An adaptive local meshfree updated Lagrangian approach for large deformation analysis of metal forming

The large deformation analysis is one of major challenges in numerical modelling and simulation of metal forming. Because no mesh is used, the meshfree methods show good potential for the large deformation analysis. In this paper, a local meshfree formulation, based on the local weak-forms and the updated Lagrangian (UL) approach, is developed for the large deformation analysis. To fully employ the advantages of meshfree methods, a simple and effective adaptive technique is proposed, and this procedure is much easier than the re-meshing in FEM. Numerical examples of large deformation analysis are presented to demonstrate the effectiveness of the newly developed nonlinear meshfree approach. It has been found that the developed meshfree technique provides a superior performance to the conventional FEM in dealing with large deformation problems for metal forming.

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.

Built to last versus meant to end : time bounds specification in strategic alliances

This article explores an important temporal aspect of the design of strategic alliances by focusing on the issue of time bounds specification. Time bounds specification refers to a choice on behalf of prospective alliance partners at the time of alliance formation to either pre-specify the duration of an alliance to a specific time window, or to keep the alliance open-ended (Reuer & Ariňo, 2007). For instance, Das (2006) mentions the example of the alliance between Telemundo Network and Mexican Argos Comunicacion (MAC). Announced in October 2000, this alliance entailed a joint production of 1200 hours of comedy, news, drama, reality and novella programs (Das, 2006). Conditioned on the projected date of completing the 1200 hours of programs, Telemundo Network and MAC pre-specified the time bounds of the alliance ex ante. Such time-bound alliances are said to be particularly prevalent in project-based industries, like movie production, construction, telecommunications and pharmaceuticals (Schwab & Miner, 2008). In many other instances, however, firms may choose to keep their alliances open-ended, not specifying a specific time bound at the time of alliance formation. The choice between designing open-ended alliances that are “built to last”, versus time bound alliances that are “meant to end” is important. Seminal works like Axelrod (1984), Heide & Miner (1992), and Parkhe (1993) demonstrated that the choice to place temporal bounds on a collaborative venture has important implications. More specifically, collaborations that have explicit, short term time bounds (i.e. what is termed a shorter “shadow of the future”) are more likely to experience opportunism (Axelrod, 1984), are more likely to focus on the immediate present (Bakker, Boros, Kenis & Oerlemans, 2012), and are less likely to develop trust (Parkhe, 1993) than alliances for which time bounds are kept indeterminate. These factors, in turn, have been shown to have important implications for the performance of alliances (e.g. Kale, Singh & Perlmutter, 2000). Thus, there seems to be a strong incentive for organizations to form open-ended strategic alliances. And yet, Reuer & Ariňo (2007), one of few empirical studies that details the prevalence of time-bound and open-ended strategic alliances, found that about half (47%) of the alliances in their sample were time bound, the other half were open-ended. What conditions, then, determine this choice?

Filter and control performance bounds in the presence of model uncertainties with aerospace applications

This thesis establishes performance properties for approximate filters and controllers that are designed on the basis of approximate dynamic system representations. These performance properties provide a theoretical justification for the widespread application of approximate filters and controllers in the common situation where system models are not known with complete certainty. This research also provides useful tools for approximate filter designs, which are applied to hybrid filtering of uncertain nonlinear systems. As a contribution towards applications, this thesis also investigates air traffic separation control in the presence of measurement uncertainties.

Entropic bounds for multi-scale and multi-physics coupling in earth sciences

The ability to understand and predict how thermal, hydrological,mechanical and chemical (THMC) processes interact is fundamental to many research initiatives and industrial applications. We present (1) a new Thermal– Hydrological–Mechanical–Chemical (THMC) coupling formulation, based on non-equilibrium thermodynamics; (2) show how THMC feedback is incorporated in the thermodynamic approach; (3) suggest a unifying thermodynamic framework for multi-scaling; and (4) formulate a new rationale for assessing upper and lower bounds of dissipation for THMC processes. The technique is based on deducing time and length scales suitable for separating processes using a macroscopic finite time thermodynamic approach. We show that if the time and length scales are suitably chosen, the calculation of entropic bounds can be used to describe three different types of material and process uncertainties: geometric uncertainties,stemming from the microstructure; process uncertainty, stemming from the correct derivation of the constitutive behavior; and uncertainties in time evolution, stemming from the path dependence of the time integration of the irreversible entropy production. Although the approach is specifically formulated here for THMC coupling we suggest that it has a much broader applicability. In a general sense it consists of finding the entropic bounds of the dissipation defined by the product of thermodynamic force times thermodynamic flux which in material sciences corresponds to generalized stress and generalized strain rates, respectively.