Towards a Geometric Approach to Strassen's Asymptotic Rank Conjecture

We make a first geometric study of three varieties in $\mathbb{C}^m \otimes \mathbb{C}^m \otimes \mathbb{C}^m$ (for each $m$), including the Zariski closure of the set of tight tensors, the tensors with continuous regular symmetry. Our motivation is to develop a geometric framework for Strassen's Asymptotic Rank Conjecture that the asymptotic rank of any tight tensor is minimal. In particular, we determine the dimension of the set of tight tensors. We prove that this dimension equals the dimension of the set of oblique tensors, a less restrictive class introduced by Strassen.Comment: Final version. Revisions in Section 1 and Section

Emphasizing Extension\u27s Unbiased, Research-Based Recommendations Is Critical

With a multitude of information sources available to stakeholders, it is critical that Extension emphasize the supporting work and unbiased approach that comprise the backbone of our recommendations. In Alabama, management of target spot, a disease that can devastate cotton, is the result of 100 field trials, 6,700 man-hours, and $485,800 in grants. The team involved delivered 94 associated publications and stakeholder activities and posted information via YouTube and Twitter. For Cooperative Extension to remain relevant, we must emphasize our strong experiment station partnership that ensures a foundation firmly planted in unbiased, research-based information that is not influenced by outside, market-driven interests

Polynomial systems admitting a simultaneous solution

We provide a complete description of the ideal that serves as the resultant ideal for n univariate polynomials of degree d. We in particular describe a set of generators of this resultant ideal arising as maximal minors of a set of cascading matrices formed from the coefficients of the polynomials, generalising the classical Sylvester resultant of two polynomials.Comment: 9 page

The Evolution of Telepractice Use during the COVID-19 Pandemic: Perspectives of Pediatric Speech-Language Pathologists

The study investigated how pediatric speech-language pathologists (SLPs) applied telepractice to compensate for the loss of in-person services and the dynamics of telepractice use during the COVID-19 pandemic in a rural state. We conducted interviews with 10 SLPs and then a statewide survey in which 51 SLPs participated. The qualitative interviews revealed themes including changes in service environment due to the pandemic (e.g., transition to telepractice, losing clients), challenges in the transition to telepractice (e.g., limited training, difficulty engaging clients), worsening wellbeing of clinicians and clients, and SLPs’ perspectives and suggestions towards telepractice in the future. Survey results showed service disruptions and transition dynamics during the pandemic. SLPs’ weekly caseloads reduced from an average of 42.3 clients prior to the pandemic to 25.9 and 23.4 from March to May and from June to September 2020, respectively, and then recovered to 37.2 clients from October to December 2020. In contrast, the number of telepractice caseloads sharply increased from 0.2 clients per week prior to the pandemic to 14.8 from March to May 2020. The weekly telepractice caseloads then declined to 5.5 clients from June to September and 7.9 clients from October to December 2020. In the months right after the pandemic outbreak (i.e., March to May), client children struggled with treatment gains and behavioral wellbeing. However, their outcomes gradually improved by October to December and approached pre-pandemic levels. About one-third of the SLPs reported that they would be more likely or much more likely to use telepractice in the future regardless of the pandemic. However, only about a quarter perceived telepractice as comparable to in-person services. We concluded that the transition from in-person services to telepractice substantially mitigated service disruptions right after the pandemic outbreak and that telepractice’s substitute role evolved over time

The evolution of telepractice use during the covid-19 pandemic: Perspectives of pediatric speech-language pathologists

The study investigated how pediatric speech-language pathologists (SLPs) applied teleprac-tice to compensate for the loss of in-person services and the dynamics of telepractice use during the COVID-19 pandemic in a rural state. We conducted interviews with 10 SLPs and then a statewide survey in which 51 SLPs participated. The qualitative interviews revealed themes including changes in service environment due to the pandemic (e.g., transition to telepractice, losing clients), challenges in the transition to telepractice (e.g., limited training, difficulty engaging clients), worsening well-being of clinicians and clients, and SLPs’ perspectives and suggestions towards telepractice in the future. Survey results showed service disruptions and transition dynamics during the pandemic. SLPs’ weekly caseloads reduced from an average of 42.3 clients prior to the pandemic to 25.9 and 23.4 from March to May and from June to September 2020, respectively, and then recovered to 37.2 clients from October to December 2020. In contrast, the number of telepractice caseloads sharply increased from 0.2 clients per week prior to the pandemic to 14.8 from March to May 2020. The weekly telepractice caseloads then declined to 5.5 clients from June to September and 7.9 clients from October to December 2020. In the months right after the pandemic outbreak (i.e., March to May), client children struggled with treatment gains and behavioral wellbeing. However, their outcomes gradually improved by October to December and approached pre-pandemic levels. About one-third of the SLPs reported that they would be more likely or much more likely to use telepractice in the future regardless of the pandemic. However, only about a quarter perceived telepractice as comparable to in-person services. We concluded that the transition from in-person services to telepractice substantially mitigated service disruptions right after the pandemic outbreak and that telepractice’s substitute role evolved over time

nduction and Characterization of Mutations Related to Dwarf Habit in Hardy Hibiscus (Muenchhusia section)

Hybrids between various species of Hibiscus in the Muenchhusia section are popular in commercial markets due to their colorful, floriferous blooms. However, many commercial cultivars are too vigorous for use in smaller garden spaces and often have only a few flowers in bloom. Stable, heritable mutants exhibiting dwarf stature and better branching architecture will be valuable to the commercial production of hardy Hibiscus. The goal of this project was to induce stable, heritable mutations using ethyl methanesulfonate that result in increased branching and a dwarf compact phenotype and introgress the compact phenotypes into lines of hardy Hibiscus to generate a series of diverse compact cultivars for use in commercial markets. Multiple mutations associated with dwarf, compact phenotypes were successfully induced. Hybridizations were made between M2 plants displaying a dwarf phenotype and hybrids developed through conventional breeding that do not possess the dwarf mutation in their background to develop diverse selections of dwarf plants. Inheritance patterns of the dwarf genes were determined through the segregation ratios of the dwarf phenotype in the F1 and F2 generations of these hybrids. Compared with wild-type progeny, dwarf progeny had shorter internode lengths and a greater number of primary branches