Improved Generalization via Tolerant Training

Theoretical and computational justification is given for improved generalization when the training set is learned with less accuracy. The model used for this investigation is a simple linear one. It is shown that learning a training set with a tolerance improves generalization, over zero-tolerance training, for any testing set satisfying a certain closeness condition to the training set. These results, obtained via a mathematical programming formulation, are placed in the context of some well-known machine learning results. Computational confirmation of improved generalization is given for linear systems (including nine of the twelve real-world data sets tested), as well as for nonlinear systems such as neural networks for which no theoretical results are available at present. In particular, the tolerant training method improves generalization on noisy, sparse, and overparameterized problems.     

Galois theory in variable categories

The order-reversing bijection between field extensions and subgroups of the Galois group G follows from the equivalence between the opposite of the category of étale algebras and the category of discrete G-spaces [2]. We show that the basic ingredient for this equivalence of categories, and for various known generalizations, is a factorization system for variable categories.     

Designing protein beta-sheet surfaces by Z-score optimization

Studies of lattice models of proteins have suggested that the appropriate energy expression for protein design may include nonthermodynamic terms to accommodate negative design concerns. One method, developed in lattice model studies, maximizes a quantity known as the " Z-score," which compares the lowest energy sequence whose ground state structure is the target structure to an ensemble of random sequences. Here we show that, in certain circumstances, the technique can be applied to real proteins. The resulting energy expression is used to design the beta-sheet surfaces of two real proteins. We find experimentally that the designed proteins are stable and well folded, and in one case is even more thermostable than the wild type.     

New compounds in the Mn-X-Bi system where X = Ni, Cu, RhorPd

A new class of magnetic compounds has been discovered in the temary system Mn-X-Bi where X is Ni, Cu, Rh or Pd. The approximate compositions of these compounds are Mn₅Ni₂Bi₄, Mn₃Cu₄Bi₄, Mn₅Rh₂Bi₄, and Mn₅Pd₂Bi₄. The Bravais lattice is face-centered cubic, and the lattice constants are 12.16 Å (X = Ni), 12.18 Å (X = Cu), 12.31 Å (X = Rh) and 12.44 Å (X = Pd). These compounds are probably ferromagnetic and have Curie temperatures in the range -7°C to 183°C. A crystal structure is proposed for these compounds which contains 88 atoms/unit cell.     

Conductivity and Hall effect measurements in doped polyacetylene

Conductivity and Hall effect measurements are reported for polyacetylene films heavily doped with AsF₅. The Hall coefficient is anomalously small, however, it is p-type and relatively temperature insensitive in the range 4–300 K indicative of metallic conduction. The effects of film degration by heating and air exposure are also investigated.     

Mössbauer effect studies of spin disturbances in dilute ferromagnetic alloys

¹¹⁹Sn Mössbauer effect studies of dilute Pt Fe, Pd Fe and Ni Fe alloys are reported. For Pt Fe an oscillatory spatial dependence of the spin-polarization about the Fe atoms is observed. The range increases with increasing temperature. For Pd Fe and Ni Fe the host properties are masked by the magnetic disturbances induced by the tin probe atoms.     

The Remarkable Stable Emerald Green C60F15[CBr(CO2Et)2]3: The First [60]Fullerene That Is also the First [18]Trannulene

No Abstract     

Duals Invert

Monoidal objects (or pseudomonoids) in monoidal bicategories share many of the properties of the paradigmatic example: monoidal categories. The existence of (say, left) duals in a monoidal category leads to a dualization operation which was abstracted to the context of monoidal objects by Day et al. (Appl Categ Struct 11:229–260, 2003). We define a relative version of this called exact pairing for two arrows in a monoidal bicategory; when one of the arrows is an identity, the other is a dualization. In this context we supplement results of Day et al. (Appl Categ Struct 11:229–260, 2003) (and even correct one of them) and only assume the existence of biduals in the bicategory where necessary. We also abstract recent work of Day and Pastro (New York J Math 14:733–742, 2008) on Frobenius monoidal functors to the monoidal bicategory context. Our work began by focusing on the invertibility of components at dual objects of monoidal natural transformations between Frobenius monoidal functors. As an application of the abstraction, we recover a theorem of Walters and Wood (Theory Appl Categ 3:25–47, 2008) asserting that, for objects A and X in a cartesian bicategory , if A is Frobenius then the category Map(X,A) of left adjoint arrows is a groupoid. Also, the characterization in Walters and Wood (Theory Appl Categ 3:25–47, 2008) of left adjoint arrows between Frobenius objects of a cartesian bicategory is put into our current setting. In the same spirit, we show that when a monoidal object admits a dualization, its lax centre coincides with the centre defined in Street (Theory Appl Categ 13:184–190, 2004). Finally we look at the relationship between lax duals for objects and adjoints for arrows in a monoidal bicategory.