Nathan Witkin, in his article The Cost of Closed Doors…, attempts to reframe the question of whether child dependency proceedings should be open or closed to the public and press by positing a balancing test between “dependent families seeking privacy…and the macro-level benefits of a more transparent system.” Witkin’s hypothesis is that opening dependency proceedings educates the public that child welfare spending must be increased, that transparency leads to “greater per capita” spending in open versus closed dependency systems, and finally, that more child welfare spending will result in fewer per capita child welfare fatalities in open court states. This article will examine both sides of Witkin’s proposed balancing test to demonstrate that his approach fails to prove his hypotheses. First, it will discuss how Witkin’s almost total reliance on twenty-five to thirty-year-old psychological studies rather than on contemporary mental health research substantially understates the potential dangers to child abuse victims, especially LGBTQ+ and polyvictimized children, from opening child dependency proceedings. Second, it will present evidence that the welfare budgets did not constantly increase in some closed court states that were later opened to the public, but rather fluctuated through sporadic ups and downs which over time resulted in almost no net longitudinal budgetary increases. Second, those originally closed courts that were later opened had their child fatality rates actually increase which is the opposite of Witkin’s predictions.

Comic opera from the first half of the eighteenth century borrowed many of the structural and formal features of the dramma per musica. The arias of early comic opera were almost exclusively set in da capo form, which had become ubiquitous near the end of the seventeenth century. Although commentators and librettists frequently lamented the banality of this inherited convention, it persisted until about 1750, when, over the course of approximately a decade, it was replaced by a much more flexible approach to the formal organization of arias. This article investigates that period of experimentation and identifies the individuals who drove the innovations. I argue that two singers in particular, Francesco Baglioni and Serafina Penna, provided the impetus to break away from da capo form. Their desire for arias that displayed their dramatic and musical abilities to the greatest advantage led the librettist Carlo Goldoni to provide them with textual prompts that required new approaches to musical form. By emphasizing the connection between singers and librettists, I draw attention to the collaborative nature of operatic production. This approach also demonstrates the ways in which musical form, usually considered the purview of the composer, is in fact rooted in the features of the libretto and inspired by the inclinations and abilities of singers.

We argue that logicism, the thesis that mathematics is reducible to logic and analytic truths, is true. We do so by (a) developing a formal framework with comprehension and abstraction principles, (b) giving reasons for thinking that this framework is part of logic, (c) showing how the denotations for predicates and individual terms of an arbitrary mathematical theory can be viewed as logical objects that exist in the framework, and (d) showing how each theorem of a mathematical theory can be given an analytically true reading in the logical framework.

We prove new statistical results about the distribution of the cokernel of a random integral matrix with a concentrated residue. Given a prime p and a positive integer n, consider a random $n \times n$ matrix $X_n$ over the ring $\mathbb{Z}_p$ of p-adic integers whose entries are independent. Previously, Wood showed that as long as each entry of $X_n$ is not too concentrated on a single residue modulo p, regardless of its distribution, the distribution of the cokernel $\mathrm{cok}(X_n)$ of $X_n$, up to isomorphism, weakly converges to the Cohen–Lenstra distribution, as $n \rightarrow \infty$. Here on the contrary, we consider the case when $X_n$ has a concentrated residue $A_n$ so that $X_n = A_n + pB_n$. When $B_n$ is a Haar-random $n \times n$ matrix over $\mathbb{Z}_p$, we explicitly compute the distribution of $\mathrm{cok}(P(X_n))$ for every fixed n and a non-constant monic polynomial $P(t) \in \mathbb{Z}_p[t]$. We deduce our result from an interesting equidistribution result for matrices over $\mathbb{Z}_p[t]/(P(t))$, which we prove by establishing a version of the Weierstrass preparation theorem for the noncommutative ring $\mathrm{M}_n(\mathbb{Z}_p)$ of $n \times n$ matrices over $\mathbb{Z}_p$. We also show through cases the subtlety of the “universality” behavior when $B_n$ is not Haar-random.

Purulia, a district in the southwestern part of West Bengal, is popular for the renowned chhou dance. Despite the prevalent notion that chhou is exclusively a war dance, it dynamically incorporates contemporary social and political issues, and has undergone significant changes such as new musical instruments and technologies, lighting, costume transformations, and female performers.