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Yiyi Zhu

Publications and source records attributed to Yiyi Zhu.

12 recordsLinked to original sources
arXiv2026

Finiteness and Construction of Internal Hom for Vertex Operator Algebras

Let $V$ be a vertex operator algebra, and let $W^1$ and $W^2$ be restricted $V$-modules. We construct a generalized $V$-module $\mathcal{H}(W^1, W^2)$ characterized by canonical universal properties. We show that, under suitable hypotheses, $ \mathcal{H}(W^1, W^2)$ realizes the internal Hom object in the tensor category of restricted $V$-modules. Although our construction differs from Li's, we show that it agrees with the natural logarithmic generalization of Li's module $Δ(W^1, W^2)$. We further establish a canonical isomorphism between $\mathcal{H} \big(W^1,(W^2 )^\prime \big)$ and the $P(z_0)$-dual product $ W^1 \pzbox_{P(z_0)} W^2 $ recently constructed by Du and Huang. Under the $C_1$-cofiniteness condition, we investigate finiteness properties of $ \mathcal H(W^1, W^2)$. As applications, we obtain a natural isomorphism between $ \mathcal H(W^1, W^2)'$ and $ W^1 \boxtimes (W^2)'$, and prove the finiteness of the corresponding fusion rules.

math.QA↗
arXiv2026

Diversity-Driven Offline Multi-Objective Optimization via Nested Pareto Set Learning

Multi-objective optimization (MOO) has emerged as a powerful approach to solving complex optimization problems involving multiple objectives. In many practical scenarios, function evaluations are unavailable or prohibitively expensive, necessitating optimization solely based on a fixed offline dataset. In this setting, known as offline MOO, the goal is to find out the Pareto set without access to the true objective functions. This setting suffers from the out-of-distribution (OOD) issue, where the surrogate model is not accurate for unseen designs. Due to the OOD issue, surrogate errors may cause the optimizer to select solutions that do not lie on the true Pareto front and are biased toward its extremes. To address this, this paper proposes Diversity-driven Offline Multi-Objective Optimization (DOMOO), which aims to find out a diverse and high-quality set of solutions. First, DOMOO incorporates an accumulative risk control module that estimates the potential risk of candidate solutions and alleviates the OOD issue between the training data and the generated solutions. In addition, a nested Pareto set learning (PSL) strategy is proposed to jointly learn preference and PSL parameters, then optimize them, enabling adaptation to diverse Pareto front geometries. To further enhance solution quality, we design a diversity-driven selection strategy that extracts a representative and well-distributed set of final solutions. To achieve this diversity-driven selection strategy, we propose $\text{IGD}_\text{offline}$, a tailored indicator for the offline setting that considers both diversity and convergence, and avoids the bias of hypervolume indicator. Extensive experiments on synthetic and real-world benchmarks show that DOMOO achieves the best average rank across tasks in both convergence and diversity among the compared methods.

cs.LG↗
arXiv2025

Cofiniteness for Twisted Fusion Products in Vertex Operator Algebra Theory

Let $V$ be a vertex operator algebra equipped with two commuting finite-order automorphisms $g_1$ and $g_2$, and set $g_3 = g_1 g_2$. For $k = 1, 2, 3$, let $W^k$ be a $g_k$-twisted $V$-module. Assuming that $W^1$ and $W^2$ are $C_1$-cofinite and that there exists a surjective twisted logarithmic intertwining operator of type $\binom{W^3}{W^1 \ W^2}$, we prove that $W^3$ is also $C_1$-cofinite. The cofiniteness follows from the finite-dimensionality of the solution space of an associated complex-coefficient linear differential equation. As an application, under the condition of $C_1$-cofiniteness, we establish the finiteness of the fusion rules and construct the fusion product.

math.QA↗
arXiv2025

Exploring $β$ decay and $β$-delayed neutron emission in exotic $^{46,47}$Cl isotopes

In this paper, $β^-$ and $β$-delayed neutron decays of $^{46,47}$Cl are reported from an experiment carried out at the National Superconducting Cyclotron Laboratory using the Beta Counting System. The half-lives of both $^{46}$Cl and $^{47}$Cl were extracted. Based on the delayed $γ$-ray transitions observed, the level structure of $N = 28$ $^{46}$Ar was determined. Completely different sets of excited states above the first $2^+$ state in $^{46}$Ar were populated in the $^{46}$Cl $\beta0n$ and $^{47}$Cl $\beta1n$ decay channels. Two new $γ$-ray transitions in $^{47}$Ar were identified from the very weak $^{47}$Cl $\beta0n$ decay. Furthermore, $^{46}$Cl $\beta1n$ and $^{47}$Cl $\beta2n$ were also observed to yield different population patterns for levels in $^{45}$Ar, including states of different parities. The experimental results allow us to address some of the open questions related to the delayed neutron emission process. For isotopes with large neutron excess and high $Q_β$ values, delayed neutron emission remains an important decay mode and can be utilized as a powerful spectroscopic tool. Experimental results were compared with shell-model calculations using the FSU and $V_{MU}$ effective interactions.

nucl-ex↗
arXiv2025

Bimodules over twisted Zhu algebras and twisted fusion rules theorem for vertex operator algebras

Let $V$ be a strongly rational vertex operator algebra, and let $g_1, g_2, g_3$ be three commuting finitely ordered automorphisms of $V$ such that $g_1g_2=g_3$ and $g_i^T=1$ for $i=1, 2, 3$ and $T\in \N$. Suppose $M^1$ is a $g_1$-twisted module. For any $n, m\in \frac{1}{T}\N$, we construct an $A_{g_3, n}(V)$-$A_{g_2, m}(V)$-bimodule $\mathcal{A}_{g_3, g_2, n, m}(M^1)$ associated to the quadruple $(M^1, g_1, g_2, g_3)$. Given an $A_{g_2, m}(V)$-module $U$, an admissible $g_3$-twisted module $\mathcal{M}(M^1, U)$ is constructed. For the quadruple $(V, 1, g, g)$ with some finitely ordered $g\in \text{Aut}(V)$, $\mathcal{A}_{g, g, n, m}(V)$ coincides with the $A_{g, n}(V)$-$A_{g, m}(V)$-bimodules $A_{g, n, m}(V)$ constructed by Dong-Jiang, and $\mathcal{M}(V, U)$ is the generalized Verma type admissible $g$-twisted module generated by $U$. When $U=M^2(m)$ is the $m$-th component of a $g_2$-twisted module $M^2$ for some $m\in\frac{1}{T}\N$, we show that the submodule of $\M(M^1, M^2(m))$ generated by the $m$-th component satisfies the universal property of the tensor product of $M^1$ and $M^2$. Using this result, we obtain a twisted version of Frenkel-Zhu-Li's fusion rules theorem.

math.QA↗
arXiv2024

Twisted restricted conformal blocks of vertex operator algebras II: twisted restricted conformal blocks on totally ramified orbicurves

In this paper, we introduce a notion of twisted restricted conformal blocks on totally ramified orbicurves and establish an isomorphism between the space of twisted restricted conformal blocks and the space of twisted conformal blocks. The relationships among twisted (restricted) conformal blocks, $g$-twisted (restricted) correlation functions, and twisted intertwining operators are explored. Furthermore, by introducing a geometric generalization of Zhu's algebra and its modules, we obtain a description of the space of coinvariants by modules over associative algebras and show it is finite-dimensional under some conditions. In particular, a more conceptual proof of the $g$-twisted fusion rules theorem in vertex operator algebra theory is provided.

math.AG↗
arXiv2023

Twisted restricted conformal blocks of vertex operator algebras I: $g$-twisted correlation functions and fusion rules

In this paper, we introduce a notion of $g$-twisted restricted conformal block on the three-pointed twisted projective line $\mathfrak{x}\colon\overline{C}\to\mathbb{P^1}$ associated with an untwisted module $M^1$ and the bottom levels of two $g$-twisted modules $M^2$ and $M^3$ over a vertex operator algebra $V$. We show that the space of twisted restricted conformal blocks is isomorphic to the space of $g$-twisted (restricted) correlation functions defined by the same datum and to the space of intertwining operators among these twisted modules. As an application, we derive a twisted version of the Fusion Rules Theorem.

math.QA↗
arXiv2023

Low spin spectroscopy of neutron-rich 43,44,45Cl via β and (β}n decay

β decay of neutron-rich isotopes 43,45 S,studied at the National Superconducting Cyclotron Laboratory is reported here. β delayed γ transitions were detected by an array of 16 clover detectors surrounding the Beta Counting Station which consists of a 40x40 Double Sided Silicon Strip Detector followed by a Single Sided Silicon Strip Detector. β decay half-lives have been extracted for 43,45 S by correlating implants and decays in the pixelated implant detector with further coincidence with γ transitions in the daughter nucleus. The level structure of 43,45 Cl is expanded by the addition of 20 new γ transitions in 43Cl and 8 in 45 Cl with the observation of core excited negative-parity states for the first time. For 45 S decay, a large fraction of the β decay strength goes to delayed neutron emission populating states in 44 Cl which are also presented. Comparison of experimental observations is made to detailed shell-model calculations using the SDPFSDG-MU interaction to highlight the role of the diminished N = 28 neutron shell gap and the near degeneracy of the proton s 1/2 and d 3/2 orbitals on the structure of the neutron-rich Cl isotopes. The current work also provides further support to a ground state spin-parity assignment of 3/2 + in 45 Cl.

nucl-ex↗
arXiv2023

$β^-$ decay of neutron-rich $^{45}$Cl at magic number N=28

Results from the study of $β^-$-decay of $^{45}$Cl, produced in the fragmentation of a 140-MeV/u $^{48}$Ca beam, are presented. The half-life for $^{45}$Cl $β$-decay is measured to be 513(36) ms. The $β^-$ and $β^- 1n$ decay of $^{45}$Cl populated excited states in $^{45,44}$Ar, respectively. On the basis of $γ$-ray singles and $γ$-$γ$ coincidence data, decay schemes for the two daughter nuclei have been established. They are compared with shell model calculations using the FSU interaction. The low-lying negative parity states for $^{45}$Ar are well described by a single particle (neutron) occupying orbitals near the Fermi surface, whereas neutron excitations across the $N = 20$ shell gap are needed to explain the positive-parity states which are expected to be populated in allowed Gamow-Teller $β$-decay of $^{45}$Cl. The highest $β$-feeding to the 5/2$^+$ state in $^{45}$Ar from the ground state of $^{45}$Cl points towards a 3/2$^+$ spin-parity assignment of the ground state of the parent over the other possibility of 1/2$^+$. The high Q$_{β^-}$ value of $^{45}$Cl decay allows for the population of $1p1h$ states above the neutron separation energy in $^{45}$Ar leading to positive parity states of $^{44}$Ar being populated by removal of one neutron from the $sd$ shell. The spin-parities of the excited levels in $^{44}$Ar are tentatively assigned for the first time by comparison with the shell model calculations. The 2978~keV level of $^{44}$Ar is identified as the excited 0$^+$ level which could correspond to a different configuration from the ground state.

nucl-ex↗
arXiv2023

Bimodues associated to twisted modules of vertex operator algebras and fusion rules

Let $V$ be a vertex operator algebra, $T\in \mathbb{N}$ and $(M^k, Y_{M^k})$ for $k=1, 2, 3$ be a $g_k$-twisted module, where $g_k$ are commuting automorphisms of $V$ such that $g_k^T=1$ for $k=1, 2, 3$ and $g_3=g_1g_2$. Suppose $I(\cdot, z)$ is an intertwining operator of type $({array}{c} M^{3} M^{1} M^{2} {array}) $. We construct an $A_{g_1g_2}(V)$-$A_{g_2}(V)$-bimodule $A_{g_1g_2, g_2}(M^1)$ which determines the action of $M^1$ from the bottom level of $M^2$ to the bottom level of $M^3$ and explored its connections with fusion rules.

math.QA↗
arXiv2019

Learned Sectors: A fundamentals-driven sector reclassification project

Market sectors play a key role in the efficient flow of capital through the modern Global economy. We analyze existing sectorization heuristics, and observe that the most popular - the GICS (which informs the S&P 500), and the NAICS (published by the U.S. Government) - are not entirely quantitatively driven, but rather appear to be highly subjective and rooted in dogma. Building on inferences from analysis of the capital structure irrelevance principle and the Modigliani-Miller theoretic universe conditions, we postulate that corporation fundamentals - particularly those components specific to the Modigliani-Miller universe conditions - would be optimal descriptors of the true economic domain of operation of a company. We generate a set of potential candidate learned sector universes by varying the linkage method of a hierarchical clustering algorithm, and the number of resulting sectors derived from the model (ranging from 5 to 19), resulting in a total of 60 candidate learned sector universes. We then introduce reIndexer, a backtest-driven sector universe evaluation research tool, to rank the candidate sector universes produced by our learned sector classification heuristic. This rank was utilized to identify the risk-adjusted return optimal learned sector universe as being the universe generated under CLINK (i.e. complete linkage), with 17 sectors. The optimal learned sector universe was tested against the benchmark GICS classification universe with reIndexer, outperforming on both absolute portfolio value, and risk-adjusted return over the backtest period. We conclude that our fundamentals-driven Learned Sector classification heuristic provides a superior risk-diversification profile than the status quo classification heuristic.

q-fin.GN↗