Scaling and Universality of the Complexity of Analog Computation

We apply a probabilistic approach to study the computational complexity of analog computers which solve linear programming problems. We analyze numerically various ensembles of linear programming problems and obtain, for each of these ensembles, the probability distribution functions of certain quantities which measure the computational complexity, known as the convergence rate, the barrier and the computation time. We find that in the limit of very large problems these probability distributions are universal scaling functions. In other words, the probability distribution function for each of these three quantities becomes, in the limit of large problem size, a function of a single scaling variable, which is a certain composition of the quantity in question and the size of the system. Moreover, various ensembles studied seem to lead essentially to the same scaling functions, which depend only on the variance of the ensemble. These results extend analytical and numerical results obtained recently for the Gaussian ensemble, and support the conjecture that these scaling functions are universal.Comment: 22 pages, latex, 12 eps fig

Accuracy of schemes for the Euler equations with non-uniform meshes

The effect of non-uniform grids on the solution of the Euler equations is analyzed. A Runge-Kutta type scheme based on a finite volume formulation is considered. It is shown that for arbitrary grids the scheme can be inconsistent even though it is second-order accurate for uniform grids. An improvement is suggested which leads to at least first-order accuracy for general grids. Test cases are presented in both two- and three-space dimensions. Applications to finite difference and implicit algorithms are also given

Tax evasion and exchange equity: a reference-dependent approach

The standard portfolio model of tax evasion with a public good produces the perverse conclusion that when taxpayers perceive the public good to be under-/overprovided, an increase in the tax rate increases/decreases evasion. The author treats taxpayers as thinking in terms of gains and losses relative to an endogenous reference level, which reflects perceived exchange equity between the value of taxes paid and the value of public goods supplied. With these alternative behavioral assumptions, the author overturns the aforementioned result in a direction consistent with the empirical evidence. The author also finds a role for relative income in determining individual responses to a change in the marginal rate of tax

Enhancing Qubit Readout with Autoencoders

In addition to the need for stable and precisely controllable qubits, quantum computers take advantage of good readout schemes. Superconducting qubit states can be inferred from the readout signal transmitted through a dispersively coupled resonator. This work proposes a novel readout classification method for superconducting qubits based on a neural network pre-trained with an autoencoder approach. A neural network is pre-trained with qubit readout signals as autoencoders in order to extract relevant features from the data set. Afterwards, the pre-trained network inner layer values are used to perform a classification of the inputs in a supervised manner. We demonstrate that this method can enhance classification performance, particularly for short and long time measurements where more traditional methods present lower performance.Comment: 16 pages, 23 figure

A global atmospheric electricity monitoring network for climate and geophysical research

The Global atmospheric Electric Circuit (GEC) is a fundamental coupling network of the climate system connecting electrically disturbed weather regions with fair weather regions across the planet. The GEC sustains the fair weather electric field (or potential gradient, PG) which is present globally and can be measured routinely at the surface using durable instrumentation such as modern electric field mills, which are now widely deployed internationally. In contrast to lightning or magnetic fields, fair weather PG cannot be measured remotely. Despite the existence of many PG datasets (both contemporary and historical), few attempts have been made to coordinate and integrate these fragmented surface measurements within a global framework. Such a synthesis is important elvinin order to fully study major influences on the GEC such as climate variations and space weather effects, as well as more local atmospheric electrical processes such as cloud electrification, lightning initiation, and dust and aerosol charging. The GloCAEM (Global Coordination of Atmospheric Electricity Measurements) project has brought together experts in atmospheric electricity to make the first steps towards an effective global network for atmospheric electricity monitoring, which will provide data in near real time. Data from all sites are available in identically-formatted files, at both one second and one minute temporal resolution, along with meteorological data (wherever available) for ease of interpretation of electrical measurements. This work describes the details of the GloCAEM database and presents what is likely to be the largest single analysis of PG data performed from multiple datasets at geographically distinct locations. Analysis of the diurnal variation in PG from all 17 GloCAEM sites demonstrates that the majority of sites show two daily maxima, characteristic of local influences on the PG, such as the sunrise effect. Data analysis methods to minimise such effects are presented and recommendations provided on the most suitable GloCAEM sites for the study of various scientific phenomena. The use of the dataset for a further understanding of the GEC is also demonstrated, in particular for more detailed characterization of day-to-day global circuit variability. Such coordinated effort enables deeper insight into PG phenomenology which goes beyond single-location PG measurements, providing a simple measurement of global thunderstorm variability on a day-to-day timescale. The creation of the GloCAEM database is likely to enable much more effective study of atmospheric electricity variables than has ever been possible before, which will improve our understanding of the role of atmospheric electricity in the complex processes underlying weather and climate

Not Just a Theory--The Utility of Mathematical Models in Evolutionary Biology

Progress in science often begins with verbal hypotheses meant to explain why certain biological phenomena exist. An important purpose of mathematical models in evolutionary research, as in many other fields, is to act as “proof-of-concept” tests of the logic in verbal explanations, paralleling the way in which empirical data are used to test hypotheses. Because not all subfields of biology use mathematics for this purpose, misunderstandings of the function of proof-of-concept modeling are common. In the hope of facilitating communication, we discuss the role of proof-of-concept modeling in evolutionary biology

Fine-mapping of the Rpt5 net blotch resistance gene region in barley

Poster