Secants of Lagrangian Grassmannians

We study the dimensions of secant varieties of the Grassmannian of Lagrangian subspaces in a symplectic vector space. We calculate these dimensions for third and fourth secant varieties. Our result is obtained by providing a normal form for four general points on such a Grassmannian and by explicitly calculating the tangent spaces at these four points

On the dimensions of secant varieties of Segre-Veronese varieties

This paper explores the dimensions of higher secant varieties to Segre-Veronese varieties. The main goal of this paper is to introduce two different inductive techniques. These techniques enable one to reduce the computation of the dimension of the secant variety in a high dimensional case to the computation of the dimensions of secant varieties in low dimensional cases. As an application of these inductive approaches, we will prove non-defectivity of secant varieties of certain two-factor Segre-Veronese varieties. We also use these methods to give a complete classification of defective s-th Segre-Veronese varieties for small s. In the final section, we propose a conjecture about defective two-factor Segre-Veronese varieties.Comment: Revised version. To appear in Annali di Matematica Pura e Applicat

Incompressible liquid state of rapidly-rotating bosons at filling factor 3/2

Bosons in the lowest Landau level, such as rapidly-rotating cold trapped atoms, are investigated numerically in the specially interesting case in which the filling factor (ratio of particle number to vortex number) is 3/2. When a moderate amount of a longer-range (e.g. dipolar) interaction is included, we find clear evidence that the ground state is in a phase constructed earlier by two of us, in which excitations possess non-Abelian statistics.Comment: 5 pages, 5 figure

Phase Separation of a Fast Rotating Boson-Fermion Mixture in the Lowest-Landau-Level Regime

By minimizing the coupled mean-field energy functionals, we investigate the ground-state properties of a rotating atomic boson-fermion mixture in a two-dimensional parabolic trap. At high angular frequencies in the mean-field-lowest-Landau-level regime, quantized vortices enter the bosonic condensate, and a finite number of degenerate fermions form the maximum-density-droplet state. As the boson-fermion coupling constant increases, the maximum density droplet develops into a lower-density state associated with the phase separation, revealing characteristics of a Landau-level structure

Data Visualization of COVID-19 Vaccination Progress and Prediction Using Linear Regression

This paper provides a data visualization and analysis of the COVID-19 vaccination program. Important information such as which countries have the highest vaccination rates and numbers. In addition to the types of vaccines used and used by countries in the world, an infographic on the geographic distribution of vaccine use is also shown. To model the obtained data, daily vaccination rates were modeled by linear regression in which five sample countries with different vaccination ranges were processed using data science approach, namely, linear regression. The modeling results show a gradient coefficient that represents an increase in vaccine rates. The prediction results showed that the highest rate of increase in daily vaccination was 1,826,126 additional vaccines per day

Systematic review of brucellosis in the Middle East: disease frequency in ruminants and humans and risk factors for human infection

This paper considers the problem of finding global states incoming to a specified global state in a Boolean network, which may be useful for pre-processing of finding a sequence of control actions for a Boolean network and for identifying the basin of attraction for a given attractor, We show that this problem is NP-hard in general along with related theoretical results, On the other hand, we present algorithms that are much faster than the naive exhaustive search-based algorithm. ©2007 IEEE.link_to_subscribed_fulltex

An asymptotic bound for secant varieties of Segre varieties

This paper studies the defectivity of secant varieties of Segre varieties. We prove that there exists an asymptotic lower estimate for the greater non-defective secant variety (without filling the ambient space) of any given Segre variety. In particular, we prove that the ratio between the greater non-defective secant variety of a Segre variety and its expected rank is lower bounded by a value depending just on the number of factors of the Segre variety. Moreover, in the final section, we present some results obtained by explicit computation, proving the non-defectivity of all the secant varieties of Segre varieties of the shape (P^n)^4, with 1 < n < 11, except at most \sigma_199((P^8)^4) and \sigma_357((P^10)^4).Comment: 14 page

Quantum theory of a vortex line in an optical lattice

We investigate the quantum theory of a vortex line in a stack of weakly-coupled two-dimensional Bose-Einstein condensates, that is created by a one-dimensional optical lattice. We derive the dispersion relation of the Kelvin modes of the vortex line and also study the coupling between the Kelvin modes and the quadrupole modes. We solve the coupled dynamics of the vortex line and the quadrupole modes, both classically as well as quantum mechanically. The quantum mechanical solution reveals the possibility of generating nonequilibrium squeezed vortex states by strongly driving the quadrupole modes.Comment: Minor changes in response to a referee repor

TOPSIS Approach for Solving Bi-Level Non-Linear Fractional MODM Problems

TOPSIS (technique for order preference similarity to ideal solution) is considered one of the known classical multiple criteria decision making (MCDM) methods to solve bi-level non-linear fractional multi-objective decision making (BL-NFMODM) problems, and in which the objective function at each level is considered nonlinear and maximization type fractional functions. The proposed approach presents the basic terminology of TOPSIS approach and the construction of membership function for the upper level decision variable vectors, the membership functions of the distance functions from the positive ideal solution (PIS) and of the distance functions from the negative ideal solution (NIS). Thereafter a fuzzy goal programming model is adopted to obtain compromise optimal solution of BL-NFMODM problems. The proposed approach avoids the decision deadlock situations in decision making process and possibility of rejecting the solution again and again by lower level decision makers. The presented TOPSIS technique for BL-NFMODM problems is a new fuzzy extension form of TOPSIS approach suggested by Baky and Abo-Sinna (2013) (Applied Mathematical Modelling, 37, 1004-1015, 2013) which dealt with bi -level multi-objective decision making (BL-MODM) problems. Also, an algorithm is presented of the new fuzzy TOPSIS approach for solving BL-NFMODM problems. Finally, an illustrative numerical example is given to demonstrate the approach