Complete Space Research Articles

Strict comparison theorems under sublinear expectations

In this paper, we consider strict comparison theorems in the framework of G-expectation, which is a type of sublinear expectation associated with fully nonlinear parabolic partial differential equations. In particular, we first apply Krylov–Safonov estimates to establish the strict comparison theorem for functions from the Lipschitz class \(Lip(\Omega )\). Then we prove generalized strict comparison theorems on the enlarged space \(L_G^1(\Omega )\), which is the Banach completion of \(Lip(\Omega )\) under the G-expectation.

Challenges and advances for transcriptome assembly in non-model species.

Analyses of high-throughput transcriptome sequences of non-model organisms are based on two main approaches: de novo assembly and genome-guided assembly using mapping to assign reads prior to assembly. Given the limits of mapping reads to a reference when it is highly divergent, as is frequently the case for non-model species, we evaluate whether using blastn would outperform mapping methods for read assignment in such situations (>15% divergence). We demonstrate its high performance by using simulated reads of lengths corresponding to those generated by the most common sequencing platforms, and over a realistic range of genetic divergence (0% to 30% divergence). Here we focus on gene identification and not on resolving the whole set of transcripts (i.e. the complete transcriptome). For simulated datasets, the transcriptome-guided assembly based on blastn recovers 94.8% of genes irrespective of read length at 0% divergence; however, assignment rate of reads is negatively correlated with both increasing divergence level and reducing read lengths. Nevertheless, we still observe 92.6% of recovered genes at 30% divergence irrespective of read length. This analysis also produces a categorization of genes relative to their assignment, and suggests guidelines for data processing prior to analyses of comparative transcriptomics and gene expression to minimize potential inferential bias associated with incorrect transcript assignment. We also compare the performances of de novo assembly alone vs in combination with a transcriptome-guided assembly based on blastn both via simulation and empirically, using data from a cyprinid fish species and from an oak species. For any simulated scenario, the transcriptome-guided assembly using blastn outperforms the de novo approach alone, including when the divergence level is beyond the reach of traditional mapping methods. Combining de novo assembly and a related reference transcriptome for read assignment also addresses the bias/error in contigs caused by the dependence on a related reference alone. Empirical data corroborate these findings when assembling transcriptomes from the two non-model organisms: Parachondrostoma toxostoma (fish) and Quercus pubescens (plant). For the fish species, out of the 31,944 genes known from D. rerio, the guided and de novo assemblies recover respectively 20,605 and 20,032 genes but the performance of the guided assembly approach is much higher for both the contiguity and completeness metrics. For the oak, out of the 29,971 genes known from Vitis vinifera, the transcriptome-guided and de novo assemblies display similar performance, but the new guided approach detects 16,326 genes where the de novo assembly only detects 9,385 genes.

The Impact of a Sparse Migration Topology on the Runtime of Island Models in Dynamic Optimization

Island models denote a distributed system of evolutionary algorithms which operate independently, but occasionally share their solutions with each other along the so-called migration topology. We investigate the impact of the migration topology by introducing a simplified island model with behavior similar to lambda islands optimizing the so-called Maze fitness function (Kötzing and Molter in Proceedings of parallel problem solving from nature (PPSN XII), Springer, Berlin, pp 113–122, 2012). Previous work has shown that when a complete migration topology is used, migration must not occur too frequently, nor too soon before the optimum changes, to track the optimum of the Maze function. We show that using a sparse migration topology alleviates these restrictions. More specifically, we prove that there exist choices of model parameters for which using a unidirectional ring of logarithmic diameter as the migration topology allows the model to track the oscillating optimum through nMaze-like phases with high probability, while using any graph of diameter less than cln n for some sufficiently small constant c>0 results in the island model losing track of the optimum with overwhelming probability. Experimentally, we show that very frequent migration on a ring topology is not an effective diversity mechanism, while a lower migration rate allows the ring topology to track the optimum for a wider range of oscillation patterns. When migration occurs only rarely, we prove that dense migration topologies of small diameter may be advantageous. Combined, our results show that the sparse migration topology is able to track the optimum through a wider range of oscillation patterns, and cope with a wider range of migration frequencies.

Convergence of functions and their Moreau envelopes on Hadamard spaces

A well known result of H. Attouch states that the Mosco convergence of a sequence of proper convex lower semicontinuous functions defined on a Hilbert space is equivalent to the pointwise convergence of the associated Moreau envelopes. In the present paper we generalize this result to Hadamard spaces. More precisely, while it has already been known that the Mosco convergence of a sequence of convex lower semicontinuous functions on a Hadamard space implies the pointwise convergence of the corresponding Moreau envelopes, the converse implication was an open question. We now fill this gap.Our result has several consequences. It implies, for instance, the equivalence of the Mosco and Frolík–Wijsman convergences of convex sets. As another application, we show that there exists a complete metric on the cone of proper convex lower semicontinuous functions on a separable Hadamard space such that a sequence of functions converges in this metric if and only if it converges in the sense of Mosco.

Boundary behaviors for Liouville's equation in planar singular domains

We study asymptotic behaviors near the boundary of complete metrics of constant curvature in planar singular domains and establish an optimal estimate of these metrics by the corresponding metrics in tangent cones near isolated singular points on boundary. The conformal structure plays an essential role.

Increasing Completion and Cutting Costs: An Examination of How the Flipped Classroom and One-Room Schoolhouse Models Benefit Community Colleges

ABSTRACTCommunity colleges continue to operate in a society of accountability and efficiencies. Throughout the country, states have implemented performance-based funding and completion agendas while also tightening or restricting funding for higher education. The state of Ohio has implemented one of the boldest performance funding plans in the country while also mandating that higher education institutions limit spending and lower costs to students. This article explores how Central Ohio Technical College has implemented the flipped classroom and one-room school house models in college-level mathematics courses and how both models of instruction can help community colleges increase successful completion rates to meet performance-based funding completion metrics while also limiting instructional cost.

Characterizations of the Borel \(\sigma\)-fields of the fuzzy number space

In this paper, we characterize Borel \(\sigma\)-fields of the set of all fuzzy numbers endowed with different metrics. The main result is that the Borel \(\sigma\)-fields with respect to all known separable metrics are identical. This Borel field is the Borel \(\sigma\)-field making all level cut functions of fuzzy mappings from any measurable spaces to the fuzzy number space measurable with respect to the Hausdorff metric on the cut sets. The relation between the Borel \(\sigma\)-field with respect to the supremum metric \(d_{\infty}\) is also demonstrated. We prove that the Borel field is induced by a separable and complete metric. A global characterization of measurability of fuzzy valued functions is given via the main result. Applications to fuzzy valued integral are given, and an approximation method is presented for integrals of fuzzy valued functions. Finally, an example is given to illustrate the applications of these results in economics. This example shows that the results in this paper are basic to the theory of fuzzy-valued functions, such as the fuzzy version of Lebesgue-like integrals of fuzzy-valued functions, and are useful in applied fields. doi:10.1017/S1446181117000189

Existance of some common Fixed Point Theorm on eleven complete Metric Spaces.

Existance of some common Fixed Point Theorm on eleven complete Metric Spaces.

Two-Type Information Fusion Based IP-to-AS Mapping Table Refining

The Internet topology at the autonomous system (AS) level is of great importance, and traceroute has been known to be a potential tool to obtain a complete AS topology. The original IP-to-AS mapping table maps the IP addresses in traceroute paths to their origin ASes, which may cause false AS links. The existing methods refine the original mapping table based on traceroute-BGP path pairs or alias resolution data. However, the information extracted from either of them is inaccurate and incomplete. In this paper, we present a two-type information fusion based method to refine the original mapping table. We extract four kinds of information from path pair and alias resolution data. Based on these information, we build a candidate AS set for each router. Then we choose the AS that is consistent with the existing information to be the owner AS of each router and map all of the IP addresses on the router to it. We validate the result with the ground truth from PeeringDB and Looking Glass severs. Compared with the existing methods, our method produces a more accurate mapping table. In addition, we discuss the coverage of our method and show that our method is convergent and more robust against the reduction of information or the increase of incorrect information.

Evaluation of advanced techniques for multi-party privacy-preserving record linkage on real-world health databases

ABSTRACT
 ObjectiveThe linking of multiple (three or more) health databases is challenging because of the increasing sizes of databases, the number of parties among which they are to be linked, and privacy concerns related to the use of personal data such as names, addresses, or dates of birth. This entails a need to develop advanced scalable techniques for linking multiple databases while preserving the privacy of the individuals they contain. In this study we empirically evaluate several state-of-the-art multi-party privacy-preserving record linkage (MP-PPRL) techniques with large real-world health databases from Australia.
 ApproachMP-PPRL is conducted such that no sensitive information is revealed about database records that can be used to infer knowledge about individuals or groups of individuals. Current state-of-the-art methods used in this evaluation use Bloom filters to encode personal identifying information. The empirical evaluation comprises of different multi-party private blocking and matching techniques that are evaluated for different numbers of parties. Each database contains more than 700,000 records extracted from ten years of New South Wales (NSW) emergency presentation data. Each technique is evaluated with regard to scalability, quality and privacy. Scalability and quality are measured using the metrics of reduction ratio, pairs completeness, precision, recall, and F-measure. Privacy is measured using disclosure risk metrics that are based on the probability of suspicion, defined as the likelihood that a record in an encoded database matches to one or more record(s) in a publicly available database such as a telephone directory. MP-PPRL techniques that either utilize a trusted linkage unit, and those that do not, are evaluated.
 ResultsExperimental results showed MP-PPRL methods are practical for linking large-scale real world data. Private blocking techniques achieved significantly higher privacy than standard hashing-based techniques with a maximum disclosure risk of 0.0003 and 1, respectively, at a small cost to linkage quality and efficiency. Similarly, private matching techniques provided a similar acceptable reduction in linkage quality compared to standard non-private matching while providing high privacy protection.
 ConclusionThe adoption of privacy-preserving linkage methods has the ability to significantly reduce privacy risks associated with linking large health databases, and enable the data linkage community to offer operational linkage services not previously possible. The evaluation results show that these state-of-the-art MP-PPRL techniques are scalable in terms of database sizes and number of parties, while providing significantly improved privacy with an associated trade-off in linkage quality compared to standard linkage techniques.

Complexity and structural properties of food webs in the Barents Sea

A food web topology describes the diversity of species and their trophic interactions, i.e. who eats whom, and structural analysis of food web topologies can provide insight into ecosystem structure and function. It appears simple, at first sight, to list all species and their trophic interactions. However, the very large number of species at low trophic levels and the impossibility to monitor all trophic interactions in the ocean makes it impossible to construct complete food web topologies. In practice, food web topologies are simplified by aggregating species into groups termed trophospecies. It is not clear though, how much simplified versions of food webs retain the structural properties of more detailed networks. Using the most comprehensive Barents Sea food web to date, we investigate the performance of methods to construct simplified food webs using three approaches: taxonomic, structural and regular clustering. We then evaluate how topological properties vary with the level of network simplification. Results show that alteration of food web structural properties due to aggregation are highly sensitive to the methodology used for grouping species and trophic links. In the specific case of the Barents Sea, we show that it is possible to preserve key structural properties of the original complex food web in simplified versions when using taxonomic or structural clustering combined with intermediate 25% linkage for trophic aggregation.

Geodesics and nodal sets of Laplace eigenfunctions on hyperbolic manifolds

Let X be a manifold equipped with a complete Riemannian metric of constant negative curvature and finite volume. We demonstrate the finiteness of the collection of totally geodesic immersed hypersurfaces in X that lie in the zero-level set of some Laplace eigenfunction. For surfaces, we show that the number can be bounded just in terms of the area of the surface. We also provide constructions of geodesics in hyperbolic surfaces that lie in a nodal set but that do not lie in the fixed point set of a reflection symmetry.

Non metrizable topologies on Z with countable dual group.

In this paper we give two families of non-metrizable topologies on the group of the integers having a countable dual group which is isomorphic to a infinite torsion subgroup of the unit circle in the complex plane. Both families are related to D-sequences, which are sequences of natural numbers such that each term divides the following. The first family consists of locally quasi-convex group topologies. The second consists of complete topologies which are not locally quasi-convex. In order to study the dual groups for both families we need to make numerical considerations of independent interest.<br /><br />

A New Type of Tripled Fixed Point Theorem in Partially Ordered Complete Metric Space

A New Type of Tripled Fixed Point Theorem in Partially Ordered Complete Metric Space

CHARACTERIZATIONS OF THE BOREL -FIELDS OF THE FUZZY NUMBER SPACE

In this paper, we characterize Borel $\unicode[STIX]{x1D70E}$-fields of the set of all fuzzy numbers endowed with different metrics. The main result is that the Borel $\unicode[STIX]{x1D70E}$-fields with respect to all known separable metrics are identical. This Borel field is the Borel $\unicode[STIX]{x1D70E}$-field making all level cut functions of fuzzy mappings from any measurable space to the fuzzy number space measurable with respect to the Hausdorff metric on the cut sets. The relation between the Borel $\unicode[STIX]{x1D70E}$-field with respect to the supremum metric $d_{\infty }$ is also demonstrated. We prove that the Borel field is induced by a separable and complete metric. A global characterization of measurability of fuzzy-valued functions is given via the main result. Applications to fuzzy-valued integrals are given, and an approximation method is presented for integrals of fuzzy-valued functions. Finally, an example is given to illustrate the applications of these results in economics. This example shows that the results in this paper are basic to the theory of fuzzy-valued functions, such as the fuzzy version of Lebesgue-like integrals of fuzzy-valued functions, and are useful in applied fields.

Complete topology inversion can be part of normal membrane protein biogenesis.

The topology of helical membrane proteins is generally defined during insertion of the transmembrane helices, yet it is now clear that it is possible for topology to change under unusual circumstances. It remains unclear, however, if topology reorientation is part of normal biogenesis. For dual topology dimer proteins such as the multidrug transporter EmrE, there may be evolutionary pressure to allow topology flipping so that the populations of both orientations can be equalized. We previously demonstrated that when EmrE is forced to insert in a distorted topology, topology flipping of the first transmembrane helix can occur during translation. Here, we show that topological malleability also extends to the C-terminal helix and that even complete topology inversion of the entire EmrE protein can occur after the full protein is translated and inserted. Thus, topology rearrangements are possible during normal biogenesis. Wholesale topology flipping is remarkable given the physical constraints of the membrane and expands the range of possible membrane protein folding pathways, both productive and detrimental.

English

English

A generalization of Reich’s fixed point theorem for multi-valued mappings

Motivated by a problem concerning multi-valued mappings posed by Reich [S. Reich, Some fixed point problems, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. 57 (1974) 194-198] and a paper of Jleli and Samet [M. Jleli, B. Samet, A new generalization of the Banach contraction principle, J. Inequal. Appl. 2014:38 (2014) 1-8], we consider a new class of multi-valued mappings that satisfy a ?-contractive condition in complete metric spaces and prove some fixed point theorems. These results generalize Reich?s and Mizoguchi-Takahashi?s fixed point theorems. Some examples are given to show the usability of the obtained results.

Fixed points of set-valued F-contractions and its application to non-linear integral equations

We observe that the assumption of set-valued F-contractions (Sgroi and Vetro [13]) is actually very strong for the existence of fixed point and can be weakened. In this connection, we introduce the notion of set-valued ?-F-contractions and prove a corresponding fixed point theorem in complete metric spaces. Consequently, we derive several fixed point theorems in metric spaces. Some examples are given to illustrate the new theory. Then we apply our results to establishing the existence and uniqueness of solutions for a certain type of non-linear integral equations.

A new perspective for multivalued weakly Picard operators

This research contains some recent developments about multivalued weakly Picard operators on complete metric spaces. In addition, taking into account both multivalued ?-contraction and almost contraction on complete metric spaces, we present a new perspective for multivalued weakly Picard operators. Finally, we give a nontrivial example showing that the investigation of this paper is significant.