Self-exciting price impact via negative resilience in stochastic order books

Most of the existing literature on optimal trade execution in limit order book models assumes that resilience is positive. But negative resilience also has a natural interpretation, as it models self-exciting behaviour of the price impact, where trading activities of the large investor stimulate other market participants to trade in the same direction. In the paper we discuss several new qualitative effects on optimal trade execution that arise when we allow resilience to take negative values. We do this in a framework where both market depth and resilience are stochastic processes.Comment: 27 pages; title of first version: On effects of negative resilience on optimal trade execution in stochastic order book

Deep neural networks with ReLU, leaky ReLU, and softplus activation provably overcome the curse of dimensionality for Kolmogorov partial differential equations with Lipschitz nonlinearities in the LpL^p-sense

Recently, several deep learning (DL) methods for approximating high-dimensional partial differential equations (PDEs) have been proposed. The interest that these methods have generated in the literature is in large part due to simulations which appear to demonstrate that such DL methods have the capacity to overcome the curse of dimensionality (COD) for PDEs in the sense that the number of computational operations they require to achieve a certain approximation accuracy $\varepsilon\in(0,\infty)$ grows at most polynomially in the PDE dimension $d\in\mathbb N$ and the reciprocal of $\varepsilon$. While there is thus far no mathematical result that proves that one of such methods is indeed capable of overcoming the COD, there are now a number of rigorous results in the literature that show that deep neural networks (DNNs) have the expressive power to approximate PDE solutions without the COD in the sense that the number of parameters used to describe the approximating DNN grows at most polynomially in both the PDE dimension $d\in\mathbb N$ and the reciprocal of the approximation accuracy $\varepsilon>0$. Roughly speaking, in the literature it is has been proved for every $T>0$ that solutions $u_d\colon [0,T]\times\mathbb R^d\to \mathbb R$, $d\in\mathbb N$, of semilinear heat PDEs with Lipschitz continuous nonlinearities can be approximated by DNNs with ReLU activation at the terminal time in the $L^2$-sense without the COD provided that the initial value functions $\mathbb R^d\ni x\mapsto u_d(0,x)\in\mathbb R$, $d\in\mathbb N$, can be approximated by ReLU DNNs without the COD. It is the key contribution of this work to generalize this result by establishing this statement in the $L^p$-sense with $p\in(0,\infty)$ and by allowing the activation function to be more general covering the ReLU, the leaky ReLU, and the softplus activation functions as special cases.Comment: 52 page

Paving the way : a future without inertia is closer than you think

Unless you have been hibernating in a remote cave for the past decade, you will have noticed the explosion of variable renewable generation. Wind power and solar photovoltaics (PVs) have been the subject of dozens of articles, just within the pages of IEEE Power & Energy Magazine. Charts illustrating relentless growth, such as the example from the United States shown in Figure 1 with futures tending toward 100% renewable energy, are common. This figure, provided by the National Renewable Energy Laboratory (NREL), reflects a low-cost, high-renewable projection scenario

Sex-dependent dissociation between emotional appraisal and memory: a large-scale behavioral and fMRI study

Extensive evidence indicates that women outperform men in episodic memory tasks. Furthermore, women are known to evaluate emotional stimuli as more arousing than men. Because emotional arousal typically increases episodic memory formation, the females' memory advantage might be more pronounced for emotionally arousing information than for neutral information. Here, we report behavioral data from 3398 subjects, who performed picture rating and memory tasks, and corresponding fMRI data from up to 696 subjects. We were interested in the interaction between sex and valence category on emotional appraisal, memory performances, and fMRI activity. The behavioral results showed that females evaluate in particular negative (p < 10(-16)) and positive (p = 2 × 10(-4)), but not neutral pictures, as emotionally more arousing (pinteraction < 10(-16)) than males. However, in the free recall females outperformed males not only in positive (p < 10(-16)) and negative (p < 5 × 10(-5)), but also in neutral picture recall (p < 3.4 × 10(-8)), with a particular advantage for positive pictures (pinteraction < 4.4 × 10(-10)). Importantly, females' memory advantage during free recall was absent in a recognition setting. We identified activation differences in fMRI, which corresponded to the females' stronger appraisal of especially negative pictures, but no activation differences that reflected the interaction effect in the free recall memory task. In conclusion, females' valence-category-specific memory advantage is only observed in a free recall, but not a recognition setting and does not depend on females' higher emotional appraisal

Reproductive success of Bornean orangutan males: scattered in time but clustered in space

The social and mating systems of orangutans, one of our closest relatives, remain poorly understood. Orangutans (Pongo spp.) are highly sexually dimorphic and females are philopatric and maintain individual, but overlapping home ranges, whereas males disperse, are non-territorial and wide-ranging, and show bimaturism, with many years between reaching sexual maturity and attaining full secondary sexual characteristics (including cheek pads (flanges) and emitting long calls). We report on 21 assigned paternities, among 35 flanged and 15 unflanged, genotyped male Bornean orangutans (Pongo pygmaeus wurmbii), studied from 2003 to 2018 in Tuanan (Central Kalimantan, Indonesia). All 10 infants born since mid-2003 with an already identified sire were sired by flanged males. All adult males ranged well beyond the study area (c. 1000 ha), and their dominance relations fluctuated even within short periods. However, 5 of the 10 identified sires had multiple offspring within the monitored area. Several sired over a period of c. 10 years, which overlapped with siring periods of other males. The long-calling behavior of sires indicated they were not consistently dominant over other males in the area around the time of known conceptions. Instead, when they were seen in the area, the known sires spent most of their time within the home ranges of the females whose offspring they sired. Overall, successful sires were older and more often resident than others. Significance statement It is difficult to assess reproductive success for individuals of long-lived species, especially for dispersing males, who cannot be monitored throughout their lives. Due to extremely long interbirth intervals, orangutans have highly male-skewed operational sex ratios and thus intensive male-male competition for every conception. Paternity analyses matched 21 immature Bornean orangutans with their most likely sire (only 10 of 50 genotyped males) in a natural population. Half of these identified sires had multiple offspring in the study area spread over periods of at least 10 years, despite frequently ranging outside this area. Dominance was a poor predictor of success, but, consistent with female mating tactics to reduce the risk of infanticide, known “sires” tended to have relatively high local presence, which seems to contribute to the males’ siring success. The results highlight the importance of large protected areas to enable a natural pattern of dispersal and ranging

Cosmic ray transport and anisotropies

We show that the large-scale cosmic ray anisotropy at ~10 TeV can be explained by a modified Compton-Getting effect in the magnetized flow field of old supernova remnants. This approach suggests an optimum energy scale for detecting the anisotropy. Two key assumptions are that propagation is based on turbulence following a Kolmogorov law and that cosmic ray interactions are dominated by transport through stellar winds of the exploding stars. A prediction is that the amplitude is smaller at lower energies due to incomplete sampling of the velocity field and also smaller at larger energies due to smearing.Comment: 6 pages, 1 figur

Reduced expression of C/EBPβ-LIP extends health- and lifespan in mice

Ageing is associated with physical decline and the development of age-related diseases such as metabolic disorders and cancer. Few conditions are known that attenuate the adverse effects of ageing, including calorie restriction (CR) and reduced signalling through the mechanistic target of rapamycin complex 1 (mTORC1) pathway. Synthesis of the metabolic transcription factor C/EBPβ-LIP is stimulated by mTORC1, which critically depends on a short upstream open reading frame (uORF) in the Cebpb-mRNA. Here we describe that reduced C/EBPβ-LIP expression due to genetic ablation of the uORF delays the development of age-associated phenotypes in mice. Moreover, female C/EBPβΔuORF mice display an extended lifespan. Since LIP levels increase upon aging in wild type mice, our data reveal an important role for C/EBPβ in the aging process and suggest that restriction of LIP expression sustains health and fitness. Thus, therapeutic strategies targeting C/EBPβ-LIP may offer new possibilities to treat age-related diseases and to prolong healthspan