Quiver GIT for varieties with tilting bundles

In the setting of a variety X admitting a tilting bundle T we consider the problem of constructing X as a quiver GIT quotient of the algebra A:=EndX(T)opA:=EndX(T)op . We prove that if the tilting equivalence restricts to a bijection between the skyscraper sheaves of X and the closed points of a quiver representation moduli functor for A=EndX(T)opA=EndX(T)op then X is indeed a fine moduli space for this moduli functor, and we prove this result without any assumptions on the singularities of X. As an application we consider varieties which are projective over an affine base such that the fibres are of dimension 1, and the derived pushforward of the structure sheaf on X is the structure sheaf on the base. In this situation there is a particular tilting bundle on X constructed by Van den Bergh, and our result allows us to reconstruct X as a quiver GIT quotient for an easy to describe stability condition and dimension vector. This result applies to flips and flops in the minimal model program, and in the situation of flops shows that both a variety and its flop appear as moduli spaces for algebras produced from different tilting bundles on the variety. We also give an application to rational surface singularities, showing that their minimal resolutions can always be constructed as quiver GIT quotients for specific dimension vectors and stability conditions. This gives a construction of minimal resolutions as moduli spaces for all rational surface singularities, generalising the G-Hilbert scheme moduli space construction which exists only for quotient singularities

Consultant-2: pre- and post processing of machine learning applications.

The knowledge acquisition bottleneck in the development of large knowledge-based applications has not yet been resolved. One approach which has been advocated is the systematic use of Machine Learning (ML) techniques. However, ML technology poses difficulties to domain experts and knowledge engineers who are not familiar with it. This paper discusses Consultant-2, a system which makes a first step towards providing system support for a pre- and post-processing methodology where a cyclic process of experiments with an ML tool, its data, data description language and parameters attempts to optimize learning performance. Consultant-2 has been developed to support the use of Machine Learning Toolbox (MLT), an integrated architecture of 10 ML tools, and has evolved from a series of earlier systems. Consultant-0 and Consultant-1 had knowledge only about how to choose an ML algorithm based on the nature of the domain data. Consultant-2 is the most sophisticated. It, additionally, has knowledge about how ML experts and domain experts pre-process domain data before a run with the ML algorithm, and how they further manipulate the data and reset parameters after a run of the selected ML algorithm, to achieve a more acceptable result. How these several KBs were acquired and encoded is described. In fact, this knowledge has been acquired by interacting both with the ML algorithm developers and with domain experts who had been using the MLT toolbox on real-world tasks. A major aim of the MLT project was to enable a domain expert to use the toolbox directly; i.e. without necessarily having to involve either a ML specialist or a knowledge engineer. Consultant's principal goal was to provide specific advice to ease this process

Case-base maintenance with multi-objective evolutionary algorithms.

Case-Base Reasoning is a problem-solving methodology that uses old solved problems, called cases, to solve new problems. The case-base is the knowledge source where the cases are stored, and the amount of stored cases is critical to the problem-solving ability of the Case-Base Reasoning system. However, when the case-base has many cases, then performance problems arise due to the time needed to find those similar cases to the input problem. At this point, Case-Base Maintenance algorithms can be used to reduce the number of cases and maintain the accuracy of the Case-Base Reasoning system at the same time. Whereas Case-Base Maintenance algorithms typically use a particular heuristic to remove (or select) cases from the case-base, the resulting maintained case-base relies on the proportion of redundant and noisy cases that are present in the case-base, among other factors. That is, a particular Case-Base Maintenance algorithm is suitable for certain types of case-bases that share some indicators, such as redundancy and noise levels. In the present work, we consider Case-Base Maintenance as a multi-objective optimization problem, which is solved with a Multi-Objective Evolutionary Algorithm. To this end, a fitness function is introduced to measure three different objectives based on the Complexity Profile model. Our hypothesis is that the Multi-Objective Evolutionary Algorithm performing Case-Base Maintenance may be used in a wider set of case-bases, achieving a good balance between the reduction of cases and the problem-solving ability of the Case-Based Reasoning system. Finally, from a set of the experiments, our proposed Multi-Objective Evolutionary Algorithm performing Case-Base Maintenance shows regularly good results with different sets of case-bases with different proportion of redundant and noisy cases

On Dimer Models and Closed String Theories

We study some aspects of the recently discovered connection between dimer models and D-brane gauge theories. We argue that dimer models are also naturally related to closed string theories on non compact orbifolds of \BC^2 and \BC^3, via their twisted sector R charges, and show that perfect matchings in dimer models correspond to twisted sector states in the closed string theory. We also use this formalism to study the combinatorics of some unstable orbifolds of \BC^2.Comment: 1 + 25 pages, LaTeX, 11 epsf figure

Lathe converted for grinding aspheric surfaces

A standard overarm tracing lathe converted by the addition of an independently driven diamond grinding wheel is used for grinding aspheric surfaces. The motion of the wheel is controlled by the lathe air tracer following the template which produces the desired aspheric profile

Noncommutative resolutions of ADE fibered Calabi-Yau threefolds

In this paper we construct noncommutative resolutions of a certain class of Calabi-Yau threefolds studied by F. Cachazo, S. Katz and C. Vafa. The threefolds under consideration are fibered over a complex plane with the fibers being deformed Kleinian singularities. The construction is in terms of a noncommutative algebra introduced by V. Ginzburg, which we call the "N=1 ADE quiver algebra"

The genomic footprint of coastal earthquake uplift

Theory suggests that catastrophic earth-history events can drive rapid biological evolution, but empirical evidence for such processes is scarce. Destructive geological events such as earthquakes can represent large-scale natural experiments for inferring such evolutionary processes. We capitalized on a major prehistoric (800 yr BP) geological uplift event affecting a southern New Zealand coastline to test for the lasting genomic impacts of disturbance. Genome-wide analyses of three co-distributed keystone kelp taxa revealed that post-earthquake recolonization drove the evolution of novel, large-scale intertidal spatial genetic ‘sectors’ which are tightly linked to geological fault boundaries. Demographic simulations confirmed that, following widespread extirpation, parallel expansions into newly vacant habitats rapidly restructured genome-wide diversity. Interspecific differences in recolonization mode and tempo reflect differing ecological constraints relating to habitat choice and dispersal capacity among taxa. This study highlights the rapid and enduring evolutionary effects of catastrophic ecosystem disturbance and reveals the key role of range expansion in reshaping spatial genetic patterns

Remarks on quiver gauge theories from open topological string theory

We study effective quiver gauge theories arising from a stack of D3-branes on certain Calabi-Yau singularities. Our point of view is a first principle approach via open topological string theory. This means that we construct the natural A-infinity-structure of open string amplitudes in the associated D-brane category. Then we show that it precisely reproduces the results of the method of brane tilings, without having to resort to any effective field theory computations. In particular, we prove a general and simple formula for effective superpotentials

RPA using a multiplexed cartridge for low cost point of care diagnostics in the field

A point of care device utilising Lab-on-a-Chip technologies that is applicable for biological pathogens was designed, fabricated and tested showing sample in to answer out capabilities. The purpose of the design was to develop a cartridge with the capability to perform nucleic acid extraction and purification from a sample using a chitosan membrane at an acidic pH. Waste was stored within the cartridge with the use of sodium polyacrylate to solidify or gelate the sample in a single chamber. Nucleic acid elution was conducted using the RPA amplification reagents (alkaline pH). Passive valves were used to regulate the fluid flow and a multiplexer was designed to distribute the fluid into six microchambers for amplification reactions. Cartridges were produced using soft lithography of silicone from 3D printed moulds, bonded to glass substrates. The isothermal technique, RPA is employed for amplification. This paper shows the results from two separate experiments: the first using the RPA control nucleic acid, the second showing successful amplification from Chlamydia Trachomatis. Endpoint analysis conducted for the RPA analysis was gel electrophoresis that showed 143 base pair DNA was amplified successfully for positive samples whilst negative samples did not show amplification. End point analysis for Chlamydia Trachomatis samples was fluorescence detection that showed successful detection of 1 copy/μL and 10 copies/μL spiked in a MES buffer.Medical Research Counci

On the geometry of C^3/D_27 and del Pezzo surfaces

We clarify some aspects of the geometry of a resolution of the orbifold X = C3/D_27, the noncompact complex manifold underlying the brane quiver standard model recently proposed by Verlinde and Wijnholt. We explicitly realize a map between X and the total space of the canonical bundle over a degree 1 quasi del Pezzo surface, thus defining a desingularization of X. Our analysis relys essentially on the relationship existing between the normalizer group of D_27 and the Hessian group and on the study of the behaviour of the Hesse pencil of plane cubic curves under the quotient.Comment: 23 pages, 5 figures, 2 tables. JHEP style. Added references. Corrected typos. Revised introduction, results unchanged