New analytic solutions of the collective Bohr hamiltonian for a beta-soft, gamma-soft axial rotor

New analytic solutions of the quadrupole collective Bohr hamiltonian are proposed, exploiting an approximate separation of the beta and gamma variables to describe gamma-soft prolate axial rotors. The model potential is a sum of two terms: a beta-dependent term taken either with a Coulomb-like or a Kratzer-like form, and a gamma-dependent term taken as an harmonic oscillator. In particular it is possible to give a one parameter paradigm for a beta-soft, gamma-soft axial rotor that can be applied, with a considerable agreement, to the spectrum of 234U.Comment: (Dipartimento di Fisica ``G.Galilei'' and INFN, via Marzolo 8, I-35131 Padova, Italy) 10 pages, 3 figure

Does invariant recognition predict tuning of neurons in sensory cortex?

Tuning properties of simple cells in cortical V1 can be described in terms of a "universal shape" characterized by parameter values which hold across different species. This puzzling set of findings begs for a general explanation grounded on an evolutionarily important computational function of the visual cortex. We ask here whether these properties are predicted by the hypothesis that the goal of the ventral stream is to compute for each image a "signature" vector which is invariant to geometric transformations, with the the additional assumption that the mechanism for continuously learning and maintaining invariance consists of the memory storage of a sequence of neural images of a few objects undergoing transformations (such as translation, scale changes and rotation) via Hebbian synapses. For V1 simple cells the simplest version of this hypothesis is the online Oja rule which implies that the tuning of neurons converges to the eigenvectors of the covariance of their input. Starting with a set of dendritic fields spanning a range of sizes, simulations supported by a direct mathematical analysis show that the solution of the associated "cortical equation" provides a set of Gabor-like wavelets with parameter values that are in broad agreement with the physiology data. We show however that the simple version of the Hebbian assumption does not predict all the physiological properties. The same theoretical framework also provides predictions about the tuning of cells in V4 and in the face patch AL which are in qualitative agreement with physiology data

Direct observation of the high magnetic field effect on the Jahn-Teller state in TbVO4

We report the first direct observation of the influence of high magnetic fields on the Jahn-Teller (JT) transition in TbVO4. Contrary to spectroscopic and magnetic methods, X-ray diffraction directly measures the JT distortion; the splitting between the (311)/(131) and (202)/(022) pairs of Bragg reflections is proportional to the order parameter. Our experimental results are compared to mean field calculations, taking into account all possible orientations of the grains relative to the applied field, and qualitative agreement is obtained.Comment: 11 pages, 4 figures, submitted to Phys. Rev. Let

Nodes Effect on the Bending Performance of Laminated Bamboo Lumber Unit

This research studied the ultimate bearing capacity of laminated bamboo lumber (LBL) unit and thereby calculated the maximum bending moment. The load-displacement chart for all specimens was obtained. Then the flexural capacity of members with and without bamboo nodes in the middle section was coMPared. The bending experiment phenomenon of LBL unit was concluded. Different failure modes of bending components were analysed and concluded. Finally, the bending behaviour of LBL units is coMPared with other bamboo and timber products. It is shown that the average ultimate load of BS members is 866.1 N, the average flexural strength is 101 MPa, the average modulus of elasticity is 8.3 GPa, and the average maximum displacement is 17.02 mm. The average ultimate load of BNS members is 1008.1 N, the average flexural strength is 118.02 MPa, the average modulus of elasticity is 9.9 GPa, and the average maximum displacement is 18.26 mm. Laminated bamboo lumber (LBL) unit without bamboo nodes (BNS) has relatively higher flexural strength coMPared with LBL unit with bamboo nodes (BS). The presence of bamboo nodes reduces the strength of the entire structure. Three failure modes were concluded for BS members, and two failure modes were observed for BNS members during the experimental process. According to a coMParison between the LBL unit and other products, the flexural strength and bending modulus of elasticity of the LBL unit are similar as bamboo scrimber and raw bamboo components, which is much higher than timber components

Quantum criticality as a resource for quantum estimation

We address quantum critical systems as a resource in quantum estimation and derive the ultimate quantum limits to the precision of any estimator of the coupling parameters. In particular, if L denotes the size of a system and \lambda is the relevant coupling parameters driving a quantum phase transition, we show that a precision improvement of order 1/L may be achieved in the estimation of \lambda at the critical point compared to the non-critical case. We show that analogue results hold for temperature estimation in classical phase transitions. Results are illustrated by means of a specific example involving a fermion tight-binding model with pair creation (BCS model).Comment: 7 pages. Revised and extended version. Gained one author and a specific exampl

Fine properties of self-similar solutions of the Navier-Stokes equations

We study the solutions of the nonstationary incompressible Navier--Stokes equations in $\R^d$, $d\ge2$, of self-similar form $u(x,t)=\frac{1}{\sqrt t}U\bigl(\frac{x}{\sqrt t}\bigr)$, obtained from small and homogeneous initial data $a(x)$. We construct an explicit asymptotic formula relating the self-similar profile $U(x)$ of the velocity field to its corresponding initial datum $a(x)$

Tangent Bundle Filters and Neural Networks: From Manifolds to Cellular Sheaves and Back

In this work we introduce a convolution operation over the tangent bundle of Riemannian manifolds exploiting the Connection Laplacian operator. We use this convolution operation to define tangent bundle filters and tangent bundle neural networks (TNNs), novel continuous architectures operating on tangent bundle signals, i.e. vector fields over manifolds. We discretize TNNs both in space and time domains, showing that their discrete counterpart is a principled variant of the recently introduced Sheaf Neural Networks. We formally prove that this discrete architecture converges to the underlying continuous TNN. We numerically evaluate the effectiveness of the proposed architecture on a denoising task of a tangent vector field over the unit 2-sphere

A quantum solution to the arrow-of-time dilemma

The arrow of time dilemma: the laws of physics are invariant for time inversion, whereas the familiar phenomena we see everyday are not (i.e. entropy increases). I show that, within a quantum mechanical framework, all phenomena which leave a trail of information behind (and hence can be studied by physics) are those where entropy necessarily increases or remains constant. All phenomena where the entropy decreases must not leave any information of their having happened. This situation is completely indistinguishable from their not having happened at all. In the light of this observation, the second law of thermodynamics is reduced to a mere tautology: physics cannot study those processes where entropy has decreased, even if they were commonplace.Comment: Contains slightly more material than the published version (the additional material is clearly labeled in the latex source). Because of PRL's title policy, the leading "A" was left out of the title in the published pape

On the possibility of measuring the Earth's gravitomagnetic force in a new laboratory experiment

In this paper we propose, in a preliminary way, a new Earth-based laboratory experiment aimed to the detection of the gravitomagnetic field of the Earth. It consists of the measurement of the difference of the circular frequencies of two rotators moving along identical circular paths, but in opposite directions, on a horizontal friction-free plane in a vacuum chamber placed at South Pole. The accuracy of our knowledge of the Earth's rotation from VLBI and the possibility of measuring the rotators'periods over many revolutions should allow for the feasibility of the proposed experiment.Comment: Latex2e, 8 pages, no figures, no tables, accepted for publication by Classical and Quantum Gravity. Typo corrected in the formula of the error in the difference of the orbital period

A New Method of Measuring 81Kr and 85Kr Abundances in Environmental Samples

We demonstrate a new method for determining the 81Kr/Kr ratio in environmental samples based upon two measurements: the 85Kr/81Kr ratio measured by Atom Trap Trace Analysis (ATTA) and the 85Kr/Kr ratio measured by Low-Level Counting (LLC). This method can be used to determine the mean residence time of groundwater in the range of 10^5 - 10^6 a. It requires a sample of 100 micro-l STP of Kr extracted from approximately two tons of water. With modern atmospheric Kr samples, we demonstrate that the ratios measured by ATTA and LLC are directly proportional to each other within the measurement error of +/- 10%; we calibrate the 81Kr/Kr ratio of modern air measured using this method; and we show that the 81Kr/Kr ratios of samples extracted from air before and after the development of the nuclear industry are identical within the measurement error