Geometric frustration produces long-sought Bose metal phase of quantum matter

Two of the most prominent phases of bosonic matter are the superfluid with perfect flow and the insulator with no flow. A now decades-old mystery unexpectedly arose when experimental observations indicated that bosons could organize into the formation of an entirely different intervening third phase: the Bose metal with dissipative flow. The most viable theory for such a Bose metal to date invokes the use of the extrinsic property of impurity-based disorder; however, a generic intrinsic quantum Bose metal state is still lacking. We propose a universal homogeneous theory for a Bose metal in which geometric frustration confines the essential quantum coherence to a lower dimension. The result is a gapless insulator characterized by dissipative flow that vanishes in the low-energy limit. This failed insulator exemplifies a frustration-dominated regime that is only enhanced by additional scattering sources at low energy and therefore produces a Bose metal that thrives under realistic experimental conditions.

Multilevel Laser Induced Continuum Structure

Laser-induced-continuum-structure (LICS) allows for coherent control techniques to be applied in a Raman type system with an intermediate continuum state. The standard LICS problem involves two bound states coupled to one or more continua. In this paper, we discuss the simplest non-trivial multistate generalization of LICS which couples two bound levels, each composed of two degenerate states through a common continuum state. We reduce the complexity of the system by switching to a rotated basis of the bound states, in which different sub-systems of lower dimension evolve independently. We derive the trapping condition and explore the dynamics of the sub-systems under different initial conditions.

The Concept of Ibnu Miskawaih Moral Education For Students

Although both education and morality are different, in practice they are closely related and synergistic. In the Islamic world, even education is in a lower dimension than morality. This shows that the importance of morality is so important that knowledge seems to fade away its essence without morality. Ibn Miskawaih is a thinker who is concerned with the moral dimension. The idea of morals boils down to divine values and Islamic ethics. Ibn Miskawaih offers his character concept emphasizing psychological and religious aspects to improve the character quality of students. This research is a literature study with a descriptive text analysis method. The results showed that Ibn Miskawaih was very intense in applying the habit method to explore the character of students. According to Ibnu Miskawaih, environmental habits, friends and family are the most important media in educational media

The close relation between border and Pommaret marked bases

Given a finite order ideal $${\mathcal {O}}$$ O in the polynomial ring $$K[x_1,\ldots , x_n]$$ K [ x 1 , … , x n ] over a field K, let $$\partial {\mathcal {O}}$$ ∂ O be the border of $${\mathcal {O}}$$ O and $${\mathcal {P}}_{\mathcal {O}}$$ P O the Pommaret basis of the ideal generated by the terms outside $${\mathcal {O}}$$ O . In the framework of reduction structures introduced by Ceria, Mora, Roggero in 2019, we investigate relations among $$\partial {\mathcal {O}}$$ ∂ O -marked sets (resp. bases) and $${\mathcal {P}}_{\mathcal {O}}$$ P O -marked sets (resp. bases). We prove that a $$\partial {\mathcal {O}}$$ ∂ O -marked set B is a marked basis if and only if the $${\mathcal {P}}_{\mathcal {O}}$$ P O -marked set P contained in B is a marked basis and generates the same ideal as B. Using a functorial description of these marked bases, as a byproduct we obtain that the affine schemes respectively parameterizing $$\partial {\mathcal {O}}$$ ∂ O -marked bases and $${\mathcal {P}}_{\mathcal {O}}$$ P O -marked bases are isomorphic. We are able to describe this isomorphism as a projection that can be explicitly constructed without the use of Gröbner elimination techniques. In particular, we obtain a straightforward embedding of border schemes in affine spaces of lower dimension. Furthermore, we observe that Pommaret marked schemes give an open covering of Hilbert schemes parameterizing 0-dimensional schemes without any group actions. Several examples are given throughout the paper.

On Integration of the Loaded mKdV Equation in the Class of Rapidly Decreasing Functions

The paper is devoted to the integration of the loaded modified Kortewegde Vries equation in the class of rapidly decreasing functions. It is well known that loaded differential equations in the literature are usually called equations containing in the coefficients or in the right-hand side any functionals of the solution, in particular, the values of the solution or its derivatives on manifolds of lower dimension. In this paper, we consider the Cauchy problem for the loaded modified Korteweg-de Vries equation. The problem is solved using the inverse scattering method, i.e. the evolution of the scattering data of a non-self-adjoint Dirac operator is derived, the potential of which is a solution to the loaded modified Korteweg-de Vries equation in the class of rapidly decreasing functions. A specific example is given to illustrate the application of the results obtained.

Independent Skill Transfer for Deep Reinforcement Learning

Recently, diverse primitive skills have been learned by adopting the entropy as intrinsic reward, which further shows that new practical skills can be produced by combining a variety of primitive skills. This is essentially skill transfer, very useful for learning high-level skills but quite challenging due to the low efficiency of transferring primitive skills. In this paper, we propose a novel efficient skill transfer method, where we learn independent skills and only independent components of skills are transferred instead of the whole set of skills. More concretely, independent components of skills are obtained through independent component analysis (ICA), which always have a smaller amount (or lower dimension) compared with their mixtures. With a lower dimension, independent skill transfer (IST) exhibits a higher efficiency on learning a given task. Extensive experiments including three robotic tasks demonstrate the effectiveness and high efficiency of our proposed IST method in comparison to direct primitive-skill transfer and conventional reinforcement learning.

Online Metric Learning for Multi-Label Classification

Existing research into online multi-label classification, such as online sequential multi-label extreme learning machine (OSML-ELM) and stochastic gradient descent (SGD), has achieved promising performance. However, these works lack an analysis of loss function and do not consider label dependency. Accordingly, to fill the current research gap, we propose a novel online metric learning paradigm for multi-label classification. More specifically, we first project instances and labels into a lower dimension for comparison, then leverage the large margin principle to learn a metric with an efficient optimization algorithm. Moreover, we provide theoretical analysis on the upper bound of the cumulative loss for our method. Comprehensive experiments on a number of benchmark multi-label datasets validate our theoretical approach and illustrate that our proposed online metric learning (OML) algorithm outperforms state-of-the-art methods.

RELATIVE UNITARY RZ-SPACES AND THE ARITHMETIC FUNDAMENTAL LEMMA

We prove a comparison isomorphism between certain moduli spaces of $p$ -divisible groups and strict ${\mathcal{O}}_{K}$ -modules (RZ-spaces). Both moduli problems are of PEL-type (polarization, endomorphism, level structure) and the difficulty lies in relating polarized $p$ -divisible groups and polarized strict ${\mathcal{O}}_{K}$ -modules. We use the theory of relative displays and frames, as developed by Ahsendorf, Lau and Zink, to translate this into a problem in linear algebra. As an application of these results, we verify new cases of the arithmetic fundamental lemma (AFL) of Wei Zhang: The comparison isomorphism yields an explicit description of certain cycles that play a role in the AFL. This allows, under certain conditions, to reduce the AFL identity in question to an AFL identity in lower dimension.

FRACTAL STOKES’ THEOREM BASED ON INTEGRALS ON FRACTAL MANIFOLDS

In this paper, with the Hausdorff measure, the Hausdorff integral on fractal sets with one or lower dimension is firstly introduced via measure theory. Then the definition of the integral on fractal sets in [Formula: see text] is given. With the variable substitution theorem in the Riemann integral generalized to the integral on fractal sets, the integral on fractal manifolds is defined. As a result, with the generalization of Gauss’ theorem, Stokes’ theorem is generalized to the integral on fractal manifolds in [Formula: see text].