Mapping Criteria Research Articles

Univalence criterion for harmonic mappings and Φ-like functions

In this paper, we obtain a new characterization for univalent harmonic mappings and obtain a structural formula for the associated function which defines the analytic -like functions in the unit disk. The new criterion stated in this article for the injectivity of harmonic mappings implies the well-known results of Kas’yanyuk [10] and Brickman [3] for analytic functions, but with a simpler proof than theirs. A number of consequences of the characterization, and examples are also presented. Further investigation provides a new method to construct univalent harmonic mappings with the help of an improved distortion theorem.

Secret Key Exchange and Authentication via Randomized Spatial Modulation and Phase Shifting

Advances in physical layer security techniques have increasingly demonstrated their potential to replace security functionalities that are traditionally included in the upper layers of the Open Systems Interconnection model. This has made it possible for devices with limited layer structures or/and restricted hardware components to offer security measures. In this paper, we consider spatial modulation (SM) systems and propose a unique physical layer technique that uses a random constellation mapping criterion for secret key exchange. The principle idea here is to exploit the inherent symbol-antenna mapping feature of the SM technique to encode the secret key. Specifically, a random phase shift is imposed on each of the modulated symbols using a channel driven approach to uniquely authenticate the transmitted key bits or/and the encrypted confidential data. The results demonstrate that the proposed technique is superior to benchmark techniques in terms of computational complexity and key bit error rate. It will also be shown that the proposed technique offers greater flexibility in terms of the authentication process preference, which is normally unattainable in most of the key exchange proposed techniques.

On plotting the scheme of fracture-mega-block tectonics of the Ukrainian Shield in a scale 1 : 500 000

The main principles have been proposed for discussion on composing the Scheme of fracrture-mega-block tectonics of the Ukrainian Shield in a scale 1 : 500 000 supported by a decision of Inter-departmental tectonic committee of Ukraine as a basis for plotting the Tectonic map of the Ukrainian Shield in the mentioned scale. The existing maps and schemes of the blocky subdivision of the Ukrainian Shield considerably differ from each other especially because the fact that the unified principles of blocky and especially mega-blocky subdivision for the whole shield were not yet formulated then and the criteria for subdivision and mapping of inter-mega-block fracture zones were not supported. Such criteria are being considered in this work, and examples of schemes of fracture-block tectonics of three sheets in a scale 1 : 200 000 composed on their base have been given. It is proved that the Scheme of fracture-mega-block structure of the Ukrainian Shield must reflect the present-day blocky subdivision of the earth crust formed at the border of Early and Middle Proterozoic, at the very end of establishment of the granite socle of the shield. Only such mega-blocks and blocks and in the first place fault zones, which separate them, may be exactly identified and mapped that is an important condition, because the most part of deposits and ore manifestations of the shield are just related to the fracture zones. More ancient margins of mega-blocks and fault zones in the areas of Early Proterozoic tectonic-magmatic activation are hypothetical and cannot be mapped unambiguously. It has been shown that while plotting the Scheme of fracture-mega-block tectonics of the Ukrainian Shield the priority belongs to geophysical methods.

Influence of Intramyocardial Adipose Tissue on the Accuracy of Endocardial Contact Mapping of the Chronic Myocardial Infarction Substrate.

Recent studies have demonstrated that intramyocardial adipose tissue (IMAT) may contribute to ventricular electrophysiological remodeling in patients with chronic myocardial infarction. Using an ovine model of myocardial infarction, we aimed to determine the influence of IMAT on scar tissue identification during endocardial contact mapping and optimal voltage-based mapping criteria for defining IMAT dense regions. In 7 sheep, left ventricular endocardial and transmural mapping was performed 84 weeks (15-111 weeks) post-myocardial infarction. Spearman rank correlation coefficient was used to assess the relationship between endocardial contact electrogram amplitude and histological composition of myocardium. Receiver operator characteristic curves were used to derive optimal electrogram thresholds for IMAT delineation during endocardial mapping and to describe the use of endocardial mapping for delineation of IMAT dense regions within scar. Endocardial electrogram amplitude correlated significantly with IMAT (unipolar r=-0.48±0.12, P<0.001; bipolar r=-0.45±0.22, P=0.04) but not collagen (unipolar r=-0.36±0.24, P=0.13; bipolar r=-0.43±0.31, P=0.16). IMAT dense regions of myocardium reliably identified using endocardial mapping with thresholds of <3.7 and <0.6 mV, respectively, for unipolar, bipolar, and combined modalities (single modality area under the curve=0.80, P<0.001; combined modality area under the curve=0.84, P<0.001). Unipolar mapping using optimal thresholding remained significantly reliable (area under the curve=0.76, P<0.001) during mapping of IMAT, confined to putative scar border zones (bipolar amplitude, 0.5-1.5 mV). These novel findings enhance our understanding of the confounding influence of IMAT on endocardial scar mapping. Combined bipolar and unipolar voltage mapping using optimal thresholds may be useful for delineating IMAT dense regions of myocardium, in postinfarct cardiomyopathy.

Harmonic mappings of bounded boundary rotation

The purpose of this paper is to investigate the valency of planar harmonic mappings of bounded boundary rotation of the open unit disc D . \mathbb {D}. The paper is motivated by the earlier work of the first two authors [Complex Analysis Oper. Theory 5 (2011), 767–774] and the recent work of T. Hayami [Complex Var. Elliptic Equ. 59 (2014), 1214–1222]. First, the authors give a counterexample showing that both the main result of Hayami, Theorem 2.1, and the related conjecture, Conjecture 4.1, are false. Second, the authors give a valency criterion for planar harmonic mappings of bounded boundary rotation of D \mathbb {D} , proving an ameliorated statement of Theorem 2.1 and settling a modified version of Conjecture 4.1.

Application of land-use management scenarios to mitigate desertification risk in northern Iran

The environmentally sensitive areas (ESAs) model has been applied to evaluate the risk of desertification in the Chehel-Chai Watershed, northern Iran. This research is mainly conducted to quantify and assess the effect of land-use change processes on desertification risk in areas with humid climate. Water erosion, soil, vegetation, climate and management practices were used as five main criteria for desertification mapping in this study. The degree of sensitivity to desertification was determined for each land unit using the categorization table of desertification intensity. For providing insights into optimal management programs, the desertification sensitivity map was used to analyze different scenarios of management strategies. By assuming that other indices are constant, these scenarios were replaced by altering land-use intensity parameter. Based on five above-mentioned criteria, the mean weight of quantitative value for desertification sensitivity was calculated, which was 1.32 for the research location. By comparing this value to ESAs table, the desertification class of the study area was determined as fragile (type 2). Scenario analysis results indicated that the relative frequencies of areas with critical states of desertification (i.e., classes 1, 2 and 3) are reduced by 18.84 and 14.27% in vegetation management scenario and land ecological capability evaluation scenario, respectively. Results of this study also highlighted that scenario maps are efficient tools for analyzing and identifying areas at high risk of desertification in Chehel-Chai Watershed, where desertification process could be alleviated if appropriate land-use planning and vegetation management programs are adopted.

Generation of simple structured information retrieval functions by genetic algorithm without stagnation

Abstract This paper investigates an approach to construct new ranking models for Information Retrieval. The IR ranking model depends on the document description. It includes the term frequency and document frequency. The model ranks documents upon a user request. The quality of the model is defined by the difference between the documents, which experts assess as relative to the request, and the ranked ones. To boost the model quality a modified genetic algorithm was developed. It generates models as superpositions of primitive functions and selects the best according to the quality criterion. The main impact of the research if the new technique to avoid stagnation and to control structural complexity of the consequently generated models. To solve problems of stagnation and complexity, a new criterion of model selection was introduced. It uses structural metric and penalty functions, which are defined in space of generated superpositions. To show that the newly discovered models outperform the other state-of-the-art IR scoring models the authors perform a computational experiment on TREC datasets. It shows that the resulted algorithm is significantly faster than the exhaustive one. It constructs better ranking models according to the MAP criterion. The obtained models are much simpler than the models, which were constructed with alternative approaches. The proposed technique is significant for developing the information retrieval systems based on expert assessments of the query-document relevance.

Indo-Iranian Parallels of the Slavic Water Rites of the Oath and Guilt Confirmation Attested in Medieval Latin Accounts and Slavic Law Codices&lt;br&gt;Indo-iranskie paralleli slavjanskih vodnyh ritualov kljatvoprinošenija i priznanija viny, opisannyh v srednevekovyh latinskih istočnikah i predstavlennyh v slavjanskih juridičeskih kodeksah&lt;/br&gt;

In this article are presented Slavic rituals of the contract, and confirmation of oaths through water, mentioned in the historic accounts and law codices. Connections between the deities given in the historic accounts and descriptions of the rituals are proposed. Parallels between the Slavic and Indo-Iranian water oath rites, as well as their semantics and related deities, are offered. An attempt to justify the validity of the reconstruction of the missing elements of one mytho-religious space with the use of another, a better-known space, is presented, given that the elements of the interest satisfy the homomorphic mapping between the spaces. It is suggested that the mapping of the water oath rites and their associated deities in the Slavic and Indo-Iranian mytho-religious spaces satisfy the homomorphic mapping criteria.

Bromodomain protein 4 discriminates tissue-specific super-enhancers containing disease-specific susceptibility loci in prostate and breast cancer

BackgroundEpigenetic information can be used to identify clinically relevant genomic variants single nucleotide polymorphisms (SNPs) of functional importance in cancer development. Super-enhancers are cell-specific DNA elements, acting to determine tissue or cell identity and driving tumor progression. Although previous approaches have been tried to explain risk associated with SNPs in regulatory DNA elements, so far epigenetic readers such as bromodomain containing protein 4 (BRD4) and super-enhancers have not been used to annotate SNPs. In prostate cancer (PC), androgen receptor (AR) binding sites to chromatin have been used to inform functional annotations of SNPs.ResultsHere we establish criteria for enhancer mapping which are applicable to other diseases and traits to achieve the optimal tissue-specific enrichment of PC risk SNPs. We used stratified Q-Q plots and Fisher test to assess the differential enrichment of SNPs mapping to specific categories of enhancers. We find that BRD4 is the key discriminant of tissue-specific enhancers, showing that it is more powerful than AR binding information to capture PC specific risk loci, and can be used with similar effect in breast cancer (BC) and applied to other diseases such as schizophrenia.ConclusionsThis is the first study to evaluate the enrichment of epigenetic readers in genome-wide associations studies for SNPs within enhancers, and provides a powerful tool for enriching and prioritizing PC and BC genetic risk loci. Our study represents a proof of principle applicable to other diseases and traits that can be used to redefine molecular mechanisms of human phenotypic variation.

An improved data-driven fuzzy mineral prospectivity mapping procedure; cosine amplitude-based similarity approach to delineate exploration targets

Weighting and synthesizing exploration evidence criteria for mineral prospectivity mapping (MPM) are affected by complexity and ambiguity of ore mineralization processes. In this regard, fuzziness could facilitate the modeling of such vague processes for MPM. Furthermore, imprecise selection of the exploration criteria to be used in MPM has negative influence on the efficiency of the generated prospectivity models. In this paper, of various exploration criteria, a coherent set of exploration features were recognized by using the distance distribution analysis. Then, the application of cosine amplitude-based similarity procedure was adapted as a data-driven fuzzy logic approach for predictive mapping of porphyry-Cu prospectivity in Arasbaran metallogenic zone, NW Iran. In addition, a conventional data-driven fuzzy prospectivity model was generated for comparison purpose. Comparison of the two models demonstrated the superiority of the cosine amplitude-based fuzzy procedure for MPM.

Analog Network-Coded Modulation With Maximum Euclidean Distance: Mapping Criterion and Constellation Design

Physical-layer network coding holds the great potential of improving the power efficiency and the spectral efficiency for the two-stage transmission scheme. The first stage is the multiple access stage, where two source nodes (SN1 and SN2) simultaneously transmit to the relay node (RN). The second stage is the Broadcast stage, where the RN broadcasts to the two destination nodes (DN1 and DN2), after a denoising-and-mapping operation. In this paper, we investigate the joint network-coded modulation design of the two stages. A universal modulation framework is built, referred to as analog network-coded modulation strategy, which is more general than the former modulation design mechanism. More explicitly, we propose a joint design criterion to guarantee the forwarding reliability at the RN. The criterion ensures that the neighboring constellation points superposed at the RN are mapped to an identical constellation point for broadcasting if their Euclidean distance (ED) is less than a given threshold. This yields a non-convex polynomial optimization problem by minimizing the average transmission power and constraining the ED among the constellation points. By solving the problem, we propose two joint modulation design algorithms, termed as the Enhanced Semidefinite Relaxation Algorithm and the Fast-Relaxation Algorithm, respectively. The two algorithms can achieve the tradeoff between the communication performance and the computation resources. As for the Fast-Relaxation Algorithm, the theoretical performance boundary is derived in detail. Simulation results demonstrate the effectiveness of both the proposed algorithms by comparing symbol error rate performance with the existing modulation design methods.

Research of short-term heart rate variability during sleep based on limited penetrable horizontal visibility graph

Heart rate is one of the most easily accessed human physiological data. In recent years, the analysis of sleep function based on heart rate variability has become a new popular feature of wearable devices used for daily health management. Consequently, it is needed to explore various types of short-term characteristic parameters which can be applied to the heartbeat interval time series within the standard sleep staging time window (about 30 s). Utilizing the recently reported limited penetrable horizontal visibility graph (LPHVG) algorithm, together with a weighted limited penetrable horizontal visibility graph (WLPHVG) algorithm proposed in this paper, the short-term heartbeat interval time series in different sleep stages are mapped to networks respectively. Then, 6 characteristic parameters, including the average clustering coefficient C, the characteristic path length L, the clustering coefficient entropy Ec, the distance distribution entropy Ed, the weighted clustering coefficient entropy ECw and the weight distribution entropy Ew are calculated and analyzed. The results show that the values of these characteristic parameters are significantly different in the states of wakefulness, light sleep, deep sleep and rapid eye movement, especially in the case of the limited penetrable distance Lp=1, indicating the effectiveness of LPHVG and WLPHVG algorithm in sleep staging based on short-term heartbeat interval time series. In addition, a preliminary comparison between proposed algorithm and the basic visibility graph (VG) algorithm shows that in this case, the LPHVG and WLPHVG algorithm are superior to the basic VG algorithm both in performance and in calculation speed. Meanwhile, based on the LPHVG and WLPHVG algorithm, the values of network parameters (the clustering coefficient entropy Ec and the weighted clustering coefficient entropy ECw) are calculated from heartbeat interval time series of healthy young and elder subjects in different sleep stages, to further study the aging effect on and sleep regulation over cardiac dynamics. It is found that despite an overall level difference between the values of Ec and ECw in young and elder groups, the stratification patterns across different sleep stages almost do not break down with advanced age, suggesting that the effect of sleep regulation on cardiac dynamics is significantly stronger than the effect of healthy aging. In addition, compared with the clustering coefficient entropy Ec based on LPHVG algorithm, the weighted clustering coefficient entropy ECw based on WLPHVG algorithm shows higher sensitivity to discriminating subtle differences in cardiac dynamics among different sleep states. Overall, it is shown that with the simple mapping criteria and low computational complexity, the proposed method could be used as a new auxiliary tool for sleep studies based on heart rate variability, and the corresponding network parameters could be used in wearable device as new auxiliary parameters for sleep staging.

IUCN guidelines using for assessment of plants from the Red Book of Russian Federation at regional level: a case study for the Republic of Mordovia (Russia)

AbstractThere are 15 plant species included in the Russian Red Book, which occur in the Republic of Mordovia:Najas tenuissima,Koeleria sclerophylla,Stipa dasyphylla,S. pennata,S. pulcherrima,S. zalesskii,Fritillaria ruthenica,Iris aphylla,Cypripedium calceolus,Cephalanthera rubra,Epipogium aphyllum,Neottianthe cucullata,Orchis militaris,Neotinea ustulata,Thymus cimicinus. Of these, onlyC. calceolusis included in the Global Red List as Critically Endangered. Threat status for studied species in Mordovia was assessed, and their distribution dynamics in this region throughout 12 years was described. Recent floristic studies, inspections of herbariums and literature were used for searches all provided data. Grid mapping and IUCN criteria were used. Nine taxa were determined as Critically Endangered, three as Endangered, one as Vulnerable, one as Near Threatened and one as Data Deficient. The areas of occupancy and extent of occurrence in Mordovia were assessed for each taxon. All studied species should be included in the next edition of the Mordovian Red Book.F. ruthenica,E. aphyllum,N. ustulata,T. cimicinusrequire additional studies to confirm earlier observations.

The 1000 Genomes Project: Prediction of Known and Novel Blood Group Continental Distribution By Next Generation Sequencing

▪Background:The 1000 Genomes Project provides a database of over 80 million genomic variants found across 2504 individuals from 26 populations. A current priority of the genomics field is to design information systems to translate this knowledge into clinical significance and patient care. The applications and advantages of red blood cell (RBC) antigen prediction through genotyping are widely accepted in transfusion medicine. Current technologies address a limited number of single nucleotide polymorphisms (SNPs) in 12 blood group genes, and our background knowledge of RBC phenotype distribution is often limited to a few populations. We analyzed the 1000 Genomes database with 4 objectives: 1) determine allele distributions of 46 blood group-related genes across the 5 genotyped superpopulations: Africa, East Asia, Europe, South Asia and the Americas; 2) identify possible new blood group alleles and their geographic association; 3) determine the feasibility of blood group genotyping by NGS; and 4) establish a scaffold of chromosomal coordinates to interpret NGS output files into a predicted RBC phenotype.Results:From the initial list of 46 blood group-related genes, we eliminated the five genes with known rearrangements and focused only on regions that met the strict criteria for accessibility through short, paired-end NGS reads (77% of 80.4kb). We mapped over 800 known alleles in coding and non-coding regions, and documented the 80 variants that were both present in the 1000 Genomes database and met the strict accessibility criteria. Sixty-four of these 80 variants are not addressed by current RBC genotyping technology. All 80 variants, including the ACKR1 promoter silencing mutation, are located within exon pull-down boundaries. The average low-coverage sequencing depth was 18,424x, with exome-sequencing confirmation at 65.7x depth. Twenty-three alleles had at least one novel population distribution, such as documentation of the Kpaallele for the first time in Africa and South Asia. From a total of 30 novel blood group continental frequencies, 14 correspond to a newfound presence in South Asia.1000 Genomes identified a total of 926 missense mutations in blood group genes that met strict NGS mapping criteria, as well as multiple deletions. Two novel missense mutations in ERMAP and SLC14A1 are classified as likely antigenic, since they target the same amino acids responsible for the SCER- and Cr(a-) alleles. Six novel deletions involving the Lewis, H, Cromer, Indian and OK systems are also classified as likely-deleterious after careful analysis. For example, a novel in-frame 24bp deletion in SLC14A1 eliminates part of the intracytoplasmic tail, which is required for membrane localization and includes the 28G residue that defines JK*01W.03. Thus, this novel deletion is predicted to alter Kidd protein expression. The 8 novel alleles are distributed throughout the five superpopulations but are most frequently found in Africa. Four standard bioinformatics programs named SIFT, PolyPhen-2, Mutation Taster, and Mutation Assessor failed to detect half of the control known blood group alleles and thus are not adequate for the analysis of novel blood group variants in the transfusion medicine context.Conclusions:NGS can allow comprehensive, fast, and high-throughput RBC antigen prediction. All queried blood group alleles are amenable to targeted exome sequencing, and 77% of blood group coding sequences can be addressed with a short, paired-end NGS strategy. Based on 1000 Genomes, we created a database of the worldwide distribution of 80 known and 8 novel blood group variants, along with their chromosomal coordinates in the hg19 and GRCh38 assemblies. This database is the scaffold for the creation of a new transfusion medicine bioinformatics pipeline that will translate NGS .vcf output files into a predicted RBC phenotype. New algorithms that focus on exposed peptides and antigenicity are required for the analysis of novel variants identified by NGS in the immunohematology context. DisclosuresNo relevant conflicts of interest to declare.

Metabarcoding of Fecal Samples to Determine Herbivore Diets: A Case Study of the Endangered Pacific Pocket Mouse.

Understanding the diet of an endangered species illuminates the animal’s ecology, habitat requirements, and conservation needs. However, direct observation of diet can be difficult, particularly for small, nocturnal animals such as the Pacific pocket mouse (Heteromyidae: Perognathus longimembris pacificus). Very little is known of the dietary habits of this federally endangered rodent, hindering management and restoration efforts. We used a metabarcoding approach to identify source plants in fecal samples (N = 52) from the three remaining populations known. The internal transcribed spacers (ITS) of the nuclear ribosomal loci were sequenced following the Illumina MiSeq amplicon strategy and processed reads were mapped to reference databases. We evaluated a range of threshold mapping criteria and found the best-performing setting generally recovered two distinct mock communities in proportions similar to expectation. We tested our method on captive animals fed a known diet and recovered almost all plant sources, but found substantial heterogeneity among fecal pellets collected from the same individual at the same time. Observed richness did not increase with pooling of pellets from the same individual. In field-collected samples, we identified 4–14 plant genera in individual samples and 74 genera overall, but over 50 percent of reads mapped to just six species in five genera. We simulated the effects of sequencing error, variable read length, and chimera formation to infer taxon-specific rates of misassignment for the local flora, which were generally low with some exceptions. Richness at the species and genus levels did not reach a clear asymptote, suggesting that diet breadth remained underestimated in the current pool of samples. Large numbers of scat samples are therefore needed to make inferences about diet and resource selection in future studies of the Pacific pocket mouse. We conclude that our minimally invasive method is promising for determining herbivore diets given a library of sequences from local plants.

Integrating Metacognitive and Psychometric Decision-Making Approaches for Bank Customer Loyalty Measurement

Greater competition and the aftermath of the financial crisis have meant that banks are increasingly focused on improving service quality and achieving higher levels of customer loyalty. Doing so requires being able to identify, understand and measure the determinants of such loyalty, however; and given the variety of multi-faceted factors involved, and the interrelationships among them, this is a complex undertaking. This paper proposes and tests an integrated application of cognitive mapping and multiple criteria decision analysis (MCDA), thus combining metacognitive and psychometric decision-making approaches, to create a framework for the assessment of bank customer loyalty, which identifies its determinants and allows the trade-offs among them to be calculated. Practical advantages and limitations of our proposal are also discussed.

Humans on Earth: Global extents of anthropogenic land cover from remote sensing

Abstract This review provides a perspective of the current state of the art in remote sensing of anthropogenic land cover and human-modified landscapes at global scales. The fact that humans have adapted to almost all of Earth’s environments, yet remain strongly clustered within each of these environments influences both the nature of anthropogenic impact on Earth’s landscapes and the challenges of mapping it. Remote sensing provides a consistent synoptic view of these environments by mapping the land cover associated with the anthropogenic land uses of settlement and food production, as well as their complement in forest cover. We give brief descriptions and illustrative comparisons of several current land cover products representing the global extents of settlements, agriculture and forests derived from remote sensing. To accommodate the challenges inherent to mapping any land cover at widely varying scales, we compare size distributions of spatially contiguous land cover (rather than total area) for several global land cover products. Despite the use of different sensors and different mapping criteria, there is remarkable consistency in the size distributions of these products – both within and across land cover class. Rank-size distributions of settlements, agricultural areas and forests are all well-described by power laws spanning more than four orders of magnitude in both area and number. This consistency in the form of the distributions suggests fundamental similarities among different types of land cover. The observed similarities can be explained by depicting land cover mosaics as co-evolving spatial networks sharing common processes of nucleation, growth and connection.

Union score and fuzzy logic mineral prospectivity mapping using discretized and continuous spatial evidence values

Two common problems affect integration of exploration criteria for mineral prospectivity mapping (MPM) in geographic information system (GIS): (a) stochastic error associated with sufficiency in number of known mineral occurrences (KMOs) used to estimate evidential weights and (b) systemic error associated with subjectivity of expert judgment applied to process, analyze, and assign weights to evidential data. In this paper we used logistic sigmoid (or S-shaped) function to transform continuous-value evidential data into logistic space without using KMOs as in data-driven MPM and without discretization of evidential data into classes by using arbitrary intervals based on expert judgment as in knowledge-driven MPM. We generated a prospectivity model using discretized evidential data as well. Then, we compared the prospectivity models generated using continuous- and discretized-value evidential data and demonstrated that the former is better model for selecting target areas for further exploration.

Mapping ecosystem service indicators in a Great Lakes estuarine Area of Concern

Abstract Estuaries provide multiple ecosystem services from which humans benefit. Twenty-seven Great Lakes coastal systems in the United States and Canada, many of them estuarine, are currently designated as Areas of Concern (AOCs) due to a legacy of chemical contamination, degraded habitat, and non-point-source pollution. The ecosystem benefits that current and future human communities can receive from these degraded ecosystems are diminished. For an AOC to be delisted, it is generally necessary to restore aquatic habitat, among other actions. Ecosystem service mapping and assessment can inform AOC restoration and management. We describe an approach, with examples, for assessing how local-scale actions affect the extent and distribution of coastal ecosystem services, using the estuarine portion of St. Louis River AOC of western Lake Superior as a case study. We applied mapping criteria derived from locally validated predictive models, published relationships, local experts, and other sources to spatially explicit biophysical data to map indicators of ecosystem services at high resolution across aquatic and riparian habitats. We mapped indicators for 23 biophysical services in the estuary (e.g., natural views, boating, game and non-game fish and wildlife species, wild rice, parks and trails, beaches, property protection, sacred sites). Most 10 × 10 m aquatic pixel locations had 3–7 overlapping services; riparian locations had fewer mapped services. To examine tradeoffs in services associated with management actions, we quantified the changes in the area of the AOC providing each ecosystem service for scenarios based on planned sediment remediation and habitat restoration projects. Some aspects of our approach can be adapted by Great Lakes coastal communities to support local environmental decision-making.

Linear connectivity, Schwarz–Pick lemma and univalency criteria for planar harmonic mapping

In this paper, we first establish a Schwarz–Pick lemma for higher-order derivatives of planar harmonic mappings, and apply it to obtain univalency criteria. Then we discuss distortion theorems, Lipschitz continuity and univalency of planar harmonic mappings defined in the unit disk with linearly connected images.