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Yanxin Liu

Publications and source records attributed to Yanxin Liu.

14 recordsLinked to original sources

Preservation of log-concavity under Hadamard products

For a nonzero real polynomial $p$, let $\W(p)$ denote the numerator of its ordinary generating function. We prove that if the coefficients of both $\W(p)$ and $\W(q)$ are nonnegative and log-concave with no internal zeros, then so are the coefficients of $\W(pq)$. This provides an affirmative answer to a question of Br\"and\'en, Ferroni, and Jochemko. As applications, we derive corresponding results for finite products and for Cartesian products of lattice polytopes, answering a question of Ferroni and Higashitani.

math.CO

Pfaffian--Toeplitz identities, Schur positivity, and the $q$-log-convexity of Baxter polynomials

We use the Pfaffian minor summation formula together with Jacobi--Trudi Toeplitz matrices to derive Pfaffian expansions in skew Schur functions. This yields explicit Schur expansions for several generating functions involving products of skew Schur functions. In particular, using sparse skew-symmetric matrices, we provide a Pfaffian proof of a Schur-positive identity arising in the study of the $q$-log-convexity of the Narayana polynomials. As the main application, we prove that the Baxter polynomials form a $q$-log-convex sequence. We further show that the Baxter transformation defined by the refined Baxter numbers preserves log-convexity. Finally, by realizing the $q$-refined Baxter numbers as principal specializations of rectangular Schur functions, we prove that the array of $q$-refined Baxter numbers is $q$-log-concave both along each row and along each column. Both $q$-log-concavity results extend naturally to the $q$-analogues of the $d$-Hoggatt numbers.

math.CO

Total positivity of transformation matrices for uniform subdivisions

The transformation of the $h$-vector of a finite simplicial complex under an $\mathcal{F}$-uniform subdivision is encoded by a transformation matrix. Mu and Welker conjectured that the transformation matrix of the barycentric subdivision is totally positive. In this paper, we give a new combinatorial proof of this conjecture. We also prove the total positivity of the transformation matrix of the interval subdivision. In addition, we establish a sufficient condition for the transformation matrix of a uniform subdivision to be totally positive of order $2$ (TP$_2$), thereby partially answering a question of Mu and Welker. As an application, we show that the transformation matrix of the $r$-colored barycentric subdivision is TP$_2$.

math.CO

Exceptional-point-constrained locking of boundary-sensitive topological transitions in chiral non-Hermitian SSH-type lattices

Topological transitions in non-Hermitian systems are generally boundary sensitive: a point-gap winding transition under periodic boundary condition (PBC) and a non-Bloch bulk real-line-gap transition under open boundary condition (OBC) at $\mathrm{Re}(E)=0$ are governed by different spectra and therefore need not coincide. Here we show, for a class of chiral non-Hermitian Su--Schrieffer--Heeger (SSH)-type lattices, that these two criticalities can be locked by an exceptional-point-constrained (EP-constrained) parameter evolution. The key requirement is not the occurrence of isolated exceptional points, but the persistence of a zero-energy Bloch degeneracy along the entire sweep, which is generically exceptional in the non-Hermitian regime. In an analytically tractable limit of an extended non-Hermitian SSH chain, the EP-constrained manifolds and both transition boundaries are obtained in closed form, making the locking explicit. Away from this limit, numerical generalized-Brillouin-zone (GBZ) calculations confirm the correspondence for representative constrained sweeps, whereas unconstrained paths show that isolated exceptional points or Hermitian degeneracies do not enforce locking. We further verify the mechanism in a spinful four-band extension with branch-resolved GBZs, including strongly branch-imbalanced regimes. These results establish a path-dependent diagnostic principle: along EP-constrained sweeps in this SSH-type class, changes in PBC point-gap winding can indicate OBC non-Bloch bulk real-line-gap transitions and the corresponding changes in zero-energy boundary modes.

physics.optics

The Long Shadow of Pandemic: Understanding the lingering effects of cause-specific mortality shocks

In the aftermath of the COVID-19 pandemic, empirical data have revealed that large-scale health crises not only cause immediate disruptions in mortality dynamics but also have persistent effects that may last for several years. Existing mortality models largely assume that mortality shocks are transitory and overlook how their effects can be long-lasting and heterogeneous across age groups and causes of death. In response to this limitation, we propose a novel stochastic mortality model that captures age- and cause-specific long-lasting effects of mortality jumps through a gamma-density-like decay function, estimated via a customized conditional maximum likelihood algorithm. Applying the model to recent U.S. mortality data, we reveal divergent persistence patterns across demographic groups and provide key insights into the tail risk profiles of life insurance and annuity products. Our scenario-based analyses further show that neglecting persistent shock effects can lead to suboptimal hedging, while the proposed model enables what-if testing to analyze such effects under potential future health crises.

stat.AP

BPE: Behavioral Profiling Ensemble

In the field of machine learning, ensemble learning is widely recognized as a pivotal strategy for pushing the boundaries of predictive performance. Traditional static ensemble methods typically assign weights by treating each base learner as a whole, thereby overlooking that individual models exhibit varying competence across different regions of the instance space. Dynamic Ensemble Selection (DES) was introduced to address this limitation. However, both static and dynamic approaches predominantly rely on inter-model differences as the basis for integration; this inter-model perspective neglects models' intrinsic characteristics and often requires heavy reliance on reference sets for competence estimation. We propose the Behavioral Profiling Ensemble (BPE) framework, which introduces a model-centric integration paradigm. Unlike traditional methods, BPE constructs an intrinsic behavioral profile $\mathcal{P}_k$ for each model and derives aggregation weights from the deviation between a model's response to a test instance and its established profile; in this work, we instantiate $\mathcal{P}_k$ with entropy-based summary statistics (e.g., mean and variance). Extensive experiments on 42 real-world datasets show that BPE-derived algorithms outperform state-of-the-art DES baselines, increasing predictive accuracy while reducing computational and storage overhead.

cs.LG

Accept-Reject Lasso

The Lasso method is known to exhibit instability in the presence of highly correlated features, often leading to an arbitrary selection of predictors. This issue manifests itself in two primary error types: the erroneous omission of features that lack a true substitutable relationship (falsely redundant features) and the inclusion of features with a true substitutable relationship (truly redundant features). Although most existing methods address only one of these challenges, we introduce the Accept-Reject Lasso (ARL), a novel approach that resolves this dilemma. ARL operationalizes an Accept-Reject framework through a fine-grained analysis of feature selection across data subsets. This framework is designed to partition the output of an ensemble method into beneficial and detrimental components through fine-grained analysis. The fundamental challenge for Lasso is that inter-variable correlation obscures the true sources of information. ARL tackles this by first using clustering to identify distinct subset structures within the data. It then analyzes Lasso's behavior across these subsets to differentiate between true and spurious correlations. For truly correlated features, which induce multicollinearity, ARL tends to select a single representative feature and reject the rest to ensure model stability. Conversely, for features linked by spurious correlations, which may vanish in certain subsets, ARL accepts those that Lasso might have incorrectly omitted. The distinct patterns arising from true versus spurious correlations create a divisible separation. By setting an appropriate threshold, our framework can effectively distinguish between these two phenomena, thereby maximizing the inclusion of informative variables while minimizing the introduction of detrimental ones. We illustrate the efficacy of the proposed method through extensive simulation and real-data experiments.

stat.ME

Relative Overfitting and Accept-Reject Framework

The scaling of Large Language Models (LLMs) currently faces significant challenges. Model assembly is widely considered a promising solution to break through these performance bottlenecks. However, current ensembling methods are primarily guided by the statistical expectation that combining multiple models over large samples will lead to performance gains. We propose an ensemble framework that transitions from such stochastic, sample-dependent methods to a regular, controllable approach based on fine-grained model segmentation. This regularity governs how models are segmented to ensure performance improvement, how the magnitude of this improvement varies with model selection, and what factors determine its theoretical maximum. To formalize this pattern, we introduce the concept of'relative overfitting,' which is derived from the performance discrepancies between constituent models and builds a bridge between ensemble outcomes and the inherent attributes of these models. We detail the patterns of this framework within the domain of NLP and briefly describe its extensibility to other fields, such as computer vision (CV) and AI for science. Our approach was validated using both custom-built and pre-trained mainstream models across diverse benchmarks, including language modeling, long-context tasks, and question-answering (QA). The results indicate that the ensemble rules we proposed are generally effective and that we provide a rigorous proof of these rules in certain experimental scenarios. The proposed framework offers a new perspective for understanding ensemble theory and provides a systematic approach to addressing the performance bottlenecks of LLMs.

cs.LG

Magnetodynamics of short nanoparticle chains

In recent years, there has been increasing interest in the understanding and application of nanoparticle assemblies driven by external fields. Although these systems can exhibit marked transitions in behavior compared to non-interacting counterparts, it has often proven challenging to connect their dynamics with underlying physical mechanisms or even to verifiably establish their structure under realistic experimental conditions. We have studied colloidal iron oxide nanoparticles that assemble into ordered, few-particle linear chains under the influence of oscillating and pulsed magnetic fields. In this work, our goal has been to answer the following question: by what physical mechanisms does the magnetic switching of a linear chain evolve from the switching of its constituent particles? Cryo-TEM has been used to flash freeze and image the structures formed by oscillatory drive fields, and magnetic relaxometry has been used to extract the multiple time constants associated with magnetic switching of the short chains. Armed with the physical structure from microscopy and the field-dependent switching times from magnetic measurements, we have conducted extensive micromagnetic simulations, revealing probable physical mechanisms for each time constant regime spanning ~1 microsecond to 1 s in time. These types of magnetic nanomaterials have great potential for biomedical technologies, particularly magnetic particle imaging and hyperthermia, and rigorous elucidation of their physics will hasten their optimization.

cond-mat.mtrl-sci

Automated Evaluation of Large Vision-Language Models on Self-driving Corner Cases

Large Vision-Language Models (LVLMs) have received widespread attention for advancing the interpretable self-driving. Existing evaluations of LVLMs primarily focus on multi-faceted capabilities in natural circumstances, lacking automated and quantifiable assessment for self-driving, let alone the severe road corner cases. In this work, we propose CODA-LM, the very first benchmark for the automatic evaluation of LVLMs for self-driving corner cases. We adopt a hierarchical data structure and prompt powerful LVLMs to analyze complex driving scenes and generate high-quality pre-annotations for the human annotators, while for LVLM evaluation, we show that using the text-only large language models (LLMs) as judges reveals even better alignment with human preferences than the LVLM judges. Moreover, with our CODA-LM, we build CODA-VLM, a new driving LVLM surpassing all open-sourced counterparts on CODA-LM. Our CODA-VLM performs comparably with GPT-4V, even surpassing GPT-4V by +21.42% on the regional perception task. We hope CODA-LM can become the catalyst to promote interpretable self-driving empowered by LVLMs.

cs.CV

Realization of strong coupling between deterministic single-atom arrays and a high-finesse miniature optical cavity

We experimentally demonstrate strong coupling between a one-dimensional (1D) single-atom array and a high-finesse miniature cavity. The atom array is obtained by loading single atoms into a 1D optical tweezer array with dimensions of 1$\times$11. Therefore, a deterministic number of atoms is obtained, and the atom number is determined by imaging the atom array on a CCD camera in real time. By precisely controlling the position and spacing of the atom array in the high finesse Fabry--Perot cavity, all the atoms in the array are strongly coupled to the cavity simultaneously. The vacuum Rabi splitting spectra are discriminated for deterministic atom numbers from 1 to 8, and the $\sqrt{N}$ dependence of the collective enhancement of the coupling strength on atom number $N$ is validated at the single-atom level.

quant-ph

Weighted Dyck paths with special restrictions on the levels of valleys

This paper concentrates on the set $\mathcal{V}_n$ of weighted Dyck paths of length $2n$ with special restrictions on the level of valleys. We first give its explicit formula of the counting generating function in terms of certain weight functions. When the weight functions are specialized, some connections are builded between $\mathcal{V}_n$ and other classical combinatorial structures such as $(a,b)$-Motzkin paths, $q$-Schröder paths, Delannoy paths and complete $k$-ary trees. Some bijections are also established between these settings and $\mathcal{V}_n$ subject to certain special weight functions.

math.CO

Triply magic conditions for microwave transitions of optically trapped alkali-metal atoms

We report the finding of "triply magic" conditions (the doubly magic frequency-intensity conditions of an optical dipole trap plus the magic magnetic field) for the microwave transitions of optically trapped alkali-metal atoms. The differential light shift (DLS) induced by a degenerate two-photon process is adopted to compensate a DLS associated with the one-photon process. Thus, doubly magic conditions for the intensity and frequency of the optical trap beam can be found. Moreover, the DLS decouples from the magnetic field in a linearly polarized optical dipole trap, so that the magic condition of the magnetic field can be applied independently. Therefore, the "triply magic" conditions can be realized simultaneously. We also experimentally demonstrate the doubly magic frequency-intensity conditions as well as the independence of the magnetic field. When the triply magic conditions are fulfilled, the inhomogeneous and homogeneous decoherences for the optically trapped atom will be dramatically suppressed, and the coherence time can be extended significantly.

quant-ph

Single Molecule FRET Reveals Pore Size and Opening Mechanism of MscL

The mechanosensitive channel of large conductance, which serves as a model system for mechanosensitive channels, has previously been crystallized in the closed form, but not in the open form. Ensemble measurements and electrophysiological sieving experiments show that the open-diameter of the channel pore is >25Å, but the exact size and whether the conformational change follows a helix-tilt or barrel-stave model are unclear. Here we report measurements of the distance changes on liposome-reconstituted MscL transmembrane α-helices, using a "virtual sorting" single-molecule fluorescence energy transfer. We observed directly that the channel opens via the helix-tilt model and the open pore reaches 2.8 nm in diameter. In addition, based on the measurements, we developed a molecular dynamics model of the channel structure in the open state which confirms our direct observations.

q-bio.BM