Deep Bilevel Learning

We present a novel regularization approach to train neural networks that enjoys better generalization and test error than standard stochastic gradient descent. Our approach is based on the principles of cross-validation, where a validation set is used to limit the model overfitting. We formulate such principles as a bilevel optimization problem. This formulation allows us to define the optimization of a cost on the validation set subject to another optimization on the training set. The overfitting is controlled by introducing weights on each mini-batch in the training set and by choosing their values so that they minimize the error on the validation set. In practice, these weights define mini-batch learning rates in a gradient descent update equation that favor gradients with better generalization capabilities. Because of its simplicity, this approach can be integrated with other regularization methods and training schemes. We evaluate extensively our proposed algorithm on several neural network architectures and datasets, and find that it consistently improves the generalization of the model, especially when labels are noisy.Comment: ECCV 201

Group Theory and Quasiprobability Integrals of Wigner Functions

The integral of the Wigner function of a quantum mechanical system over a region or its boundary in the classical phase plane, is called a quasiprobability integral. Unlike a true probability integral, its value may lie outside the interval [0,1]. It is characterized by a corresponding selfadjoint operator, to be called a region or contour operator as appropriate, which is determined by the characteristic function of that region or contour. The spectral problem is studied for commuting families of region and contour operators associated with concentric disks and circles of given radius a. Their respective eigenvalues are determined as functions of a, in terms of the Gauss-Laguerre polynomials. These polynomials provide a basis of vectors in Hilbert space carrying the positive discrete series representations of the algebra su(1,1)or so(2,1). The explicit relation between the spectra of operators associated with disks and circles with proportional radii, is given in terms of the dicrete variable Meixner polynomials.Comment: 11 pages, latex fil

A new approach to quantum backflow

We derive some rigorous results concerning the backflow operator introduced by Bracken and Melloy. We show that it is linear bounded, self adjoint, and not compact. Thus the question is underlined whether the backflow constant is an eigenvalue of the backflow operator. From the position representation of the backflow operator we obtain a more efficient method to determine the backflow constant. Finally, detailed position probability flow properties of a numerical approximation to the (perhaps improper) wave function of maximal backflow are displayed.Comment: 12 pages, 8 figure

Solutions to the Quantum Yang-Baxter Equation with Extra Non-Additive Parameters

We present a systematic technique to construct solutions to the Yang-Baxter equation which depend not only on a spectral parameter but in addition on further continuous parameters. These extra parameters enter the Yang-Baxter equation in a similar way to the spectral parameter but in a non-additive form. We exploit the fact that quantum non-compact algebras such as $U_q(su(1,1))$ and type-I quantum superalgebras such as $U_q(gl(1|1))$ and $U_q(gl(2|1))$ are known to admit non-trivial one-parameter families of infinite-dimensional and finite dimensional irreps, respectively, even for generic $q$. We develop a technique for constructing the corresponding spectral-dependent R-matrices. As examples we work out the the $R$-matrices for the three quantum algebras mentioned above in certain representations.Comment: 13 page

Trauma as counter-revolutionary colonisation: narratives from (post)revolutionary Egypt

We argue that multiple levels of trauma were present in Egypt before, during and after the 2011 revolution. Individual, social and political trauma constitute a triangle of traumatisation which was strategically employed by the Egyptian counter-revolutionary forces – primarily the army and the leadership of the Muslim Brotherhood – to maintain their political and economic power over and above the social, economic and political interests of others. Through the destruction of physical bodies, the fragmentation and polarisation of social relations and the violent closure of the newly emerged political public sphere, these actors actively repressed the potential for creative and revolutionary transformation. To better understand this multi-layered notion of trauma, we turn to Habermas’ ‘colonisation of the lifeworld’ thesis which offers a critical lens through which to examine the wider political and economic structures and context in which trauma occurred as well as its effects on the personal, social and political realms. In doing so, we develop a novel conception of trauma that acknowledges individual, social and political dimensions. We apply this conceptual framing to empirical narratives of trauma in Egypt’s pre- and post-revolutionary phases, thus both developing a non-Western application of Habermas’ framework and revealing ethnographic accounts of the revolution by activists in Cairo

Comments on Drinfeld Realization of Quantum Affine Superalgebra Uq[gl(m∣n)(1)]U_q[gl(m|n)^{(1)}] and its Hopf Algebra Structure

By generalizing the Reshetikhin and Semenov-Tian-Shansky construction to supersymmetric cases, we obtain Drinfeld current realization for quantum affine superalgebra $U_q[gl(m|n)^{(1)}]$. We find a simple coproduct for the quantum current generators and establish the Hopf algebra structure of this super current algebra.Comment: Some errors and misprints corrected and a remark in section 4 removed. 12 pages, Latex fil

Uqosp(2,2)U_q osp(2,2) Lattice Models

In this paper I construct lattice models with an underlying $U_q osp(2,2)$ superalgebra symmetry. I find new solutions to the graded Yang-Baxter equation. These {\it trigonometric} $R$-matrices depend on {\it three} continuous parameters, the spectral parameter, the deformation parameter $q$ and the $U(1)$ parameter, $b$, of the superalgebra. It must be emphasized that the parameter $q$ is generic and the parameter $b$ does not correspond to the `nilpotency' parameter of \cite{gs}. The rational limits are given; they also depend on the $U(1)$ parameter and this dependence cannot be rescaled away. I give the Bethe ansatz solution of the lattice models built from some of these $R$-matrices, while for other matrices, due to the particular nature of the representation theory of $osp(2,2)$, I conjecture the result. The parameter $b$ appears as a continuous generalized spin. Finally I briefly discuss the problem of finding the ground state of these models.Comment: 19 pages, plain LaTeX, no figures. Minor changes (version accepted for publication

Tina Fuchs Interview 2016

A 2016 interview with Tina Fuchs, the Dean of Students at Western Oregon University. In her interview, she discusses her career and the changes in student diversity and sustainability that she has witnessed over her 27 years at as an administrator at Western Oregon University

Localization and Causality for a free particle

Theorems (most notably by Hegerfeldt) prove that an initially localized particle whose time evolution is determined by a positive Hamiltonian will violate causality. We argue that this apparent paradox is resolved for a free particle described by either the Dirac equation or the Klein-Gordon equation because such a particle cannot be localized in the sense required by the theorems.Comment: 9 pages,no figures,new section adde