A Perron-Frobenius Theorem for Positive Quasipolynomial Matrices Associated with Homogeneous Difference Equations

We extend the classical Perron-Frobenius theorem for positive quasipolynomial matrices associated with homogeneous difference equations. Finally, the result obtained is applied to derive necessary and sufficient conditions for the stability of positive system

Two Gap State Density in MgB2_{2}: A True Bulk Property or A Proximity Effect?

We report on the temperature dependence of the quasiparticle density of states (DOS) in the simple binary compound MgB2 directly measured using scanning tunneling microscope (STM). To achieve high quality tunneling conditions, a small crystal of MgB2 is used as a tip in the STM experiment. The ``sample'' is chosen to be a 2H-NbSe2 single crystal presenting an atomically flat surface. At low temperature the tunneling conductance spectra show a gap at the Fermi energy followed by two well-pronounced conductance peaks on each side. They appear at voltages V$_{S}\simeq \pm 3.8$ mV and V$_{L}\simeq \pm 7.8$ mV. With rising temperature both peaks disappear at the Tc of the bulk MgB2, a behavior consistent with the model of two-gap superconductivity. The explanation of the double-peak structure in terms of a particular proximity effect is also discussed.Comment: 4 pages, 3 figure

Deep Metric Learning Meets Deep Clustering: An Novel Unsupervised Approach for Feature Embedding

Unsupervised Deep Distance Metric Learning (UDML) aims to learn sample similarities in the embedding space from an unlabeled dataset. Traditional UDML methods usually use the triplet loss or pairwise loss which requires the mining of positive and negative samples w.r.t. anchor data points. This is, however, challenging in an unsupervised setting as the label information is not available. In this paper, we propose a new UDML method that overcomes that challenge. In particular, we propose to use a deep clustering loss to learn centroids, i.e., pseudo labels, that represent semantic classes. During learning, these centroids are also used to reconstruct the input samples. It hence ensures the representativeness of centroids - each centroid represents visually similar samples. Therefore, the centroids give information about positive (visually similar) and negative (visually dissimilar) samples. Based on pseudo labels, we propose a novel unsupervised metric loss which enforces the positive concentration and negative separation of samples in the embedding space. Experimental results on benchmarking datasets show that the proposed approach outperforms other UDML methods.Comment: Accepted in BMVC 202

Assessment of the Effectiveness of Ich Tam Khang as a Supportive Therapy for Chronic Heart Failure

Background: Heart failure is a chronic disease needing lifelong management. Despite the advances that have been made in the treatment of the disease, both the longevity and quality of life for those with chronic heart failure remain impaired. A more effective therapeutic approach with less negative side effects is still needed. In this study, we evaluate Ich Tam Khang (ITK), the poly-ingredient herbal and nutritional preparation with multiple physiological actions, as a supportive therapy for patients with chronic heart failure.Aims of Study: To evaluate the effectiveness and safety of Ich Tam Khang as an adjunctive treatment of chronic heart failure.Methods: A total of 60 patients with chronic congestive heart failure were enrolled in this open label, cross-sectional and prospective study. All patients were treated with a conventional regimen (digoxin, diuretics, angiotensin-converting-enzyme (ACE) inhibitors or angiotensin II receptor blockers (ARBs), beta blockers) for at least 4 weeks before being divided into two equal groups. In the treated patients with ITK, patients received conventional therapy plus 4 tablets ITK per day added in two divided doses. In the control patients, all patients kept the same conventional regimen without ITK. All patients were followed up for 3 months for clinical and para-clinical outcomes.Result: The symptoms of heart failure (dyspnea, palpitation, peripheral edema, neck vein distention, heptojugular reflex) decreased. Heart rate and blood pressure stabilized during treatment in the treated patients with ITK. Additionally, total cholesterol and HDL-cholesterol normalized in the patients treated with ITK. Most of echocardiography parameters in the ITK treated patients were superior to the control patients. ITK is safe and it has no side effects.Conclusion: ITK as a combination of herbal and nutritional preparation is effective in reducing heart failure symptoms, improving patient's quality of life for the patients with decompensated heart failure and reducing total cholesterol and LDL-C

q-Deformation of W(2,2) Lie algebra associated with quantum groups

An explicit realization of the W(2,2) Lie algebra is presented using the famous bosonic and fermionic oscillators in physics, which is then used to construct the q-deformation of this Lie algebra. Furthermore, the quantum group structures on the q-deformation of this Lie algebra are completely determined.Comment: 12 page