An explicit computation of the Bergman kernel function

We give an explicit computation of the Bergman kernel function on the domain

A classification-based privacy-preserving decision-making for secure data sharing in Internet of Things assisted applications

The introduction of the Internet of Things (IoT) paradigm serves as pervasive resource access and sharing platform for different real-time applications. Decentralized resource availability, access, and allocation provide a better quality of user experience regardless of the application type and scenario. However, privacy remains an open issue in this ubiquitous sharing platform due to massive and replicated data availability. In this paper, privacy-preserving decision-making for the data-sharing scheme is introduced. This scheme is responsible for improving the security in data sharing without the impact of replicated resources on communicating users. In this scheme, classification learning is used for identifying replicas and accessing granted resources independently. Based on the trust score of the available resources, this classification is recurrently performed to improve the reliability of information sharing. The user-level decisions for information sharing and access are made using the classification of the resources at the time of availability. This proposed scheme is verified using the metrics access delay, success ratio, computation complexity, and sharing loss.     

CPFinder: Finding an unknown caller's profession from anonymized mobile phone data

Identifying an unfamiliar caller's profession is important to protect citizens' personal safety and property. Owing to the limited data protection of various popular online services in some countries, such as taxi hailing and ordering takeouts, many users presently encounter an increasing number of phone calls from strangers. The situation may be aggravated when criminals pretend to be such service delivery staff, threatening the user individuals as well as the society. In addition, numerous people experience excessive digital marketing and fraudulent phone calls because of personal information leakage. However, previous works on malicious call detection only focused on binary classification, which does not work for the identification of multiple professions. We observed that web service requests issued from users' mobile phones might exhibit their application preferences, spatial and temporal patterns, and other profession-related information. This offers researchers and engineers a hint to identify unfamiliar callers. In fact, some previous works already leveraged raw data from mobile phones (which includes sensitive information) for personality studies. However, accessing users' mobile phone raw data may violate the more and more strict private data protection policies and regulations (e.g., General Data Protection Regulation). We observe that appropriate statistical methods can offer an effective means to eliminate private information and preserve personal characteristics, thus enabling the identification of the types of mobile phone callers without privacy concerns. In this paper, we develop CPFinder —- a system that exploits privacy-preserving mobile data to automatically identify callers who are divided into four categories of users: taxi drivers, delivery and takeouts staffs, telemarketers and fraudsters, and normal users (other professions). Our evaluation of an anonymized dataset of 1,282 users over a period of 3 months in Shanghai City shows that the CPFinder can achieve accuracies of more than 75.0% and 92.4% for multiclass and binary classifications, respectively.     

Approximation by translates of refinable functions

Summary. The functions are refinable if they are combinations of the rescaled and translated functions . This is very common in scientific computing on a regular mesh. The space of approximating functions with meshwidth is a subspace of with meshwidth . These refinable spaces have refinable basis functions. The accuracy of the computations depends on , the order of approximation, which is determined by the degree of polynomials that lie in . Most refinable functions (such as scaling functions in the theory of wavelets) have no simple formulas. The functions are known only through the coefficients in the refinement equation – scalars in the traditional case, matrices for multiwavelets. The scalar "sum rules" that determine are well known. We find the conditions on the matrices that yield approximation of order from . These are equivalent to the Strang–Fix conditions on the Fourier transforms , but for refinable functions they can be explicitly verified from the . Received August 31, 1994 / Revised version received May 2, 1995     

Unitary invariants of spectral measures with the CGS-property

A «CGS-property» for the spectral measures is introduced and the classical results of determining complete systems of unitary invariants for self-adjoint and bounded normal operators on separable Hilbert spaces are extended to the class of spectral measures with this property. As a consequence, the above mentioned results are extended to unbounded normal operators on separable Hilbert spaces. Moreover, three different kinds of multiplicity are defined and it is shown that for the measures with the «CGS-property» they all coincide. In the last section some analogues of the multiplicity functions defined by Stone [14] are related to the total multiplicity.     

On measurable multifunctions in countably separated spaces

We use an idea of countable separability of points and sets in topological spaces to prove results on intersection of measurable multifunctions and an implicit function theorem. We generalize or extend in part some well known Himmelberg's theorems.     

The coefficients of the Laurent series expansions of real analytic functions

Letf be a real analytic function of a real variable such that 0 is an isolated (possibly essential) singularity off. In the existing literature the coefficients of the Laurent series expansion off around 0 are obtained by applying Cauchy's integral formula to the analytic continuation off on the complex plane. Here by means of a conformal mapping we derive a formula which determines the Laurent coefficients off solely in terms of the values off and the derivatives off at a real point of analyticity off. Using a more complicated mapping, we similarly determine the coefficients of the Laurent expansion off around 0 where now 0 is a singularity off which is not necessarily isolated.     

Properties of compact complex manifolds carrying closed positive currents

We show that a compact complex manifold is Moishezon if and only if it carries a strictly positive, integral (1, 1)-current. We then study holomorphic line bundles carrying singular hermitian metrics with semi-positive curvature currents, and we give some cases in which these line bundles are big. We use these cases to provide sufficient conditions for a compact complex manifold to be Moishezon in terms of the existence of certain semi-positive, integral (1,1)-currents. We also show that the intersection number of two closed semi-positive currents of complementary degrees on a compact complex manifold is positive when the intersection of their singular supports is contained in a Stein domain. The first author was partially supported by National Science Foundation Grant Nos. DMS-8922760 and DMS-9204273. The second author was partially supported by National Science Foundation Grant Nos. DMS-9001365 and DMS-9204037.     

Local analyticity for the [`(?)]\overline \partial -Neumann problem in completely decoupled pseudoconvex domains-Neumann problem in completely decoupled pseudoconvex domains

In this paper we prove local analyticity of solutions to the -Neumann problem up to the boundary of rigid, completely decoupled pseudoconvex domains with real-analytic boundary. These are domains that are locally of the form Imw > Σ |h _k (z _k )|² with eachh _k holomorphic and vanishing only at 0. As in those earlier papers, we use purelyL ² methods and must construct a special holomorphic vector fieldM and then use carefully balanced polynomials inM to localize high powers ofT = ∂/∂t effectively, wheret = Rew.     

Unique continuation theorems for the\bar \partial - Operator and applications

We formulate a unique continuation principle for the inhomogeneous Cauchy-Riemann equations near a boundary pointz ₀ of a smooth domain in complex euclidean space. The principle implies that the Bergman projection of a function supported away fromz ₀ cannot vanish to infinite order atz ₀ unless it vanishes identically. We prove that the principle holds in planar domains and in domains where the problem is known to be analytic hypoelliptic. We also demonstrate the relevance of such questions to mapping problems in several complex variables. The last section of the paper deals with unique continuation properties of the Szegő projection and kernel in planar domains. Research supported by NSF Grant DMS-8922810.