AutonoVi: Autonomous Vehicle Planning with Dynamic Maneuvers and Traffic Constraints

We present AutonoVi:, a novel algorithm for autonomous vehicle navigation that supports dynamic maneuvers and satisfies traffic constraints and norms. Our approach is based on optimization-based maneuver planning that supports dynamic lane-changes, swerving, and braking in all traffic scenarios and guides the vehicle to its goal position. We take into account various traffic constraints, including collision avoidance with other vehicles, pedestrians, and cyclists using control velocity obstacles. We use a data-driven approach to model the vehicle dynamics for control and collision avoidance. Furthermore, our trajectory computation algorithm takes into account traffic rules and behaviors, such as stopping at intersections and stoplights, based on an arc-spline representation. We have evaluated our algorithm in a simulated environment and tested its interactive performance in urban and highway driving scenarios with tens of vehicles, pedestrians, and cyclists. These scenarios include jaywalking pedestrians, sudden stops from high speeds, safely passing cyclists, a vehicle suddenly swerving into the roadway, and high-density traffic where the vehicle must change lanes to progress more effectively.Comment: 9 pages, 6 figure

The evolution of costly acquired immune memory

A key feature of the vertebrate adaptive immune system is acquired immune memory, whereby hosts launch a faster and heightened response when challenged by previously encountered pathogens, preventing full infection. Here, we use a mathematical model to explore the role of ecological and epidemiological processes in shaping selection for costly acquired immune memory. Applying the framework of adaptive dynamics to the classic SIR (Susceptible-Infected-Recovered) epidemiological model, we focus on the conditions that may lead hosts to evolve high levels of immunity. Linking our work to previous theory, we show how investment in immune memory may be greatest at long or intermediate host lifespans depending on whether immunity is long lasting. High initial costs to gain immunity are also found to be essential for a highly effective immune memory. We also find that high disease infectivity and sterility, but intermediate virulence and immune period, increase selection for immunity. Diversity in host populations through evolutionary branching is found to be possible but only for a limited range of parameter space. Our model suggests that specific ecological and epidemiological conditions have to be met for acquired immune memory to evolve

On the Polynomial Szemer\'edi Theorem in Finite Commutative Rings

The polynomial Szemer\'{e}di theorem implies that, for any $\delta \in (0,1)$, any family $\{P_1,\ldots, P_m\} \subset \mathbb{Z}[y]$ of nonconstant polynomials with constant term zero, and any sufficiently large $N$, every subset of $\{1,\ldots, N\}$ of cardinality at least $\delta N$ contains a nontrivial configuration of the form $\{x,x+P_1(y),\ldots, x+P_m(y)\}$. When the polynomials are assumed independent, one can expect a sharper result to hold over finite fields, special cases of which were proven recently, culminating with arXiv:1802.02200, which deals with the general case of independent polynomials. One goal of this article is to explain these theorems as the result of joint ergodicity in the presence of asymptotic total ergodicity. Guided by this concept, we establish, over general finite commutative rings, a version of the polynomial Szemer\'{e}di theorem for independent polynomials $\{P_1,\ldots, P_m\} \subset \mathbb{Z}[y_1,\ldots, y_n]$, deriving new combinatorial consequences, such as the following. Let $\mathcal R$ be a collection of finite commutative rings subject to a mild condition on their torsion. There exists $\gamma \in (0,1)$ such that, for every $R \in \mathcal R$, every subset $A \subset R$ of cardinality at least $|R|^{1-\gamma}$ contains a nontrivial configuration $\{x,x+P_1(y),\ldots, x+P_m(y)\}$ for some $(x,y) \in R \times R^n$, and, moreover, for any subsets $A_0,\ldots, A_m \subset R$ such that $|A_0|\cdots |A_m| \geq |R|^{(m+1)(1-\gamma)}$, there is a nontrivial configuration $(x, x+P_1(y), \ldots, x+P_m(y)) \in A_0\times \cdots \times A_m$. The fact that general rings have zero divisors is the source of many obstacles, which we overcome; for example, by studying character sums, we develop a bound on the number of roots of an integer polynomial over a general finite commutative ring, a result which is of independent interest.Comment: 110 page

The emergence of 4-cycles in polynomial maps over the extended integers

Let $f(x) \in \mathbb{Z}[x]$; for each integer $\alpha$ it is interesting to consider the number of iterates $n_{\alpha}$, if possible, needed to satisfy $f^{n_{\alpha}}(\alpha) = \alpha$. The sets $\{\alpha, f(\alpha), \ldots, f^{n_{\alpha} - 1}(\alpha), \alpha\}$ generated by the iterates of $f$ are called cycles. For $\mathbb{Z}[x]$ it is known that cycles of length 1 and 2 occur, and no others. While much is known for extensions to number fields, we concentrate on extending $\mathbb{Z}$ by adjoining reciprocals of primes. Let $\mathbb{Z}[1/p_1, \ldots, 1/p_n]$ denote $\mathbb{Z}$ extended by adding in the reciprocals of the $n$ primes $p_1, \ldots, p_n$ and all their products and powers with each other and the elements of $\mathbb{Z}$. Interestingly, cycles of length 4, called 4-cycles, emerge for polynomials in $\mathbb{Z}\left[1/p_1, \ldots, 1/p_n\right][x]$ under the appropriate conditions. The problem of finding criteria under which 4-cycles emerge is equivalent to determining how often a sum of four terms is zero, where the terms are $\pm 1$ times a product of elements from the list of $n$ primes. We investigate conditions on sets of primes under which 4-cycles emerge. We characterize when 4-cycles emerge if the set has one or two primes, and (assuming a generalization of the ABC conjecture) find conditions on sets of primes guaranteed not to cause 4-cycles to emerge.Comment: 14 pages, 1 figur

Study protocol for a randomised controlled trial evaluating the effect of prenatal omega-3 LCPUFA supplementation to reduce the incidence of preterm birth: The ORIP trial

Introduction: Preterm birth accounts for more than 85% of all perinatal complications and deaths. Seventy-five per cent of early preterm births (EPTBs) occur spontaneously and without identifiable risk factors. The need for a broadly applicable, effective strategy for primary prevention is paramount. Secondary outcomes from the docosahexaenoic acid (DHA) to Optimise Mother Infant Outcome trial showed that maternal supplementation until delivery with omega-3 (ω-3) long chain polyunsaturated fatty acid (LCPUFA), predominantly as DHA, resulted in a 50% reduction in the incidence of EPTB and an increase in the incidence of post-term induction or post-term prelabour caesarean section due to extended gestation. We aim to determine the effectiveness of supplementing the maternal diet with ω-3 LCPUFA until 34 weeks’ gestation on the incidence of EPTB. Methods and analysis: This is a multicentre, parallel group, randomised, blinded and controlled trial. Women less than 20 weeks’ gestation with a singleton or multiple pregnancy and able to give informed consent are eligible to participate. Women will be randomised to receive high DHA fish oil capsules or control capsules without DHA. Capsules will be taken from enrolment until 34 weeks’ gestation. The primary outcome is the incidence of EPTB, defined as delivery before 34 completed weeks’ gestation. Key secondary outcomes include length of gestation, incidence of post-term induction or prelabour caesarean section and spontaneous EPTB. The target sample size is 5540 women (2770 per group), which will provide 85% power to detect an absolute reduction in the incidence of preterm birth of 1.16% (from 2.45% to 1.29%) between the DHA and control group (two sided α=0.05). The primary analysis will be based on the intention-to-treat principle. Trial registration number: Australia and New Zealand Clinical Trial Registry Number: 2613001142729; Pre-results

Ramsey Theory Problems over the Integers: Avoiding Generalized Progressions

Two well studied Ramsey-theoretic problems consider subsets of the natural numbers which either contain no three elements in arithmetic progression, or in geometric progression. We study generalizations of this problem, by varying the kinds of progressions to be avoided and the metrics used to evaluate the density of the resulting subsets. One can view a 3-term arithmetic progression as a sequence $x, f_n(x), f_n(f_n(x))$, where $f_n(x) = x + n$, $n$ a nonzero integer. Thus avoiding three-term arithmetic progressions is equivalent to containing no three elements of the form $x, f_n(x), f_n(f_n(x))$ with $f_n \in\mathcal{F}_{\rm t}$, the set of integer translations. One can similarly construct related progressions using different families of functions. We investigate several such families, including geometric progressions ($f_n(x) = nx$ with $n > 1$ a natural number) and exponential progressions ($f_n(x) = x^n$). Progression-free sets are often constructed "greedily," including every number so long as it is not in progression with any of the previous elements. Rankin characterized the greedy geometric-progression-free set in terms of the greedy arithmetic set. We characterize the greedy exponential set and prove that it has asymptotic density 1, and then discuss how the optimality of the greedy set depends on the family of functions used to define progressions. Traditionally, the size of a progression-free set is measured using the (upper) asymptotic density, however we consider several different notions of density, including the uniform and exponential densities.Comment: Version 1.0, 13 page

SPA: Verbal Interactions between Agents and Avatars in Shared Virtual Environments using Propositional Planning

We present a novel approach for generating plausible verbal interactions between virtual human-like agents and user avatars in shared virtual environments. Sense-Plan-Ask, or SPA, extends prior work in propositional planning and natural language processing to enable agents to plan with uncertain information, and leverage question and answer dialogue with other agents and avatars to obtain the needed information and complete their goals. The agents are additionally able to respond to questions from the avatars and other agents using natural-language enabling real-time multi-agent multi-avatar communication environments. Our algorithm can simulate tens of virtual agents at interactive rates interacting, moving, communicating, planning, and replanning. We find that our algorithm creates a small runtime cost and enables agents to complete their goals more effectively than agents without the ability to leverage natural-language communication. We demonstrate quantitative results on a set of simulated benchmarks and detail the results of a preliminary user-study conducted to evaluate the plausibility of the virtual interactions generated by SPA. Overall, we find that participants prefer SPA to prior techniques in 84\% of responses including significant benefits in terms of the plausibility of natural-language interactions and the positive impact of those interactions

Evolution of host resistance towards pathogen exclusion: the role of predators

Question: Can increased host resistance drive a pathogen to extinction? Do more complex ecosystems lead to significantly different evolutionary behaviour and new potential extinctions? Mathematical method: Merging host-parasite models with predator-prey models. Analytically studying evolution using adaptive dynamics and trade-off and invasion plots, and carrying out numerical simulations. Key assumptions: Mass action (general mixing). All individuals of a given phenotype are identical. Only prey vulnerable to infection. Mutations are small and rare (however, the assumption on the size of mutation is relaxed later). In simulations, very small (negligible) populations are at risk of extinction. Conclusions: The presence of the predator can significantly change evolutionary outcomes for host resistance to a pathogen and can create branching points where none occurred previously. The pathogen (and sometimes the predator) is protected from exclusion if we take mutations to be arbitrarily small; however, relaxing the assumption on mutation size can lead to its exclusion. Increased resistance can drive the predator and/or pathogen to extinction depending on inter-species dynamics, such as the predator's preference for infected prey. Predator co-evolution can move exclusion boundaries and prevent the predator's own extinction if its rate of mutation is high enough (with respect to that of the prey)