A topological characterization of modulo-p arguments and implications for necklace splitting

The classes PPA-p have attracted attention lately, because they are the main candidates for capturing the complexity of Necklace Splitting with p thieves, for prime p. However, these classes were not known to have complete problems of a topological nature, which impedes any progress towards settling the complexity of the Necklace Splitting problem. On the contrary, topological problems have been pivotal in obtaining completeness results for PPAD and PPA, such as the PPAD-completeness of finding a Nash equilibrium [18, 15] and the PPA-completeness of Necklace Splitting with 2 thieves [24]. In this paper, we provide the first topological characterization of the classes PPA-p. First, we show that the computational problem associated with a simple generalization of Tucker's Lemma, termed p-polygon-Tucker, as well as the associated Borsuk-Ulam-type theorem, p-polygon-Borsuk-Ulam, are PPA-p-complete. Then, we show that the computational version of the well-known BSS Theorem [8], as well as the associated BSS-Tucker problem are PPA-p-complete. Finally, using a different generalization of Tucker's Lemma (termed Zp-star-Tucker), which we prove to be PPA-p-complete, we prove that p-thief Necklace Splitting is in PPA-p. This latter result gives a new combinatorial proof for the Necklace Splitting theorem, the only proof of this nature other than that of Meunier [42]. All of our containment results are obtained through a new combinatorial proof for Zp-versions of Tucker's lemma that is a natural generalization of the standard combinatorial proof of Tucker's lemma by Freund and Todd [27]. We believe that this new proof technique is of independent interest

Three-Dimensional Printable Enzymatically Active Plastics

[Image: see text] Here, we describe a facile route to the synthesis of enzymatically active highly fabricable plastics, where the enzyme is an intrinsic component of the material. This is facilitated by the formation of an electrostatically stabilized enzyme–polymer surfactant nanoconstruct, which, after lyophilization and melting, affords stable macromolecular dispersions in a wide range of organic solvents. A selection of plastics can then be co-dissolved in the dispersions, which provides a route to bespoke 3D enzyme plastic nanocomposite structures using a wide range of fabrication techniques, including melt electrowriting, casting, and piston-driven 3D printing. The resulting constructs comprising active phosphotriesterase (arPTE) readily detoxify organophosphates with persistent activity over repeated cycles and for long time periods. Moreover, we show that the protein guest molecules, such as arPTE or sfGFP, increase the compressive Young’s modulus of the plastics and that the identity of the biomolecule influences the nanomorphology and mechanical properties of the resulting materials. Overall, we demonstrate that these biologically active nanocomposite plastics are compatible with state-of-the-art 3D fabrication techniques and that the methodology could be readily applied to produce robust and on-demand smart nanomaterial structures

Doing it for us: community identification predicts willingness to receive a COVID‐19 vaccination via perceived sense of duty to the community

The COVID-19 pandemic has presented huge challenges for communities across the world. Vaccines offer the best hope for controlling its deleterious effects, but not everybody is willing to be vaccinated, so it is important to explore variables that might predict vaccination willingness. The present study addressed this by drawing upon the Social Identity Approach, which posits that people’s membership of social groups is consequential for their thoughts and behaviour. Specifically, it was predicted that people’s strength of identification with their local community (a social group that came to particular prominence during the pandemic) would positively predict their willingness to engage in community-related prosocial normative behaviour (i.e., their perceived sense of duty, as a community member, to get vaccinated), and that this, in turn, would predict higher levels of vaccination willingness. Participants (N = 130) completed an online survey, which supported the hypothesised mediation model, even after controlling for subjective neighbourhood socio-economic status and age (two variables that are particularly likely to impact upon vaccination willingness). To our knowledge, this is the first study to apply Social Identity Approach principles to the study of COVID-19 vaccination willingness. The implications of the findings for governments’ efforts to boost vaccine uptake are discussed. Please refer to the Supplementary Material section to find this article’s Community and Social Impact Statement

Creativity and entrepreneurial intention in young people: empirical insights from business school students

The authors examine the link between creativity and entrepreneurial intention in young people and the roles that family and education may play in encouraging this link. The results from a survey of 180 undergraduate business school students show that the more creative young people consider themselves to be, the higher are their entrepreneurial intentions. Students' creativity also fully mediates the effect of family support for creativity on their entrepreneurial intention. Support for creativity in the university is found to have no effect on their creativity or on their entrepreneurial intention. Entrepreneurship course attendance moderates the effect of individual creativity on entrepreneurial intention

Bootstrapping EM via power EM and convergence in the naive bayes model

Copyright 2018 by the author(s). We study the convergence properties of the Expectation-Maximization algorithm in the Naive Bayes model. We show that EM can get stuck in regions of slow convergence, even when the features are binary and i.i.d. conditioning on the class label, and even under random (i.e. non worst-case) initialization. In turn, we show that EM can be bootstrapped in a pre-training step that computes a good initialization. From this initialization we show theoretically and experimentally that EM converges exponentially fast to the true model parameters. Our bootstrapping method amounts to running the EM algorithm on appropriately centered iterates of small magnitude, which as we show corresponds to effectively performing power iteration on the covariance matrix of the mixture model, although power iteration is performed under the hood by EM itself. As such, we call our bootstrapping approach “power EM.” Specifically for the case of two binary features, we show global exponentially fast convergence of EM, even without bootstrapping. Finally, as the Naive Bayes model is quite expressive, we show as corollaries of our convergence results that the EM algorithm globally converges to the true model parameters for mixtures of two Gaussians, recovering recent results of [XHM16, DTZ17]

Interplay of Space Charge and Intra-Beam Scattering in the LHC ion injector chain

The ion injectors of the CERN accelerator chain, in particular the Super Proton Synchrotron (SPS) and the Low Energy Ion Ring (LEIR), operate in a strong Space Charge (SC) and Intra-Beam Scattering (IBS) regime, which can degrade beam quality. Optimizing the ion beam performance requires thus to study the interplay of these two effects in tracking simulations by incorporating both SC and IBS effects interleaved with lattice non-linearities. In this respect, the kinetic theory approach of treating IBS effects has been deployed. A new, modified approach has been introduced using the formalism of the Bjorken and Mtingwa model and the complete integrals of the second kind for faster numerical evaluation. This IBS kick is implemented in PyORBIT and extensive benchmarking cases against analytical models are shown. Results of combined space charge and intra-beam scattering simulations for the SPS and LEIR are presented and compared with observations from beam measurements

Status of the High Energy Booster of the lepton option of the future circular collider

In the context of the FCC IS European study, which investigates the feasibility of a 100 km circular +− collider for the future high-energy physics research, we present the status of the High Energy Booster (HEB) ring. In order to perform precision measurements of the Z, W and H bosons, as well as of the top quark, unprecedented luminosities are required. To reach this goal and to fill the collider, it is mandatory to continuously top up inject some beams with a comparable emittance to the collider ones and a bunch-by-bunch intensity variation below few %. The main challenges of the HEB are the fast cycling time to reach the collider equilibrium emittances and the minimum injection energy into the booster that allows a stable operation. We present the status of the optics design of the HEB taking into account these challenges, and the impact of magnetic field imperfections on the dynamic aperture at injection