Functional Identity Research Articles

Proof of a conjecture on congruences of the sum of minimal excludants

Very recently, Baruah et al. refined a result of Andrews and Newman on the sum of minimal excludants over all the partitions of a positive integer [Formula: see text] by establishing the generating functions of two functions [Formula: see text] and [Formula: see text] which denote the sum of odd minimal excludants and the sum of even minimal excludants, respectively. They proved some congruences on [Formula: see text] and [Formula: see text] modulo 4 and 8 and posed a conjecture on [Formula: see text] and [Formula: see text] at the end of their paper. In this paper, we confirm this conjecture by using theta function identities.

Proofs of three conjectured internal congruences modulo 32 for Schur-type overpartitions

Let S(n) denote the number of overpartitions of Schur-type. Recently, Chern, da Silva and Sellers proved many congruences modulo 8 and 16 for S(n). At the end of their paper, they also posed a conjecture on internal congruences modulo 32 for S(n). In this paper, we confirm their conjecture by using theta function identities and the (p, k)-parameterization of theta functions given by Alaca and Williams. In particular, we show that for any integer j with 0 ≤ j ≤ 31, there are infinitely many integers uj such that S(uj ) ≡ j (mod 32).

Symmetric Reverse n-Derivations on Ideals of Semiprime Rings

This paper focuses on examining a new type of n-additive map called the symmetric reverse n-derivation. As implied by its name, it combines the ideas of n-additive maps and reverse derivations, with a 1-reverse derivation being the ordinary reverse derivation. We explore several findings that expand our knowledge of these maps, particularly their presence in semiprime rings and the way rings respond to specific functional identities involving elements of ideals. Also, we provide examples to help clarify the concept of symmetric reverse n-derivations. This study aims to deepen our understanding of these symmetric maps and their properties within mathematical structures.

Independent effects of tree diversity on aboveground and soil carbon pools after six years of experimental afforestation.

Planting diverse forests has been proposed as a means to increase long-term carbon (C) sequestration while providing many co-benefits. Positive tree diversity-productivity relationships are well established, suggesting more diverse forests will lead to greater aboveground C sequestration. However, the effects of tree diversity on belowground C storage have the potential to either complement or offset aboveground gains, especially during early stages of afforestation when potential exists for large losses in soil C due to soil decomposition. Thus, experimental tests of the effects of planted tree biodiversity on changes in whole-ecosystem C balance are needed. Here, we present changes in above- and belowground C pools 6 years after the initiation of the Forests and Biodiversity experiment (FAB1), consisting of high-density plots of one, two, five, or 12 tree species planted in a common garden. The trees included a diverse range of native species, including both needle-leaf conifer and broadleaf angiosperm species, and both ectomycorrhizal and arbuscular mycorrhizal species. We quantified the effects of species richness, phylogenetic diversity, and functional diversity on aboveground woody C, as well as on mineral soil C accumulation, fine root C, and soil aggregation. Surprisingly, changes in aboveground woody C pools were uncorrelated to changes in mineral soil C pools, suggesting that variation in soil C accumulation was not driven by the quantity of plant litter inputs. Aboveground woody C accumulation was strongly driven by species and functional identity; however, plots with higher species richness and functional diversity accumulated more C in aboveground wood than expected based on monocultures. We also found weak but significant effects of tree species richness, identity, and mycorrhizal type on soil C accumulation. To assess the role of the microbial community in mediating these effects, we further compared changes in soil C pools to phospholipid fatty acid (PLFA) profiles. Soil C pools and accumulation were more strongly correlated with specific microbial clades than with total microbial biomass or plant diversity. Our results highlight rapidly emerging and microbially mediated effects of tree biodiversity on soil C storage in the early years of afforestation that are independent of gains in aboveground woody biomass.

Interpreting the shifts in forest structure, plant community composition, diversity, and functional identity by using remote sensing-derived wildfire severity

BackgroundWildfires are increasingly impacting ecosystems worldwide especially in temperate dry habitats, often interplaying with other global changes (e.g., alien plant invasions). Understanding the ecological consequences of wildfires is crucial for effective conservation and management strategies. The aim of this study was to investigate the impacts of wildfire severity on plant community (both the canopy trees and herbaceous layer) and alien plant invasion, combining field observations and remotely sensed data.We conducted an observational study in the Karst forests (North-East Italy) 1 year after the large wildfire which affected the area in 2022. We assessed the impact through 35 field plots (200 m2 each) distributed among different fire severity (i.e., the loss of organic matter) classes assessed using the differenced normalized burn ratio (dNBR) calculated from satellite images. In each plot, tree species, diameter, vitality, resprouting capacity, and seedling density were measured. In addition, herb species richness (taxonomical diversity) was quantified, and plant cover was visually estimated. Functional diversity was also assessed considering six functional traits retrieved from databases.ResultsSome woody species (e.g., Quercus pubescens) showed a higher resistance to the fire (i.e., lower mortality rate), while others showed a higher resilience (i.e., recovery after fire through resprouting or seedlings, e.g., Cotinus coggygria). The transition to a shrub-dominated community (i.e., Cotinus coggygria) where fire severity was the highest underlines the dynamic nature of the post-fire succession. We detected a significant variation in the herbaceous plant community composition, diversity, and functional identity (i.e., community-weighted mean of trait) along the fire severity gradient. In particular, high-fire severity areas exhibited higher species richness compared to low-severity or unburned areas. Total alien plant cover increased with fire severity, while native cover remained constant. We also found shifts in species that enhance traits related to germination potential and growth strategy.ConclusionsOur results highlight the vulnerability of the forest stands to an increase in wildfire severity, resulting in significant mortality and changes in tree community structure. This study contributes to the understanding of ecological processes after wildfires using a novel remote sensing approach in a temperate forest, emphasizing the need for conservation strategies aimed at mitigating high severity wildfires.

Investigating how consumption values and place identity shape long-haul truck drivers’ intention to visit roadside rest areas

Transportation business organisations, policymakers, and government entities attempt to enhance the welfare of long-haul truck drivers (LHTDs) by promoting safe driving practices. LHTDs spend long hours on goods delivery journeys, and that causes various health and in-route safety issues for drivers. For improved LHTD health and safety, many developed nations introduced the concept of roadside rest areas (RRAs) for regulated, safe, and enhanced driving experience for LHTDs, whereas developing nations’ research on RRAs development is nascent. The RRAs offer a chance to reduce negative truck driving impacts and promote wellbeing among LHTDs, but why drivers will visit RRAs during their tracking journey is a question for policymakers. Hence, the present study tries to comprehend the significance of drivers’ visit consumption values in terms of functional, social, emotional, epistemic, conditional value, and place identity concerning visit intentions towards RRAs. In addition, the present work examines the influence of consumption values on word of mouth (WoM) for RRAs by LHTDs. The research problem is examined via the lens of the theory of consumption values. The study utilised 247 valid responses for model analysis, using the partial least squares-structural equation modelling (PLS-SEM) technique. The findings establish that consumption value is a formative construct that further positively influences place identity, intentions to visit RRAs, and WoM for RRAs by LHTDs. This implies that the intentions of LHTDs to visit relaxation sites are mostly influenced by the values they perceive from such places. This perception of consumption values also helps LHTDs develop place identity with RRAs and influences them to spread positive WoM about it. However, the results of the present study did not find the mediation role of place identity. This implies that Indian LHTDs will develop the intention to visit RRAs because of the consumption values rather than any attachment to the place. The findings of this paper will help transport policymakers develop adequate measures for developing rest areas on major transport routes to improve road safety and drivers’ wellbeing.

Modelling human diabetes ex vivo: a glance at maturity onset diabetes of the young.

Diabetes is a complex metabolic disease which most commonly has a polygenic origin; however, in rare cases, diabetes may be monogenic. This is indeed the case in both Maturity Onset Diabetes of the Young (MODY) and neonatal diabetes. These disease subtypes are believed to be simpler than Type 1 (T1D) and Type 2 Diabetes (T2D), which allows for more precise modelling. During the three last decades, many studies have focused on rodent models. These investigations provided a wealth of knowledge on both pancreas development and beta cell function. In particular, they allowed the establishment of a hierarchy of the transcription factors and highlighted the role of microenvironmental factors in the control of progenitor cell proliferation and differentiation. Transgenic mice also offered the possibility to decipher the mechanisms that define the functional identity of the pancreatic beta cells. Despite such interest in transgenic mice, recent data have also indicated that important differences exist between mice and human. To overcome these limitations, new human models are necessary. In the present review, we describe these ex vivo models, which are created using stem cells and organoids, and represent an important step toward islet cell therapy and drug discovery.

Spatial structuring of coral traits along a subtropical-temperate transition zone persists despite localised signs of tropicalisation

AbstractClimate-driven species range expansions are underway with more tropically affiliated species, including Scleractinian corals, becoming increasingly abundant at higher latitudes. However, uncertainty remains on how these range shifts will affect reef-scale ecosystem processes, which will ultimately depend on the traits of the taxa that dominate these assemblages. Here, we quantified spatiotemporal patterns in the taxonomic and trait structure of coral assemblages along the subtropical-temperate coast of Western Australia (27°–34°S). Coral abundance was generally low and coral cover < 5% across our study sites. Coral assemblages shared similarities in morphological trait structures across the latitudinal gradient, mostly characterised by taxa with simple morphologies; yet subtle differences were also observed across latitudes, with high-latitude corals characterised by slower growth rates and reduced maximum colony sizes. We found a 3.4-fold increase (from 1 to 3.4 individuals m−2) in coral abundance at one heavily disturbed location, where canopy-forming seaweeds were replaced by turfing algae, a pattern that was partly driven by an increase in the relative contribution of warm affinity taxa, such as Acropora spp. We predicted these changes would be reflected in different components of functional diversity; yet, despite a localised signal of tropicalisation, we only observed subtle changes in the functional identity, richness, evenness, and divergence. The spatially invariant trait structure of coral assemblages suggests that the nature of ecosystem functions will likely remain unchanged during early stages of tropicalisation, and hence their contribution to temperate reef-scale ecological processes will depend on dominance over other benthic foundational species.

Distinct brain-wide presynaptic networks underlie the functional identity of individual cortical neurons.

Neuronal connections provide the scaffolding for neuronal function. Revealing the connectivity of functionally identified individual neurons is necessary to understand how activity patterns emerge and support behavior. Yet, the brain-wide presynaptic wiring rules that lay the foundation for the functional selectivity of individual neurons remain largely unexplored. Cortical neurons, even in primary sensory cortex, are heterogeneous in their selectivity, not only to sensory stimuli but also to multiple aspects of behavior. Here, to investigate presynaptic connectivity rules underlying the selectivity of pyramidal neurons to behavioral state 1-12 in primary somatosensory cortex (S1), we used two-photon calcium imaging, neuropharmacology, single-cell based monosynaptic input tracing, and optogenetics. We show that behavioral state-dependent neuronal activity patterns are stable over time. These are minimally affected by neuromodulatory inputs and are instead driven by glutamatergic inputs. Analysis of brain-wide presynaptic networks of individual neurons with distinct behavioral state-dependent activity profiles revealed characteristic patterns of anatomical input. While both behavioral state-related and unrelated neurons had a similar pattern of local inputs within S1, their long-range glutamatergic inputs differed. Individual cortical neurons, irrespective of their functional properties, received converging inputs from the main S1-projecting areas. Yet, neurons that tracked behavioral state received a smaller proportion of motor cortical inputs and a larger proportion of thalamic inputs. Optogenetic suppression of thalamic inputs reduced behavioral state-dependent activity in S1, but this activity was not externally driven. Our results revealed distinct long-range glutamatergic inputs as a substrate for preconfigured network dynamics associated with behavioral state.

Perceived Impacts of Tourism on Community Identity: Perspectives of Two Scottish Highland Communities

ABSTRACT The Scottish Highlands tourism industry has grown significantly due to the successful launch of the North Coast 500 route. This study investigates the perceived tourism impact on rural communities based on a survey and semi-structured interviews conducted in Elphin and Ullapool in 2021. By approaching community identity as a combination of emotional identity, functional identity, and community participation, the paper identifies key differences in the identities of two communities usually framed as belonging to one homogenous region. This provides host community perspectives on which aspects of their identities may be targeted to support effective tourism developments. We conclude that although the overall strength of both communities identities seem unaffected by growing tourism levels, they do shape their nature, particularly when different concerns intersect such as environmental degradation and limited affordable housing. Addressing resident concerns through meaningful contributions to decision-making processes is key to the success of regional tourism policies.

Coordinated Tbx3 / Tbx5 transcriptional control of the adult ventricular conduction system.

The cardiac conduction system (CCS) orchestrates the electrical impulses that enable coordinated contraction of the cardiac chambers. The T-box transcription factors TBX3 and TBX5 are required for cardiac conduction system development and associated with overlapping and distinct human cardiac conduction system diseases. We evaluated the coordinated role of Tbx3 and Tbx5 in the murine ventricular conduction system (VCS). We engineered a compound Tbx3:Tbx5 conditional knockout allele for both genes located in cis on mouse chromosome 5. Conditional deletion of both T-box transcriptional factors in the ventricular conduction system, using the VCS-specific Mink:Cre, caused loss of VCS function and molecular identity. Combined Tbx3 and Tbx5 deficiency in the adult VCS led to conduction defects, including prolonged PR and QRS intervals and elevated susceptibility to ventricular tachycardia. These electrophysiologic defects occurred prior to detectable alterations in cardiac contractility or histologic morphology, indicative of a primary conduction system defect. Tbx3:Tbx5 double knockout VCS cardiomyocytes revealed a transcriptional shift towards non-CCS-specialized working myocardium, suggesting reprogramming of their cellular identity. Furthermore, optical mapping revealed a loss of VCS-specific conduction system propagation. Collectively, these findings indicate that Tbx3 and Tbx5 coordinate to control VCS molecular fate and function, with implications for understanding cardiac conduction disorders in humans.

Pfaffians are Pfine

Summary Pfaffians are less familiar functions on skew-symmetric matrices, and yet Donald Knuth claims they are more fundamental than determinants. We explore connections between determinants and Pfaffians. Along the way, the reader will encounter combinatorial proofs of identities for both matrix functions and play with permutations, matchings, Reidemeister moves, and game theory.

Considerations for trustworthy cross-border interoperability of digital identity systems in developing countries

AbstractIn developing nations, the implementation of Foundational Identity Systems (FIDS) has optimised service delivery and inclusive economic growth. Cross-border e-government will gain traction as developing countries increasingly look to identity federation and trustworthy interoperability through FIDS for the identification and authentication of identity holders. Despite this potential, the interoperability of FIDS in the African identity ecosystem has not been well-studied. Among the difficulties in this situation are the intricate internal political dynamics that have led to weak institutions, suggesting that FIDS could be used for political purposes; additionally, citizens’ or identity holders’ habitual low trust in the government raises concerns about data security and privacy protection. Similarly, vendor lock-in, cross-system compatibility, and ambiguous legislative rules for data exchange are other concerns. Interoperability is fundamentally necessary as a precondition for e-government services and serves as the foundation for the best possible service delivery in the areas of social security, education, and finance, as well as gender equality as demonstrated by the European Union (EU). Moreover, the integration of cross-border FIDS and an ecosystem of effective data governance will be created by unified data sharing via an interoperable identity system. Thus, in this study, we point to the challenges, opportunities, and requirements for cross-border interoperability in an African setting. Furthermore, we investigated current interoperability solutions such as the EU’s eIDAS and Estonian X-Road and proposed an approach for scoping requirements to achieve a fully functional interoperable identity ecosystem in the African setting. Our findings show that interoperability in the African identity ecosystem is essential for expanding the scope of e-government throughout the continent and for bolstering the smooth authentication and verification of identity holders for inclusive economic growth.

Optogenetic hedonic hotspots in orbitofrontal cortex and insula: causing enhancement of sweetness 'liking'.

Hedonic hotspots are brain subregions that causally amplify the hedonic impact of palatable tastes, measured as increases in affective orofacial 'liking' reactions to sweetness. Previously, two cortical hedonic hotspots in orbitofrontal cortex and insula were identified by neurochemical stimulation using opioid or orexin microinjections. Here we used optogenetic stimulation in rats as an independent neurobiological technique for activating cortical hedonic hotspots to identify hedonic functions and map boundaries. We report that channelrhodopsin stimulations within rostral orbitofrontal and caudal insula hotspots doubled the number of hedonic 'liking' reactions elicited by sucrose taste. This independently confirms their robust functional identity as causal amplifiers of hedonic 'liking' and confirms their anatomical boundaries. Additionally, we confirmed an intervening suppressive hedonic coldstrip, to stretching from caudal orbitofrontal cortex to rostral insula. By contrast to localized hedonic hotspots for 'liking' enhancement, motivational 'wanting' for reward, measured as laser self-stimulation, was mediated by more widely distributed anatomical sites.

A quadratic transformation for a special confluent Heun function

We report a functional identity involving a quadratic transformation of the argument for the confluent Heun function. This identity is the first of its kind to be discovered for the confluent Heun function, and it has the potential to be useful in a variety of applications.

A novel integral identity for circular and diamond symmetric functions

A novel integral identity is introduced that can be applied to circular and diamond symmetric functions. It is demonstrated how this new identity and its alternative representations can be employed to facilitate integral derivations, including available examples in the literature as its special cases. As another application of the presented integral identities, a new integral transform is introduced that transforms circular symmetric functions to corresponding diamond symmetric functions. It is also illustrated how other integral equalities can be developed based on the introduced identities and using known integral transform kernels. Then, two-dimensional Mellin and Fourier transform kernels are adopted as case studies.

Crop functional structure predicts the provision of Nature´s material Contribution to People in diversified agroforestry

Applying concepts from natural ecosystem ecology, particularly through diversified cropping systems that integrate woody crops with other crops, can enhance agrobiodiversity and significantly contribute to multifunctional agriculture. The ecological and, more recently, the agronomic literature have indicated that functional trait aspects of diversity offer a more comprehensive explanation for ecosystem functions compared to species richness alone. In this study, we apply the trait-based approach during experimental agroforest succession in subtropical Southern Brazil to investigate the main factors of crop functional structure, differentiating the effects of functional diversity (FD) from functional identity (CWM - community weighted mean), on Nature's Contributions to People (NCP). The experiment was designed varying crop FD, based on leaf nitrogen concentration, while maintaining crop species richness constant across all treatments. To assess FD and CWM, we measured six crop traits; maximum plant height, leaf area, specific leaf area, leaf nitrogen content, leaf dry-matter content, and stem-specific density. Additionally, we evaluated four material NCP (green manure, forage, germplasm, and food) based on data collected during the initial four years of the experiment (2017–2020). To analyze the data, we employed principal component analysis to reduce the number of variables and subsequently fitted linear mixed-effect models. Our findings provide support for the hypothesis that crop functional structure, particularly in relation to leaf traits (leaf area and leaf nitrogen content) and vegetative height, significantly influences material outputs and predicts above-ground biomass production that can be utilized as green manure and animal feed in agroforestry and silvopastoral systems. Both FD and CWM were important drivers of NCPs, showing that both niche complementarity and selection effects contribute to explain agroecosystem functioning. By utilizing functional traits, we reached valuable insights for generating agronomical recommendations and enhancing cropping system diversification through effective trait-based management.

S-move matrix in the NS sector of N = 1 super Liouville field theory

In this paper we calculate matrix of modular transformations of the one-point toric conformal blocks in the Neveu-Schwarz sector of N = 1 super Liouville field theory. For this purpose we use explicit expression for this matrix as integral of product of certain elements of fusion matrix. This integral is computed using the chain of integral identities for supersymmetric hyperbolic gamma functions derived by the degeneration of the integrals of parafermionic elliptic gamma functions.

Landscape planning and polycentricity: potentialities for regional integration in transboundary natural resources

This article proposes a discussion on the potential application of polycentricity strategies in the management of strategic transboundary natural resources, such as shared water bodies and river basins with regional potential for water supply and energy production.As a method, it presents a review of the literature on polycentricity, focusing on the challenges and opportunities of governance of shared territories among polycentric cities. It identifies key aspects of polycentricity, focusing on topics such as the integration of cities in polycentric urban regions, regional policies and governance in polycentric regions, and polycentricity and natural resource management.Complementarily, potential landscape planning strategies that can be applied to strengthen regional identity between centralities, as well as to strengthen the functional, institutional and cultural identity and integration of a polycentric region, are also presented.

Eulerian series as Hecke-type double sums through the transformation formulas

Recently, establishing the Hecke-type double sums forms for Eulerian series has received a great deal of attention to seek special cases of [Formula: see text]-hypergeometric series. In this paper, with the aid of some basic hypergeometric series identities given by Chen and Wang, and Liu, we discover many new Eulerian series and express them in terms of Hecke-type double sums and Appell–Lerch sums. Based on the modern sense for the mock theta functions, we find that some of these series are mock theta functions and the others are mixed mock theta functions. Furthermore, from the viewpoint of Hecke-type double sums, we find three string function identities with levels [Formula: see text], [Formula: see text], and [Formula: see text].