Asymptotic growth and least common multiples in groups

In this article we relate word and subgroup growth to certain functions that arise in the quantification of residual finiteness. One consequence of this endeavor is a pair of results that equate the nilpotency of a finitely generated group with the asymptotic behavior of these functions. The second half of this article investigates the asymptotic behavior of two of these functions. Our main result in this arena resolves a question of Bogopolski from the Kourovka notebook concerning lower bounds of one of these functions for nonabelian free groups.Comment: 13 page

Bertrand's postulate and subgroup growth

In this article we investigate the L^1-norm of certain functions on groups called divisibility functions. Using these functions, their connection to residual finiteness, and integration theory on profinite groups, we define the residual average of a finitely generated group. One of the main results in this article is the finiteness of residual averages on finitely generated linear groups. Whether or not the residual average is finite depends on growth rates of indices of finite index subgroups. Our results on index growth rates are analogous to results on gaps between primes, and provide a variant of the subgroup growth function, which may be of independent interest.Comment: 33 page

Memory-enhancing intra-basolateral amygdala infusions of clenbuterol increase Arc and CaMKIIα protein expression in the rostral anterior cingulate cortex

Activation of β-adrenoceptors in the basolateral complex of the amygdala (BLA) modulates memory through interactions with multiple memory systems. The cellular mechanisms for this interaction remain unresolved. Memory-modulating BLA manipulations influence expression of the protein product of the immediate early gene activity-regulated cytoskeletal-associated protein (Arc) in the dorsal hippocampus, and hippocampal expression of Arc protein is critically involved in memory consolidation and long-term potentiation. The present studies examined whether this influence of the BLA is specific to the hippocampus and to Arc protein. Like the hippocampus, the rostral portion of the anterior cingulate cortex (rACC) is involved in the consolidation of inhibitory avoidance (IA) memory, and IA training increases Arc protein in the rACC. Because the BLA interacts with the rACC in the consolidation of IA memory, the rACC is a potential candidate for further studies of BLA modulation of synaptic plasticity. The alpha isoform of the Calcium/Calmodulin-dependent protein kinase II (CaMKIIα) and the immediate early gene c-Fos are involved in long-term potentiation and memory. Both Arc and CaMKIIα proteins can be translated in isolated synapses, where the mRNA is localized, but c-Fos protein remains in the soma. To examine the influence of memory-modulating manipulations of the BLA on expression of these memory and plasticity-associated proteins in the rACC, male Sprague–Dawley rats were trained on an IA task and given intra-BLA infusions of either clenbuterol or lidocaine immediately after training. Findings suggest that noradrenergic stimulation of the BLA may modulate memory consolidation through effects on both synaptic proteins Arc and CaMKIIα, but not the somatic protein c-Fos. Furthermore, protein changes observed in the rACC following BLA manipulations suggest that the influence of the BLA on synaptic proteins is not limited to those in the dorsal hippocampus

Exploring Collaborative Professionalism as a Means of Virtually Supporting Rural Teachers

Thirty percent of US teachers work in rural schools where geographic isolation and lack of peers can make it difficult for them to engage in collaborative professional relationships with colleagues. Facilitated professional development can be used as a way to build these networks. Using a situative perspective in which teachers are viewed as experts and agents in their own professional learning and by capitalizing on the rapid increase in understanding and use of video conferencing in 2021, the research team developed an open-enrollment, co-designed series of workshops for rural teachers in the intermountain West. The team was interested in how collaborative professionalism (Hargreaves & O’Connor, 2018a) could be built and used to bring these rural teachers together to support each other as they explored their own identified problems of practice. The analysis of the collected qualitative and quantitative data (including videos, reflections, and documents used and created in the sessions) revealed initial trends that supported the development of solidarity and solidity in this group of teachers and facilitators. The authors posit that this perspective could be productive in connecting rural teachers in collaborative professional relationships despite their isolation

Virus protein of mosaic disease of tobacco

Publication authorized February 9, 1939.Digitized 2007 AES.Includes bibliographical references (page 12)

Effect of bismuth citrate, lactose, and organic acid on necrotic enteritis in broilers

Clostridium perfringens-associated ne- crotic enteritis causes significant economic losses. The objective of this study was to evaluate the effect of bismuth citrate, lactose, and organic acid on the devel- opment of necrotic enteritis in broilers. The first study was a dose response that evaluated bismuth citrate at 50, 100, or 200 ppm on bacterial intestinal coloniza- tion and lesion development associated with our C. perfringens challenge model. The second study evalu- ated bismuth citrate, lactose, and citric acid on intes- tinal pH and lesion development. For the third study, we determined if lactose would enhance the efficacy of bismuth citrate against intestinal colonization and lesion development associated with C. perfringens. In study 1, intestinal lesion scores at the 50, 100, and 200 ppm bismuth citrate treatment level were reduced (P ≤ 0.05) when compared with the birds fed 0 ppm bismuth citrate. Intestinal C. perfringens colonization of the 100 and 200 ppm bismuth citrate treatment group was sig- nificantly reduced when compared with birds fed 0 ppm bismuth citrate. In study 2, we found no significant differences in lesion development, after C. perfringens challenge, between birds fed 100 ppm bismuth citrate or fed a combination of 100 ppm bismuth citrate with dietary lactose or citric acid relative to the controls. The intestinal pH of birds fed 100 ppm bismuth cit- rate or fed a combination of 100 ppm bismuth citrate with dietary lactose or citric acid was not significantly reduced when compared with the controls. However, a significant reduction in pH was observed in birds fed a combination of 100 ppm bismuth citrate and lactose relative to the negative controls. In study 3, a decrease (P ≤ 0.05) in intestinal lesion scores occurred in birds fed lactose with 100 ppm bismuth citrate, compared with the positive controls. There were no significant differences in intestinal bacterial colonization. These preliminary data suggest that bismuth citrate may re- duce intestinal lesion development and C. perfringens colonization in broilers infected with necrotic enteritis

Optical spectroscopic analysis for the discrimination of Extra-Virgin Olive Oil

We thank the UK Engineering and Physical Sciences Research Council and the European Union FAMOS project (FP7 ICT, 317744) for funding.We demonstrate the ability to discriminate between five brands of commercially available extra-virgin olive oil (EVOO) using Raman spectroscopy or fluorescence spectroscopy. Data was taken on both a ‘bulk optics’ free space system and on a compact handheld device, each capable of taking both Raman and fluorescence data. With the compact Raman device we achieved an average sensitivity and specificity of 98.4% and 99.6% for discrimination, respectively. Our approach illustrates that both Raman and fluorescence spectroscopy can be used for portable discrimination of EVOOs. This technique may enable detection of EVOO that has undergone counterfeiting or adulteration. The main challenge with this technique is that oxidation of EVOO causes a shift in the Raman signal over time. It would therefore be necessary to retrain the database regularly.We demonstrate preliminary data to address this issue, which may enable successful discrimination over time. We show that by discarding the first principal component, which contains information on the variations due to oxidation, we can improve discrimination efficiency.PostprintPeer reviewe

Unified N=2 Maxwell-Einstein and Yang-Mills-Einstein Supergravity Theories in Four Dimensions

We study unified N=2 Maxwell-Einstein supergravity theories (MESGTs) and unified Yang-Mills Einstein supergravity theories (YMESGTs) in four dimensions. As their defining property, these theories admit the action of a global or local symmetry group that is (i) simple, and (ii) acts irreducibly on all the vector fields of the theory, including the ``graviphoton''. Restricting ourselves to the theories that originate from five dimensions via dimensional reduction, we find that the generic Jordan family of MESGTs with the scalar manifolds [SU(1,1)/U(1)] X [SO(2,n)/SO(2)X SO(n)] are all unified in four dimensions with the unifying global symmetry group SO(2,n). Of these theories only one can be gauged so as to obtain a unified YMESGT with the gauge group SO(2,1). Three of the four magical supergravity theories defined by simple Euclidean Jordan algebras of degree 3 are unified MESGTs in four dimensions. Two of these can furthermore be gauged so as to obtain 4D unified YMESGTs with gauge groups SO(3,2) and SO(6,2), respectively. The generic non-Jordan family and the theories whose scalar manifolds are homogeneous but not symmetric do not lead to unified MESGTs in four dimensions. The three infinite families of unified five-dimensional MESGTs defined by simple Lorentzian Jordan algebras, whose scalar manifolds are non-homogeneous, do not lead directly to unified MESGTs in four dimensions under dimensional reduction. However, since their manifolds are non-homogeneous we are not able to completely rule out the existence of symplectic sections in which these theories become unified in four dimensions.Comment: 47 pages; latex fil

Substance Use Prevention Services in Juvenile Justice and Behavioral Health: Results from a National Survey

BACKGROUND: This study examined the national availability of substance use prevention (SUP) within juvenile justice (JJ) and their primary behavioral health (BH) providers, and the relationships between the availability of SUP and agency-level measures of organizational structure, staffing, and youth characteristics. A three-stage national probability sampling process was used to select participants for a national survey that included, among other facets of community supervision (CS) and BH practices, questions on agency characteristics, youth characteristics, whether the agency/provider directly provided SUP services, and whether the agency/provider directly provided substance use and/or mental health treatment. This paper focuses on SUP services along with agency/provider and youth characteristics related to providing SUP. RESULTS: The response rate for both CS agencies (n = 195) and BH providers (n = 271) was 96%. Complex samples logistic regression initially examined univariate associations of each variable and identified candidates for a final multivariate model. Overall, only one-third of CS and BH providers reported offering SUP services, with BH providers being significantly more likely than CS agencies to provide SUP services. In addition, likelihood of SUP was significantly lower among agencies where the substance use distribution of the caseload was below the median. Controlling for master\u27s level staff and the substance use distribution, CS agencies were about 67% less likely to offer SUP when compared to BH providers. CONCLUSIONS: Given the high rates of substance use among justice-involved youth and that substance use is an established risk for several negative behaviors, outcomes, and health conditions, these findings suggest that evidence-based prevention services should likely be expanded in justice settings, and perhaps included as part of CS programs, even when youth do not initially present with SU service needs

Generative Use of Locatives in Multiword Utterances in Agrammatism: A Matrix Training Approach

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