arXiv subjects

Tianqi Zhao

Publications and source records attributed to Tianqi Zhao.

At least 37 records · Page 2Linked to original sources

arXiv2025

Characterizing the nuclear models informed by PREX and CREX: a view from Bayesian inference

New measurements of the weak charge density distributions of $^{48}$Ca and $^{208}$Pb challenge existing nuclear models. In the post-PREX-CREX era, it is unclear if current models can simultaneously describe weak charge distributions along with accurate measurements of binding energy and charge radii. In this letter, we explore the parameter space of relativistic and non-relativistic models to study the differences between the electric and weak form factors, $ΔF=F_{ch}-F_{W}$, in $^{48}$Ca and $^{208}$Pb. We show, for the first time, which aspects of mean-field models are the most important in determining the relative magnitude of the neutron skin in lead and calcium nuclei. We carefully disentangle the tension between the PREX-2/CREX constraints and the ability of the RMF and Skyrme models to accurately describe binding energies and charge radii. We find that the nuclear symmetry energy coefficient $S_V$ and the isovector spin-orbit coefficient $b'_4$ play different roles in determining $ΔF$ of $^{48}$Ca and $^{208}$Pb. Consequently, adjusting $S_V$ or $b'_4$ shifts predicted $ΔF$ values toward or away from PREX-2/CREX measurements. Additionally, $S_V$ and the slope L are marginally correlated given the prior constraints of our Bayesian inference, allowing us to infer them separately from PREX-2/CREX data.

nucl-th↗

arXiv2025

Suppression of composition $g$-modes in chemically-equilibrating warm neutron stars

We investigate the impact of chemical equilibration and the resulting bulk viscosity on non-radial oscillation modes of warm neutron stars at temperatures up to $T\approx 5$ MeV, relevant for protoneutron stars and neutron-star post-merger remnants. In this regime, the relaxation rate of weak interactions becomes comparable to the characteristic frequencies of composition $g$-modes in the core, resulting in resonant damping. To capture this effect, we introduce the dynamical sound speed, a complex, frequency-dependent generalization of the adiabatic sound speed that encodes both the restoring force and the dissipative effects of bulk compression. Using realistic weak reaction rates and three representative equations of state, we compute the complex frequencies of composition $g$-modes with finite-temperature profiles. We find that bulk viscous damping becomes increasingly significant with temperature and can completely suppress composition $g$-modes. In contrast, the $f$-mode remains largely unaffected by bulk viscosity due to its nearly divergence-free character. Our results highlight the sensitivity of $g$-mode behavior to thermal structure, weak reaction rates, and the equation of state, and establish the dynamical sound speed as a valuable descriptor characterizing oscillation properties in dissipative neutron star matter.

astro-ph.HE↗

arXiv2025

A Hybrid SMT-NRA Solver: Integrating 2D Cell-Jump-Based Local Search, MCSAT and OpenCAD

In this paper, we propose a hybrid framework for Satisfiability Modulo the Theory of Nonlinear Real Arithmetic (SMT-NRA for short). First, we introduce a two-dimensional cell-jump move, called \emph{$2d$-cell-jump}, generalizing the key operation, cell-jump, of the local search method for SMT-NRA. Then, we propose an extended local search framework, named \emph{$2d$-LS} (following the local search framework, LS, for SMT-NRA), integrating the model constructing satisfiability calculus (MCSAT) framework to improve search efficiency. To further improve the efficiency of MCSAT, we implement a recently proposed technique called \emph{sample-cell projection operator} for MCSAT, which is well suited for CDCL-style search in the real domain and helps guide the search away from conflicting states. Finally, we present a hybrid framework for SMT-NRA integrating MCSAT, $2d$-LS and OpenCAD, to improve search efficiency through information exchange. The experimental results demonstrate improvements in local search performance, highlighting the effectiveness of the proposed methods.

cs.AI↗

arXiv2025

OSVAuto: automatic proofs about functional specifications in OS verification

We present OSVAuto for automatic proofs about functional specifications that commonly arise when verifying operating system kernels. The algorithm behind OSVAuto is designed to support natively those data types that commonly occur in OS verification, including sequences, maps, structures and enumerations. Propositions about these data are encoded into a form that is suitable for SMT solving. For quantifier instantiation, we propose an extension of recent work for automatic proofs about sequences. We evaluate the algorithm on proof obligations adapted from existing verification of the uC-OS/II kernel in Coq, demonstrating that a large number of proof obligations can be solved automatically, significantly reducing the proof effort on the functional side.

cs.SC↗

arXiv2024

GNN-MultiFix: Addressing the pitfalls for GNNs for multi-label node classification

Graph neural networks (GNNs) have emerged as powerful models for learning representations of graph data showing state of the art results in various tasks. Nevertheless, the superiority of these methods is usually supported by either evaluating their performance on small subset of benchmark datasets or by reasoning about their expressive power in terms of certain graph isomorphism tests. In this paper we critically analyse both these aspects through a transductive setting for the task of node classification. First, we delve deeper into the case of multi-label node classification which offers a more realistic scenario and has been ignored in most of the related works. Through analysing the training dynamics for GNN methods we highlight the failure of GNNs to learn over multi-label graph datasets even for the case of abundant training data. Second, we show that specifically for transductive node classification, even the most expressive GNN may fail to learn in absence of node attributes and without using explicit label information as input. To overcome this deficit, we propose a straightforward approach, referred to as GNN-MultiFix, that integrates the feature, label, and positional information of a node. GNN-MultiFix demonstrates significant improvement across all the multi-label datasets. We release our code at https://anonymous.4open.science/r/Graph-MultiFix-4121.

cs.LG↗

arXiv2024

A data-centric approach for assessing progress of Graph Neural Networks

Graph Neural Networks (GNNs) have achieved state-of-the-art results in node classification tasks. However, most improvements are in multi-class classification, with less focus on the cases where each node could have multiple labels. The first challenge in studying multi-label node classification is the scarcity of publicly available datasets. To address this, we collected and released three real-world biological datasets and developed a multi-label graph generator with tunable properties. We also argue that traditional notions of homophily and heterophily do not apply well to multi-label scenarios. Therefore, we define homophily and Cross-Class Neighborhood Similarity for multi-label classification and investigate $9$ collected multi-label datasets. Lastly, we conducted a large-scale comparative study with $8$ methods across nine datasets to evaluate current progress in multi-label node classification. We release our code at \url{https://github.com/Tianqi-py/MLGNC}.

cs.LG↗

arXiv2024

AGALE: A Graph-Aware Continual Learning Evaluation Framework

In recent years, continual learning (CL) techniques have made significant progress in learning from streaming data while preserving knowledge across sequential tasks, particularly in the realm of euclidean data. To foster fair evaluation and recognize challenges in CL settings, several evaluation frameworks have been proposed, focusing mainly on the single- and multi-label classification task on euclidean data. However, these evaluation frameworks are not trivially applicable when the input data is graph-structured, as they do not consider the topological structure inherent in graphs. Existing continual graph learning (CGL) evaluation frameworks have predominantly focussed on single-label scenarios in the node classification (NC) task. This focus has overlooked the complexities of multi-label scenarios, where nodes may exhibit affiliations with multiple labels, simultaneously participating in multiple tasks. We develop a graph-aware evaluation (\agale) framework that accommodates both single-labeled and multi-labeled nodes, addressing the limitations of previous evaluation frameworks. In particular, we define new incremental settings and devise data partitioning algorithms tailored to CGL datasets. We perform extensive experiments comparing methods from the domains of continual learning, continual graph learning, and dynamic graph learning (DGL). We theoretically analyze \agale and provide new insights about the role of homophily in the performance of compared methods. We release our framework at https://github.com/Tianqi-py/AGALE.

cs.LG↗

arXiv2024

Multi-label Node Classification On Graph-Structured Data

Graph Neural Networks (GNNs) have shown state-of-the-art improvements in node classification tasks on graphs. While these improvements have been largely demonstrated in a multi-class classification scenario, a more general and realistic scenario in which each node could have multiple labels has so far received little attention. The first challenge in conducting focused studies on multi-label node classification is the limited number of publicly available multi-label graph datasets. Therefore, as our first contribution, we collect and release three real-world biological datasets and develop a multi-label graph generator to generate datasets with tunable properties. While high label similarity (high homophily) is usually attributed to the success of GNNs, we argue that a multi-label scenario does not follow the usual semantics of homophily and heterophily so far defined for a multi-class scenario. As our second contribution, we define homophily and Cross-Class Neighborhood Similarity for the multi-label scenario and provide a thorough analyses of the collected $9$ multi-label datasets. Finally, we perform a large-scale comparative study with $8$ methods and $9$ datasets and analyse the performances of the methods to assess the progress made by current state of the art in the multi-label node classification scenario. We release our benchmark at https://github.com/Tianqi-py/MLGNC.

cs.LG↗

arXiv2024

Exploring Radial Oscillations in Slow Stable and Hybrid Neutron Stars

In the era of gravitational wave astronomy, radial oscillations hold significant potential for not only uncovering the microphysics behind the internal structure but also investigating the stability of neutron stars (NSs). We start by constructing families of static NSs following nucleonic, quarkyonic, and hybrid equations of state and then subject them to radial perturbations in order to explore the stability of these stars. Unlike other literature where the fluid elements are assumed to be in chemical equilibrium, we consider the out-of-equilibrium effects on the chemical composition of fluid elements for the calculation of radial modes. Taking these considerations into account, we observe that the sound speed ($c^2_s$) and adiabatic index ($γ$) avoid singularities and discontinuities over the equilibrium case. We elucidate the response of the fundamental radial modes by examining the out-of-equilibrium matter distribution scenario, offering insights into its dynamic variations. We also demonstrate that this approach extends the stable branches of stellar models, enabling stars to sustain stable higher-order mass doublets, shedding some light on observation and existence of PSR J0740+6620.

nucl-th↗

arXiv2023

Radial Oscillations of Dark Matter admixed Neutron Stars

Within the relativistic mean-field model, we investigate the properties of dark matter (DM) admixed neutron stars, considering non-rotating objects made of isotropic matter. We adopt the IOPB-I hadronic equation of state (EOS) by assuming that the fermionic DM within super-symmetric models has already been accreted inside the neutron star (NS). The impact of DM on the mass-radius relationships and the radial oscillations of pulsating DM admixed neutron stars (with and without the crust) are explored. It is observed that the presence of DM softens the EOS, which in turn lowers the maximum mass and its corresponding radius. Moreover, adding DM results in higher frequencies of pulsating objects and hence we show the linearity of fundamental mode frequency of canonical NS with DM Fermi momentum. We also investigate the profile of eigenfunctions solving the Sturm-Liouville boundary value problem, and verify its validity. Further, we study the stability of NSs considering the fundamental mode frequency variation with the mass of the star, and verify the stability criterion $\partial M/\partialρ_c > 0$. Finally, the effect of the crust on the large frequency separation for different DM Fermi momenta is shown as well.

nucl-th↗

arXiv2023

Framework for phase transitions between the Maxwell and Gibbs constructions

By taking the nucleon-to-quark phase transition within a neutron star as an example, we present a thermodynamically consistent method to calculate the equation of state of ambient matter so that transitions that are intermediate to those of the familiar Maxwell and Gibbs constructions can be described. This method does not address the poorly known surface tension between the two phases microscopically (as, for example, in the calculation of the core pasta phases via the Wigner-Seitz approximation) but instead combines the local and global charge neutrality conditions characteristic of the Maxwell and Gibbs constructions, respectively. Overall charge neutrality is achieved by dividing the leptons to those that obey local charge neutrality (Maxwell) and those that maintain global charge neutrality (Gibbs). The equation of state is obtained by using equilibrium constraints derived from minimizing the total energy density. The results of this minimization are then used to calculate neutron star mass-radius curves, tidal deformabilities, equilibrium and adiabatic sound speeds, and nonradial $g$-mode oscillation frequencies for several intermediate constructions. Various quantities of interest transform smoothly from their Gibbs structures to those of Maxwell as the local-to-total electron ratio $η$, introduced to mimic the hadron-to-quark interface tension from $0$ (Gibbs) to $\infty$ (Maxwell), is raised from $0$ to $1$. A notable exception is the $g$-mode frequency for the specific case of $η=1$ for which a gap appears between the quark and hadronic branches.

nucl-th↗

arXiv2023

Local Search for Solving Satisfiability of Polynomial Formulas

Satisfiability Modulo the Theory of Nonlinear Real Arithmetic, SMT(NRA) for short, concerns the satisfiability of polynomial formulas, which are quantifier-free Boolean combinations of polynomial equations and inequalities with integer coefficients and real variables. In this paper, we propose a local search algorithm for a special subclass of SMT(NRA), where all constraints are strict inequalities. An important fact is that, given a polynomial formula with $n$ variables, the zero level set of the polynomials in the formula decomposes the $n$-dimensional real space into finitely many components (cells) and every polynomial has constant sign in each cell. The key point of our algorithm is a new operation based on real root isolation, called cell-jump, which updates the current assignment along a given direction such that the assignment can `jump' from one cell to another. One cell-jump may adjust the values of several variables while traditional local search operations, such as flip for SAT and critical move for SMT(LIA), only change that of one variable. We also design a two-level operation selection to balance the success rate and efficiency. Furthermore, our algorithm can be easily generalized to a wider subclass of SMT(NRA) where polynomial equations linear with respect to some variable are allowed. Experiments show the algorithm is competitive with state-of-the-art SMT solvers, and performs particularly well on those formulas with high-degree polynomials.

cs.LO↗

arXiv2023

Isolating Bounded and Unbounded Real Roots of a Mixed Trigonometric-Polynomial

Mixed trigonometric-polynomials (MTPs) are functions of the form $f(x,\sin{x}, \cos{x})$ with $f\in\mathbb{Q}[x_1,x_2,x_3]$. In this paper, an algorithm ``isolating" all the real roots of an MTP is provided and implemented. It automatically divides the real roots into two parts: one consists of finitely many ``bounded" roots in an interval $[μ_-,μ_+]$ while the other consists of probably countably many ``periodic" roots in $\mathbb{R}\backslash[μ_-,μ_+]$. For bounded roots, the algorithm returns isolating intervals and corresponding multiplicities while for periodic roots, it returns finitely many mutually disjoint small intervals $I_i\subset[-π,π]$, integers $c_i>0$ and multisets of root multiplicity $\{m_{j,i}\}_{j=1}^{c_i}$ such that any periodic root $t>μ_+$ is in the set $(\sqcup_i\cup_{k\in\mathbb{N}}(I_i+2kπ))$ and any interval $I_i+2kπ\subset(μ_+,\infty)$ contains exactly $c_i$ periodic roots with multiplicities $m_{1,i},...,m_{c_i,i}$, respectively. The effectiveness and efficiency of the algorithm are shown by experiments. %In particular, our results indicate that the ``distributions" of the roots of an MTP in the ``periods" $(-π,π]+2kπ$ sufficiently far from $0$ share a same pattern. Besides, the method used to isolate the roots in $[μ_-,μ_+]$ is applicable to any other bounded interval as well. The algorithm takes advantages of the weak Fourier sequence technique and deals with the intervals period-by-period without scaling the coordinate so to keep the length of the sequence short. The new approaches can easily be modified to decide whether there is any root, or whether there are infinitely many roots in unbounded intervals of the form $(-\infty,a)$ or $(a,\infty)$ with $a\in\mathbb{Q}$.

cs.SC↗

arXiv2022

Radial oscillations in neutron stars from unified hadronic and quarkyonic equation of states

We study radial oscillations in non-rotating neutron stars by considering the unified equation of states (EoSs), which support the 2 M$_\odot$ star criterion. We solve the Sturm-Liouville problem to compute 20 lowest radial oscillation modes and their eigenfunctions for neutron star modelled with eight selected unified EoSs from distinct Skyrme-Hartree Fock, Relativistic Mean-Field and quarkyonic models. We compare the behavior of the computed eigenfrequency for NS modelled with hadronic to that with quarkyonic EoSs while varying central densities. The lowest order, f-mode frequency varies substantially between the two classes of the of EoS at 1.4 M$_\odot$ but vanishes at their respective maximum masses, consistent with the stability criterion $\partial M/\partialρ_c > 0$. Moreover, we also computed large frequency separation and discovered that higher-order mode frequencies are significantly reduced by incorporating crust in the EoS.

nucl-th↗

arXiv2022

Impact of the equation of state on $f$- and $p$- mode oscillations of neutron stars

We investigate the impact of the neutron-star matter equation of state on the $f$- and $p_1$-mode oscillations of neutron stars obtained within the Cowling approximation and linearized general relativity. The $f$- and $p_1$-mode oscillation frequencies, and their damping times are calculated using representative sets of Skyrme Hartree-Fock and relativistic mean-field models, all of which reproduce nuclear systematics and support $2M_\odot$ neutron stars. Our study shows strong correlations between the frequencies of $f$- and $p_1$-modes and their damping times with the pressure of $β$-equilibrated matter at densities equal to or slightly higher than the nuclear saturation density $ρ_0$. Such correlations are found to be almost independent of the composition of the stars. The frequency of the $p_1$-mode of $1.4M_\odot$ star is strongly correlated with the slope of the symmetry energy $L_0$ and $β$-equilibrated pressure at density $ρ_0$. Compared to GR calculations, the error in the Cowling approximation for the $f$-mode is about 30\% for neutron stars of low mass, whereas it decreases with increasing mass. The accuracy of the $p_1$-mode is better than 15\% for neutron stars of maximum mass, and improves for lower masses and higher number of radial nodes.

nucl-th↗

arXiv2022

ECG Heartbeat classification using deep transfer learning with Convolutional Neural Network and STFT technique

Electrocardiogram (ECG) is a simple non-invasive measure to identify heart-related issues such as irregular heartbeats known as arrhythmias. While artificial intelligence and machine learning is being utilized in a wide range of healthcare related applications and datasets, many arrhythmia classifiers using deep learning methods have been proposed in recent years. However, sizes of the available datasets from which to build and assess machine learning models is often very small and the lack of well-annotated public ECG datasets is evident. In this paper, we propose a deep transfer learning framework that is aimed to perform classification on a small size training dataset. The proposed method is to fine-tune a general-purpose image classifier ResNet-18 with MIT-BIH arrhythmia dataset in accordance with the AAMI EC57 standard. This paper further investigates many existing deep learning models that have failed to avoid data leakage against AAMI recommendations. We compare how different data split methods impact the model performance. This comparison study implies that future work in arrhythmia classification should follow the AAMI EC57 standard when using any including MIT-BIH arrhythmia dataset.

cs.LG↗

arXiv2022

Universal Relations for Neutron Star F-Mode and G-Mode Oscillations

Among the various oscillation modes of neutron stars, f- and g- modes are the most likely to be ultimately observed in binary neutron star mergers. The f-mode is known to correlate in normal neutron stars with their tidal deformability, moment of inertia and quadrupole moment. Using a piecewise polytropic parameterization scheme to model the uncertain hadronic high-density EOS and a constant sound-speed scheme to model pure quark matter, we refine this correlation and show that these universal relations also apply to both self-bound stars and hybrid stars containing phase transitions. We identify a novel 1-node branch of the f-mode that occurs in low-mass hybrid stars in a narrow mass range just beyond the critical mass necessary for a phase transition to appear. This 1-node branch shows the largest, but still small, deviations from the universal correlation we have found. The g-mode frequency only exists in matter with a non-barotropic equation of state involving temperature, chemical potential or composition, or a phase transition in barotropic matter. The g-mode therefore could serve as a probe for studying phase transitions in hybrid stars. In contrast with the f-mode, discontinuity g-mode frequencies depend strongly on properties of the transition (the density and the magnitude of the discontinuity) at the transition. Imposing causality and maximum mass constraints, the g-mode frequency in hybrid stars is found to have an upper bound of about 1.25 kHz. However, if the sound speed c_s in the inner core at densities above the phase transition density is restricted to c_s^2 < c^2/3, the g-mode frequencies can only reach about 0.8 kHz, which are significantly lower than f-mode frequencies, 1.3-2.8 kHz. Also, g-mode gravitational wave damping times are extremely long, >10^4 s (10^2 s) in the inner core with c_s^2< c^{2/3} (c^2), in comparison with the f-mode damping time, 0.1-1 s.

astro-ph.HE↗

arXiv2022

Square-free Strong Triangular Decomposition of Zero-dimensional Polynomial Systems

Triangular decomposition with different properties has been used for various types of problem solving, e.g. geometry theorem proving, real solution isolation of zero-dimensional polynomial systems, etc. In this paper, the concepts of strong chain and square-free strong triangular decomposition (SFSTD) of zero-dimensional polynomial systems are defined. Because of its good properties, SFSTD may be a key way to many problems related to zero-dimensional polynomial systems, such as real solution isolation and computing radicals of zero-dimensional ideals. Inspired by the work of Wang and of Dong and Mou, we propose an algorithm for computing SFSTD based on Gröbner bases computation. The novelty of the algorithm is that we make use of saturated ideals and separant to ensure that the zero sets of any two strong chains have no intersection and every strong chain is square-free, respectively. On one hand, we prove that the arithmetic complexity of the new algorithm can be single exponential in the square of the number of variables, which seems to be among the rare complexity analysis results for triangular-decomposition methods. On the other hand, we show experimentally that, on a large number of examples in the literature, the new algorithm is far more efficient than a popular triangular-decomposition method based on pseudo-division. Furthermore, it is also shown that, on those examples, the methods based on SFSTD for real solution isolation and for computing radicals of zero-dimensional ideals are very efficient.

cs.SC↗