Classical Case Research Articles

Enabling Adaptive Sampling for Intra-Window Join: Simultaneously Optimizing Quantity and Quality

>Sampling is one of the most widely employed approximations in big data processing. Among various challenges in sampling design, sampling for join is particularly intriguing yet complex. This perplexing problem starts with a classical case where the join of two Bernoulli samples shrinks its output size quadratically and exhibits a strong dependency on the input data, presenting a unique challenge that necessitates adaptive sampling to guarantee both the quantity and quality of the sampled data. The community has made strides in achieving this goal by constructing offline samples and integrating support from indexes or key frequencies. However, when dealing with stream data, due to the need for real-time processing and high-quality analysis, methods developed for processing static data become unavailable. Consequently, a fundamental question arises: Is it possible to achieve adaptive sampling in stream data without relying on offline techniques? To address this problem, we propose FreeSam, which couples hybrid sampling with intra-window join, a key stream join operator. Our focus lies on two widely used metrics: output size, ensuring quantity, and variance, ensuring quality. FreeSam enables adaptability in both the desired quantity and quality of data sampling by offering control on the two-dimensional space spanned by these metrics. Meanwhile, adjustable trade-offs between quality and performance make FreeSam practical for use. Our experiments show that, for every 1% increase in latency limitation, FreeSam can yield a 3.83% increase in the output size while maintaining the level of the estimator's variance. Additionally, we give FreeSam a multi-core implementation and ensure predictability of its latency through both an analytic model and a neural network model. The accuracy of these models is 88.05% and 96.75% respectively.

On a non-local problem for a fractional differential equation of the Boussinesq type

In recent years, the fractional partial differential equation of the Boussinesq type has attracted much attention from researchers due to its practical importance. In this paper, we study a non-local problem for the Boussinesq type equation Dtαu(t)+A Dtαu(t)+ν2Au(t) =0, 0<t<T, 1<α<3∕2, where Dtα is the Caputo fractional derivative, and A is an abstract operator. In the classical case, i.e., when α = 2, this problem has been studied previously, and an interesting effect has been discovered: the existence and uniqueness of a solution depend significantly on the length of the time interval and the parameter ν. In this note, we show that in the case of a fractional equation, there is no such effect: a solution of the problem exists and is unique for any T and ν.

Environmental Lighting Conditions, Phenomenal Contrast, and the Conscious Perception of Near and Far.

Recent evidence in systems neuroscience suggests that lighting conditions affect the whole chain of brain processing, from retina to high-level cortical networks, for perceptual and cognitive function. Here, visual adaptation levels to three different environmental lighting conditions, (1) darkness, (2) daylight, and (3) prolonged exposure to very bright light akin to sunlight, were simulated in lab to investigate the effects of light adaptation levels on classic cases of subjective contrast, assimilation, and contrast-induced relative depth in achromatic, i.e., ON-OFF pathway mediated visual configurations. After adaptation/exposure to a given lighting condition, configurations were shown in grouped and ungrouped conditions in random order to healthy young humans in computer-controlled two-alternative forced-choice procedures that consisted of deciding, as quickly as possible, which of two background patterns in a given configuration of achromatic contrast appeared lighter, or which of two foreground patterns appeared to stand out in front, as if it were nearer to the observer. We found a statistically significant effect of the adaptation levels on the consciously perceived subjective contrast (F(2,23) = 20.73; p < 0.001) and the relative depth (F(2,23) = 12.67; p < 0.001), a statistically significant interaction between the adaptation levels and the grouping factor (F(2,23) = 4.73; p < 0.05) on subjective contrast, and a statistically significant effect of the grouping factor on the relative depth (F(2,23) = 13.71; p < 0.01). Visual adaption to different lighting conditions significantly alters the conscious perception of contrast and assimilation, classically linked to non-linear functional synergies between ON and OFF processing channels in the visual brain, and modulates the repeatedly demonstrated effectiveness of luminance contrast as a depth cue; the physically brighter pattern regions in the configurations are no longer consistently perceived as nearer to a conscious observer under daylight and extreme bright light adapted (rod-saturated) conditions.

On Non-Commutative Multi-Rings with Involution

The primary motivation for this work is to develop the concept of Marshall’s quotient applicable to non-commutative multi-rings endowed with involution, expanding upon the main ideas of the classical case—commutative and without involution—presented in Marshall’s seminal paper. We define two multiplicative properties to address the involutive case and characterize their Marshall quotient. Moreover, this article presents various cases demonstrating that the “multi” version of rings with involution offers many examples, applications, and relatives in (multi)algebraic structures. Therefore, we established the first steps toward the development of an expansion of real algebra and real algebraic geometry to a non-commutative and involutive setting.

Thermodynamic quantum Fokker–Planck equations and their application to thermostatic Stirling engine

We developed a computer code for the thermodynamic quantum Fokker–Planck equations (T-QFPE), derived from a thermodynamic system–bath model. This model consists of an anharmonic subsystem coupled to multiple Ohmic baths at different temperatures, which are connected to or disconnected from the subsystem as a function of time. The code numerically integrates the T-QFPE and their classical expression to simulate isothermal, isentropic, thermostatic, and entropic processes in both quantum and classical cases. The accuracy of the results was verified by comparing the analytical solutions of the Brownian oscillator. In addition, we illustrated a breakdown of the Markovian Lindblad-master equation in the pure quantum regime. As a demonstration, we simulated a thermostatic Stirling engine employed to develop non-equilibrium thermodynamics [S. Koyanagi and Y. Tanimura, J. Chem. Phys. 161, 114113 (2024)] under quasi-static conditions. The quasi-static thermodynamic potentials, described as intensive and extensive variables, were depicted as work diagrams. In the classical case, the work done by the external field is independent of the system–bath coupling strength. In contrast, in the quantum case, the work decreases as the coupling strength increases due to quantum entanglement between the subsystem and bath. The codes were developed for multicore processors using Open Multi-Processing (OpenMP) and for graphics processing units using the Compute Unified Device Architecture. These codes are provided in the supplementary material.

Q\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varvec{q}$$\\end{document}-rational Functions and Interpolation with Complete Nevanlinna–Pick Kernels

In this paper we introduce the concept of matrix-valued q-rational functions. In comparison to the classical case, we give different characterizations with principal emphasis on realizations and discuss algebraic manipulations. We also study the concept of Schur multipliers and complete Nevanlinna–Pick kernels in the context of q-deformed reproducing kernel Hilbert spaces and provide first applications in terms of an interpolation problem using Schur multipliers and complete Nevanlinna–Pick kernels.

Progress in application of machine learning in epidemiology

Population based health data collection and analysis are important in epidemiological research. In recent years, with the rapid development of big data, Internet and cloud computing, artificial intelligence has gradually attracted attention of epidemiological researchers. More and more researchers are trying to use artificial intelligence algorithms for genome sequencing and medical image data mining, and for disease diagnosis, risk prediction and others. In recent years, machine learning, a branch of artificial intelligence, has been widely used in epidemiological research. This paper summarizes the key fields and progress in the application of machine learning in epidemiology, reviews the development history of machine learning, analyzes the classic cases and current challenges in its application in epidemiological research, and introduces the current application scenarios and future development trends of machine learning and artificial intelligence algorithms for the better exploration of the epidemiological research value of massive medical health data in China.

Bayesian inversion of a fractional elliptic system derived from seismic exploration

In this paper, we concentrate on the Bayesian inversion of a dispersion‐dominated fractional Helmholtz (DDFH) equation, which has been introduced in studies concerning seismic exploration. To establish the inversion theory, we meticulously examine the DDFH equation. We transform it into a system comprising both fractional‐ and integer‐order elliptic equations, extending the conventional definition of the spectral fractional Laplace operator to accommodate non‐homogeneous boundary conditions. Subsequently, we establish the well‐posedness theory for scenarios involving both small and large wavenumbers. Our proof hinges upon the regularity attributes of select fractional elliptic equations and capitalizes fully on the structural peculiarities of the elliptic system, which distinguish it from classical cases. Thereafter, we focus on the inverse medium scattering problem pertinent to the DDFH equation, framed within the Bayesian statistical framework. We address two scenarios: one devoid of model reduction errors and another characterized by such errors—arising from the implementation of certain absorbing boundary conditions. More precisely, based on the properties of the forward operator, well‐posedness of the posterior measures have been proved in both cases, which provide an opportunity to quantify the uncertainties of this problem.

A NEW ALGORITHM FOR GENERATING POWER SERIES SOLUTIONS FOR A BROAD CLASS OF FRACTIONAL PDES: APPLICATIONS TO INTERESTING PROBLEMS

This research offers a precise analytical solution for initial value problems of both linear and nonlinear fractional order partial differential equations. A new approach called the limit residual function method is developed and utilized to generate a series solution for the equations. The key tools of this method are the concepts of power series, residual function, and the limit at zero. The new method is characterized by the speed of determining the series solution coefficients and the limited mathematical operations used. The study examines five significant applications of fractional partial differential equations using this new method. To validate the accuracy of the results, they are compared with exact solutions in the classical case for the discussed applications. We conclude that the proposed approach is straightforward, effective, and successful in solving linear and nonlinear fractional differential equations.

Digamma function and general Fischer series in the theory of Kempner sums

The harmonic sum of the integers which are missing p given digits in a base b is expressed as blog(b)/p plus corrections indexed by the excluded digits and expressed as integrals involving the digamma function and a suitable measure. A number of consequences are derived, such as explicit bounds, monotony, series representations and asymptotic expansions involving the zeta values at integers, and suitable moments of the measure. In the classic Kempner case of b=10 and 9 as the only excluded digit, the series representation turns out to be exactly identical with a result obtained by Fischer already in 1993. Extending this work is indeed the goal of the present contribution.

Research on Risk Management of Equity Pledge in Listed Companies: A Case Study of Guirenniao

In the present financial market, the financial needs of listed companies are expanding rapidly. Equity pledge, as a commonly used means of financing for listed companies, is becoming increasingly significant. As an emerging form of guarantee, equity pledge allows listed companies to pledge their own equity as collateral to obtain financing from external financial institutions. Equity pledge has many advantages, such as universality, fast financing speed, strong security, and effective risk diversification. However, equity pledge not only meets the financing needs of listed companies, but also brings corresponding risks to them. this paper selects the classic case of Guirenniao Co., Ltd. as the research object and adopts the literature analysis method to review relevant research on equity pledge both domestically and internationally. Based on the leverage cycle theory, PBC (Private Benefits of Control) theory, and asymmetric information theory, the article analyzes the risks associated with equity pledge and identifies excessive pledge by Guirenniao as an important factor contributing to the failure of company operation. Finally, based on the research findings, risk response measures are proposed from the main aspects of external information disclosure, internal supervision and control, enhancement of enterprise value, and dynamic monitoring of business operations. It aims to raise awareness among other listed companies and their stakeholders, prevent risks, effectively supervise the equity pledge behavior of listed companies, and ensure the sustainable development of equity pledge.

Aggregate Estimates of Reflexive Collective Behavior Dynamics in a Cournot Oligopoly Model

This paper considers an oligopoly model with an arbitrary number of Cournotreflexive agents under incomplete information in the classical case of linear cost and demand functions. Agents make decisions based on a collective behavior model. The problem of identifying convergence conditions to the model equilibrium is studied, with an emphasis placed on the trajectory of the sum of the action residuals of all agents. Aggregate estimates of this trajectory are obtained. They can be used to judge how the trajectory of each agent evolves towards the equilibrium.

On the radicality property for spaces of symbols of bounded Volterra operators

In [1] it is shown that the Bloch space B in the unit disc has the following radicality property: if an analytic function g satisfies that gn∈B, then gm∈B, for all m≤n. Since B coincides with the space T(Aαp) of analytic symbols g such that the Volterra-type operator Tgf(z)=∫0zf(ζ)g′(ζ)dζ is bounded on the classical weighted Bergman space Aαp, the radicality property was used to study the composition of paraproducts Tg and Sgf=Tfg on Aαp. Motivated by this fact, we prove that T(Aωp) also has the radicality property, for any radial weight ω. Unlike the classical case, the lack of a precise description of T(Aωp) for a general radial weight, induces us to prove the radicality property for Aωp from precise norm-operator results for compositions of analytic paraproducts.

Desmoplastic Melanoma

Desmoplastic melanoma is a rare fibrosing variant of melanoma. It typically affects elderly patients but can occasionally affect young or middle-aged individuals. Desmoplastic melanoma is relevant as a diagnostic pitfall for pure tumor variants' distinct histopathologic and clinical features. The latter includes a lower regional lymph node involvement frequency and a more favorable prognosis among thick melanomas. Classic cases of desmoplastic melanoma tend to carry a high mutation burden. Patients with metastases from those tumors tend to respond favorably to novel immunotherapies.

Deterministic Record-and-Replay

This column describes three recent research advances related to deterministic record-and-replay, with the goal of showing both classical use cases and emerging use cases. A growing number of systems use a weaker form of deterministic record-and-replay. Essentially, these systems exploit the determinism that exists across many program executions but intentionally allow some nondeterminism for performance reasons. This trend is exemplified in GPUReplay in particular, but also in systems such as ShortCut and Dora.

Erdheim-chester disease with bilateral proptosis, coated aorta and hairy kidney

Erdheim-Chester disease (ECD) is a rare histiocytic disorder with a spectrum of clinical manifestations, ranging from asymptomatic single-organ involvement to multisystem disease. We present a classic case of ECD with detailed radiographic and histopathologic findings. A 63-year-old Thai female with a history of triple vessel disease post-PCI presented with bilateral proptosis and blurred vision for one year. On admission, she exhibited marked proptosis epiblepharon, lagophthalmos, conjunctival injection, chemosis, limited extraocular movement and cranial nerve II palsy. Imaging showed increased bilateral retro-orbital infiltrative lesions, osteosclerotic changes, and soft tissue thickening along the great vessels and retroperitoneum. A retro-orbital soft tissue biopsy showed foamy histiocytic proliferation with Touton giant cells. EDC was confirmed by next-generation sequencing revealing a BRAF V600E mutation. This patient received pegylated interferon-alpha. At 1-year follow-up visit, the disease remained stable. In this report, we present a classic case of EDC. The rarity of this disease makes it challenging to diagnose. The typical presentation characteristics raise awareness for the diagnosis of EDC, which is based on features such as osteosclerotic lesions in the long bones, soft tissue infiltration in medium to large vessels (coated aorta) and the bilateral pelvicalyceal systems (hairy kidney). These findings were confirmed through tissue pathology and molecular diagnostics.

Effect of Hopf-Hopf bifurcation on the post-flutter behavior of a three-degree-of-freedom airfoil

The post-flutter dynamics of a three-degree-of-freedom nonlinear airfoil with unsteady aerodynamics are investigated based on the Hopf-Hopf bifurcation theory. Many prior works have relied on Hopf bifurcation theory to predict flutter behavior in airfoil systems. Although this approach facilitates flutter prediction and characterization of post-flutter behavior in numerous scenarios, it may be invalid in specific instances, such as when the Hopf bifurcation of the system degenerates. Therefore, this study focuses on a classical degenerate case of Hopf bifurcation in airfoil systems, specifically the Hopf-Hopf bifurcation. We show that the system undergoes various Hopf-Hopf bifurcations under specific parameter conditions as the center of gravity shifts. The local dynamics near the Hopf-Hopf bifurcation points are represented, including quasiperiodic oscillations on a three-dimensional torus. The airfoil begins to oscillate quasiperiodically after the airflow speed crosses specific Hopf-Hopf bifurcation points. The study also uncovers complex quasiperiodic crises and quasiperiodic hysteresis loops, which have not been reported in previous studies of aeroelastic systems. Then, many singularities and bifurcation curves are obtained near the Hopf-Hopf bifurcation point by semiglobal unfolding. Furthermore, the influence of stall effects on the bifurcation structure of the system is represented. It is shown that the types of Hopf-Hopf bifurcations may vary with the changes of stall effects, influencing the system's semiglobal bifurcation structures consequently. For all Hopf-Hopf bifurcation scenarios, stall effects affect one of the Neimark-Sacker bifurcation curve structures unfolded from the Hopf-Hopf bifurcation point significantly, while the other Neimark-Sacker bifurcation curve experiences minimal impact from stall effects. Moreover, a large nonlinear stall coefficient will postpone the onset of quasiperiodic/chaotic oscillations.

A Real-Time Inverted Velocity Model for Fault Detection in Deep-Buried Hard Rock Tunnels Based on a Microseismic Monitoring System

Microseismic monitoring is an effective and widely used technology for dynamic fault disaster early warning and prevention in deep-buried hard rock tunnels. However, the insufficient understanding of the distribution of native faults poses a major challenge to yielding precise early warnings of disasters using an MS (Microseismic Monitoring System). Velocity field inversion is a reliable means to reflect fault information, and there is an urgent need to establish a real-time velocity field inversion method during tunnel excavation. In this paper, a method based on an MS is proposed to achieve the inversion of the velocity field in the monitoring area using microseismic event and excavation blasting data. The velocity field inversion method integrates the reflected wave ray-tracing method based on PSO (Particle Swarm Optimization) theory and FWI (Full-Waveform Inversion) theory. The accuracy of the proposed velocity inversion method was verified by various classic numerical simulation cases. In numerical simulations, the robustness of our method is evident in its ability to identify anomalous structural surfaces and velocity discontinuities ahead of the tunnel face.

Level-2 IFS thermodynamic formalism: Gibbs probabilities in the space of probabilities and the push-forward map

We will denote by M the space of Borel probabilities on the symbolic space Ω = { 1 , 2 ⋯ , m } N . M is equipped Monge–Kantorovich metric. We consider here the push-forward map T : M → M as a dynamical system. The space of Borel probabilities on M is denoted by M . Given a continuous function A : M → R , an a priori probability Π 0 on M , and a certain convolution operation acting on pairs of probabilities on M , we define an associated Level-2 IFS Ruelle operator. We show the existence of an eigenfunction and an eigenprobability Π ^ ∈ M for such an operator. Under a normalization condition for A, we show the existence of some T -invariant probabilities Π ^ ∈ M . We are able to define the variational entropy of such Π ^ and a related maximization pressure problem associated to A. In some particular examples, we show how to get eigenprobabilities solutions on M for the Level-2 Thermodynamic Formalism problem from eigenprobabilities on M for the classical (Level-1) Thermodynamic Formalism; this shows that our approach is a natural generalization of the classic case.

On the Approximation of the Hardy Z-Function via High-Order Sections

The Z-function is the real function given by Z(t)=eiθ(t)ζ12+it, where ζ(s) is the Riemann zeta function, and θ(t) is the Riemann–Siegel theta function. The function, central to the study of the Riemann hypothesis (RH), has traditionally posed significant computational challenges. This research addresses these challenges by exploring new methods for approximating Z(t) and its zeros. The sections of Z(t) are given by ZN(t):=∑k=1Ncos(θ(t)−ln(k)t)k for any N∈N. Classically, these sections approximate the Z-function via the Hardy–Littlewood approximate functional equation (AFE) Z(t)≈2ZN˜(t)(t) for N˜(t)=t2π. While historically important, the Hardy–Littlewood AFE does not sufficiently discern the RH and requires further evaluation of the Riemann–Siegel formula. An alternative, less common, is Z(t)≈ZN(t)(t) for N(t)=t2, which is Spira’s approximation using higher-order sections. Spira conjectured, based on experimental observations, that this approximation satisfies the RH in the sense that all of its zeros are real. We present a proof of Spira’s conjecture using a new approximate equation with exponentially decaying error, recently developed by us via new techniques of acceleration of series. This establishes that higher-order approximations do not need further Riemann–Siegel type corrections, as in the classical case, enabling new theoretical methods for studying the zeros of zeta beyond numerics.