arXiv subjects

Yilong Zhang

Publications and source records attributed to Yilong Zhang.

36 records · Page 2Linked to original sources

arXiv2024

Monodromy of Primitive Vanishing Cycles for Hypersurfaces in $\mathbb P^4$

Let X be a complex submanifold of projective space. Schnell showed that the middle-dimensional primitive cohomology of X is generated by tube classes, which arise from the monodromy of the vanishing homology on hyperplane sections. Clemens asks if the theorem is still true when we restrict the generating set to the tube classes over the class of a single vanishing sphere of nodal degeneration. We prove this is true for hypersurfaces in CP^4. The proof is based on the degeneration of a hypersurface to the union of hypersurfaces of lower degrees.

math.AG↗

arXiv2024

Extension of the Topological Abel-Jacobi Map for Cubic Threefolds

The difference $[L_1]-[L_2]$ of a pair of skew lines on a cubic threefold defines a vanishing cycle on the cubic surface as the hyperplane section spanned by the two lines. By deforming the hyperplane, the flat translation of such vanishing cycle forms a 72-to-1 covering space $T_v$ of a Zariski open subspace of $(\mathbb P^4)^*$. Based on a lemma of Stein on the compactification of finite analytic covers, we found a compactification of $T_v$ to which the topological Abel-Jacobi map extends. Moreover, the boundary points of the compactification can be interpreted in terms of local monodromy and the singularities on cubic surfaces. We prove the associated map on fundamental groups of topological Abel-Jacobi map is surjective.

math.AG↗

arXiv2023

Degeneration of Dual Varieties of Hypersurfaces

Consider a one-parameter family of smooth projective varieties X_t which degenerate into a simple normal crossing divisor at t=0. What is the dual variety in the limit? We answer this question for a hypersurface of degree d degenerate to the union of two hypersurfaces of degree d_1 and d-d_1 meeting transversely. We find all the irreducible components of the dual variety in the limit and their multiplicities.

math.AG↗

arXiv2023

Multiply robust estimators in longitudinal studies with missing data under control-based imputation

Longitudinal studies are often subject to missing data. The ICH E9(R1) addendum addresses the importance of defining a treatment effect estimand with the consideration of intercurrent events. Jump-to-reference (J2R) is one classically envisioned control-based scenario for the treatment effect evaluation using the hypothetical strategy, where the participants in the treatment group after intercurrent events are assumed to have the same disease progress as those with identical covariates in the control group. We establish new estimators to assess the average treatment effect based on a proposed potential outcomes framework under J2R. Various identification formulas are constructed under the assumptions addressed by J2R, motivating estimators that rely on different parts of the observed data distribution. Moreover, we obtain a novel estimator inspired by the efficient influence function, with multiple robustness in the sense that it achieves $n^{1/2}$-consistency if any pairs of multiple nuisance functions are correctly specified, or if the nuisance functions converge at a rate not slower than $n^{-1/4}$ when using flexible modeling approaches. The finite-sample performance of the proposed estimators is validated in simulation studies and an antidepressant clinical trial.

stat.ME↗

arXiv2023

Deep-Learning-based Vasculature Extraction for Single-Scan Optical Coherence Tomography Angiography

Optical coherence tomography angiography (OCTA) is a non-invasive imaging modality that extends the functionality of OCT by extracting moving red blood cell signals from surrounding static biological tissues. OCTA has emerged as a valuable tool for analyzing skin microvasculature, enabling more accurate diagnosis and treatment monitoring. Most existing OCTA extraction algorithms, such as speckle variance (SV)- and eigen-decomposition (ED)-OCTA, implement a larger number of repeated (NR) OCT scans at the same position to produce high-quality angiography images. However, a higher NR requires a longer data acquisition time, leading to more unpredictable motion artifacts. In this study, we propose a vasculature extraction pipeline that uses only one-repeated OCT scan to generate OCTA images. The pipeline is based on the proposed Vasculature Extraction Transformer (VET), which leverages convolutional projection to better learn the spatial relationships between image patches. In comparison to OCTA images obtained via the SV-OCTA (PSNR: 17.809) and ED-OCTA (PSNR: 18.049) using four-repeated OCT scans, OCTA images extracted by VET exhibit moderate quality (PSNR: 17.515) and higher image contrast while reducing the required data acquisition time from ~8 s to ~2 s. Based on visual observations, the proposed VET outperforms SV and ED algorithms when using neck and face OCTA data in areas that are challenging to scan. This study represents that the VET has the capacity to extract vascularture images from a fast one-repeated OCT scan, facilitating accurate diagnosis for patients.

eess.IV↗

arXiv2023

Topological Abel-Jacobi Map and Mixed Hodge Structures

For a smooth projective variety X of dimension 2n-1 over complex field, Zhao defined the topological Abel-Jacobi map, which sends vanishing cycles on a smooth hyperplane section Y to the middle dimensional primitive intermediate Jacobian of X. It agrees with Griffiths' Abel-Jacobi map on vanishing cycles that are algebraic and varies holomorphically on the locus of Hodge classes as hyperplane section deforms. On the other hand, Schnell proposed an alternative construction using the real-splitting property of the mixed Hodge structure on H^{2n-1}(X\Y). We show that the two definitions coincide, which answers a question of Schnell.

math.AG↗

arXiv2023

Measuring the speed of light with updated Hubble diagram of high-redshift standard candles

The possible time variation of the fundamental constants of nature has been an active subject of research in modern physics. In this paper, we propose a new method to investigate such possible time variation of the speed of light $c$ using the updated Hubble diagram of high-redshift standard candles including Type Ia Supernovae (SNe Ia) and high-redshift quasars (based on UV-X relation). Our findings show that the SNe Ia Pantheon sample, combined with currently available sample of cosmic chronometers, would produce robust constraints on the speed of light at the level of $c/c_0=1.03\pm0.03$. For the Hubble diagram of UV+X ray quasars acting as a new type of standard candles, we obtain $c/c_0=1.19\pm0.07$. Therefore, our results confirm that there is no strong evidence for the deviation from the constant speed of light up to $z\sim 2$. Moreover, we discuss how our technique might be improved at much higher redshifts ($z\sim5$), focusing on future measurements of the acceleration parameter $X(z)$ with gravitational waves (GWs) from binary neutron star mergers. In particular, in the framework of the second-generation space-based GW detector, DECi-hertz Interferometer Gravitational-wave Observatory (DECIGO), the speed of light is expected to be constrained with the precision of $Δ{c}/c=10^{-3}$.

astro-ph.CO↗

arXiv2023

Internal Structure Attention Network for Fingerprint Presentation Attack Detection from Optical Coherence Tomography

As a non-invasive optical imaging technique, optical coherence tomography (OCT) has proven promising for automatic fingerprint recognition system (AFRS) applications. Diverse approaches have been proposed for OCT-based fingerprint presentation attack detection (PAD). However, considering the complexity and variety of PA samples, it is extremely challenging to increase the generalization ability with the limited PA dataset. To solve the challenge, this paper presents a novel supervised learning-based PAD method, denoted as ISAPAD, which applies prior knowledge to guide network training and enhance the generalization ability. The proposed dual-branch architecture can not only learns global features from the OCT image, but also concentrate on layered structure feature which comes from the internal structure attention module (ISAM). The simple yet effective ISAM enables the proposed network to obtain layered segmentation features belonging only to Bonafide from noisy OCT volume data directly. Combined with effective training strategies and PAD score generation rules, ISAPAD obtains optimal PAD performance in limited training data. Domain generalization experiments and visualization analysis validate the effectiveness of the proposed method for OCT PAD.

cs.CV↗

arXiv2023

Number of Repetitions in Re-randomization Tests

In covariate-adaptive or response-adaptive randomization, the treatment assignment and outcome can be correlated. Under this situation, re-randomization tests are a straightforward and attractive method to provide valid statistical inference. In this paper, we investigate the number of repetitions in the re-randomization tests. This is motivated by the group sequential design in clinical trials, where the nominal significance bound can be very small at an interim analysis. Accordingly, re-randomization tests lead to a very large number of required repetitions, which may be computationally intractable. To reduce the number of repetitions, we propose an adaptive procedure and compare it with multiple approaches under pre-defined criteria. Monte Carlo simulations are conducted to show the performance of different approaches in a limited sample size. We also suggest strategies to reduce total computation time and provide practical guidance in preparing, executing and reporting before and after data are unblinded at an interim analysis, so one can complete the computation within a reasonable time frame.

stat.ME↗

arXiv2022

Impact of impurities on drift wave instabilities in reversed-field pinch plasmas

The drift wave in the presence of impurity ions was investigated numerically in reversed field pinch (RFP) plasmas, using the gyrokinetic integral eigenmode equation. It was found that in RFP plasmas with hollow density profiles, an increase in $k_θρ_s$ increases the growth rate of the ion temperature gradient (ITG). Comparing the results of regular and hollow plasma density profile shows that the ITG mode under the hollow density profile is much harder to be excited. For the impurities' effects, when the impurities' density gradient is opposite to the primary ions, namely when $L_{ez}$ is negative, impurities could enhance the instability. On the contrary, when $L_{ez}$ is positive, the instability is stabilized. Regarding the trapped electron mode (TEMs), the growth rate under the plasma with hollow density profile remained minor than that for the standard density gradient. There exists a threshold of $L_{ez}$. When $L_{ez}$ is less than this value, impurity destabilizes TEMs, while as $L_{ez}$ is greater than this, impurity stabilizes TEMs. The effects of $L_{ez}$ on TEM also depend on both the plasma density gradient and the impurity species. In addition, the influence of collisionality on TEMs was also studied.

physics.plasm-ph↗

arXiv2022

Multiple measurements of gravitational waves acting as standard probes: model-independent constraints on the cosmic curvature with DECIGO

Although the spatial curvature has been precisely determined via the cosmic microwave background (CMB) observation by Planck satellite, it still suffers from the well-known cosmic curvature tension. As a standard siren, gravitational waves (GWs) from binary neutron star mergers provide a direct way to measure the luminosity distance. In addition, the accelerating expansion of the universe may cause an additional phase shift in the gravitational waveform, which allows us to measure the acceleration parameter. This measurement provides an important opportunity to determine the curvature parameter $Ω_k$ in the GW domain based on the combination of two different observables for the same objects at high redshifts. In this study, we investigate how such an idea could be implemented with future generation of space-based DECi-hertz Interferometer Gravitational-wave Observatory (DECIGO) in the framework of two model-independent methods. Our results show that DECIGO could provide a reliable and stringent constraint on the cosmic curvature at a precision of $ΔΩ_k$=0.12, which is comparable to existing results based on different electromagnetic data. Our constraints are more stringent than the traditional electromagnetic method from the Pantheon SNe Ia sample, which shows no evidence for the deviation from the flat universe at $z\sim 2.3$. More importantly, with our model-independent method, such a second-generation space-based GW detector would also be able to explore the possible evolution $Ω_k$ with redshifts, through direct measurements of cosmic curvature at different redshifts ($z\sim 5$). Such a model-independent $Ω_k$ reconstruction to the distance past can become a milestone in gravitational-wave cosmology.

astro-ph.CO↗

arXiv2022

Robust analyses for longitudinal clinical trials with missing and non-normal continuous outcomes

Missing data is unavoidable in longitudinal clinical trials, and outcomes are not always normally distributed. In the presence of outliers or heavy-tailed distributions, the conventional multiple imputation with the mixed model with repeated measures analysis of the average treatment effect (ATE) based on the multivariate normal assumption may produce bias and power loss. Control-based imputation (CBI) is an approach for evaluating the treatment effect under the assumption that participants in both the test and control groups with missing outcome data have a similar outcome profile as those with an identical history in the control group. We develop a general robust framework to handle non-normal outcomes under CBI without imposing any parametric modeling assumptions. Under the proposed framework, sequential weighted robust regressions are applied to protect the constructed imputation model against non-normality in both the covariates and the response variables. Accompanied by the subsequent mean imputation and robust model analysis, the resulting ATE estimator has good theoretical properties in terms of consistency and asymptotic normality. Moreover, our proposed method guarantees the analysis model robustness of the ATE estimation, in the sense that its asymptotic results remain intact even when the analysis model is misspecified. The superiority of the proposed robust method is demonstrated by comprehensive simulation studies and an AIDS clinical trial data application.

stat.ME↗

arXiv2022

Sensitivity analysis in longitudinal clinical trials via distributional imputation

Missing data is inevitable in longitudinal clinical trials. Conventionally, the missing at random assumption is assumed to handle missingness, which however is unverifiable empirically. Thus, sensitivity analysis is critically important to assess the robustness of the study conclusions against untestable assumptions. Toward this end, regulatory agencies often request using imputation models such as return-to-baseline, control-based, and washout imputation. Multiple imputation is popular in sensitivity analysis; however, it may be inefficient and result in an unsatisfying interval estimation by Rubin's combining rule. We propose distributional imputation (DI) in sensitivity analysis, which imputes each missing value by samples from its target imputation model given the observed data. Drawn on the idea of Monte Carlo integration, the DI estimator solves the mean estimating equations of the imputed dataset. It is fully efficient with theoretical guarantees. Moreover, we propose weighted bootstrap to obtain a consistent variance estimator, taking into account the variabilities due to model parameter estimation and target parameter estimation. The finite-sample performance of DI inference is assessed in the simulation study. We apply the proposed framework to an antidepressant longitudinal clinical trial involving missing data to investigate the robustness of the treatment effect. Our proposed DI approach detects a statistically significant treatment effect in both the primary analysis and sensitivity analysis under certain prespecified sensitivity models in terms of the average treatment effect, the risk difference, and the quantile treatment effect in lower quantiles of the responses, uncovering the benefit of the test drug for curing depression.

stat.ME↗

arXiv2021

Consistency testing for invariance of the speed of light at different redshifts: the newest results from strong lensing and type Ia supernovae observations

The invariance of the speed of light in the distant universe has profound significance for fundamental physics. In this paper, we propose a new model-independent method to test the invariance of the speed of light $c$ at different redshifts by combining the strong gravitational lensing (SGL) systems and the observations of type-Ia supernovae (SNe Ia). All the quantities used to test the deviation of $c$ come from the direct observations, and the absolute magnitudes of SNe Ia need not to be calibrated. Our results show that the speed of light in the distant universe is no obvious deviation from the constant value $c_0$ within the uncertainty based on current observations. Moreover, we conclude that the currently compiled SGL and SNe Ia Pantheon samples may achieve much higher precision $Δc/c\sim10^{-2}$ for the deviation of $c$ than all previously considered approaches. The forthcoming data from the Legacy Survey of Space and Time and Wide-Field InfraRed Space Telescope will achieve more stringent testing for deviation of the SOL (at the level of $Δc/c \sim10^{-3}$) by using our model-independent method. Finally, we discuss the potential ways in which our technique might be improved, focusing on the treatment of possible sources of systematic uncertainties.

astro-ph.CO↗

arXiv2021

SMIM: a unified framework of Survival sensitivity analysis using Multiple Imputation and Martingale

Censored survival data are common in clinical trial studies. We propose a unified framework for sensitivity analysis to censoring at random in survival data using multiple imputation and martingale, called SMIM. The proposed framework adopts the δ-adjusted and control-based models, indexed by the sensitivity parameter, entailing censoring at random and a wide collection of censoring not at random assumptions. Also, it targets for a broad class of treatment effect estimands defined as functionals of treatment-specific survival functions, taking into account of missing data due to censoring. Multiple imputation facilitates the use of simple full-sample estimation; however, the standard Rubin's combining rule may overestimate the variance for inference in the sensitivity analysis framework. We decompose the multiple imputation estimator into a martingale series based on the sequential construction of the estimator and propose the wild bootstrap inference by resampling the martingale series. The new bootstrap inference has a theoretical guarantee for consistency and is computationally efficient compared to the non-parametric bootstrap counterpart. We evaluate the finite-sample performance of the proposed SMIM through simulation and an application on a HIV clinical trial.

stat.ME↗

arXiv2021

Probing modified gravity theories with multiple measurements of high-redshift quasars

In this paper, we quantify the ability of multiple measurements of high-redshift quasars (QSOs) to constrain several theories of modified gravity, including the Dvali-Gabadadze-Porrati braneworld scenario, generalized Chaplygin gas, $f(T)$ modified gravity, and Modified Polytropic Cardassian model. Recently released sample of 1598 quasars with X-ray and UV flux measurements in the redshift range of $0.036\leq z \leq 5.1003$, as well as a compilation of 120 intermediate-luminosity radio quasars covering the redshift of $0.46 < z < 2.76$ are respectively used as standard probes at higher redshifts. For all considered modified gravity theories, our results show that there is still some possibility that the standard $Λ$CDM scenario might not be the best cosmological model preferred by the current quasar observations. In order to improve cosmological constraints, the quasar data are also combined with the latest observations of baryon acoustic oscillations (BAO), which strongly complement the constraints. Finally, we discuss the support given by the data to modified gravity theories, applying different information theoretic techniques like the Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC) and Jensen-Shannon divergence (JSD).

astro-ph.CO↗

arXiv2017

Sparse Convex Clustering

Convex clustering, a convex relaxation of k-means clustering and hierarchical clustering, has drawn recent attentions since it nicely addresses the instability issue of traditional nonconvex clustering methods. Although its computational and statistical properties have been recently studied, the performance of convex clustering has not yet been investigated in the high-dimensional clustering scenario, where the data contains a large number of features and many of them carry no information about the clustering structure. In this paper, we demonstrate that the performance of convex clustering could be distorted when the uninformative features are included in the clustering. To overcome it, we introduce a new clustering method, referred to as Sparse Convex Clustering, to simultaneously cluster observations and conduct feature selection. The key idea is to formulate convex clustering in a form of regularization, with an adaptive group-lasso penalty term on cluster centers. In order to optimally balance the tradeoff between the cluster fitting and sparsity, a tuning criterion based on clustering stability is developed. In theory, we provide an unbiased estimator for the degrees of freedom of the proposed sparse convex clustering method. Finally, the effectiveness of the sparse convex clustering is examined through a variety of numerical experiments and a real data application.

stat.ME↗

arXiv2015

A Survey of directed graphs invariants

In this paper, various kinds of invariants of directed graphs are summarized. In the first topic, the invariant w(G) for a directed graph G is introduced, which is primarily defined by S. Chen and X.M. Chen to solve a problem of weak connectedness of tensor product of two directed graphs. Further, we present our recent studies on the invariant w(G) in categorical view. In the second topic, Homology theory on directed graph is introduced, and we also cast on categorical view of the definition. The third topic mainly focuses on Laplacians on graphs, including traditional work and latest result of 1-laplacian by K.C.Chang. Finally, Zeta functions and Graded graphs are introduced, inclduing Bratteli-Vershik diagram, dual graded graphs and differential posets, with some applications in dynamic system.

math.CO↗