Given a unital $C^*$-algebra and a faithful trace, we prove that the topology on the associated density space induced by the $C^*$-norm is finer than the Bures metric topology. We also provide an example when this containment is strict. Next, we provide a metric on the density space induced by a quantum metric in the sense of Rieffel and prove that the induced topology is the same as the topology induced by the Bures metric and $C^*$-norm when the $C^*$-algebra is assumed to be finite dimensional. Finally, we provide an example where the Bures metric and induced quantum metric are not metric equivalent. Thus, we provide a bridge between these aspects of quantum information theory and noncommutative metric geometry.

The overuse and inappropriate use of antimicrobials have led to environmental waste and drug shortages. This challenges the ecological and economical sustainability of our healthcare system and worsens antimicrobial resistance.

Antimicrobial stewardship programs (ASP) commonly consider the cost of drug acquisition but may be failing to recognize the hidden costs of multi-dose intravenous regimens including additional nursing administration time, tubing and fluids, and potentially increased hospital length of stay. They also rarely consider the environmental impact of medical waste creation and disposal, which contributes to the global antimicrobial resistance crisis. These costs are harder to calculate but crucial to a comprehensive assessment of a medication’s total impact. In this invited commentary, we provide an example of a stewardship evaluation at our institution focused on changing from meropenem (MER) to ertapenem (ETP) for infections caused by extended-spectrum beta-lactamase producing organisms. We found that despite an increase in acquisition costs, changing from MER to ETP is associated with overall savings and decreased waste production. A secondary analysis suggests that stay length may also be improved with this substitution.

We present a holistic approach to antimicrobial stewardship that considers the total cost of an antimicrobial. By broadening their view to include hidden costs and secondary effects, ASPs can further demonstrate their value to the healthcare system, reduce resistance, and improve their environmental impact.

Epistemic trust in others frequently cannot be disentangled from interpersonal trust more generally, but the epistemic implications of how we affectively express our trust in others are under-investigated. This essay claims that gratitude, despite its empirically undeniable importance to human flourishing generally, is also important epistemically and in several intersecting ways. To be grateful to a person is to represent the world differently in key respects. Gratitude, even if it is for past non-epistemic benefits, should play an important role in shaping who we epistemically rely on. Gratitude for specifically epistemic benefits is an important way in which we show our attunement to epistemic value and contribute to the incentive structures that make much of our public knowledge and informational ecosystems possible. Likewise, ingratitude is a crippling epistemic vice that renders our dependence on quality sources of information fragile and vulnerable to capture by misinformation.

A defeater is, very broadly, a consideration that reduces or completely takes away justification from a subject’s belief about a certain proposition. According to a widely endorsed view, justifiers and defeaters require evidential support. However, a number of philosophers argue that unjustified beliefs can serve as defeaters as well. Call the former type of defeater an ‘evidential defeater’ and the latter a ‘doxastic defeater’. Doxastic defeaters are highly controversial. First of all, they seem to be flatly incompatible with evidentialism. Moreover and more alarmingly, if we accept that unjustified beliefs can be defeaters, we have to accept that unjustified beliefs can serve as justifiers as well. A further unwelcome implication is that epistemically irresponsible subjects could immunise themselves from defeat by generating their own defeater-defeaters. Problems like these have led philosophers to reject doxastic defeaters altogether. This paper argues that doxastic defeaters are intelligible given a dualistic conception of rationality.

A 69-year-old man had an abnormal intracardiac course of a pacemaker lead. CT angiography demonstrated a window between the right upper pulmonary vein and the superior caval vein. The window was treated with covered stents in the superior caval vein, which was complicated by a chronic pericardial effusion that was treated with a pericardial window 6 months later.

Together Cæsar and Cotton left an immense trove of English state papers on all matters of subjects. While Cæsar spent much of his lifetime as an officer of state, e.g., Master of the Rolls, they both devised innumerable works of great value. For instance, both he and Cotton expounded upon the issue of the post-nati and other arguments made in the conferences on the union with Scotland in Parliament. With their cessation in 1607, Cæsar undertook his most significant follow-up work: “That neither any General Statute nor Nativity only make a Man (whose Parents were Strangers) to be a Natural Subject in any Country.” Later duplicated by Cotton in Titus, F. IV., the intricacies of its two pages remained long-guarded in the private possession of such great men as Lords, Secretaries of State, and Prime Ministers. Only two centuries after Cæsar commenced its work did it come full circle to the British Museum—itself, ironically, formed from the seized library of Cotton. As for legal precedent, it is unique in that its broad historical scope predated the complexities of England's permanent royal colonies in America. During this period, every regnant—except for Charles I and James II—would assent unto major naturalization or alien statutes during their reign, all of which remained common law throughout England, the Empire, and America until, at the least, 1863.

This study presents a simple frequency-dependent regime-switching vector autoregression (VAR) model, where each regime and its associated parameters in the VAR are characterized by their distinct spectral properties. Empirical applications to several key macroeconomic variables reveal clear frequency-dependent switching dynamics, with each regime exhibiting distinctive features regarding spectral properties, volatility, and impulse responses. We compare this model with a conventional regime-switching model (typically studied in the time domain) and highlight several key differences between the two approaches.

North Carolina growers have long struggled to control Italian ryegrass, and recent research has confirmed Italian ryegrass biotypes resistant to nicosulfuron, glyphosate, clethodim, and paraquat. Integrating alternative management strategies is crucial to effectively control such biotypes. The objectives of this study were to evaluate Italian ryegrass control with cover crops and fall-applied residual herbicides and investigate cover crop injury from residual herbicides. This study was conducted during the fall/winter of 2021-22 in Salisbury and fall/winter of 2021-22 and 2022-23 at Clayton, NC. The study was designed as a 3x5 split-plot, where the main plot consisted of three cover crop treatments (no-cover, cereal rye at 80 kg ha-1, and crimson clover at 18 kg ha-1), and the subplots consisted of five residual herbicide treatments (S-metolachlor, flumioxazin, metribuzin, pyroxasulfone, and nontreated). In the 2021-22 season at Clayton, metribuzin injured cereal rye and crimson clover 65% and 55%, respectively. However, metribuzin injured both cover crops ≤6% in 2022-23. Flumioxazin resulted in unacceptable crimson clover injury with 50% and 38% in 2021-22 and 2022-23 in Clayton and 40% at Salisbury, respectively. Without preemergence herbicides, cereal rye controlled Italian ryegrass 85% and 61% at 24 WAP in 2021-22 and 2022-23 at Clayton and 82% in Salisbury, respectively. In 2021-22, Italian ryegrass seed production was lowest in cereal rye treatments at both locations, except when cover crop was treated with metribuzin. For example, in Salisbury, cereal rye plus metribuzin resulted in 39324 seeds m–2, compared to ≤4386 seeds m–2 from all other cereal rye treatments. In 2022-23, Italian ryegrass seed production in cereal rye was lower when either metribuzin or pyroxasulfone were used PRE (2670 and 1299 seeds m–2, respectively) when compared to cereal rye without herbicides (5600 seeds m–2).

Pot studies outdoors under natural environmental conditions were conducted to determine leafy spurge biomass reduction resulting from broadcast application of 2,4-D (2,244 g ae ha-1) with and without wiper-applied glyphosate. Glyphosate (575 g ae L-1) was applied at 0, 33, 50, and 75% diluted concentrate with a wiper 24 hrs after 2,4-D was broadcast applied. Injury estimates and shoot biomass did not differ between plants treated with 2,4-D-only or the addition of wiper-applied glyphosate 21 days after treatment. Shoot regrowth biomass of plants treated with 2,4-D-only was approximately 560% greater compared to nontreated plants three months after treatment. Plants treated with wiper-applied glyphosate had shoot regrowth biomass of less than 10% compared to the nontreated plants 3 months after treatment. Root biomass of 2,4-D-only treated plants (160% of nontreated plants) followed a similar pattern of shoot regrowth biomass. Root biomass of plants treated with wiper-applied glyphosate exhibited approximately 50% reductions compared to nontreated plants. The concentrations of glyphosate tested reduced all vegetative metrics equally; therefore, all labeled concentrations should be effective. The results of the experiment show that broadcast-applied 2,4-D is more effective at reducing leafy spurge biomass with the addition of wiper-applied glyphosate.

A left-variable word over an alphabet A is a word over $A \cup \{\star \}$ whose first letter is the distinguished symbol $\star $ standing for a placeholder. The ordered variable word theorem ($\mathsf {OVW}$), also known as Carlson–Simpson’s theorem, is a tree partition theorem, stating that for every finite alphabet A and every finite coloring of the words over A, there exists a word $c_0$ and an infinite sequence of left-variable words $w_1, w_2, \dots $ such that $\{ c_0 \cdot w_1[a_1] \cdot \dots \cdot w_k[a_k] : k \in \mathbb {N}, a_1, \dots , a_k \in A \}$ is monochromatic.

In this article, we prove that $\mathsf {OVW}$ is $\Pi ^0_4$-conservative over $\mathsf {RCA}_0 + \mathsf {B}\Sigma ^0_2$. This implies in particular that $\mathsf {OVW}$ does not imply $\mathsf {ACA}_0$ over $\mathsf {RCA}_0$. This is the first principle for which the only known separation from $\mathsf {ACA}_0$ involves non-standard models.

For a given graph $H$, we say that a graph $G$ has a perfect $H$-subdivision tiling if $G$ contains a collection of vertex-disjoint subdivisions of $H$ covering all vertices of $G.$ Let $\delta _{\mathrm {sub}}(n, H)$ be the smallest integer $k$ such that any $n$-vertex graph $G$ with minimum degree at least $k$ has a perfect $H$-subdivision tiling. For every graph $H$, we asymptotically determined the value of $\delta _{\mathrm {sub}}(n, H)$. More precisely, for every graph $H$ with at least one edge, there is an integer $\mathrm {hcf}_{\xi }(H)$ and a constant $1 \lt \xi ^*(H)\leq 2$ that can be explicitly determined by structural properties of $H$ such that $\delta _{\mathrm {sub}}(n, H) = \left (1 - \frac {1}{\xi ^*(H)} + o(1) \right )n$ holds for all $n$ and $H$ unless $\mathrm {hcf}_{\xi }(H) = 2$ and $n$ is odd. When $\mathrm {hcf}_{\xi }(H) = 2$ and $n$ is odd, then we show that $\delta _{\mathrm {sub}}(n, H) = \left (\frac {1}{2} + o(1) \right )n$.

In 1206 Chinggis Khan replaced the warring factions of Mongolia with a single polity, the Great Mongol Realm (Yeke Mongqol Ulus). The ulus was ruled by a khan, who allocated pastures, households and revenues to his relatives as shares (qubi). Chinggis granted the first allocation to his brothers and senior sons in 1207 but many more redistributions took place in the coming decades. Many of these appanages grew so large that their holders challenged the khan's dominance and even broke free of his control to form their own polities (uluses). This article will explore the fluidity of the Mongol appanage system by taking the qubi of Chinggis Khan's grandson Ariq Böke (d. 1266) as a case study. The Ariq Bökids established their own secondary ulus in Inner Asia, before fragmenting and lending their support to neighbouring khans in the fourteenth century.

This article analyses the struggle for possession of the House of Baha’u’llah in Baghdad during the 1920s and 1930s. One of the Bahai religion’s most sacred sites, the House of Baha’u’llah was the subject of protracted legal and political-diplomatic disputes following efforts by anti-Bahai activists to appropriate it from its Bahai custodians in 1921. The ensuing case touched almost every facet of the Iraqi judicial system, galvanised the international Bahai community and captured the attention of the British colonial state, the Iraqi government and the League of Nations. This article explores the causes and implications of the dispute, which can be considered one of the first incidents of religious persecution in modern Iraq. Rather than explaining the incident with reference to the intolerant attitudes of the Shi`i majority, the article argues for the role of the institutions of colonial modernity – the Mandates system, the new minorities regime, the praxis and discourse of colonial expansion, and the internationalism of the interwar period – for the unravelling of the case itself and for affecting modern, secular articulations of anti-Bahai prejudice.

This is a reply to Komárek’s criticism of our article “Europe’s political constitution”. We address the issues raised by our critic one by one. The topics range from the definition of the public sphere to the role that law blogs and social media play in it. The reply concludes by examining what it means to pursue truth in legal scholarship based on contrasting the views of Hans Kelsen und Stanley Fish.