Ultimate shear strength of LiteSteel beams

This paper presents the details of an investigation on the shear behaviour of a recently developed, cold-formed steel beam known as LiteSteel Beam (LSB).The LSB section has a unique shape of a channel beam with two rectangular hollow flanges and is produced by a patented manufacturing process involving simultaneous cold-forming and dual electric resistance welding. In the present investigation, a series of numerical analyses based on three-dimensional finite element modeling and an experimental study were carried out to investigate the shear behaviour of 10 different LSB sections. It was found that the current design rules in cold-formed steel structures design codes are very conservative for the shear design of LiteSteel beams. Significant improvements to web shear buckling occurred due to the presence of rectangular hollow flanges while considerable post-buckling strength was also observed. Therefore the design rules were further modified to include the available post-buckling strength. Suitable design rules were also developed under the direct strength method format. This paper presents the details of this investigation and the results including the final design rules for the shear capacity of LSBs. It also presents new shear strength formulae for lipped channel beams based on the current design equations for shear strength given in AISI (2007) using the same approach used for LSBs.

Convexity, Classification, and Risk Bounds

Many of the classification algorithms developed in the machine learning literature, including the support vector machine and boosting, can be viewed as minimum contrast methods that minimize a convex surrogate of the 0–1 loss function. The convexity makes these algorithms computationally efficient. The use of a surrogate, however, has statistical consequences that must be balanced against the computational virtues of convexity. To study these issues, we provide a general quantitative relationship between the risk as assessed using the 0–1 loss and the risk as assessed using any nonnegative surrogate loss function. We show that this relationship gives nontrivial upper bounds on excess risk under the weakest possible condition on the loss function—that it satisfies a pointwise form of Fisher consistency for classification. The relationship is based on a simple variational transformation of the loss function that is easy to compute in many applications. We also present a refined version of this result in the case of low noise, and show that in this case, strictly convex loss functions lead to faster rates of convergence of the risk than would be implied by standard uniform convergence arguments. Finally, we present applications of our results to the estimation of convergence rates in function classes that are scaled convex hulls of a finite-dimensional base class, with a variety of commonly used loss functions.

Rademacher and Gaussian complexities: Risk bounds and structural results

We investigate the use of certain data-dependent estimates of the complexity of a function class, called Rademacher and Gaussian complexities. In a decision theoretic setting, we prove general risk bounds in terms of these complexities. We consider function classes that can be expressed as combinations of functions from basis classes and show how the Rademacher and Gaussian complexities of such a function class can be bounded in terms of the complexity of the basis classes. We give examples of the application of these techniques in finding data-dependent risk bounds for decision trees, neural networks and support vector machines.

Shifting : one-inclusion mistake bounds and sample compression

We present new expected risk bounds for binary and multiclass prediction, and resolve several recent conjectures on sample compressibility due to Kuzmin and Warmuth. By exploiting the combinatorial structure of concept class F, Haussler et al. achieved a VC(F)/n bound for the natural one-inclusion prediction strategy. The key step in their proof is a d = VC(F) bound on the graph density of a subgraph of the hypercube—oneinclusion graph. The first main result of this paper is a density bound of n [n−1 <=d-1]/[n <=d] < d, which positively resolves a conjecture of Kuzmin and Warmuth relating to their unlabeled Peeling compression scheme and also leads to an improved one-inclusion mistake bound. The proof uses a new form of VC-invariant shifting and a group-theoretic symmetrization. Our second main result is an algebraic topological property of maximum classes of VC-dimension d as being d contractible simplicial complexes, extending the well-known characterization that d = 1 maximum classes are trees. We negatively resolve a minimum degree conjecture of Kuzmin and Warmuth—the second part to a conjectured proof of correctness for Peeling—that every class has one-inclusion minimum degree at most its VCdimension. Our final main result is a k-class analogue of the d/n mistake bound, replacing the VC-dimension by the Pollard pseudo-dimension and the one-inclusion strategy by its natural hypergraph generalization. This result improves on known PAC-based expected risk bounds by a factor of O(logn) and is shown to be optimal up to an O(logk) factor. The combinatorial technique of shifting takes a central role in understanding the one-inclusion (hyper)graph and is a running theme throughout.

Corrigendum to “Shifting : one-inclusion mistake bounds and sample compression” [J. Comput. System Sci. 75 (1) (2009) 37–59]

H. Simon and B. Szörényi have found an error in the proof of Theorem 52 of “Shifting: One-inclusion mistake bounds and sample compression”, Rubinstein et al. (2009). In this note we provide a corrected proof of a slightly weakened version of this theorem. Our new bound on the density of one-inclusion hypergraphs is again in terms of the capacity of the multilabel concept class. Simon and Szörényi have recently proved an alternate result in Simon and Szörényi (2009).

Optimal strategies and minimax lower bounds for online convex games

A number of learning problems can be cast as an Online Convex Game: on each round, a learner makes a prediction x from a convex set, the environment plays a loss function f, and the learner’s long-term goal is to minimize regret. Algorithms have been proposed by Zinkevich, when f is assumed to be convex, and Hazan et al., when f is assumed to be strongly convex, that have provably low regret. We consider these two settings and analyze such games from a minimax perspective, proving minimax strategies and lower bounds in each case. These results prove that the existing algorithms are essentially optimal.

Shifting : one-inclusion mistake bounds and sample compression

We present new expected risk bounds for binary and multiclass prediction, and resolve several recent conjectures on sample compressibility due to Kuzmin and Warmuth. By exploiting the combinatorial structure of concept class F, Haussler et al. achieved a VC(F)/n bound for the natural one-inclusion prediction strategy. The key step in their proof is a d=VC(F) bound on the graph density of a subgraph of the hypercube—one-inclusion graph. The first main result of this report is a density bound of n∙choose(n-1,≤d-1)/choose(n,≤d) < d, which positively resolves a conjecture of Kuzmin and Warmuth relating to their unlabeled Peeling compression scheme and also leads to an improved one-inclusion mistake bound. The proof uses a new form of VC-invariant shifting and a group-theoretic symmetrization. Our second main result is an algebraic topological property of maximum classes of VC-dimension d as being d-contractible simplicial complexes, extending the well-known characterization that d=1 maximum classes are trees. We negatively resolve a minimum degree conjecture of Kuzmin and Warmuth—the second part to a conjectured proof of correctness for Peeling—that every class has one-inclusion minimum degree at most its VC-dimension. Our final main result is a k-class analogue of the d/n mistake bound, replacing the VC-dimension by the Pollard pseudo-dimension and the one-inclusion strategy by its natural hypergraph generalization. This result improves on known PAC-based expected risk bounds by a factor of O(log n) and is shown to be optimal up to a O(log k) factor. The combinatorial technique of shifting takes a central role in understanding the one-inclusion (hyper)graph and is a running theme throughout

High-probability regret bounds for bandit online linear optimization

We present a modification of the algorithm of Dani et al. [8] for the online linear optimization problem in the bandit setting, which with high probability has regret at most O ∗ ( √ T) against an adaptive adversary. This improves on the previous algorithm [8] whose regret is bounded in expectation against an oblivious adversary. We obtain the same dependence on the dimension (n 3/2) as that exhibited by Dani et al. The results of this paper rest firmly on those of [8] and the remarkable technique of Auer et al. [2] for obtaining high probability bounds via optimistic estimates. This paper answers an open question: it eliminates the gap between the high-probability bounds obtained in the full-information vs bandit settings.

To bound or not to bound: preliminary Theory of Time Bounds Specification in strategic alliances

This article augments Resource Dependence Theory with Real Options reasoning in order to explain time bounds specification in strategic alliances. Whereas prior work has found about a 50/50 split between alliances that are time bound and those that are open-ended, their substantive differences and antecedents are ill understood. To address this, we suggest that the two alliance modes present different real options trade-offs in adaptation to environmental uncertainty: ceteris paribus, time-bound alliances are likely to provide abandonment options over open-ended alliances, but require additional investments to extend the alliance when this turns out to be desirable after formation. Open-ended alliances are likely to provide growth options over open-ended alliances, but they demand additional effort to abandon the alliance if post-formation circumstances so desire. Therefore, we expect time bounds specification to be a function of environmental uncertainty: organizations in more uncertain environments will be relatively more likely to place time bounds on their strategic alliances. Longitudinal archival and survey data collected amongst 39 industry clusters provides empirical support for our claims, which contribute to the recent renaissance of resource dependence theory by specifying the conditions under which organizations choose different time windows in strategic partnering.

Perceptions of charities and the ultimate gift : the use of the Repertory Test to elicit salient bequest decision criteria

This paper reports a practitioner/academic collaboration that sought to identify the attributes salient in the decision-making process of individuals considering a charitable bequest in Australia. Philanthropy scholars concur that bequest making behaviour is generally not well understood or researched and is fertile terrain for new enquiry. They urge scholars and practitioners to integrate learning from other relevant disciplines to reveal new insights and understandings into why so many individuals elect to make a testamentary gift to a charity in their will or other planned giving instrument. This research draws on the branding literature; and effectively trialed the use of Kelly’s (1955) Repertory Test from clinical psychology, the results of which will provide researchers and charity marketing practitioners with an enhanced understanding of bequest decision criteria.