Precalculus (Albany State University)

This Grants Collection for Precalculus was created under a Round Two ALG Textbook Transformation Grant. Affordable Learning Georgia Grants Collections are intended to provide faculty with the frameworks to quickly implement or revise the same materials as a Textbook Transformation Grants team, along with the aims and lessons learned from project teams during the implementation process. Documents are in .pdf format, with a separate .docx (Word) version available for download. Each collection contains the following materials: Linked Syllabus Initial Proposal Final Reporthttps://oer.galileo.usg.edu/mathematics-collections/1002/thumbnail.jp

Nonfragile Robust H

The nonfragile H∞ filtering problem for a kind of Takagi-Sugeno (T-S) fuzzy stochastic system which has a time-varying delay and parameter uncertainties has been studied in this paper. Sufficient conditions for stochastic input-to-state stability (SISS) of the fuzzy stochastic systems are obtained. Attention is focused on the design of a nonfragile H∞ filter such that the filtering error system can tolerate some level of the gain variations in the filter and the H∞ performance level also could be satisfied. By using the SISS result, the approach to design the nonfragile filter is proposed in terms of linear matrix inequalities. Finally, an illustrative example is given to demonstrate the effectiveness of the proposed method

Maximal independent families and a topological consequence

AbstractFor κ⩾ω and X a set, a family A⊆P(X) is said to be κ-independent on X if |⋂A∈FAf(A)|⩾κ for each F∈[A]<ω and f∈{−1,+1}F; here A+1=A and A−1=X⧹A.Theorem 3.6For κ⩾ω, some A⊆P(κ) with |A|=2κ is simultaneously maximal κ-independent and maximal ω-independent on κ. The family A may be chosen so that every two elements of κ are separated by 2κ-many elements of A.Corollary 5.4For κ⩾ω there is a dense subset D of {0,1}2κ such that each nonempty open U⊆D satisfies |U|=d(U)=κ and no subset of D is resolvable. The set D may be chosen so that every two of its elements differ in 2κ-many coordinates.Remarks(a) Theorem 3.6 answers affirmatively a question of Eckertson [Topology Appl. 79 (1997) 1–11]. Two proofs are given here. (b) Parts of Corollary 5.4 have been obtained by other methods by Feng [Topology Appl. 105 (2000) 31–36] and (for κ=ω) by Alas et al. [Topology Appl. 107 (2000) 259–273]

A CD8 T Cell/Indoleamine 2,3-Dioxygenase Axis Is Required for Mesenchymal Stem Cell Suppression of Human Systemic Lupus Erythematosus

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Nonlocal Detection of Interlayer Three-Magnon Coupling

A leading nonlinear effect in magnonics is the interaction that splits a high-frequency magnon into two low-frequency magnons with conserved linear momentum. Here, we report experimental observation of nonlocal three-magnon scattering between spatially separated magnetic systems, viz. a CoFeB nanowire and a yttrium iron garnet (YIG) thin film. Above a certain threshold power of an applied microwave field, a CoFeB Kittel magnon splits into a pair of counterpropagating YIG magnons that induce voltage signals in Pt electrodes on each side, in excellent agreement with model calculations based on the interlayer dipolar interaction. The excited YIG magnon pairs reside mainly in the first excited (n=1) perpendicular standing spin-wave mode. With increasing power, the n=1 magnons successively scatter into nodeless (n=0) magnons through a four-magnon process. Our results demonstrate nonlocal detection of two separately propagating magnons emerging from one common source that may enable quantum entanglement between distant magnons for quantum information applications.</p

Voxel-based, brain-wide association study of aberrant functional connectivity in schizophrenia implicates thalamocortical circuitry

Background: Wernicke\u27s concept of \u27sejunction\u27 or aberrant associations among specialized brain regions is one of the earliest hypotheses attempting to explain the myriad of symptoms in psychotic disorders. Unbiased data mining of all possible brain-wide connections in large data sets is an essential first step in localizing these aberrant circuits. Methods: We analyzed functional connectivity using the largest resting-state neuroimaging data set reported to date in the schizophrenia literature (415 patients vs. 405 controls from UK, USA, Taiwan, and China). An exhaustive brain-wide association study at both regional and voxel-based levels enabled a continuous data-driven discovery of the key aberrant circuits in schizophrenia. Results: Results identify the thalamus as the key hub for altered functional networks in patients. Increased thalamus-primary somatosensory cortex connectivity was the most significant aberration in schizophrenia (P=10-18). Overall, a number of thalamic links with motor and sensory cortical regions showed increased connectivity in schizophrenia, whereas thalamo-frontal connectivity was weakened. Network changes were correlated with symptom severity and illness duration, and support vector machine analysis revealed discrimination accuracies of 73.53-80.92%. Conclusions: Widespread alterations in resting-state thalamocortical functional connectivity is likely to be a core feature of schizophrenia that contributes to the extensive sensory, motor, cognitive, and emotional impairments in this disorder. Changes in this schizophrenia-associated network could be a reliable mechanistic index to discriminate patients from healthy controls

Dense sampling of bird diversity increases power of comparative genomics

© 2020, The Author(s). Whole-genome sequencing projects are increasingly populating the tree of life and characterizing biodiversity1–4. Sparse taxon sampling has previously been proposed to confound phylogenetic inference5, and captures only a fraction of the genomic diversity. Here we report a substantial step towards the dense representation of avian phylogenetic and molecular diversity, by analysing 363 genomes from 92.4% of bird families—including 267 newly sequenced genomes produced for phase II of the Bird 10,000 Genomes (B10K) Project. We use this comparative genome dataset in combination with a pipeline that leverages a reference-free whole-genome alignment to identify orthologous regions in greater numbers than has previously been possible and to recognize genomic novelties in particular bird lineages. The densely sampled alignment provides a single-base-pair map of selection, has more than doubled the fraction of bases that are confidently predicted to be under conservation and reveals extensive patterns of weak selection in predominantly non-coding DNA. Our results demonstrate that increasing the diversity of genomes used in comparative studies can reveal more shared and lineage-specific variation, and improve the investigation of genomic characteristics. We anticipate that this genomic resource will offer new perspectives on evolutionary processes in cross-species comparative analyses and assist in efforts to conserve species

Optimization of 4-( N -Cycloamino)phenylquinazolines as a Novel Class of Tubulin-Polymerization Inhibitors Targeting the Colchicine Site

The 6-methoxy-1,2,3,4-tetrahydroquinoline moiety in prior leads 2-chloro- and 2-methyl-4-(6-methoxy-3,4-dihydroquinolin-1(2H)-yl)quinazoline (1a and 1b) was modified to produce 4-(N-cycloamino)quinazolines (4a–c and 5a–m). The new compounds were evaluated in cytotoxicity and tubulin inhibition assays, resulting in the discovery of new tubulin-polymerization inhibitors. 7-Methoxy-4-(2-methylquinazolin-4-yl)-3,4-dihydroquinoxalin- 2(1H)-one (5f), the most potent compound, exhibited high in vitro cytotoxic activity (GI50 1.9–3.2 nM), significant potency against tubulin assembly (IC50 0.77 μM), and substantial inhibition of colchicine binding (99% at 5 μM). In mechanism studies, 5f caused cell arrest in G2/M phase, disrupted microtubule formation, and competed mostly at the colchicine site on tubulin. Compound 5f and N-methylated analogue 5g were evaluated in nude mouse MCF7 xenograft models to validate their antitumor activity. Compound 5g displayed significant in vivo activity (tumor inhibitory rate 51%) at a dose of 4 mg/kg without obvious toxicity, whereas 5f unexpectedly resulted in toxicity and death at the same dose