Separability problem for multipartite states of rank at most four

One of the most important problems in quantum information is the separability problem, which asks whether a given quantum state is separable. We investigate multipartite states of rank at most four which are PPT (i.e., all their partial transposes are positive semidefinite). We show that any PPT state of rank two or three is separable and has length at most four. For separable states of rank four, we show that they have length at most six. It is six only for some qubit-qutrit or multiqubit states. It turns out that any PPT entangled state of rank four is necessarily supported on a 3x3 or a 2x2x2 subsystem. We obtain a very simple criterion for the separability problem of the PPT states of rank at most four: such a state is entangled if and only if its range contains no product vectors. This criterion can be easily applied since a four-dimensional subspace in the 3x3 or 2x2x2 system contains a product vector if and only if its Pluecker coordinates satisfy a homogeneous polynomial equation (the Chow form of the corresponding Segre variety). We have computed an explicit determinantal expression for the Chow form in the former case, while such expression was already known in the latter case.Comment: 19 page

High-Performance Multi-Mode Ptychography Reconstruction on Distributed GPUs

Ptychography is an emerging imaging technique that is able to provide wavelength-limited spatial resolution from specimen with extended lateral dimensions. As a scanning microscopy method, a typical two-dimensional image requires a number of data frames. As a diffraction-based imaging technique, the real-space image has to be recovered through iterative reconstruction algorithms. Due to these two inherent aspects, a ptychographic reconstruction is generally a computation-intensive and time-consuming process, which limits the throughput of this method. We report an accelerated version of the multi-mode difference map algorithm for ptychography reconstruction using multiple distributed GPUs. This approach leverages available scientific computing packages in Python, including mpi4py and PyCUDA, with the core computation functions implemented in CUDA C. We find that interestingly even with MPI collective communications, the weak scaling in the number of GPU nodes can still remain nearly constant. Most importantly, for realistic diffraction measurements, we observe a speedup ranging from a factor of $10$ to $10^3$ depending on the data size, which reduces the reconstruction time remarkably from hours to typically about 1 minute and is thus critical for real-time data processing and visualization.Comment: work presented in NYSDS 201

Selection of earthquake ground motions for multiple objectives using genetic algorithms

Existing earthquake ground motion (GM) selection methods for the seismic assessment of structural systems focus on spectral compatibility in terms of either only central values or both central values and variability. In this way, important selection criteria related to the seismology of the region, local soil conditions, strong GM intensity and duration as well as the magnitude of scale factors are considered only indirectly by setting them as constraints in the pre-processing phase in the form of permissible ranges. In this study, a novel framework for the optimum selection of earthquake GMs is presented, where the aforementioned criteria are treated explicitly as selection objectives. The framework is based on the principles of multi-objective optimization that is addressed with the aid of the Weighted Sum Method, which supports decision making both in the pre-processing and post-processing phase of the GM selection procedure. The solution of the derived equivalent single-objective optimization problem is performed by the application of a mixed-integer Genetic Algorithm and the effects of its parameters on the efficiency of the selection procedure are investigated. Application of the proposed framework shows that it is able to track GM sets that not only provide excellent spectral matching but they are also able to simultaneously consider more explicitly a set of additional criteria

Sleep hygiene behaviours in Iranian adolescents: an application of the Theory of Planned Behavior

Poor sleep quality and inadequate sleep in adolescents are a rising trend globally. The Theory of Planned Behaviour (TPB)—which centres on an individual’s attitude toward performing the behaviour, subjective norms and perceived behavioural control—has been applied to examine sleep hygiene behaviours in young adults. We expanded on prior works by using a longitudinal design to examine the effects of TPB factors, together with sleep hygiene knowledge and planning constructs, on sleep hygiene behaviours and on sleep quality and health in a group of Iranian adolescents. A total of 1822 healthy adolescents (mean age = 13.97) from 25 high schools in Qazvin, Iran, completed a selfreported survey at baseline and 6 months later. Structural equation modelling (SEM) was used to delineate the pathway from adolescents’ sleep hygiene knowledge, TPB constructs of their behavioural intentions and sleep hygiene behaviours and their sleep quality and self-reported health. The SEM model demonstrated that although behavioural intention, coping planning and action planning predicted the sleep hygiene behaviours positively 6 months later with acceptable model fit [comparative fit index (CFI) = 0.936; Tucker–Lewis index (TLI) = 0.902; root mean square error of approximation (RMSEA) = 0.080; standardized root mean square residual (SRMR) = 0.044], sleep hygiene knowledge did not predict behavioural intentions significantly. Sleep hygiene behaviours were associated with sleep quality and psychiatric wellbeing. Thus, the TPB, combined with coping and action planning, is useful in understanding the sleep hygiene behaviours of adolescents. Health-care providers may want to emphasize TPB constructs and coping and action planning to improve adolescents’ sleep hygiene behaviours, rather than rely solely upon increasing adolescents’ sleep hygiene knowledge

Internet banking acceptance model: Cross-market examination

This article proposes a revised technology acceptance model to measure consumers’ acceptance of Internet banking, the Internet Banking Acceptance Model (IBAM). Data was collected from 618 university students in the United Kingdom and Saudi Arabia. The results suggest the importance of attitude, such that attitude and behavioral intentions emerge as a single factor, denoted as “attitudinal intentions” (AI). Structural equation modeling confirms the fit of the model, in which perceived usefulness and trust fully mediate the impact of subjective norms and perceived manageability on AI. The invariance analysis demonstrates the psychometric equivalence of the IBAM measurements between the two country groups. At the structural level, the influence of trust and system usefulness on AI vary between the two countries, emphasizing the potential role of cultures in IS adoption. The IBAM is robust and parsimonious, explaining over 80% of AI

Long Range Interaction Models and Yangian Symmetry

The generalized Sutherland-Romer models and Yan models with internal spin degrees are formulated in terms of the Polychronakos' approach and RTT relation associated to the Yang-Baxter equation in consistent way. The Yangian symmetry is shown to generate both models. We finally introduce the reflection algebra K(u) to the long range models.Comment: 13 pages, preprint of Nankai Institute of Mathematics ( Theoretical Physics Division ), published in Physical Review E of 1995. For hard copy, write to Prof. Mo-lin GE directly. Do not send emails to this accoun

Polynomial Growth Harmonic Functions on Finitely Generated Abelian Groups

In the present paper, we develop geometric analytic techniques on Cayley graphs of finitely generated abelian groups to study the polynomial growth harmonic functions. We develop a geometric analytic proof of the classical Heilbronn theorem and the recent Nayar theorem on polynomial growth harmonic functions on lattices \mathds{Z}^n that does not use a representation formula for harmonic functions. We also calculate the precise dimension of the space of polynomial growth harmonic functions on finitely generated abelian groups. While the Cayley graph not only depends on the abelian group, but also on the choice of a generating set, we find that this dimension depends only on the group itself.Comment: 15 pages, to appear in Ann. Global Anal. Geo