1,575,078 research outputs found
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 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
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