8200849
Error Bound Moduli for Conic Convex Systems on Banach Spaces
We give two explicit formulas which express the error bound moduli for conic convex systems, one in terms of directional derivative, and the other in terms of the coderivative. As applications, we study error bounds for systems of infinitely many convex inequalities.
14909738
Regularities and their relations to error bounds
Abstract.In this paper, we mainly study various notions of regularity for a finite collection {C1,⋯,Cm} of closed convex subsets of a Banach space X and their relations with other fundamental concepts. We show that a proper lower semicontinuous function f on X has a Lipschitz error bound (resp., ϒ-error bound) if and only if the pair {epi(f),X×{0}} of sets in the product space X×ℝ is linearly regular (resp., regular). Similar results for multifunctions are also established. Next, we prove that {C1,⋯,Cm} is linearly regular if and only if it has the strong CHIP and the collection {NC1(z),⋯,NCm(z)} of normal cones at z has property (G) for each z∈C:=∩i=1mCi. Provided that C1 is a closed convex cone and that C2=Y is a closed vector subspace of X, we show that {C1,Y} is linearly regular if and only if there exists α>0 such that each positive (relative to the order induced by C1) linear functional on Y of norm one can be extended to a positive linear functional on X with norm bounded by α. Similar characterization is given in terms of normal cones.
16910052
On best restricted range approximation in continuous complex-valued function spaces
To provide a Kolmogorov-type condition for characterizing a best approximation in a continuous complex-valued function space, it is usually assumed that the family of closed convex sets in the complex plane used to restrict the range satisfies a strong interior-point condition, and this excludes the interesting case when some @W"t is a line-segment or a singleton. The main aim of the present paper is to remove this restriction by virtue of a study of the notion of the strong CHIP for an infinite system of closed convex sets in a continuous complex-valued function space.
20652786
The iterative development of a tangible pin-board to symmetrically link physical and digital documents
There is an asymmetry in many tangible interfaces: while physical objects can be used to manipulate digital information, the reverse is often not possible—the digital world cannot push back. We introduce a new push-back tangible technology, a pin-board that physically ejects paper documents. This is realized by extending the Pin&Play technology to support ‘pouts’, addressable pin-like devices that can remove themselves from a board using muscle wire actuators. We describe how this technology has been developed through two iterations of prototyping, application and formative study. An initial study revealed how potential mismatches between the physical and digital characteristics of pouts caused difficulties with users predicting pop-out events and reasoning about the state of pouts. This led us to extend pouts to reveal more of their internal state, an approach verified through a second study. It also raises more general issues for the design of pushback tangible technologies and ubiquitous interfaces.
7581866
The orientation number of two complete graphs with linkages
For a connected graph G containing no bridges, let D(G) be the family of strong orientations of G; and for any D@?D(G), we denote by d(D) the diameter of D. The orientation number d->(G) of G is defined by d->(G)=min{d(D)|D@?D(G)}. In this paper, we study the orientation numbers of a family of graphs, denoted by G(p,q;m), that are obtained from the disjoint union of two complete graphs K"p and K"q by adding m edges linking them in an arbitrary manner. Define d->(m)=min{d->(G):G@?G(p,q;m)}. We prove that d->(2)=4 and min{m:d->(m)=3}=4. Let @a=min{m:d->(m)=2}. We evaluate the exact value of @a when p==p+4.
10675081
The applicability of universal pragmatics in information retrieval interaction: a pilot study
This article discusses the possibility and usefulness of applying Habermas' universal pragmatics to analyze information retrieval interaction. The first part of the article is theoretical argumentation. It examines the current common schemes of studies of human computer interaction (HCI), inspects their appropriateness and limitations, argues for a pragmatic perspective, and elaborates some of Habermas' idea of universal pragmatics. The second part is a case study. It reports an investigation of the initiation and development of verification of validity claims in HCI from the universal pragmatics perspective. It describes some patterns in which a user deals with what may be considered as invalid claims of an IR system outputs. A typical sequence consists of the following pattern: (1) user invokes a simple request; (2) system replies with a questionable answer; leading to (3) user tries to verify the validity claims of truth, truthfulness, and/ or rightness of the system output; and (4) when the available interaction channels cannot support the validation, the interaction becomes a non-communicative process which discourages further interaction.
8169680
PINS push in and POUTS pop out: creating a tangible pin-board that ejects physical documents
There is an asymmetry in many tangible interfaces: while phicons can be used to manipulate digital information, the reverse is often not possible - the digital world cannot push back. We describe a tangible pin-board that pushes back by physically ejecting paper documents when they are digitally deleted. This is realized using pouts, addressable pin-like devices that communicate with a Pin&Play board and that can eject themselves by contracting an internal Muscle Wire actuator to trigger a mechanical latch. To demonstrate and begin to evaluate the technology we have developed an initial application of pouts involving a game where online players vote to eject physical pictures from a pin-board.
12496765
A practical implementation of a 3D game engine
Creating a 3D game engine is not a trivial task as gamers often demand for high quality output with top notch performance in games. In this paper, we show how various real-time rendering algorithms can be applied to implement a practical 3D game engine. We explore the general architecture of a 3D engine and discuss the role of a scene graph in a 3D engine. We look at scene graph from the software engineering perspective. In particular, we show the way to design a scene graph that is object-oriented and portable across different rendering engine. Then, we explain the algorithms that we apply to speed up the performance of our 3D engine. We optimize the 3D engine on the scene graph and object geometry levels. The algorithms that we propose are expected to perform reasonably well for both static and dynamic scenes. Finally, we give a brief preview on the possibility of parallel processing in scene graph to create a 3D engine with multiprocessing capability.