Let [Formula: see text] be the finite field with [Formula: see text] elements and consider the rational function field [Formula: see text]. For a Drinfeld module [Formula: see text] defined over [Formula: see text], we study the transcendence of special values of the Goss [Formula: see text]-function attached to the abelian [Formula: see text]-motive [Formula: see text] of [Formula: see text]. Moreover, when [Formula: see text] is a Drinfeld module of rank [Formula: see text] defined over [Formula: see text] which has everywhere good reduction, we prove that the value of the Goss [Formula: see text]-function attached to the [Formula: see text]-st exterior power of [Formula: see text] at any positive integer is transcendental over [Formula: see text].
Sol-gel-derived aerogels are three-dimensional, nanoscale materials that combine large surface areas and high porosities. These traits make them useful for any rate-critical chemical process, particularly sensing or electrochemical applications, once physical or chemical moieties are incorporated into the gels to add their functionality into the ultraporous scaffold. Incorporating biomolecules into aerogels has been challenging due to the inability of most biomolecules to remain structurally intact within the gels during the necessary supercritical fluid processing. However, the heme protein cytochrome c (cyt. c) forms self-organized superstructures around gold (or silver) nanoparticles in buffer that can be encapsulated within silica and processed to form aerogels in which cyt. c retains its characteristic visible absorption. The gold (or silver) nanoparticle-nucleated superstructures protect the majority of the protein from the harsh physicochemical conditions necessary to form an aerogel. The Au∼cyt. c superstructures exhibit rapid gas-phase recognition of nitric oxide (NO) within the aerogel matrix, as facilitated by the high-quality pore structure of the aerogel, and remain viable for weeks at room temperature.
Erdős proved an upper bound on the number of edges in an n-vertex non-Hamiltonian graph with given minimum degree and showed sharpness via two members of a particular graph family. Füredi, Kostochka and Luo showed that these two graphs play the same role when “number of edges” is replaced by “number of t-stars,” and that two members of a more general graph family maximize the number of edges among non-k-edge-Hamiltonian graphs. In this paper we generalize their former result from Hamiltonicity to related properties (traceability, Hamiltonian-connectedness, k-edge Hamiltonicity, k-Hamiltonicity) and their latter result from edges to t-stars. We identify a family of extremal graphs for each property that is forbidden. This problem without the minimum degree condition was also open; here we conjecture a complete description of the extremal family for each property, and prove the characterization in some cases. Finally, using a different family of extremal graphs, we find the maximum number of t-stars in non-k-connected graphs.
PURPOSE:Ring 14 Syndrome is a rare genetic disorder caused by an anomaly in the 14th chromosome that often leads to intractable epilepsy, moderate to severe intellectual disabilities, slow growth, ocular abnormalities, and more. The presentation and severity of symptoms can greatly vary, making Ring 14 syndrome a complex condition to understand, manage, and treat. Conceptual disease models, also known as disease concept models, provide a formal framework based on the lived experience of patients and families that helps to describe the functional and quality of life impacts of a disease across various domains using qualitative methods. METHODS:To inform the development of a conceptual disease model on Ring 14 Syndrome, 17 caregivers representing 12 patients with Ring 14 Syndrome participated in semi-structured interviews over the course of four months. Data were analyzed using a mix of deductive and inductive inquiry through NVivo Software. Concepts were grouped into domains of patient symptoms and caregiver symptoms, with patient symptoms consisting of two sub-domains: functional impacts (which included cognitive impacts, physical impacts, behavioral impacts, and social-emotional-expressive impacts) and quality of life impacts (which included ADLs, medication side effects, and school/social/community). Caregiver impacts were categorized by mental health, family and social aspects, and medical care. RESULTS:Patient impacts listed under the cognitive and physical categories align closely with patient impacts referenced in the medical literature. However, impacts listed under the patient quality of life domain as well as the caregiver domain are inadequately represented in the literature, suggesting that the patient perspective has previously been neglected in the medical literature on Ring 14 Syndrome. Further, the numerous mental and physical health impacts on caregivers, grouped with the negative quality of life impacts on Ring 14 patients themselves, warrants further attention, as both have profound effects on health-related quality of life. Finally, while many of the impacts listed in the conceptual disease model may be considered negative aspects of the disorder, there were also positive impacts identified (such as happy demeanor, resilience, and social support) by the community as well.
Turbulence refers to the endogenous reallocation of resources (such as jobs) across firms due to entry, exit, and churning (movements within the firm-size distribution). The paper develops a model of turbulent endogenous growth in which firms invest in in-house innovation to cut costs and gain market share. As firms grow, the marginal return to market share declines due to downward-sloping demand, weakening the incentive to innovate. This mechanism, combined with idiosyncratic shocks, generates endogenous churning while preserving a stationary firm-size distribution. The results are robust to introducing entry and exit, which amplify churning and affect growth through selection. In a counterfactual exercise, I model the observed decline in high-growth startups as a thinning of the right tail of the R&D productivity distribution. While eliminating skewness can generate large reductions in aggregate outcomes, matching its decline explains only 15% of the post-2000 slowdown, suggesting a limited aggregate role for fast-growing startups.
