This document summarizes a presentation on testing cosmology using galaxy clusters, the cosmic microwave background, and galaxy clustering. It discusses combining measurements of cosmic growth and expansion from these sources to constrain departures from general relativity. Models are presented for linear, time-dependent departures from GR. Constraints on parameters like the growth index γ are shown from combinations of clusters, CMB, and galaxy data. Tightening constraints are achieved by adding baryon acoustic oscillation, supernova, and Hubble constant data. The document also briefly discusses using cluster counts to constrain primordial non-Gaussianity.
Gauss–Bonnet Boson Stars in AdS, Bielefeld, Germany, 2014Jurgen Riedel
Strong coupling to gravity: self-interacting rotating boson
stars are destabilized.
Sufficiently small AdS radius: self-interacting rotating boson
stars are destabilized.
Sufficiently strong rotation stabilizes self-interacting rotating
boson stars.
Onset of ergoregions can occur on the main branch of boson
star solutions, supposed to be classically stable.
Radially excited self-interacting rotating boson stars can be
classically stable in aAdS for sufficiently large AdS radius and
sufficiently small backreaction.
Gauss–Bonnet Boson Stars in AdS - Ibericos, Portugal, 2014Jurgen Riedel
Describe the model to construct non-rotating
Gauss-Bonnet boson stars in AdS
Describe effect of Gauss-Bonnet term to boson star
solutions
Stability analysis of rotating Gauss-Bonnet boson star
solutions (ignoring the Gauss-Bonnet coupling for now)
Simple toy models for a wide range of objects such as
particles, compact stars, e.g. neutron stars and even
centres of galaxies
Gauss-Bonnet gravity: its spectrum does not include
new propagating degrees of freedom besides
gravitation
Toy models for AdS/CFT correspondence. Planar boson
stars in AdS have been interpreted as Bose-Einstein
condensates of glueballs
The Evolving Relation between Star Formation Rates and Stellar Mass Russell Johnston
Quantifying the interplay between star formation and stellar mass is a crucial component to understanding the build up of galaxies over cosmic time. There have been many investigations of this relationship, using both observations and simulations, with the aim of shedding light on how it connects with the underlying physical processes governing galaxy evolution.
In this talk I will present recent work where we have examined the star formation rate (SFR) - stellar mass (M∗) relation of star-forming galaxies in the XMM-LSS field to z ∼ 3.0 using the near-infrared data from the VISTA Deep Extragalactic Observations (VIDEO) survey. Combining VIDEO with broad-band photometry, we have used the SED fitting algorithm CIGALE to derive SFRs and M∗ and have adapted it to account for the full photometric redshift PDF uncertainty.
We have also compared our results to a range of simulations where I will show that the analytical scaling relation approaches, that invoke an equilibrium model, a good fit to our data. Within a simplified framework, such a model does not include the modelling of e.g. halos, cooling, or galaxy mergers, suggesting that a continual smooth accretion regulated by continual outflows may be a key driver in the overall growth of SFGs.
Gauss–Bonnet Boson Stars in AdS, Bielefeld, Germany, 2014Jurgen Riedel
Strong coupling to gravity: self-interacting rotating boson
stars are destabilized.
Sufficiently small AdS radius: self-interacting rotating boson
stars are destabilized.
Sufficiently strong rotation stabilizes self-interacting rotating
boson stars.
Onset of ergoregions can occur on the main branch of boson
star solutions, supposed to be classically stable.
Radially excited self-interacting rotating boson stars can be
classically stable in aAdS for sufficiently large AdS radius and
sufficiently small backreaction.
Gauss–Bonnet Boson Stars in AdS - Ibericos, Portugal, 2014Jurgen Riedel
Describe the model to construct non-rotating
Gauss-Bonnet boson stars in AdS
Describe effect of Gauss-Bonnet term to boson star
solutions
Stability analysis of rotating Gauss-Bonnet boson star
solutions (ignoring the Gauss-Bonnet coupling for now)
Simple toy models for a wide range of objects such as
particles, compact stars, e.g. neutron stars and even
centres of galaxies
Gauss-Bonnet gravity: its spectrum does not include
new propagating degrees of freedom besides
gravitation
Toy models for AdS/CFT correspondence. Planar boson
stars in AdS have been interpreted as Bose-Einstein
condensates of glueballs
The Evolving Relation between Star Formation Rates and Stellar Mass Russell Johnston
Quantifying the interplay between star formation and stellar mass is a crucial component to understanding the build up of galaxies over cosmic time. There have been many investigations of this relationship, using both observations and simulations, with the aim of shedding light on how it connects with the underlying physical processes governing galaxy evolution.
In this talk I will present recent work where we have examined the star formation rate (SFR) - stellar mass (M∗) relation of star-forming galaxies in the XMM-LSS field to z ∼ 3.0 using the near-infrared data from the VISTA Deep Extragalactic Observations (VIDEO) survey. Combining VIDEO with broad-band photometry, we have used the SED fitting algorithm CIGALE to derive SFRs and M∗ and have adapted it to account for the full photometric redshift PDF uncertainty.
We have also compared our results to a range of simulations where I will show that the analytical scaling relation approaches, that invoke an equilibrium model, a good fit to our data. Within a simplified framework, such a model does not include the modelling of e.g. halos, cooling, or galaxy mergers, suggesting that a continual smooth accretion regulated by continual outflows may be a key driver in the overall growth of SFGs.
Hidden gates in universe: Wormholes UCEN 2017 by Dr. Ali Ovgun
Gravity at UCEN 2017: Black holes and Cosmology, November 22, 23 and 24, 2017
The meeting take place at Universidad Central de Chile.
http://www2.udec.cl/~juoliva/gravatucen2017.html
Spectroscopic confirmation of an ultra-faint galaxy at the epoch of reionizationSérgio Sacani
Within one billion years of the Big Bang, intergalactic hydrogen
was ionized by sources emitting ultraviolet and higher energy
photons. This was the final phenomenon to globally affect all
the baryons (visible matter) in the Universe. It is referred to
as cosmic reionization and is an integral component of cosmology.
It is broadly expected that intrinsically faint galaxies
were the primary ionizing sources due to their abundance
in this epoch1,2. However, at the highest redshifts (z > 7.5;
lookback time 13.1 Gyr), all galaxies with spectroscopic confirmations
to date are intrinsically bright and, therefore, not
necessarily representative of the general population3. Here,
we report the unequivocal spectroscopic detection of a low
luminosity galaxy at z > 7.5. We detected the Lyman-α emission
line at ∼10,504 Å in two separate observations with
MOSFIRE4 on the Keck I Telescope and independently with
the Hubble Space Telescope’s slitless grism spectrograph,
implying a source redshift of z = 7.640 ± 0.001. The galaxy
is gravitationally magnified by the massive galaxy cluster
MACS J1423.8+2404 (z = 0.545), with an estimated intrinsic
luminosity of MAB = −19.6 ± 0.2 mag and a stellar mass of
☆ = × − +
M 3.0 0.8 10
1.5 8 solar masses. Both are an order of magnitude
lower than the four other Lyman-α emitters currently
known at z > 7.5, making it probably the most distant representative
source of reionization found to date.
The widespread popularity of Bayesian tree-structured regression methods has raised considerable interest in theoretical understanding of their empirical success. However, theoretical literature on methods such as Bayesian CART and BART is still in its infancy. This paper affords new insights about Bayesian CART in the context of structured wavelet shrinkage under the white noise model. We exhibit precise connections between tree-shaped sparsity priors and unstructured spike-and-slab priors, which are regarded as ideal but are rather theoretical in nature. We show that the more practical Bayesian CART priors lead to adaptive rate-minimax posterior concentration in the l∞sense, performing nearly as well as the theoretical ideal (up to a log term). To further explore the benefits of structured shrinkage, we propose the g-prior for trees, which departs from the typical wavelet product priors by harnessing correlation structure induced by the tree topology. While the majority of wavelet type theoretical results for CART focus on dyadic trees, here we do not require that splits are at dyadic locations. We introduce the library of weakly balanced Haar wavelets and show that Bayesian CART is equivalent to Bayesian basis selection from this library. To illustrate that l∞adaptation is an intricate phenomenon, where internal sparsity plays a key role, we show that dense trees are incapable of adaptation. While one of the major appeals of BART is uncertainty quantification via credible sets, asymptotic normality justifications have thus far been unavailable. Building on the l∞adaptation property, we provide new fully non-parametric and adaptive Bernstein-von Mises statements for Bayesian CART using multiscale techniques.
(Joint work with Ismael Castillo)
Detection of lyman_alpha_emission_from_a_triply_imaged_z_6_85_galaxy_behind_m...Sérgio Sacani
We report the detection of Ly emission at 9538A
in the Keck/DEIMOS and HST WFC3
G102 grism data from a triply-imaged galaxy at z = 6:846 0:001 behind galaxy cluster MACS
J2129.4 0741. Combining the emission line wavelength with broadband photometry, line ratio upper
limits, and lens modeling, we rule out the scenario that this emission line is [O II] at z = 1:57. After
accounting for magnication, we calculate the weighted average of the intrinsic Ly luminosity to be
1:31042 erg s 1 and Ly equivalent width to be 7415A. Its intrinsic UV absolute magnitude at
1600A
is 18:60:2 mag and stellar mass (1:50:3)107 M, making it one of the faintest (intrinsic
LUV 0:14 L
UV) galaxies with Ly detection at z 7 to date. Its stellar mass is in the typical range
for the galaxies thought to dominate the reionization photon budget at z & 7; the inferred Ly escape
fraction is high (& 10%), which could be common for sub-L z & 7 galaxies with Ly emission. This
galaxy oers a glimpse of the galaxy population that is thought to drive reionization, and it shows
that gravitational lensing is an important avenue to probe the sub-L galaxy population.
Hidden gates in universe: Wormholes UCEN 2017 by Dr. Ali Ovgun
Gravity at UCEN 2017: Black holes and Cosmology, November 22, 23 and 24, 2017
The meeting take place at Universidad Central de Chile.
http://www2.udec.cl/~juoliva/gravatucen2017.html
Spectroscopic confirmation of an ultra-faint galaxy at the epoch of reionizationSérgio Sacani
Within one billion years of the Big Bang, intergalactic hydrogen
was ionized by sources emitting ultraviolet and higher energy
photons. This was the final phenomenon to globally affect all
the baryons (visible matter) in the Universe. It is referred to
as cosmic reionization and is an integral component of cosmology.
It is broadly expected that intrinsically faint galaxies
were the primary ionizing sources due to their abundance
in this epoch1,2. However, at the highest redshifts (z > 7.5;
lookback time 13.1 Gyr), all galaxies with spectroscopic confirmations
to date are intrinsically bright and, therefore, not
necessarily representative of the general population3. Here,
we report the unequivocal spectroscopic detection of a low
luminosity galaxy at z > 7.5. We detected the Lyman-α emission
line at ∼10,504 Å in two separate observations with
MOSFIRE4 on the Keck I Telescope and independently with
the Hubble Space Telescope’s slitless grism spectrograph,
implying a source redshift of z = 7.640 ± 0.001. The galaxy
is gravitationally magnified by the massive galaxy cluster
MACS J1423.8+2404 (z = 0.545), with an estimated intrinsic
luminosity of MAB = −19.6 ± 0.2 mag and a stellar mass of
☆ = × − +
M 3.0 0.8 10
1.5 8 solar masses. Both are an order of magnitude
lower than the four other Lyman-α emitters currently
known at z > 7.5, making it probably the most distant representative
source of reionization found to date.
The widespread popularity of Bayesian tree-structured regression methods has raised considerable interest in theoretical understanding of their empirical success. However, theoretical literature on methods such as Bayesian CART and BART is still in its infancy. This paper affords new insights about Bayesian CART in the context of structured wavelet shrinkage under the white noise model. We exhibit precise connections between tree-shaped sparsity priors and unstructured spike-and-slab priors, which are regarded as ideal but are rather theoretical in nature. We show that the more practical Bayesian CART priors lead to adaptive rate-minimax posterior concentration in the l∞sense, performing nearly as well as the theoretical ideal (up to a log term). To further explore the benefits of structured shrinkage, we propose the g-prior for trees, which departs from the typical wavelet product priors by harnessing correlation structure induced by the tree topology. While the majority of wavelet type theoretical results for CART focus on dyadic trees, here we do not require that splits are at dyadic locations. We introduce the library of weakly balanced Haar wavelets and show that Bayesian CART is equivalent to Bayesian basis selection from this library. To illustrate that l∞adaptation is an intricate phenomenon, where internal sparsity plays a key role, we show that dense trees are incapable of adaptation. While one of the major appeals of BART is uncertainty quantification via credible sets, asymptotic normality justifications have thus far been unavailable. Building on the l∞adaptation property, we provide new fully non-parametric and adaptive Bernstein-von Mises statements for Bayesian CART using multiscale techniques.
(Joint work with Ismael Castillo)
Detection of lyman_alpha_emission_from_a_triply_imaged_z_6_85_galaxy_behind_m...Sérgio Sacani
We report the detection of Ly emission at 9538A
in the Keck/DEIMOS and HST WFC3
G102 grism data from a triply-imaged galaxy at z = 6:846 0:001 behind galaxy cluster MACS
J2129.4 0741. Combining the emission line wavelength with broadband photometry, line ratio upper
limits, and lens modeling, we rule out the scenario that this emission line is [O II] at z = 1:57. After
accounting for magnication, we calculate the weighted average of the intrinsic Ly luminosity to be
1:31042 erg s 1 and Ly equivalent width to be 7415A. Its intrinsic UV absolute magnitude at
1600A
is 18:60:2 mag and stellar mass (1:50:3)107 M, making it one of the faintest (intrinsic
LUV 0:14 L
UV) galaxies with Ly detection at z 7 to date. Its stellar mass is in the typical range
for the galaxies thought to dominate the reionization photon budget at z & 7; the inferred Ly escape
fraction is high (& 10%), which could be common for sub-L z & 7 galaxies with Ly emission. This
galaxy oers a glimpse of the galaxy population that is thought to drive reionization, and it shows
that gravitational lensing is an important avenue to probe the sub-L galaxy population.
Prospects for CMB lensing-galaxy clustering cross-correlations and initial co...Marcel Schmittfull
The lensing convergence measurable with future CMB experiments will be highly correlated with the clustering of galaxies that will be observed by imaging surveys such as LSST. I will discuss prospects for using that cross-correlation signal to constrain local primordial non-Gaussianity, the amplitude of matter fluctuations as a function of redshift, halo bias, and possibly the sum of neutrino masses. A key limitation for such analyses and large-scale structure analyses in general is that the mapping from initial conditions to observables is nonlinear for wavenumbers k>0.1h/Mpc. This can destroy cosmological information or move it to non-Gaussian tails of the probability distribution that are difficult to measure. I will describe how we can use recently developed initial condition reconstruction methods to help us recover some of that information in the nonlinear regime.
Unification Scheme in Double Radio Sources: Bend Angle versus Arm Length Rati...IOSR Journals
From radio source unification scheme, asymmetries are more pronounced in quasars than in radio galaxies. Using a sample of 625 double radio sources (316 radio galaxies and 309 quasars), we investigated the variations between bend angle, arm-length ratio and redshift. We find no significant correlation (0.045) between bend angle and redshift for the entire sample and at low z for radio galaxies while a weak correlation (0.121) between bend angle and redshift for quasars for the entire sampleis observed. A weak correlation (radio galaxies, r = 0.173 and quasars, r = 0.102) between the bend angle and arm-length ratio for the double radio sources used in this study is observed. Kharbet al. (2008) in their study of powerful classical double radio galaxies noted that this correlation could suggest that the environmental asymmetries that give rise to the arm-length ratio could be contributory to the misalignment angles in these sources. Quasars appear much more bent and misaligned. This is consistent with quasars being radio galaxies viewed at small angles.
The build up_of_the_c_d_halo_of_m87_evidence_for_accretion_in_the_last_gyrSérgio Sacani
Observações recentes obtidas com o Very Large Telescope do ESO mostraram que Messier 87, a galáxia elíptica gigante mais próximo de nós, engoliu uma galáxia inteira de tamanho médio no último bilhão de anos. Uma equipe de astrônomos conseguiu pela primeira vez seguir o movimento de 300 nebulosas planetárias brilhantes, encontrando evidências claras deste evento e encontrando também excesso de radiação emitida pelos restos da vítima completamente desfeita.
SPECTROSCOPIC CONFIRMATION OF THE EXISTENCE OF LARGE, DIFFUSE GALAXIES IN THE...Sérgio Sacani
We recently identified a population of low surface brightness objects in the field of the z = 0.023 Coma cluster,
using the Dragonfly Telephoto Array. Here we present Keck spectroscopy of one of the largest of these “ultradiffuse
galaxies” (UDGs), confirming that it is a member of the cluster. The galaxy has prominent absorption
features, including the Ca II H+K lines and the G-band, and no detected emission lines. Its radial velocity of
cz=6280±120 km s−1 is within the 1σ velocity dispersion of the Coma cluster. The galaxy has an effective
radius of 4.3 ± 0.3 kpc and a Sérsic index of 0.89 ± 0.06, as measured from Keck imaging. We find no indications
of tidal tails or other distortions, at least out to a radius of ∼2re. We show that UDGs are located in a previously
sparsely populated region of the size—magnitude plane of quiescent stellar systems, as they are ∼6 mag fainter
than normal early-type galaxies of the same size. It appears that the luminosity distribution of large quiescent
galaxies is not continuous, although this could largely be due to selection effects. Dynamical measurements are
needed to determine whether the dark matter halos of UDGs are similar to those of galaxies with the same
luminosity or to those of galaxies with the same size.
The Scale Invariant Vacuum Theory as viable Cosmology Model VGG Consulting
Recent studies in applying the Weyl's original gauge symmetry idea within the framework of the Weyl's Integrable Geometry to modern observational data in cosmology has resulted in the Scale Invariant Vacuum (SIV) paradigm. A sequence of papers by Prof. André Maeder has shown that SIV is a viable contender to standard LamdaCDM model see [1] for recent review. It has been also shown that the growth of the density perturbations of the early universe can be modeled within SIV without the need of dark matter [2]. Furthermore, SIV has been able to explain the asymptotic limit of the Radial Acceleration Relation (RAR) in Dwarf Spheroidals better than MOND and Dark Matter models [3]. An overview of the SIV results will be summarized and discussed subject to the time constraints of the workshop. \\
[1] Universe 2020, 6 (3), 46; https://doi.org/10.3390/universe6030046;\\
[2] Physics of the Dark Universe 25 (2019) 100315; https://doi.org/10.1016/j.dark.2019.100315;\\
[3] MNRAS 492 (2) February 2020, Pages 2698–2708, https://doi.org/10.1093/mnras/stz3613;
A tale of scale & speed: How the US Navy is enabling software delivery from l...sonjaschweigert1
Rapid and secure feature delivery is a goal across every application team and every branch of the DoD. The Navy’s DevSecOps platform, Party Barge, has achieved:
- Reduction in onboarding time from 5 weeks to 1 day
- Improved developer experience and productivity through actionable findings and reduction of false positives
- Maintenance of superior security standards and inherent policy enforcement with Authorization to Operate (ATO)
Development teams can ship efficiently and ensure applications are cyber ready for Navy Authorizing Officials (AOs). In this webinar, Sigma Defense and Anchore will give attendees a look behind the scenes and demo secure pipeline automation and security artifacts that speed up application ATO and time to production.
We will cover:
- How to remove silos in DevSecOps
- How to build efficient development pipeline roles and component templates
- How to deliver security artifacts that matter for ATO’s (SBOMs, vulnerability reports, and policy evidence)
- How to streamline operations with automated policy checks on container images
Full-RAG: A modern architecture for hyper-personalizationZilliz
Mike Del Balso, CEO & Co-Founder at Tecton, presents "Full RAG," a novel approach to AI recommendation systems, aiming to push beyond the limitations of traditional models through a deep integration of contextual insights and real-time data, leveraging the Retrieval-Augmented Generation architecture. This talk will outline Full RAG's potential to significantly enhance personalization, address engineering challenges such as data management and model training, and introduce data enrichment with reranking as a key solution. Attendees will gain crucial insights into the importance of hyperpersonalization in AI, the capabilities of Full RAG for advanced personalization, and strategies for managing complex data integrations for deploying cutting-edge AI solutions.
Enchancing adoption of Open Source Libraries. A case study on Albumentations.AIVladimir Iglovikov, Ph.D.
Presented by Vladimir Iglovikov:
- https://www.linkedin.com/in/iglovikov/
- https://x.com/viglovikov
- https://www.instagram.com/ternaus/
This presentation delves into the journey of Albumentations.ai, a highly successful open-source library for data augmentation.
Created out of a necessity for superior performance in Kaggle competitions, Albumentations has grown to become a widely used tool among data scientists and machine learning practitioners.
This case study covers various aspects, including:
People: The contributors and community that have supported Albumentations.
Metrics: The success indicators such as downloads, daily active users, GitHub stars, and financial contributions.
Challenges: The hurdles in monetizing open-source projects and measuring user engagement.
Development Practices: Best practices for creating, maintaining, and scaling open-source libraries, including code hygiene, CI/CD, and fast iteration.
Community Building: Strategies for making adoption easy, iterating quickly, and fostering a vibrant, engaged community.
Marketing: Both online and offline marketing tactics, focusing on real, impactful interactions and collaborations.
Mental Health: Maintaining balance and not feeling pressured by user demands.
Key insights include the importance of automation, making the adoption process seamless, and leveraging offline interactions for marketing. The presentation also emphasizes the need for continuous small improvements and building a friendly, inclusive community that contributes to the project's growth.
Vladimir Iglovikov brings his extensive experience as a Kaggle Grandmaster, ex-Staff ML Engineer at Lyft, sharing valuable lessons and practical advice for anyone looking to enhance the adoption of their open-source projects.
Explore more about Albumentations and join the community at:
GitHub: https://github.com/albumentations-team/albumentations
Website: https://albumentations.ai/
LinkedIn: https://www.linkedin.com/company/100504475
Twitter: https://x.com/albumentations
LF Energy Webinar: Electrical Grid Modelling and Simulation Through PowSyBl -...DanBrown980551
Do you want to learn how to model and simulate an electrical network from scratch in under an hour?
Then welcome to this PowSyBl workshop, hosted by Rte, the French Transmission System Operator (TSO)!
During the webinar, you will discover the PowSyBl ecosystem as well as handle and study an electrical network through an interactive Python notebook.
PowSyBl is an open source project hosted by LF Energy, which offers a comprehensive set of features for electrical grid modelling and simulation. Among other advanced features, PowSyBl provides:
- A fully editable and extendable library for grid component modelling;
- Visualization tools to display your network;
- Grid simulation tools, such as power flows, security analyses (with or without remedial actions) and sensitivity analyses;
The framework is mostly written in Java, with a Python binding so that Python developers can access PowSyBl functionalities as well.
What you will learn during the webinar:
- For beginners: discover PowSyBl's functionalities through a quick general presentation and the notebook, without needing any expert coding skills;
- For advanced developers: master the skills to efficiently apply PowSyBl functionalities to your real-world scenarios.
Essentials of Automations: The Art of Triggers and Actions in FMESafe Software
In this second installment of our Essentials of Automations webinar series, we’ll explore the landscape of triggers and actions, guiding you through the nuances of authoring and adapting workspaces for seamless automations. Gain an understanding of the full spectrum of triggers and actions available in FME, empowering you to enhance your workspaces for efficient automation.
We’ll kick things off by showcasing the most commonly used event-based triggers, introducing you to various automation workflows like manual triggers, schedules, directory watchers, and more. Plus, see how these elements play out in real scenarios.
Whether you’re tweaking your current setup or building from the ground up, this session will arm you with the tools and insights needed to transform your FME usage into a powerhouse of productivity. Join us to discover effective strategies that simplify complex processes, enhancing your productivity and transforming your data management practices with FME. Let’s turn complexity into clarity and make your workspaces work wonders!
Generative AI Deep Dive: Advancing from Proof of Concept to ProductionAggregage
Join Maher Hanafi, VP of Engineering at Betterworks, in this new session where he'll share a practical framework to transform Gen AI prototypes into impactful products! He'll delve into the complexities of data collection and management, model selection and optimization, and ensuring security, scalability, and responsible use.
In the rapidly evolving landscape of technologies, XML continues to play a vital role in structuring, storing, and transporting data across diverse systems. The recent advancements in artificial intelligence (AI) present new methodologies for enhancing XML development workflows, introducing efficiency, automation, and intelligent capabilities. This presentation will outline the scope and perspective of utilizing AI in XML development. The potential benefits and the possible pitfalls will be highlighted, providing a balanced view of the subject.
We will explore the capabilities of AI in understanding XML markup languages and autonomously creating structured XML content. Additionally, we will examine the capacity of AI to enrich plain text with appropriate XML markup. Practical examples and methodological guidelines will be provided to elucidate how AI can be effectively prompted to interpret and generate accurate XML markup.
Further emphasis will be placed on the role of AI in developing XSLT, or schemas such as XSD and Schematron. We will address the techniques and strategies adopted to create prompts for generating code, explaining code, or refactoring the code, and the results achieved.
The discussion will extend to how AI can be used to transform XML content. In particular, the focus will be on the use of AI XPath extension functions in XSLT, Schematron, Schematron Quick Fixes, or for XML content refactoring.
The presentation aims to deliver a comprehensive overview of AI usage in XML development, providing attendees with the necessary knowledge to make informed decisions. Whether you’re at the early stages of adopting AI or considering integrating it in advanced XML development, this presentation will cover all levels of expertise.
By highlighting the potential advantages and challenges of integrating AI with XML development tools and languages, the presentation seeks to inspire thoughtful conversation around the future of XML development. We’ll not only delve into the technical aspects of AI-powered XML development but also discuss practical implications and possible future directions.
Unlocking Productivity: Leveraging the Potential of Copilot in Microsoft 365, a presentation by Christoforos Vlachos, Senior Solutions Manager – Modern Workplace, Uni Systems
GDG Cloud Southlake #33: Boule & Rebala: Effective AppSec in SDLC using Deplo...James Anderson
Effective Application Security in Software Delivery lifecycle using Deployment Firewall and DBOM
The modern software delivery process (or the CI/CD process) includes many tools, distributed teams, open-source code, and cloud platforms. Constant focus on speed to release software to market, along with the traditional slow and manual security checks has caused gaps in continuous security as an important piece in the software supply chain. Today organizations feel more susceptible to external and internal cyber threats due to the vast attack surface in their applications supply chain and the lack of end-to-end governance and risk management.
The software team must secure its software delivery process to avoid vulnerability and security breaches. This needs to be achieved with existing tool chains and without extensive rework of the delivery processes. This talk will present strategies and techniques for providing visibility into the true risk of the existing vulnerabilities, preventing the introduction of security issues in the software, resolving vulnerabilities in production environments quickly, and capturing the deployment bill of materials (DBOM).
Speakers:
Bob Boule
Robert Boule is a technology enthusiast with PASSION for technology and making things work along with a knack for helping others understand how things work. He comes with around 20 years of solution engineering experience in application security, software continuous delivery, and SaaS platforms. He is known for his dynamic presentations in CI/CD and application security integrated in software delivery lifecycle.
Gopinath Rebala
Gopinath Rebala is the CTO of OpsMx, where he has overall responsibility for the machine learning and data processing architectures for Secure Software Delivery. Gopi also has a strong connection with our customers, leading design and architecture for strategic implementations. Gopi is a frequent speaker and well-known leader in continuous delivery and integrating security into software delivery.
How to Get CNIC Information System with Paksim Ga.pptxdanishmna97
Pakdata Cf is a groundbreaking system designed to streamline and facilitate access to CNIC information. This innovative platform leverages advanced technology to provide users with efficient and secure access to their CNIC details.
In his public lecture, Christian Timmerer provides insights into the fascinating history of video streaming, starting from its humble beginnings before YouTube to the groundbreaking technologies that now dominate platforms like Netflix and ORF ON. Timmerer also presents provocative contributions of his own that have significantly influenced the industry. He concludes by looking at future challenges and invites the audience to join in a discussion.
Building RAG with self-deployed Milvus vector database and Snowpark Container...Zilliz
This talk will give hands-on advice on building RAG applications with an open-source Milvus database deployed as a docker container. We will also introduce the integration of Milvus with Snowpark Container Services.
DevOps and Testing slides at DASA ConnectKari Kakkonen
My and Rik Marselis slides at 30.5.2024 DASA Connect conference. We discuss about what is testing, then what is agile testing and finally what is Testing in DevOps. Finally we had lovely workshop with the participants trying to find out different ways to think about quality and testing in different parts of the DevOps infinity loop.
Communications Mining Series - Zero to Hero - Session 1DianaGray10
This session provides introduction to UiPath Communication Mining, importance and platform overview. You will acquire a good understand of the phases in Communication Mining as we go over the platform with you. Topics covered:
• Communication Mining Overview
• Why is it important?
• How can it help today’s business and the benefits
• Phases in Communication Mining
• Demo on Platform overview
• Q/A
Climate Impact of Software Testing at Nordic Testing DaysKari Kakkonen
My slides at Nordic Testing Days 6.6.2024
Climate impact / sustainability of software testing discussed on the talk. ICT and testing must carry their part of global responsibility to help with the climat warming. We can minimize the carbon footprint but we can also have a carbon handprint, a positive impact on the climate. Quality characteristics can be added with sustainability, and then measured continuously. Test environments can be used less, and in smaller scale and on demand. Test techniques can be used in optimizing or minimizing number of tests. Test automation can be used to speed up testing.
Climate Impact of Software Testing at Nordic Testing Days
Testing cosmology with galaxy clusters, the CMB and galaxy clustering
1. July 4, 2013 SuperJEDI Mauritius
Testing cosmology with galaxy clusters,
the CMB and galaxy clustering
David Rapetti
DARK Fellow
Dark Cosmology Centre, Niels Bohr Institute
University of Copenhagen
In collaboration with
Steve Allen (KIPAC), Adam Mantz (KICP), Chris Blake
(Swinburne), David Parkinson (Queensland), Florian Beutler
(LBNL), Sarah Shandera (Pennsylvania)
2. July 4, 2013 SuperJEDI Mauritius
Combined constraints on growth and
expansion: breaking degeneracies
A combined measurement of cosmic growth and expansion
from clusters of galaxies, the CMB and galaxy clustering ,
MNRAS 2013 (arXiv:1205.4679)
David Rapetti, Chris Blake, Steven Allen, Adam Mantz, David Parkinson, Florian Beutler
3. July 4, 2013 SuperJEDI Mauritius
GR γ~0.55
Modeling linear, time-dependent
departures from GR
Linear power spectrum
Variance of the
density fluctuations
General Relativity Phenomenological parameterization
Growth rate
Scale independent in the
synchronous gauge
Number density of
galaxy clusters
4. July 4, 2013 SuperJEDI Mauritius
Modeling linear, time-dependent
departures from GR
Having measurements of σ8(z)
allows us to obtain f(z)
To measure g we need growth, f(z),
and expansion, Ωm(z), measurements
From measurements of the shape of the galaxy power spec-
trum and correlation function, we use constraints on the
product f(z) σ8(z) and on the quantity F(z), where the lat-
ter are purely expansion history constraints, i.e. on Ωm(z).
For this data set, both of these constraints are crucial to
measure γ = ln f(z)/ ln Ωm(z).10
However, having a con-
straint on f(z) σ8(z), instead of on f(z), yields a positive cor-
relation between γ and σ8 (see Figure 1) as long as Ωm < 1.
The faster the perturbations grow (small γ), the smaller
the perturbation amplitude, σ8, needs to be to provide the
same amount of anisotropy in the distribution of galaxies,
f(z) σ8(z). Note that the current uncertainty on the bias of
baryonic matter limits the ability of using the normaliza-
tion of the galaxy power spectrum to measure σ8, and thus
to break the degeneracy with γ.
3.3 Cluster abundance and masses
For clusters, we have direct constraints on σ8(z) and Ωm(z)
from abundance, mass calibration and gas mass fraction
data (see Sections 2.2 and 4.1). σ8(z) measurements pro-
vide us with constraints not only on σ8(z = 0), from
the local cluster mass function, but also on the growth
rate f(z) = −(1 + z)d ln σ8(z)/dz, from which together
with those on Ωm(z), we can constrain γ. The evolution of
σ8(z) = σ8e−g(z)
depends on γ, Ωm and w as follows
10 Note that without the AP effect constraints on Ωm(z), no rel-
evant constraints on γ can be obtained from RSD measurements
alone. For the same reason, the addition of the BAO constraints
on Ωm(z) improves significantly the measurement of γ for the
combination gal+BAO (see the right panel of Figure 1).
ation function
ameters in the
ell as the non-
lie within the
ies in F(z) and
(2011) used in
sses a range of
3.3 Cluster abundance and masses
For clusters, we have direct constraints on σ
from abundance, mass calibration and ga
data (see Sections 2.2 and 4.1). σ8(z) mea
vide us with constraints not only on σ8
the local cluster mass function, but also
rate f(z) = −(1 + z)d ln σ8(z)/dz, from
with those on Ωm(z), we can constrain γ. T
σ8(z) = σ8e−g(z)
depends on γ, Ωm and w a
10 Note that without the AP effect constraints
evant constraints on γ can be obtained from RS
alone. For the same reason, the addition of the
on Ωm(z) improves significantly the measurem
combination gal+BAO (see the right panel of F
Growth and e
g(z) =
z
0
(1 + z )−1
p(z ) − 1
−γ
p(z )γ
dz (8)
= (3wγ)−1
[λ(z) − λ(0)] , (9)
where λ(z) = [p(z) − 1]1−γ
p(z)γ
2F1 [1, 1; 1 + γ; p(z)], 2F1
is a hypergeometric function, p(z) = p0(1 + z)−3w
and
p0 = Ωm/(Ωm − 1). In practice, a negative degeneracy be-
tween σ8 and γ exists due to the limited precision of clus-
ter mass estimates, but it is notably smaller than those de-
scribed above (see Figure 1). Within the precision of the
data, indistinguishable cluster mass functions can be pro-
Growth
g(z) =
z
0
(1 + z )−1
p(z ) − 1
−γ
p(z )γ
dz
= (3wγ)−1
[λ(z) − λ(0)] ,
where λ(z) = [p(z) − 1]1−γ
p(z)γ
2F1 [1,1;1 + γ;p(z
is a hypergeometric function, p(z) = p0(1 + z)−3
p0 = Ωm/(Ωm − 1). In practice, a negative degenera
tween σ8 and γ exists due to the limited precision o
Growth and ex
g(z) =
z
0
(1 + z )−1
p(z ) − 1
−γ
p(z )γ
dz (8)
= (3wγ)−1
[λ(z) − λ(0)] , (9)
where λ(z) = [p(z) − 1]1−γ
p(z)γ
2F1 [1, 1; 1 + γ; p(z)], 2F1
is a hypergeometric function, p(z) = p0(1 + z)−3w
and
p0 = Ωm/(Ωm − 1). In practice, a negative degeneracy be-
tween σ8 and γ exists due to the limited precision of clus-
ter mass estimates, but it is notably smaller than those de-
scribed above (see Figure 1). Within the precision of the
Growth and expansion
g(z) =
z
0
(1 + z )−1
p(z ) − 1
−γ
p(z )γ
dz (8)
= (3wγ)−1
[λ(z) − λ(0)] , (9)
where λ(z) = [p(z) − 1]1−γ
p(z)γ
2F1 [1, 1; 1 + γ; p(z)], 2F1
is a hypergeometric function, p(z) = p0(1 + z)−3w
and
p0 = Ωm/(Ωm − 1). In practice, a negative degeneracy be-
tween σ8 and γ exists due to the limited precision of clus-
ter mass estimates, but it is notably smaller than those de-
scribed above (see Figure 1). Within the precision of the
data, indistinguishable cluster mass functions can be pro-
4.1.1
We mo
with a
where
log10[E
Growth and expansion from clu
z
0
(1 + z )−1
p(z ) − 1
−γ
p(z )γ
dz (8)
(3wγ)−1
[λ(z) − λ(0)] , (9)
= [p(z) − 1]1−γ
p(z)γ
2F1 [1, 1; 1 + γ; p(z)], 2F1
geometric function, p(z) = p0(1 + z)−3w
and
Ωm − 1). In practice, a negative degeneracy be-
nd γ exists due to the limited precision of clus-
timates, but it is notably smaller than those de-
ove (see Figure 1). Within the precision of the
4.1.1 Scaling re
We model the L
(m) =
with a log-norma
where ≡ lo
Growth an
g(z) =
z
0
(1 + z )−1
p(z ) − 1
−γ
p(z )γ
dz
= (3wγ)−1
[λ(z) − λ(0)] ,
where λ(z) = [p(z) − 1]1−γ
p(z)γ
2F1 [1, 1; 1 + γ; p(z)],
is a hypergeometric function, p(z) = p0(1 + z)−3w
p0 = Ωm/(Ωm − 1). In practice, a negative degeneracy
tween σ8 and γ exists due to the limited precision of c
ter mass estimates, but it is notably smaller than those
scribed above (see Figure 1). Within the precision of
Rapetti et al 13
6. July 4, 2013 SuperJEDI Mauritius
Flat ΛCDM + γ: full pdf’s
Gold, solid line:
clusters+CMB (ISW)+galaxies
Red, dashed line:
clusters
Blue, dotted line:
CMB (ISW)
Green, long-dashed line:
galaxies
Rapetti et al 13
7. July 4, 2013 SuperJEDI Mauritius
Gold, solid line:
clusters+CMB (ISW)+galaxies
Red, dashed line:
clusters
Blue, dotted line:
CMB (ISW)
Green, long-dashed line:
galaxies
Flat ΛCDM + γ: full pdf’s
Rapetti et al 13
8. July 4, 2013 SuperJEDI Mauritius
Flat ΛCDM + growth index γ
Rapetti et al 13
clusters (XLF+fgas): BCS+REFLEX
+MACS
CMB (ISW): WMAP
galaxies (RSD+AP): WiggleZ
+6dFGS+BOSS
For General Relativity γ~0.55
Magenta: clusters+galaxies
Purple: clusters+CMB
Turquoise: CMB+galaxies
Gold: clusters+CMB+galaxies
9. July 4, 2013 SuperJEDI Mauritius
Rapetti et al 13
For General Relativity γ~0.55
Magenta: clusters+galaxies
Purple: clusters+CMB
Turquoise: CMB+galaxies
Gold: clusters+CMB+galaxies
Platinum: clusters+CMB+galaxies
+BAO (Reid et al 12; Percival et al
10)+SNIa (Suzuki et al 12)
+SH0ES (Riess et al 11)
Flat wCDM + growth index γ: growth plane
10. July 4, 2013 SuperJEDI Mauritius
Rapetti et al 13
Flat wCDM + growth index γ: expansion planes
Platinum: clusters + CMB + galaxies + BAO (Reid et al 12; Percival et al 10)
+ SNIa (Suzuki et al 12) + SH0ES (Riess et al 11)
11. July 4, 2013 SuperJEDI Mauritius
Rapetti et al 13
For General Relativity γ~0.55
Magenta: clusters+galaxies
Purple: clusters+CMB
Turquoise: CMB+galaxies
Gold: clusters+CMB+galaxies
Flat wCDM + growth index γ: expansion+growth
12. July 4, 2013 SuperJEDI Mauritius
Rapetti et al 13
Flat wCDM + growth index γ: expansion+growth
For General Relativity γ~0.55
For ΛCDM w=-1
Gold: clusters+CMB+galaxies
Platinum: clusters+CMB+galaxies
+BAO+SNIa+SH0ES
! = 0.604± 0.078
"8 = 0.789 ± 0.019
w = !0.967!0.053
+0.054
"m = 0.278!0.011
+0.012
H0 = 70.0 ±1.3
13. July 4, 2013 SuperJEDI Mauritius
Flat wCDM + γ: full pdf’s
Red, dashed line: clusters; Purple, dotted line: clusters+CMB; Gold, solid line:
clusters+CMB+galaxies; Platinum, long-dashed line: all
Rapetti et al 13
14. July 4, 2013 SuperJEDI Mauritius
Beyond ΛCDM: Primordial non-Gaussianity
X-ray cluster constraints on non-Gaussianity ,
arXiv:1304.1216
Sarah Shandera, Adam Mantz, David Rapetti, Steven Allen
15. July 4, 2013 SuperJEDI Mauritius
Testing the Gaussianity of the
primordial fluctuations
1. When cumulants beyond skewness (correlations beyond the
bispectrum) are important, we can only properly describe the non-
Gaussianity with a one-parameter model if we can use this
parameter to specify the amplitude of all the correlations.
2. We assume two different ways to scale higher moments with the
skewness based on particle physics models of inflation.
3. Cluster counts probe smaller scales (0.1-0.5h/Mpc) than the CMB
and the galaxy bias.
4. Cluster counts are sensitive to any non-Gaussianity and to higher
order moments of the probability distribution of primordial
fluctuations.
16. July 4, 2013 SuperJEDI Mauritius
Testing the Gaussianity of the
primordial fluctuations
D D
spectrum. The three-point correlation is then just a function of two independent momenta
and is called the bispectrum.
The local, equilateral and orthogonal bispectra are shown in Eq.(2.3) below. Inter-
estingly, though, object number counts are not sensitive to the details of the bispectrum’s
momentum dependence. Instead, only the integrated moments of the smoothed density fluc-
tuations δR are relevant. For example,
δ3
R =
d3k1
(2π)3
d3k2
(2π)3
d3k3
(2π)3
M(k1, R, z)M(k2, R, z)M(k3, R, z)Φ(k1)Φ(k2)Φ(k3)c
(1.1)
where the terms M(ki, R, z) contain a window function, the corresponding factors from the
Poisson equation, the transfer function and the growth factor converting the linear perturba-
tion in the gravitational potential to the smoothed density perturbation. (The full expressions
for these quantities can be found in Appendix A.) We characterize the non-Gaussianity by
the dimensionless ratios of the cumulants of the density field
Mn,R =
δn
Rc
δ2
Rn/2
(1.2)
which are by construction redshift independent and nearly independent of the smoothing
scale, R, if the primordial bispectrum is scale independent.1
When cumulants beyond the skewness (correlations beyond the bispectrum) are relevant,
a one-parameter model is only useful if we can use it to specify the amplitude of all the
correlations. In this paper we use M3 and a choice for how higher moments scale with M3
to describe non-Gaussian fluctuations. The scalings we consider are motivated by particle
1
Scale independence means that the bispectrum (e.g., those in Eq.(2.3)) contains no length scale other
than the factors k−1
i in the P(ki) terms.
trum.
eral and orthogonal bispectra are shown in Eq.(2.3) below. Inter-
t number counts are not sensitive to the details of the bispectrum’s
. Instead, only the integrated moments of the smoothed density fluc-
t. For example,
3k2
π)3
d3k3
(2π)3
M(k1, R, z)M(k2, R, z)M(k3, R, z)Φ(k1)Φ(k2)Φ(k3)c
(1.1)
R, z) contain a window function, the corresponding factors from the
ansfer function and the growth factor converting the linear perturba-
potential to the smoothed density perturbation. (The full expressions
be found in Appendix A.) We characterize the non-Gaussianity by
s of the cumulants of the density field
Mn,R =
δn
Rc
δ2
Rn/2
(1.2)
ion redshift independent and nearly independent of the smoothing
ial bispectrum is scale independent.1
eyond the skewness (correlations beyond the bispectrum) are relevant,
is only useful if we can use it to specify the amplitude of all the
per we use M3 and a choice for how higher moments scale with M3
an fluctuations. The scalings we consider are motivated by particle
ans that the bispectrum (e.g., those in Eq.(2.3)) contains no length scale other
P(ki) terms.
effect of Primordial non-Gaussianity on object number counts
tool is a series expansion for the ratio of the non-Gaussian mass function to
sian one. The expansion we use is based on a Press-Schechter model for halo
applied to non-Gaussian probability distributions for the primordial fluctuations.
d derivation of the non-Gaussian mass function we use is given in Appendix A
developed in [30–32]. The weakly non-Gaussian probability distributions that the
tion is based on are asymptotic expansions that deviate substantially from the
bability density function (PDF) for sufficiently rare fluctuations. Fortunately, our
is already sufficiently constrained to determine that the clusters in our sample
in that regime. However, the clusters are sufficiently rare that truncating the
below at a single term (the skewness) is not sufficient to test the full range of
at are only as skewed as current CMB constraints allow.
dd non-Gaussianity to the cosmology by considering a mass function of the form
dn
dM
NG
=
dn
dM
T,M300
nNG
nG
Edgeworth
(2.1)
first term on the right hand side is the Gaussian mass function of Tinker et al.
usters identified as spheres containing a mean density 300 times that of the mean
nsity of the Universe, 300 ¯ρm(z). The ratio of the non-Gaussian mass function to
ian one will be given as a series expansion, defined below. This factor will be
n of mass, redshift, and parameters that characterize the amplitude of the non-
ty, which we define next.
ametrizing the level of non-Gaussianity
ect number counts are not sensitive to the details of the momentum space corre-
Hierarchical scaling (local)
Feeder scaling (two field model)
Non-Gaussian mass function
Dimensionless ratios of the cumulants of the density field
Since object number counts are not sensitive to the details of the momentum space corre-
lations, we consider the dimensionless, connected moments (the cumulants, divided by the
appropriate power of the amplitude of fluctuations) of the density fluctuations smoothed on
a given scale R, as defined in Eq.(1.2). Most constraints on non-Gaussianity have so far been
reported for a parameter that measures the size of the three-point correlation in momentum
space, or bispectrum. This is an extremely useful first statistic because this correlation should
be exactly zero if the fluctuations were exactly Gaussian. However, because the bispectrum
is a function of two momenta, the non-Gaussian parameters most often quoted assume a
shape for the bispectrum.
A generic homogeneous and isotropic bispectrum for the potential Φ can be written as
Φ(k1)Φ(k2)Φ(k3)
c
= (2π)3
δ3
D(k1 + k2 + k3) B(k1, k2, k3) (2.2)
where the function B(k1, k2, k3) determines the shape. Bispectra are colloquially named by
the (triangle) configuration of the three momentum vectors that are most strongly correlated.
To interpret our constraints on M3 in terms of familiar bispectra, we consider the templates
for ‘local’, ‘equilateral’ and ‘orthogonal’ bispectra:
Blocal = 2flocal
NL (P(k1)P(k2) + P(k1)P(k3) + P(k2)P(k3)) (2.3)
Bequil = 6fequil
NL [−P(k1)P(k2) + 2 perm. − 2(P(k1)P(k2)P(k3))2/3
+P(k1)1/3
P(k2)2/3
P(k3) + 5 perm.]
Borth = 6forth
NL [−3P(k1)P(k2) + 2 perm. − 8(P(k1)P(k2)P(k3))2/3
+3P(k1)1/3
P(k2)2/3
P(k3) + 5 perm.]
– 4 –
Integrated moments of the smoothed density fluctuations
Generic homogeneous and isotropic bispectrum of the potential
r counts are sensitive to the value of the total skewness and to the scaling of
ts, rather than any details of the momentum space correlations.
on to the dependence on a parameter like fNL, the cumulants also have nu-
ients that typically have to do with combinatorics. For example, beginning
the bispectrum contains three terms linear in flocal
NL , each with two equivalent
the expectation value of pairs of fields ΦG. We will the choose the constants
ality equal to combinatoric factors for the moments that are generated in the
nd a simple two-field extension that gives feeder scaling:4
Hierarchical Mh
n = n! 2n−3
Mh
3
6
n−2
(2.7)
Feeder Mf
n = (n − 1)! 2n−1
Mf
3
8
n/3
. (2.8)
aling of the moments, we can determine a series expansion for the probability
nd for the mass function that can be consistently truncated at some order in
single parameter scenarios, we report constraints in terms of the scaling as-
umber counts are sensitive to the value of the total skewness and to the scaling of
oments, rather than any details of the momentum space correlations.
ddition to the dependence on a parameter like fNL, the cumulants also have nu-
oefficients that typically have to do with combinatorics. For example, beginning
1.3), the bispectrum contains three terms linear in flocal
NL , each with two equivalent
ake the expectation value of pairs of fields ΦG. We will the choose the constants
tionality equal to combinatoric factors for the moments that are generated in the
atz and a simple two-field extension that gives feeder scaling:4
Hierarchical Mh
n = n! 2n−3
Mh
3
6
n−2
(2.7)
Feeder Mf
n = (n − 1)! 2n−1
Mf
3
8
n/3
. (2.8)
en scaling of the moments, we can determine a series expansion for the probability
on and for the mass function that can be consistently truncated at some order in
ents.
the single parameter scenarios, we report constraints in terms of the scaling as-
physics models of inflation, and our constraints on the total dimensionless skewness can
always be re-written in terms of a particular bispectrum using Eq. (1.1) and Eq. (1.2).
Most previous work on the utility of cluster counts to constrain non-Gaussianity has
focused on the local ansatz [18, 19], where one assumes that the non-Gaussian field Φ(x) is
a simple, local transformation of a Gaussian field ΦG(x):
Φ(x) = ΦG(x) + flocal
NL [ΦG(x)2
− ΦG(x)2
]. (1.3)
In this useful model, flocal
NL is the single parameter that all correlation functions depend on,
and the cumulants scale2 as (flocal
NL )n−2. Non-Gaussianity of the local type has a bispectrum
that most strongly correlates Fourier modes of very different wavelengths. This particular
mode coupling generates strong signals in other large scale structure observables – most no-
tably introducing a scale dependence in the bias of any biased tracer of the underlying dark
matter distribution [11, 14, 20]. For this reason, papers that have analyzed the potential for
17. July 4, 2013 SuperJEDI Mauritius
Testing the Gaussianity of the
primordial fluctuations
Hierarchical scaling (local)
Feeder scaling (two field model)
reported for a parameter that measures the size of the three-point correlation in momentum
space, or bispectrum. This is an extremely useful first statistic because this correlation should
be exactly zero if the fluctuations were exactly Gaussian. However, because the bispectrum
is a function of two momenta, the non-Gaussian parameters most often quoted assume a
shape for the bispectrum.
A generic homogeneous and isotropic bispectrum for the potential Φ can be written as
Φ(k1)Φ(k2)Φ(k3)
c
= (2π)3
δ3
D(k1 + k2 + k3) B(k1, k2, k3) (2.2)
where the function B(k1, k2, k3) determines the shape. Bispectra are colloquially named by
the (triangle) configuration of the three momentum vectors that are most strongly correlated.
To interpret our constraints on M3 in terms of familiar bispectra, we consider the templates
for ‘local’, ‘equilateral’ and ‘orthogonal’ bispectra:
Blocal = 2flocal
NL (P(k1)P(k2) + P(k1)P(k3) + P(k2)P(k3)) (2.3)
Bequil = 6fequil
NL [−P(k1)P(k2) + 2 perm. − 2(P(k1)P(k2)P(k3))2/3
+P(k1)1/3
P(k2)2/3
P(k3) + 5 perm.]
Borth = 6forth
NL [−3P(k1)P(k2) + 2 perm. − 8(P(k1)P(k2)P(k3))2/3
+3P(k1)1/3
P(k2)2/3
P(k3) + 5 perm.]
– 4 –
Generic homogeneous and isotropic bispectrum of the potential
r counts are sensitive to the value of the total skewness and to the scaling of
ts, rather than any details of the momentum space correlations.
on to the dependence on a parameter like fNL, the cumulants also have nu-
ients that typically have to do with combinatorics. For example, beginning
the bispectrum contains three terms linear in flocal
NL , each with two equivalent
the expectation value of pairs of fields ΦG. We will the choose the constants
ality equal to combinatoric factors for the moments that are generated in the
nd a simple two-field extension that gives feeder scaling:4
Hierarchical Mh
n = n! 2n−3
Mh
3
6
n−2
(2.7)
Feeder Mf
n = (n − 1)! 2n−1
Mf
3
8
n/3
. (2.8)
aling of the moments, we can determine a series expansion for the probability
nd for the mass function that can be consistently truncated at some order in
single parameter scenarios, we report constraints in terms of the scaling as-
umber counts are sensitive to the value of the total skewness and to the scaling of
oments, rather than any details of the momentum space correlations.
ddition to the dependence on a parameter like fNL, the cumulants also have nu-
oefficients that typically have to do with combinatorics. For example, beginning
1.3), the bispectrum contains three terms linear in flocal
NL , each with two equivalent
ake the expectation value of pairs of fields ΦG. We will the choose the constants
tionality equal to combinatoric factors for the moments that are generated in the
atz and a simple two-field extension that gives feeder scaling:4
Hierarchical Mh
n = n! 2n−3
Mh
3
6
n−2
(2.7)
Feeder Mf
n = (n − 1)! 2n−1
Mf
3
8
n/3
. (2.8)
en scaling of the moments, we can determine a series expansion for the probability
on and for the mass function that can be consistently truncated at some order in
ents.
the single parameter scenarios, we report constraints in terms of the scaling as-
physics models of inflation, and our constraints on the total dimensionless skewness can
always be re-written in terms of a particular bispectrum using Eq. (1.1) and Eq. (1.2).
Most previous work on the utility of cluster counts to constrain non-Gaussianity has
focused on the local ansatz [18, 19], where one assumes that the non-Gaussian field Φ(x) is
a simple, local transformation of a Gaussian field ΦG(x):
Φ(x) = ΦG(x) + flocal
NL [ΦG(x)2
− ΦG(x)2
]. (1.3)
In this useful model, flocal
NL is the single parameter that all correlation functions depend on,
and the cumulants scale2 as (flocal
NL )n−2. Non-Gaussianity of the local type has a bispectrum
that most strongly correlates Fourier modes of very different wavelengths. This particular
mode coupling generates strong signals in other large scale structure observables – most no-
tably introducing a scale dependence in the bias of any biased tracer of the underlying dark
matter distribution [11, 14, 20]. For this reason, papers that have analyzed the potential for
A generic homogeneous and isotropic bispectrum for the potential Φ can be written as
Φ(k1)Φ(k2)Φ(k3)
c
= (2π)3
δ3
D(k1 + k2 + k3) B(k1, k2, k3) (2.2)
where the function B(k1, k2, k3) determines the shape. Bispectra are colloquially named by
the (triangle) configuration of the three momentum vectors that are most strongly correlated.
To interpret our constraints on M3 in terms of familiar bispectra, we consider the templates
for ‘local’, ‘equilateral’ and ‘orthogonal’ bispectra:
Blocal = 2flocal
NL (P(k1)P(k2) + P(k1)P(k3) + P(k2)P(k3)) (2.3)
Bequil = 6fequil
NL [−P(k1)P(k2) + 2 perm. − 2(P(k1)P(k2)P(k3))2/3
+P(k1)1/3
P(k2)2/3
P(k3) + 5 perm.]
Borth = 6forth
NL [−3P(k1)P(k2) + 2 perm. − 8(P(k1)P(k2)P(k3))2/3
+3P(k1)1/3
P(k2)2/3
P(k3) + 5 perm.]
where the power spectrum, P(k), is defined from the two-point correlation function by
Φ(k1)Φ(k2)
= (2π)3
δ3
D(k1 + k2)P(k1) ≡ (2π)3
δ3
D(k1 + k2)2π2 ∆2
Φ(k0)
k3
1
k1
k0
ns−1
(2.4)
where ∆Φ(k0) is the RMS amplitude of fluctuations at a pivot point k0 and any running
of that amplitude with scale is parametrized with the spectral index ns. In the best fit
cosmology from the seven-year WMAP data, baryon acoustic oscillations and Hubble pa-
rameter measurements, the pivot point is k0 = 0.002 Mpc−1
, the spectral index is a constant
18. July 4, 2013 SuperJEDI Mauritius
Testing the Gaussianity of the
primordial fluctuations
oments.
or the single parameter scenarios, we report constraints in terms of the scaling as-
and the parameter M3, which can be compared with other constraints on particular
trum shapes using Table 1.
The mass function in terms of M3 and the scaling of higher moments
l assume the non-Gaussian factor in the mass function of Eq.(2.1) takes the following
nNG
nG
Edgeworth
≈ 1 +
Fh,f
1 (M)
F
0(M)
+
Fh,f
2 (M)
F
0(M)
+ . . . (2.9)
term in the series is normalized by the Press-Schechter Gaussian term, F
0(M) =
2/
√
2π)(dσ/dM)(νc/σ), where νc = δc/σ, δc = 1.686 is the collapse threshold, and σ =
is the variance in density fluctuations smoothed on the appropriate scale (Eq.(A.4)).
ugh the first term, Fh
1 (M) or Ff
1 (M), is proportional to M3 regardless of how the
moments scale, the exact form of all higher order terms depends on the choice of
. For the hierarchical and feeder scaling, Fh
n (M) and Ff
n (M) are given in Eq.(A.14)
Appendix. Truncating this series after the first term is clearly unphysical since no
bility distribution with only a non-zero skewness can be positive everywhere. Although
me objects (low mass, low redshift) this truncation does not cause a significant error,
er fluctuations it does. Keeping higher terms in the series is therefore important. How
cant these terms are in the context of cluster constraints depends on the mass and red-
f the objects as well as the amplitude and scaling of the non-Gaussianity considered.
tion 5, we show several examples to illustrate how relevant the higher terms are as a
on of mass, redshift, skewness and scaling. Although this mass function has been shown
ee reasonably well with simulations, it does not come from a first principles derivation.
tion 5 we also contrast it to the Dalal et al mass function from simulations of the local
[20].
For the single parameter scenarios, we report constraints in terms of
sumed and the parameter M3, which can be compared with other constrain
bispectrum shapes using Table 1.
2.2 The mass function in terms of M3 and the scaling of higher m
We will assume the non-Gaussian factor in the mass function of Eq.(2.1) tak
form:
nNG
nG
Edgeworth
≈ 1 +
Fh,f
1 (M)
F
0(M)
+
Fh,f
2 (M)
F
0(M)
+ . . .
Each term in the series is normalized by the Press-Schechter Gaussian t
(e−ν2
c /2/
√
2π)(dσ/dM)(νc/σ), where νc = δc/σ, δc = 1.686 is the collapse thr
σ(M) is the variance in density fluctuations smoothed on the appropriate s
Although the first term, Fh
1 (M) or Ff
1 (M), is proportional to M3 regard
higher moments scale, the exact form of all higher order terms depends o
scaling. For the hierarchical and feeder scaling, Fh
n (M) and Ff
n (M) are giv
of the Appendix. Truncating this series after the first term is clearly unph
probability distribution with only a non-zero skewness can be positive everyw
for some objects (low mass, low redshift) this truncation does not cause a s
for rarer fluctuations it does. Keeping higher terms in the series is therefore i
significant these terms are in the context of cluster constraints depends on th
shift of the objects as well as the amplitude and scaling of the non-Gaussia
In Section 5, we show several examples to illustrate how relevant the higher
function of mass, redshift, skewness and scaling. Although this mass function
to agree reasonably well with simulations, it does not come from a first princ
In Section 5 we also contrast it to the Dalal et al mass function from simulat
terms of the scaling as-
constraints on particular
higher moments
.(2.1) takes the following
. . . (2.9)
aussian term, F
0(M) =
lapse threshold, and σ =
opriate scale (Eq.(A.4)).
M3 regardless of how the
epends on the choice of
M) are given in Eq.(A.14)
arly unphysical since no
ve everywhere. Although
cause a significant error,
herefore important. How
nds on the mass and red-
-Gaussianity considered.
he higher terms are as a
function has been shown
first principles derivation.
Now for either scaling, truncating the series at some finite s in the sums above keeps all terms
up to the same order in M3: Ms
3 for hierarchical scalings and M
s/3
3 for feeder scalings.
To write the mass function we will need derivatives of all the terms in the expansion
with respect to mass (or smoothing scale). In general, the derivatives can be found using the
relationship for the Hermite polynomials:
νHn(ν) −
dHn(ν)
dν
= Hn+1(ν) . (A.12)
The ratio of the non-Gaussian Edgeworth mass function to the Gaussian has the same struc-
tural form for either scaling:
nNG
nG
Edgeworth
≈ 1 +
Fh,f
1 (M)
F
0(M)
+
Fh,f
2 (M)
F
0(M)
+ . . . (A.13)
with the derivatives of each term F
s = dFs/dM for s ≥ 1:
Fh
s (ν) = F
0
{km}h
Hs+2r
s
m=1
1
km!
Mm+2,R
(m + 2)!
km
(A.14)
+Hs+2r−1
σ
ν
d
dσ
s
m=1
1
km!
Mm+2,R
(m + 2)!
km
Ff
s (ν) = F
0
{km}f
Hs+2
s
m=1
1
km!
Mm+2,R
(m + 2)!
km
+Hs+1
σ
ν
d
dσ
s
m=1
1
km!
Mm+2,R
(m + 2)!
km
where the {km} again satisfy the relationships given below Eq.(A.11) and we have used
F
0 =
e−
ν2
c
2
√
dσ νc
. (A.15)
Press-Schechter normalization
Edgeworth expansion
Hierarchical scaling
Feeder scaling
19. July 4, 2013 SuperJEDI Mauritius
Shandera et al 13
Gaussian distribution Μ3=0
Purple: clusters
Gold: clusters+CMB
Flat ΛCDM + beyond skewness: hierarchical
−0.2 −0.1 0.0 0.1 0.2
0.70.80.91.01.1
M3
σ8
●
●
clusters
clusters+CMB
●
●
●
●
●
●
Hierarchical model
−600 −300 0 300 600
fNL
local
103
M3 = !1!28
+24
!8 = 0.81!0.03
+0.02
fNL
local
= !3!91
+78
20. July 4, 2013 SuperJEDI Mauritius
Shandera et al 13
Gaussian distribution Μ3=0
Purple: clusters
Gold: clusters+CMB
Flat ΛCDM + beyond skewness: feeder
−0.04 −0.02 0.00 0.02 0.04
0.70.80.91.01.1
M3
σ8
●
●
clusters
clusters+CMB
●
●
●
●
●
●
Feeder model
−100 −50 0 50 100
fNL
local
103
M3 = !1!28
+24
!8 = 0.81!0.03
+0.02
fNL
local
= !14!21
+22
21. July 4, 2013 SuperJEDI Mauritius
Shandera et al 13
Gaussian distribution Μ3=0
Purple: clusters
Gold: clusters+CMB
Flat ΛCDM + beyond skewness: hierarchical
−0.2 −0.1 0.0 0.1 0.2
1.11.21.31.41.51.6
M3
βlm
●
●
clusters
clusters+CMB
●
●
●
●
●
●
Hierarchical model
−600 −300 0 300 600
fNL
local
103
M3 = !1!28
+24
!lm =1.33!0.08
+0.07
fNL
local
= !3!91
+78
22. July 4, 2013 SuperJEDI Mauritius
Shandera et al 13
Gaussian distribution Μ3=0
Purple: clusters
Gold: clusters+CMB
Flat ΛCDM + beyond skewness: feeder
−0.04 −0.02 0.00 0.02 0.04
1.11.21.31.41.51.6
M3
βlm
●
●
clusters
clusters+CMB
●
●
●
●
●
●
Feeder model
−100 −50 0 50 100
fNL
local
103
M3 = !1!28
+24
!lm =1.32!0.05
+0.06
fNL
local
= !14!21
+22
23. July 4, 2013 SuperJEDI Mauritius
Flat ΛCDM + beyond skewness: redshift
−0.2 −0.1 0.0 0.1 0.2 0.3
0.60.70.80.91.01.1
M3
σ8
●
●
clusters (all)
clusters (z 0.3)
●
●
●
●
●
●
Hierarchical model
−600 −300 0 300 600 900
fNL
local
Shandera et al 13
−0.04 −0.02 0.00 0.02 0.04
0.60.70.80.91.01.1 M3
σ8
●
●
clusters (all)
clusters (z 0.3)
●
●
●
●
●
●
Feeder model
−150 −100 −50 0 50 100 150
fNL
local
24. July 4, 2013 SuperJEDI Mauritius
Shandera et al 13
13.5 13.75 14. 14.25 14.5 14.75 15. 15.25 15.5
1.0
1.1
1.2
1.3
1.4
z0, fNL30
dn
dM
NG dn
dM
G
z = 0 , flocal
NL = 30
LMSV, skew only
LMSV, hierarchical
LMSV, feeder
Dalal et al.
Log10(M/M⊙ h−1
)
13.5 13.75 14. 14.25 14.5 14.75 15. 15.25 15.5
1.0
1.1
1.2
1.3
1.4
z1, fNL30
dn
dM
NG dn
dM
G
z = 1.0 , flocal
NL = 30
Log10(M/M⊙ h−1
)
13.5 13.75 14. 14.25 14.5 14.75 15. 15.25 15.5
1.0
1.2
1.4
1.6
1.8
2.0
2.2
2.4
z0, fNL100
dn
dM
NG dn
dM
G
z = 0 , flocal
NL = 100
Log10(M/M⊙ h−1
)
13.5 13.75 14. 14.25 14.5 14.75 15. 15.25 15.5
1.0
1.2
1.4
1.6
1.8
2.0
2.2
2.4
z1, fNL100
dn
dM
NG dn
dM
G
z = 1.0 , flocal
NL = 100
Log10(M/M⊙ h−1
)
25. July 4, 2013 SuperJEDI Mauritius
Shandera et al 13
Table 3. The constraints on the skewness can be converted to constraints on the amplitude of any
bispectrum. The shape of the bispectrum is independent of the scaling, although the usual local
ansatz corresponds to a local-shape bispectrum with hierarchical moments.
Scaling Data Local Bispectrum Equil. Bispectrum Orthog. Bispectrum
h CL −73+129
−113 −271+482
−422 346+538
−615
h CL+CMB −3+78
−91 −12+289
−338 15+430
−369
f CL −28+35
−13 −106+134
−48 130+60
−164
f CL+CMB −14+22
−21 −52+85
−79 63+97
−104
skew-only CL −29+532
−78 −105+1916
−280 146+389
−2658
skew-only CL+CMB −9+234
−65 −35+841
−234 48+324
−1167
ensity
1.01.5
Hierarchical
Feeder
tes from follow-up data, or the mass/redshift ranges
on the full set of cosmological and scaling relation
urselves to a single, limited, but informative compar-
ge when data at z ≥ 0.3 are excluded. In detail, this
s, of which 61 have follow-up data, compared to 237
Figure 5 for single-parameter non-Gaussian models
ings, the constraining power of this low-redshift data
he low-redshift clusters only are shown in Table 2.
re
-Gaussianity from cluster counts have been done by
y mission, Sartoris et al. [43] for future X-ray surveys
pe concept, Oguri [44] for a variety of future optical
elected clusters in the Dark Energy Survey (DES),
veys using the Sunyaev-Zel’dovich effect. There have
on non-Gaussianity: two based on clusters detected
who find flocal
NL = −192±310, and Williamson et al.
one based on the SDSS maxBCG cluster catalogue,
82 ± 317.8
ts use a variety of prescriptions for the non-Gaussian
e mass functions are given in Eq.(A.19) in the Ap-
e levels of non-Gaussianity shown are M3 = 0.009
nly cluster number counts, without including either the cluster
Benson et al 13 (SPT+CMB)
mber of clusters with mass estimates from follow-up data, or the mass/redshift ranges
, necessarily impacts constraints on the full set of cosmological and scaling relation
ters. Consequently, we confine ourselves to a single, limited, but informative compar-
asking how our constraints change when data at z ≥ 0.3 are excluded. In detail, this
shift sample contains 203 clusters, of which 61 have follow-up data, compared to 237
for the full data set. As shown in Figure 5 for single-parameter non-Gaussian models
he full hierarchical and feeder scalings, the constraining power of this low-redshift data
gnificantly reduced. Results for the low-redshift clusters only are shown in Table 2.
mparison with the literature
s forecasts for constraints on non-Gaussianity from cluster counts have been done by
h et al. [7] for the eROSITA X-ray mission, Sartoris et al. [43] for future X-ray surveys
ing the Wide Field X-ray Telescope concept, Oguri [44] for a variety of future optical
, Cunha et al. [6] for optically selected clusters in the Dark Energy Survey (DES),
k and Pierpaoli [8] for future surveys using the Sunyaev-Zel’dovich effect. There have
ree previous cluster constraints on non-Gaussianity: two based on clusters detected
PT survey, by Benson et al. [15], who find flocal
NL = −192±310, and Williamson et al.
ho report flocal
NL = 20 ± 450; and one based on the SDSS maxBCG cluster catalogue,
a et al. [17], who have flocal
NL = 282 ± 317.8
he existing forecasts and constraints use a variety of prescriptions for the non-Gaussian
nction (listed in Table 4). These mass functions are given in Eq.(A.19) in the Ap-
and are plotted in Figure 6. The levels of non-Gaussianity shown are M3 = 0.009
result corresponds to their analysis of only cluster number counts, without including either the cluster
Williamson et al 11 (SPT+CMB)
n, however, since any attempt to reduce the overall size of the sample,
s with mass estimates from follow-up data, or the mass/redshift ranges
mpacts constraints on the full set of cosmological and scaling relation
ently, we confine ourselves to a single, limited, but informative compar-
r constraints change when data at z ≥ 0.3 are excluded. In detail, this
ontains 203 clusters, of which 61 have follow-up data, compared to 237
a set. As shown in Figure 5 for single-parameter non-Gaussian models
ical and feeder scalings, the constraining power of this low-redshift data
uced. Results for the low-redshift clusters only are shown in Table 2.
ith the literature
constraints on non-Gaussianity from cluster counts have been done by
the eROSITA X-ray mission, Sartoris et al. [43] for future X-ray surveys
Field X-ray Telescope concept, Oguri [44] for a variety of future optical
[6] for optically selected clusters in the Dark Energy Survey (DES),
li [8] for future surveys using the Sunyaev-Zel’dovich effect. There have
luster constraints on non-Gaussianity: two based on clusters detected
Benson et al. [15], who find flocal
NL = −192±310, and Williamson et al.
= 20 ± 450; and one based on the SDSS maxBCG cluster catalogue,
who have flocal
NL = 282 ± 317.8
casts and constraints use a variety of prescriptions for the non-Gaussian
in Table 4). These mass functions are given in Eq.(A.19) in the Ap-
d in Figure 6. The levels of non-Gaussianity shown are M3 = 0.009
Mana et al 13 (MaXBCG)
and only for non-Gaussianity of the local type. A more precisely calibrated, more general
non-Gaussian mass function will be important for any future analysis of non-Gaussianity
with clusters.
Table 4. Gaussian mass functions and non-Gaussian extensions used in the literature. The non-
Gaussian mass functions are either the first order semi-analytic expression from LoVerde et al. [30]
(LMSV) or the mass function calibrated on N-body simulations of the local ansatz by Dalal et al.
[20]. All non-Gaussian mass functions also make use of a Gaussian mass function such as those fit by
Sheth and Tormen [46], Warren et al. [47], Jenkins et al. [48] or Tinker et al. [33, 49].
Author Mass Function used
Benson [15] Jenkins + fDalal
Cunha [6] Jenkins + fDalal
Mak [8] Tinker + fLMSV,skew only
Mana [17] Tinker + fLMSV,skew only
Oguri [44] Warren +fLMSV,skew only
Pillepich [7] Tinker + fLMSV,skew only
Sartoris [43] Sheth-Tormen + fLMSV,skew only
Williamson [16] Jenkins + fDalal
This work Tinker + fLMSV,many terms
Apart from the non-Gaussian mass function, these forecasts and analyses differ from
one another and from ours in two principal ways: the form and complexity assumed for the
mass–observable relation and its intrinsic scatter, and priors on the associated parameters.
The most pessimistic forecasts in the literature find marginalized one sigma errors on flocal
NL
calibrated on simulations of the local ansatz, in principle it should include information about
higher moments. This technique, though, has only been tried against one set of simulations
and only for non-Gaussianity of the local type. A more precisely calibrated, more genera
non-Gaussian mass function will be important for any future analysis of non-Gaussianity
with clusters.
Table 4. Gaussian mass functions and non-Gaussian extensions used in the literature. The non
Gaussian mass functions are either the first order semi-analytic expression from LoVerde et al. [30
(LMSV) or the mass function calibrated on N-body simulations of the local ansatz by Dalal et al
[20]. All non-Gaussian mass functions also make use of a Gaussian mass function such as those fit by
Sheth and Tormen [46], Warren et al. [47], Jenkins et al. [48] or Tinker et al. [33, 49].
Author Mass Function used
Benson [15] Jenkins + fDalal
Cunha [6] Jenkins + fDalal
Mak [8] Tinker + fLMSV,skew only
Mana [17] Tinker + fLMSV,skew only
Oguri [44] Warren +fLMSV,skew only
Pillepich [7] Tinker + fLMSV,skew only
Sartoris [43] Sheth-Tormen + fLMSV,skew only
Williamson [16] Jenkins + fDalal
This work Tinker + fLMSV,many terms
Apart from the non-Gaussian mass function, these forecasts and analyses differ from
one another and from ours in two principal ways: the form and complexity assumed for the
mass–observable relation and its intrinsic scatter, and priors on the associated parameters
better with simulation results if a reduced collapse threshold, δc ∼ 1.5, is used. If that ad
justment is made, the Dalal et al mass function would deviate more from the Gaussian tha
LMSV; see [45] for a comparison of all these cases. Since the Dalal et al. mass function wa
calibrated on simulations of the local ansatz, in principle it should include information abou
higher moments. This technique, though, has only been tried against one set of simulation
and only for non-Gaussianity of the local type. A more precisely calibrated, more genera
non-Gaussian mass function will be important for any future analysis of non-Gaussianit
with clusters.
Table 4. Gaussian mass functions and non-Gaussian extensions used in the literature. The non
Gaussian mass functions are either the first order semi-analytic expression from LoVerde et al. [30
(LMSV) or the mass function calibrated on N-body simulations of the local ansatz by Dalal et a
[20]. All non-Gaussian mass functions also make use of a Gaussian mass function such as those fit b
Sheth and Tormen [46], Warren et al. [47], Jenkins et al. [48] or Tinker et al. [33, 49].
Author Mass Function used
Benson [15] Jenkins + fDalal
Cunha [6] Jenkins + fDalal
Mak [8] Tinker + fLMSV,skew only
Mana [17] Tinker + fLMSV,skew only
Oguri [44] Warren +fLMSV,skew only
Pillepich [7] Tinker + fLMSV,skew only
Sartoris [43] Sheth-Tormen + fLMSV,skew only
Williamson [16] Jenkins + f
Mana [17] Tinker + fLMSV,skew only
Oguri [44] Warren +fLMSV,skew only
Pillepich [7] Tinker + fLMSV,skew only
Sartoris [43] Sheth-Tormen + fLMSV,skew only
Williamson [16] Jenkins + fDalal
This work Tinker + fLMSV,many terms
he non-Gaussian mass function, these forecasts and analyses differ from
om ours in two principal ways: the form and complexity assumed for the
lation and its intrinsic scatter, and priors on the associated parameters.
tic forecasts in the literature find marginalized one sigma errors on flocal
NL
g, some cases analyzed in [6, 7]). Those results assume that the scaling
onstrained solely through self-calibration [50] rather than with estimates
which can significantly boost the constraining power [51]. In addition,
ume significant photometric redshift errors [7]. As outlined in Section 4,
n our sample have spectroscopic redshifts and for nearly half we also have
ta that significantly improve the mass determinations.
PT results, Benson et al. use a smaller area of the survey than Williamson
improved mass calibration and extend their sample to lower SZ detection
wer mass). In comparison, our cluster data set is significantly larger than
cluster samples, contains more massive clusters (although at lower red-
intrinsic scatter in the mass–observable relation (although the parameters