“Workers without Borders:” Envisioning Sociality in Xiao Hai’s Poems

New worker poetry has emerged as a unique literary voice in contemporary China. This paper places Chinese new workers as the global working class and focuses on the poetics of their global vision. Through a close reading of poems written by Xiao Hai (1980-), one of the prolific worker poets, I argue that the new worker poet constructs global sociality at the levels of aesthetics, social critique, and cultural proposal. Aesthetically, Xiao Hai has borrowed inspiration from classical Chinese poetry, western counter-culture icons, and contemporary avant-garde spirit in his writings on laborers’ ordeals. Global sociality embodies a powerful critique of hierarchical global systems in which laborers are positioned at the bottom. It is also a cultural ideal rooted in revolutionary nostalgia and classical notions, a passionate call for connection among like-minded people, and an awareness of workers’ shared identity. Raising their voices in poetry, Xiao Hai, as well as other worker poets, actively explore opportunities to make their voices heard on a broader scal

Decompositions of periodic matrices into a sum of special matrices

We study the problem of when a periodic square matrix of order $n\times n$ over an arbitrary field $\mathbb{F}$ is decomposable into the sum of a square-zero matrix and a torsion matrix and show that this decomposition can always be obtained for matrices of rank at least $\frac{n}{2}$ when $\mathbb{F}$ is either a field of prime characteristic, or the field of rational numbers, or an algebraically closed field of zero characteristic. We also provide a counterexample to such a decomposition when $\mathbb{F}$ equals the field of the real numbers

Domination number and (signless Laplacian) spectral radius of cactus graphs

A cactus graph is a connected graph whose block is either an edge or a cycle. A vertex set $S\subseteq V(G)$ is said to be a dominating set of a graph $G$ if every vertex in $V(G)\setminus S$ is adjacent to a vertex in $S$. There are several results on the (signless Laplacian) spectral radius and domination number in graph theory. In this paper, we determine the unique graph with the maximum adjacency spectral radius and signless Laplacian spectral radius among all cactus graphs with fixed domination number

Expressing matrices in SLn(F)\mathrm{SL}_{n}(F) as products of commutators of unipotent matrices

This paper aims to show that for two positive integers $n \ge k$, every nonscalar matrix in the special linear group of degree $n$ over a field can be written as a product of a maximum of two commutators of unipotent matrices of index $k$. This fact also holds for scalar matrices over a quadratically closed field. Using GAP, some examples are provided to highlight the significance of the field's cardinality and to show that the assumption of quadratically closed fields is essential

Edge-disjoint spanning trees and balloons in (multi-)graphs from size or spectral radius

A multigraph is a graph that may have multiple edges, but has no loops. The multiplicity of a multigraph is the maximum number of edges between any pair of vertices. The spanning tree packing number of a graph $G$, denoted by $\tau(G)$, is the maximum number of edge-disjoint spanning trees contained in $G$. A balloon of a graph $G$ is a maximal 2-edge-connected subgraph that is joined to the rest of $G$ by exactly one cut edge. By $b(G)$, $e(G)$, and $\kappa(G)$, we denote the number of balloons, the size, and the vertex-connectivity of $G$, respectively. In this paper, we show that for a positive integer $k$ and any multigraph $G$ of order $n\geq 2r$ with multiplicity $m\leq k$ and minimum degree $\delta \geq2k$, if $e(G)\geq m[\binom{r}{2}+\binom{n-r}{2}]+k,$ then $\tau(G)\geq k$, where $r=\lceil(\delta+1)/m\rceil$. This extends the result of Fan, Gu and Lin (J. Graph Theory, 2023). Analogous results involving the size to characterize $\kappa(G)\geq k$ or $b(G)\leq k-1$ of a multigraph $G$ are also presented. In addition, we prove a tight sufficient condition to guarantee $b(G)\leq k-1$ in terms of the spectral radius of a simple graph $G$, with extremal graphs characterized

Probabilistic zero forcing with vertex reversion

Probabilistic zero forcing is a graph coloring process in which blue vertices "infect" (color blue) white vertices with a probability proportional to the number of neighboring blue vertices. This paper introduces reversion probabilistic zero forcing (RPZF), which shares the same infection dynamics but also allows for blue vertices to revert to being white in each round. A threshold number of blue vertices is produced such that the complete graph is entirely blue in the next round of RPZF with high probability. Utilizing Markov chain theory, a tool is formulated which, given a graph's RPZF Markov transition matrix, calculates the probability of whether the graph becomes all white or all blue as well as the time at which this is expected to occur

Semirings in which the permanent of invertible matrices is multiplicative

We show that, if $1+2xy=1$ holds for all elements $x,\,y$ with additive inverses in a commutative semiring $\mathcal{S}$, then the function of permanent is multiplicative on the matrices with multiplicative inverses over $\mathcal{S}$

Godsil-McKay switchings for gain graphs

We introduce a switching operation, inspired by the Godsil-McKay switching, in order to obtain pairs of $G$-cospectral gain graphs, that are gain graphs cospectral with respect to every representation of the gain group $G$. For instance, for two signed graphs, this notion of cospectrality is equivalent to the cospectrality of their signed adjacency matrices together with the cospectrality of their underlying graphs. Moreover, we introduce another more flexible switching in order to obtain pairs of gain graphs cospectral with respect to some fixed unitary representation. Many existing notions of spectrum for graphs and gain graphs are indeed special cases of these spectra associated with particular representations, therefore our construction recovers the classical Godsil-McKay switching and the Godsil-McKay switching for signed and complex unit gain graphs. As in the classical case, not all gain graphs are suitable for these switchings: we analyze the relationships between the properties that make the graph suitable for the one or the other switching. Finally, we apply our construction in order to define a Godsil-McKay switching for the right spectrum of quaternion unit gain graphs

Topics of Interest Formative Assessment, Single-Point Rubric

For some years, the need for deeper thought and personal reflection on the mission and purpose of formal education has become grist for the political mill. Germane here are issues related not only to what to teach, but how to teach it; thornier decisions must be grappled with in the wrestling rings of assessment and of equity.  Among other domains in education, critical thinking and formative assessment hold meaning for me. The scholarship of teaching and learning (SoTL) carries promise, at least possibly for the short term

Graph products that allow two distinct eigenvalues

The parameter $q(G)$ of a graph $G$ is the minimum number of distinct eigenvalues of a symmetric matrix whose pattern is given by $G$. We introduce a novel graph product by which we construct new infinite families of graphs that achieve $q(G)=2$. Several graph families for which it is already known that $q(G)=2$ can also be thought of as arising from this new product