Succinct Representation of Codes with Applications to Testing

Motivated by questions in property testing, we search for linear error-correcting codes that have the "single local orbit" property: i.e., they are specified by a single local constraint and its translations under the symmetry group of the code. We show that the dual of every "sparse" binary code whose coordinates are indexed by elements of F_{2^n} for prime n, and whose symmetry group includes the group of non-singular affine transformations of F_{2^n} has the single local orbit property. (A code is said to be "sparse" if it contains polynomially many codewords in its block length.) In particular this class includes the dual-BCH codes for whose duals (i.e., for BCH codes) simple bases were not known. Our result gives the first short (O(n)-bit, as opposed to the natural exp(n)-bit) description of a low-weight basis for BCH codes. The interest in the "single local orbit" property comes from the recent result of Kaufman and Sudan (STOC 2008) that shows that the duals of codes that have the single local orbit property under the affine symmetry group are locally testable. When combined with our main result, this shows that all sparse affine-invariant codes over the coordinates F_{2^n} for prime n are locally testable. If, in addition to n being prime, if 2^n-1 is also prime (i.e., 2^n-1 is a Mersenne prime), then we get that every sparse cyclic code also has the single local orbit. In particular this implies that BCH codes of Mersenne prime length are generated by a single low-weight codeword and its cyclic shifts

Statistical mechanics and thermodynamics of viral evolution

This paper uses methods drawn from physics to study the life cycle of viruses. The paper analyzes a model of viral infection and evolution using the "grand canonical ensemble" and formalisms from statistical mechanics and thermodynamics. Using this approach we enumerate all possible genetic states of a model virus and host as a function of two independent pressures-immune response and system temperature. We prove the system has a real thermodynamic temperature, and discover a new phase transition between a positive temperature regime of normal replication and a negative temperature "disordered" phase of the virus. We distinguish this from previous observations of a phase transition that arises as a function of mutation rate. From an evolutionary biology point of view, at steady state the viruses naturally evolve to distinct quasispecies. This paper also reveals a universal relationship that relates the order parameter (as a measure of mutational robustness) to evolvability in agreement with recent experimental and theoretical work. Given that real viruses have finite length RNA segments that encode proteins which determine virus fitness, the approach used here could be refined to apply to real biological systems, perhaps providing insight into immune escape, the emergence of novel pathogens and other results of viral evolution

The cost of simplifying air travel when modeling disease spread

Background: Air travel plays a key role in the spread of many pathogens. Modeling the long distance spread of infectious disease in these cases requires an air travel model. Highly detailed air transportation models can be over determined and computationally problematic. We compared the predictions of a simplified air transport model with those of a model of all routes and assessed the impact of differences on models of infectious disease. Methodology/Principal Findings: Using U.S. ticket data from 2007, we compared a simplified "pipe" model, in which individuals flow in and out of the air transport system based on the number of arrivals and departures from a given airport, to a fully saturated model where all routes are modeled individually. We also compared the pipe model to a "gravity" model where the probability of travel is scaled by physical distance; the gravity model did not differ significantly from the pipe model. The pipe model roughly approximated actual air travel, but tended to overestimate the number of trips between small airports and underestimate travel between major east and west coast airports. For most routes, the maximum number of false (or missed) introductions of disease is small (<1 per day) but for a few routes this rate is greatly underestimated by the pipe model. Conclusions/Significance: If our interest is in large scale regional and national effects of disease, the simplified pipe model may be adequate. If we are interested in specific effects of interventions on particular air routes or the time for the disease to reach a particular location, a more complex point-to-point model will be more accurate. For many problems a hybrid model that independently models some frequently traveled routes may be the best choice. Regardless of the model used, the effect of simplifications and sensitivity to errors in parameter estimation should be analyzed

The \u3ci\u3eExxon Valdez\u3c/i\u3e Reopener: Natural Resources Damage Settlements and Roads Not Taken

The 1989 Exxon Valdez oil spill caused extensive natural resource damage to the Prince William Sound. Lawsuits addressing this natural resource damage resulted in a settlement that required Exxon to pay $900 million over time to trustees charged with spending this money to restore the damaged environment of the Sound and nearby areas. The settlement included a “Reopener Clause,” which pledges Exxon to spend an additional$100 million to fund restoration or rehabilitation of resources whose injuries were not foreseeable in 1989. This Article urges the State of Alaska and the United States to seek enforcement of the Reopener Clause, to restore natural resources and Native subsistence uses that were not addressed in the initial settlement and have not recovered from the Exxon Valdez oil spill. Alternatively, this Article urges Native entities to intervene in the case and seek enforcement of the Reopener Clause. To date, neither Alaska nor the federal government have requested any of the $100 million Exxon may be required to pay to compensate for additional damages resulting from the oil spill. We offer extended comment on this most famous of all natural resource damage cases. Special attention will be paid to legal roads not taken

A global model of malaria climate sensitivity: Comparing malaria response to historic climate data based on simulation and officially reported malaria incidence

Background: The role of the Anopheles vector in malaria transmission and the effect of climate on Anopheles populations are well established. Models of the impact of climate change on the global malaria burden now have access to high-resolution climate data, but malaria surveillance data tends to be less precise, making model calibration problematic. Measurement of malaria response to fluctuations in climate variables offers a way to address these difficulties. Given the demonstrated sensitivity of malaria transmission to vector capacity, this work tests response functions to fluctuations in land surface temperature and precipitation. Methods. This study of regional sensitivity of malaria incidence to year-to-year climate variations used an extended Macdonald Ross compartmental disease model (to compute malaria incidence) built on top of a global Anopheles vector capacity model (based on 10years of satellite climate data). The predicted incidence was compared with estimates from the World Health Organization and the Malaria Atlas. The models and denominator data used are freely available through the Eclipse Foundations Spatiotemporal Epidemiological Modeller (STEM). Results: Although the absolute scale factor relating reported malaria to absolute incidence is uncertain, there is a positive correlation between predicted and reported year-to-year variation in malaria burden with an averaged root mean square (RMS) error of 25% comparing normalized incidence across 86 countries. Based on this, the proposed measure of sensitivity of malaria to variations in climate variables indicates locations where malaria is most likely to increase or decrease in response to specific climate factors. Bootstrapping measures the increased uncertainty in predicting malaria sensitivity when reporting is restricted to national level and an annual basis. Results indicate a potential 20x improvement in accuracy if data were available at the level ISO 3166-2 national subdivisions and with monthly time sampling. Conclusions: The high spatial resolution possible with state-of-the-art numerical models can identify regions most likely to require intervention due to climate changes. Higher-resolution surveillance data can provide a better understanding of how climate fluctuations affect malaria incidence and improve predictions. An open-source modelling framework, such as STEM, can be a valuable tool for the scientific community and provide a collaborative platform for developing such models

Long Range Magnetic Order and the Darwin Lagrangian

We simulate a finite system of $N$ confined electrons with inclusion of the Darwin magnetic interaction in two- and three-dimensions. The lowest energy states are located using the steepest descent quenching adapted for velocity dependent potentials. Below a critical density the ground state is a static Wigner lattice. For supercritical density the ground state has a non-zero kinetic energy. The critical density decreases with $N$ for exponential confinement but not for harmonic confinement. The lowest energy state also depends on the confinement and dimension: an antiferromagnetic cluster forms for harmonic confinement in two dimensions.Comment: 5 figure

Gender moderates the relationship between empathy and aggressiveness in sport: The mediating role of anger

This research investigated whether gender moderates, and anger mediates, the relationship between empathy (i.e., perspective taking and empathic concern) and aggressiveness in sport. In Study 1, perspective taking and empathic concern were negatively associated with aggressiveness, and this effect was stronger in women compared to men. In Study 2, perspective taking was a negative predictor of aggressiveness and antisocial behavior in sport, and anger mediated these relationships in women, but not in men. Our findings suggest that empathy and emotion-based strategies targeted at reducing aggressiveness in sport need to be tailored for males and females

A terminal assessment of stages theory : introducing a dynamic states approach to entrepreneurship

Stages of Growth models were the most frequent theoretical approach to understanding entrepreneurial business growth from 1962 to 2006; they built on the growth imperative and developmental models of that time. An analysis of the universe of such models (N=104) published in the management literature shows no consensus on basic constructs of the approach, nor is there any empirical confirmations of stages theory. However, by changing two propositions of the stages models, a new dynamic states approach is derived. The dynamic states approach has far greater explanatory power than its precursor, and is compatible with leading edge research in entrepreneurship

Tune in to your emotions: a robust personalized affective music player

The emotional power of music is exploited in a personalized affective music player (AMP) that selects music for mood enhancement. A biosignal approach is used to measure listeners’ personal emotional reactions to their own music as input for affective user models. Regression and kernel density estimation are applied to model the physiological changes the music elicits. Using these models, personalized music selections based on an affective goal state can be made. The AMP was validated in real-world trials over the course of several weeks. Results show that our models can cope with noisy situations and handle large inter-individual differences in the music domain. The AMP augments music listening where its techniques enable automated affect guidance. Our approach provides valuable insights for affective computing and user modeling, for which the AMP is a suitable carrier application