Next Generation Evaluation: Embracing Complexity, Connectivity, and Change

This Learning Brief draws from literature and research, as well as more than a dozen interviews with foundation leaders, evaluation practitioners, and social sector thought leaders, with the intention of starting the conversation in the field around Next Generation Evaluation characteristics and approaches

Generalized Jordan derivations on prime rings and standard operator algebras

In this paper we initiate the study of generalized Jordan derivations and generalized Jordan triple derivations on prime rings and standard operator algebras

Evaluating Ecosystem Investments

This report focuses on what was learned about best practices for evaluating the effects of ecosystem investments along with examples of how others are using these practicesin their work.MethodologyThree research questions guided this engagement:What are the new / best practices in evaluating the effects of ecosystem invest­ments?Which organizations are evaluating these investments well? What can they teach us?What relevant outcomes and indicators could Omidyar Network use to evaluate its ecosystem investments?To answer these questions, FSG conducted the following activities, in addition to drawing on our experience supporting strategic learning and evaluation in complex environments. Appendix A includes a complete list of grants reviewed and interviewees.Grants analysis: FSG analyzed Omidyar Network's Initiative Results Architecture frameworks and 23 grants within its ecosystem investment portfolio. These docu­ments helped ground our research in an understanding of the different types of ecosystem investments Omidyar Network is making, as well as how the organiza­tion currently evaluates the impact of its ecosystem investments.Literature review: FSG reviewed more than 60 publications to identify best practices in evaluating ecosystem investments—these publications included both peer-reviewed journal articles and "grey literature" (conference presentations, blog posts) by organizations employing advocacy-type strategies.Interviews: FSG conducted interviews with nine external experts (listed in Appen­dix A) to more deeply understand effective practices in evaluating the effects of eco­system investments and to identify leading organizations in this area. Interviewees were identified to glean best practices from both within and outside the traditional social sector

Accurate determination of the Gaussian transition in spin-1 chains with single-ion anisotropy

The Gaussian transition in the spin-one Heisenberg chain with single-ion anisotropy is extremely difficult to treat, both analytically and numerically. We introduce an improved DMRG procedure with strict error control, which we use to access very large systems. By considering the bulk entropy, we determine the Gaussian transition point to 4-digit accuracy, $D_{c}/J = 0.96845(8)$, resolving a long-standing debate in quantum magnetism. With this value, we obtain high-precision data for the critical behavior of quantities including the ground-state energy, gap, and transverse string-order parameter, and for the critical exponent, $\nu = 1.472(2)$. Applying our improved technique at $J_{z} = 0.5$ highlights essential differences in critical behavior along the Gaussian transition line.Comment: 4 pages and 4 figure

Constraining the Star Formation Histories in Dark Matter Halos: I. Central Galaxies

Using the self-consistent modeling of the conditional stellar mass functions across cosmic time by Yang et al. (2012), we make model predictions for the star formation histories (SFHs) of {\it central} galaxies in halos of different masses. The model requires the following two key ingredients: (i) mass assembly histories of central and satellite galaxies, and (ii) local observational constraints of the star formation rates of central galaxies as function of halo mass. We obtain a universal fitting formula that describes the (median) SFH of central galaxies as function of halo mass, galaxy stellar mass and redshift. We use this model to make predictions for various aspects of the star formation rates of central galaxies across cosmic time. Our main findings are the following. (1) The specific star formation rate (SSFR) at high $z$ increases rapidly with increasing redshift [$\propto (1+z)^{2.5}$] for halos of a given mass and only slowly with halo mass ($\propto M_h^{0.12}$) at a given $z$, in almost perfect agreement with the specific mass accretion rate of dark matter halos. (2) The ratio between the star formation rate (SFR) in the main-branch progenitor and the final stellar mass of a galaxy peaks roughly at a constant value, $\sim 10^{-9.3} h^2 {\rm yr}^{-1}$, independent of halo mass or the final stellar mass of the galaxy. However, the redshift at which the SFR peaks increases rapidly with halo mass. (3) More than half of the stars in the present-day Universe were formed in halos with 10^{11.1}\msunh < M_h < 10^{12.3}\msunh in the redshift range $0.4 < z < 1.9$. (4) ... [abridged]Comment: 15 figures, 22 pages, Accepted for publication in Ap

Revealing the cosmic web dependent halo bias

Halo bias is the one of the key ingredients of the halo models. It was shown at a given redshift to be only dependent, to the first order, on the halo mass. In this study, four types of cosmic web environments: clusters, filaments, sheets and voids are defined within a state of the art high resolution $N$-body simulation. Within those environments, we use both halo-dark matter cross-correlation and halo-halo auto correlation functions to probe the clustering properties of halos. The nature of the halo bias differs strongly among the four different cosmic web environments we describe. With respect to the overall population, halos in clusters have significantly lower biases in the {$10^{11.0}\sim 10^{13.5}h^{-1}\rm M_\odot$} mass range. In other environments however, halos show extremely enhanced biases up to a factor 10 in voids for halos of mass {$\sim 10^{12.0}h^{-1}\rm M_\odot$}. Such a strong cosmic web environment dependence in the halo bias may play an important role in future cosmological and galaxy formation studies. Within this cosmic web framework, the age dependency of halo bias is found to be only significant in clusters and filaments for relatively small halos \la 10^{12.5}\msunh.Comment: 14 pages, 14 figures, ApJ accepte

Adaptive Multi-source Predictor for Zero-shot Video Object Segmentation

Static and moving objects often occur in real-life videos. Most video object segmentation methods only focus on extracting and exploiting motion cues to perceive moving objects. Once faced with the frames of static objects, the moving object predictors may predict failed results caused by uncertain motion information, such as low-quality optical flow maps. Besides, different sources such as RGB, depth, optical flow and static saliency can provide useful information about the objects. However, existing approaches only consider either the RGB or RGB and optical flow. In this paper, we propose a novel adaptive multi-source predictor for zero-shot video object segmentation (ZVOS). In the static object predictor, the RGB source is converted to depth and static saliency sources, simultaneously. In the moving object predictor, we propose the multi-source fusion structure. First, the spatial importance of each source is highlighted with the help of the interoceptive spatial attention module (ISAM). Second, the motion-enhanced module (MEM) is designed to generate pure foreground motion attention for improving the representation of static and moving features in the decoder. Furthermore, we design a feature purification module (FPM) to filter the inter-source incompatible features. By using the ISAM, MEM and FPM, the multi-source features are effectively fused. In addition, we put forward an adaptive predictor fusion network (APF) to evaluate the quality of the optical flow map and fuse the predictions from the static object predictor and the moving object predictor in order to prevent over-reliance on the failed results caused by low-quality optical flow maps. Experiments show that the proposed model outperforms the state-of-the-art methods on three challenging ZVOS benchmarks. And, the static object predictor precisely predicts a high-quality depth map and static saliency map at the same time.Comment: Accepted to IJCV 2024. Code is available at: https://github.com/Xiaoqi-Zhao-DLUT/Multi-Source-APS-ZVOS. arXiv admin note: substantial text overlap with arXiv:2108.0507

Mapping the real space distributions of galaxies in SDSS DR7: I. Two Point Correlation Functions

Using a method to correct redshift space distortion (RSD) for individual galaxies, we mapped the real space distributions of galaxies in the Sloan Digital Sky Survey (SDSS) Data Release 7 (DR7). We use an ensemble of mock catalogs to demonstrate the reliability of our method. Here as the first paper in a series, we mainly focus on the two point correlation function (2PCF) of galaxies. Overall the 2PCF measured in the reconstructed real space for galaxies brighter than $^{0.1}{\rm M}_r-5\log h=-19.0$ agrees with the direct measurement to an accuracy better than the measurement error due to cosmic variance, if the reconstruction uses the correct cosmology. Applying the method to the SDSS DR7, we construct a real space version of the main galaxy catalog, which contains 396,068 galaxies in the North Galactic Cap with redshifts in the range $0.01 \leq z \leq 0.12$. The Sloan Great Wall, the largest known structure in the nearby Universe, is not as dominant an over-dense structure as appears to be in redshift space. We measure the 2PCFs in reconstructed real space for galaxies of different luminosities and colors. All of them show clear deviations from single power-law forms, and reveal clear transitions from 1-halo to 2-halo terms. A comparison with the corresponding 2PCFs in redshift space nicely demonstrates how RSDs boost the clustering power on large scales (by about $40-50\%$ at scales $\sim 10 h^{-1}{\rm {Mpc}}$) and suppress it on small scales (by about $70-80\%$ at a scale of $0.3 h^{-1}{\rm {Mpc}}$).Comment: 19 pages, 13 figure