arXiv subjects

Bo Hou

Publications and source records attributed to Bo Hou.

At least 19 recordsLinked to original sources

arXiv2026

Construction of diassociative bialgebras from antisymmetric infinitesimal bialgebras and related algebra structures

There is a diassociative algebra structure on the tensor product of an associative algebra and a perm algebra. In this paper, we elevate this conclusion to the level of bialgebra.We prove that the tensor product of an antisymmetric infinitesimal bialgebra and a quadratic perm algebra has a diassociative bialgebra structure, and this diassociative bialgebra structure is coboundary (resp. quasi-triangular, triangular, factorizable) if the original antisymmetric infinitesimal bialgebra is coboundary (resp. quasi-triangular,triangular, factorizable). As an application, we provide the close relationship between Lie bialgebras, Leibniz bialgebras, diassociative bialgebras and antisymmetric infinitesimal bialgebras, and the close relationship between symplectic Lie algebras, symplectic Leibniz algebras, symplectic associative algebras and symplectic diassociative algebras.

math.RA↗

arXiv2026

Leibniz bialgebras constructed by tensor product from Lie bialgebras and perm bialgebras

The construction problem of Leibniz bialgebras from Lie bialgebras and perm bialgebras is considered in this paper. We show that there is a Leibniz algebra structure on the tensor product of a Lie algebra and a perm algebra, and elevate this conclusion to the level of bialgebra. We prove that the tensor product of a quadratic Lie algebra and a perm bialgebra has a Leibniz bialgebra structure, and this Leibniz bialgebra structure is coboundary (resp. quasi-triangular, triangular, factorizable) if the original perm bialgebra is coboundary (resp. quasi-triangular, triangular, factorizable). Moreover, we constructed an infinite-dimensional Leibniz bialgebra using the tensor product of a finite-dimensional Lie bialgebra and a quadratic $\bz$-graded perm algebra. Quasi-triangular and triangular infinite-dimensional Leibniz bialgebras are considered.

math.RA↗

arXiv2026

Lie bialgebras constructed from Zinbiel bialgebras and Leibniz bialgebras

There is a Lie algebra structure on the tensor product of a Leibniz algebra and a Zinbiel algebra for the operads of Leibniz algebras and Zinbiel algebras are Koszul dual. In this paper, we extend such conclusion to the context of bialgebras. We show that there is a Lie bialgebra structure on the tensor product of a Leibniz bialgebra and a quadratic Zinbiel algebra; there is an infinite-dimensional Lie bialgebra structure on the tensor product of a Zinbiel bialgebra and a quadratic $\mathbb{Z}$-graded Leibniz algebra. For special quadratic $\mathbb{Z}$-graded Leibniz algebra, the tensor product with a Zinbiel bialgebra being a Lie bialgebra characterizes the Zinbiel bialgebra. By analyzing the relationship between solutions of the classical Yang-Baxter equation in a Zinbiel algebra (resp. a Leibniz algebra) and solutions of the classical Yang-Baxter equation in the induced Lie algebra, we prove that the induced Lie bialgebra is quasi-triangular (resp. triangular, factorizable) if the original Zinbiel bialgebra (resp. Leibniz bialgebra) is quasi-triangular (resp. triangular, factorizable). Finally, we provide a construction of a quasi-Frobenius Lie algebra on the tensor product of a quasi-Frobenius Zinbiel algebra and a quadratic Leibniz algebra.

math.RT↗

arXiv2026

Quasi-triangular dual pre-Poisson bialgebras and its connection with Poisson bialgebras

In this paper, the notions of quasi-triangular and factorizable dual pre-Poisson bialgebras are introduced. A factorizable dual pre-Poisson bialgebra induces a factorization of the underlying dual pre-Poisson algebra, and the double of any dual pre-Poisson bialgebra is factorizable. We introduce the notion of quadratic Rota-Baxter dual pre-Poisson algebras and show that there is a one-to-one correspondence between factorizable dual pre-Poisson bialgebras and quadratic Rota-Baxter Poisson algebras of nonzero weights. Moreover, a method of constructing infinite-dimensional dual pre-Poisson bialgebras using finite-dimensional Poisson bialgebras is given. We prove that there is a completed dual pre-Poisson bialgebra structure the tensor product of a Poisson bialgebra and a quadratic $\bz$-graded perm algebra, and this completed dual pre-Poisson bialgebra structure is coboundary (resp. quasi-triangular, triangular) if the original Poisson bialgebra is coboundary (resp. quasi-triangular, triangular). The induced factorizable finite-dimensional dual pre-Poisson bialgebras are considered.

math.RA↗

arXiv2026

Affinization of dendriform $\md$-bialgebras, Lie bialgebras and solutions of classical Yang-Baxter equation

In this paper, we mainly discuss how to use dendriform $\md$-bialgebras to construct Lie bialgebras and the relationship between the solutions of their corresponding Yang-Baxter equations. We provide two methods for obtaining Lie algebras from dendriform algebras using the tensor product with perm algebras, one by means of associative algebras and the other by means of pre-Lie algebras. We elevate both approaches to the level of bialgebras and prove that the Lie bialgebraa obtained using these two approaches are the same. There is a correspondence between symmetric solutions of the dendriform Yang-Baxter equation in dendriform algebras and certain skew-symmetric solutions of the classical Yang-Baxter equation in the Lie algebras induced from the dendriform algebras. The connections between triangular bialgebra structures, $\mathcal{O}$-operators related to the solutions of these Yang-Baxter equations are discussed in detail. During the discussion, we also present a method for constructing infinite-dimensional antisymmetric infinitesimal bialgebra by using the affineization of dendriform $\md$-bialgebras.

math.RA↗

arXiv2025

Affinization of Zinbiel bialgebras and pre-Poisson bialgebras, infinite-dimensional Poisson bialgebras

The purpose of this paper is to construct infinite-dimensional Poisson bialgebras by the affinization of pre-Poisson algebras. There is a natural Poisson algebra structure on the tensor product of a pre-Poisson algebra and a perm algebra, and the Poisson algebra structure on the tensor product of a pre-Poisson algebra and a special perm algebra characterizes the pre-Poisson algebra. We extend such correspondences to the context of bialgebras, that is, there is a Poisson bialgebra structure on the tensor product of a pre-Poisson bialgebra and a quadratic $\bz$-graded perm algebra.In this process, we provide the affinization of Zinbiel bialgebras, and give a correspondence between symmetric solutions of the Yang-Baxter equation in pre-Poisson algebras and certain skew-symmetric solutions of the Yang-Baxter equation in the induced infinite-dimensional Poisson algebras. The similar correspondences for the related triangular bialgebra structures and $\mathcal{O}$-operators are given.

math.RA↗

arXiv2025

Unveiling spin-orbital angular momentum locking in photonic Dirac vortex cavities

Dirac vortices, originally studied in quantum field theories to predict localized zero-energy modes, were recently realized in photonics, leading to Dirac vortex cavities. With topological protection, Dirac vortex cavities offer robust single-mode large-area localized modes appealing for high-performance micro-lasers and other applications. As a spectrally-isolated single mode, the radiation of a Dirac vortex cavity mode was believed as having vanishing orbital angular momentum due to time-reversal symmetry. Here, we report the direct observation of orbital angular momentum radiation of a Dirac vortex cavity through spin-resolved measurements. Remarkably, we confirm the spin-orbital angular momentum locking in such radiation due to the spin-valley locking and inter-valley couplings. We demonstrate that the spin-orbital angular momentum locking is controlled by the chirality of the Kekul\'e modulation and propose design schemes for arbitrary-order single-mode OAM radiation.

physics.optics↗

arXiv2025

LLM-Driven Collaborative Model for Untangling Commits via Explicit and Implicit Dependency Reasoning

Atomic commits, which address a single development concern, are a best practice in software development. In practice, however, developers often produce tangled commits that mix unrelated changes, complicating code review and maintenance. Prior untangling approaches (rule-based, feature-based, or graph-based) have made progress but typically rely on shallow signals and struggle to distinguish explicit dependencies (e.g., control/data flow) from implicit ones (e.g., semantic or conceptual relationships). In this paper, we propose ColaUntangle, a new collaborative consultation framework for commit untangling that models both explicit and implicit dependencies among code changes. ColaUntangle integrates Large Language Model (LLM)-driven agents in a multi-agent architecture: one agent specializes in explicit dependencies, another in implicit ones, and a reviewer agent synthesizes their perspectives through iterative consultation. To capture structural and contextual information, we construct Explicit and Implicit Contexts, enabling agents to reason over code relationships with both symbolic and semantic depth. We evaluate ColaUntangle on two widely-used datasets (1,612 C# and 14k Java tangled commits). Experimental results show that ColaUntangle outperforms the best-performing baseline, achieving an improvement of 44% on the C# dataset and 82% on the Java dataset. These findings highlight the potential of LLM-based collaborative frameworks for advancing automated commit untangling tasks.

cs.AI↗

arXiv2025

Quasi-triangular Novikov bialgebras and related bialgebra structures

We introduce the notion of quasi-triangular Novikov bialgebras, which constructed from solutions of the Novikov Yang-Baxter equation whose symmetric parts are invariant. Triangular Novikov bialgebras and factorizable Novikov bialgebras are important subclasses of quasi-triangular Novikov bialgebras. A factorizable Novikov bialgebra induces a factorization of the underlying Novikov algebra and the double of any Novikov bialgebra naturally admits a factorizable Novikov bialgebra structure. Moreover, we introduce the notion of quadratic Rota-Baxter Novikov algebras and show that there is an one-to-one correspondence between factorizable Novikov bialgebras and quadratic Rota-Baxter Novikov algebras of nonzero weights. Finally, we obtain that the Lie bialgebra induced by a Novikov bialgebra and a quadratic right Novikov algebra is quasi-triangular (resp. triangular, factorizable) if the Novikov bialgebra is quasi-triangular (resp. triangular, factorizable), and under certain conditions, the Novikov bialgebra induced by a differential infinitesimal bialgebra is quasi-triangular (resp. triangular, factorizable) if the differential infinitesimal bialgebra is quasi-triangular (resp. triangular, factorizable).

math.RA↗

arXiv2025

Giant and Rapidly Switching Intrinsic Chirality Enabled by Toroidal Quasi-Bound States in the Continuum

Circular dichroism (CD), arising from spin-selective light-matter interactions controlled by chirality, is critical for advanced applications such as chiral imaging and ultrasensitive biosensing. However, CD of chiral natural materials is inherently constrained owing to molecular symmetry and thermodynamic stability. Recently, artificially engineered metasurfaces incorporating chiral quasi-bound states in the continuum (Q-BICs) have emerged as a promising solution, which enables near-unity CD responses. However, their current designs heavily rely on complex three-dimensional geometries, posing significant challenges for integration with planar on-chip platforms. To address the stringent challenges, we demonstrate a truly planar metasurface that achieves giant intrinsic chiral responses by utilizing a chiral Q-BIC dominated by out-of-plane toroidal dipoles (Tz). With deep-subwavelength ({\lambda}/20) thickness, our metasurface exhibits outstanding intrinsic CD values in both simulations (>0.90) and experiments (~0.80). Moreover, in contrast to previous electric or magnetic chiral Q-BICs, the toroidal Q-BIC produces a rapidly switching CD response - transitioning sharply between positive and negative giant CD values within ~0.2 GHz, and the switching is highly sensitive to small oblique incidence of opposite angles. Therefore, our scheme provides a planar platform for studying chiral light-matter interactions involving toroidal dipoles, important for future development of polarization- and angle-sensitive photonic and optoelectronic devices.

physics.optics↗

arXiv2025

The non-abelian extension and Wells map of Leibniz conformal algebra

In this paper, we study the theory of non-abelian extensions of a Leibniz conformal algebra $R$ by a Leibniz conformal algebra $H$ and prove that all the non-abelian extensions are classified by non-abelian $2$nd cohomology $H^2_{nab}(R,H)$ in the sense of equivalence. Then we introduce a differential graded Lie algebra $\mathfrak{L}$ and show that the set of its Maurer-Cartan elements in bijection with the set of non-abelian extensions. Finally, as an application of non-abelian extension, we consider the inducibility of a pair of automorphisms about a non-abelian extension, and give the fundamental sequence of Wells of Leibniz conformal algebra $R$. Especially, we discuss the extensibility problem of derivations about an abelian extension of $R$.

math.RA↗

arXiv2025

Direct Observation of Strongly Tilted Dirac Points at General Positions in the Reciprocal Space

Type-II Dirac points (DPs), which occur at the intersection of strongly tilted and touching energy bands, exhibit many intriguing physical phenomena fundamentally different from the non-tilted type-I counterparts. Over the past decade, their discovery has spurred extensive research into electronic systems and other Bloch-wave systems, such as photonic and phononic crystals. However, current studies typically focus on type-II DPs along high-symmetry directions in the first Brillouin zone (FBZ) under mirror symmetry conditions, which are highly restrictive and limit further investigations and applications. To overcome the stringent constraint, here we identify and demonstrate the emergence of type-II DPs at general positions inside the FBZ without requiring the mirror symmetry. The type-II DPs, being accidental degeneracies, are experimentally realized on a metacrystal slab with H-shaped metallic patterns. Our findings indicate that even in the absence of mirror symmetry, type-II DPs can emerge at designated locations inside the FBZ by simply rotating the H-shaped patterns and adjusting geometrical and physical parameters. Furthermore, based on the rotated type-II DPs, off-axis conical diffractions have been both realized and experimentally observed. Meanwhile, we discovered that during the rotation process, the type-II DPs transform into off-axis type-I DPs, but still strongly tilted, resulting in the emergence of negative refractions. Hence, the generic method we propose for inducing type-II or strongly tilted type-I DPs without the high-symmetry limitations opens potential avenues for related research. For example, the observed off-axis conical diffraction and negative refraction could inspire future development and applications in photonics and other Bloch-wave systems.

physics.optics↗

arXiv2024

Quasi-triangular, triangular, factorizable anti-Leibniz bialgebras and anti-Leibniz Yang-Baxter equation

We introduce the notion of an anti-Leibniz bialgebra which is equivalent to a Manin triple of anti-Leibniz algebras, is equivalent to a matched pair of anti-Leibniz algebras. The study of some special anti-Leibniz bialgebras leads to the introduction of the anti-Leibniz Yang-Baxter equation in an anti-Leibniz algebra. A symmetric (or an invariant) solution of the anti-Leibniz Yang-Baxter equation gives an anti-Leibniz bialgebra. The notion of a relative Rota-Baxter operator of an anti-Leibniz algebra is introduced to construct symmetric solutions of the anti-Leibniz Yang-Baxter equation. Moreover, we introduce the notions of factorizable anti-Leibniz bialgebras and skew-symmetric Rota-Baxter anti-Leibniz algebras, and show that a factorizable anti-Leibniz bialgebra leads to a factorization of the underlying anti-Leibniz algebra. There is a one-to-one correspondence between factorizable anti-Leibniz bialgebras and skew-quadratic Rota-Baxter anti-Leibniz algebras. Finally, we constrict anti-Leibniz bialgebras form Leibniz bialgebras by the tensor product and constrict infinite-dimensional anti-Leibniz bialgebras form finite-dimensional anti-Leibniz bialgebras by the completed tensor product.

math.RA↗

arXiv2024

Averaging antisymmetric infinitesimal bialgebra and perm bialgebras

We establish a bialgebra theory for averaging algebras, called averaging antisymmetric infinitesimal bialgebras by generalizing the study of antisymmetric infinitesimal bialgebras to the context of averaging algebras. They are characterized by double constructions of averaging Frobenius algebras as well as matched pairs of averaging algebras. Antisymmetric solutions of the Yang-Baxter equation in averaging algebras provide averaging antisymmetric infinitesimal bialgebras. The notions of an $\mathcal{O}$-operator of an averaging algebra and an averaging dendriform algebra are introduced to construct antisymmetric solutions of the Yang-Baxter equation in an averaging algebra and hence averaging antisymmetric infinitesimal bialgebras. Moreover, we introduce the notion of factorizable averaging antisymmetric infinitesimal bialgebras and show that a factorizable averaging antisymmetric infinitesimal bialgebra leads to a factorization of the underlying averaging algebra. We establish a one-to-one correspondence between factorizable averaging antisymmetric infinitesimal bialgebras and symmetric averaging Frobenius algebras with a Rota-Baxter operator of nonzero weight. Finally, we apply the study of averaging antisymmetric infinitesimal bialgebras to perm bialgebras, extending the construction of perm algebras from commutative averaging algebras to the context of bialgebras, which is consistent with the well constructed theory of perm bialgebras.

math.RA↗

arXiv2024

Dissolution of the non-Hermitian skin effect in one-dimensional lattices with linearly varying nonreciprocal hopping

We study the one-dimensional non-Hermitian lattices with linearly varying nonreciprocal hopping, where the non-Hermitian skin effect (NHSE) is found to be dissolved gradually as the strength of nonreciprocity increases. The energy spectrum under the open boundary condition is composed of real and imaginary eigenenergies when the nonreciprocal hopping is weak. Interestingly, the real eigenenergies form an equally spaced ladder, and the corresponding eigenstates are localized at the boundary with a Gaussian distribution due to NHSE. By increasing the nonreciprocity, the number of real eigenenergies will decrease while more and more eigenenergies become imaginary. Accompanied by the real-imaginary transition in the spectrum, the eigenstates are shifted from the boundary into the bulk of the lattice. When the nonreciprocity gets strong enough, the whole spectrum will be imaginary and the NHSE disappears completely in the system; i.e., all the eigenstates become Gaussian bound states localized inside the bulk. Our work unveils the exotic properties of non-Hermitian systems with spatially varying nonreciprocal hopping.

quant-ph↗

arXiv2023

Extending structures for perm algebras and perm bialgebras

We investigate the theory of extending structures by the unified product for perm algebras, and the factorization problem as well as the classifying complements problem in the setting of perm algebras. For a special extending structure, non-abelian extension, we study the inducibility of a pair of automorphisms associated to a non-abelian extension of perm algebras, and give the fundamental sequence of Wells in the context of perm algebras. For a special extending structure, bicrossed product, we introduce the concept of perm bialgebras, equivalently characterized by Manin triples of perm algebras and certain matched pairs of perm algebras. We introduce and study coboundary perm bialgebras, and our study leads to the ''$\mathcal{S}$-equation" in perm algebras, which is an analogue of the classical Yang-Baxter equation. A symmetric solution of $\mathcal{S}$-equation gives a perm bialgebra.

math.RA↗

arXiv2023

Wannier-Stark localization in one-dimensional amplitude-chirped lattices

We study the Wannier-Stark (WS) localization in one-dimensional amplitude-chirped lattices with the $j$th onsite potential modulated by a function $Fj\cos(2\pi \alpha j)$, where $F$ is the external field with a period determined by $\alpha=p/q$ ($p$ and $q$ are coprime integers). In the Hermitian (or non-Hermitian) systems with real (or imaginary) fields, we can obtain real (or imaginary) WS ladders in the eigenenergy spectrum. In most cases with $q \geq 2$, there are multiple WS ladders with all the eigenstates localized in the strong field limit. However, in the lattices with $q=4$, the energy-dependent localization phenomenon emerges due to the presence of both spatially periodic and linearly increasing behaviors in the onsite potential. About half the number of eigenstates are gathered at the band center and can extend over a wide region or even the full range of the lattice, even when the field becomes very strong. Moreover, in the non-Hermitian lattices with odd $q$, some of the WS ladders become doubly degenerate, where the eigenstates are evenly distributed at two neighboring sites in a wide regime of field strength. Our work opens an avenue for exploring WS localization in both Hermitian and non-Hermitian amplitude-chirped lattices.

cond-mat.dis-nn↗

arXiv2023

M$^3$Fair: Mitigating Bias in Healthcare Data through Multi-Level and Multi-Sensitive-Attribute Reweighting Method

In the data-driven artificial intelligence paradigm, models heavily rely on large amounts of training data. However, factors like sampling distribution imbalance can lead to issues of bias and unfairness in healthcare data. Sensitive attributes, such as race, gender, age, and medical condition, are characteristics of individuals that are commonly associated with discrimination or bias. In healthcare AI, these attributes can play a significant role in determining the quality of care that individuals receive. For example, minority groups often receive fewer procedures and poorer-quality medical care than white individuals in US. Therefore, detecting and mitigating bias in data is crucial to enhancing health equity. Bias mitigation methods include pre-processing, in-processing, and post-processing. Among them, Reweighting (RW) is a widely used pre-processing method that performs well in balancing machine learning performance and fairness performance. RW adjusts the weights for samples within each (group, label) combination, where these weights are utilized in loss functions. However, RW is limited to considering only a single sensitive attribute when mitigating bias and assumes that each sensitive attribute is equally important. This may result in potential inaccuracies when addressing intersectional bias. To address these limitations, we propose M3Fair, a multi-level and multi-sensitive-attribute reweighting method by extending the RW method to multiple sensitive attributes at multiple levels. Our experiments on real-world datasets show that the approach is effective, straightforward, and generalizable in addressing the healthcare fairness issues.

cs.LG↗