We consider a population constituted by two types of individuals; each of them can produce offspring in two different islands (as a particular case the islands can be interpreted as active or dormant individuals). We model the evolution of the popula
tion of each type using a two-type Feller diffusion with immigration, and we study the frequency of one of the types, in each island, when the total population size in each island is forced to be constant at a dense set of times. This leads to the solution of a SDE which we call the asymmetric two-island frequency process. We derive properties of this process and obtain a large population limit when the total size of each island tends to infinity. Additionally, we compute the fluctuations of the process around its deterministic limit. We establish conditions under which the asymmetric two-island frequency process has a moment dual. The dual is a continuous-time two-dimensional Markov chain that can be interpreted in terms of mutation, branching, pairwise branching, coalescence, and a novel mixed selection-migration term. Also, we conduct a stability analysis of the limiting deterministic dynamical system and present some numerical results to study fixation and a new form of balancing selection. When restricting to the seedbank model, we observe that some combinations of the parameters lead to balancing selection. Besides finding yet another way in which genetic reservoirs increase the genetic variability, we find that if a population that sustains a seedbank competes with one that does not, the seed producers will have a selective advantage if they reproduce faster, but will not have a selective disadvantage if they reproduce slower: their worst case scenario is balancing selection.
In game development, designing compelling visual assets that convey gameplay-relevant features requires time and experience. Recent image generation methods that create high-quality content could reduce development costs, but these approaches do not
consider game mechanics. We propose a Convolutional Variational Autoencoder (CVAE) system to modify and generate new game visuals based on their gameplay relevance. We test this approach with Pokemon sprites and Pokemon type information, since types are one of the games core mechanics and they directly impact the games visuals. Our experimental results indicate that adopting a transfer learning approach can help to improve visual quality and stability over unseen data.
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Fernando Cordero
, Adrian Gonzalez Casanova
, Jason Schweinsberg andn Maite Wilke-Berenguer
2020
Consider a population evolving from year to year through three seasons: spring, summer and winter. Every spring starts with $N$ dormant individuals waking up independently of each other according to a given distribution. Once an individual is awake,
it starts reproducing at a constant rate. By the end of spring, all individuals are awake and continue reproducing independently as Yule processes during the whole summer. In the winter, $N$ individuals chosen uniformly at random go to sleep until the next spring, and the other individuals die. We show that because an individual that wakes up unusually early can have a large number of surviving descendants, for some choices of model parameters the genealogy of the population will be described by a $Lambda$-coalescent. In particular, the beta coalescent can describe the genealogy when the rate at which individuals wake up increases exponentially over time. We also characterize the set of all $Lambda$-coalescents that can arise in this framework.
Humans can infer a great deal about the meaning of a word, using the syntax and semantics of surrounding words even if it is their first time reading or hearing it. We can also generalise the learned concept of the word to new tasks. Despite great pr
ogress in achieving human-level performance in certain tasks (Silver et al., 2016), learning from one or few examples remains a key challenge in machine learning, and has not thoroughly been explored in Natural Language Processing (NLP). In this work we tackle the problem of oneshot learning for an NLP task by employing ideas from recent developments in machine learning: embeddings, attention mechanisms (softmax) and similarity measures (cosine, Euclidean, Poincare, and Minkowski). We adapt the framework suggested in matching networks (Vinyals et al., 2016), and explore the effectiveness of the aforementioned methods in one, two and three-shot learning problems on the task of predicting missing word explored in (Vinyals et al., 2016) by using the WikiText-2 dataset. Our work contributes in two ways: Our first contribution is that we explore the effectiveness of different distance metrics on k-shot learning, and show that there is no single best distance metric for k-shot learning, which challenges common belief. We found that the performance of a distance metric depends on the number of shots used during training. The second contribution of our work is that we establish a benchmark for one, two, and three-shot learning on a language task with a publicly available dataset that can be used to benchmark against in future research.
We analyse a family of two-types Wright-Fisher models with selection in a random environment and skewed offspring distribution. We provide a calculable criterion to quantify the impact of different shapes of selection on the fate of the weakest allel
e, and thus compare them. The main mathematical tool is duality, which we prove to hold, also in presence of random environment (quenched and in some cases annealed), between the populations allele frequencies and genealogy, both in the case of finite population size and in the scaling limit for large size. Duality also yields new insight on properties of branching-coalescing processes in random environment, such as their long term behaviour.
We introduce a new Wright-Fisher type model for seed banks incorporating simultaneous switching, which is motivated by recent work on microbial dormancy. We show that the simultaneous switching mechanism leads to a new jump-diffusion limit for the sc
aled frequency processes, extending the classical Wright-Fisher and seed bank diffusion limits. We further establish a new dual coalescent structure with multiple activation and deactivation events of lineages. While this seems reminiscent of multiple merger events in general exchangeable coalescents, it actually leads to an entirely new class of coalescent processes with unique qualitative and quantitative behaviour. To illustrate this, we provide a novel kind of condition for coming down from infinity for these coalescents using recent results of Griffiths.
DNA is a flexible molecule, but the degree of its flexibility is subject to debate. The commonly-accepted persistence length of $l_p approx 500,$AA is inconsistent with recent studies on short-chain DNA that show much greater flexibility but do not p
robe its origin. We have performed X-ray and neutron small-angle scattering on a short DNA sequence containing a strong nucleosome positioning element, and analyzed the results using a modified Kratky-Porod model to determine possible conformations. Our results support a hypothesis from Crick and Klug in 1975 that some DNA sequences in solution can have sharp kinks, potentially resolving the discrepancy. Our conclusions are supported by measurements on a radiation-damaged sample, where single-strand breaks lead to increased flexibility and by an analysis of data from another sequence, which does not have kinks, but where our method can detect a locally enhanced flexibility due to an $AT$-domain.
We revisit the model by Wiser, Ribeck, and Lenski (Science textbf{342} (2013), 1364--1367), which describes how the mean fitness increases over time due to beneficial mutations in Lenskis long-term evolution experiment. We develop the model further b
oth conceptually and mathematically. Conceptually, we describe the experiment with the help of a Cannings model with mutation and selection, where the latter includes diminishing returns epistasis. The analysis sheds light on the growth dynamics within every single day and reveals a runtime effect, that is, the shortening of the daily growth period with increasing fitness; and it allows to clarify the contribution of epistasis to the mean fitness curve. Mathematically, we explain rigorous results in terms of a law of large numbers (in the limit of infinite population size and for a certain asymptotic parameter regime), and present approximations based on heuristics and supported by simulations for finite populations.
We investigate various aspects of the (biallelic) Wright-Fisher diffusion with seed bank in conjunction with and contrast to the two-island model analysed e.g. in Kermany, Zhou and Hickey, 2008, and Nath and Griffiths, 1993, including moments, statio
nary distribution and reversibility, for which our main tool is duality. Further, we show that the Wright-Fisher diffusion with seed bank can be reformulated as a one-dimensional stochastic delay differential equation, providing an elegant interpretation of the age structure in the seed bank also forward in time in the spirit of Kaj, Krone and Lascoux, 2001. We also provide a complete boundary classification for this two-dimensional SDE using martingale-based reasoning known as McKeans argument.
We investigate the behaviour of the genealogy of a Wright-Fisher population model under the influence of a strong seed-bank effect. More precisely, we consider a simple seed-bank age distribution with two atoms, leading to either classical or long ge
nealogical jumps (the latter modeling the effect of seed-dormancy). We assume that the length of these long jumps scales like a power $N^beta$ of the original population size $N$, thus giving rise to a `strong seed-bank effect. For a certain range of $beta$, we prove that the ancestral process of a sample of $n$ individuals converges under a non-classical time-scaling to Kingmans $n-$coalescent. Further, for a wider range of parameters, we analyze the time to the most recent common ancestor of two individuals analytically and by simulation.
