Entropy measures for complex networks: Toward an information theory of complex topologies

The quantification of the complexity of networks is, today, a fundamental problem in the physics of complex systems. A possible roadmap to solve the problem is via extending key concepts of information theory to networks. In this paper we propose how to define the Shannon entropy of a network ensemble and how it relates to the Gibbs and von Neumann entropies of network ensembles. The quantities we introduce here will play a crucial role for the formulation of null models of networks through maximum-entropy arguments and will contribute to inference problems emerging in the field of complex networks.Comment: (4 pages, 1 figure

An exponential lower bound for Individualization-Refinement algorithms for Graph Isomorphism

The individualization-refinement paradigm provides a strong toolbox for testing isomorphism of two graphs and indeed, the currently fastest implementations of isomorphism solvers all follow this approach. While these solvers are fast in practice, from a theoretical point of view, no general lower bounds concerning the worst case complexity of these tools are known. In fact, it is an open question whether individualization-refinement algorithms can achieve upper bounds on the running time similar to the more theoretical techniques based on a group theoretic approach. In this work we give a negative answer to this question and construct a family of graphs on which algorithms based on the individualization-refinement paradigm require exponential time. Contrary to a previous construction of Miyazaki, that only applies to a specific implementation within the individualization-refinement framework, our construction is immune to changing the cell selector, or adding various heuristic invariants to the algorithm. Furthermore, our graphs also provide exponential lower bounds in the case when the $k$-dimensional Weisfeiler-Leman algorithm is used to replace the standard color refinement operator and the arguments even work when the entire automorphism group of the inputs is initially provided to the algorithm.Comment: 21 page

Random access quantum information processors

Qubit connectivity is an important property of a quantum processor, with an ideal processor having random access -- the ability of arbitrary qubit pairs to interact directly. Here, we implement a random access superconducting quantum information processor, demonstrating universal operations on a nine-bit quantum memory, with a single transmon serving as the central processor. The quantum memory uses the eigenmodes of a linear array of coupled superconducting resonators. The memory bits are superpositions of vacuum and single-photon states, controlled by a single superconducting transmon coupled to the edge of the array. We selectively stimulate single-photon vacuum Rabi oscillations between the transmon and individual eigenmodes through parametric flux modulation of the transmon frequency, producing sidebands resonant with the modes. Utilizing these oscillations for state transfer, we perform a universal set of single- and two-qubit gates between arbitrary pairs of modes, using only the charge and flux bias of the transmon. Further, we prepare multimode entangled Bell and GHZ states of arbitrary modes. The fast and flexible control, achieved with efficient use of cryogenic resources and control electronics, in a scalable architecture compatible with state-of-the-art quantum memories is promising for quantum computation and simulation.Comment: 7 pages, 5 figures, supplementary information ancillary file, 21 page

Extension of the sun-synchronous Orbit

Through careful consideration of the orbit perturbation force due to the oblate nature of the primary body a secular variation of the ascending node angle of a near-polar orbit can be induced without expulsion of propellant. Resultantly, the orbit perturbations can be used to maintain the orbit plane in, for example, a near-perpendicular (or at any other angle) alignment to the Sun-line throughout the full year of the primary body; such orbits are normally termed Sun-synchronous orbits [1, 2]. Sun-synchronous orbits about the Earth are typically near-circular Low-Earth Orbits (LEOs), with an altitude of less than 1500 km. It is normal to design a LEO such that the orbit period is synchronised with the rotation of the Earth‟s surface over a given period, such that a repeating ground-track is established. A repeating ground-track, together with the near-constant illumination conditions of the ground-track when observed from a Sun-synchronous orbit, enables repeat observations of a target over an extended period under similar illumination conditions [1, 2]. For this reason, Sun-synchronous orbits are extensively used by Earth Observation (EO) platforms, including currently the Environmental Satellite (ENVISAT), the second European Remote Sensing satellite (ERS-2) and many more. By definition, a given Sun-synchronous orbit is a finite resource similar to a geostationary orbit. A typical characterising parameter of a Sun-synchronous orbit is the Mean Local Solar Time (MLST) at descending node, with a value of 1030 hours typical. Note that ERS-1 and ERS-2 used a MLST at descending node of 1030 hours ± 5 minutes, while ENVISAT uses a 1000 hours ± 5 minutes MLST at descending node [3]. Following selection of the MLST at descending node and for a given desired repeat ground-track, the orbit period and hence the semi-major axis are fixed, thereafter assuming a circular orbit is desired it is found that only a single orbit inclination will enable a Sun-synchronous orbit [2]. As such, only a few spacecraft can populate a given repeat ground-track Sun-synchronous orbit without compromise, for example on the MLST at descending node. Indeed a notable feature of on-going studies by the ENVISAT Post launch Support Office is the desire to ensure sufficient propellant remains at end-of-mission for re-orbiting to a graveyard orbit to ensure the orbital slot is available for future missions [4]. An extension to the Sun-synchronous orbit is considered using an undefined, non-orientation constrained, low-thrust propulsion system. Initially the low-thrust propulsion system will be considered for the free selection of orbit inclination and altitude while maintaining the Sun-synchronous condition. Subsequently the maintenance of a given Sun-synchronous repeat-ground track will be considered, using the low-thrust propulsion system to enable the free selection of orbit altitude. An analytical expression will be developed to describe these extensions prior to then validating the analytical expressions within a numerical simulation of a spacecraft orbit. Finally, an analysis will be presented on transfer and injection trajectories to these orbits

Lumikot : Fast Auroral Transients During the Growth Phase of Substorms

The development of a magnetospheric substorm may be classified into three phases: growth, expansion, and recovery. The growth phase is important as it includes processes that lead to the expansion. In a recent growth-phase study, a type of fast discrete auroral transient phenomena-referred to as Lumikot-were observed. The Lumikot are several kilometers across and move in the high-energy precipitation region, parallel to the main growth-phase arc, with both east-west and west-east directions of travel during the same event. Their apparent transverse movement and quasi-stable intensity make them distinct from cooccurring optical pulsating aurorae. Comparison to other studies show that they occur in the cosmic noise absorption region and it is likely that the Lumikot are colocated with high-energy particle populations on the boundary between the outer radiation belt and the plasmasheet.Peer reviewe

PPC: an algorithm for accurate estimation of SNP allele frequencies in small equimolar pools of DNA using data from high density microarrays

Robust estimation of allele frequencies in pools of DNA has the potential to reduce genotyping costs and/or increase the number of individuals contributing to a study where hundreds of thousands of genetic markers need to be genotyped in very large populations sample sets, such as genome wide association studies. In order to make accurate allele frequency estimations from pooled samples a correction for unequal allele representation must be applied. We have developed the polynomial based probe specific correction (PPC) which is a novel correction algorithm for accurate estimation of allele frequencies in data from high-density microarrays. This algorithm was validated through comparison of allele frequencies from a set of 10 individually genotyped DNA's and frequencies estimated from pools of these 10 DNAs using GeneChip 10K Mapping Xba 131 arrays. Our results demonstrate that when using the PPC to correct for allelic biases the accuracy of the allele frequency estimates increases dramatically

Human papillomavirus infection in esophageal squamous cell carcinoma and esophageal adenocarcinoma: a concise review

The causal link between high-risk human papillomavirus (hr-HPV) infection and cervical, anogenital, and some oropharyngeal malignancies has been established by both molecular and epidemiological data. The association between HPV and esophageal squamous cell carcinoma (ESCC) remains controversial, as is the true prevalence of HPV infection in ESCC. The wide range in reported rates reflects variability in the primary literature, with some larger scale case–control studies suggesting the infection rates range from 0% to 78%. Interactions between HPV and the Barrett's metaplasia–dysplasia–carcinoma sequence have been explored, and these studies have shown some conflicting data. Overall, systematic reviews have reported the prevalence of HPV-positive DNA in esophageal adenocarcinoma patients of between 13% and 35%. Postulated reasons for discrepancies in HPV prevalence rates in esophageal cancer include variations in testing methodology and assay sensitivities; technical issues, including the lack of a gold-standard primer; types of specimens utilized (fresh-frozen versus formalin-fixed tissue); geographical variation; cross-contamination; and small sample sizes. Thus, efforts must be undertaken to (1) standardize HPV testing, ideally in a central laboratory and utilizing tests that detect viral transcriptional activity; (2) avoid cross-contamination; and (3) recruit large numbers of patients to accurately ascertain HPV rates in esophageal malignancy

Kochen-Specker Vectors

We give a constructive and exhaustive definition of Kochen-Specker (KS) vectors in a Hilbert space of any dimension as well as of all the remaining vectors of the space. KS vectors are elements of any set of orthonormal states, i.e., vectors in n-dim Hilbert space, H^n, n>3 to which it is impossible to assign 1s and 0s in such a way that no two mutually orthogonal vectors from the set are both assigned 1 and that not all mutually orthogonal vectors are assigned 0. Our constructive definition of such KS vectors is based on algorithms that generate MMP diagrams corresponding to blocks of orthogonal vectors in R^n, on algorithms that single out those diagrams on which algebraic 0-1 states cannot be defined, and on algorithms that solve nonlinear equations describing the orthogonalities of the vectors by means of statistically polynomially complex interval analysis and self-teaching programs. The algorithms are limited neither by the number of dimensions nor by the number of vectors. To demonstrate the power of the algorithms, all 4-dim KS vector systems containing up to 24 vectors were generated and described, all 3-dim vector systems containing up to 30 vectors were scanned, and several general properties of KS vectors were found.Comment: 19 pages, 6 figures, title changed, introduction thoroughly rewritten, n-dim rotation of KS vectors defined, original Kochen-Specker 192 (117) vector system translated into MMP diagram notation with a new graphical representation, results on Tkadlec's dual diagrams added, several other new results added, journal version: to be published in J. Phys. A, 38 (2005). Web page: http://m3k.grad.hr/pavici