Characterizations of Super-regularity and its Variants

Convergence of projection-based methods for nonconvex set feasibility problems has been established for sets with ever weaker regularity assumptions. What has not kept pace with these developments is analogous results for convergence of optimization problems with correspondingly weak assumptions on the value functions. Indeed, one of the earliest classes of nonconvex sets for which convergence results were obtainable, the class of so-called super-regular sets introduced by Lewis, Luke and Malick (2009), has no functional counterpart. In this work, we amend this gap in the theory by establishing the equivalence between a property slightly stronger than super-regularity, which we call Clarke super-regularity, and subsmootheness of sets as introduced by Aussel, Daniilidis and Thibault (2004). The bridge to functions shows that approximately convex functions studied by Ngai, Luc and Th\'era (2000) are those which have Clarke super-regular epigraphs. Further classes of regularity of functions based on the corresponding regularity of their epigraph are also discussed.Comment: 15 pages, 2 figure

The Radius of Metric Subregularity

There is a basic paradigm, called here the radius of well-posedness, which quantifies the "distance" from a given well-posed problem to the set of ill-posed problems of the same kind. In variational analysis, well-posedness is often understood as a regularity property, which is usually employed to measure the effect of perturbations and approximations of a problem on its solutions. In this paper we focus on evaluating the radius of the property of metric subregularity which, in contrast to its siblings, metric regularity, strong regularity and strong subregularity, exhibits a more complicated behavior under various perturbations. We consider three kinds of perturbations: by Lipschitz continuous functions, by semismooth functions, and by smooth functions, obtaining different expressions/bounds for the radius of subregularity, which involve generalized derivatives of set-valued mappings. We also obtain different expressions when using either Frobenius or Euclidean norm to measure the radius. As an application, we evaluate the radius of subregularity of a general constraint system. Examples illustrate the theoretical findings.Comment: 20 page

Immobile indices and CQ-free optimality criteria for linear copositive programming problems

We consider problems of linear copositive programming where feasible sets consist of vectors for which the quadratic forms induced by the corresponding linear matrix combinations are nonnegative over the nonnegative orthant. Given a linear copositive problem, we define immobile indices of its constraints and a normalized immobile index set. We prove that the normalized immobile index set is either empty or can be represented as a union of a finite number of convex closed bounded polyhedra. We show that the study of the structure of this set and the connected properties of the feasible set permits to obtain new optimality criteria for copositive problems. These criteria do not require the fulfillment of any additional conditions (constraint qualifications or other). An illustrative example shows that the optimality conditions formulated in the paper permit to detect the optimality of feasible solutions for which the known sufficient optimality conditions are not able to do this. We apply the approach based on the notion of immobile indices to obtain new formulations of regularized primal and dual problems which are explicit and guarantee strong duality.publishe

A conceptual framework for the adoption of big data analytics by e-commerce startups: a case-based approach

E-commerce start-ups have ventured into emerging economies and are growing at a significantly faster pace. Big data has acted like a catalyst in their growth story. Big data analytics (BDA) has attracted e-commerce firms to invest in the tools and gain cutting edge over their competitors. The process of adoption of these BDA tools by e-commerce start-ups has been an area of interest as successful adoption would lead to better results. The present study aims to develop an interpretive structural model (ISM) which would act as a framework for efficient implementation of BDA. The study uses hybrid multi criteria decision making processes to develop the framework and test the same using a real-life case study. Systematic review of literature and discussion with experts resulted in exploring 11 enablers of adoption of BDA tools. Primary data collection was done from industry experts to develop an ISM framework and fuzzy MICMAC analysis is used to categorize the enablers of the adoption process. The framework is then tested by using a case study. Thematic clustering is performed to develop a simple ISM framework followed by fuzzy analytical network process (ANP) to discuss the association and ranking of enablers. The results indicate that access to relevant data forms the base of the framework and would act as the strongest enabler in the adoption process while the company rates technical skillset of employees as the most important enabler. It was also found that there is a positive correlation between the ranking of enablers emerging out of ISM and ANP. The framework helps in simplifying the strategies any e-commerce company would follow to adopt BDA in future. © 2019, Springer-Verlag GmbH Germany, part of Springer Nature

Brains Emerging: On Modularity and Self-organisation of Neural Development In Vivo and In Vitro

Molecular developmental biology has expanded our conceptions of gene actions, underpinning that embryonic development is not only governed by a set of specific genes, but as much by space–time conditions of its developing modules. Typically, formation of cellular spheres, their transformation into planar epithelia, followed by tube formations and laminations are modular steps leading to the development of nervous tissues. Thereby, actions of organising centres, morphogenetic movements, inductive events between epithelia, tissue polarity reversal, widening of epithelia, and all these occurring orderly in space and time, are driving forces of emergent laminar neural tissues, e.g. the vertebrate retina. Analyses of self-organisational formation of retina-like 3D structures from dispersed cells under defined cell culture conditions demonstrate that not only particular genetic networks, but—at least as important—the applied culture conditions define phenotypes of emergent tissues. Such in vitro approaches allow assigning emerging tissue formation to ground-laying genetic networks separately from contributions by conditional constraints

About intrinsic transversality of pairs of sets

The article continues the study of the ‘regular’ arrangement of a collection of sets near a point in their intersection. Such regular intersection or, in other words, transversality properties are crucial for the validity of qualification conditions in optimization as well as subdifferential, normal cone and coderivative calculus, and convergence analysis of computational algorithms. One of the main motivations for the development of the transversality theory of collections of sets comes from the convergence analysis of alternating projections for solving feasibility problems. This article targets infinite dimensional extensions of the intrinsic transversality property introduced recently by Drusvyatskiy, Ioffe and Lewis as a sufficient condition for local linear convergence of alternating projections. Several characterizations of this property are established involving new limiting objects defined for pairs of sets. Special attention is given to the convex case

Approximate Web Database Snapshots

The amount of data stored in databases is increasing at a tremendous rate. They are oftentimes stored over the web to be accessed by various clients. One useful and interesting query to a collection of databases is to capture a consistent snapshot of a set of interested attributes across the databases. While traditional snapshot algorithms for a distributed database could be adopted, they are mainly designed for database recovery and are costly to execute. We need efficient algorithms to return good-enough snapshots for querying purposes, in the absence of a consistent but costly snapshot as defined in distributed systems. In this paper, we propose the notion of an approximate consistent snapshot by considering and minimizing the deviation of the collected snapshot covering the interested attributes from a reference absolute snapshot. There are several variations of this kind of approximate snapshots. We propose effective algorithms to capture such snapshots in a collection of databases and then conduct performance evaluation on their efficiency. We believe that this notion of approximate consistency would be useful in practical situations.Department of Computin

Your Eye Tells How Well You Comprehend

Systems that adapt to changes in human needs automatically are useful, built upon advancements in human-computer interaction research. In this paper, we investigate the problem of how well the eye movement of a user when reading an article can predict the level of reading comprehension, which could be exploited in intelligent adaptive e-learning systems. We characterize the eye movement pattern in the form of eye gaze signal. We invite human subjects in reading articles of different difficulty levels being induced to different comprehension levels. Machine-learning techniques are applied to identify useful features to recognize when readers are experiencing difficulties in understanding their reading material. Finally, a detection model that can identify different levels of user comprehension is built. We achieve a performance improvement of over 30% above the baseline, translating over 50% reduction in detection error.Department of Computin

Detecting handwriting errors with visual feedback in early childhood for Chinese characters

This paper presents KID, an interactive app on a smart device, designed to facilitate and encourage young children to learn and practice Chinese characters. It relies on pen dynamics to extract the strokes and map the written character to the proper one. The stroke orientation is also analyzed for ordering and spatial alignment features that pinpoint common errors. A visual pictorial feedback is then provided to motivate children and to arouse their interest. We iterate the prototype design and implementation upon collecting feedback from focus group interviews, from where the system is greeted with positive comments.Department of ComputingRefereed conference pape