Discrimination decisions for 100,000-dimensional spaces

Discrimination decisions arise in many natural language processing tasks. Three classical tasks are discriminating texts by their authors (author identification), discriminating documents by their relevance to some query (information retrieval), and discriminating multi-meaning words by their meanings (sense discrimination). Many other discrimination tasks arise regularly, such as determining whether a particular proper noun represents a person or a place, or whether a given work from some teletype text would be capitalized if both cases had been used.We [9] introduced a method designed for the sense discrimination problems mentioned.We also discuss areas for research based on observed shortcomings of the method. In particular, an example in the author identification task shows the need for a robust version of the method. Also, the method makes an assumption of independence which is demonstrably false, yet there has been no careful study of the results of this assumption.     

Atomic and electronic structure of the corundum (0001) surface: comparison with surface spectroscopies

The electronic structure and geometry of the Al-terminated corundum (0001) surface were studied using a slab model within the ab-initio Hartree-Fock technique. The distance between the top Al plane and the next O basal plane is found to be considerably reduced on relaxation (by 0.57 Å, i.e. by 68% of the corresponding interlayer distance in the bulk). An interpretation of experimental photoelectron spectra (UPS He I) and metastable impact electron spectra (MIES) is given using the calculated total density of states of the slab and the projections to the atoms, atomic orbitals, and He 1s floating atomic orbital at different positions above the surface. Calculated projected densities of states exhibit a strong dependence on the relaxation of surface atoms. The good agreement of simulated and experimental UPS and MIES spectra supports the correctness of calculated surface relaxation.     

Equilibrium in a discrete exchange economy with money

We consider a market in which there aren traders each of whom owns an object and some amount of money. It is shown that under rather mild conditions on demand the market will have a price equilibrium. The proof makes use of a generalization of a well known result of combinatorial topology.     

Some remarks on the stable matching problem

The stable matching problem is that of matching two sets of agents in such a manner that no two unmatched agents prefer each other to their mates. We establish three results on properties of these matchings and present two short proofs of a recent theorem of Dubins and Freedman.     

CrystalGrower: a generic computer program for Monte Carlo modelling of crystal growth

A Monte Carlo crystal growth simulation tool, CrystalGrower, is described which is able to simultaneously model both the crystal habit and nanoscopic surface topography of any crystal structure under conditions of variable supersaturation or at equilibrium. This tool has been developed in order to permit the rapid simulation of crystal surface maps generated by scanning probe microscopies in combination with overall crystal habit. As the simulation is based upon a coarse graining at the nanoscopic level features such as crystal rounding at low supersaturation or undersaturation conditions are also faithfully reproduced. CrystalGrower permits the incorporation of screw dislocations with arbitrary Burgers vectors and also the investigation of internal point defects in crystals. The effect of growth modifiers can be addressed by selective poisoning of specific growth sites. The tool is designed for those interested in understanding and controlling the outcome of crystal growth through a deeper comprehension of the key controlling experimental parameters.

Generic in silico methodology – CrystalGrower – for simulating crystal habit and nanoscopic surface topology to determine crystallisation free energies.     

Thermodynamics of catalytic formation of dimethyl ether from methanol in acidic zeolites

We present a theoretical study of the formation of the first intermediate, dimethyl ether, in the methanol to gasoline conversion within the framework of an ab initio molecular dynamics approach. The study is performed under conditions that closely resemble the reaction conditions in the zeolite catalyst including the full topology of the framework. The use of the method of thermodynamic integration allows us to extract the free-energy profile along the reaction coordinate. We find that the entropic contribution qualitatively alters the free-energy profile relative to the total energy profile. Different transition states are found from the internal and free energy profiles. The entropy contribution varies significantly along the reaction coordinate and is responsible for stabilizing the products and for lowering the energy barrier. The hugely inhomogeneous variation of the entropy can be understood in terms of elementary processes that take place during the chemical reaction. Our simulations provide new insights into the complex nature of this chemical reaction.     

On the existence of Analytic Semigroups Bounded on the Half-Disc in some Banach Algebras

Let G be a locally compact group. We show that L¹(G) does notcontain any analytic semigroups which are bounded on the half-disc,by using some facts about the analytic Radon-Nikodm propertyin Banach spaces. This solves a question raised by J. Esterle.