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We prove a Poisson process approximation result for stabilising functionals of a determinantal point process. Our results use concrete couplings of determinantal processes with different Palm measures and exploit their association properties. Second, we focus on the Ginibre process and show in the asymptotic scenario of an increasing observation window that the process of points with a large nearest neighbour distance converges after a suitable scaling to a Poisson point process. As a corollary, we obtain the scaling of the maximum nearest neighbour distance in the Ginibre process, which turns out to be different from its analogue for independent points.
For a Sunday morning drive sometime in May 2023, the busy Outer Ring Road in Bengaluru seemed much more congested than usual. Vehicles were coming from everywhere and spilling into and out of this main road, and what was surreal was that this congestion was without the usual levels of nudging, shoving, shouting, and scraping on the road. For one, the road was crawling with traffic police, being, I should add, ably assisted by burly Bharatiya Janata Party (BJP) party workers. For another, it was one among Narendra Modi's several visits to the state as part of his campaigning for the assembly elections, and so it looked like everyone knew the reason behind the congestion and everyone seemed resigned to it, happily or otherwise. Modi was going to go through one of the perpendicular roads as part of his Bengaluru road show.
And as is typical of most Bengaluru drivers, I also took the chance of exiting the main road, into the narrow alleyways, hoping that I could get to another road that I presumed would be out of the vicinity of the road show. At the end of this alleyway maze, I suddenly found myself in the middle of a much wider road, again overflowing with cops and BJP party workers. With no traffic around, strangely, they casually gave me a glance as if my car was intruding upon something. Clearly it looked like I was.
I found myself on the road that Modi's procession had just crossed barely a few minutes ago, and those public officials were possibly breathing a sigh of relief when my car came in as an unwelcome pull back to reality. It was very quiet, with absolutely no traffic on the road.
Modeling detailed chemical kinetics is a primary challenge in combustion simulations. We present a novel framework to enforce physical constraints, specifically total mass and elemental conservation, during the reaction of ML models’ training for the reduced composition space chemical kinetics of large chemical mechanisms in combustion. In these models, the transport equations for a subset of representative species are solved with the ML approaches, while the remaining nonrepresentative species are “recovered” with a separate artificial neural network trained on data. Given the strong correlation between full and reduced solution vectors, our method utilizes a small neural network to establish an accurate and physically consistent mapping. By leveraging this mapping, we enforce physical constraints in the training process of the ML model for reduced composition space chemical kinetics. The framework is demonstrated here for methane, CH4, and oxidation. The resulting solution vectors from our deep operator networks (DeepONet)-based approach are accurate and align more consistently with physical laws.
As part of my dissertation research many summers ago, I lived for a couple of months in a few villages that straddled the borders of Karnataka, Tamil Nadu, and Andhra Pradesh. I was initiated into the political economy of this region by Mr Krishne Gowda of Bathlahalli village, an elderly patron of the region, who lived with his married sons and their families. Armed with a law degree from decades ago and a towel over the armpit (Manor 2004) now, Mr Gowda was the quintessential mover-and-shaker politician. On one post-lunch afternoon in the early days, he asked me what subject I was studying, and I told him “Political Science.” He looked at me, and then, in his earnestness to educate me, he said what I remember as the following:
Look, you are studying politics but let me tell you that we villagers know a lot about politics and data because we vote on many things. We vote in the panchayat elections, Assembly elections, and Lok Sabha of course. But we also have votes for cooperative bank elections, committees within panchayats, and so on.
We also know how to deal with the government. When they come and ask us how many members there are in my household, I decide the answer according to who is asking. If it is the forest official who asks, I will say one household. If it is for rations, I will say multiple households. If it is for elections, I will say three households. If it is for census, I will say one household and so on … it really depends on what the benefit is.
To compare is to “assimilate” and to discover deeper or fundamental similarities below the surface of secondary diversities (Sartori 1970). This chapter will discuss the underlying conceptual attributes of populism and how they have been constructed as they provide the background for indexing the cases in Chapter 4. The intention behind parsing populism into its underlying conceptual attributes is to be able to identify how they configure with each other to constitute the various populisms in India. And since set theoretic analysis is the approach adopted here to understand these configurations, this chapter will also translate these attributes and their constructs as necessary and sufficient conditions.
At this point, it may be helpful to step back from populism and understand the construction and the kind of concept structure being used and why that justifies the need for sufficient and necessary conditions and the downstream analysis that follows. The description provided here is a simple adaptation of the framework outlined by Goertz (2006). The concept structure being used here is multilevel and multidimensional. A multilevel concept has a basic structure, reflected through the secondary level as visible attributes whereby each attribute in turn can be measured through indicators as membership scores (in this project) or as variables in projects with a quantitative design. A multidimensional concept has different dimensions that constitute the basic level of the concept. The nature of the relationship between the attributes and the basic level can be causal, ontological, and substitutable. In this project, the attributes share an ontological relationship with the basic concept, according to which the various attributes are not just the defining features of the basic concept but in fact are the elements that compose the basic level.
Below are some clarificatory notes related to the dataset.
Populist Outcome Related
Clarifications on Electoral Data
A few additional clarifications, as background information, are necessary to understand some of the measures related to the electoral data.
1. Bal Thackeray had never contested an election. But it seemed unjustifiable to ignore him, as he was clearly a populist leader of some measure in Maharashtra. Thus, I took the first electoral victory of the Shiv Sena in the assembly elections of 1995 as the populist instance, because Bal Thackeray reigned supreme for many years prior to and after this victory. And I took the electoral statistics of the incumbent chief minister and loyalist, Manohar Joshi, as the proxy for Bal Thackeray, assuming that the party chief that has got the assembly majority for the first time in its history would have its most trusted loyalist as the chief minister.
2. Jayalalitha's elections in 2001, 2011, and 2016 also need clarifications. In 2001, Jayalalitha was disqualified from competing in the election in May 2001 but was acquitted in December 2001 and thereafter won the byelections from Andipatti in 2002. In 2011, even though Jayalalitha won from the Srirangam constituency (which was the constituency included in the dataset), she was convicted by the Karnataka High Court soon thereafter and acquitted subsequently. She then contested from the RK Nagar constituency and resumed her chief ministership and contested from RK Nagar again in 2016.
In this chapter, I will present the results of the qualitative comparative analysis (QCA) and then interpret them to describe the configurations that constitute populism in India. I will then provide the results of the tests for necessary and sufficient conditions and discuss the parameters of fit in terms of consistency and coverage. Finally, I will cover the various solution terms that indicate the pathways to populism.
The Sets of Data
Table 5.1 presents the data, that is, the sets of data, comprising 37 cases along five conditions and a populist outcome. Describing the worksheet as comprising sets of data instead of a dataset seems more accurate because each of the columns in the sheet is a set and its members are points of data (as fuzzy scores or as percentage scores) along the rows as constituent parts of the unit of analysis. The unit of analysis is an instance of a party candidate contesting elections at the state or at the national level. The cases have been purposively selected by reviewing the scholarship that explicitly indicates that the cases can be identified as instances of populism. And the conditions described earlier—electoral invocation to their people (P), antagonistic boundary setting (B), populist political leadership (L), populist attitude (A), and anxiety about the future (F)—are some of the commonly accepted attributes in the comparative scholarship on populism. In set theoretic terms, we will explore if P, B, L, A, and F are the conditions that constitute the membership of the populist outcome Y.
When we see data on a spreadsheet, concepts and methods associated with standard quantitative techniques inevitably come to mind. Usually and by default, we try to make sense of the data by deriving the summary statistics to understand what has gone up or down, we explore associations between factors by identifying correlations, and administer technical tests to see if the results confirm, reinterpret, or nullify our research questions and hypotheses.
But is it possible to look at a dataset “qualitatively”? And what would that imply? Is it possible to look at columns and rows and identify relations and configurations between them that are more than associational? At first glance, the possibility of this approach seems incongruous because we usually associate qualitative methods with text and quantitative methods with numbers.
This chapter introduces the reader to a qualitative approach by providing an overview of the set theoretic methodology and the QCA method. An introduction to the methodology and the method is important not just because it is mostly an unfamiliar method to many social scientists, particularly those who work in the Indian context, but also because, as a methodology, its philosophical and conceptual roots are somewhat distinct from standard social science approaches. And, equally important, because QCA relies on numbers and software codes for analysis, it misconstrues expectations since the use of numbers can inadvertently lead to interpretations based on quantitative reasoning.
Over the past 75 years, there have been at least 800 state government terms ruled by around 375 political leaders as chief ministers and counting. Populist leaders are a small but pivotal subset among these leaders. Scholarship on such leaders has necessarily been long on descriptive accounts because of their exceptional rise to and stay in political office. Such accounts are the basis upon which this comparative account is built.
The unit of analysis in this study is not a populist personality over a period of time, but a personality in a particular year that corresponds with either an assembly or a national election year. For example, a single case would not be “Kejriwal,” but would instead be cases like “Kejriwal 2015” or “Kejriwal 2020.” This chapter, therefore, does not aim to provide elaborate accounts of the leaders, but tries to strike a balance with the details and their relevance and, in doing so, provide a narrative of each that is tenable for comparative analysis.
This “case by year” approach seems justified for a couple of reasons. First, while almost all populist leaders come to power riding a wave, they inevitably routinize into the mainstream over successive elections. The fever breaks. Second, it may appear that the period of such long-term leaders is linear, that is, from the heights of riding a wave to come to power, and subsequently routinizing into a banal steady but sustained popularity over time. Breaking this narrative into multiple periods provides space for curvilinear possibilities because it allows for a closer look into the ups and downs of political life in that declining trajectory.
In this paper, we aim to investigate the fluid model associated with an open large-scale storage network of non-reliable file servers with finite capacity, where new files can be added, and a file with only one copy can be lost or duplicated. The Skorokhod problem with oblique reflection in a bounded convex domain is used to identify the fluid limits. This analysis involves three regimes: the under-loaded, the critically loaded, and the overloaded regimes. The overloaded regime is of particular importance. To identify the fluid limits, new martingales are derived, and an averaging principle is established. This paper extends the results of El Kharroubi and El Masmari [7].
As the population ages, the provision of adult long-term care (LTC) is one of the major challenges facing the UK and other developed nations. LTC funding for the elderly is complex, reflecting the range and level of services provided, with the total cost depending on the duration of LTC required. Institutional care settings (e.g., nursing/residential care homes) represent the most expensive form of LTC. Planning and funding for institutional LTC requires an understanding of the factors affecting the mortality (and hence duration and cost of care) of such LTC recipients. Using data provided by Bupa, one of the largest LTC providers in Britain, this paper investigates factors affecting the mortality of residents of institutional LTC facilities over the period 2016-2019. Consistent with existing research, most residents were female and had a higher average age profile compared with male residents. For those residents who died during the investigation period, the average length of stay was approximately 1.6 times longer for females relative to males. For both males and females, new residents experienced higher mortality in the first-year post admission compared to existing residents. Variations in the mortality of the residents were analysed by condition, funding status and care type on admission.
Counting independent sets in graphs and hypergraphs under a variety of restrictions is a classical question with a long history. It is the subject of the celebrated container method which found numerous spectacular applications over the years. We consider the question of how many independent sets we can have in a graph under structural restrictions. We show that any $n$-vertex graph with independence number $\alpha$ without $bK_a$ as an induced subgraph has at most $n^{O(1)} \cdot \alpha ^{O(\alpha )}$ independent sets. This substantially improves the trivial upper bound of $n^{\alpha },$ whenever $\alpha \le n^{o(1)}$ and gives a characterisation of graphs forbidding which allows for such an improvement. It is also in general tight up to a constant in the exponent since there exist triangle-free graphs with $\alpha ^{\Omega (\alpha )}$ independent sets. We also prove that if one in addition assumes the ground graph is chi-bounded one can improve the bound to $n^{O(1)} \cdot 2^{O(\alpha )}$ which is tight up to a constant factor in the exponent.
This article studies estimation and inference in the autoregressive (AR) models with unspecified and heavy-tailed heteroskedastic noises. A piece-wise locally stationary structure of the noise is constructed to capture various forms of heterogeneity, without imposing any restrictions on the tail index. The new nonstationary AR model allows for not only time-varying conditional features but also unconditional variance and tail index. This makes it appealing in practice, with wide applications in economics and finance. To obtain a feasible inference, we investigate the self-weighted least absolute deviation estimator and derive its asymptotic normality. Since the asymptotic variance relies on an unobserved density, a bootstrap method is proposed to approximate the limiting distribution. Based on the conditional moment condition, a portmanteau test from residuals is further proposed to detect misspecifications in the proposed model. A simulation study and two applications to time series illustrate our inference procedures.