor diffusion factor, rotor inlet airflow angle, relative Mach number on S1 surface of the first 1.5 stages, and the limit streamlines on blade suction surfaces are analyzed for different IGV angles. It is observed that minor IGV adjustment can regulate the distribution of aerodynamic parameters and internal flow of the first stage without significantly affecting the distribution of aerodynamic parameters in the subsequent stages. However, significant changes in the aerodynamic parameters of all stages occur when large adjustments are made to the IGV. Finally, the distribution characteristics of losses on the blade suction surface, meridional flow channel, and IGV for different angles are studied. When the IGV are adjusted from −10° to +35°, the high-entropy region on the IGV suction surface gradually increases, while the high-entropy region on the leading edge of the first-stage rotors decreases. The changes in aerodynamic parameters at each stage during large angle adjustments exacerbate the deterioration of internal flow, leading to a significant increase in the high-entropy region in the meridional flow channel. The loss ratio fitting curve provides a quantitative basis for evaluating the IGV losses at different adjustment angles.

Entropy: An Inspiring Tool for Characterizing Turbulence-Combustion Interaction in Swirling Flames via Direct Numerical Simulations of Non-Premixed and Premixed Flames.

This article focuses on entropy generation in the combustion field, which serves as a useful indicator to quantify the interaction between turbulence and combustion. The study is performed on the direct numerical simulations (DNS) of high pressure non-premixed and premixed swirling flames. By analyzing the entropy generation in thermal transport, mass transport, and chemical reactions, it is found that the thermal transport, driven by the temperature gradient, plays a dominant role. The enstrophy transport analysis reveals that the responses of individual terms to combustion can be measured by the entropy: the vortex stretching and the dissipation terms increase monotonically with the increasing entropy. In high entropy regions, the turbulence behaves as the "cigar shaped" state in the non-premixed flame, while as the axisymmetric state in the premixed flame. A substantial increase in the normal Reynolds stress with the entropy is observed. This is due to the competition between two terms promoted by the entropy, i.e., the velocity-pressure gradient correlation term and the shear production term. As a result, the velocity-pressure gradient correlation tends to isotropize turbulence by transferring energy increasingly from the largest streamwise component to the other smaller normal components of Reynolds stress and is dominated by the fluctuating pressure gradient that increases along the entropy. The shear production term increases with the entropy due to the upgrading alignment of the eigenvectors of strain rate and Reynolds stress tensors.

Synergistic Label-Stability Learning for Semi-supervised Left Atrium Segmentation.

Recent semi-supervised learning approaches appealingly advance medical image segmentation for their effectiveness in alleviating the need for a large amount of expert-demanding annotations. However, most of them have two limitations: (i) neglect of the intra-class variation caused by different patients and scanning protocols, which makes the pixel-level label propagation difficult; (ii) non-selective stability learning (a.k.a., consistency regularization), resulting in distraction by the redundant easy regions. To address these, in this work, we propose a novel synergistic label-stability learning (SLSL) framework for semi-supervised medical image segmentation. Specifically, our method is built upon the teacher-student framework. Then, the label learning process includes the typical pseudo label learning that reinforces confirmation of well-classified easy regions and the cyclic real label learning that takes advantage of real labels and class prototypes to regularize the distribution of intra-class features from unlabeled data to facilitate label propagation. In addition, the difficulty-selective stability learning aims to regularize the perturbed stability only at the high-entropy (can be regarded as difficult) regions, rather than being distracted by the less-informative easy regions. Extensive experiments on left atrium segmentation from MRI show that our method can effectively exploit the unlabeled data and outperform other semi-supervised medical image segmentation methods.Clinical relevance- The proposed method can help develop a high-performance automatic left atrium segmentation model for treating atrial fibrillation under limited expert-demanding annotation budgets.

Study on flow characteristics of leakage in the last stage inner blade tip clearance of steam turbine

Internal steam leakage in steam turbines from the high-pressure side to the low-pressure side through clearances causes loss, resulting in reduced efficiency and potentially compromising the safe operation of the turbine. Therefore, a comprehensive understanding of the flow characteristics of leakage through blade tip clearances is crucial to improve the efficiency of steam turbines. In this paper, the last stage blades of the low-pressure cylinder of a certain 600 MW ultra-supercritical steam turbine unit were studied. A wet steam flow model and a turbulence model were established, and the flow characteristics of the last stage under different inlet parameters, outlet parameters, and tip clearance sizes were analyzed. The results showed that an increase in the clearance size affects the inlet and outlet steam angles of the rotor blades, with significant changes occurring near the blade tip. The main flow velocity inside the rotor blade channel fluctuates violently starting from the 70% axial position. The high entropy region is located near the exit flow region of the rotor blade, with its range expanding as the clearance size increases. The entropy change is significant at 60% blade height and above, with more intense changes occurring in the blade tip area. The relative leakage amount and efficiency change uniformly with clearance variation. Generally, for every 0.1% increase in clearance height, the relative leakage amount increases by ∼0.31%–0.42%, and the stage efficiency decreases by 0.34%–0.44%. The results of this study can provide a theoretical basis and guidance for improving the flow efficiency of steam turbines.

Seagull optimization-based near-duplicate image detection in large image databases

ABSTRACT Many of the near-duplicate (ND) image detection methods involve a greater number of interest points (IPs) and large dimensions of the feature descriptors requiring huge computations and are unsuitable for large image databases. They may fail to detect NDs if the query and images in the database contain sparse IPs due to low entropy. Besides, the k-means algorithm used for the quantization of visual words may land at a sub-optimal minimum for descriptors because of their distance distribution in feature space. This article presents a new ND image detection method, which uniformly distributes the IPs over low and high entropy regions, reduces the dimension of feature descriptors using discrete wavelet transform (DWT) and employs Seagull Optimization algorithm (SOA) for optimally forming the visual words. It examines proposed method performs on image databases of various sizes and shows that the developed method is more reliable and computationally efficient than the alternatives.

Control of Inner Flow Field Inside A Transonic Centrifugal Compressor with Splitter Through Chordwise Sweep

The strategy of sweep design should be based on the inner flow field of the compressor. In this paper, a transonic centrifugal compressor within the splitter is discussed in detail, and both forward sweep and backward sweep are studied with numerical simulation for optimization. Splitter introduces extra leakage and it’s worth noting that the high-entropy region is shifted from the suction side of the main blade to the suction side of the splitter. Different from the transonic axial rotor, the leakage of the main blade mainly occurs after the passage shock and will be mixed with the leakage of the splitter in the suction side of the splitter. Therefore, the flow control on the middle and rare part of the compressor is more essential for the performance of the stage. In this regard, the backward sweep of the main blade exhibits a good effect by reducing the mixing loss of secondary leakage. Due to the redistribution of the airflow, the mainstream velocity in the tip area is accelerated in the forepart and reduced in the rare part, the aerodynamic loss in the high-entropy zone is then improved, and the flow capacity of the compressor is also increased. The best performance is achieved by an 8° backward sweep for the centrifugal compressor in this work, the pressure ratio is increased by 2.84% and isentropic efficiency is increased by 1.40%, compared to the prototype.

Estimation of the Grüneisen Parameter of High-Entropy Alloy-Type Functional Materials: The Cases of REO0.7F0.3BiS2 and MTe

In functional materials such as thermoelectric materials and superconductors, the interplay between functionality, electronic structure, and phonon characteristics is one of the key factors to improve functionality and to understand the underlying mechanisms. In the first part of this article, we briefly review investigations on lattice anharmonicity in functional materials on the basis of the Grüneisen parameter (γG). We show that γG can be a good index for large lattice anharmonicity and for detecting a change in anharmonicity amplitude in functional materials. Then, we show original results on the estimation of γG for recently developed high-entropy alloy-type (HEA-type) functional materials with a layered structure and a NaCl-type structure. As a common trend for those two systems with two- and three-dimensional structures, we found that γG increased with a slight increase in the configurational entropy of mixing (ΔSmix) and then decreased with increasing ΔSmix in the high-entropy region.

Self-Organization, Entropy Generation Rate, and Boundary Defects: A Control Volume Approach.

Self-organization that leads to the discontinuous emergence of optimized new patterns is related to entropy generation and the export of entropy. Compared to the original pattern that the new, self-organized pattern replaces, the new features could involve an abrupt change in the pattern-volume. There is no clear principle of pathway selection for self-organization that is known for triggering a particular new self-organization pattern. The new pattern displays different types of boundary-defects necessary for stabilizing the new order. Boundary-defects can contain high entropy regions of concentrated chemical species. On the other hand, the reorganization (or refinement) of an established pattern is a more kinetically tractable process, where the entropy generation rate varies continuously with the imposed variables that enable and sustain the pattern features. The maximum entropy production rate (MEPR) principle is one possibility that may have predictive capability for self-organization. The scale of shapes that form or evolve during self-organization and reorganization are influenced by the export of specific defects from the control volume of study. The control volume (CV) approach must include the texture patterns to be located inside the CV for the MEPR analysis to be applicable. These hypotheses were examined for patterns that are well-characterized for solidification and wear processes. We tested the governing equations for bifurcations (the onset of new patterns) and for reorganization (the fine tuning of existing patterns) with published experimental data, across the range of solidification morphologies and nonequilibrium phases, for metallic glass and featureless crystalline solids. The self-assembling features of surface-texture patterns for friction and wear conditions were also modeled with the entropy generation (MEPR) principle, including defect production (wear debris). We found that surface texture and entropy generation in the control volume could be predictive for self-organization. The main results of this study provide support to the hypothesis that self-organized patterns are a consequence of the maximum entropy production rate per volume principle. Patterns at any scale optimize a certain outcome and have utility. We discuss some similarities between the self-organization behavior of both inanimate and living systems, with ideas regarding the optimizing features of self-organized pattern features that impact functionality, beauty, and consciousness.

Wide flat minima and optimal generalization in classifying high-dimensional Gaussian mixtures

We analyze the connection between minimizers with good generalizing properties and high local entropy regions of a threshold-linear classifier in Gaussian mixtures with the mean squared error loss function. We show that there exist configurations that achieve the Bayes-optimal generalization error, even in the case of unbalanced clusters. We explore analytically the error-counting loss landscape in the vicinity of a Bayes-optimal solution, and show that the closer we get to such configurations, the higher the local entropy, implying that the Bayes-optimal solution lays inside a wide flat region. We also consider the algorithmically relevant case of targeting wide flat minima of the (differentiable) mean squared error loss. Our analytical and numerical results show not only that in the balanced case the dependence on the norm of the weights is mild, but also, in the unbalanced case, that the performances can be improved.

Large positive correlation between the effective electron mass and the multipolar fluctuation in the heavy-fermion metal Ce1\u2212xLaxB6

For the last few decades, researchers have been intrigued by multipolar ordering phenomena and related quantum phase transitions in heavy-fermion Kondo systems. However, a criticality induced by substitution level (x), temperature (T), or magnetic field (B) is poorly understood even in the prototypical material, Ce1−xLaxB6, despite a large collection of experimental results is available. In this work, we present T–B, x–T, and x–B phase diagrams of Ce1−xLaxB6 (B || [110]). These are completed by investigating heat capacity, magnetocaloric effect (MCE), and elastic neutron scattering. A drastic increase of the Sommerfeld coefficient γ0, which is estimated from the heat capacity down to 0.05 K, is observed with increasing x. The precise T–B phase diagram including a high-entropy region is derived from the MCE analysis in which a knowledge beyond the equilibrium thermodynamics is involved. Finally, the x–B phase diagram at T = 0, which supports the existence of a quantum critical point at x > 0.75, is obtained by the same analysis. A detailed interpretation of phase diagrams strongly indicates positive correlation between the fluctuating multipoles and the effective electron mass.

LiDAR-derived surface roughness signatures of basaltic lava types at the Muliwai a Pele Lava Channel, Mauna Ulu, Hawai‘i

We used light detection and ranging (LiDAR) data to calculate roughness patterns (homogeneity, mean-roughness, and entropy) for five lava types at two different resolutions (1.5 and 0.1 m/pixel). We found that end-member types (ʻaʻā and pāhoehoe) are separable (with 95% confidence) at both scales, indicating that roughness patterns are well suited for analyzing types of lava. Intermediate lavas were also explored, and we found that slabby-pāhoehoe is separable from the other end-members using 1.5 m/pixel data, but not in the 0.1 m/pixel analysis. This suggests that the conversion from pāhoehoe to slabby-pāhoehoe is a meter-scale process, and the finer roughness characteristics of pāhoehoe, such as ropes and toes, are not significantly affected. Furthermore, we introduce the ratio $$ \frac{ENT}{HOM} $$ (derived from lava roughness) as a proxy for assessing local lava flow rate from topographic data. High entropy and low homogeneity regions correlate with high flow rate while low entropy and high homogeneity regions correlate with low flow rate. We suggest that this relationship is not directional, rather it is apparent through roughness differences of the associated lava type emplaced at the high and low rates, respectively.

Bayesian framework inspired no-reference region-of-interest quality measure for brain MRI images.

We describe a postacquisition, attribute-based quality assessment method for brain magnetic resonance imaging (MRI) images. It is based on the application of Bayes theory to the relationship between entropy and image quality attributes. The entropy feature image of a slice is segmented into low- and high-entropy regions. For each entropy region, there are three separate observations of contrast, standard deviation, and sharpness quality attributes. A quality index for a quality attribute is the posterior probability of an entropy region given any corresponding region in a feature image where quality attribute is observed. Prior belief in each entropy region is determined from normalized total clique potential (TCP) energy of the slice. For TCP below the predefined threshold, the prior probability for a region is determined by deviation of its percentage composition in the slice from a standard normal distribution built from 250 MRI volume data provided by Alzheimer's Disease Neuroimaging Initiative. For TCP above the threshold, the prior is computed using a mathematical model that describes the TCP-noise level relationship in brain MRI images. Our proposed method assesses the image quality of each entropy region and the global image. Experimental results demonstrate good correlation with subjective opinions of radiologists for different types and levels of quality distortions.

Noninvasive microwave ablation zone radii estimation using x-ray CT image analysis.

The aims of this study were to noninvasively and automatically estimate both the radius of the ablated liver tissue and the radius encircling the treated zone, which also defines where the tissue is definitely untreated during a microwave (MW) thermal ablation procedure. Fourteen ex vivo bovine fresh liver specimens were ablated at 40 W using a 14 G microwave antenna, for durations of 3, 6, 8, and 10 min. The tissues were scanned every 5 s during the ablation using an x-ray CT scanner. In order to estimate the radius of the ablation zone, the acquired images were transformed into a polar presentation by displaying the Hounsfield units (HU) as a function of angle and radius. From this polar presentation, the average HU radial profile was analyzed at each time point and the ablation zone radius was estimated. In addition, textural analysis was applied to the original CT images. The proposed algorithm identified high entropy regions and estimated the treated zone radius per time. The estimated ablated zone radii as a function of treatment durations were compared, by means of correlation coefficient and root mean square error (RMSE) to gross pathology measurements taken immediately post-treatment from similarly ablated tissue. Both the estimated ablation radii and the treated zone radii demonstrated strong correlation with the measured gross pathology values (R(2) ≥ 0.89 and R(2) ≥ 0.86, respectively). The automated ablation radii estimation had an average discrepancy of less than 1 mm (RMSE = 0.65 mm) from the gross pathology measured values, while the treated zone radii showed a slight overestimation of approximately 1.5 mm (RMSE = 1.6 mm). Noninvasive monitoring of MW ablation using x-ray CT and image analysis is feasible. Automatic estimations of the ablation zone radius and the radius encompassing the treated zone that highly correlate with actual ablation measured values can be obtained. This technique can therefore potentially be used to obtain real time monitoring and improve the clinical outcome.

INTRACLUSTER MEDIUM OF THE MERGING CLUSTER A3395

We present a detailed imaging and spectral analysis of the merging environment of the bimodal cluster A3395 using X-ray and radio observations. X-ray images of the cluster show five main constituents of diffuse emission : A3395 NE, A3395 SW, A3395 NW, A3395 W, and a filament connecting NE to W. X-ray surface-brightness profiles of the cluster did not show any shock fronts in the cluster. Temperature and entropy maps show high temperature and high entropy regions in the W, the NW, the filament and between the NE and SW subclusters. The NE, SW and W components have X-ray bolometric luminosities similar to those of rich clusters of galaxies but have relatively higher temperatures. Similarly, the NW component has X-ray bolometric luminosity similar to that of isolated groups but with much higher temperature. It is, therefore, possible that all the components of the cluster have been heated by the ongoing mergers. The NE subcluster is the most massive and luminous constituent and other subclusters are found to be gravitationally bound to it. The W component is most probably either a clump of gas stripped off the SW due to ram pressure or a separate subcluster that has merged or is merging with the SW. No X-ray cavities are seen associated with the Wide Angle Tailed (WAT) radio source near the centre of the SW subcluster. Minimum energy pressure in the radio emission-peaks of the WAT galaxy is comparable with the external thermal pressure. The radio spectrum of the WAT suggests a spectral age of ~10Myr.

A Hybrid Approach of DWT and DCT for Rational Dither Modulation Watermarking

In this paper, on the basis of the theories and methods of Watson’s perceptual model and rational dither modulation (RDM), a hybrid quantization-based watermarking in the discrete wavelet transform (DWT) and discrete cosine transform (DCT) domains is studied. In the design of the quantization-based watermarking, quantization step-size plays an important role in many watermarking algorithms. RDM at both the embedder and decoder adopts a gain-invariant adaptive quantization step-size. Therefore, we investigated combining the modified Watson’s perceptual model with RDM. Its improved robustness is due to the embedding in the high entropy region of low-frequency sub-band image and adaptive control of its quantization step-size. The Euclidean distance decoder is used to extract the watermark data. The performance of the proposed scheme is analytically calculated and verified by simulation. Experimental results confirm the imperceptibility of the proposed watermarking and its higher robustness against attacks compared to alternative watermarking methods in the literature.

Evidence for a merger-revived radio phoenix in MaxBCG J217.95869+13.53470

We use XMM-Newton observations of the galaxy cluster MaxBCG J217.95869+13.53470 to analyze its physical properties and dynamical state. MaxBCG J217.95869+13.53470 is found at a redshift of 0.16, has a mass of ~1x10^14 Msun, and a luminosity of 7.9x10^43 erg/s. The temperature map shows the presence of hot regions towards the north and west of the brightest cluster galaxy (BCG). From the entropy distribution, regions of high entropy match the location of the hot regions; more high entropy regions are found to the west, and ~165 kpc to the southwest of the central AGN. A second X-ray bright galaxy is visible ~90 kpc to the northeast of the BCG, at a redshift of 0.162. This galaxy is likely to be the BCG of a smaller, infalling galaxy cluster. The mass of the smaller cluster is ~10 percent the mass of MaxBCG J217.95869+13.53470, yielding an impact parameter of ~30-100 kpc. We compare the results of our X-ray observations with GMRT observations of the radio source VLSS J1431.8+1331, located at the center of the cluster. Two sources are visible in the radio: a central elongated source that bends at its northern and southern ends, and a southwestern source that coincides with a region of high entropy. The radio sources are connected by a bridge of faint radio emission. We speculate that the southwestern radio source is a radio relic produced by compression of old radio plasma by a merger shock.

SUZAKUOBSERVATION OF A1689: ANISOTROPIC TEMPERATURE AND ENTROPY DISTRIBUTIONS ASSOCIATED WITH THE LARGE-SCALE STRUCTURE

(Abridged) We present results of Suzaku observations of the intracluster medium (ICM) in Abell 1689, combined with complementary analysis of the SDSS data and weak and strong lensing analysis of Subaru/Suprime-Cam and HST/ACS observations. Faint X-ray emission from the ICM around the virial radius is detected at 4.0 sigma significance. We find anisotropic gas temperature and entropy distributions in cluster outskirts correlated with large-scale structure of galaxies. The high temperature and entropy region in the northeastern (NE) outskirts is connected to an overdense filamentary structure. The outskirt regions in contact with low density void environments have low gas temperatures and entropies, deviating from hydrostatic equilibrium. These results suggest that thermalization of the ICM occurs faster along the filamentary structures than the void regions. A joint X-ray and lensing analysis shows that the hydrostatic mass is $\sim60-90%$ of spherical lensing one but comparable to a triaxial halo mass within errors in $0.6r_{2500} \simlt r \simlt 0.8r_{500}$, and that it is significantly biased as low as $\simlt60%$ within $0.4r_{2500}$, irrespective of mass models. The thermal gas pressure within $r_{500}$ is, at most, $\sim50$--60% of the total pressure to balance fully the gravity of the spherical lensing mass, and $\sim30$--40% around the virial radius. Although these constitute lower limits when one considers the possible halo triaxiality, these small relative contributions of thermal pressure would require additional sources of pressure, such as bulk and/or turbulent motions.

Simulating independence

We present new explicit constructions of deterministic randomness extractors, dispersers and related objects. We say that a distribution X on binary strings of length n is a δ-source if X assigns probability at most 2 −δ n to any string of length n . For every δ>0, we construct the following poly( n )-time computable functions: 2-source disperser: D:({0, 1} n ) 2 → {0, 1} such that for any two independent δ-sources X 1 , X 2 we have that the support of D ( X 1 , X 2 ) is {0, 1}. Bipartite Ramsey graph: Let N =2 n . A corollary is that the function D is a 2-coloring of the edges of K N,N (the complete bipartite graph over two sets of N vertices) such that any induced subgraph of size N δ by N δ is not monochromatic. 3-source extractor: E :({0, 1} n ) 3 → {0, 1} such that for any three independent δ-sources X 1 , X 2 , X 3 we have that E ( X 1 , X 2 , X 3 ) is o (1)-close to being an unbiased random bit. No previous explicit construction was known for either of these for any δ<1/2, and these results constitute significant progress to long-standing open problems. A component in these results is a new construction of condensers that may be of independent interest: This is a function C :{0, 1} n → ({0, 1} n/c ) d (where c and d are constants that depend only on δ) such that for every δ-source X one of the output blocks of C(X) is (exponentially close to) a 0.9-source. (This result was obtained independently by Ran Raz.) The constructions are quite involved and use as building blocks other new and known objects. A recurring theme in these constructions is that objects that were designed to work with independent inputs, sometimes perform well enough with correlated, high entropy inputs. The construction of the disperser is based on a new technique which we call “the challenge-response mechanism” that (in some sense) allows “identifying high entropy regions” in a given pair of sources using only one sample from the two sources.