Equilibrium states of the pressure function for products of matrices

Let $\{M_i\}_{i=1}^\ell$ be a non-trivial family of $d\times d$ complex matrices, in the sense that for any $n\in \N$, there exists $i_1... i_n\in \{1,..., \ell\}^n$ such that $M_{i_1}... M_{i_n}\neq {\bf 0}$. Let $P \colon (0,\infty)\to \R$ be the pressure function of $\{M_i\}_{i=1}^\ell$. We show that for each $q>0$, there are at most $d$ ergodic $q$-equilibrium states of $P$, and each of them satisfies certain Gibbs property.Comment: 12 pages. To appear in DCD

Global behavior of cosmological dynamics with interacting Veneziano ghost

In this paper, we shall study the dynamical behavior of the universe accelerated by the so called Veneziano ghost dark energy component locally and globally by using the linearization and nullcline method developed in this paper. The energy density is generalized to be proportional to the Hawking temperature defined on the trapping horizon instead of Hubble horizon of the Friedmann-Robertson-Walker (FRW) universe. We also give a prediction of the fate of the universe and present the bifurcation phenomenon of the dynamical system of the universe. It seems that the universe could be dominated by dark energy at present in some region of the parameter space.Comment: 8 pages, 7 figures, accepted for publication in JHE

Anticipating a New Golden Age

The standard model of fundamental interactions is remarkably successful, but it leaves an unfinished agenda. Several major questions seem ripe for exploration in the near future. I anticipate that the coming decade will be a Golden Age of discovery in fundamental physics.Comment: 25 pages, 15 figures. Version 3: Added references, caption to Figure 14 correcte

A citizen-science approach to muon events in imaging atmospheric Cherenkov telescope data: the Muon Hunter

Event classification is a common task in gamma-ray astrophysics. It can be treated with rapidly-advancing machine learning algorithms, which have the potential to outperform traditional analysis methods. However, a major challenge for machine learning models is extracting reliably labelled training examples from real data. Citizen science offers a promising approach to tackle this challenge. We present "Muon Hunter", a citizen science project hosted on the Zooniverse platform, where VERITAS data are classified multiple times by individual users in order to select and parameterize muon events, a product from cosmic ray induced showers. We use this dataset to train and validate a convolutional neural-network model to identify muon events for use in monitoring and calibration. The results of this work and our experience of using the Zooniverse are presented.Comment: 8 pages, 3 figures, in Proceedings of the 35th International Cosmic Ray Conference (ICRC 2017), Busan, South Kore

Single spin detection by qubit SWAP to a molecular nanomagnet

Spin state detection is a key but very challenging step for any spin-based solid-state quantum computing technology. In fullerene based quantum computer technologies, we here propose to detect the single spin inside a fullerene by transferring the quantum information from the endohedral spin to the ground states of a molecular nanomagnet Fe$_{8}$, with large spin S=10. We show how to perform the required SWAP operation and how to read out the information through state-of-the-art techniques such as micro-SQUID.Comment: Europhysics Letters 69,699 (2005

A new approach to investigate wave dissipation in viscoelastic tubes: Application of wave intensity analysis

Wave dissipation in elastic and viscoelastic medium has been investigated extensively in the frequency domain. The aim of this study is to examine the pattern of wave dissipation in the time-domain using wave intensity analysis. A single semi-sinusoidal pulse was generated in 8 mm and 16 mm diameter tubes; each is of 200 cm in length. Pressure and flow measurements were taken at intervals of 5 cm along the tube. In order to examine the effect of the wall mechanical properties on wave dissipation, we also modified the wall of the 16 mm tube; a thread of strong cotton was wound with a pitch of approximately 30deg around the circumference of the tube in the longitudinal direction. The separated forward pressure, wave intensity and wave energy were calculated using wave intensity analysis. The amplitudes of the forward pressure wave, wave intensity and wave energy dissipated exponentially with distance. In the 8 mm diameter tube, the dissipation of forward pressure, wave intensity and wave energy were greater than those in 16 mm tube. For the same sized of tube, there was no significant difference in the dissipation of forward pressure, wave intensity and wave energy between the modified and normal wall tubes. It is concluded that the size of tube has a significant effect on the wave dissipation but the mechanical properties of the wall do not have a discernable effect on wave dissipatio

On the signature of certain intersection forms

We prove a conjecture of Zuber on the signature of intersection froms associated with affine algebras of type A.Comment: 10 pages, Amste

Determination of wave intensity in flexible tubes using measured diameter and velocity

Wave intensity (WI) is a hemodynamics index, which is the product of changes in pressure and velocity across the wave-front. Wave Intensity Analysis, which is a time domain technique allows for the separation of running waves into their forward and backward directions and traditionally uses the measured pressure and velocity waveforms. However, due to the possible difficulty in obtaining reliable pressure waveforms non-invasively, investigating the use of wall displacement instead of pressure signals in calculating WI may have clinical merits. In this paper, we developed an algorithm in which we use the measured diameter of flexible tube's wall and flow velocity to separate the velocity waveform into its forward and backward directions. The new algorithm is also used to separate wave intensity into its forward and backward directions. In vitro experiments were carried out in two sized flexible tubes, 12 mm and 16 mm in diameters, each is of 2 m in length. Pressure, velocity and diameter were taken at three measuring sites. A semi-sinusoidal wave was generated using a piston pump, which ejected 40 cc water into each tube. The results show that separated wave intensity into the forward and backward directions of the new algorithm using the measured diameter and velocity are almost identical in shape to those traditionally using the measured pressure and velocity. We conclude that the new algorithm presented in this work, could have clinical advantages since the required information can be obtained non-invasively

Two closed forms for the Bernoulli polynomials

In the paper, the authors find two closed forms involving the Stirling numbers of the second kind and in terms of a determinant of combinatorial numbers for the Bernoulli polynomials and numbers.Comment: 7 page