An exomoon survey of 70 cool giant exoplanets and the new candidate Kepler-1708 b-i

Exomoons represent a crucial missing puzzle piece in our efforts to understand extrasolar planetary systems. To address this deficiency, we here describe an exomoon survey of 70 cool, giant transiting exoplanet candidates found by Kepler. We identify only one exhibiting a moon-like signal that passes a battery of vetting tests: Kepler-1708 b. We show that Kepler-1708 b is a statistically validated Jupiter-sized planet orbiting a Sun-like quiescent star at 1.6 au. The signal of the exomoon candidate, Kepler-1708 b-i, is a 4.8σ effect and is persistent across different instrumental detrending methods, with a 1% false-positive probability via injection–recovery. Kepler-1708 b-i is ~2.6 Earth radii and is located in an approximately coplanar orbit at ~12 planetary radii from its ~1.6 au Jupiter-sized host. Future observations will be necessary to validate or reject the candidate.

Influence of sequencing depth on the fidelity and sensitivity of 1%-5% low-frequency mutation detection and recommendation for standardization of sequencing depth

Sequencing depth has always played an important role in the accurate detection of low-frequency mutations. The increase of sequencing depth and the reasonable setting of threshold can maximize the probability of true positive mutation, or sensitivity. Here, we found that when the threshold was set as a fixed number of positive mutated reads, the probability of both true and false-positive mutations increased with depth. However, When the number of positive mutated reads increased in an equal proportion with depth (the threshold was transformed from a fixed number to a fixed percentage of mutated reads), the true positive probability still increased while false positive probability decreased. Through binomial distribution simulation and experimental test, it is found that the "fidelity" of detected-VAFs is the cause of this phenomenon. Firstly, we used the binomial distribution to construct a model that can easily calculate the relationship between sequencing depth and probability of true positive (or false positive), which can standardize the minimum sequencing depth for different low-frequency mutation detection. Then, the effect of sequencing depth on the fidelity of NA12878 with 3% mutation frequency and circulating tumor DNA (ctDNA of 1%, 3% and 5%) showed that the increase of sequencing depth reduced the fluctuation range of detected-VAFs around the expected VAFs, that is, the fidelity was improved. Finally, based on our experiment result, the consistency of single-nucleotide variants (SNVs) between paired FF and FFPE samples of mice increased with increasing depth, suggesting that increasing depth can improve the precision and sensitivity of low-frequency mutations.

Stochastic rumors on random trees

The Maki–Thompson rumor model is defined by assuming that a population represented by a graph is subdivided into three classes of individuals; namely, ignorants, spreaders and stiflers. A spreader tells the rumor to any of its nearest ignorant neighbors at rate one. At the same rate, a spreader becomes a stifler after a contact with other nearest neighbor spreaders, or stiflers. In this work we study the model on random trees. As usual we define a critical parameter of the model as the critical value around which the rumor either becomes extinct almost-surely or survives with positive probability. We analyze the existence of phase-transition regarding the survival of the rumor, and we obtain estimates for the mean range of the rumor. The applicability of our results is illustrated with examples on random trees generated from some well-known discrete distributions.

Quasi-stationary probability distribution for the SIR epidemic model

In this paper, we propose two new approximations to the joint quasi-stationary distribution (QSD) of the number susceptible and infected individuals in the Susceptible-Infected-Recovered (SIR) stochastic epidemic model and we derive the marginal QSD of the infected individuals. These two approximations depend on the basic reproduction number [Formula: see text] and give a positive probability of the QSD to all the transient states. Numerical comparisons are presented to check the accuracy of these approximations.

Lack of Commitment, Retroactive Taxation, and Macroeconomic Instability

Retroactive tax legislation is constitutional in most high-income countries. In this paper we are concerned with the fiscal and macroeconomic consequences stemming from retroactive income taxation. Within the context of a real neoclassical economy, we find that if the government can set taxes retroactively within the fiscal year—or if there is a positive probability that a future government will be able to use retroactive taxation—then there exists a multiplicity of expectations-driven equilibria. In this case, neither fiscal policy nor macroeconomic aggregates are uniquely pinned down by economic fundamentals. Rather, they are determined by expectations about current and future fiscal policy. This implies that the government is a source of macroeconomic instability. By contrast, a constitutional reform banning the government from using retroactive tax legislation would yield a unique equilibrium, thus removing the possibility of expectations-driven fluctuations.

Planarity and non-separating cycles in uniform high genus quadrangulations

We study large uniform random bipartite quadrangulations whose genus grows linearly with the number of faces. Their local convergence was recently established by Budzinski and the author [9, 10]. Here we study several properties of these objects which are not captured by the local topology. Namely we show that balls around the root are planar with high probability up to logarithmic radius, and we prove that there exist non-contractible cycles of constant length with positive probability.

Heterogeneous coalitions and social revolutions

We have explained the presence of heterogeneous winning coalitions in social revolutions. In an overcrowded agrarian society, two almost identical non-productive enforcers, the landed political elite, collude and bargain over transfers with one of the two peasants to contest over a piece of land, as property rights for land are not well defined. In any other scenario, neither the grand coalition nor the coalition of two peasants and one enforcer forms, thereby deposing the other enforcer with positive probability. So, social revolutions never occur. If foreign wars weaken an enforcer, such as in China (1911), France, and Russia, adding one unit of capital makes the coalition of the peasant, the now worker, and one of the enforcers (now an industrial political elite) attractive: The excess labor can work with it; the weaker enforcer retaliates less and the stronger one more, if excluded. However, if the weaker one (the still-landed political elite) proposes first, a grand coalition forms in which he or she gets less than the other members do (desertion). There is conflict among peasants and among landed elites; thus, the concept of a coalition is more appropriate than that of a class.

ON PROFITABILITY OF NAKAMOTO DOUBLE SPEND

Nakamoto doublespend strategy, described in Bitcoin foundational article, leads to total ruin with positive probability. The simplest strategy that avoids this risk incorporates a stopping threshold when success is unlikely. We compute the exact profitability and the minimal double spend that is profitable for this strategy. For a given amount of the transaction, we determine the minimal number of confirmations to be requested by the recipient that makes the double-spend strategy non-profitable. This number of confirmations is only 1 or 2 for average transactions and for a small relative hashrate of the attacker. This is substantially lower than the original Nakamoto number, which is about six confirmations and is widely used. Nakamoto analysis is only based on the success probability of the attack instead of on a profitability analysis that we carry out.

Pattanaik’s axioms and existence of preferred with probability at least half winners

In this paper we show that three conditions due to Pattanaik, when satisfied by a given profile of state-dependent preferences (linear orders) on a given and fixed set of alternatives and a probability distribution with which the various states of nature occur, are individually sufficient, for the non-emptiness of the set of alternative(s) which are individually preferred to all alternatives other than itself with probability at least half. Prior to this, we show that since each axiom individually implies Sen-Coherence, then, as a consequence of a result obtained earlier, each axiom along with asymmetry of the ‘preferred with at probability at least half” relation implies the transitivity of the relation. All the sufficient conditions discussed here are required to be applicable at least to all those otherwise relevant events that have positive probability. This observation also applies to a sufficient condition for the non-emptiness of the set of alternative(s) which are individually preferred to all alternatives other than itself with probability at least half, called Generalised Sen Coherence introduced and discussed in earlier research.

Limit Points of Endogenous Misspecified Learning

We study how an agent learns from endogenous data when their prior belief is misspecified. We show that only uniform Berk–Nash equilibria can be long‐run outcomes, and that all uniformly strict Berk–Nash equilibria have an arbitrarily high probability of being the long‐run outcome for some initial beliefs. When the agent believes the outcome distribution is exogenous, every uniformly strict Berk–Nash equilibrium has positive probability of being the long‐run outcome for any initial belief. We generalize these results to settings where the agent observes a signal before acting.