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Frequency-division duplexing (FDD) remains the de facto standard in modern low Earth orbit (LEO) satellite communication (SatCom) systems, such as SpaceX's Starlink, OneWeb, and Amazon's Project Kuiper. While time-division duplexing (TDD) is often regarded as superior in today's terrestrial networks, its viability in future LEO SatCom systems remains unclear. This article details how the long propagation delays and high orbital velocities exhibited by LEO SatCom systems impedes the adoption of TDD, due to challenges involving the frame structure and synchronization. We then present potential approaches to overcome these challenges, which vary in terms of resource efficiency and operational/device complexity and thus would likely be application-specific. We conclude by assessing the performance of these proposed approaches, putting into perspective the tradeoff between complexity and performance gains over FDD. Overall, this article aims to motivate future investigation into the prospects of TDD in LEO SatCom systems and solutions to enable such, with the goal of enhancing future systems and unifying them with terrestrial networks.

By utilizing the recently developed hypergraph analogue of Godsil's identity by the second author, we prove that for all $n \geq k \geq 2$, one can reconstruct the matching polynomial of an $n$-vertex $k$-uniform hypergraph from the multiset of all induced sub-hypergraphs on $\lfloor \frac{k-1}{k}n \rfloor + 1$ vertices. This generalizes the well-known result of Godsil on graphs in 1981 to every uniform hypergraph. As a corollary, we show that for every graph $F$, one can reconstruct the number of $F$-factors in a graph under analogous conditions. We also constructed examples that imply the number $\lfloor \frac{k-1}{k}n \rfloor + 1$ is the best possible for all $n\geq k \geq 2$ with $n$ divisible by $k$., Comment: 11 pages, 3 figures

In this note, we obtain a quantitative improvement on the hypergraph variant of the Balog-Szemer\'{e}di-Gowers theorem due to Sudakov, Szemer\'{e}di, and Vu [Duke Math. J.129.1 (2005): 129-155]. Additionally, we prove the hypergraph variant of the ``almost all'' version of Balog-Szemer\'{e}redi-Gowers theorem., Comment: 13 pages

As a neural network's depth increases, it can achieve strong generalization performance. Training, however, becomes challenging due to gradient issues. Theoretical research and various methods have been introduced to address this issues. However, research on weight initialization methods that can be effectively applied to tanh neural networks of varying sizes still needs to be completed. This paper presents a novel weight initialization method for Feedforward Neural Networks with tanh activation function. Based on an analysis of the fixed points of the function $\tanh(ax)$, our proposed method aims to determine values of $a$ that prevent the saturation of activations. A series of experiments on various classification datasets demonstrate that the proposed method is more robust to network size variations than the existing method. Furthermore, when applied to Physics-Informed Neural Networks, the method exhibits faster convergence and robustness to variations of the network size compared to Xavier initialization in problems of Partial Differential Equations.

Body composition analysis is vital in assessing health conditions such as obesity, sarcopenia, and metabolic syndromes. MRI provides detailed images of skeletal muscle (SKM), visceral adipose tissue (VAT), and subcutaneous adipose tissue (SAT), but their manual segmentation is labor-intensive and limits clinical applicability. This study validates an automated tool for MRI-based 2D body composition analysis- (Data Analysis Facilitation Suite (DAFS) Express), comparing its automated measurements with expert manual segmentations using UK Biobank data. A cohort of 399 participants from the UK Biobank dataset was selected, yielding 423 single L3 slices for analysis. DAFS Express performed automated segmentations of SKM, VAT, and SAT, which were then manually corrected by expert raters for validation. Evaluation metrics included Jaccard coefficients, Dice scores, Intraclass Correlation Coefficients (ICCs), and Bland-Altman Plots to assess segmentation agreement and reliability. High agreements were observed between automated and manual segmentations with mean Jaccard scores: SKM 99.03%, VAT 95.25%, and SAT 99.57%; and mean Dice scores: SKM 99.51%, VAT 97.41%, and SAT 99.78%. Cross-sectional area comparisons showed consistent measurements with automated methods closely matching manual measurements for SKM and SAT, and slightly higher values for VAT (SKM: Auto 132.51 cm^2, Manual 132.36 cm^2; VAT: Auto 137.07 cm^2, Manual 134.46 cm^2; SAT: Auto 203.39 cm^2, Manual 202.85 cm^2). ICCs confirmed strong reliability (SKM: 0.998, VAT: 0.994, SAT: 0.994). Bland-Altman plots revealed minimal biases, and boxplots illustrated distribution similarities across SKM, VAT, and SAT areas. On average DAFS Express took 18 seconds per DICOM. This underscores its potential to streamline image analysis processes in research and clinical settings, enhancing diagnostic accuracy and efficiency.

This paper introduces a new integer programming game (IPG) named the Edge-weighted Budgeted Maximum Coverage (EBMC) game and proposes a new algorithm, the Best Response Plus (BR-plus) algorithm, for finding the best Pure Nash Equilibrium (PNE). We demonstrate this methodology by optimizing county-level decisions to prevent aquatic invasive species (AIS) in Minnesota lakes, where each county-level decision makers has self-serving objectives while AIS is an interconnected issue that crosses county borders. Specifically, we develop EBMC games to model the strategic interactions among county-level decision-makers with two variations in utility functions. We also study and prove the existence of a PNE in these models under specified conditions. We advance the current state-of-the-art, which is limited to only a few players, by presenting the BR-plus algorithm that can handle a large set of players via utilizing the best response dynamics for finding PNE in normal-form games. Experimental results show that our BR-plus algorithm offers computational advantages over the ZR algorithm, especially in larger games, on both random and real-world networks.

Thomason [$\textit{Trans. Amer. Math. Soc.}$ 296.1 (1986)] proved that every sufficiently large tournament contains Hamilton paths and cycles with all possible orientations, except possibly the consistently oriented Hamilton cycle. This paper establishes $\textit{transversal}$ generalizations of these classical results. For a collection $\mathbf{T}=\{T_1,\dots,T_m\}$ of not-necessarily distinct tournaments on the common vertex set $V$, an $m$-edge directed subgraph $\mathcal{D}$ with the vertices in $V$ is called a transversal if there exists an bijection $\varphi\colon E(\mathcal{D})\to [m]$ such that $e\in E(T_{\varphi(e)})$ for all $e\in E(\mathcal{D})$. We prove that for sufficiently large $n$, there exist transversal Hamilton cycles of all possible orientations possibly except the consistently oriented one. We also obtain a similar result for the transversal Hamilton paths of all possible orientations. These results generalize the classical theorem of Thomason, and our approach provides another proof of this theorem.

The recent advancements in large language models (LLMs) have brought significant progress in solving NLP tasks. Notably, in-context learning (ICL) is the key enabling mechanism for LLMs to understand specific tasks and grasping nuances. In this paper, we propose a simple yet effective method to contextualize a task toward a specific LLM, by (1) observing how a given LLM describes (all or a part of) target datasets, i.e., open-ended zero-shot inference, and (2) aggregating the open-ended inference results by the LLM, and (3) finally incorporate the aggregated meta-information for the actual task. We show the effectiveness of this approach in text clustering tasks, and also highlight the importance of the contextualization through examples of the above procedure., Comment: ARR Submitted

For a given hypergraph $H$ and a vertex $v\in V(H)$, consider a random matching $M$ chosen uniformly from the set of all matchings in $H.$ In $1995,$ Kahn conjectured that if $H$ is a $d$-regular linear $k$-uniform hypergraph, the probability that $M$ does not cover $v$ is $(1 + o_d(1))d^{-1/k}$ for all vertices $v\in V(H).$ This conjecture was proved for $k = 2$ by Kahn and Kim in $1998.$ In this paper, we disprove this conjecture for all $k \geq 3.$ For infinitely many values of $d,$ we construct $d$-regular linear $k$-uniform hypergraph $H$ containing two vertices $v_1$ and $v_2$ such that $\mathcal{P}(v_1 \notin M) = 1 - \frac{(1 + o_d(1))}{d^{k-2}}$ and $\mathcal{P}(v_2 \notin M) = \frac{(1 + o_d(1))}{d+1}.$ The gap between $\mathcal{P}(v_1 \notin M)$ and $\mathcal{P}(v_2 \notin M)$ in this $H$ is best possible. In the course of proving this, we also prove a hypergraph analog of Godsil's result on matching polynomials and paths in graphs, which is of independent interest., Comment: 15 pages

Most prior safety research of large language models (LLMs) has focused on enhancing the alignment of LLMs to better suit the safety requirements of humans. However, internalizing such safeguard features into larger models brought challenges of higher training cost and unintended degradation of helpfulness. To overcome such challenges, a modular approach employing a smaller LLM to detect harmful user queries is regarded as a convenient solution in designing LLM-based system with safety requirements. In this paper, we leverage a smaller LLM for both harmful query detection and safeguard response generation. We introduce our safety requirements and the taxonomy of harmfulness categories, and then propose a multi-task learning mechanism fusing the two tasks into a single model. We demonstrate the effectiveness of our approach, providing on par or surpassing harmful query detection and safeguard response performance compared to the publicly available LLMs.

Although there has been a growing interest among industries in integrating generative LLMs into their services, limited experience and scarcity of resources act as a barrier in launching and servicing large-scale LLM-based services. In this paper, we share our experiences in developing and operating generative AI models within a national-scale search engine, with a specific focus on the sensitiveness of user queries. We propose a taxonomy for sensitive search queries, outline our approaches, and present a comprehensive analysis report on sensitive queries from actual users. We believe that our experiences in launching generative AI search systems can contribute to reducing the barrier in building generative LLM-based services., Comment: NAACL2025(Findings)

Dirac's theorem states that any $n$-vertex graph $G$ with even integer $n$ satisfying $\delta(G) \geq n/2$ contains a perfect matching. We generalize this to $k$-uniform linear hypergraphs by proving the following. Any $n$-vertex $k$-uniform linear hypergraph $H$ with minimum degree at least $\frac{n}{k} + \Omega(1)$ contains a matching that covers at least $(1-o(1))n$ vertices. This minimum degree condition is asymptotically tight and obtaining perfect matching is impossible with any degree condition. Furthermore, we show that if $\delta(H) \geq (\frac{1}{k}+o(1))n$, then $H$ contains almost spanning linear cycles, almost spanning hypertrees with $o(n)$ leaves, and ``long subdivisions'' of any $o(\sqrt{n})$-vertex graphs., Comment: 13 pages

In 1994, Alon construct a triangle-free $(n,d,\lambda)$-graph with $d = \Omega(n^{2/3})$ and $\lambda = O(d^{1/2})$ for an exponentially increasing sequence of integers $n$. Using his ingenious construction, we deduce that there exist triangle-free $(n,d,\lambda)$-graphs with $d = \Omega(n^{2/3})$ and $\lambda = O( (d \log n)^{1/2} )$ for all sufficiently large $n$., Comment: 9 pages

For a given collection $\mathcal{G} = (G_1,\dots, G_k)$ of graphs on a common vertex set $V$, which we call a \emph{graph system}, a graph $H$ on a vertex set $V(H) \subseteq V$ is called a \emph{rainbow subgraph} of $\mathcal{G}$ if there exists an injective function $\psi:E(H) \rightarrow [k]$ such that $e \in G_{\psi(e)}$ for each $e\in E(H)$. The maximum value of $\min_{i}\{|E(G_i)|\}$ over $n$-vertex graph systems $\mathcal{G}$ having no rainbow subgraph isomorphic to $H$ is called the rainbow Tur\'{a}n number $\mathrm{ex}_k^{\ast}(n, H)$ of $H$. In this article, we study the rainbow Tur\'{a}n density $\pi_k^{\ast}(T) = \lim_{n \rightarrow \infty} \frac{\mathrm{ex}_k^{\ast}(n, T)}{\binom{n}{2}}$ of a tree $T$. While the classical Tur\'{a}n density $\pi(H)$ of a graph $H$ lies in the set $\{1-\frac{1}{t} : t\in \mathbb{N}\}$, the rainbow Tur\'{a}n density exhibits different behaviors as it can even be an irrational number. Nevertheless, we conjecture that the rainbow Tur\'{a}n density is always an algebraic number. We provide evidence for this conjecture by proving that the rainbow Tur\'{a}n density of a tree is an algebraic number. To show this, we identify the structure of extremal graphs for rainbow trees. Moreover, we further determine all tuples $(\alpha_1,\dots, \alpha_k)$ such that every graph system $(G_1,\dots,G_k)$ satisfying $|E(G_i)|>(\alpha_i+o(1))\binom{n}{2}$ contains all rainbow $k$-edge trees. In the course of proving these results, we also develop the theory on the limit of graph systems., Comment: 24pages + 9 page appendix, 2 figures

Appropriate weight initialization settings, along with the ReLU activation function, have become cornerstones of modern deep learning, enabling the training and deployment of highly effective and efficient neural network models across diverse areas of artificial intelligence. The problem of \textquotedblleft dying ReLU," where ReLU neurons become inactive and yield zero output, presents a significant challenge in the training of deep neural networks with ReLU activation function. Theoretical research and various methods have been introduced to address the problem. However, even with these methods and research, training remains challenging for extremely deep and narrow feedforward networks with ReLU activation function. In this paper, we propose a novel weight initialization method to address this issue. We establish several properties of our initial weight matrix and demonstrate how these properties enable the effective propagation of signal vectors. Through a series of experiments and comparisons with existing methods, we demonstrate the effectiveness of the novel initialization method., Comment: 13 pages

Dirac's theorem determines the sharp minimum degree threshold for graphs to contain perfect matchings and Hamiltonian cycles. There have been various attempts to generalize this theorem to hypergraphs with larger uniformity by considering hypergraph matchings and Hamiltonian cycles. In this paper, we consider another natural generalization of the perfect matchings, Steiner triple systems. As a Steiner triple system can be viewed as a partition of pairs of vertices, it is a natural high-dimensional analogue of a perfect matching in graphs. We prove that for sufficiently large integer $n$ with $n \equiv 1 \text{ or } 3 \pmod{6},$ any $n$-vertex $3$-uniform hypergraph $H$ with minimum codegree at least $\left(\frac{3 + \sqrt{57}}{12} + o(1) \right)n = (0.879... + o(1))n$ contains a Steiner triple system. In fact, we prove a stronger statement by considering transversal Steiner triple systems in a collection of hypergraphs. We conjecture that the number $\frac{3 + \sqrt{57}}{12}$ can be replaced with $\frac{3}{4}$ which would provide an asymptotically tight high-dimensional generalization of Dirac's theorem.

It is well-known that every tournament contains a Hamilton path, and every strongly connected tournament contains a Hamilton cycle. This paper establishes transversal generalizations of these classical results. For a collection $\mathbf{T}=\{T_1,\dots,T_m\}$ of not-necessarily distinct tournaments on a common vertex set $V$, an $m$-edge directed graph $\mathcal{D}$ with vertices in $V$ is called a $\mathbf{T}$-transversal if there exists a bijection $\phi\colon E(\mathcal{D})\to [m]$ such that $e\in E(T_{\phi(e)})$ for all $e\in E(\mathcal{D})$. We prove that for sufficiently large $m$ with $m=|V|-1$, there exists a $\mathbf{T}$-transversal Hamilton path. Moreover, if $m=|V|$ and at least $m-1$ of the tournaments $T_1,\ldots,T_m$ are assumed to be strongly connected, then there is a $\mathbf{T}$-transversal Hamilton cycle. In our proof, we utilize a novel way of partitioning tournaments which we dub $\mathbf{H}$-partition.

We prove that an $n$-vertex digraph $D$ with minimum semi-degree at least $\left(\frac{1}{2} + \varepsilon \right)n$ and $n = \Omega_{\varepsilon}(m)$ contains a subdivision of all $m$-arc digraphs. This is the best possible and settles a conjecture raised by Pavez-Sing\'{e} in a stronger form., Comment: 5 pages

Hansel's lemma states that $\sum_{H\in \mathcal{H}}|H| \geq n \log_2 n$ holds where $\mathcal{H}$ is a collection of bipartite graphs covering all the edges of $K_n$. We generalize this lemma to the corresponding multigraph covering problem and the graphon covering problem. We also prove an upper bound on $\sum_{H\in \mathcal{H}}|H|$ which shows that our generalization is asymptotically tight in some sense., Comment: 13 pages

For a given graph $H$, we say that a graph $G$ has a perfect $H$-subdivision tiling if $G$ contains a collection of vertex-disjoint subdivisions of $H$ covering all vertices of $G.$ Let $\delta_{sub}(n, H)$ be the smallest integer $k$ such that any $n$-vertex graph $G$ with minimum degree at least $k$ has a perfect $H$-subdivision tiling. For every graph $H$, we asymptotically determined the value of $\delta_{sub}(n, H)$. More precisely, for every graph $H$ with at least one edge, there is a constant $1 < \xi^*(H)\leq 2$ such that $\delta_{sub}(n, H) = \left(1 - \frac{1}{\xi^*(H)} + o(1) \right)n$ if $H$ has a bipartite subdivision with two parts having different parities. Otherwise, the threshold depends on the parity of $n.$, Comment: 23 pages, supporting information added and some minor mistakes corrected

Dementia of Alzheimer's Type (DAT) is a complex disorder influenced by numerous factors, but it is unclear how each factor contributes to disease progression. An in-depth examination of these factors may yield an accurate estimate of time-to-conversion to DAT for patients at various disease stages. We used 401 subjects with 63 features from MRI, genetic, and CDC (Cognitive tests, Demographic, and CSF) data modalities in the Alzheimer's Disease Neuroimaging Initiative (ADNI) database. We used a deep learning-based survival analysis model that extends the classic Cox regression model to predict time-to-conversion to DAT. Our findings showed that genetic features contributed the least to survival analysis, while CDC features contributed the most. Combining MRI and genetic features improved survival prediction over using either modality alone, but adding CDC to any combination of features only worked as well as using only CDC features. Consequently, our study demonstrated that using the current clinical procedure, which includes gathering cognitive test results, can outperform survival analysis results produced using costly genetic or CSF data.

There has been extensive studies on the following question: given $k$ graphs $G_1,\dots, G_k$ over a common vertex set of size $n$, what conditions on $G_i$ ensures a `colorful' copy of $H$, i.e., a copy of $H$ containing at most one edge from each $G_i$? A lower bound on $\sum_{i\in [k]} e(G_i)$ enforcing a colorful copy of a given graph $H$ was considered by Keevash, Saks, Sudakov, and Verstra\"{e}te. They defined $\operatorname{ex}_k(n,H)$ to be the maximum total number of edges of the graphs $G_1,\dots, G_k$ on a common vertex set of size $n$ having no colorful copy of $H$. They completely determined $\operatorname{ex}_k(n,K_r)$ for large $n$ by showing that, depending on the value of $k$, one of the two natural constructions is always the extremal construction. Moreover, they conjectured the same holds for every color-critical graphs and proved it for 3-color-critical graphs. We prove their conjecture for 4-color-critical graphs and for almost all $r$-color-critical graphs when $r > 4$. Moreover, we show that for every non-color-critical non-bipartite graphs, none of the two natural constructions is extremal for certain values of $k$. This answers a question of Keevash, Saks, Sudakov, and Verstra\"{e}te.

Background: The increasing availability of databases containing both magnetic resonance imaging (MRI) and genetic data allows researchers to utilize multimodal data to better understand the characteristics of dementia of Alzheimer's type (DAT). Objective: The goal of this study was to develop and analyze novel biomarkers that can help predict the development and progression of DAT. Methods: We used feature selection and ensemble learning classifier to develop an image/genotype-based DAT score that represents a subject's likelihood of developing DAT in the future. Three feature types were used: MRI only, genetic only, and combined multimodal data. We used a novel data stratification method to better represent different stages of DAT. Using a pre-defined 0.5 threshold on DAT scores, we predicted whether or not a subject would develop DAT in the future. Results: Our results on Alzheimer's Disease Neuroimaging Initiative (ADNI) database showed that dementia scores using genetic data could better predict future DAT progression for currently normal control subjects (Accuracy=0.857) compared to MRI (Accuracy=0.143), while MRI can better characterize subjects with stable mild cognitive impairment (Accuracy=0.614) compared to genetics (Accuracy=0.356). Combining MRI and genetic data showed improved classification performance in the remaining stratified groups. Conclusion: MRI and genetic data can contribute to DAT prediction in different ways. MRI data reflects anatomical changes in the brain, while genetic data can detect the risk of DAT progression prior to the symptomatic onset. Combining information from multimodal data in the right way can improve prediction performance.

Message forwarding protocols are protocols in which a chain of agents handles transmission of a message. Each agent forwards the received message to the next agent in the chain. For example, TLS middleboxes act as intermediary agents in TLS, adding functionality such as filtering or compressing data. In such protocols, an attacker may attempt to bypass one or more intermediary agents. Such an agent-skipping attack can the violate security requirements of the protocol. Using the multiset rewriting model in the symbolic setting, we construct a comprehensive framework of such path protocols. In particular, we introduce a set of security goals related to path integrity: the notion that a message faithfully travels through participants in the order intended by the initiating agent. We perform a security analysis of several such protocols, highlighting key attacks on modern protocols.

The oriented Ramsey number $\vec{r}(H)$ for an acyclic digraph $H$ is the minimum integer $n$ such that any $n$-vertex tournament contains a copy of $H$ as a subgraph. We prove that the $1$-subdivision of the $k$-vertex transitive tournament $H_k$ satisfies $\vec{r}(H_k)= O(k^2\log\log k)$. This is tight up to multiplicative $\log\log k$-term. We also show that if $T$ is an $n$-vertex tournament with $\Delta^+(T)-\delta^+(T)= O(n/k) - k^2$, then $T$ contains a $1$-subdivision of $\vec{K}_k$, a complete $k$-vertex digraph with all possible $k(k-1)$ arcs. This is also tight up to multiplicative constant.

The max-cut problem is a classical graph theory problem which is NP-complete. The best polynomial time approximation scheme relies on \emph{semidefinite programming} (SDP). We study the conditions under which graphs of certain classes have rank~1 solutions to the max-cut SDP. We apply these findings to look at how solutions to the max-cut SDP behave under simple combinatorial constructions. Our results determine when solutions to the max-cut SDP for cycle graphs are rank~1. We find the solutions to the max-cut SDP of the vertex~sum of two graphs. We then characterize the SDP solutions upon joining two triangle graphs by an edge~sum., Comment: 18 pages, 1 figure