Torsion as a dynamic degree of freedom of quantum gravity

The gauge approach to gravity based on the local Lorentz group with a general independent affine connection A_{\mu cd} is developed. We consider SO(1,3) gauge theory with a Lagrangian quadratic in curvature as a simple model of quantum gravity. The torsion is proposed to represent a dynamic degree of freedom of quantum gravity at scales above the Planckian energy. The Einstein-Hilbert theory is induced as an effective theory due to quantum corrections of torsion via generating a stable gravito-magnetic condensate. We conjecture that torsion possesses an intrinsic quantum nature and can be confined. A minimal Abelian projection for the Lorentz gauge model has been constructed, and an effective theory of the cosmic knot at the Planckian scale is proposed.Comment: 13 pages, reduced final versio

Magic polarization for optical trapping of atoms without Stark-induced dephasing

We demonstrate that the differential ac-Stark shift of a ground-state hyperfine transition in an optical trap can be eliminated by using properly polarized trapping light. We use the vector polarizability of an alkali-metal atom to produce a polarization-dependent ac-Stark shift that resembles a Zeeman shift. We study a transition from the |2S1/2,F=2,mF=-2> to the |2S1/2,F=1,mF=-1> state of 7Li to observe 0.59+-0.02 Hz linewidth with interrogation time of 2 s and 0.82+-0.06 s coherence time of a superposition state. Implications of the narrow linewidth and the long coherence time for precision spectroscopy and quantum information processing using atoms in an optical lattice are discussed

Disorder dependence of the ferromagnetic quantum phase transition

We quantitatively discuss the influence of quenched disorder on the ferromagnetic quantum phase transition in metals, using a theory that describes the coupling of the magnetization to gapless fermionic excitations. In clean systems, the transition is first order below a tricritical temperature T_tc. Quenched disorder is predicted to suppress T_tc until it vanishes for residual resistivities rho_0 on the order of several microOhmcm for typical quantum ferromagnets. We discuss experiments that allow to distinguish the mechanism considered from other possible realizations of a first-order transition.Comment: 5pp, 1 figure; additional reference

JOBS: Joint-Sparse Optimization from Bootstrap Samples

Classical signal recovery based on $\ell_1$ minimization solves the least squares problem with all available measurements via sparsity-promoting regularization. In practice, it is often the case that not all measurements are available or required for recovery. Measurements might be corrupted/missing or they arrive sequentially in streaming fashion. In this paper, we propose a global sparse recovery strategy based on subsets of measurements, named JOBS, in which multiple measurements vectors are generated from the original pool of measurements via bootstrapping, and then a joint-sparse constraint is enforced to ensure support consistency among multiple predictors. The final estimate is obtained by averaging over the $K$ predictors. The performance limits associated with different choices of number of bootstrap samples $L$ and number of estimates $K$ is analyzed theoretically. Simulation results validate some of the theoretical analysis, and show that the proposed method yields state-of-the-art recovery performance, outperforming $\ell_1$ minimization and a few other existing bootstrap-based techniques in the challenging case of low levels of measurements and is preferable over other bagging-based methods in the streaming setting since it performs better with small $K$ and $L$ for data-sets with large sizes

Reducing Sampling Ratios Improves Bagging in Sparse Regression

Bagging, a powerful ensemble method from machine learning, improves the performance of unstable predictors. Although the power of Bagging has been shown mostly in classification problems, we demonstrate the success of employing Bagging in sparse regression over the baseline method (L1 minimization). The framework employs the generalized version of the original Bagging with various bootstrap ratios. The performance limits associated with different choices of bootstrap sampling ratio L/m and number of estimates K is analyzed theoretically. Simulation shows that the proposed method yields state-of-the-art recovery performance, outperforming L1 minimization and Bolasso in the challenging case of low levels of measurements. A lower L/m ratio (60% - 90%) leads to better performance, especially with a small number of measurements. With the reduced sampling rate, SNR improves over the original Bagging by up to 24%. With a properly chosen sampling ratio, a reasonably small number of estimates K = 30 gives satisfying result, even though increasing K is discovered to always improve or at least maintain the performance.Comment: arXiv admin note: substantial text overlap with arXiv:1810.0374

Combinatorial Proofs of Two Overpartition Theorems Connected by a Universal Mock Theta Function

In 2015, Bringmann, Lovejoy and Mahlburg considered certain kinds overpartitions, which can been seen as the overpartition analogue of Schur's partition. The motivation of their work is that the difference between the generating function of Schur's classical partitions and the generating functions of the partitions in which the smallest part is excluded. The difference between the two generating functions of partitions is a specialization of the "universal" mock theta function g_3 which introduced by Hickerson. To give an analogue of this, by using another universal mock theta function g_2 instead of g_3, Bringmann Lovejoy and Mahlburg introduced two kinds of overpartitions, which satisfy certain congruence conditions and difference conditions with the smallest parts different. They prove these theorems by using the q-differential equations. In this paper, we will give the generating functions of these two kinds of overpartitions by combinatorial technique.Comment: 12pages. arXiv admin note: text overlap with arXiv:1311.5483 by other author

Parity Considerations in Rogers-Ramanujan-Gordon Type Overpartitions

In 2010, Andrews considers a variety of parity questions connected to classical partition identities of Euler, Rogers, Ramanujan and Gordon. As a large part in his paper, Andrews considered the partitions by restricting the parity of occurrences of even numbers or odd numbers in the Rogers-Ramanujan-Gordon type. The Rogers-Ramanujan-Gordon type partition was defined by Gordon in 1961 as a combinatorial generalization of the Rogers-Ramaujan identities with odd moduli. In 1974, Andrews derived an identity which can be considered as the generating function counterpart of the Rogers-Ramanujan-Gordon theorem, and since then it has been called the Andrews--Gordon identity. By revisting the Andrews--Gordon identity Andrews extended his results by considering some additional restrictions involving parities to obtain some Rogers-Ramanujan-Gordon type theorems and Andrews--Gordon type identities. In the end of Andrews' paper, he posed $15$ open problems. Most of Andrews' $15$ open problems have been settled, but the $11$th that "extend the parity indices to overpartitions in a manner" has not. In 2013, Chen, Sang and Shi, derived the overpartition analogues of the Rogers-Ramanujan-Gordon theorem and the Andrews-Gordon identity. In this paper, we post some parity restrictions on these overpartitions analogues to get some Rogers-Ramanujan-Gordon type overpartition theorems

Benchmarking strong-field ionisation with atomic hydrogen

As the simplest atomic system, the hydrogen atom plays a key benchmarking role in laser and quantum physics. Atomic hydrogen is a widely used atomic test system for theoretical calculations of strong-field ionization, since approximate theories can be directly compared to numerical solutions of the time-dependent Schr\"odinger equation. However, relatively little experimental data is available for comparison to these calculations, since atomic hydrogen sources are difficult to construct and use. We review the existing experimental results on strong-field ionization of atomic hydrogen in multi-cycle and few-cycle laser pulses. Quantitative agreement has been achieved between experiment and theoretical predictions at the 10% uncertainty level, and has been used to develop an intensity calibration method with 1% uncertainty. Such quantitative agreement can be used to certify experimental techniques as being free from systematic errors, guaranteeing the accuracy of data obtained on species other than H. We review the experimental and theoretical techniques that enable these results.Comment: invited revie

Congruences modulo 44 for Rogers--Ramanujan--Gordon type overpartitions

In a recent work, Andrews defined the singular overpartitions with the goal of presenting an overpartition analogue to the theorems of Rogers--Ramanujan type for ordinary partitions with restricted successive ranks. As a small part of his work, Andrews noted two congruences modulo $3$ for the number of singular overpartitions prescribed by parameters $k=3$ and $i=1$. It should be noticed that this number equals the number of the Rogers--Ramanujan--Gordon type overpartitions with $k=i=3$ which come from the overpartition analogue of Gordon's Rogers--Ramanujan partition theorem introduced by Chen, Sang and Shi. In this paper, we derive numbers of congruence identities modulo $4$ for the number of Rogers--Ramanujan--Gordon type overpartitions

Mesoscale analyses of fungal networks as an approach for quantifying phenotypic traits

We investigate the application of mesoscopic response functions (MRFs) to characterize a large set of networks of fungi and slime moulds grown under a wide variety of different experimental treatments, including inter-species competition and attack by fungivores. We construct 'structural networks' by estimating cord conductances (which yield edge weights) from the experimental data, and we construct 'functional networks' by calculating edge weights based on how much nutrient traffic is predicted to occur along each edge. Both types of networks have the same topology, and we compute MRFs for both families of networks to illustrate two different ways of constructing taxonomies to group the networks into clusters of related fungi and slime moulds. Although both network taxonomies generate intuitively sensible groupings of networks across species, treatments and laboratories, we find that clustering using the functional-network measure appears to give groups with lower intra-group variation in species or treatments. We argue that MRFs provide a useful quantitative analysis of network behaviour that can (1) help summarize an expanding set of increasingly complex biological networks and (2) help extract information that captures subtle changes in intra- and inter-specific phenotypic traits that are integral to a mechanistic understanding of fungal behaviour and ecology. As an accompaniment to our paper, we also make a large data set of fungal networks available in the public domain.Comment: 16 pages, 3 figures, 1 tabl