A Stochastic Subgradient Method for Distributionally Robust Non-convex and Non-smooth Learning

Journal of Optimization Theory and Applications - We consider a distributionally robust formulation of stochastic optimization problems arising in statistical learning, where robustness is with...     

TBOR-shaped electro-optic modulator with dual output based on double-layer graphene

We proposed an electro-optic modulator with two-bus one-ring (TBOR) structure to improve the extinction ratio and reduce insert loss. It has a dual output compared with one-bus one-ring structure. In addition, double-layer graphene makes it possible for the modulation in the visible to mid-infrared wavelength range. It shows that this new electro-optic modulator can present two switching states well with low insertion loss, high absorption and high extinction ratio. At $\lambda =1550\text{ nm}$, when the switching states are based on the chemical potential, ${\mu }_{\mathrm{c}}=0.38\text{ eV}$ and ${\mu }_{\mathrm{c}}=0.4\text{ eV}$, the insertion losses of both output ports are less than 2 dB, the absorption of the output port coupled via a micro-ring reaches 45 dB and the extinction ratio reaches 14 dB. When the refractive index of the dielectric material is 4.2, the applied voltage will be less than 1.2 V, thus can be used in low-voltage CMOS technology.     

Transition metal complexes with long-chain amines thermal behaviour and crystal structure of (n-CaH2a+1NH2)2ZnCl2

The thermal behaviour of (n-C_aH_2n+1NH₂)₂ZnCl₂ complexes with n = 6, 8, … 16 has been investigated by DSC and by temperature variable IR and X-ray powder diffraction techniques. Complexes with n = 12,14,16 show solid—solid phase transition which are “melting” transitions of the hydrocarbon regions of the structure. The crystal structure of both the low and the high temperature polymorphs is characterized by the piling of sandwiches, each formed by an “inorganic” layer sandwiched between two alkylammonium layers.     

Regioselective cis-trans isomerization of arachidonic double bonds by thiyl radicals: the influence of phospholipid supramolecular organization

Trans unsaturated fatty acids in humans may be originated by two different contributions. The exogenous track is due to dietary supplementation of trans fats and the endogenous path deals with free-radical-catalyzed cis-trans isomerization of fatty acids. Arachidonic acid residue (5c,8c,11c,14c-20:4), which has only two out of the four double bonds deriving from the diet, was used to differentiate the two paths and to assess the importance of a radical reaction. A detailed study on the formation of trans phospholipids catalyzed by the HOCH2CH2S* radical was carried out on L-alpha-phosphatidylcholine from egg lecithin and 1-stearoyl-2-arachidonoyl-L-alpha-phosphatidylcholine (SAPC) in homogeneous solution or in large unilamellar vesicles (LUVET). Thiyl radicals were generated from the corresponding thiol by either gamma-irradiation or UV photolysis, and the reaction course was followed by GC, Ag/TLC, and 13C NMR analyses. The isomerization was found to be independent of cis double bond location (random process) in i-PrOH solution. In the case of vesicles, the supramolecular organization of lipids produced a dramatic change of the isomerization outcome: (i) in egg lecithin, the reactivity of arachidonate moieties is higher than that of oleate and linoleate residues, (ii) in the linoleate residues of egg lecithin, the 9t,12c-18:2 isomer prevailed on the 9c,12t-18:2 isomer (3:1 ratio), and (iii) a regioselective isomerization of SAPC arachidonate residues occurred in the 5 and 8 positions. This effect of "positional preference" indicates that thiyl radicals entering the hydrophobic region of the membrane bilayer start to isomerize polyunsaturated fatty acid residues having the double bonds nearest to the membrane surfaces. We propose that arachidonic acid and its trans isomers can function as biomarkers in membranes for distinguishing the two trans fatty acid-forming pathways.     

The natural spinor connection on S 8 is a gauge field

We show that the natural spinor connection on S ₈ gives the solution of the Yang-Mills equations in eight dimensions recently found by Grossman, Kephart, and Stasheff. We compute explicitly its Euler number.     

Dimensional Reduction Over the Quantum Sphere and Non-Abelian q-Vortices

We extend equivariant dimensional reduction techniques to the case of quantum spaces which are the product of a K?hler manifold M with the quantum two-sphere. We work out the reduction of bundles which are equivariant under the natural action of the quantum group SU _q (2), and also of invariant gauge connections on these bundles. The reduction of Yang–Mills gauge theory on the product space leads to a q-deformation of the usual quiver gauge theories on M. We formulate generalized instanton equations on the quantum space and show that they correspond to q-deformations of the usual holomorphic quiver chain vortex equations on M. We study some topological stability conditions for the existence of solutions to these equations, and demonstrate that the corresponding vacuum moduli spaces are generally better behaved than their undeformed counterparts, but much more constrained by the q-deformation. We work out several explicit examples, including new examples of non-abelian vortices on Riemann surfaces, and q-deformations of instantons whose moduli spaces admit the standard hyper-K?hler quotient construction.     

Quasi-Newton projection methods and the discrepancy principle in image restoration

In this work, the problem of the restoration of images corrupted by space invariant blur and noise is considered. This problem is ill-posed and regularization is required. The image restoration problem is formulated as a nonnegatively constrained minimization problem whose objective function depends on the statistical properties of the noise corrupting the observed image. The cases of Gaussian and Poisson noise are both considered. A Newton-like projection method with early stopping of the iterates is proposed as an iterative regularization method in order to determine a nonnegative approximation to the original image. A suitable approximation of the Hessian of the objective function is proposed for a fast solution of the Newton system. The results of the numerical experiments show the effectiveness of the method in computing a good solution in few iterations, when compared with some methods recently proposed as best performing.     

Natural Pseudo-Distance and Optimal Matching between Reduced Size Functions

This paper studies the properties of a new lower bound for the natural pseudo-distance. The natural pseudo-distance is a dissimilarity measure between shapes, where a shape is viewed as a topological space endowed with a real-valued continuous function. Measuring dissimilarity amounts to minimizing the change in the functions due to the application of homeomorphisms between topological spaces, with respect to the L _∞-norm. In order to obtain the lower bound, a suitable metric between size functions, called matching distance, is introduced. It compares size functions by solving an optimal matching problem between countable point sets. The matching distance is shown to be resistant to perturbations, implying that it is always smaller than the natural pseudo-distance. We also prove that the lower bound so obtained is sharp and cannot be improved by any other distance between size functions.     

The Weil Algebra of a Hopf Algebra I: A Noncommutative Framework

We generalize the notion, introduced by Henri Cartan, of an operation of a Lie algebra ${\mathfrak{g}}$ in a graded differential algebra Ω. We define the notion of an operation of a Hopf algebra ${\mathcal{H}}$ in a graded differential algebra Ω which is referred to as a ${\mathcal{H}}$ -operation. We then generalize for such an operation the notion of algebraic connection. Finally we discuss the corresponding noncommutative version of the Weil algebra: The Weil algebra ${W(\mathcal{H})}$ of the Hopf algebra ${\mathcal{H}}$ is the universal initial object of the category of ${\mathcal{H}}$ -operations with connections.