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Sets and Numbers

This chapter covers set theory. The topics include set algebra, relations, orderings and mappings, countability and sequences, real numbers, sequences and limits, and set classes including monotone classes, rings, fields, and sigma fields. The final section introduces the basic ideas of real analysis including Euclidean distance, sets of the real line, coverings, and compactness.

International Conference on Mathematical and Statistical Sciences (ICMSS) 2021 Study Program of Mathematics and the Study Program of Statistics Faculty of Mathematics and Natural Sciences Universitas Lambung Mangkurat Banjarbaru - Indonesia, 15 - 16 September 2021 The International Conference on Mathematical and Statistical Sciences (ICMSS) 2021 was organized through a collaboration between the Study Program of Mathematics and the Study Program of Statistics, Faculty of Mathematics and Natural Sciences - Universitas Lambung Mangkurat (ULM). The theme raised was “Mathematical and Statistical Sciences in Multidisciplinary Research”, with the aims are to acknowledge, learn, share, and transfer the results of scientific knowledge and research among academia and practitioners who have used or implemented Mathematical and Statistical Sciences to solve real-world problems and improve the quality of life. The scopes of our conference are Mathematical modeling, Artificial intelligence, Mathematical physics, Algebra and its applications, Statistics and its applications, Computational fluid dynamics, Data mining and its applications, Dynamical nonlinear systems, Mathematics Educations, Financial mathematics, Mathematical biology, Numerical methods and analysis, Operation research and optimizations, and Real analysis. On behalf of the committee, we would like to thank the Rector of Universitas Lambung Mangkurat, the Dean of Faculty of Mathematics and Natural Sciences, Coordinator of the Study Program of Mathematics and Coordinator of the Study Program of Statistics, advisory board, steering committee, all committee members, reviewers, presenters, and participants. We also would thank the Indonesian Mathematical Society (IndoMS), The Indonesian Algebra Society (IAS), and The Forum Pendidikan Tinggi Statistika (Forstat). Special thanks are also given to the Journal of Physics: Conference Series. We, on behalf of the ICMSS 2021 committee, would like to thank all parties for their participation in supporting this publication. We hope to see you all at the next conference. Kind regards, Dr. Muhammad Ahsar Karim Chair of the ICMSS 2021 List of Organizing Committees, Photographs and Peer review statement are available in this pdf.

Roadmap to glory: scaffolding real analysis for deeper learning

Real analysis, analisis kemampuan berpikir tingkat tinggi mahasiswa dalam mengkonstruksi representasi biner bilangan real.

Higher-order thinking skills (HOTS) are needed to determine the student's ability to construct an answer. In this study, researchers analyzed the higher-order thinking skills of students of the Mathematics Education Study Program in constructing one of the test answers, namely constructing a binary representation of real numbers in the Introduction to Real Analysis course. Fifty-two students taking the Introduction to Real Analysis course in the odd semester 2020/2021 are the subjects of this research. Data was collected using a test that was analyzed based on the indicator of higher-order thinking ability created (C6). It was revealed that the students' higher-order thinking skills were in the sufficient category. This means that most students have not been able to construct and analyze information into the right strategy. The results of this study are expected to be a reference for the lecture process where students are familiarized with giving HOTS-oriented questions during exams and practice questions for lectures to help develop higher-order thinking skills.Keywords: Bloom's taxonomy-C6; higher order thinking skill; binary representation Kemampuan berpikir tingkat tinggi diperlukan untuk mengetahui kemampuan mahasiswa mengkonstruksi suatu jawaban. Pada studi ini, peneliti menganalisis kemampuan berpikir tingkat tinggi mahasiswa Program Studi Pendidikan Matematika dalam mengkonstruksi salah satu jawaban tes yaitu mengkonstruksi representasi biner bilangan real pada mata kuliah Pengantar Analisis Real. Lima puluh dua mahasiswa yang sedang mengambil mata kuliah Pengantar Analisis Real pada semester ganjil 2020/2021 sebagai subjek penelitian ini. Data dikumpulkan dengan tes yang dianalisis berdasarkan indikator kemampuan berpikir tingkat tinggi create (C6). Terungkap bahwa kemampuan berpikir tingkat tinggi mahasiswa berada pada kategori cukup. Ini berarti sebagian besar mahasiswa belum mampu mengkonstruksi dan menganalisis informasi menjadi strategi yang tepat. Hasil penelitian ini diharapkan menjadi acuan untuk proses perkuliahan dimana mahasiswa dibiasakan dengan pemberian soal yang berorientasi HOTS baik itu pada saat ujian maupun latihan-latihan soal perkuliahan untuk membantu mengembangkan kemampuan berpikir tingkat tinggi.Kata Kunci:  taksonomi Bloom-C6; kemampuan berpikir tingkat tinggi; representasi biner

On two kinds of the reverse half-discrete Mulholland-type inequalities involving higher-order derivative function

AbstractBy means of the weight functions, Hermite–Hadamard’s inequality, and the techniques of real analysis, a new more accurate reverse half-discrete Mulholland-type inequality involving one higher-order derivative function is given. The equivalent statements of the best possible constant factor related to a few parameters, the equivalent forms, and several particular inequalities are provided. Another kind of the reverses is also considered.

Real Analysis, Harmonic Analysis and Applications

Ε and δ real analysis, mathematical-analytical thinking skills: the impacts and interactions of open-ended learning method & self-awareness (its application on bilingual test instruments).

Analytical thinking is a skill to unite the initial process, plan solutions, produce solutions, and conclude something to produce conclusions or correct answers. This research aims to 1) determine whether there are differences in students' mathematical, analytical thinking skills between classes that use the Open-ended learning method and classes that use the lecturing method, 2) to find out whether there are mathematical, analytical thinking skills differences between students with high, moderate, and low self-awareness criteria, and 3) to find out whether there is an interaction between Open-ended learning method and self-awareness toward students' mathematical-analytical thinking skills. This research employs a quasi-experimental design. Based on the data and data analysis, this research is mixed-method research, and the design used in this research is the posttest control group design. This research was conducted on students who have studied the Real Analysis Courses. Based on the results of hypothesis testing, it was found out that, first, there are differences in students' mathematical-analytical thinking skills between the class that uses the Open-ended learning method and the class that uses the lecturing method. Second, there are mathematical-analytical thinking skills differences between high, moderate, and low self-awareness criteria. Third, there is no interaction between the Open-ended learning method with self-awareness of students' mathematical-analytical thinking skills.

Equivalent Properties of Two Kinds of Hardy-Type Integral Inequalities

In this paper, using weight functions as well as employing various techniques from real analysis, we establish a few equivalent conditions of two kinds of Hardy-type integral inequalities with nonhomogeneous kernel. To prove our results, we also deduce a few equivalent conditions of two kinds of Hardy-type integral inequalities with a homogeneous kernel in the form of applications. We additionally consider operator expressions. Analytic inequalities of this nature and especially the techniques involved have far reaching applications in various areas in which symmetry plays a prominent role, including aspects of physics and engineering.

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5.3: Real Analysis - Convergent Sequences

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• Page ID 62293

• Dave Witte Morris & Joy Morris
• University of Lethbridge

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Notation \(5.3.1\).

For \(x \in \mathbb{R}\), \(|x|\) denotes the absolute value of \(x\): \[|x|=\left\{\begin{aligned} x & \text { if } x \geq 0 , \\ -x & \text { if } x<0 . \end{aligned}\right.\]

You may assume the following basic properties of absolute value (without proof):

Lemma \(5.3.2\).

For \(x, y, z \in \mathbb{R}\) , we have:

• \(|x| \geq 0\) ( and \(|x|=0 \Leftrightarrow x=0\)).
• \(|x| = |−x|\).
• \(|x+y| \leq |x|+|y|\). (“ triangle inequality ”)
• \(|x y|=|x| \cdot|y|\).
• \(−|x| \leq x \leq |x|\).
• \(\exists N \in \mathbb{N}, N>|x|\).
• If \(|x| < |y|\) and \(z \neq 0\) , then \(|xz| < |yz|\).
• If \(|x| > |y| \neq 0\) , then \(1/|x| < 1/|y|\).

Definition \(5.3.3\).

Assume \(a_{1}, a_{2}, a_{3}, \ldots\) is an infinite sequence of real numbers, and \(L \in \mathbb{R}\). We say that the sequence converges to \(L\) (and write \(a_{n} \rightarrow L\)) iff \[\forall \epsilon>0, \exists N \in \mathbb{N}, \forall n>N,\left|a_{n}-L\right|<\epsilon .\]

Other Terminology.

When \(a_{n} \rightarrow L\), we can also say that the limit of the sequence is \(L\).

Example \(5.3.4\).

Let \(t \in \mathbb{R}\). If \(a_{n} = t\) for all \(n\), then \(a_{n} \rightarrow t\).

Given\(\epsilon>0\), let \(N = 0\). Given \(n > N\), we have \(\left|a_{n}-t\right|=|t-t|=|0|=0<\epsilon\).

Example \(5.3.5\).

If \(a_{n} = 1/n\) for all \(n\), then \(a_{n} \rightarrow 0\).

Scratchwork . To prove \(a_{n} \rightarrow 0\), we want: \[\left|a_{n}-0\right| \stackrel{?}{<} \epsilon \quad 1 / n \stackrel{?}{<} \epsilon \quad 1 / \epsilon \stackrel{?}{<} n\] Since \(n > N\), it suffices to choose \(N > 1 / \epsilon\).

Given \(\epsilon > 0\), Lemma \(5.3.2(6)\) tells us there exists \(N \in \mathbb{N}\), such that \(N > 1 / \epsilon\). Given \(n > N\), we have \[\begin{aligned} \left|a_{n}-0\right| &=1 / n & &\left(a_{n}=1 / n>0\right) \\ &<1 / N & &(n>N \text { and Lemma 5.3.2(8)) }\\ &<\epsilon & &(N>1 / \epsilon \text { and Lemma 5.3.2(8)) } \end{aligned}\]

Exercise \(5.3.6\).

Show that if \(a_{n} = n/(n + 1)\) for all \(n\), then \(a_{n} \rightarrow 1\).

Proposition \(5.3.7\).

If \(a_{n} \rightarrow L\) and \(b_{n} \rightarrow M\) , then \(a_{n} + b_{n} \rightarrow L + M\).

Scratchwork . To prove \(a_{n} + b_{n} \rightarrow L + M\), \[\text { we want to make }\left|\left(a_{n}+b_{n}\right)-(L+M)\right| \text { small (less than } \epsilon \text { ). }\] What we know is that we can make \(\left|a_{n}-L\right|\) and \(\left|b_{n}-M\right|\) as small as we like. By the triangle inequality, we have \[\left|\left(a_{n}-L\right)+\left(b_{n}-M\right)\right|<\left|a_{n}-L\right|+\left|b_{n}-M\right|\] By simple algebra, the left-hand side is equal to \(\left|\left(a_{n}+b_{n}\right)-(L+M)\right|\), so we just need to make the right-hand side less than \(\epsilon\). This will be true if \(\left|a_{n}-L\right|\) and \(\left|b_{n}-M\right|\) are both less than \(\epsilon / 2\).

Since \(a_{n} \rightarrow L\), there is some large \(N_{a}\), such that \(\left|a_{n}-L\right|<\epsilon / 2\) for all \(n > N_{a}\). Similarly, since \(b_{n} \rightarrow M\), there is some large \(N_{b}\), such that \(\left|b_{n}-M\right|<\epsilon / 2\) for all \(n > N_{b}\). Now, we just need know that \(n\) will be larger than both \(N_{a}\) and \(N_{b}\) whenever \(n > N\). So we should choose \(N\) to be whichever of \(N_{a}\) and \(N_{b}\) is larger. That is, we let \(N\) be the maximum of \(N_{a}\) and \(N_{b}\), which is denoted max(Na, Nb).

Given \(\epsilon > 0\), we know that \(\epsilon / 2 > 0\). Hence:

• Since \(a_{n} \rightarrow L\), we know \(\exists N_{a} \in \mathbb{N}, \forall n>N_{a},\left|a_{n}-L\right|<\epsilon / 2\).
• Since \(b_{n} \rightarrow M\), we know \(\exists N_{b} \in \mathbb{N}, \forall n>N_{b},\left|b_{n}-M\right|<\epsilon / 2\).

Let \(N=\max \left(N_{a}, N_{b}\right) \in \mathbb{N}\), so \(N \geq N_{a}\) and \(N \geq N_{b}\).

Given \(n > N\):

• We have \(n > N \geq N_{a}\), so \(\left|a_{n}-L\right|<\epsilon / 2\).
• We have \(n > N \geq N_{b}\), so \(\left|b_{n}-M\right|<\epsilon / 2\).

Therefore \[\begin{aligned} \left|\left(a_{n}+b_{n}\right)-(L+M)\right| &=\left|\left(a_{n}-L\right)+\left(b_{n}-M\right)\right| & & \text { (high-school algebra) } \\ & \leq\left|a_{n}-L\right|+\left|b_{n}-M\right| & & \text { (triangle inequality) } \\ &<\epsilon / 2+\epsilon / 2 & &((*) \text { and }(* *)) \\ &=\epsilon . & & \end{aligned}\]

Exercise \(5.3.8\).

Assume \(a_{n} \rightarrow L\), and \(c \in \mathbb{R}\). Do these proofs directly from the definition of convergence .

• Show \(−a_{n} \rightarrow −L\).
• Show \(a_{n} + c \rightarrow L + c\).
• Show \(2a_{n} \rightarrow 2L\).
• Show \(ca_{n} \rightarrow cL\) if \(c \neq 0\).
• Show that if \(L > 0\), then \(\exists N \in \mathbb{N}\), such that \(a_{n} > 0\) for all \(n > N\).
• (harder) Show that if \(L = 1\), then \(1/a_{n} \rightarrow 1\).

Exercise \(5.3.9\).

Assume \(a_{n} \rightarrow L\) and \(b_{n} \rightarrow M\).

• Show that if \(M = 0\), and \(|a_{n}| \leq 2\) for all \(n\), then \(a_{n}b_{n} \rightarrow 0\).
• (harder) Show \(a_{n}b_{n} \rightarrow LM\).

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Research Topics & Ideas: Data Science

50 Topic Ideas To Kickstart Your Research Project

If you’re just starting out exploring data science-related topics for your dissertation, thesis or research project, you’ve come to the right place. In this post, we’ll help kickstart your research by providing a hearty list of data science and analytics-related research ideas , including examples from recent studies.

PS – This is just the start…

We know it’s exciting to run through a list of research topics, but please keep in mind that this list is just a starting point . These topic ideas provided here are intentionally broad and generic , so keep in mind that you will need to develop them further. Nevertheless, they should inspire some ideas for your project.

To develop a suitable research topic, you’ll need to identify a clear and convincing research gap , and a viable plan to fill that gap. If this sounds foreign to you, check out our free research topic webinar that explores how to find and refine a high-quality research topic, from scratch. Alternatively, consider our 1-on-1 coaching service .

Data Science-Related Research Topics

• Developing machine learning models for real-time fraud detection in online transactions.
• The use of big data analytics in predicting and managing urban traffic flow.
• Investigating the effectiveness of data mining techniques in identifying early signs of mental health issues from social media usage.
• The application of predictive analytics in personalizing cancer treatment plans.
• Analyzing consumer behavior through big data to enhance retail marketing strategies.
• The role of data science in optimizing renewable energy generation from wind farms.
• Developing natural language processing algorithms for real-time news aggregation and summarization.
• The application of big data in monitoring and predicting epidemic outbreaks.
• Investigating the use of machine learning in automating credit scoring for microfinance.
• The role of data analytics in improving patient care in telemedicine.
• Developing AI-driven models for predictive maintenance in the manufacturing industry.
• The use of big data analytics in enhancing cybersecurity threat intelligence.
• Investigating the impact of sentiment analysis on brand reputation management.
• The application of data science in optimizing logistics and supply chain operations.
• Developing deep learning techniques for image recognition in medical diagnostics.
• The role of big data in analyzing climate change impacts on agricultural productivity.
• Investigating the use of data analytics in optimizing energy consumption in smart buildings.
• The application of machine learning in detecting plagiarism in academic works.
• Analyzing social media data for trends in political opinion and electoral predictions.
• The role of big data in enhancing sports performance analytics.
• Developing data-driven strategies for effective water resource management.
• The use of big data in improving customer experience in the banking sector.
• Investigating the application of data science in fraud detection in insurance claims.
• The role of predictive analytics in financial market risk assessment.
• Developing AI models for early detection of network vulnerabilities.

Data Science Research Ideas (Continued)

• The application of big data in public transportation systems for route optimization.
• Investigating the impact of big data analytics on e-commerce recommendation systems.
• The use of data mining techniques in understanding consumer preferences in the entertainment industry.
• Developing predictive models for real estate pricing and market trends.
• The role of big data in tracking and managing environmental pollution.
• Investigating the use of data analytics in improving airline operational efficiency.
• The application of machine learning in optimizing pharmaceutical drug discovery.
• Analyzing online customer reviews to inform product development in the tech industry.
• The role of data science in crime prediction and prevention strategies.
• Developing models for analyzing financial time series data for investment strategies.
• The use of big data in assessing the impact of educational policies on student performance.
• Investigating the effectiveness of data visualization techniques in business reporting.
• The application of data analytics in human resource management and talent acquisition.
• Developing algorithms for anomaly detection in network traffic data.
• The role of machine learning in enhancing personalized online learning experiences.
• Investigating the use of big data in urban planning and smart city development.
• The application of predictive analytics in weather forecasting and disaster management.
• Analyzing consumer data to drive innovations in the automotive industry.
• The role of data science in optimizing content delivery networks for streaming services.
• Developing machine learning models for automated text classification in legal documents.
• The use of big data in tracking global supply chain disruptions.
• Investigating the application of data analytics in personalized nutrition and fitness.
• The role of big data in enhancing the accuracy of geological surveying for natural resource exploration.
• Developing predictive models for customer churn in the telecommunications industry.
• The application of data science in optimizing advertisement placement and reach.

Recent Data Science-Related Studies

While the ideas we’ve presented above are a decent starting point for finding a research topic, they are fairly generic and non-specific. So, it helps to look at actual studies in the data science and analytics space to see how this all comes together in practice.

Below, we’ve included a selection of recent studies to help refine your thinking. These are actual studies,  so they can provide some useful insight as to what a research topic looks like in practice.

• Data Science in Healthcare: COVID-19 and Beyond (Hulsen, 2022)
• Auto-ML Web-application for Automated Machine Learning Algorithm Training and evaluation (Mukherjee & Rao, 2022)
• Survey on Statistics and ML in Data Science and Effect in Businesses (Reddy et al., 2022)
• Visualization in Data Science VDS @ KDD 2022 (Plant et al., 2022)
• An Essay on How Data Science Can Strengthen Business (Santos, 2023)
• A Deep study of Data science related problems, application and machine learning algorithms utilized in Data science (Ranjani et al., 2022)
• You Teach WHAT in Your Data Science Course?!? (Posner & Kerby-Helm, 2022)
• Statistical Analysis for the Traffic Police Activity: Nashville, Tennessee, USA (Tufail & Gul, 2022)
• Data Management and Visual Information Processing in Financial Organization using Machine Learning (Balamurugan et al., 2022)
• A Proposal of an Interactive Web Application Tool QuickViz: To Automate Exploratory Data Analysis (Pitroda, 2022)
• Applications of Data Science in Respective Engineering Domains (Rasool & Chaudhary, 2022)
• Jupyter Notebooks for Introducing Data Science to Novice Users (Fruchart et al., 2022)
• Towards a Systematic Review of Data Science Programs: Themes, Courses, and Ethics (Nellore & Zimmer, 2022)
• Application of data science and bioinformatics in healthcare technologies (Veeranki & Varshney, 2022)
• TAPS Responsibility Matrix: A tool for responsible data science by design (Urovi et al., 2023)
• Data Detectives: A Data Science Program for Middle Grade Learners (Thompson & Irgens, 2022)
• MACHINE LEARNING FOR NON-MAJORS: A WHITE BOX APPROACH (Mike & Hazzan, 2022)
• COMPONENTS OF DATA SCIENCE AND ITS APPLICATIONS (Paul et al., 2022)
• Analysis on the Application of Data Science in Business Analytics (Wang, 2022)

As you can see, these research topics are a lot more focused than the generic topic ideas we presented earlier. So, for you to develop a high-quality research topic, you’ll need to get specific and laser-focused on a specific context with specific variables of interest.  In the video below, we explore some other important things you’ll need to consider when crafting your research topic.

Get 1-On-1 Help

If you’re still unsure about how to find a quality research topic, check out our Research Topic Kickstarter service, which is the perfect starting point for developing a unique, well-justified research topic.

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Topology in Real-World Machine Learning and Data Analysis

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Topological Data Analysis (TDA) and Topological Machine Learning (TML) comprise a set of powerful techniques whose ability to extract robust geometric information has led to novel insights in the analysis of complex data. Topology is concerned with understanding the global shape and structure of ...

Keywords : topological data analysis, computational topology, machine learning, algebraic topology, nonlinear dimensionality reduction

Important Note : All contributions to this Research Topic must be within the scope of the section and journal to which they are submitted, as defined in their mission statements. Frontiers reserves the right to guide an out-of-scope manuscript to a more suitable section or journal at any stage of peer review.

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Published: 5 April 2024 Contributors: Tim Mucci, Cole Stryker

Big data analytics refers to the systematic processing and analysis of large amounts of data and complex data sets, known as big data, to extract valuable insights. Big data analytics allows for the uncovering of trends, patterns and correlations in large amounts of raw data to help analysts make data-informed decisions. This process allows organizations to leverage the exponentially growing data generated from diverse sources, including internet-of-things (IoT) sensors, social media, financial transactions and smart devices to derive actionable intelligence through advanced analytic techniques.

In the early 2000s, advances in software and hardware capabilities made it possible for organizations to collect and handle large amounts of unstructured data. With this explosion of useful data, open-source communities developed big data frameworks to store and process this data. These frameworks are used for distributed storage and processing of large data sets across a network of computers. Along with additional tools and libraries, big data frameworks can be used for:

• Predictive modeling by incorporating artificial intelligence (AI) and statistical algorithms
• Statistical analysis for in-depth data exploration and to uncover hidden patterns
• What-if analysis to simulate different scenarios and explore potential outcomes
• Processing diverse data sets, including structured, semi-structured and unstructured data from various sources.

Four main data analysis methods  – descriptive, diagnostic, predictive and prescriptive  – are used to uncover insights and patterns within an organization's data. These methods facilitate a deeper understanding of market trends, customer preferences and other important business metrics.

IBM named a Leader in the 2024 Gartner® Magic Quadrant™ for Augmented Data Quality Solutions.

Structured vs unstructured data

What is data management?

The main difference between big data analytics and traditional data analytics is the type of data handled and the tools used to analyze it. Traditional analytics deals with structured data, typically stored in relational databases . This type of database helps ensure that data is well-organized and easy for a computer to understand. Traditional data analytics relies on statistical methods and tools like structured query language (SQL) for querying databases.

Big data analytics involves massive amounts of data in various formats, including structured, semi-structured and unstructured data. The complexity of this data requires more sophisticated analysis techniques. Big data analytics employs advanced techniques like machine learning and data mining to extract information from complex data sets. It often requires distributed processing systems like Hadoop to manage the sheer volume of data.

These are the four methods of data analysis at work within big data:

The "what happened" stage of data analysis. Here, the focus is on summarizing and describing past data to understand its basic characteristics.

The “why it happened” stage. By delving deep into the data, diagnostic analysis identifies the root patterns and trends observed in descriptive analytics.

The “what will happen” stage. It uses historical data, statistical modeling and machine learning to forecast trends.

Describes the “what to do” stage, which goes beyond prediction to provide recommendations for optimizing future actions based on insights derived from all previous.

The following dimensions highlight the core challenges and opportunities inherent in big data analytics.

The sheer volume of data generated today, from social media feeds, IoT devices, transaction records and more, presents a significant challenge. Traditional data storage and processing solutions are often inadequate to handle this scale efficiently. Big data technologies and cloud-based storage solutions enable organizations to store and manage these vast data sets cost-effectively, protecting valuable data from being discarded due to storage limitations.

Data is being produced at unprecedented speeds, from real-time social media updates to high-frequency stock trading records. The velocity at which data flows into organizations requires robust processing capabilities to capture, process and deliver accurate analysis in near real-time. Stream processing frameworks and in-memory data processing are designed to handle these rapid data streams and balance supply with demand.

Today's data comes in many formats, from structured to numeric data in traditional databases to unstructured text, video and images from diverse sources like social media and video surveillance. This variety demans flexible data management systems to handle and integrate disparate data types for comprehensive analysis. NoSQL databases , data lakes and schema -on-read technologies provide the necessary flexibility to accommodate the diverse nature of big data.

Data reliability and accuracy are critical, as decisions based on inaccurate or incomplete data can lead to negative outcomes. Veracity refers to the data's trustworthiness, encompassing data quality, noise and anomaly detection issues. Techniques and tools for data cleaning, validation and verification are integral to ensuring the integrity of big data, enabling organizations to make better decisions based on reliable information.

Big data analytics aims to extract actionable insights that offer tangible value. This involves turning vast data sets into meaningful information that can inform strategic decisions, uncover new opportunities and drive innovation. Advanced analytics, machine learning and AI are key to unlocking the value contained within big data, transforming raw data into strategic assets.

Data professionals, analysts, scientists and statisticians prepare and process data in a data lakehouse, which combines the performance of a data lakehouse with the flexibility of a data lake to clean data and ensure its quality. The process of turning raw data into valuable insights encompasses several key stages:

• Collect data: The first step involves gathering data, which can be a mix of structured and unstructured forms from myriad sources like cloud, mobile applications and IoT sensors. This step is where organizations adapt their data collection strategies and integrate data from varied sources into central repositories like a data lake, which can automatically assign metadata for better manageability and accessibility.
• Process data: After being collected, data must be systematically organized, extracted, transformed and then loaded into a storage system to ensure accurate analytical outcomes. Processing involves converting raw data into a format that is usable for analysis, which might involve aggregating data from different sources, converting data types or organizing data into structure formats. Given the exponential growth of available data, this stage can be challenging. Processing strategies may vary between batch processing, which handles large data volumes over extended periods and stream processing, which deals with smaller real-time data batches.
• Clean data: Regardless of size, data must be cleaned to ensure quality and relevance. Cleaning data involves formatting it correctly, removing duplicates and eliminating irrelevant entries. Clean data prevents the corruption of output and safeguard’s reliability and accuracy.
• Analyze data: Advanced analytics, such as data mining, predictive analytics, machine learning and deep learning, are employed to sift through the processed and cleaned data. These methods allow users to discover patterns, relationships and trends within the data, providing a solid foundation for informed decision-making.

Under the Analyze umbrella, there are potentially many technologies at work, including data mining, which is used to identify patterns and relationships within large data sets; predictive analytics, which forecasts future trends and opportunities; and deep learning , which mimics human learning patterns to uncover more abstract ideas.

Deep learning uses an artificial neural network with multiple layers to model complex patterns in data. Unlike traditional machine learning algorithms, deep learning learns from images, sound and text without manual help. For big data analytics, this powerful capability means the volume and complexity of data is not an issue.

Natural language processing (NLP) models allow machines to understand, interpret and generate human language. Within big data analytics, NLP extracts insights from massive unstructured text data generated across an organization and beyond.

Structured Data

Structured data refers to highly organized information that is easily searchable and typically stored in relational databases or spreadsheets. It adheres to a rigid schema, meaning each data element is clearly defined and accessible in a fixed field within a record or file. Examples of structured data include:

• Customer names and addresses in a customer relationship management (CRM) system
• Transactional data in financial records, such as sales figures and account balances
• Employee data in human resources databases, including job titles and salaries

Structured data's main advantage is its simplicity for entry, search and analysis, often using straightforward database queries like SQL. However, the rapidly expanding universe of big data means that structured data represents a relatively small portion of the total data available to organizations.

Unstructured Data

Unstructured data lacks a pre-defined data model, making it more difficult to collect, process and analyze. It comprises the majority of data generated today, and includes formats such as:

• Textual content from documents, emails and social media posts
• Multimedia content, including images, audio files and videos
• Data from IoT devices, which can include a mix of sensor data, log files and time-series data

The primary challenge with unstructured data is its complexity and lack of uniformity, requiring more sophisticated methods for indexing, searching and analyzing. NLP, machine learning and advanced analytics platforms are often employed to extract meaningful insights from unstructured data.

Semi-structured data

Semi-structured data occupies the middle ground between structured and unstructured data. While it does not reside in a relational database, it contains tags or other markers to separate semantic elements and enforce hierarchies of records and fields within the data. Examples include:

• JSON (JavaScript Object Notation) and XML (eXtensible Markup Language) files, which are commonly used for web data interchange
• Email, where the data has a standardized format (e.g., headers, subject, body) but the content within each section is unstructured
• NoSQL databases, can store and manage semi-structured data more efficiently than traditional relational databases

Semi-structured data is more flexible than structured data but easier to analyze than unstructured data, providing a balance that is particularly useful in web applications and data integration tasks.

Ensuring data quality and integrity, integrating disparate data sources, protecting data privacy and security and finding the right talent to analyze and interpret data can present challenges to organizations looking to leverage their extensive data volumes. What follows are the benefits organizations can realize once they see success with big data analytics:

Real-time intelligence

One of the standout advantages of big data analytics is the capacity to provide real-time intelligence. Organizations can analyze vast amounts of data as it is generated from myriad sources and in various formats. Real-time insight allows businesses to make quick decisions, respond to market changes instantaneously and identify and act on opportunities as they arise.

Better-informed decisions

With big data analytics, organizations can uncover previously hidden trends, patterns and correlations. A deeper understanding equips leaders and decision-makers with the information needed to strategize effectively, enhancing business decision-making in supply chain management, e-commerce, operations and overall strategic direction.  

Cost savings

Big data analytics drives cost savings by identifying business process efficiencies and optimizations. Organizations can pinpoint wasteful expenditures by analyzing large datasets, streamlining operations and enhancing productivity. Moreover, predictive analytics can forecast future trends, allowing companies to allocate resources more efficiently and avoid costly missteps.

Better customer engagement

Understanding customer needs, behaviors and sentiments is crucial for successful engagement and big data analytics provides the tools to achieve this understanding. Companies gain insights into consumer preferences and tailor their marketing strategies by analyzing customer data.

Optimized risk management strategies

Big data analytics enhances an organization's ability to manage risk by providing the tools to identify, assess and address threats in real time. Predictive analytics can foresee potential dangers before they materialize, allowing companies to devise preemptive strategies.

As organizations across industries seek to leverage data to drive decision-making, improve operational efficiencies and enhance customer experiences, the demand for skilled professionals in big data analytics has surged. Here are some prominent career paths that utilize big data analytics:

Data scientist

Data scientists analyze complex digital data to assist businesses in making decisions. Using their data science training and advanced analytics technologies, including machine learning and predictive modeling, they uncover hidden insights in data.

Data analyst

Data analysts turn data into information and information into insights. They use statistical techniques to analyze and extract meaningful trends from data sets, often to inform business strategy and decisions.

Data engineer

Data engineers prepare, process and manage big data infrastructure and tools. They also develop, maintain, test and evaluate data solutions within organizations, often working with massive datasets to assist in analytics projects.

Machine learning engineer

Machine learning engineers focus on designing and implementing machine learning applications. They develop sophisticated algorithms that learn from and make predictions on data.

Business intelligence analyst

Business intelligence (BI) analysts help businesses make data-driven decisions by analyzing data to produce actionable insights. They often use BI tools to convert data into easy-to-understand reports and visualizations for business stakeholders.

Data visualization specialist

These specialists focus on the visual representation of data. They create data visualizations that help end users understand the significance of data by placing it in a visual context.

Data architect

Data architects design, create, deploy and manage an organization's data architecture. They define how data is stored, consumed, integrated and managed by different data entities and IT systems.

IBM and Cloudera have partnered to create an industry-leading, enterprise-grade big data framework distribution plus a variety of cloud services and products — all designed to achieve faster analytics at scale.

IBM Db2 Database on IBM Cloud Pak for Data combines a proven, AI-infused, enterprise-ready data management system with an integrated data and AI platform built on the security-rich, scalable Red Hat OpenShift foundation.

IBM Big Replicate is an enterprise-class data replication software platform that keeps data consistent in a distributed environment, on-premises and in the hybrid cloud, including SQL and NoSQL databases.

A data warehouse is a system that aggregates data from different sources into a single, central, consistent data store to support data analysis, data mining, artificial intelligence and machine learning.

Business intelligence gives organizations the ability to get answers they can understand. Instead of using best guesses, they can base decisions on what their business data is telling them — whether it relates to production, supply chain, customers or market trends.

Cloud computing is the on-demand access of physical or virtual servers, data storage, networking capabilities, application development tools, software, AI analytic tools and more—over the internet with pay-per-use pricing. The cloud computing model offers customers flexibility and scalability compared to traditional infrastructure.

Purpose-built data-driven architecture helps support business intelligence across the organization. IBM analytics solutions allow organizations to simplify raw data access, provide end-to-end data management and empower business users with AI-driven self-service analytics to predict outcomes.

TOPICS IN MEASURE THEORY AND REAL ANALYSIS

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• Alexander B. Kharazishvili 0

A. Razmadze Mathematical Institute, Tbilisi, Republic of Georgia

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Part of the book series: Atlantis Studies in Mathematics (ATLANTISSM, volume 2)

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Table of contents (20 chapters)

Front matter, the problem of extending partial functions.

Alexander B. Kharazishvili

Some aspects of the measure extension problem

Invariant measures, quasi-invariant measures, measurability properties of real-valued functions, some properties of step-functions connected with extensions of measures, almost measurable real-valued functions, several facts from general topology, weakly metrically transitive measures and nonmeasurable sets, nonmeasurable subgroups of uncountable solvable groups, algebraic sums of measure zero sets, the absolute nonmeasurability of minkowski’s sum of certain universal measure zero sets, absolutely nonmeasurable additive sierpiński-zygmund functions, relatively measurable sierpiński-zygmund functions, a nonseparable extension of the lebesgue measure without new null-sets, metrical transitivity and nonseparable extensions of invariant measures, nonseparable left invariant measures on uncountable solvable groups, universally measurable additive functionals, some subsets of the euclidean plane.

• Lebesgue measure
• boundary element method
• information
• measure theory
• metric space

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Book Title : TOPICS IN MEASURE THEORY AND REAL ANALYSIS

Authors : Alexander B. Kharazishvili

Series Title : Atlantis Studies in Mathematics

DOI : https://doi.org/10.2991/978-94-91216-36-7

Publisher : Atlantis Press Paris

eBook Packages : Mathematics and Statistics , Mathematics and Statistics (R0)

Copyright Information : Atlantis Press and the authors 2009

eBook ISBN : 978-94-91216-36-7 Published: 01 November 2009

Series ISSN : 1875-7634

Series E-ISSN : 2215-1885

Edition Number : 1

Number of Pages : XI, 461

Topics : Measure and Integration

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McKinsey Global Private Markets Review 2024: Private markets in a slower era

At a glance, macroeconomic challenges continued.

McKinsey Global Private Markets Review 2024: Private markets: A slower era

If 2022 was a tale of two halves, with robust fundraising and deal activity in the first six months followed by a slowdown in the second half, then 2023 might be considered a tale of one whole. Macroeconomic headwinds persisted throughout the year, with rising financing costs, and an uncertain growth outlook taking a toll on private markets. Full-year fundraising continued to decline from 2021’s lofty peak, weighed down by the “denominator effect” that persisted in part due to a less active deal market. Managers largely held onto assets to avoid selling in a lower-multiple environment, fueling an activity-dampening cycle in which distribution-starved limited partners (LPs) reined in new commitments.

About the authors

This article is a summary of a larger report, available as a PDF, that is a collaborative effort by Fredrik Dahlqvist , Alastair Green , Paul Maia, Alexandra Nee , David Quigley , Aditya Sanghvi , Connor Mangan, John Spivey, Rahel Schneider, and Brian Vickery , representing views from McKinsey’s Private Equity & Principal Investors Practice.

Performance in most private asset classes remained below historical averages for a second consecutive year. Decade-long tailwinds from low and falling interest rates and consistently expanding multiples seem to be things of the past. As private market managers look to boost performance in this new era of investing, a deeper focus on revenue growth and margin expansion will be needed now more than ever.

Perspectives on a slower era in private markets

Global fundraising contracted.

Fundraising fell 22 percent across private market asset classes globally to just over $1 trillion, as of year-end reported data—the lowest total since 2017. Fundraising in North America, a rare bright spot in 2022, declined in line with global totals, while in Europe, fundraising proved most resilient, falling just 3 percent. In Asia, fundraising fell precipitously and now sits 72 percent below the region’s 2018 peak.

Despite difficult fundraising conditions, headwinds did not affect all strategies or managers equally. Private equity (PE) buyout strategies posted their best fundraising year ever, and larger managers and vehicles also fared well, continuing the prior year’s trend toward greater fundraising concentration.

The numerator effect persisted

Despite a marked recovery in the denominator—the 1,000 largest US retirement funds grew 7 percent in the year ending September 2023, after falling 14 percent the prior year, for example 1 “U.S. retirement plans recover half of 2022 losses amid no-show recession,” Pensions and Investments , February 12, 2024. —many LPs remain overexposed to private markets relative to their target allocations. LPs started 2023 overweight: according to analysis from CEM Benchmarking, average allocations across PE, infrastructure, and real estate were at or above target allocations as of the beginning of the year. And the numerator grew throughout the year, as a lack of exits and rebounding valuations drove net asset values (NAVs) higher. While not all LPs strictly follow asset allocation targets, our analysis in partnership with global private markets firm StepStone Group suggests that an overallocation of just one percentage point can reduce planned commitments by as much as 10 to 12 percent per year for five years or more.

Despite these headwinds, recent surveys indicate that LPs remain broadly committed to private markets. In fact, the majority plan to maintain or increase allocations over the medium to long term.

Investors fled to known names and larger funds

Fundraising concentration reached its highest level in over a decade, as investors continued to shift new commitments in favor of the largest fund managers. The 25 most successful fundraisers collected 41 percent of aggregate commitments to closed-end funds (with the top five managers accounting for nearly half that total). Closed-end fundraising totals may understate the extent of concentration in the industry overall, as the largest managers also tend to be more successful in raising non-institutional capital.

While the largest funds grew even larger—the largest vehicles on record were raised in buyout, real estate, infrastructure, and private debt in 2023—smaller and newer funds struggled. Fewer than 1,700 funds of less than $1 billion were closed during the year, half as many as closed in 2022 and the fewest of any year since 2012. New manager formation also fell to the lowest level since 2012, with just 651 new firms launched in 2023.

Whether recent fundraising concentration and a spate of M&A activity signals the beginning of oft-rumored consolidation in the private markets remains uncertain, as a similar pattern developed in each of the last two fundraising downturns before giving way to renewed entrepreneurialism among general partners (GPs) and commitment diversification among LPs. Compared with how things played out in the last two downturns, perhaps this movie really is different, or perhaps we’re watching a trilogy reusing a familiar plotline.

Dry powder inventory spiked (again)

Private markets assets under management totaled $13.1 trillion as of June 30, 2023, and have grown nearly 20 percent per annum since 2018. Dry powder reserves—the amount of capital committed but not yet deployed—increased to $3.7 trillion, marking the ninth consecutive year of growth. Dry powder inventory—the amount of capital available to GPs expressed as a multiple of annual deployment—increased for the second consecutive year in PE, as new commitments continued to outpace deal activity. Inventory sat at 1.6 years in 2023, up markedly from the 0.9 years recorded at the end of 2021 but still within the historical range. NAV grew as well, largely driven by the reluctance of managers to exit positions and crystallize returns in a depressed multiple environment.

Private equity strategies diverged

Buyout and venture capital, the two largest PE sub-asset classes, charted wildly different courses over the past 18 months. Buyout notched its highest fundraising year ever in 2023, and its performance improved, with funds posting a (still paltry) 5 percent net internal rate of return through September 30. And although buyout deal volumes declined by 19 percent, 2023 was still the third-most-active year on record. In contrast, venture capital (VC) fundraising declined by nearly 60 percent, equaling its lowest total since 2015, and deal volume fell by 36 percent to the lowest level since 2019. VC funds returned –3 percent through September, posting negative returns for seven consecutive quarters. VC was the fastest-growing—as well as the highest-performing—PE strategy by a significant margin from 2010 to 2022, but investors appear to be reevaluating their approach in the current environment.

Private equity entry multiples contracted

PE buyout entry multiples declined by roughly one turn from 11.9 to 11.0 times EBITDA, slightly outpacing the decline in public market multiples (down from 12.1 to 11.3 times EBITDA), through the first nine months of 2023. For nearly a decade leading up to 2022, managers consistently sold assets into a higher-multiple environment than that in which they had bought those assets, providing a substantial performance tailwind for the industry. Nowhere has this been truer than in technology. After experiencing more than eight turns of multiple expansion from 2009 to 2021 (the most of any sector), technology multiples have declined by nearly three turns in the past two years, 50 percent more than in any other sector. Overall, roughly two-thirds of the total return for buyout deals that were entered in 2010 or later and exited in 2021 or before can be attributed to market multiple expansion and leverage. Now, with falling multiples and higher financing costs, revenue growth and margin expansion are taking center stage for GPs.

Real estate receded

Demand uncertainty, slowing rent growth, and elevated financing costs drove cap rates higher and made price discovery challenging, all of which weighed on deal volume, fundraising, and investment performance. Global closed-end fundraising declined 34 percent year over year, and funds returned −4 percent in the first nine months of the year, losing money for the first time since the 2007–08 global financial crisis. Capital shifted away from core and core-plus strategies as investors sought liquidity via redemptions in open-end vehicles, from which net outflows reached their highest level in at least two decades. Opportunistic strategies benefited from this shift, with investors focusing on capital appreciation over income generation in a market where alternative sources of yield have grown more attractive. Rising interest rates widened bid–ask spreads and impaired deal volume across food groups, including in what were formerly hot sectors: multifamily and industrial.

Private debt pays dividends

Debt again proved to be the most resilient private asset class against a turbulent market backdrop. Fundraising declined just 13 percent, largely driven by lower commitments to direct lending strategies, for which a slower PE deal environment has made capital deployment challenging. The asset class also posted the highest returns among all private asset classes through September 30. Many private debt securities are tied to floating rates, which enhance returns in a rising-rate environment. Thus far, managers appear to have successfully navigated the rising incidence of default and distress exhibited across the broader leveraged-lending market. Although direct lending deal volume declined from 2022, private lenders financed an all-time high 59 percent of leveraged buyout transactions last year and are now expanding into additional strategies to drive the next era of growth.

Infrastructure took a detour

After several years of robust growth and strong performance, infrastructure and natural resources fundraising declined by 53 percent to the lowest total since 2013. Supply-side timing is partially to blame: five of the seven largest infrastructure managers closed a flagship vehicle in 2021 or 2022, and none of those five held a final close last year. As in real estate, investors shied away from core and core-plus investments in a higher-yield environment. Yet there are reasons to believe infrastructure’s growth will bounce back. Limited partners (LPs) surveyed by McKinsey remain bullish on their deployment to the asset class, and at least a dozen vehicles targeting more than $10 billion were actively fundraising as of the end of 2023. Multiple recent acquisitions of large infrastructure GPs by global multi-asset-class managers also indicate marketwide conviction in the asset class’s potential.

Private markets still have work to do on diversity

Private markets firms are slowly improving their representation of females (up two percentage points over the prior year) and ethnic and racial minorities (up one percentage point). On some diversity metrics, including entry-level representation of women, private markets now compare favorably with corporate America. Yet broad-based parity remains elusive and too slow in the making. Ethnic, racial, and gender imbalances are particularly stark across more influential investing roles and senior positions. In fact, McKinsey’s research  reveals that at the current pace, it would take several decades for private markets firms to reach gender parity at senior levels. Increasing representation across all levels will require managers to take fresh approaches to hiring, retention, and promotion.

Artificial intelligence generating excitement

The transformative potential of generative AI was perhaps 2023’s hottest topic (beyond Taylor Swift). Private markets players are excited about the potential for the technology to optimize their approach to thesis generation, deal sourcing, investment due diligence, and portfolio performance, among other areas. While the technology is still nascent and few GPs can boast scaled implementations, pilot programs are already in flight across the industry, particularly within portfolio companies. Adoption seems nearly certain to accelerate throughout 2024.

Private markets in a slower era

If private markets investors entered 2023 hoping for a return to the heady days of 2021, they likely left the year disappointed. Many of the headwinds that emerged in the latter half of 2022 persisted throughout the year, pressuring fundraising, dealmaking, and performance. Inflation moderated somewhat over the course of the year but remained stubbornly elevated by recent historical standards. Interest rates started high and rose higher, increasing the cost of financing. A reinvigorated public equity market recovered most of 2022’s losses but did little to resolve the valuation uncertainty private market investors have faced for the past 18 months.

Within private markets, the denominator effect remained in play, despite the public market recovery, as the numerator continued to expand. An activity-dampening cycle emerged: higher cost of capital and lower multiples limited the ability or willingness of general partners (GPs) to exit positions; fewer exits, coupled with continuing capital calls, pushed LP allocations higher, thereby limiting their ability or willingness to make new commitments. These conditions weighed on managers’ ability to fundraise. Based on data reported as of year-end 2023, private markets fundraising fell 22 percent from the prior year to just over $1 trillion, the largest such drop since 2009 (Exhibit 1).

The impact of the fundraising environment was not felt equally among GPs. Continuing a trend that emerged in 2022, and consistent with prior downturns in fundraising, LPs favored larger vehicles and the scaled GPs that typically manage them. Smaller and newer managers struggled, and the number of sub–$1 billion vehicles and new firm launches each declined to its lowest level in more than a decade.

Despite the decline in fundraising, private markets assets under management (AUM) continued to grow, increasing 12 percent to $13.1 trillion as of June 30, 2023. 2023 fundraising was still the sixth-highest annual haul on record, pushing dry powder higher, while the slowdown in deal making limited distributions.

Investment performance across private market asset classes fell short of historical averages. Private equity (PE) got back in the black but generated the lowest annual performance in the past 15 years, excluding 2022. Closed-end real estate produced negative returns for the first time since 2009, as capitalization (cap) rates expanded across sectors and rent growth dissipated in formerly hot sectors, including multifamily and industrial. The performance of infrastructure funds was less than half of its long-term average and even further below the double-digit returns generated in 2021 and 2022. Private debt was the standout performer (if there was one), outperforming all other private asset classes and illustrating the asset class’s countercyclical appeal.

Private equity down but not out

Higher financing costs, lower multiples, and an uncertain macroeconomic environment created a challenging backdrop for private equity managers in 2023. Fundraising declined for the second year in a row, falling 15 percent to $649 billion, as LPs grappled with the denominator effect and a slowdown in distributions. Managers were on the fundraising trail longer to raise this capital: funds that closed in 2023 were open for a record-high average of 20.1 months, notably longer than 18.7 months in 2022 and 14.1 months in 2018. VC and growth equity strategies led the decline, dropping to their lowest level of cumulative capital raised since 2015. Fundraising in Asia fell for the fourth year of the last five, with the greatest decline in China.

Despite the difficult fundraising context, a subset of strategies and managers prevailed. Buyout managers collectively had their best fundraising year on record, raising more than $400 billion. Fundraising in Europe surged by more than 50 percent, resulting in the region’s biggest haul ever. The largest managers raised an outsized share of the total for a second consecutive year, making 2023 the most concentrated fundraising year of the last decade (Exhibit 2).

Despite the drop in aggregate fundraising, PE assets under management increased 8 percent to $8.2 trillion. Only a small part of this growth was performance driven: PE funds produced a net IRR of just 2.5 percent through September 30, 2023. Buyouts and growth equity generated positive returns, while VC lost money. PE performance, dating back to the beginning of 2022, remains negative, highlighting the difficulty of generating attractive investment returns in a higher interest rate and lower multiple environment. As PE managers devise value creation strategies to improve performance, their focus includes ensuring operating efficiency and profitability of their portfolio companies.

Deal activity volume and count fell sharply, by 21 percent and 24 percent, respectively, which continued the slower pace set in the second half of 2022. Sponsors largely opted to hold assets longer rather than lock in underwhelming returns. While higher financing costs and valuation mismatches weighed on overall deal activity, certain types of M&A gained share. Add-on deals, for example, accounted for a record 46 percent of total buyout deal volume last year.

Real estate recedes

For real estate, 2023 was a year of transition, characterized by a litany of new and familiar challenges. Pandemic-driven demand issues continued, while elevated financing costs, expanding cap rates, and valuation uncertainty weighed on commercial real estate deal volumes, fundraising, and investment performance.

Managers faced one of the toughest fundraising environments in many years. Global closed-end fundraising declined 34 percent to $125 billion. While fundraising challenges were widespread, they were not ubiquitous across strategies. Dollars continued to shift to large, multi-asset class platforms, with the top five managers accounting for 37 percent of aggregate closed-end real estate fundraising. In April, the largest real estate fund ever raised closed on a record $30 billion.

Capital shifted away from core and core-plus strategies as investors sought liquidity through redemptions in open-end vehicles and reduced gross contributions to the lowest level since 2009. Opportunistic strategies benefited from this shift, as investors turned their attention toward capital appreciation over income generation in a market where alternative sources of yield have grown more attractive.

In the United States, for instance, open-end funds, as represented by the National Council of Real Estate Investment Fiduciaries Fund Index—Open-End Equity (NFI-OE), recorded $13 billion in net outflows in 2023, reversing the trend of positive net inflows throughout the 2010s. The negative flows mainly reflected $9 billion in core outflows, with core-plus funds accounting for the remaining outflows, which reversed a 20-year run of net inflows.

As a result, the NAV in US open-end funds fell roughly 16 percent year over year. Meanwhile, global assets under management in closed-end funds reached a new peak of $1.7 trillion as of June 2023, growing 14 percent between June 2022 and June 2023.

Real estate underperformed historical averages in 2023, as previously high-performing multifamily and industrial sectors joined office in producing negative returns caused by slowing demand growth and cap rate expansion. Closed-end funds generated a pooled net IRR of −3.5 percent in the first nine months of 2023, losing money for the first time since the global financial crisis. The lone bright spot among major sectors was hospitality, which—thanks to a rush of postpandemic travel—returned 10.3 percent in 2023. 2 Based on NCREIFs NPI index. Hotels represent 1 percent of total properties in the index. As a whole, the average pooled lifetime net IRRs for closed-end real estate funds from 2011–20 vintages remained around historical levels (9.8 percent).

Global deal volume declined 47 percent in 2023 to reach a ten-year low of $650 billion, driven by widening bid–ask spreads amid valuation uncertainty and higher costs of financing (Exhibit 3). 3 CBRE, Real Capital Analytics Deal flow in the office sector remained depressed, partly as a result of continued uncertainty in the demand for space in a hybrid working world.

During a turbulent year for private markets, private debt was a relative bright spot, topping private markets asset classes in terms of fundraising growth, AUM growth, and performance.

Fundraising for private debt declined just 13 percent year over year, nearly ten percentage points less than the private markets overall. Despite the decline in fundraising, AUM surged 27 percent to $1.7 trillion. And private debt posted the highest investment returns of any private asset class through the first three quarters of 2023.

Private debt’s risk/return characteristics are well suited to the current environment. With interest rates at their highest in more than a decade, current yields in the asset class have grown more attractive on both an absolute and relative basis, particularly if higher rates sustain and put downward pressure on equity returns (Exhibit 4). The built-in security derived from debt’s privileged position in the capital structure, moreover, appeals to investors that are wary of market volatility and valuation uncertainty.

Direct lending continued to be the largest strategy in 2023, with fundraising for the mostly-senior-debt strategy accounting for almost half of the asset class’s total haul (despite declining from the previous year). Separately, mezzanine debt fundraising hit a new high, thanks to the closings of three of the largest funds ever raised in the strategy.

Over the longer term, growth in private debt has largely been driven by institutional investors rotating out of traditional fixed income in favor of private alternatives. Despite this growth in commitments, LPs remain underweight in this asset class relative to their targets. In fact, the allocation gap has only grown wider in recent years, a sharp contrast to other private asset classes, for which LPs’ current allocations exceed their targets on average. According to data from CEM Benchmarking, the private debt allocation gap now stands at 1.4 percent, which means that, in aggregate, investors must commit hundreds of billions in net new capital to the asset class just to reach current targets.

Private debt was not completely immune to the macroeconomic conditions last year, however. Fundraising declined for the second consecutive year and now sits 23 percent below 2021’s peak. Furthermore, though private lenders took share in 2023 from other capital sources, overall deal volumes also declined for the second year in a row. The drop was largely driven by a less active PE deal environment: private debt is predominantly used to finance PE-backed companies, though managers are increasingly diversifying their origination capabilities to include a broad new range of companies and asset types.

Infrastructure and natural resources take a detour

For infrastructure and natural resources fundraising, 2023 was an exceptionally challenging year. Aggregate capital raised declined 53 percent year over year to $82 billion, the lowest annual total since 2013. The size of the drop is particularly surprising in light of infrastructure’s recent momentum. The asset class had set fundraising records in four of the previous five years, and infrastructure is often considered an attractive investment in uncertain markets.

While there is little doubt that the broader fundraising headwinds discussed elsewhere in this report affected infrastructure and natural resources fundraising last year, dynamics specific to the asset class were at play as well. One issue was supply-side timing: nine of the ten largest infrastructure GPs did not close a flagship fund in 2023. Second was the migration of investor dollars away from core and core-plus investments, which have historically accounted for the bulk of infrastructure fundraising, in a higher rate environment.

The asset class had some notable bright spots last year. Fundraising for higher-returning opportunistic strategies more than doubled the prior year’s total (Exhibit 5). AUM grew 18 percent, reaching a new high of $1.5 trillion. Infrastructure funds returned a net IRR of 3.4 percent in 2023; this was below historical averages but still the second-best return among private asset classes. And as was the case in other asset classes, investors concentrated commitments in larger funds and managers in 2023, including in the largest infrastructure fund ever raised.

The outlook for the asset class, moreover, remains positive. Funds targeting a record amount of capital were in the market at year-end, providing a robust foundation for fundraising in 2024 and 2025. A recent spate of infrastructure GP acquisitions signal multi-asset managers’ long-term conviction in the asset class, despite short-term headwinds. Global megatrends like decarbonization and digitization, as well as revolutions in energy and mobility, have spurred new infrastructure investment opportunities around the world, particularly for value-oriented investors that are willing to take on more risk.

Private markets make measured progress in DEI

Diversity, equity, and inclusion (DEI) has become an important part of the fundraising, talent, and investing landscape for private market participants. Encouragingly, incremental progress has been made in recent years, including more diverse talent being brought to entry-level positions, investing roles, and investment committees. The scope of DEI metrics provided to institutional investors during fundraising has also increased in recent years: more than half of PE firms now provide data across investing teams, portfolio company boards, and portfolio company management (versus investment team data only). 4 “ The state of diversity in global private markets: 2023 ,” McKinsey, August 22, 2023.

In 2023, McKinsey surveyed 66 global private markets firms that collectively employ more than 60,000 people for the second annual State of diversity in global private markets report. 5 “ The state of diversity in global private markets: 2023 ,” McKinsey, August 22, 2023. The research offers insight into the representation of women and ethnic and racial minorities in private investing as of year-end 2022. In this chapter, we discuss where the numbers stand and how firms can bring a more diverse set of perspectives to the table.

The statistics indicate signs of modest advancement. Overall representation of women in private markets increased two percentage points to 35 percent, and ethnic and racial minorities increased one percentage point to 30 percent (Exhibit 6). Entry-level positions have nearly reached gender parity, with female representation at 48 percent. The share of women holding C-suite roles globally increased 3 percentage points, while the share of people from ethnic and racial minorities in investment committees increased 9 percentage points. There is growing evidence that external hiring is gradually helping close the diversity gap, especially at senior levels. For example, 33 percent of external hires at the managing director level were ethnic or racial minorities, higher than their existing representation level (19 percent).

Yet, the scope of the challenge remains substantial. Women and minorities continue to be underrepresented in senior positions and investing roles. They also experience uneven rates of progress due to lower promotion and higher attrition rates, particularly at smaller firms. Firms are also navigating an increasingly polarized workplace today, with additional scrutiny and a growing number of lawsuits against corporate diversity and inclusion programs, particularly in the US, which threatens to impact the industry’s pace of progress.

Fredrik Dahlqvist is a senior partner in McKinsey’s Stockholm office; Alastair Green  is a senior partner in the Washington, DC, office, where Paul Maia and Alexandra Nee  are partners; David Quigley  is a senior partner in the New York office, where Connor Mangan is an associate partner and Aditya Sanghvi  is a senior partner; Rahel Schneider is an associate partner in the Bay Area office; John Spivey is a partner in the Charlotte office; and Brian Vickery  is a partner in the Boston office.

The authors wish to thank Jonathan Christy, Louis Dufau, Vaibhav Gujral, Graham Healy-Day, Laura Johnson, Ryan Luby, Tripp Norton, Alastair Rami, Henri Torbey, and Alex Wolkomir for their contributions

The authors would also like to thank CEM Benchmarking and the StepStone Group for their partnership in this year's report.

This article was edited by Arshiya Khullar, an editor in the Gurugram office.

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Academics Use Imaginary Data in Their Research

Academia values the appearance of truth over actual truth..

Aaron Brown | 5.7.2024 10:45 AM

After surviving a disastrous congressional hearing, Claudine Gay was forced to resign as the president of Harvard for repeatedly copying and pasting language used by other scholars and passing it off as her own. She's hardly alone among elite academics, and plagiarism has become a roiling scandal in academia.

There's another common practice among professional researchers that should be generating even more outrage: making up data. I'm not talking about explicit fraud, which also happens way too often, but about openly inserting fictional data into a supposedly objective analysis.

Instead of doing the hard work of gathering data to test hypotheses, researchers take the easy path of generating numbers to support their preconceptions or to claim statistical significance. They cloak this practice in fancy-sounding words like "imputation," "ecological inference," "contextualization," and "synthetic control."

They're actually just making stuff up.

Claudine Gay was accused of plagiarizing sections of her Ph.D. thesis, for which she was awarded Harvard's Toppan Prize for the best dissertation in political science. She has since requested three corrections . More outrageous is that she wrote a paper on white voter participation without having any data on white voter participation.

In an article in the American Political Science Review that was based on her dissertation, Gay set out to investigate "the link between black congressional representation and political engagement," finding that "the election of blacks to Congress negatively affects white political involvement and only rarely increases political engagement among African Americans."

To arrive at that finding, you might assume that Gay had done the hard work of measuring white and black voting patterns in the districts she was studying. You would assume wrong.

Instead, Gay used regression analysis to estimate white voting patterns. She analyzed 10 districts with black representatives and observed that those with more voting-age whites had lower turnout at the polls than her model predicted. So she concludes that whites must be the ones not voting.

She committed what in statistics is known as the "ecological fallacy"—you see two things occurring in the same place and assume a causal relationship. For example, you notice a lot of people dying in hospitals, so you assume hospitals kill people. The classic example is Jim Crow laws were strictest in states that skewed black. Ecological inference leads to the false conclusion that blacks supported Jim Crow.

Gay's theory that a black congressional representative depresses white voter turnout could be true, but there are other plausible explanations for what she observed. The point is that we don't know. The way to investigate white voter turnout is to measure white voter turnout. 

Gay is hardly the only culprit. Because she was the president of Harvard, it's worth making an example of her work, but it reflects broad trends in academia. Unlike the academic crime of plagiarism, students are taught and encouraged to invent data under the guise of statistical sophistication. Academia values the appearance of truth over actual truth.

You need real data to understand the world. The process of gathering real data also leads to essential insights. Researchers pick up on subtleties that often cause them to shift their hypotheses. Armchair investigators, on the other hand, build neat rows and columns that don't say anything about what's happening outside their windows.

Another technique for generating rather than collecting data is called "imputation," which was used in a paper titled "Green innovations and patents in OECD countries" by economists Almas Heshmati and Mike Shinas. The authors wanted to analyze the number of "green" patents issued by different countries in different years. But the authors only had data for some countries and some years.

"Imputation" means filling in data gaps with educated guesses. It can be defensible if you have a good basis for your guesses and they don't affect your conclusions strongly. For example, you can usually guess gender based on a person's name. But if you're studying the number of green patents, and you don't know that number, imputation isn't an appropriate tool for solving the problem.

The use of imputation allowed them to publish a paper arguing that environmentalist policies lead to innovation—which is likely the conclusions they had hoped for—and to do so with enough statistical significance to pass muster with journal editors.

A graduate student in economics working with the same data as Heshmati and Shinas recounted being "dumbstruck" after reading their paper. The student, who wants to remain anonymous for career reasons, reached out to HeshmAati to find out how he and Shinas had filled in the data gaps. The research accountability site Retraction Watch reported that they had used the Excel "autofill" function.

According to an analysis by the economist Gary Smith, altogether there were over 2,000 fictional data points amounting to 13 percent of all the data used in the paper.

The Excel autofill function is a lot of fun and genuinely handy in some situations. When you enter 1, 2, 3, it guesses 4. But it doesn't work when the data—like much of reality—have no simple or predictable pattern.

When you give Excel a list of U.S. presidents, it can't predict the next one. I did give it a try though. Why did Excel think that William Henry Harrison' would retake the White House in 1941? Harrison died in office just 31 days after his inauguration—in 1841. Most likely, autofill figured it was only fair that he be allowed to serve out his remaining years. Why did it pick 1941? That's when FDR began his third term, which apparently Excel considered to be illegitimate, so it exhumed Harrison and put him back in the White House.

In a paper published in the journal of the American Medical Association and written up by CNN and the New York Post , a team of academics claimed to show that age-adjusted death rates soared 106 percent during the pandemic among renters who had received eviction filing notices, compared to 25 percent for a control group.

The authors got 483,408 eviction filings, and asked the U.S. Census how many of the tenants had died. The answer was 0.3 percent, and that 58 percent were still alive. The status of about 42 percent was unknown—usually because the tenant had moved without filing a change of address. If the authors had assumed that all the unknowns were still alive, the COVID-era mortality increase would be 22 percent for tenants who got eviction notices versus 25 percent who didn't. This would have been a statistically insignificant finding, wouldn't have been publishable, and certainly wouldn't have gotten any press attention.

Some of the tenants that the Census couldn't find probably did die, though likely not many, since most dead people end up with death certificates—and people who are dead can't move, so you'd expect most of them to to be linked to their census addresses. But some might move or change their names and then die, or perhaps they were missing from the Census database before receiving an eviction notice.

But whatever the reality, the authors didn't have the data. The entire result of their paper—the 106 percent claimed increase in mortality for renters with eviction filings versus the 22 percent observed rate—comes from a guess about how many of the unknown tenants had died.

How did they guess? They made the wildly implausible assumption that the Census and the Social Security Administration are equally likely to lose track of a dead person and a living one. Yet the government is far more interested in when people die than when they move, especially because they don't want to keep cutting them Social Security checks. Also, dead people don't move or change their names.

Whether or not their assumption was plausible, the paper reported a guess as if it reflected objective data. That's considered acceptable in academia, but it shouldn't be.

Another paper , titled "Association Between Connecticut's Permit-to-Purchase Handgun Law and Homicides," was published in the American Journal of Public Health. It cooked up data to use as a control. The study claimed to show that a 1994 gun control law passed in Connecticut cut firearm homicides by 40 percent. But firearm homicide rates in Connecticut followed national trends, with no obvious change after the 1994 law.

Forty percent compared to what? The authors arrived at their conclusion by concocting an imaginary state to serve as the control group, combining numbers from California, Maryland, Nevada, New Hampshire, and Rhode Island. This fictional state had 40 percent more homicides than the real Connecticut.

Reality is too messy for a technique like this to tell us anything meaningful. The author's entire finding derived from the fact that Rhode Island, which comprised most of "synthetic Connecticut," experienced a temporary spate of about 20 extra murders from 1999 to 2003, a large percentage increase in such a small state. Since the temporary spike in murders wasn't the result of a change in gun control policy, it tells us little about the efficacy of Connecticut's 1994 law or the policy issue at hand.

Is it always wrong to guess about missing data? No, not under conditions of extreme uncertainty in which data collection is impossible before a decision has to be made. For example, if you're considering taking a potentially life-saving medicine that hasn't been properly studied, you make the best guess you can with the information you have. But difficult decisions that have to be made with scarce information shouldn't influence public policy and aren't worthy of publication.

Yet researchers routinely rely on these methods to generate results on matters of no great urgency, because in academia publishing matters more than truth. Which is a shame. Progress in human knowledge requires real-world observations, not clicking a mouse and dragging it to the bottom of the screen.

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Spain | Analysis of national tourist flows in real time between January and April of 2024

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Published on Tuesday, May 14, 2024 | Updated on Tuesday, May 14, 2024

According to BBVA credit card data, the first months of the year have been characterized by a slowdown in the growth of tourist spending in Spain compared to the last months of 2023, weighed down by the decline in consumption by Spaniards and despite the rebound of foreign tourism.

• Key points:
• Between January and April 2024, total tourist spending (domestic and foreign) grew by 8.1% y/y (5 pp less than in the previous quarter).
• In the same period, tourist spending by Spaniards outside their usual province of residence registered a drop of 2.7% y/y (+9.3% y/y in the previous quarter), while spending by foreigners in Spain accelerated its growth to 20.0% y/y, 2 pp more than the previous period.
• During Easter 2024, total tourist spending fell 1.4% year-on-year compared to the same holiday period last year. The drop was entirely due to the domestic segment, while the foreign segment showed progress.
• National tourist spending grew in only five communities in the first four months of 2024. The Balearic Islands stood out, which is also the only region where growth accelerated compared to the previous period. On the other hand, Madrid, the Canary Islands and Aragón registered the greatest declines.
• All regions except Madrid presented an increase in total tourist spending (national plus foreigners) in the first four months of the year. The growth in the islands, C. Valenciana and Andalusia, stood out. Foreign tourism supported growth in all regions and especially in the islands, Navarra and the Mediterranean coast.

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• Giancarlo Carta BBVA Research - Senior Economist

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