The importance of being zero

2018 International Symposium on Symbolic and Algebraic Computation (ISSAC), July 2018, New York, NY, United StatesWe present a deterministic algorithm for deciding if a polynomial ideal, with coefficients in an algebraically closed field K of characteristic zero, of which we know just some very limited data, namely:the number n of variables, and some upper bound for the geometric degree of its zero set in Kn, is or not the zero ideal. The algorithm performs just a finite number of decisions to check whether a point is or not in the zero set of the ideal. Moreover, we extend this technique to test, in the same fashion, if the elimination of some variables in the given ideal yields or not the zero ideal. Finally, the role of this technique in the context of automated theorem proving of elementary geometry statements, is presented, with references to recent documents describing the excellent performance of the already existing prototype version, implemented in GeoGebra.Ministerio de Economía y CompetitividadEuropean Regional Development Fun

Towards Physical Hybrid Systems

Some hybrid systems models are unsafe for mathematically correct but physically unrealistic reasons. For example, mathematical models can classify a system as being unsafe on a set that is too small to have physical importance. In particular, differences in measure zero sets in models of cyber-physical systems (CPS) have significant mathematical impact on the mathematical safety of these models even though differences on measure zero sets have no tangible physical effect in a real system. We develop the concept of "physical hybrid systems" (PHS) to help reunite mathematical models with physical reality. We modify a hybrid systems logic (differential temporal dynamic logic) by adding a first-class operator to elide distinctions on measure zero sets of time within CPS models. This approach facilitates modeling since it admits the verification of a wider class of models, including some physically realistic models that would otherwise be classified as mathematically unsafe. We also develop a proof calculus to help with the verification of PHS.Comment: CADE 201

Shot Noise in Magnetic Tunnel Junctions: Evidence for Sequential Tunneling

We report the experimental observation of sub-Poissonian shot noise in single magnetic tunnel junctions, indicating the importance of tunneling via impurity levels inside the tunnel barrier. For junctions with weak zero-bias anomaly in conductance, the Fano factor (normalized shot noise) depends on the magnetic configuration being enhanced for antiparallel alignment of the ferromagnetic electrodes. We propose a model of sequential tunneling through nonmagnetic and paramagnetic impurity levels inside the tunnel barrier to qualitatively explain the observations.Comment: 5 pages, 5 figure

Zero-sum thinking, the evolution of effort suppressing beliefs, and economic development

We study the evolution of belief systems that suppress productive effort. These include concerns about the envy of others, beliefs in the importance of luck for success, disdain for competitive effort, and traditional beliefs in witchcraft. We show that such demotivating beliefs can evolve when interactions are zero-sum in nature, i.e., gains for one individual tend to come at the expense of others. Within a population, our model predicts a divergence between material and subjective payoffs, with material welfare being hump-shaped and subjective well-being being decreasing in demotivating beliefs. Across societies, our model predicts a positive relationship between zero-sum thinking and demotivating beliefs and a negative relationship between zero-sum thinking (or demotivating beliefs) and both material welfare and subjective well-being. We test the model’s predictions using data from two samples in the Democratic Republic of Congo and from the World Values Survey. In the DRC, we find a positive relationship between zero-sum thinking and the presence of demotivating beliefs, such as concerns about envy and beliefs in witchcraft. Globally, zero-sum thinking is associated with skepticism about the importance of hard work for success, lower income, less educational attainment, less financial security, and lower life satisfaction. Comparing individuals in the same zero-sum environment, we observe the divergence between material outcomes and subjective well-being predicted by our model

Acoustic Supercoupling in a Zero-Compressibility Waveguide

Funneling acoustic waves through largely mismatched channels is of fundamental importance to tailor and transmit sound for a variety of applications. In electromagnetics, zero-permittivity metamaterials have been used to enhance the coupling of energy in and out of ultranarrow channels, based on a phenomenon known as supercoupling. These metamaterial channels can support total transmission and complete phase uniformity, independent of the channel length, despite being geometrically mismatched to their input and output ports. In the field of acoustics, this phenomenon is challenging to achieve, since it requires zero-density metamaterials, typically realized with waveguides periodically loaded with membranes or resonators. Compared to electromagnetics, the additional challenge is due to the fact that conventional acoustic waveguides do not support a cut-off for the dominant mode of propagation, and therefore zero-index can be achieved only based on a collective resonance of the loading elements. Here we propose and experimentally realize acoustic supercoupling in a dual regime, using a compressibility-near-zero acoustic channel. Rather than engineering the channel with subwavelength inclusions, we operate at the cut-off of a higher-order acoustic mode, demonstrating the realization and efficient excitation of a zero-compressibility waveguide with effective soft boundaries. We experimentally verify strong transmission through a largely mismatched channel and uniform phase distribution, independent of the channel length. Our results open interesting pathways towards the realization of extreme acoustic parameters, and their implementation in relevant applications, such as ultrasound imaging, sonar technology, and sound transmission

Dynamical stabilisation of complex Langevin simulations of QCD

The ability to describe strongly interacting matter at finite temperature and baryon density provides the means to determine, for instance, the equation of state of QCD at non-zero baryon chemical potential. From a theoretical point of view, direct lattice simulations are hindered by the numerical sign problem, which prevents the use of traditional methods based on importance sampling. Despite recent successes, simulations using the complex Langevin method have been shown to exhibit instabilities, which cause convergence to wrong results. We introduce and discuss the method of Dynamic Stabilisation (DS), a modification of the complex Langevin process aimed at solving these instabilities. We present results of DS being applied to the heavy-dense approximation of QCD, as well as QCD with staggered fermions at zero chemical potential and finite chemical potential at high temperature. Our findings show that DS can successfully deal with the aforementioned instabilities, opening the way for further progress.Comment: 11 pages, 15 figures and 2 tables; Added acknowledgment

Rotational effects in thermonuclear Type I Bursts: equatorial crossing and directionality of flame spreading

In a previous study on thermonuclear (type I) nursts on accreting neutron stars we addressed and demonstrated the importance of the effects of rotation, through the Coriolis force, on the propagation of the burning flame. However, that study only analysed cases of longitudinal propagation, where the Coriolis force coefficient $2\Omega\cos\theta$ was constant. In this paper, we study the effects of rotation on propagation in the meridional (latitudinal) direction, where the Coriolis force changes from its maximum at the poles to zero at the equator. We find that the zero Coriolis force at the equator, while affecting the structure of the flame, does not prevent its propagation from one hemisphere to another. We also observe structural differences between the flame propagating towards the equator and that propagating towards the pole, the second being faster. In the light of the recent discovery of the low spin frequency of burster IGR~J17480-2446 rotating at 11 Hz (for which Coriolis effects should be negligible) we also extend our simulations to slow rotation.Comment: Accepted for publication by MNRA