Survival Probabilities of History-Dependent Random Walks

We analyze the dynamics of random walks with long-term memory (binary chains with long-range correlations) in the presence of an absorbing boundary. An analytically solvable model is presented, in which a dynamical phase-transition occurs when the correlation strength parameter \mu reaches a critical value \mu_c. For strong positive correlations, \mu > \mu_c, the survival probability is asymptotically finite, whereas for \mu < \mu_c it decays as a power-law in time (chain length).Comment: 3 pages, 2 figure

Survival probabilities in time-dependent random walks

We analyze the dynamics of random walks in which the jumping probabilities are periodic {\it time-dependent} functions. In particular, we determine the survival probability of biased walkers who are drifted towards an absorbing boundary. The typical life-time of the walkers is found to decrease with an increment of the oscillation amplitude of the jumping probabilities. We discuss the applicability of the results in the context of complex adaptive systems.Comment: 4 pages, 3 figure

Phase-Transition in Binary Sequences with Long-Range Correlations

Motivated by novel results in the theory of correlated sequences, we analyze the dynamics of random walks with long-term memory (binary chains with long-range correlations). In our model, the probability for a unit bit in a binary string depends on the fraction of unities preceding it. We show that the system undergoes a dynamical phase-transition from normal diffusion, in which the variance D_L scales as the string's length L, into a super-diffusion phase (D_L ~ L^{1+|alpha|}), when the correlation strength exceeds a critical value. We demonstrate the generality of our results with respect to alternative models, and discuss their applicability to various data, such as coarse-grained DNA sequences, written texts, and financial data.Comment: 4 pages, 4 figure

Hyperbolic planforms in relation to visual edges and textures perception

We propose to use bifurcation theory and pattern formation as theoretical probes for various hypotheses about the neural organization of the brain. This allows us to make predictions about the kinds of patterns that should be observed in the activity of real brains through, e.g. optical imaging, and opens the door to the design of experiments to test these hypotheses. We study the specific problem of visual edges and textures perception and suggest that these features may be represented at the population level in the visual cortex as a specific second-order tensor, the structure tensor, perhaps within a hypercolumn. We then extend the classical ring model to this case and show that its natural framework is the non-Euclidean hyperbolic geometry. This brings in the beautiful structure of its group of isometries and certain of its subgroups which have a direct interpretation in terms of the organization of the neural populations that are assumed to encode the structure tensor. By studying the bifurcations of the solutions of the structure tensor equations, the analog of the classical Wilson and Cowan equations, under the assumption of invariance with respect to the action of these subgroups, we predict the appearance of characteristic patterns. These patterns can be described by what we call hyperbolic or H-planforms that are reminiscent of Euclidean planar waves and of the planforms that were used in [1, 2] to account for some visual hallucinations. If these patterns could be observed through brain imaging techniques they would reveal the built-in or acquired invariance of the neural organization to the action of the corresponding subgroups.Comment: 34 pages, 11 figures, 2 table

On the Necessary Memory to Compute the Plurality in Multi-Agent Systems

We consider the Relative-Majority Problem (also known as Plurality), in which, given a multi-agent system where each agent is initially provided an input value out of a set of $k$ possible ones, each agent is required to eventually compute the input value with the highest frequency in the initial configuration. We consider the problem in the general Population Protocols model in which, given an underlying undirected connected graph whose nodes represent the agents, edges are selected by a globally fair scheduler. The state complexity that is required for solving the Plurality Problem (i.e., the minimum number of memory states that each agent needs to have in order to solve the problem), has been a long-standing open problem. The best protocol so far for the general multi-valued case requires polynomial memory: Salehkaleybar et al. (2015) devised a protocol that solves the problem by employing $O(k 2^k)$ states per agent, and they conjectured their upper bound to be optimal. On the other hand, under the strong assumption that agents initially agree on a total ordering of the initial input values, Gasieniec et al. (2017), provided an elegant logarithmic-memory plurality protocol. In this work, we refute Salehkaleybar et al.'s conjecture, by providing a plurality protocol which employs $O(k^{11})$ states per agent. Central to our result is an ordering protocol which allows to leverage on the plurality protocol by Gasieniec et al., of independent interest. We also provide a $\Omega(k^2)$-state lower bound on the necessary memory to solve the problem, proving that the Plurality Problem cannot be solved within the mere memory necessary to encode the output.Comment: 14 pages, accepted at CIAC 201

Self-Gravitating Strings In 2+1 Dimensions

We present a family of classical spacetimes in 2+1 dimensions. Such a spacetime is produced by a Nambu-Goto self-gravitating string. Due to the special properties of three-dimensional gravity, the metric is completely described as a Minkowski space with two identified worldsheets. In the flat limit, the standard string is recovered. The formalism is developed for an open string with massive endpoints, but applies to other boundary conditions as well. We consider another limit, where the string tension vanishes in geometrical units but the end-masses produce finite deficit angles. In this limit, our open string reduces to the free-masses solution of Gott, which possesses closed timelike curves when the relative motion of the two masses is sufficiently rapid. We discuss the possible causal structures of our spacetimes in other regimes. It is shown that the induced worldsheet Liouville mode obeys ({\it classically}) a differential equation, similar to the Liouville equation and reducing to it in the flat limit. A quadratic action formulation of this system is presented. The possibility and significance of quantizing the self-gravitating string, is discussed.Comment: 55 page

The Medium Is the Danger: Discourse about Television among Amish and Ultra-Orthodox (Haredi) Women

This study shows how Old Order Amish and ultra-Orthodox women’s discourse about television can help develop a better understanding of the creation, construction, and strengthening of limits and boundaries separating enclave cultures from the world. Based on questionnaires containing both closed- and open-ended questions completed by 82 participants, approximately half from each community, I argue that both communities can be understood as interpretive communities that negatively interpret not only television content, like other religious communities, but also the medium itself. Their various negative interpretive strategies is discussed and the article shows how they are part of an “us-versus-them” attitude created to mark the boundaries and walls that enclave cultures build around themselves. The comparison between the two communities found only a few small differences but one marked similarity: The communities perceive avoidance of a tool for communication, in this case television, as part of the communities’ sharing, participation, and common culture

How Insurance Substitutes For Regulation

Legal regulation of behavior requires information. Acquiring information about the regulated party\u27s conduct, setting benchmarks by which that conduct is measured, and establishing the correct scale of payoffs for violating or following regulation are costly and require expertise and motivation. Thus, economic theories of rulemaking are often based on the relative information advantages that different regulatory bodies have and how that information can be harnessed to enhance incentives and thereby improve welfare. Government regulators, on average, do not have informational advantages. They are not paid for performance and thus may lack adequate incentives. They are not disciplined by market forces and are only imperfectly disciplined by career concerns or by the political process. Moreover, they commonly lack the most advanced tools for information acquisition, aggregation, and prediction. Courts, for example, do not search for information independently, but instead receive only what parries present to them through the litigation process, which is costly, ad hoc, and as a result often bypassed by crude settlements. Courts are also ill-equipped to recognize the distribution of characreristics from which any given case is sampled

The Unintended Effects of Government-Subsidized Weather Insurance

Catastrophes from severe weather are perhaps the costliest accidents humanity faces. While we are still a long way from technologies that would abate the destructive force of storms, there is much we can do to reduce their effect. True, we cannot regulate the weather, but through smart governance and correct incentives we can influence human exposure to the risk of bad weather. We may not be able to control wind or storm surge, but we can prompt people to build sturdier homes with stronger roofs far from floodplains. We call these catastrophes natural disasters, but they are the result of a combination of natural forces and, we show here, often imprudent and shortsighted human decisions induced by questionable government policies. Regulating weather risk is an increasingly urgent social issue. Hurricane Katrina in 2005 and Hurricane Sandy in 2012 brought unprecedented property damage to the Gulf and coastal northeastern states. As a result of an enormous development enterprise, the majority of Florida real estate now lies in coastal areas affected by hurricane activity. And the potential rise of sea level and the resulting erosion of the coastline are putting at risk large chunks of prime real estate in numerous regions. Our thesis is simple: the most effective way to prepare for storms is through disaster insurance. But this preparation would not simply take the form that is commonly thought: insurance as a form of post-disaster relief. Rather, we see insurance as a form of private regulation of safety - a contractual device controlling and incentivizing behavior prior to the occurence of losses

Under the Weather: Government Insurance and the Regulation of Climate Risks

This Article explores the role of insurance as substitute for direct regulation of risks posed by severe weather. In pricing the risk of human activity along the predicted path of storms, insurance can provide incentives for efficient location decisions