Worldsheet Instantons and Torsion Curves

We study aspects of worldsheet instantons relevant to a heterotic standard model. The non-simply connected Calabi-Yau threefold used admits Z_3 x Z_3 Wilson lines, and a more detailed investigation shows that the homology classes of curves are H_2(X,Z)=Z^3+Z_3+Z_3. We compute the genus-0 prepotential, this is the first explicit calculation of the Gromov-Witten invariants of homology classes with torsion (finite subgroups). In particular, some curve classes contain only a single instanton. This ensures that the Beasley-Witten cancellation of instanton contributions cannot happen on this (non-toric) Calabi-Yau threefold.Comment: 9 pages. To appear in the proceedings of the first Sowers Theoretical Physics workshop, Virginia Tech, May 200

Seismic evidence for the tectonics of Central and Western Asia

A statistical analysis of the null axes of the fault-plane solutions of earthquakes in any one area permits determination of the average tectonic motion direction of that area. In the present paper this method has been applied to areas in central and western Asia for which several hundred fault-plane solutions are readily available in the literature. The investigation yields the result that (seismically) calculated tectonic motion directions in a series of small areas that are part of a larger unit are consistent with each other and that there is in every case an excellent correlation with the tectonic motion of the area as postulated from geological studies. This appears to justify completely the seismic method. The seismically determined tectonic motion in central Asia appears to be mainly in a north-south direction. The motion refers to the present time (since the earthquakes occur at the present time), but it is the same as that postulated in geology for an explanation of the folding of the central Asian mountain ranges. This demonstrates that the stress system which created the central Asian mountains is active at the present time

Runaway Feedback Loops in Predictive Policing

Predictive policing systems are increasingly used to determine how to allocate police across a city in order to best prevent crime. Discovered crime data (e.g., arrest counts) are used to help update the model, and the process is repeated. Such systems have been empirically shown to be susceptible to runaway feedback loops, where police are repeatedly sent back to the same neighborhoods regardless of the true crime rate. In response, we develop a mathematical model of predictive policing that proves why this feedback loop occurs, show empirically that this model exhibits such problems, and demonstrate how to change the inputs to a predictive policing system (in a black-box manner) so the runaway feedback loop does not occur, allowing the true crime rate to be learned. Our results are quantitative: we can establish a link (in our model) between the degree to which runaway feedback causes problems and the disparity in crime rates between areas. Moreover, we can also demonstrate the way in which \emph{reported} incidents of crime (those reported by residents) and \emph{discovered} incidents of crime (i.e. those directly observed by police officers dispatched as a result of the predictive policing algorithm) interact: in brief, while reported incidents can attenuate the degree of runaway feedback, they cannot entirely remove it without the interventions we suggest.Comment: Extended version accepted to the 1st Conference on Fairness, Accountability and Transparency, 2018. Adds further treatment of reported as well as discovered incident

Statistical analysis of recent fault-plane solutions of earthquakes

The large number of fault-plane solutions at present available in the literature permit one to calculate several statistical averages that have an important bearing upon geotectonics. The present paper represents a continuation of earlier work in this direction: 101 new fault-plane solutions are listed and the ratio of pressure to tension, strike slip to dip slip, and the average slip angle have been calculated for nine earthquake areas. Some of the older results are thereby corroborated, viz., that the “normal” character of earthquakes is to represent strike-slip faulting, and that the central Asian regions constitute an exception to this rule. In addition, it is now possible to make a breakdown with regard to depth. In this, a peculiar situation is found at 0.03 R depth, where the slip angle reaches a maximum. If the relationship between shallow and deep earthquakes be considered for any one area, however, it turns out that they are on the whole of the same character. Thus, whatever it is that causes earthquakes, acts in a similar fashion at all depths in any one area, but differs from one area to another

Interface Equations for Capillary Rise in Random Environment

We consider the influence of quenched noise upon interface dynamics in 2D and 3D capillary rise with rough walls by using phase-field approach, where the local conservation of mass in the bulk is explicitly included. In the 2D case the disorder is assumed to be in the effective mobility coefficient, while in the 3D case we explicitly consider the influence of locally fluctuating geometry along a solid wall using a generalized curvilinear coordinate transformation. To obtain the equations of motion for meniscus and contact lines, we develop a systematic projection formalism which allows inclusion of disorder. Using this formalism, we derive linearized equations of motion for the meniscus and contact line variables, which become local in the Fourier space representation. These dispersion relations contain effective noise that is linearly proportional to the velocity. The deterministic parts of our dispersion relations agree with results obtained from other similar studies in the proper limits. However, the forms of the noise terms derived here are quantitatively different from the other studies

Auditing Black-box Models for Indirect Influence

Data-trained predictive models see widespread use, but for the most part they are used as black boxes which output a prediction or score. It is therefore hard to acquire a deeper understanding of model behavior, and in particular how different features influence the model prediction. This is important when interpreting the behavior of complex models, or asserting that certain problematic attributes (like race or gender) are not unduly influencing decisions. In this paper, we present a technique for auditing black-box models, which lets us study the extent to which existing models take advantage of particular features in the dataset, without knowing how the models work. Our work focuses on the problem of indirect influence: how some features might indirectly influence outcomes via other, related features. As a result, we can find attribute influences even in cases where, upon further direct examination of the model, the attribute is not referred to by the model at all. Our approach does not require the black-box model to be retrained. This is important if (for example) the model is only accessible via an API, and contrasts our work with other methods that investigate feature influence like feature selection. We present experimental evidence for the effectiveness of our procedure using a variety of publicly available datasets and models. We also validate our procedure using techniques from interpretable learning and feature selection, as well as against other black-box auditing procedures.Comment: Final version of paper that appears in the IEEE International Conference on Data Mining (ICDM), 201

Directed Fixed Energy Sandpile Model

We numerically study the directed version of the fixed energy sandpile. On a closed square lattice, the dynamical evolution of a fixed density of sand grains is studied. The activity of the system shows a continuous phase transition around a critical density. While the deterministic version has the set of nontrivial exponents, the stochastic model is characterized by mean field like exponents.Comment: 5 pages, 6 figures, to be published in Phys. Rev.

Bayesian uncertainty assessment of flood predictions in ungauged urban basins for conceptual rainfall-runoff models

Urbanization and the resulting land-use change strongly affect the water cycle and runoff-processes in watersheds. Unfortunately, small urban watersheds, which are most affected by urban sprawl, are mostly ungauged. This makes it intrinsically difficult to assess the consequences of urbanization. Most of all, it is unclear how to reliably assess the predictive uncertainty given the structural deficits of the applied models. In this study, we therefore investigate the uncertainty of flood predictions in ungauged urban basins from structurally uncertain rainfall-runoff models. To this end, we suggest a procedure to explicitly account for input uncertainty and model structure deficits using Bayesian statistics with a continuous-time autoregressive error model. In addition, we propose a concise procedure to derive prior parameter distributions from base data and successfully apply the methodology to an urban catchment in Warsaw, Poland. Based on our results, we are able to demonstrate that the autoregressive error model greatly helps to meet the statistical assumptions and to compute reliable prediction intervals. In our study, we found that predicted peak flows were up to 7 times higher than observations. This was reduced to 5 times with Bayesian updating, using only few discharge measurements. In addition, our analysis suggests that imprecise rainfall information and model structure deficits contribute mostly to the total prediction uncertainty. In the future, flood predictions in ungauged basins will become more important due to ongoing urbanization as well as anthropogenic and climatic changes. Thus, providing reliable measures of uncertainty is crucial to support decision making

Evolutionary Trends in the Physciaceae

The current delimitation of the family Physciaceae has been generally accepted since detailed descriptions of ascus characters allowed for a more natural circumscription of lichenized ascomycetes. The generic relations within the family are, however, still controversial and depend on the importance different authors attribute to specific morphological or chemical characteristics. The aim of this paper is to describe ascospore ontogeny and to test the present taxonomic structure of the family against a parsimony-based cladistic analysis, which includes three different scenarios of a priori character weighting. A study of ascospore ontogeny revealed two distinct developmental lines. One line revealed a delayed septum formation, which clearly showed transitions from spores with apical and median thickenings to spores without apical, but still well developed median thickenings, and to spores without any thickenings. In the second developmental line with an early septum formation again taxa with no thickenings, median thickenings, and both median and apical thickenings were found. Although these characters were constant at a species level, median wall thickenings especially varied among otherwise closely related taxa. In the cladistic analyses the current taxonomic structure of the Physciaceae was only obtained after the five character groups, namely morphology and anatomy of the vegetative thallus, conidiomata and conidia, morphology and anatomy of the apothecia, ontogeny of the ascospores, and secondary metabolites of the thallus, were given equal importance, and after a subjective a priori weighting further increased the weight of the three characters ‘conidial shape', ‘presence of apical thickenings', and ‘spore septation delayed'. This structure was not supported by a cladistic analysis with equally weighted characters but reflected the biased character weighting of the present day Physdaceae taxonomy. The taxonomic importance of conidial characters and of anatomical and ontogenetical spore characteristics need, therefore, a careful reconsideration in futur