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Let 퐺 be a finite group. Recall that an 퐴-group is a group whose Sylow subgroups are all abelian. In this paper, we investigate the upper bound on the diameter of the commuting graph of a solvable 퐴-group. Assuming that the commuting graph is connected, we show when the derived length of 퐺 is 2, the diameter of the commuting graph will be at most 4. In the general case, we show that the diameter of the commuting graph will be at most 6. In both cases, examples are provided to show that the upper bound of the commuting graph cannot be improved. [ABSTRACT FROM AUTHOR]

Insects, especially forest pests, are frequently characterized by eruptive dynamics. These types of species can stay at low, endemic population densities for extended periods of time before erupting in large-scale outbreaks. We here present a mechanistic model of these dynamics for mountain pine beetle. This extends a recent model that describes key aspects of mountain pine beetle biology coupled with a forest growth model by additionally including a fraction of low-vigor trees. These low-vigor trees, which may represent hosts with weakened defenses from drought, disease, other bark beetles, or other stressors, give rise to an endemic equilibrium in biologically plausible parameter ranges. The mechanistic nature of the model allows us to study how each model parameter affects the existence and size of the endemic equilibrium. We then show that under certain parameter shifts that are more likely under climate change, the endemic equilibrium can disappear entirely, leading to an outbreak. [ABSTRACT FROM AUTHOR]

Insects, especially forest pests, are frequently characterized by eruptive dynamics. These types of species can stay at low, endemic population densities for extended periods of time before erupting in large-scale outbreaks. We here present a mechanistic model of these dynamics for mountain pine beetle. This extends a recent model that describes key aspects of mountain pine beetle biology coupled with a forest growth model by additionally including a fraction of low-vigor trees. These low-vigor trees, which may represent hosts with weakened defenses from drought, disease, other bark beetles, or other stressors, give rise to an endemic equilibrium in biologically plausible parameter ranges. The mechanistic nature of the model allows us to study how each model parameter affects the existence and size of the endemic equilibrium. We then show that under certain parameter shifts that are more likely under climate change, the endemic equilibrium can disappear entirely, leading to an outbreak. [ABSTRACT FROM AUTHOR]

In a letter of Robert Southey, the first English translator of the Cantar de Mio Cid, appears a curious anecdote concerning the theft of the eponymous hero’s sword Tizona from the castle of Béjar during the Peninsular War. Contemporary memoirs identify the alleged culprit as Colonel William Mayne of the Loyal Lusitanian Legion, while suggesting a more benign interpretation of the episode. The actual weapon in question can be traced in records of the duchy of Béjar, and now belongs to the British Royal Collection. Though traditionally attributed to Diego López de Zúñiga, hero of Las Navas de Tolosa, the sword can be properly identified as having belonged to Rodrigo de Vivar y Mendoza, 1st marquis of Cenete and count of Cid. [ABSTRACT FROM AUTHOR]

Bio-optical and physical measurements were collected in the Mississippi Sound (Northern Gulf of Mexico) during the spring of 2018 as part of the Integrated Coastal Bio-Optical Dynamics project. The goal was to examine the impact of atmospheric and tidal fronts on fine-scale physical and bio-optical property distributions in a shallow, dynamic, coastal environment. During a 25-day experiment, eight moorings were deployed in the vicinity of a frontal zone. For a one-week period in the middle of the mooring deployment, focused ship sampling was conducted with aircraft and unmanned aerial vehicle overflights, acquiring hyperspectral optical and thermal data. The personnel in the aircraft located visible color fronts indicating the convergence of two water masses and directed the ship to the front. Dye releases were performed on opposite sides of a front, and coincident aircraft and unmanned aerial vehicle overflights were collected to facilitate visualization of advection/mixing/dispersion processes. Radiometric calibration of the optical hyperspectral sensor was performed. Empirical Line Calibration was also performed to atmospherically correct the aircraft imagery using in situ remote sensing reflectance measurements as calibration sources. Bio-optical properties were subsequently derived from the atmospherically corrected aircraft and unmanned aerial vehicle imagery using the Naval Research Laboratory Automated Processing System. [ABSTRACT FROM AUTHOR]

Background: Hospital medication errors are frequent and may result in adverse events. Data on non-prescription of regular medications to emergency department short stay unit patients is lacking. In response to local reports of regular medication omissions, a multi-disciplinary team was tasked to introduce corrective emergency department (ED) process changes, but with no additional financing or resources. Aim: To reduce the rate of non-prescription of regular medications for patients admitted to the ED Short Stay Unit (SSU), through process change within existing resource constraints. Methods: A pre- and post-intervention observational study compared regular medication omission rates for patients admitted to the ED SSU. Included patients were those who usually took regular home medications at 08:00 or 20:00. Omissions were classified as clinically significant medications (CSMs) or non-clinically significant medications (non-CSMs). The intervention included reinforcement that the initially treating acute ED doctor was responsible for prescription completion, formal checking of prescription presence at SSU handover rounds, double-checking of prescription completeness by the overnight SSU lead nurse and junior doctor, and ED pharmacist medication reconciliation for those still identified as having regular medication non-prescription at 07:30. Results: For the 110 and 106 patients in the pre- and post-intervention periods, there was a non-significant reduction in the CSM omission rate of −11% (95% CI: −23 to 2), from 41% (95% CI: 32-50) to 30% (95% CI: 21-39). Conclusion: Non-prescription of regular CSMs for SSU patients was not significantly reduced by institution of work practice changes within existing resource constraints. [ABSTRACT FROM AUTHOR]

At the core of contemporary U.S. language education policy is the dichotomous dividing of bilingual students into English Learners (ELs) who are entitled to extra support and non-ELs who are not entitled to this support. In this article, we genealogically trace the normative assumptions that go into this framing of the issue. We begin by examining the historical development of this dichotomous grouping of bilingual students within the remedial framing of the Bilingual Education Act that, building on the verbal deprivation theory that was prominent at the time, reproduced raciolinguistic ideologies that framed the language practices of racialized bilingual students as deficient and in need of remediation. We then examine how this remedial framing provided incentives for proponents of bilingual education to advocate for limited English proficiency as broadly as possible to ensure that more students were deemed eligible for these programs. We then examine contemporary vignettes that point to the tensions that this ideological underpinning has created for contemporary U.S. language education policymakers. We end with a discussion of ways of reconceptualizing U.S. language education policy that reject the remedial orientation that has informed this dichotomous framing and is responsive to the tensions reported by these educators. [ABSTRACT FROM AUTHOR]

We are interested in determining the bound of the average of the degrees of the irreducible characters whose degrees are not divisible by some prime p that guarantees a finite group G of odd order is p-nilpotent. There was found to be a bound which depends on the prime p. By further restricting the average by fixing a subfield k of the complex numbers and then computing the average of the degrees of the irreducible characters whose degrees are not divisible by p and have values in k, then a bound was obtained which depends on both p and k. Examples are provided which show best possible bounds. [ABSTRACT FROM AUTHOR]

In this note, we prove that if G is solvable and cod(χ) is a p-power for every nonlinear, monomial, monolithic χ e Irr(G) or every nonlinear, monomial, monolithic χ e IBr(G), then P is normal in G, where p is a prime and P is a Sylow p-subgroup of G. [ABSTRACT FROM AUTHOR]

An increasing number of commercial nanosatellite-based Earth-observing sensors are providing high-resolution images for much of the coastal ocean region. Traditionally, to improve the accuracy of normalized water-leaving radiance ( n L w ) estimates, sensor gains are computed using in-orbit vicarious calibration methods. The initial series of Planet nanosatellite sensors were primarily designed for land applications and are missing a second near-infrared band, which is typically used in selecting aerosol models for atmospheric correction over oceanographic regions. This study focuses on the vicarious calibration of Planet sensors and the duplication of its red band for use in both the aerosol model selection process and as input to bio-optical ocean product algorithms. Error measurements show the calibration performed well at the Marine Optical Buoy location near Lanai, Hawaii. Further validation was performed using in situ data from the Aerosol Robotic Network—Ocean Color platform in the northern Adriatic Sea. Bio-optical ocean color products were generated and compared with products from the Visual Infrared Imaging Radiometric Suite sensor. This approach for sensor gain generation and usage proved effective in increasing the accuracy of n L w measurements for bio-optical ocean product algorithms. [ABSTRACT FROM AUTHOR]

Mountain pine beetle (MPB) in Canada have spread well beyond their historical range. Accurate modelling of the long-term dynamics of MPB is critical for assessing the risk of further expansion and informing management strategies, particularly in the context of climate change and variable forest resilience. Most previous models have focused on capturing a single outbreak without tree replacement. While these models are useful for understanding MPB biology and outbreak dynamics, they cannot accurately model long-term forest dynamics. Past models that incorporate forest growth tend to simplify beetle dynamics. We present a new model that couples forest growth to MPB population dynamics and accurately captures key aspects of MPB biology, including a threshold for the number of beetles needed to overcome tree defenses and beetle aggregation that facilitates mass attacks. These mechanisms lead to a demographic Allee effect, which is known to be important in beetle population dynamics. We show that as forest resilience decreases, a fold bifurcation emerges and there is a stable fixed point with a non-zero MPB population. We derive conditions for the existence of this equilibrium. We then simulate biologically relevant scenarios and show that the beetle population approaches this equilibrium with transient boom and bust cycles with period related to the time of forest recovery. As forest resilience decreases, the Allee threshold also decreases. Thus, if host resilience decreases under climate change, for example under increased stress from drought, then the lower Allee threshold makes transient outbreaks more likely to occur in the future. [ABSTRACT FROM AUTHOR]

Like the First Emperor, Augustus created both the title and form of the emperor, and like the former he was both celebrated for his achievements and condemned for his cruelty and deceitfulness in climbing to power. Accounts mock the First Emperor's paranoia in hiding away behind covered passageways, but the emperor's invisibility was an ideal from the early Han. These additional approaches to examining Qin and the First Emperor are not offered as criticisms of Barbieri-Low, who has provided more than anyone could demand, but instead as further demonstrations of the validity of his argument that the First Emperor is indeed "good to think.". [Extracted from the article]

In the last few decades, mountain pine beetle (MPB) have spread into novel regions in Canada. An important aspect seldom captured in models of MPB spread is host resistance. Lodgepole pine, the predominant host of MPB, varies in resistance across the landscape. There is evidence for a genetic component of resistance, as well as evidence that hosts in areas where MPB has not been present historically are at risk of increased susceptibility. In addition to the spatially varying resistance of the primary host species, the eastward spread of MPB has brought them into jack pine forests. Host resistance in jack pine remains uncertain, but experiments indicate jack pine could be a suitable host. We develop a model of pine beetle spread that links pine beetle population dynamics and forest structure and resistance. We find that beetle outbreaks in the model are characterized by large transient outbreaks that move through the forest. We show how the speed of these outbreaks changes with host resistance and find that biologically plausible values for host resistance are able to stop the wave from advancing. We also find that near the threshold of resistance where the wave is able to advance, small changes in host resistance dramatically decrease the severity of the outbreak. These results indicate that planting trees selected for higher MPB resistance on the landscape may be able to slow or even stop the local spread of MPB. In terms of further eastward spread, our results indicate future outbreaks may move more quickly and be more severe if novel lodgepole pine hosts are indeed more susceptible to beetle attacks, although more research is needed into the susceptibility of jack pine. • Mountain pine beetle has spread into novel regions in Canada. • Further spread depends on host susceptibility. • Spatially explicit mechanistic model to predict spread speed and severity. • Spread speed and severity can increase quickly with host resistance. • Biologically plausible values of host resistance can slow or stop local spread. [ABSTRACT FROM AUTHOR]

In this note, we prove that if G is solvable and cod(X) is a p-power for every nonlinear, monomial, monolithic X 2 Irr(G) or every nonlinear, monomial, monolithic X 2 IBr(G), then P is normal in G, where p is a prime and P is a Sylow p-subgroup of G. [ABSTRACT FROM AUTHOR]

A finite group whose irreducible complex non-linear characters are rational is called a Q 1 -group. In this paper, we study Q 1 -groups via their Sylow 2-subgroups. In particular, we prove that if G is a solvable Q 1 -group that is not a rational group, then its Sylow 2-subgroups are Q 1 -groups. To prove this, we obtain information about Q 1 -groups where a Sylow 2-subgroup is contained in the vanishing off subgroup where the vanishing-off subgroup is a proper subgroup. We also obtain results about Q 1 -groups where a Sylow 2-subgroup is not contained in the vanishing off subgroup. In addition, we prove that Q 1 -groups whose Sylow 2-subgroups are dihedral and generalized quaternion groups have that all of the irreducible characters are rational groups. [ABSTRACT FROM AUTHOR]

The exceptional survival of Middle Pleistocene wooden spears at Schöningen (Germany) and Clacton-on-Sea (UK) provides tantalizing evidence for the widespread use of organic raw materials by early humans. At Clacton, less well-known organic artefacts include modified bones that were identified by the Abbé Henri Breuil in the 1920s. Some of these pieces were described and figured by Hazzledine Warren in his classic 1951 paper on the flint industry from the Clacton Channel, but they have been either overlooked in subsequent studies or dismissed as the product of natural damage. We provide the first detailed analysis of two Clactonian bone tools found by Warren and a previously unrecognized example recovered in 1934 during excavations directed by Mary Leakey. Microscopic examination of percussion damage suggests the bones were used as knapping hammers to shape or resharpen flake tools. Early Palaeolithic bone tools are exceedingly rare, and the Clacton examples are the earliest known organic knapping hammers associated with a core-and-flake (Mode 1) lithic technology. The use of soft hammers for knapping challenges the consensus that Clactonian flintknapping was undertaken solely with hard hammerstones, thus removing a major technological and behavioural difference used to distinguish the Clactonian from late Acheulean handaxe (Mode 2) industries. [ABSTRACT FROM AUTHOR]

We highlight how the use of holistic biliteracy and translanguaging perspectives can be applied in the assessment of emergent bilingual middle school students' writing to counter deficit views of their divergent repertoires. The study took place in a Mountain West middle school with a large Latinx population. We analyzed eleven emerging bilingual students' (EBs) responses to a writing prompt in an English language arts class. Findings include EBs' use of translanguaging [García, O. 2009. Bilingual Education in the 21st Century: A Global Perspective. Wiley-Blackwell], or strategic languaging, in which the students used different codes/languages in their writing. Additionally, this study found that EBs might show different patterns of spelling development as they learn to access the different alphabetic patterns of their respective repertoires. Finally, the study highlights how EBs draw from diverse discourse patterns as they compose. The analysis revealed the cultural and linguistic knowledge(s) EBs bring to developing their writing, which are often not part of monolingual English writing rubrics. Thus, the implications suggest that teachers need to develop critical sociolinguistic responsive practices as the field seeks to equitably assess the writing of EBs. Moreover, we suggest that critical cultural and linguistic awareness is needed in order to nurture the identities and competencies of EBs. [ABSTRACT FROM AUTHOR]

At the core of contemporary U.S. language education policy is the dichotomous dividing of bilingual students into English learners, who are entitled to extra support, and non-English learners, who are not entitled to this support. In this article, we genealogically trace the normative assumptions that have gone into this framing of the issue. We begin by examining the historical development of this dichotomous grouping of bilingual students within the remedial framing of the Bilingual Education Act that, building on the verbal deprivation theory that was prominent at the time, reproduced raciolinguistic ideologies that framed the language practices of bilingual students from low-income families as deficient and in need of remediation. Next, we examine how this remedial framing provided incentives for proponents of bilingual education to advocate for limited English proficiency to be defined as broadly as possible to ensure that more students were deemed eligible for these programs. We then examine contemporary vignettes that point to the tensions that this ideological underpinning has created for contemporary U.S. language education policymakers. We end with a discussion of ways of reconceptualizing U.S. language education policy that reject the remedial orientation that has informed this dichotomous framing and is responsive to the tensions illustrated in these vignettes. [ABSTRACT FROM AUTHOR]

In this paper, we obtain a characterization of GVZ-groups in terms of commutators and monolithic quotients. This characterization is based on counting formulas due to Gallagher. [ABSTRACT FROM AUTHOR]

Transient dynamics often differ drastically from the asymptotic dynamics of systems. In this paper we analyze transient dynamics in birth-jump metapopulations where dispersal occurs immediately after birth (e.g., via larval dispersal). We address the choice of appropriate norms as well as the effect of stage structure on transient dynamics. We advocate the use of the ℓ1 norm, because of its biological interpretation, and extend the transient metrics of reactivity and attenuation to birth-jump metapopulations in this norm. By way of examples we compare this norm to the more commonly used ℓ2 norm. Our focus is the case where transient dynamics are very different than asymptotic dynamics. We provide simple examples of metapopulations where this is the case and also show how increasing the number of habitat patches can increase this difference. We then connect the reactivity and attenuation of metapopulations to the source-sink classification of habitat patches and demonstrate how to meaningfully measure reactivity when metapopulations are stage-structured, with a focus on marine metapopulations. Our paper makes three primary contributions. First, it provides guidance to readers as to the appropriate norm and scalings for studying transients in birth-jump metapopulations. Second, it provides three examples of transient behavior in metapopulations involving slow-fast systems, crawl-bys, and high dimensionality. Third, it connects the concepts of reactivity and attenuation to the source-sink classification of habitat patches more commonly found in marine metapopulations [ABSTRACT FROM AUTHOR]

In this paper, we propose a novel free boundary problem to model the movement of single species with a range boundary. The spatial movement and birth/death processes of the species found within the range boundary are assumed to be governed by the classic Fisher–KPP reaction–diffusion equation, while the movement of a free boundary describing the range limit is assumed to be influenced by the weighted total population inside the range boundary and is described by an integro-differential equation. Our free boundary equation is a generalization of the classical Stefan problem that allows for nonlocal influences on the boundary movement so that range expansion and shrinkage are both possible. In this paper, we prove that the new model is well-posed and possesses steady state. We show that the spreading speed of the range boundary is smaller than that for the equivalent problem with a Stefan condition. This implies that the nonlocal effect of the weighted total population on the boundary movement slows down the spreading speed of the population. While the classical Stefan condition categorizes asymptotic behavior via a spreading–vanishing dichotomy, the new model extends this dichotomy to a spreading–balancing–vanishing trichotomy. We specifically analyze how habitat boundaries expand, balance or shrink. When the model is extended to have two free boundaries, we observe the steady state scenario, asymmetric shifts, or even boundaries moving synchronously in the same direction. These are newly discovered phenomena in the free boundary problems for animal movement. [ABSTRACT FROM AUTHOR]

For a group G , we produce upper and lower bounds for the sum of the entries of the Brauer character table of G and the projective indecomposable character table of G. When G is a π -separable group, we show that the sum of the entries in the table of Isaacs' partial characters is a real number, and we obtain upper and lower bounds for this sum. [ABSTRACT FROM AUTHOR]

For a group G, we define a graph $\Delta (G)$ by letting $G^{\scriptsize\#}=G\setminus {\{\,1\,\}} $ be the set of vertices and by drawing an edge between distinct elements $x,y\in G^{\scriptsize\#}$ if and only if the subgroup $\langle x,y\rangle $ is cyclic. Recall that a Z-group is a group where every Sylow subgroup is cyclic. In this short note, we investigate $\Delta (G)$ for a Z-group G. [ABSTRACT FROM AUTHOR]

Following the literature, a group G is called a group of central type if G has an irreducible character that vanishes on G ∖ Z (G). Motivated by this definition, we say that a character χ ∈ Irr (G) has central type if χ vanishes on G ∖ Z (χ) , where Z (χ) is the center of χ. Groups where every irreducible character has central type have been studied previously under the name GVZ-groups (and several other names) in the literature. In this paper, we study the groups G that possess a nontrivial, normal subgroup N such that every character of G either contains N in its kernel or has central type. The structure of these groups is surprisingly limited and has many aspects in common with both central type groups and GVZ-groups. [ABSTRACT FROM AUTHOR]

The mountain pine beetle (MPB) is among the most destructive eruptive forest pests in North America. A recent increase in the frequency and severity of outbreaks, combined with an eastward range expansion towards untouched boreal pine forests, has spurred a great interest by government, industry and academia into the population ecology of this tree-killing bark beetle. Modern approaches to studying the spread of the MPB often involve the analysis of large-scale, high-resolution datasets on landscape-level damage to pine forests. This creates a need for new modelling tools to handle the unique challenges associated with large sample sizes and spatial effects. In two companion papers (Koch et al. in Environ Ecol Stat. , 2020a; J R Soc Interface 17(170):20200434, 2020b), we explain how the computational challenges of dispersal and spatial autocorrelation can be addressed using separable kernels. In this paper, we use these ideas to capture nonstationary patterns in the dispersal flights of MPB. This facilitates a landscape-level inference of subtle properties of MPB attack behaviour based on aerial surveys of killed pine. Using this model, we estimate the size of the cryptic endemic MPB population, which formerly has been measurable only by means of costly and time-intensive ground surveys. [ABSTRACT FROM AUTHOR]

We consider an M/M/1 queue with a removable server that dynamically chooses its service rate from a set of finitely many rates. If the server is off, the system must warm up for a random, exponentially distributed amount of time, before it can begin processing jobs. We show under the average cost criterion, that work conserving policies are optimal. We then demonstrate the optimal policy can be characterized by a threshold for turning on the server and the optimal service rate increases monotonically with the number in system. Finally, we present some numerical experiments to provide insights into the practicality of having both a removable server and service rate control. [ABSTRACT FROM AUTHOR]

Frobenius groups are an object of fundamental importance in finite group theory. As such, several generalizations of these groups have been considered. Some examples include: A Frobenius–Wielandt group is a triple (G , H , L) where H / L is almost a Frobenius complement for G ; A Camina pair is a pair (G , N) where N is almost a Frobenius kernel for G ; A Camina triple is a triple (G , N , M) where (G , N) and (G , M) are almost Camina pairs. In this paper we study triples (G , N , M) where (G , N) and (G , M) are almost Frobenius groups. [ABSTRACT FROM AUTHOR]

We show that a group is a GVZ-group if and only if it is a flat group. We show that the nilpotence class of a GVZ-group is bounded by the number of distinct degrees of irreducible characters. We also show that certain CM-groups can be characterized as GVZ-groups whose irreducible character values lie in the prime field. [ABSTRACT FROM AUTHOR]

The cyclic graph of a group G is the graph whose vertices are the nonidentity elements of G and whose edges connect distinct elements x and y if and only if the subgroup hx; yi is cyclic. We obtain information about the cyclic graph of 2-Frobenius groups. The cyclic graph of a 2-Frobenius group is disconnected. In this paper, we determine the number of connected components of the cyclic graph of any 2-Frobenius group. [ABSTRACT FROM AUTHOR]

The solubility graph associated with a finite group G is a simple graph whose vertices are the elements of G , and there is an edge between two distinct elements x and y if and only if 〈 x , y 〉 is a soluble subgroup of G. We examine some properties of solubility graphs. [ABSTRACT FROM AUTHOR]

Let G be a p-group, and let χ be an irreducible character of G. The codegree of χ is given by |G : ker (χ)|/χ(1). Du and Lewis have shown that a p-group with exactly three codegrees has nilpotence class at most 2. Here we investigate p-groups with exactly four codegrees. If, in addition to having exactly four codegrees, G has two irreducible character degrees, G has largest irreducible character degree p2, |G : G′| = p2, or G has coclass at most 3, then G has nilpotence class at most 4. In the case of coclass at most 3, the order of G is bounded by p7. With an additional hypothesis, we can extend this result to p-groups with four codegrees and coclass at most 6. In this case, the order of G is bounded by p10. [ABSTRACT FROM AUTHOR]

Objectives: The pervasiveness of hearing loss and the development of new potential therapeutic approaches have led to increased animal studies of the inner ear. However, translational relevance of such studies depends upon verification of protein localization data in human samples. Cadavers used for anatomical education provide a potential research resource, but are limiting due to difficulties in accessing sensory tissues from the dense temporal bones. This study seeks to reduce the often months‐long process of decalcification and improve immunofluorescent staining of human cadaveric temporal bones for research use. Methods: Temporal bones were decalcified in either (a) hydrochloric acid‐containing RDO solution for 2 days followed by 0.5 M ethylenediaminetetraacetic acid (EDTA) for 3 to 5 additional days, or (b) 0.5 M EDTA alone for 2 to 4 weeks. Image‐iT FX signal enhancer (ISE) was used to improve immunofluorescent signal‐to‐noise ratios. Results: The data indicate that both methods speed decalcification and allow for immunolabeling of the extranuclear proteins neurofilament (heavy chain), myosin VIIa, oncomodulin and prestin. However, RDO decalcification was more likely to alter structural morphology of sensory tissues and hindered effective labeling of the nuclear proteins SRY‐box transcription factor 2 and GATA binding protein 3. Conclusions: Although both approaches allow for rapid decalcification, EDTA appears superior to RDO for preserving cytoarchitecture and immunogenicity. Level of evidence: NA. [ABSTRACT FROM AUTHOR]

In this paper, we study the vanishing-off subgroups of supercharacters, and use these to determine several new characterizations of supercharacter theory products. In particular, we give a character theoretic characterization that allows us to conclude that one may determine if a supercharacter theory is a Δ -product or ∗-product from the values of its corresponding supercharacters. [ABSTRACT FROM AUTHOR]

AUTH Why you should read this article: • To enhance your knowledge of the similarities and differences between borderline personality disorder (BPD) and autism spectrum disorder (ASD) • To assist you in developing effective treatment and management plans for people with BPD and/or ASD • To understand the complexities involved in diagnosing and managing people with co-morbid BPD and ASD One of the main issues that people with borderline personality disorder (BPD) and/or autism spectrum disorder (ASD) experience is that they find emotional and relational interactions challenging. This article reviews the available literature on the similarities and differences between BPD and ASD, and aims to raise awareness of the complexity of co-morbid presentations. This is important because, if a person's diagnosis is inaccurate or incomplete, their treatment may be ineffective or inappropriate. The authors provide practical guidelines to assist front-line mental health practitioners in diagnosing BPD and/or ASD, thereby enabling them to develop appropriate and effective management plans. These guidelines were drawn from the available literature and the authors' experience in clinical practice. When BPD and ASD co-occur, a formulation approach should be used to provide person-centred care, rather than an assessment approach that simply defines the issues a person is experiencing. [ABSTRACT FROM AUTHOR]

Mountain pine beetle (MPB) outbreaks have caused major economic losses and ecological consequences in North American pine forests. Ecological and environmental factors impacting MPB life-history and stands susceptibility can help with the detection of MPB infested trees and thereby, improve control. Temperatures, water stress, host characteristics, and beetle pressure are among those ecological and environmental factors. They play different roles on MPB population dynamics at the various stages of an outbreak and these roles can be affected by intensive management. However, to make detailed connections between ecological and environmental variables and MPB outbreak phases, a deeper quantitative analysis on local scales is needed. Here, we used logistic regressions on a highly-detailed and georeferenced data set to determine the factors driving MPB infestations for the different phases of the current isolated MPB outbreak in Cypress Hills. While we showed that the roles of ecological and environmental factors in a forest intensively controlled for MPB are consistent with the literature for uncontrolled forests, we determined how these factors shifted through onset, peak, and collapse phases of the intensively controlled forest. MPB presence mostly depends on nearby beetle pressure, notably for the outbreak peak. However additional weather and host variables are necessary to achieve high predictive ability for MPB outbreak locations. Our results can help managers make appropriate decisions on where and how to focus their effort, depending on which phase the outbreak is in. [ABSTRACT FROM AUTHOR]

A graph is split if there is a partition of its vertex set into a clique and an independent set. In this paper, we determine when the Gruenberg–Kegel graph, the solvable graph, and the compact forms of these graphs associated with finite nonabelian simple groups are split. In particular, it is proved that the compact form of the Gruenberg–Kegel graph of any finite simple group is split. [ABSTRACT FROM AUTHOR]

A super-Brauer character theory of a group G and a prime p is a pair consisting of a partition of the irreducible p-Brauer characters and a partition of the p-regular elements of G that satisfy certain properties. We classify the groups and primes that have exactly one super-Brauer character theory. We discuss the groups with exactly two super-Brauer character theories. [ABSTRACT FROM AUTHOR]

Let G be a solvable group, and let Δ(G) be the character degree graph of G. In this paper, we generalize the definition of a square graph to graphs that are block squares. We show that if G is a solvable group so that Δ(G) is a block square, then G has at most two normal nonabelian Sylow subgroups. Furthermore, we show that when G is a solvable group that has two normal nonabelian Sylow subgroups and Δ(G) is block square, then G is a direct product of subgroups having disconnected character degree graphs. [ABSTRACT FROM AUTHOR]

Motivated by service systems, such as telephone call centers and emergency departments, we consider admission control for a two-class multi-server loss system with periodically varying parameters and customers who may abandon from service. Assuming mild conditions for the parameters, a dynamic programming formulation is developed. We show that under the infinite horizon discounted problem, there exists an optimal threshold policy and provide conditions for a customer class to be preferred for each fixed time, extending stationary results to the non-stationary setting. We approximate the non-stationary problem by discretizing the time horizon into equally spaced intervals and examine how policies for this approximation change as a function of time and parameters numerically. We compare the performance of these approximations with several admission policies used in practice in a discrete-event simulation study. We show that simpler admission policies that ignore non-stationarity or abandonments lead to significant losses in rewards. [ABSTRACT FROM AUTHOR]

A group is nested if the centers of the irreducible characters form a chain. In this paper, we will show that there is a set of subgroups associated with the conjugacy classes of group so that a group is nested if and only if these subgroups forma chain. [ABSTRACT FROM AUTHOR]

The method of inside dynamics provides a theory that can track the dynamics of neutral gene fractions in spreading populations. However, the role of mutations has so far been absent in the study of the gene flow of neutral fractions via inside dynamics. Using integrodifference equations, we develop a neutral genetic mutation model by extending a previously established scalar inside dynamics model. To classify the mutation dynamics, we define a mutation class as the set of neutral fractions that can mutate into one another. We show that the spread of neutral genetic fractions is dependent on the leading edge of population as well as the structure of the mutation matrix. Specifically, we show that the neutral fractions that contribute to the spread of the population must belong to the same mutation class as the neutral fraction found in the leading edge of the population. We prove that the asymptotic proportion of individuals at the leading edge of the population spread is given by the dominant right eigenvector of the associated mutation matrix, independent of growth and dispersal parameters. In addition, we provide numerical simulations to demonstrate our mathematical results, to extend their generality and to develop new conjectures about our model. [ABSTRACT FROM AUTHOR]

In marine systems, adult populations confined to isolated habitat patches can be connected by larval dispersal. Source–sink theory provides effective tools to quantify the effect of specific habitat patches on the dynamics of connected populations. In this paper, we construct the next-generation matrix for a marine metapopulation and demonstrate how it can be used to calculate the source–sink dynamics of habitat patches. We investigate the effect of environmental variables on the source–sink dynamics and demonstrate how the next-generation matrix can provide useful biological insight into transient as well as asymptotic dynamics of the model. [ABSTRACT FROM AUTHOR]

Let G be a finite group. A conjugacy class of G is said to be vanishing if there exists an irreducible character of G which takes the value 0 on the elements of this class. In this note, we describe the groups whose vanishing classes all have size p for some prime p. [ABSTRACT FROM AUTHOR]

We study a hybrid impulsive reaction-advection-diffusion model given by a reaction-advection-diffusion equation composed with a discrete-time map in space dimension n ∈ N. The reaction-advection-diffusion equation takes the form ut(m)=div(A∇u(m)-qu(m))+f(u(m))for (x,t) ∈ Rn×(0,1], for some function f, a drift q and a diffusion matrix A. When the discrete-time map is local in space we use Nm(x) to denote the density of population at a point x at the beginning of reproductive season in the mth year and when the map is nonlocal we use um(x). The local discrete-time map is {u(m)(x,0)=g(Nm(x))for x ∈ Rn,Nm+1(x):=u(m)(x,1)for x ∈ Rn, for some function g. The nonlocal discrete time map is {u(m)(x,0)=um(x)for x ∈ Rn,um+1(x) := g(∫RnK(x-y)u(m)(y,1)dy) for x ∈ Rn, when K is a nonnegative normalized kernel. Here, we analyze the above model from a variety of perspectives so as to understand the phenomenon of propagation. We provide explicit formulas for the spreading speed of propagation in any direction e \in Rn. Due to the structure of the model, we apply a simultaneous analysis of the differential equation and the recurrence relation to establish the existence of traveling wave solutions. The remarkable point is that the roots of spreading speed formulas, as a function of drift, are exactly the values that yield blow-up for the critical domain dimensions, just as with the classical Fisher's equation with advection. We provide applications of our main results to impulsive reaction-advection-diffusion models describing periodically reproducing populations subject to climate change, insect populations in a stream environment with yearly reproduction, and grass growing logistically in the savannah with asymmetric seed dispersal and impacted by periodic fires. [ABSTRACT FROM AUTHOR]

Let $G$ be a group, $p$ be a prime and $P\in \text{Syl}_{p}(G)$. We say that a $p$ -Brauer character $\unicode[STIX]{x1D711}$ is monolithic if $G/\ker \unicode[STIX]{x1D711}$ is a monolith. We prove that $P$ is normal in $G$ if and only if $p\nmid \unicode[STIX]{x1D711}(1)$ for each monolithic Brauer character $\unicode[STIX]{x1D711}\in \text{IBr}(G)$. When $G$ is $p$ -solvable, we also prove that $P$ is normal in $G$ and $G/P$ is nilpotent if and only if $\unicode[STIX]{x1D711}(1)^{2}$ divides $|G:\ker \unicode[STIX]{x1D711}|$ for all monolithic irreducible $p$ -Brauer characters $\unicode[STIX]{x1D711}$ of $G$. [ABSTRACT FROM AUTHOR]

Mathematical models of spatial population dynamics typically focus on the interplay between dispersal events and birth/death processes. However, for many animal communities, significant arrangement in space can occur on shorter timescales, where births and deaths are negligible. This phenomenon is particularly prevalent in populations of larger, vertebrate animals who often reproduce only once per year or less. To understand spatial arrangements of animal communities on such timescales, we use a class of diffusion–taxis equations for modelling inter-population movement responses between N ≥ 2 populations. These systems of equations incorporate the effect on animal movement of both the current presence of other populations and the memory of past presence encoded either in the environment or in the minds of animals. We give general criteria for the spontaneous formation of both stationary and oscillatory patterns, via linear pattern formation analysis. For N = 2 , we classify completely the pattern formation properties using a combination of linear analysis and nonlinear energy functionals. In this case, the only patterns that can occur asymptotically in time are stationary. However, for N ≥ 3 , oscillatory patterns can occur asymptotically, giving rise to a sequence of period-doubling bifurcations leading to patterns with no obvious regularity, a hallmark of chaos. Our study highlights the importance of understanding between-population animal movement for understanding spatial species distributions, something that is typically ignored in species distribution modelling, and so develops a new paradigm for spatial population dynamics. [ABSTRACT FROM AUTHOR]

Let π be a set of primes, and let G be a finite π-separable group. We consider the Isaacs Bπ-characters. We show that if N is a normal subgroup of G, then Bπ (G/N) = Irr(G=N) ∩ Bπ(G). [ABSTRACT FROM AUTHOR]