Probabilistic Fréchet means for time varying persistence diagrams

© 2015, Institute of Mathematical Statistics. All rights reserved.In order to use persistence diagrams as a true statistical tool, it would be very useful to have a good notion of mean and variance for a set of diagrams. In [23], Mileyko and his collaborators made the first study of the properties of the Fréchet mean in (Dp, Wp), the space of persistence diagrams equipped with the p-th Wasserstein metric. In particular, they showed that the Fréchet mean of a finite set of diagrams always exists, but is not necessarily unique. The means of a continuously-varying set of diagrams do not themselves (necessarily) vary continuously, which presents obvious problems when trying to extend the Fréchet mean definition to the realm of time-varying persistence diagrams, better known as vineyards. We fix this problem by altering the original definition of Fréchet mean so that it now becomes a probability measure on the set of persistence diagrams; in a nutshell, the mean of a set of diagrams will be a weighted sum of atomic measures, where each atom is itself a persistence diagram determined using a perturbation of the input diagrams. This definition gives for each N a map (Dp)^N→ℙ(Dp). We show that this map is Hölder continuous on finite diagrams and thus can be used to build a useful statistic on vineyards.

Comparison of pattern detection methods in microarray time series of the segmentation clock.

While genome-wide gene expression data are generated at an increasing rate, the repertoire of approaches for pattern discovery in these data is still limited. Identifying subtle patterns of interest in large amounts of data (tens of thousands of profiles) associated with a certain level of noise remains a challenge. A microarray time series was recently generated to study the transcriptional program of the mouse segmentation clock, a biological oscillator associated with the periodic formation of the segments of the body axis. A method related to Fourier analysis, the Lomb-Scargle periodogram, was used to detect periodic profiles in the dataset, leading to the identification of a novel set of cyclic genes associated with the segmentation clock. Here, we applied to the same microarray time series dataset four distinct mathematical methods to identify significant patterns in gene expression profiles. These methods are called: Phase consistency, Address reduction, Cyclohedron test and Stable persistence, and are based on different conceptual frameworks that are either hypothesis- or data-driven. Some of the methods, unlike Fourier transforms, are not dependent on the assumption of periodicity of the pattern of interest. Remarkably, these methods identified blindly the expression profiles of known cyclic genes as the most significant patterns in the dataset. Many candidate genes predicted by more than one approach appeared to be true positive cyclic genes and will be of particular interest for future research. In addition, these methods predicted novel candidate cyclic genes that were consistent with previous biological knowledge and experimental validation in mouse embryos. Our results demonstrate the utility of these novel pattern detection strategies, notably for detection of periodic profiles, and suggest that combining several distinct mathematical approaches to analyze microarray datasets is a valuable strategy for identifying genes that exhibit novel, interesting transcriptional patterns.

Disturbance, response, and persistence in self-organized forested communities: Analysis of robustness and resilience in five communities in Southern Indiana

We develop an analytic framework for the analysis of robustness in social-ecological systems (SESs) over time. We argue that social robustness is affected by the disturbances that communities face and the way they respond to them. Using Ostrom's ontological framework for SESs, we classify the major factors influencing the disturbances and responses faced by five Indiana intentional communities over a 15-year time frame. Our empirical results indicate that operational and collective-choice rules, leadership and entrepreneurship, monitoring and sanctioning, economic values, number of users, and norms/social capital are key variables that need to be at the core of future theoretical work on robustness of self-organized systems. © 2010 by the author(s).

Exploring the effects of image persistence in low frame rate virtual environments

© 2015 IEEE.In virtual reality applications, there is an aim to provide real time graphics which run at high refresh rates. However, there are many situations in which this is not possible due to simulation or rendering issues. When running at low frame rates, several aspects of the user experience are affected. For example, each frame is displayed for an extended period of time, causing a high persistence image artifact. The effect of this artifact is that movement may lose continuity, and the image jumps from one frame to another. In this paper, we discuss our initial exploration of the effects of high persistence frames caused by low refresh rates and compare it to high frame rates and to a technique we developed to mitigate the effects of low frame rates. In this technique, the low frame rate simulation images are displayed with low persistence by blanking out the display during the extra time such image would be displayed. In order to isolate the visual effects, we constructed a simulator for low and high persistence displays that does not affect input latency. A controlled user study comparing the three conditions for the tasks of 3D selection and navigation was conducted. Results indicate that the low persistence display technique may not negatively impact user experience or performance as compared to the high persistence case. Directions for future work on the use of low persistence displays for low frame rate situations are discussed.

Institutional Persistence in Eastern Europe: Economic and Political Legacies of Empires and Communism

This dissertation seeks to advance our understanding of the roles that institutions play in economic development. How do institutions evolve? What mechanisms are responsible for their persistence? What effects do they have on economic development?

I address these questions using historical and contemporary data from Eastern Europe and Russia. This area is relatively understudied by development economists. It also has a very interesting history. For one thing, for several centuries it was divided between different empires. For another, it experienced wars and socialism in the 20th century. I use some of these exogenous shocks as quasi-natural social experiments to study the institutional transformations and its effects on economic development both in the short and long run.

This first chapter explores whether economic, social, and political institutions vary in their resistance to policies designed to remove them. The empirical context for the analysis is Romania from 1690 to the 2000s. Romania represents an excellent laboratory for studying the persistence of different types of historical institutional legacies. In the 18th and 19th centuries, Romania was split between the Habsburg and Ottoman Empires, where political and economic institutions differed. The Habsburgs imposed less extractive institutions relative to the Ottomans: stronger rule of law, a more stable and predictable state, a more developed civil society, and less corruption. In the 20th century, the Romanian Communist regime tried deliberately to homogenize the country along all relevant dimensions. It was only partially successful. Using a regression discontinuity design, I document the persistence of economic outcomes, social capital, and political attitudes. First, I document remarkable convergence in urbanization, education, unemployment, and income between the two former empires. Second, regarding social capital, no significant differences in organizational membership, trust in bureaucracy, and corruption persist today. Finally, even though the Communists tried to change all political attitudes, significant discontinuities exist in current voting behavior at the former Habsburg-Ottoman border. Using data from the parliamentary elections of 1996-2008, I find that former Habsburg rule decreases by around 6 percentage points the vote share of the major post-Communist left party and increases by around 2 and 5 percentage points the vote shares of the main anti-Communist and liberal parties, respectively.

The second chapter investigates the effects of Stalin’s mass deportations on distrust in central authority. Four deported ethnic groups were not rehabilitated after Stalin’s death; they remained in permanent exile until the disintegration of the Soviet Union. This allows one to distinguish between the effects of the groups that returned to their homelands and those of the groups that were not allowed to return. Using regional data from the 1991 referendum on the future of the Soviet Union, I find that deportations have a negative interim effect on trust in central authority in both the regions of destination and those of origin. The effect is stronger for ethnic groups that remained in permanent exile in the destination regions. Using data from the Life in Transition Survey, the chapter also documents a long-term effect of deportations in the destination regions.

The third chapter studies the short-term effect of Russian colonization of Central Asia on economic development. I use data on the regions of origin of Russian settlers and push factors to construct an instrument for Russian migration to Central Asia. This instrument allows me to interpret the outcomes causally. The main finding is that the massive influx of Russians into the region during the 1897-1926 period had a significant positive effect on indigenous literacy. The effect is stronger for men and in rural areas. Evidently, interactions between natives and Russians through the paid labor market was an important mechanism of human capital transmission in the context of colonization.

The findings of these chapters provide additional evidence that history and institutions do matter for economic development. Moreover, the dissertation also illuminates the relative persistence of institutions. In particular, political and social capital legacies of institutions might outlast economic legacies. I find that most economic differences between the former empires in Romania have disappeared. By the same token, there are significant discontinuities in political outcomes. People in former Habsburg Romania provide greater support for liberalization, privatization, and market economy, whereas voters in Ottoman Romania vote more for redistribution and government control over the economy.

In the former Soviet Union, Stalin’s deportations during World War II have a long-term negative effect on social capital. Today’s residents of the destination regions of deportations show significantly lower levels of trust in central authority. This is despite the fact that the Communist regime tried to eliminate any source of opposition and used propaganda to homogenize people’s political and social attitudes towards the authorities. In Central Asia, the influx of Russian settlers had a positive short-term effect on human capital of indigenous population by the 1920s, which also might have persisted over time.

From a development perspective, these findings stress the importance of institutions for future paths of development. Even if past institutional differences are not apparent for a certain period of time, as was the case with the former Communist countries, they can polarize society later on, hampering economic development in the long run. Different institutions in the past, which do not exist anymore, can thus contribute to current political instability and animosity.