arXiv subjects

Nathan Sun

Publications and source records attributed to Nathan Sun.

8 recordsLinked to original sources

arXiv2026

Designing Agentic AI-Based Screening for Portfolio Investment

We introduce a new agentic artificial intelligence (AI) platform for portfolio management. Our architecture consists of three layers. First, two large language model (LLM) agents are assigned specialized tasks: one agent screens for firms with desirable fundamentals, while a sentiment analysis agent screens for firms with desirable news. Second, these agents deliberate to generate and agree upon buy and sell signals from a large portfolio, substantially narrowing the pool of candidate assets. Finally, we apply a high-dimensional precision matrix estimation procedure to determine optimal portfolio weights. We show, through information acquisition theory, that screening with agentic AI can bring utility gains in screening compared with humans. We introduce the concept of \emph{sensible screening} and establish that, under mild screening errors, the squared Sharpe ratio of the screened portfolio consistently estimates its target. Empirically, our method achieves superior Sharpe ratios relative to an unscreened baseline portfolio and to conventional screening approaches, evaluated on S\&P~500 data over both short and medium terms.

q-fin.PM↗

arXiv2024

Optimizing Cycle Life Prediction of Lithium-ion Batteries via a Physics-Informed Model

Accurately measuring the cycle lifetime of commercial lithium-ion batteries is crucial for performance and technology development. We introduce a novel hybrid approach combining a physics-based equation with a self-attention model to predict the cycle lifetimes of commercial lithium iron phosphate graphite cells via early-cycle data. After fitting capacity loss curves to this physics-based equation, we then use a self-attention layer to reconstruct entire battery capacity loss curves. Our model exhibits comparable performances to existing models while predicting more information: the entire capacity loss curve instead of cycle life. This provides more robustness and interpretability: our model does not need to be retrained for a different notion of end-of-life and is backed by physical intuition.

cs.LG↗

arXiv2023

Periodic Points of Consecutive-Pattern-Avoiding Stack-Sorting Maps

West's stack-sorting map involves a stack which avoids the permutation $21$ consecutively. Defant and Zheng extended this to a consecutive-pattern-avoiding stack-sorting map $SC_\sigma$, where the stack must always avoid a given permutation $\sigma$ consecutively. We address one of the main conjectures raised by Defant and Zheng in their dynamical approach to $SC_\sigma$. Specifically, we show that the periodic points of $SC_\sigma$ are precisely the permutations that consecutively avoid $\sigma$ and its reverse.

math.CO↗

arXiv2022

The Image of the Pop Operator on Various Lattices

Extending the classical pop-stack sorting map on the lattice given by the right weak order on $S_n$, Defant defined, for any lattice $M$, a map $\mathsf{Pop}_{M}: M \to M$ that sends an element $x\in M$ to the meet of $x$ and the elements covered by $x$. In parallel with the line of studies on the image of the classical pop-stack sorting map, we study $\mathsf{Pop}_{M}(M)$ when $M$ is the weak order of type $B_n$, the Tamari lattice of type $B_n$, the lattice of order ideals of the root poset of type $A_n$, and the lattice of order ideals of the root poset of type $B_n$. In particular, we settle four conjectures proposed by Defant and Williams on the generating function \begin{equation*} \mathsf{Pop}(M; q) = \sum_{b \in \mathsf{Pop}_{M}(M)} q^{|\mathscr{U}_{M}(b)|}, \end{equation*} where $\mathscr{U}_{M}(b)$ is the set of elements of $M$ that cover $b$.

math.CO↗

arXiv2022

A Complete Enumeration of Ballot Permutations Avoiding Sets of Small Patterns

Permutations whose prefixes contain at least as many ascents as descents are called ballot permutations. Lin, Wang, and Zhao have previously enumerated ballot permutations avoiding small patterns and have proposed the problem of enumerating ballot permutations avoiding a pair of permutations of length $3$. We completely enumerate ballot permutations avoiding two patterns of length $3$ and we relate these avoidance classes with their respective recurrence relations and formulas, which leads to an interesting bijection between ballot permutations avoiding $132$ and $312$ with left factors of Dyck paths. In addition, we also conclude the Wilf-classification of ballot permutations avoiding sets of two patterns of length $3$, and we then extend our results to completely enumerate ballot permutations avoiding three patterns of length $3$.

math.CO↗

arXiv2022

On $d$-permutations and Pattern Avoidance Classes

Multidimensional permutations, or $d$-permutations, are represented by their diagrams on $[n]^d$ such that there exists exactly one point per hyperplane $x_i$ that satisfies $x_i= j$ for $i \in [d]$ and $j \in [n]$. Bonichon and Morel previously enumerated $3$-permutations avoiding small patterns, and we extend their results by first proving four conjectures, which exhaustively enumerate $3$-permutations avoiding any two fixed patterns of size $3$. We further provide a enumerative result relating $3$-permutation avoidance classes with their respective recurrence relations. In particular, we show a recurrence relation for $3$-permutations avoiding the patterns $132$ and $213$, which contributes a new sequence to the OEIS database. We then extend our results to completely enumerate $3$-permutations avoiding three patterns of size $3$.

math.CO↗

arXiv2019

A Theorem of Joseph-Alfred Serret and its Relation to Perfect Quantum State Transfer

In this paper we recast the Serret theorem about a characterization of palindromic continued fractions in the context of polynomial continued fractions. Then, using the relation between symmetric tridiagonal matrices and polynomial continued fractions we give a quick exposition of the mathematical aspect of the perfect quantum state transfer problem.

math.CA↗

arXiv2018

On Permutation Weights and $q$-Eulerian Polynomials

Weights of permutations were originally introduced by Dugan, Glennon, Gunnells, and Steingr\'imsson (Journal of Combinatorial Theory, Series A 164:24-49, 2019) in their study of the combinatorics of tiered trees. Given a permutation $\sigma$ viewed as a sequence of integers, computing the weight of $\sigma$ involves recursively counting descents of certain subpermutations of $\sigma$. Using this weight function, one can define a $q$-analog $E_n(x,q)$ of the Eulerian polynomials. We prove two main results regarding weights of permutations and the polynomials $E_n(x,q)$. First, we show that the coefficients of $E_n(x, q)$ stabilize as $n$ goes to infinity, which was conjectured by Dugan, Glennon, Gunnells, and Steingr\'imsson (Journal of Combinatorial Theory, Series A 164:24-49, 2019), and enables the definition of the formal power series $W_d(t)$, which has interesting combinatorial properties. Second, we derive a recurrence relation for $E_n(x, q)$, similar to the known recurrence for the classical Eulerian polynomials $A_n(x)$. Finally, we give a recursive formula for the numbers of certain integer partitions and, from this, conjecture a recursive formula for the stabilized coefficients mentioned above.

math.CO↗