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Universal behavior of two-dimensional bosonic gases at Berezinskii-Kosterlitz-Thouless transitions
No full textWe study the universal critical behavior of two-dimensional (2D) lattice
bosonic gases at the Berezinskii-Kosterlitz-Thouless (BKT) transition, which
separates the low-temperature superfluid phase from the high-temperature normal
phase. For this purpose, we perform quantum Monte Carlo simulations of the
hard-core Bose-Hubbard (BH) model at zero chemical potential. We determine the
critical temperature by using a matching method that relates finite-size data
for the BH model with corresponding data computed in the classical XY model. In
this approach, the neglected scaling corrections decay as inverse powers of the
lattice size L, and not as powers of 1/lnL, as in more standard approaches,
making the estimate of the critical temperature much more reliable. Then, we
consider the BH model in the presence of a trapping harmonic potential, and
verify the universality of the trap-size dependence at the BKT critical point.
This issue is relevant for experiments with quasi-2D trapped cold atoms
Twelve monotonicity conditions arising from algorithms for equilibrium problems
No full textIn the last years many solution methods for equilibrium problems (EPs) have been developed. Several different monotonicity conditions have been exploited to prove convergence. The paper investigates all the relationships between them in the framework of the so-called abstract EP. The analysis is further detailed for variational inequalities and linear equilibrium problems, which include also Nash equilibrium problems with quadratic payoffs
Pairwise Compatibility Graphs of Caterpillars
No full textA graph G = (V, E) is called a pairwise compatibility graph (PCG) if there exists an edge-weighted tree T and two non-negative real numbers dmin and dmax such that each leaf lu of T corresponds to a vertex u of V and there is an edge (u, v) in E if and only if dmin <= dT,w(lu, lv) <= dmax where dT,w(lu, lv) is the sum of the weights of the edges on the unique path from lu to lv in T. In this paper, we focus our attention on PCGs for which the witness tree is a caterpillar. We first give some properties of graphs that are PCGs of a caterpillar. We formulate this problem as an integer linear programming problem and we exploit this formulation to show that for the wheels on n vertices Wn, n = 7, ... , 11, the witness tree cannot be a caterpillar. Related to this result, we conjecture that no wheel is PCG of a caterpillar. Finally, we state a more general result proving that any pairwise compatibility graph admits a full binary tree as witness tree T
Unearthing wave-function renormalization effects in the time evolution of a Bose-Einstein condensate
No full textWe study the time evolution of a Bose-Einstein condensate in an accelerated
optical lattice. When the condensate has a narrow quasimomentum distribution
and the optical lattice is shallow, the survival probability in the ground band
exhibits a steplike structure. In this regime we establish a connection between
the wave-function renormalization parameter and the phenomenon of
resonantly enhanced tunneling
Some New Problems in Spectral Optimization
No full textSUMMARY We present some new problems in spectral optimization. The first one consists
in determining the best domain for the Dirichlet energy (or for the first
eigenvalue) of the {\it metric Laplacian}, and we consider in particular
Riemannian or Finsler manifolds, Carnot-Carath\'eodory spaces, Gaussian spaces.
The second one deals with the optimal shape of a graph when the minimization
cost is of spectral type. The third one is the optimization problem for a
Schr\"odinger potential in suitable classes
Stationary Configuration of some Optimal Shaping
No full textWe consider the problem of optimal location of a Dirichlet region in a
-dimensional domain subjected to a given right-hand side in
order to minimize some given functional of the configuration. While in the
literature the Dirichlet region is usually taken dimensional, in this
shape optimization problems, we consider two classes of control variables,
namely the class of one dimensional closed connected sets of finite one
dimensional Hausdorff measure and the class of sets of points of finite
cardinality, and we give a necessary condition of optimality
Optimal Potentials For Schrodinger Operators
No full textSUMMARY We consider the Schrodinger operator a given domain. Our goal is to study
some optimization problems where an optimal (non-negative) potential V has to
be determined in some suitable admissible classes and for some suitable
optimization criteria, like the energy or the Dirichlet eigenvalues
Cohomologies of certain orbifolds
No full textWe study the Bott–Chern cohomology of complex orbifolds obtained as a quotient of a compact complex manifold by a finite group of biholomorphisms
Data parallel patterns on CPU/GPU mix
No full textWe propose a model that uses a small set of quite simple parameters to devise a proper partitioning of the available data parallel tasks between CPU cores and GPU cores. The model takes into account both hardware and application dependent parameters. In particular, it eventually computes the percentage of tasks to be executed on CPU cores and GPU cores to achieve the better performance figures. Different experimental results on state-of-the-art CPU/GPU architectures are shown that assess the model properties
Extending a probabilistic language based upon Sampling Functions to model correlation
No full textProbability is permeating many applications of computer science, ranging from probabilistic reasoning to stochastic simulations. Therefore, researchers have started working on domain specific languages to target probabilistic computations, in order to support better understanding and development of probabilistic models. Among the proposed approaches sampling functions is one of the most promising: distributions are described as functional mappings from the unit interval (0,1] to probability domains which allows expressing a very broad class of distributions. The key advantage of this approach lies in its ability of lifting operations on values into operations on related distributions. The current state of the art frameworks, however, lack the ability to properly express variable correlation in a clean and composable way, which is a major issue of many real-world problems. In this paper we present LiXely, a probabilistic DSL which extends the sampling functions approach by providing explicit means for expressing variable correlation in a composable way and its implementation in F#