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The 3-hinge gyrus (3HG) is a newly defined folding pattern, which is the conjunction of gyri coming from three directions in cortical folding. Many studies demonstrated that 3HGs can be reliable nodes when constructing brain networks or connectome since they simultaneously possess commonality and individuality across different individual brains and populations. However, 3HGs are identified and validated within individual spaces, making it difficult to directly serve as the brain network nodes due to the absence of cross-subject correspondence. The 3HG correspondences represent the intrinsic regulation of brain organizational architecture, traditional image-based registration methods tend to fail because individual anatomical properties need to be fully respected. To address this challenge, we propose a novel self-supervised framework for anatomical feature embedding of the 3HGs to build the correspondences among different brains. The core component of this framework is to construct a structural similarity-enhanced multi-hop feature encoding strategy based on the recently developed Kolmogorov-Arnold network (KAN) for anatomical feature embedding. Extensive experiments suggest that our approach can effectively establish robust cross-subject correspondences when no one-to-one mapping exists.

A desarrangement is a permutation whose first ascent is even. Desarrangements were introduced in the 1980s by Jacques D\'{e}sarm\'{e}nien, who proved that they are in bijection with derangements. We revisit the study of desarrangements, focusing on two themes: the refined enumeration of desarrangements with respect to permutation statistics, and pattern avoidance in desarrangements. Our main results include generating function formulas for counting desarrangements by the number of descents, peaks, valleys, double ascents, and double descents, as well as a complete enumeration of desarrangements avoiding a prescribed set of length 3 patterns. We find new interpretations of the Catalan, Fine, Jacobsthal, and Fibonacci numbers in terms of pattern-avoiding desarrangements., Comment: 28 pages

This comprehensive study evaluates the performance of OpenAI's o1-preview large language model across a diverse array of complex reasoning tasks, spanning multiple domains, including computer science, mathematics, natural sciences, medicine, linguistics, and social sciences. Through rigorous testing, o1-preview demonstrated remarkable capabilities, often achieving human-level or superior performance in areas ranging from coding challenges to scientific reasoning and from language processing to creative problem-solving. Key findings include: -83.3% success rate in solving complex competitive programming problems, surpassing many human experts. -Superior ability in generating coherent and accurate radiology reports, outperforming other evaluated models. -100% accuracy in high school-level mathematical reasoning tasks, providing detailed step-by-step solutions. -Advanced natural language inference capabilities across general and specialized domains like medicine. -Impressive performance in chip design tasks, outperforming specialized models in areas such as EDA script generation and bug analysis. -Remarkable proficiency in anthropology and geology, demonstrating deep understanding and reasoning in these specialized fields. -Strong capabilities in quantitative investing. O1 has comprehensive financial knowledge and statistical modeling skills. -Effective performance in social media analysis, including sentiment analysis and emotion recognition. The model excelled particularly in tasks requiring intricate reasoning and knowledge integration across various fields. While some limitations were observed, including occasional errors on simpler problems and challenges with certain highly specialized concepts, the overall results indicate significant progress towards artificial general intelligence.

Pre-trained large language models(LLMs) have attracted increasing attention in biomedical domains due to their success in natural language processing. However, the complex traits and heterogeneity of multi-sources genomics data pose significant challenges when adapting these models to the bioinformatics and biomedical field. To address these challenges, we present GP-GPT, the first specialized large language model for genetic-phenotype knowledge representation and genomics relation analysis. Our model is fine-tuned in two stages on a comprehensive corpus composed of over 3,000,000 terms in genomics, proteomics, and medical genetics, derived from multiple large-scale validated datasets and scientific publications. GP-GPT demonstrates proficiency in accurately retrieving medical genetics information and performing common genomics analysis tasks, such as genomics information retrieval and relationship determination. Comparative experiments across domain-specific tasks reveal that GP-GPT outperforms state-of-the-art LLMs, including Llama2, Llama3 and GPT-4. These results highlight GP-GPT's potential to enhance genetic disease relation research and facilitate accurate and efficient analysis in the fields of genomics and medical genetics. Our investigation demonstrated the subtle changes of bio-factor entities' representations in the GP-GPT, which suggested the opportunities for the application of LLMs to advancing gene-phenotype research.

Air-lasing from single ionized N$_2^+$ molecules induced by laser filamentation in air has been intensively investigated and the mechanisms responsible for lasing are currently highly debated. We use ultrafast nitrogen K-edge spectroscopy to follow the strong field ionization and fragmentation dynamics of N$_2$ upon interaction with an ultrashort 800 nm laser pulse. Using probe pulses generated by extreme high-order harmonic generation, we observe transitions indicative of the formation of the electronic ground X$^2\Sigma_{g}^{+}$, first excited A$^2\Pi_u$ and second excited B$^2\Sigma^+_u$ states of N$_2^+$ on femtosecond time scales, from which we can quantitatively determine the time-dependent electronic state population distribution dynamics of N$_2^+$. Our results show a remarkably low population of the A$^2\Pi_u$ state, and nearly equal populations of the X$^2\Sigma_{g}^{+}$ and B$^2\Sigma^+_u$ states. In addition, we observe fragmentation of N$_2^+$ into N and N$^+$ on a time scale of several tens of picoseconds that we assign to significant collisional dynamics in the plasma, resulting in dissociative excitation of N$_2^+$.

A descent $k$ of a permutation $\pi=\pi_{1}\pi_{2}\dots\pi_{n}$ is called a big descent if $\pi_{k}>\pi_{k+1}+1$; denote the number of big descents of $\pi$ by $\operatorname{bdes}(\pi)$. We study the distribution of the $\operatorname{bdes}$ statistic over permutations avoiding prescribed sets of length-three patterns. Specifically, we classify all pattern sets $\Pi\subseteq\mathfrak{S}_{3}$ of size 1 and 2 into $\operatorname{bdes}$-Wilf equivalence classes, and we derive a formula for the distribution of big descents for each of these classes. Our methods include generating function techniques along with various bijections involving objects such as Dyck paths and binary words. Several future directions of research are proposed, including conjectures concerning real-rootedness, log-concavity, and Schur positivity., Comment: 36 pages

Expert-designed close-ended benchmarks are indispensable in assessing the knowledge capacity of large language models (LLMs). Despite their widespread use, concerns have mounted regarding their reliability due to limited test scenarios and an unavoidable risk of data contamination. To rectify this, we present PertEval, a toolkit devised for in-depth probing of LLMs' knowledge capacity through \textbf{knowledge-invariant perturbations}. These perturbations employ human-like restatement techniques to generate on-the-fly test samples from static benchmarks, meticulously retaining knowledge-critical content while altering irrelevant details. Our toolkit further includes a suite of \textbf{response consistency analyses} that compare performance on raw vs. perturbed test sets to precisely assess LLMs' genuine knowledge capacity. Six representative LLMs are re-evaluated using PertEval. Results reveal significantly inflated performance of the LLMs on raw benchmarks, including an absolute 25.8% overestimation for GPT-4. Additionally, through a nuanced response pattern analysis, we discover that PertEval retains LLMs' uncertainty to specious knowledge, and reveals their potential rote memorization to correct options which leads to overestimated performance. We also find that the detailed response consistency analyses by PertEval could illuminate various weaknesses in existing LLMs' knowledge mastery and guide the development of refinement. Our findings provide insights for advancing more robust and genuinely knowledgeable LLMs. Our code is available at \url{https://github.com/aigc-apps/PertEval}., Comment: Accepted by NeurIPS '24 D&B Spotlight; 28 pages, 15 figures, 14 tables

Background: Segmentation of organs and structures in abdominal MRI is useful for many clinical applications, such as disease diagnosis and radiotherapy. Current approaches have focused on delineating a limited set of abdominal structures (13 types). To date, there is no publicly available abdominal MRI dataset with voxel-level annotations of multiple organs and structures. Consequently, a segmentation tool for multi-structure segmentation is also unavailable. Methods: We curated a T1-weighted abdominal MRI dataset consisting of 195 patients who underwent imaging at National Institutes of Health (NIH) Clinical Center. The dataset comprises of axial pre-contrast T1, arterial, venous, and delayed phases for each patient, thereby amounting to a total of 780 series (69,248 2D slices). Each series contains voxel-level annotations of 62 abdominal organs and structures. A 3D nnUNet model, dubbed as MRISegmentator-Abdomen (MRISegmentator in short), was trained on this dataset, and evaluation was conducted on an internal test set and two large external datasets: AMOS22 and Duke Liver. The predicted segmentations were compared against the ground-truth using the Dice Similarity Coefficient (DSC) and Normalized Surface Distance (NSD). Findings: MRISegmentator achieved an average DSC of 0.861$\pm$0.170 and a NSD of 0.924$\pm$0.163 in the internal test set. On the AMOS22 dataset, MRISegmentator attained an average DSC of 0.829$\pm$0.133 and a NSD of 0.908$\pm$0.067. For the Duke Liver dataset, an average DSC of 0.933$\pm$0.015 and a NSD of 0.929$\pm$0.021 was obtained. Interpretation: The proposed MRISegmentator provides automatic, accurate, and robust segmentations of 62 organs and structures in T1-weighted abdominal MRI sequences. The tool has the potential to accelerate research on various clinical topics, such as abnormality detection, radiotherapy, disease classification among others., Comment: We made the segmentation model publicly available

Consider a search from the root of an ordered tree with $n$ edges to some target node at a fixed distance $\ell$ from that root. We compare the average time complexity of the breadth-first search (BFS) and depth-first search (DFS) algorithms, when the target node is selected uniformly at random among all nodes at level $\ell$ in the ordered trees with $n$ edges. Intuition suggests that BFS should have better average performance when $\ell$ is small, while DFS must have an advantage when $\ell$ is large. But where exactly is the threshold, as a function of $n$, and is it unique? We obtain explicit formulas for the expected number of steps of both BFS and DFS, by using results on the occupation measure of Brownian excursions, as well as a combinatorial proof of an identity related to lattice paths. This allows us to show that there exists a unique constant $\lambda\approx 0.789004$, such that in expectation BFS is asymptotically faster than DFS if and only if $\ell\leq \lambda\sqrt{n}$. Furthermore, we find the asymptotic average time complexity of BFS in the given setting for any class of Galton$\unicode{x2013}$Watson trees, including binary trees and ordered trees. Finally, we introduce the truncated DFS algorithm, which performs better than both BFS and DFS when $\ell$ is known in advance, and we find a formula evaluating the average time complexity of this algorithm., Comment: 32 pages

Computerized Adaptive Testing (CAT) provides an efficient and tailored method for assessing the proficiency of examinees, by dynamically adjusting test questions based on their performance. Widely adopted across diverse fields like education, healthcare, sports, and sociology, CAT has revolutionized testing practices. While traditional methods rely on psychometrics and statistics, the increasing complexity of large-scale testing has spurred the integration of machine learning techniques. This paper aims to provide a machine learning-focused survey on CAT, presenting a fresh perspective on this adaptive testing method. By examining the test question selection algorithm at the heart of CAT's adaptivity, we shed light on its functionality. Furthermore, we delve into cognitive diagnosis models, question bank construction, and test control within CAT, exploring how machine learning can optimize these components. Through an analysis of current methods, strengths, limitations, and challenges, we strive to develop robust, fair, and efficient CAT systems. By bridging psychometric-driven CAT research with machine learning, this survey advocates for a more inclusive and interdisciplinary approach to the future of adaptive testing.

Learning from point sets is an essential component in many computer vision and machine learning applications. Native, unordered, and permutation invariant set structure space is challenging to model, particularly for point set classification under spatial deformations. Here we propose a framework for classifying point sets experiencing certain types of spatial deformations, with a particular emphasis on datasets featuring affine deformations. Our approach employs the Linear Optimal Transport (LOT) transform to obtain a linear embedding of set-structured data. Utilizing the mathematical properties of the LOT transform, we demonstrate its capacity to accommodate variations in point sets by constructing a convex data space, effectively simplifying point set classification problems. Our method, which employs a nearest-subspace algorithm in the LOT space, demonstrates label efficiency, non-iterative behavior, and requires no hyper-parameter tuning. It achieves competitive accuracies compared to state-of-the-art methods across various point set classification tasks. Furthermore, our approach exhibits robustness in out-of-distribution scenarios where training and test distributions vary in terms of deformation magnitudes.

For any finite partially ordered set $P$, the $P$-Eulerian polynomial is the generating function for the descent number over the set of linear extensions of $P$, and is closely related to the order polynomial of $P$ arising in the theory of $P$-partitions. Here we study the $P$-Eulerian polynomial where $P$ is a naturally labeled zig-zag poset; we call these zig-zag Eulerian polynomials. A result of Br\"and\'en implies that these polynomials are gamma-nonnegative, and hence their coefficients are symmetric and unimodal. The zig-zag Eulerian polynomials and the associated order polynomials have appeared fleetingly in the literature in a wide variety of contexts$\unicode{x2014}$e.g., in the study of polytopes, magic labelings of graphs, and Kekul\'e structures$\unicode{x2014}$but they do not appear to have been studied systematically. In this paper, we use a "relaxed" version of $P$-partitions to both survey and unify results. Our technique shows that the zig-zag Eulerian polynomials also capture the distribution of "big returns" over the set of (up-down) alternating permutations, as first observed by Coons and Sullivant. We develop recurrences for refined versions of the relevant generating functions, which evoke similarities to recurrences for the classical Eulerian polynomials. We conclude with a literature survey and open questions., Comment: 33 pages

As a new emerging and promising type of generative models, diffusion models have proven to outperform Generative Adversarial Networks (GANs) in multiple tasks, including image synthesis. In this work, we explore semantic image synthesis for abdominal CT using conditional diffusion models, which can be used for downstream applications such as data augmentation. We systematically evaluated the performance of three diffusion models, as well as to other state-of-the-art GAN-based approaches, and studied the different conditioning scenarios for the semantic mask. Experimental results demonstrated that diffusion models were able to synthesize abdominal CT images with better quality. Additionally, encoding the mask and the input separately is more effective than na\"ive concatenating., Comment: This paper has been accepted at Deep Generative Models workshop at MICCAI 2023

Pervasive mobile AI applications primarily employ one of the two learning paradigms: cloud-based learning (with powerful large models) or on-device learning (with lightweight small models). Despite their own advantages, neither paradigm can effectively handle dynamic edge environments with frequent data distribution shifts and on-device resource fluctuations, inevitably suffering from performance degradation. In this paper, we propose ECLM, an edge-cloud collaborative learning framework for rapid model adaptation for dynamic edge environments. We first propose a novel block-level model decomposition design to decompose the original large cloud model into multiple combinable modules. By flexibly combining a subset of the modules, this design enables the derivation of compact, task-specific sub-models for heterogeneous edge devices from the large cloud model, and the seamless integration of new knowledge learned on these devices into the cloud model periodically. As such, ECLM ensures that the cloud model always provides up-to-date sub-models for edge devices. We further propose an end-to-end learning framework that incorporates the modular model design into an efficient model adaptation pipeline including an offline on-cloud model prototyping and training stage, and an online edge-cloud collaborative adaptation stage. Extensive experiments over various datasets demonstrate that ECLM significantly improves model performance (e.g., 18.89% accuracy increase) and resource efficiency (e.g., 7.12x communication cost reduction) in adapting models to dynamic edge environments by efficiently collaborating the edge and the cloud models.

In this paper, we consider the problem of estimating parameters in a linear regression model. We propose a sequential learning procedure to determine the sample size for achieving a given small estimation risk, under the widely used Gauss-Markov setup with independent normal errors. The procedure is proven to enjoy the second-order efficiency and risk-efficiency properties, which are validated through Monte Carlo simulation studies. Using e-commerce data, we implement the procedure to examine the influential factors of online sales.

In this paper, we obtain the invariant curves of quasi-periodic reversible mappings with finite smoothness. Since the reversible property is difficult to maintain in the process of approximating smooth functions by analytical ones, R\"{u}ssmann's method in \cite{HR} is invalid. Inspired by the recent work of Li, Qi and Yuan in \cite{LJ}, we turn to regard the reversible mapping as the Poincar\'{e} map of a reversible differential equation. By constructing a KAM theorem for a reversible differential equation which is quasi-periodic in time, we obtain the invariant curves of the reversible mapping. Beyond that, we establish some variants of invariant curve theorems for quasi-periodic reversible mappings.

This paper studies the relationship between the modified Foata$\unicode{x2013}$Strehl action (a.k.a. valley-hopping)$\unicode{x2014}$a group action on permutations used to demonstrate the $\gamma$-positivity of the Eulerian polynomials$\unicode{x2014}$and the number of rixed points $\operatorname{rix}$$\unicode{x2014}$a recursively-defined permutation statistic introduced by Lin in the context of an equidistribution problem. We give a linear-time iterative algorithm for computing the set of rixed points, and prove that the $\operatorname{rix}$ statistic is homomesic under valley-hopping. We also demonstrate that a bijection $\Phi$ introduced by Lin and Zeng in the study of the $\operatorname{rix}$ statistic sends orbits of the valley-hopping action to orbits of a cyclic version of valley-hopping, which implies that the number of fixed points $\operatorname{fix}$ is homomesic under cyclic valley-hopping., Comment: 27 pages

The kernel $\mathcal{K}^{\operatorname{st}}$ of a descent statistic $\operatorname{st}$, introduced by Grinberg, is a subspace of the algebra $\operatorname{QSym}$ of quasisymmetric functions defined in terms of $\operatorname{st}$-equivalent compositions, and is an ideal of $\operatorname{QSym}$ if and only if $\operatorname{st}$ is shuffle-compatible. This paper continues the study of kernels of descent statistics, with emphasis on the peak set $\operatorname{Pk}$ and the peak number $\operatorname{pk}$. The kernel $\mathcal{K}^{\operatorname{Pk}}$ in particular is precisely the kernel of the canonical projection from $\operatorname{QSym}$ to Stembridge's algebra of peak quasisymmetric functions, and is the orthogonal complement of Nyman's peak algebra. We prove necessary and sufficient conditions for obtaining spanning sets and linear bases for the kernel $\mathcal{K}^{\operatorname{st}}$ of any descent statistic $\operatorname{st}$ in terms of fundamental quasisymmetric functions, and give characterizations of $\mathcal{K}^{\operatorname{Pk}}$ and $\mathcal{K}^{\operatorname{pk}}$ in terms of the fundamental basis and the monomial basis of $\operatorname{QSym}$. Our results imply that the peak set and peak number statistics are $M$-binomial, confirming a conjecture of Grinberg., Comment: 32 pages

Given a permutation statistic $\operatorname{st}$, define its inverse statistic $\operatorname{ist}$ by $\operatorname{ist}(\pi):=\operatorname{st}(\pi^{-1})$. We give a general approach, based on the theory of symmetric functions, for finding the joint distribution of $\operatorname{st}_{1}$ and $\operatorname{ist}_{2}$ whenever $\operatorname{st}_{1}$ and $\operatorname{st}_{2}$ are descent statistics: permutation statistics that depend only on the descent composition. We apply this method to a number of descent statistics, including the descent number, the peak number, the left peak number, the number of up-down runs, and the major index. Perhaps surprisingly, in many cases the polynomial giving the joint distribution of $\operatorname{st}_{1}$ and $\operatorname{ist}_{2}$ can be expressed as a simple sum involving products of the polynomials giving the (individual) distributions of $\operatorname{st}_{1}$ and $\operatorname{st}_{2}$. Our work leads to a rederivation of Stanley's generating function for doubly alternating permutations, as well as several conjectures concerning real-rootedness and $\gamma$-positivity., Comment: 43 pages

We introduce a subfamily of skew Dyck paths called box paths and show that they are in bijection with pairs of ternary trees, confirming an observation stated previously on the On-Line Encyclopedia of Integer Sequences. More generally, we define $k$-box paths, which are in bijection with $(k+1)$-tuples of $(k+2)$-ary trees. A bijection is given between $k$-box paths and a subfamily of $k_{t}$-Dyck paths, as well as a bijection with a subfamily of $(k,\ell)$-threshold sequences. We also study the refined enumeration of $k$-box paths by the number of returns and the number of long ascents. Notably, the distribution of long ascents over $k$-box paths generalizes the Narayana distribution on Dyck paths, and we find that $(k-3)$-box paths with exactly two long ascents provide a combinatorial model for the second $k$-gonal numbers., Comment: 20 pages

As AI systems continue to grow, particularly generative models like Large Language Models (LLMs), their rigorous evaluation is crucial for development and deployment. To determine their adequacy, researchers have developed various large-scale benchmarks against a so-called gold-standard test set and report metrics averaged across all items. However, this static evaluation paradigm increasingly shows its limitations, including high computational costs, data contamination, and the impact of low-quality or erroneous items on evaluation reliability and efficiency. In this Perspective, drawing from human psychometrics, we discuss a paradigm shift from static evaluation methods to adaptive testing. This involves estimating the characteristics and value of each test item in the benchmark and dynamically adjusting items in real-time, tailoring the evaluation based on the model's ongoing performance instead of relying on a fixed test set. This paradigm not only provides a more robust ability estimation but also significantly reduces the number of test items required. We analyze the current approaches, advantages, and underlying reasons for adopting psychometrics in AI evaluation. We propose that adaptive testing will become the new norm in AI model evaluation, enhancing both the efficiency and effectiveness of assessing advanced intelligence systems.