Lower Tail Research Articles

Large deviations for the largest eigenvalue of Gaussian networks with constant average degree

Large deviation behavior of the largest eigenvalue \(\lambda _1\) of Wigner matrices including those arising from an Erdős-Rényi random graph \({\mathcal {G}}_{n,p}\) with i.i.d. random conductances on the edges has been the topic of considerable interest. However, despite several recent advances, not much is known when the underlying graph is sparse i.e., \(p\rightarrow 0\), except the recent works (Bhattacharya et al., Ann Probab 49(4):1847–1885, 2021and Bhattacharya and Ganguly, SIAM J Discret Math, 2020) which consider the simpler case of the graph without additional edge weights. Under sufficiently general conditions on the conductance distribution, one expects the ‘dense’ behavior as long as the average degree np is at least logarithmic in n. In this article we focus on the case of constant average degree i.e., \(p=\frac{d}{n}\) for some fixed \(d>0\) with standard Gaussian weights. Results in Bandeira and Van Handel (Ann Probab 44(4):2479–2506, 2016) about general non-homogeneous Gaussian matrices imply that in this regime \(\lambda _1\) scales like \(\sqrt{\log n}.\) We prove the following results towards a precise understanding of the large deviation behavior in this setting. 1. (Upper tail probabilities and structure theorem): For \(\delta >0,\) we pin down the exact exponent \(\psi (\delta )\) such that $$\begin{aligned} {\mathbb {P}}(\lambda _1\ge \sqrt{2(1+\delta )\log n})=n^{-\psi (\delta )+o(1)}. \end{aligned}$$ Further, we show that conditioned on the upper tail event, with high probability, a unique maximal clique emerges with a very precise \(\delta \) dependent size (takes either one or two possible values) and the Gaussian weights are uniformly high in absolute value on the edges in the clique. Finally, we also prove an optimal localization result for the leading eigenvector, showing that it allocates most of its mass on the aforementioned clique which is spread uniformly across its vertices. 2. (Lower tail probabilities): The exact stretched exponential behavior $$\begin{aligned} {\mathbb {P}}(\lambda _1\le \sqrt{2(1-\delta )\log n})=\exp \left( -n^{\ell (\delta )+o(1)}\right) \end{aligned}$$ is also established. As an immediate corollary, one obtains that \(\lambda _1\) is typically \((1+o(1))\sqrt{2\log n}\), a result which surprisingly appears to be new. A key ingredient in our proofs is an extremal spectral theory for weighted graphs obtained by an \(\ell _1-\)reduction of the standard \(\ell _2-\)variational formulation of the largest eigenvalue via the classical Motzkin-Straus theorem [37], which could be of independent interest.

Analysis of photoinjector transverse phase space in action and phase coordinates

Photoinjectors are the main high brightness electron sources for X-ray free electron lasers (XFEL). Photoinjector emittance reduction is one of the key knobs for improving XFEL lasing, so precise emittance measurement is critical. It's well known that rms emittance is very sensitive to low intensity tails of particle distributions in the phase space, whose measurement depend on the signal to noise ratio (SNR) and image processing procedures. Such sensitivities make the interpretations of beam transverse brightness challenging, leading to different emittance definitions to reduce the impact of tail particles. In this paper, transverse phase space is analyzed in action and phase coordinates for both analytical models and experiments, which give a more intuitive way to calculate the beam core brightness.

STUDI MORFOMETRIK UDANG CENDANA (Metapenaeus brevicornis) YANG TERTANGKAP DI PERAIRAN SAMBOJA KABUPATEN KUTAI KARTANEGARA

Yellow Shrimp (M. brevicornis) is a type of shrimp caught by Samboja fishermen which has a fairly high economic value. This study aims to provide information about the morphomorphological study of Yellow Shrimp (M. brevicornis) caught in the waters of Samboja, Kutai Kartanegara. This research was conducted in the waters of Samboja, Kutai Kartanegara, in November-December 2021, the sample used was 300 Yellow Shrimp (M. brevicornis). Morphometric study onmorphometric study Yellow Shrimp (M. brevicornis) using analysis with analysis of covariance test (ANCOVA) to see 20 morphometric covariates that affect total length (PTO). Based on the results of the analysis of the univariate ANOVA test, it is known that 20 morphometrics have a sig value <0.05, which means that H1 is accepted, that all morphometrics have an effect on PTO. Furthermore, ancova analysis was performed, obtained 5 morphometrics that have sig < 0.05, namely head length (PK), first segment length (PRP), telson length (TLS), lower head length (PKB) and tail length (PE), so from the results of the ancova test analysis showed that the most significant morphometric effect on PTO was 5 morphometers.

Top and bottom longevity of nations: a retrospective analysis of the age-at-death distribution across 18 OECD countries.

Similar to the study of the distribution of income within countries, population-level health disparities can be examined by analyzing the distribution of age at death. We sourced period-specific death counts for 18 OECD countries over 1900-2020 from the Human Mortality Database. We studied the evolution of country-year-specific distributions of age at death, with an examination of the lower and upper tails of these distributions. For each country-year, we extracted the 1st, 5th, 10th, 90th, 95th and 99th percentiles of the age-at-death distribution. We then computed the corresponding shares of longevity-the sum of the ages weighted by the age-at-death distribution as a fraction of the sum of the ages weighted by the distribution-for each percentile. For example, for the 10th percentile, this would correspond to how much longevity accrues to the bottom 10% of the age-at-death distribution in a given country-year. We expose a characterization of the age-at-death distribution across populations with a focus on the lower and upper tails of the distribution. Our metrics, specifically the gap measures in age and share across the 10th and 90th percentiles of the distribution, enable a systematic comparison of national performances, which yields information supplementary to the cross-country differences commonly pointed by traditional indicators of life expectancy and coefficient of variation. Examining the tails of age-at-death distributions can help characterize the comparative situations of the better- and worse-off individuals across nations, similarly to depictions of income distributions in economics.

Is gold still a safe haven for stock markets? New insights through the tail thickness of portfolio return distributions

This study examines the safe-haven property of gold during two deep financial crashes: the global financial crisis (GFC) and the coronavirus disease 2019 (COVID-19) pandemic. Applying extreme value theory, we analyze the tail behavior of the returns of 46 stock indices sorted by geographic location and level of market development and then investigate these portfolios with various gold allocations. We focus on changes in the tail thickness of the portfolio return distribution as an effect of an increased gold allocation. The COVID-19 crisis exhibited heavier lower tails of the stock indices than the GFC. During the GFC, gold enabled heavy Fréchet-type tails to change into thin Gumbel-type tails, whereas during the COVID-19 crash, the tails remained heavy, even after hedging. Thus, gold acted as a safe-haven asset, significantly decreasing extreme downside risk during the GFC, but the same result cannot be confirmed for the COVID-19 pandemic.

Spillovers and diversification benefits between oil futures and ASEAN stock markets

This study combines copula functions, wavelet decomposition and conditional VaR methods to examine spillovers and diversification benefits between oil futures and ASEAN stock markets (Indonesia, Philippines, Malaysia, Singapore, Vietnam and Thailand). The results show zero tail dependence between oil and stock returns at the short term. In contrast, we find a lower tail independence and an upper tail dependence at the long term. Our results highlight that oil futures serve as hedge assets at short term and a safe haven asset at the long term. Furthermore, we find significant and asymmetric risk spillovers from oil to ASEAN markets. The downside and upside spillovers are higher at the long term than short term and increase during the GFC, the recent oil crisis, and COVID-19 periods. Finally, we show that an equally weighted portfolio provides highest diversification benefits at both lower and medium tail distributions with the exception of Malaysian market. The diversification benefits of oil are sizeable for less coupling markets and fall during times of GFC and oil crisis.

Investigation of direct capture in the Na23(p,γ)Mg24 reaction

The $^{23}\mathrm{Na}(p,\ensuremath{\gamma})^{24}\mathrm{Mg}$ reaction plays an important role in the nucleosynthesis of elements in the hot bottom burning environment of asymptotic giant branch stars by providing a breakout path from the NeNa cycle to the MgAl cycle. At temperatures above $\ensuremath{\approx}0.06$ GK, the underlying nuclear reaction contributions to the rate are primarily narrow resonances, but at lower temperatures direct and broad resonance tail contributions come to dominate. While there have been recent studies to improve the uncertainties associated with these narrow resonances, little attention has been paid to the nonresonant component. In this work, experimental measurements are reported over the energy range from 0.5 and 1.05 MeV proton beam energy, with a focus on studying the off-resonance region of the cross section. Several transitions were observed where two broad resonances dominate the energy range and whose low energy tails contribute strongly to the low-energy, nonresonant, cross section. In addition, a clear signature of direct capture has been observed for the first time in the $^{23}\mathrm{Na}(p,\ensuremath{\gamma})^{24}\mathrm{Mg}$ reaction.

Z2 non-restoration and composite Higgs: singlet-assisted baryogenesis w/o topological defects

Simple scalar-singlet extensions of the Standard Model with a (spontaneously broken) Z2 symmetry allow for a strong first order electroweak phase transition, as sought in order to realize electroweak baryogenesis. However they generically also lead to the emergence of phenomenologically problematic domain walls. Here we present a framework with a real scalar singlet that features a different thermal history that avoids this problem by never restoring the Z2 symmetry in the early universe. This is accomplished by considering D > 4 operators that emerge on general grounds, understanding the model as the low energy tail of a more complete theory, like for example in composite Higgs scenarios. Sticking to the latter framework, we present a concrete SO(6)/SO(5) composite realization of the idea. To this end, we additionally provide a complete classification of the structure of the Higgs potential (and the Yukawa couplings) in SO(6)/SO(5) models with fermions in the 1, 6, 15 or 20′ of SO(6).

Mixed vine copula flows for flexible modeling of neural dependencies.

Recordings of complex neural population responses provide a unique opportunity for advancing our understanding of neural information processing at multiple scales and improving performance of brain computer interfaces. However, most existing analytical techniques fall short of capturing the complexity of interactions within the concerted population activity. Vine copula-based approaches have shown to be successful at addressing complex high-order dependencies within the population, disentangled from the single-neuron statistics. However, most applications have focused on parametric copulas which bear the risk of misspecifying dependence structures. In order to avoid this risk, we adopted a fully non-parametric approach for the single-neuron margins and copulas by using Neural Spline Flows (NSF). We validated the NSF framework on simulated data of continuous and discrete types with various forms of dependency structures and with different dimensionality. Overall, NSFs performed similarly to existing non-parametric estimators, while allowing for considerably faster and more flexible sampling which also enables faster Monte Carlo estimation of copula entropy. Moreover, our framework was able to capture low and higher order heavy tail dependencies in neuronal responses recorded in the mouse primary visual cortex during a visual learning task while the animal was navigating a virtual reality environment. These findings highlight an often ignored aspect of complexity in coordinated neuronal activity which can be important for understanding and deciphering collective neural dynamics for neurotechnological applications.

Evolution of IMF By induced asymmetries during substorms: Superposed epoch analysis at geosynchronous orbit

The By component of the magnetic field inside the magnetosphere is positively correlated with the By component of the Interplanetary Magnetic Field (IMF). This leads to asymmetries in aurora, plasma convection and electric currents between the northern and southern hemispheres It has been demonstrated that magnetic conjugate locations in the northern and southern ionosphere become less displaced during magnetospheric substorms, which are associated with enhanced reconnection in the near-Earth tail. Here we directly address how the average By component in the magnetotail evolves relative to substorm onset by performing a superposed epoch analysis of the magnetic field observed at nightside geosynchronous orbit during periods with dominant IMF By. The observations demonstrate that the average |By| in the magnetotail increases during the loading phase prior to onset. |By| maximizes in the expansion phase and is subsequently reduced during the remaining unloading phase. The observed trends become more pronounced using substorm onset lists that on average identify stronger substorms. Since dayside reconnection dominates over tail reconnection during the loading phase, whereas tail reconnection dominates during the unloading phase, the results demonstrate how asymmetries build up during periods with low tail reconnection and are reduced during periods with enhanced tail reconnection in agreement with previous case studies of conjugate auroral substorm features.

Asymmetric tail dependence modeling, with application to cryptocurrency market data

Since the inception of Bitcoin in 2008, cryptocurrencies have played an increasing role in the world of e-commerce, but the recent turbulence in the cryptocurrency market in 2018 has raised some concerns about their stability and associated risks. For investors it is crucial to uncover the dependence relationships between cryptocurrencies for a more resilient portfolio diversification. Moreover, the stochastic behavior in both tails is important, as long positions are sensitive to a decrease in prices (lower tail), while short positions are sensitive to an increase in prices (upper tail). In order to assess both risk types, we develop in this paper a flexible copula model which is able to distinctively capture asymptotic dependence or independence in its lower and upper tails simultaneously. Our proposed model is parsimonious and smoothly bridges (in each tail) both extremal dependence classes in the interior of the parameter space. Inference is performed using a full or censored likelihood approach, and we investigate by simulation the estimators’ efficiency under three different censoring schemes which reduce the impact of nonextreme observations. We also develop a local likelihood approach to capture the temporal dynamics of extremal dependence among pairs of leading cryptocurrencies. We here apply our model to historical closing prices of five leading cryotocurrencies which share large cryptocurrency market capitalizations. The results show that our proposed copula model outperforms alternative copula models and that the lower-tail dependence level between most pairs of leading cryptocurrencies and, in particular, Bitcoin and Ethereum has become stronger over time, smoothly transitioning from an asymptotic independence regime to an asymptotic dependence regime in recent years, whilst the upper tail has been relatively more stable overall at a weaker dependence level.

Global Economic Uncertainties and Exchange Rate Management in Africa: A Panel Study

Abstract This study investigates the effects of global economic uncertainties on exchange rate management in Africa from 1990 to 2021. Employing the quantile regression technique, findings show that both global and domestic economic uncertainties have significant influence on exchange rate management in Africa. The intensity of global economic uncertainty rises during the bearish and transitional markets, but dependence declines during the bullish markets. Moreover, the relationship between domestic uncertainty and African exchange rate management shows that the structure of dependence improves around the upper tails but declines around the lower tails. African countries should pay attention to global economy in order to combat any impending negative effects of global economic uncertainties. Also, attention should be paid to other uncertainties such as political, social, or other factors that may aggravate domestic economic uncertainties.

Bunching estimation of elasticities using Stata

Typical censoring models have mass points at the upper or lower tails, or at both tails, of an otherwise continuous outcome distribution. In contrast, we consider a censoring model with a mass point in the interior of the outcome distribution. We refer to this mass point as “bunching” and use it to estimate model parameters. For example, economic theory suggests that, for increasing marginal income tax rates, many taxpayers will report income exactly at the threshold where the tax rate increases. This translates into a censoring model with bunching at the threshold. The size of this mass point of taxpayers can be used to estimate an elasticity parameter that summarizes taxpayers’ responses to taxes. In this article, we introduce the command bunching, which implements new nonparametric and semiparametric identification methods for estimating elasticities developed by Bertanha, McCallum, and Seegert (2021, Technical Report 2021-002, Board of Governors of the Federal Reserve System). These methods rely on weaker assumptions than what are currently made in the literature and result in meaningfully different estimates of the elasticity.

Augmenting the Double-Gaussian Representation of Atmospheric Turbulence and Convection via a Coupled Stochastic Multi-Plume Mass-Flux Scheme

Abstract Modern general circulation models continue to require parameterizations of subgrid transport due to planetary boundary layer (PBL) turbulence and convection. Some schemes that unify these processes rely on assumed joint probability distributions of vertical velocity and moist conserved thermodynamic variables to predict the subgrid-scale contribution to the mean state of the atmosphere. The multivariate double-Gaussian mixture has been proposed as an appropriate model for PBL turbulence and shallow convection, but it is unable to reproduce important features of shallow cumulus convection. In this study, a novel unified PBL turbulence–convection–cloud macrophysics scheme is presented based on the eddy-diffusivity/mass-flux framework. The new scheme augments the double-Gaussian representation of subgrid variability with multiple stochastic mass-flux plumes at minimal added computational cost. Improved results for steady-state maritime and transient continental shallow convection from a single-column model implementation of the new scheme are shown with respect to reference large-eddy simulations. Improvements are seen in the cloud layer due to mass-flux plumes occupying the extreme moist, low liquid-water potential temperature tail of the joint temperature–moisture distribution. Significance Statement Computer models of the atmosphere used to predict future climate are unable to directly represent air motion at small spatial scales because it would take too long to run the model over the entire planet. Instead, models typically use coarse model grid spacing and a simplified statistical representation of the physical processes that cause small-scale motions. This paper improves a particular simplified representation by adding a mechanism to represent statistically rare events of strong small-scale air motion that coherently transport air from near the surface to higher in the atmosphere. This increased transport also improves the representation of clouds, a particularly difficult phenomenon to simulate in models.

An empirical investigation of market risk, dependence structure, and portfolio management between green bonds and international financial markets

The study aims to explore the market risk, dependence structure, and portfolio diversification benefits of green bonds with Islamic and conventional (equity, bonds, and energy) markets. We first examine the market risk dynamics and dependence structure between green bonds and the international financial markets by using value-at-risk (VaR), copula models, and the Copula-VaR approach over the period from July 2014 to August 2020. Findings reveal the existence of the symmetric upper (lower) tail dependence between green bonds and international financial markets, except for the conventional bonds market with zero dependence. Our empirical results suggest that international financial markets possess different risk profiles, and the investors should not treat them as homogenous assets to combine with green bonds. Moreover, we also explore the portfolio diversification benefits, using hedge ratios, optimal portfolio weights, and hedging effectiveness for all pairs of green bonds-international financial markets. The results suggest that Islamic bonds and the oil markets are best to hedge green bonds, followed by conventional bonds, conventional equity, and the Islamic equity market. These results provide implications for effective risk management and fund allocation to policymakers and socially responsible investors. The study's findings are critical for current and future investors for efficient capital allocation in the environmental and ethically responsible assets.

On the Condition Number of the Shifted Real Ginibre Ensemble

We derive an accurate lower tail estimate on the lowest singular value $\sigma_1(X-z)$ of a real Gaussian (Ginibre) random matrix $X$ shifted by a complex parameter $z$. Such shift effectively changes the upper tail behaviour of the condition number $\kappa(X-z)$ from the slower $\mathbf{P}(\kappa(X-z)\ge t)\lesssim 1/t$ decay typical for real Ginibre matrices to the faster $1/t^2$ decay seen for complex Ginibre matrices as long as $z$ is away from the real axis. This sharpens and resolves a recent conjecture in [arXiv:2005.08930] on the regularizing effect of the real Ginibre ensemble with a genuinely complex shift. As a consequence we obtain an improved upper bound on the eigenvalue condition numbers (known also as the eigenvector overlaps) for real Ginibre matrices. The main technical tool is a rigorous supersymmetric analysis from our earlier work [arXiv:1908.01653].

Study on Natural Settlement Index Characteristics of Iron-Bearing Tailings Applied to Goaf Filling Treatment

In order to provide a technical basis for the subsequent concentration and utilization of the tailings treatment process in an iron ore mine, and to achieve the objectives of cost reduction and sustainable development, the settling concentration and settling capacity of a tailings slurry with an initial concentration of 40% in its natural state were tested in conjunction with the pumping supply concentration index of the beneficiation tailings slurry in a metal mine. The test results show that the iron ore tailings particles settle at an overall fast rate: basically, within 10 to 20 min they are able to reach or approach 85 to 99.5% of the final settling state-related index. During the settling process in the fixed container, at first, the clarified water at the top of the tailings slurry is very turbid. With the passage of time, the clarified water gradually becomes blurred and clear from turbidity, and the interface between the slurry and the water gradually becomes clearer. From the phenomena observed during the settling process and the test parameters such as the net increase in clear water and slurry variation, the maximum settling concentration and settling capacity indicators of 50% and 90% can be reached or approached in 5.5 to 7.25 and 10.5 to 15.5 min after settling, and the maximum settling concentration and settling capacity can be reached or approached in 10 to 20 min after the settling process. As the settling tests and observations continued, the relevant settling parameters basically reached the final settling state within the time period of 20 to 1440 min, during which the settling concentration of the tailing sand was 71.33 to 73.42% and the settling capacity was 1.85 to 1.91 g/cm3. It can be judged from the test results that the natural settling of the low concentration tailings slurry can meet the technical specifications required for the filling process, and that the natural settling and concentration of dewatering can save the costs of the relevant facilities and flocculation chemicals, and therefore has good technical and economic feasibility.

Complex risk contagions among large international energy firms: A multi-layer network analysis

This paper introduces a multi-layer network approach to explore risk contagions in a sample of top energy firms in the world. Large energy companies play a very important role in the international energy market. Mapping their responses to different types of shocks provides profound implications for understanding how international energy markets work, and could also create significant value for investors in the energy sector. Specifically, we distinguish three layers of risk spillovers, covering return correlations as well as upper tail and lower tail dependence. Through a multi-layer network setting, we identify both within layer linkages and inter-layer linkages. In addition, the dynamic evolution of this network structure is explored through a rolling-window approach, which enables us to evaluate the level of structural stability. Our empirical results unveil three regional clusters and a dynamic power shifting pattern in the international energy sector. Overall, this multi-layer network approach allows us to detect complex risk contagion patterns in financial markets and could be generalized to other scenarios.

Total positivity of copulas from a Markov kernel perspective

The underlying dependence structure between two random variables can be described in manifold ways. This includes the examination of certain dependence properties such as lower tail decreasingness (LTD), stochastic increasingness (SI) or total positivity of order 2, the latter usually considered for a copula (TP2) or (if existent) its density (d-TP2). In the present paper we investigate total positivity of order 2 for a copula's Markov kernel (MK-TP2 for short), a positive dependence property that is stronger than TP2 and SI, weaker than d-TP2 but, unlike d-TP2, is not restricted to absolutely continuous copulas, making it presumably the strongest dependence property defined for any copula (including those with a singular part such as Marshall-Olkin copulas). We examine the MK-TP2 property for different copula families, among them the class of Archimedean copulas and the class of extreme value copulas. In particular we show that, within the class of Archimedean copulas, the dependence properties SI and MK-TP2 are equivalent.

Candidate and confirmed ultrashort period main-sequence binary stars

ABSTRACT The lower tail of the period distribution of main-sequence binary stars is poorly constrained due to the small number of such systems known. This paper deals with candidate binary stars with periods shorter than 0.2 d and colour indices consistent with them being M dwarfs. Three sources of candidates are considered – a catalogue of TESS eclipsing binaries, the ATLAS catalogue of variable stars, and binary stars from the ‘International Variable Star Index’ (VSX) website. The TESS eclipsing binary catalogue contains five new candidates satisfying the period and colour criteria. New photometry confirms one as a bona fide main-sequence system, and another as a white dwarf/red dwarf pair. New multicolour light curves of 10 ATLAS stars are presented: 7 of these are main sequence binaries with confirmed ultrashort periods (P < 0.2 d). There are 328 red VSX binary candidates with short periods. Literature searches for 77 of these with P < 0.17 d were performed: only 6 are previously studied main sequence systems, and another 14 are known red dwarf/white dwarf systems.