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Clustering is an unsupervised technique of Data Mining. It means grouping similar objects together and separating the dissimilar ones. Each object in the data set is assigned a class label in the clustering process using a distance measure.…
Cluster analysis is a popular unsupervised learning tool used in many disciplines to identify heterogeneous sub-populations within a sample. However, validating cluster analysis results and determining the number of clusters in a data set…
Cluster number counts offer sensitive probes of the dark energy if and only if the_evolution_ of the cluster mass versus observable relation(s) is well calibrated. We investigate the potential for internal calibration by demanding…
We study the stabilities of quantum states of macroscopic systems, against noises, against perturbations from environments, and against local measurements. We show that the stabilities are closely related to the cluster property, which…
We study the quantum separability problem by using general symmetric informationally complete measurements and present separability criteria for both $d$-dimensional bipartite and multipartite systems. The criterion for bipartite quantum…
The unique properties of dark matter are revealed during collisions between clusters of galaxies, like the bullet cluster (1E 0657-56) and baby bullet (MACSJ0025-12). These systems provide evidence for an additional, invisible mass in the…
Quantum incompatibility, referred as the phenomenon that some quantum measurements cannot be performed simultaneously, is necessary for various quantum information processing tasks, such as nonlocality and steering. When these applications…
Spontaneous symmetry breaking is well known to be a macroscopic phenomenon in quantum physics in many body systems. The essential features of this phenomenon are the energy degeneracy and the existence of the local operator that can modify…
We study the separability of bipartite quantum systems in arbitrary dimensions using the Bloch representation of their density matrix. This approach enables us to find an alternative characterization of the separability problem, from which…
Change detection in heterogeneous multitemporal satellite images is a challenging and still not much studied topic in remote sensing and earth observation. This paper focuses on comparison of image pairs covering the same geographical area…
A relativistically invariant quantum theory first advanced by Bakamjian and Thomas has proven very useful in modeling few-body systems. For three particles or more, this approach is known formally to fail the constraint of cluster…
We discuss the problem of determining whether the state of several quantum mechanical subsystems is entangled. As in previous work on two subsystems we introduce a procedure for checking separability that is based on finding state…
A complete apparatus is defined as reacting to every state of the measured system. Standard quantum mechanics of indistinguishable particles is shown to imply that apparatuses must be incomplete or else they would be drowned out by noise.…
In quantum sensing and metrology, an important class of measurement is the continuous linear measurement, in which the detector is coupled to the system of interest linearly and continuously in time. One key aspect involved is the quantum…
Determining whether a quantum state is separable or entangled is a problem of fundamental importance in quantum information science. It has recently been shown that this problem is NP-hard. There is a highly inefficient `basic algorithm'…
Spectral clustering is a popular unsupervised learning technique which is able to partition unlabelled data into disjoint clusters of distinct shapes. However, the data under consideration are often experimental data, implying that the data…
A Bernoulli Mixture Model (BMM) is a finite mixture of random binary vectors with independent dimensions. The problem of clustering BMM data arises in a variety of real-world applications, ranging from population genetics to activity…
We consider the problem of determining the state of a quantum system given one or more readings of the expectation value of an observable. The system is assumed to be a finite dimensional quantum control system for which we can influence…
A one-dimensional quantum oscillator is monitored by taking repeated position measurements. As a first con- tribution, it is shown that, under a quantum nondemolition measurement scheme applied to a system initially at the ground state, (i)…
Consecutive quantum measurements performed on the same system can reveal fundamental insights into quantum theory's causal structure, and probe different aspects of the quantum measurement problem. According to the Copenhagen…