Stability and Complexity of Minimising Probabilistic Automata

We consider the state-minimisation problem for weighted and probabilistic automata. We provide a numerically stable polynomial-time minimisation algorithm for weighted automata, with guaranteed bounds on the numerical error when run with floating-point arithmetic. Our algorithm can also be used for "lossy" minimisation with bounded error. We show an application in image compression. In the second part of the paper we study the complexity of the minimisation problem for probabilistic automata. We prove that the problem is NP-hard and in PSPACE, improving a recent EXPTIME-result.Comment: This is the full version of an ICALP'14 pape

Maximum Likelihood, Minimum Effort

We provide an efficient method for computing the maximum likelihood mixed quantum state (with density matrix rho) given a set of measurement outcome in a complete orthonormal operator basis subject to Gaussian noise. Our method works by first changing basis yielding a candidate density matrix mu which may have nonphysical (negative) eigenvalues, and then finding the nearest physical state under the 2-norm. Our algorithm takes at worst O(d^4) for the basis change plus O(d^3) for finding rho where d is the dimension of the quantum state. In the special case where the measurement basis is strings of Pauli operators, the basis change takes only O(d^3) as well. The workhorse of the algorithm is a new linear-time method for finding the closest probability distribution (in Euclidean distance) to a set of real numbers summing to one.Comment: 4 pages, 5 pdf figures. Replaced with corrections and expanded figure

On the Strength of Spin-Isospin Transitions in A=28 Nuclei

The relations between the strengths of spin-isospin transition operators extracted from direct nuclear reactions, magnetic scattering of electrons and processes of semi-leptonic weak interactions are discussed.Comment: LaTeX, 8 pages, 1Postscript with figur

Geometry of Polynomials and Root-Finding via Path-Lifting

Using the interplay between topological, combinatorial, and geometric properties of polynomials and analytic results (primarily the covering structure and distortion estimates), we analyze a path-lifting method for finding approximate zeros, similar to those studied by Smale, Shub, Kim, and others. Given any polynomial, this simple algorithm always converges to a root, except on a finite set of initial points lying on a circle of a given radius. Specifically, the algorithm we analyze consists of iterating $$z - \frac{f(z)-t_kf(z_0)}{f'(z)}$$ where the $t_k$ form a decreasing sequence of real numbers and $z_0$ is chosen on a circle containing all the roots. We show that the number of iterates required to locate an approximate zero of a polynomial $f$ depends only on $\log|f(z_0)/\rho_\zeta|$ (where $\rho_\zeta$ is the radius of convergence of the branch of $f^{-1}$ taking $0$ to a root $\zeta$) and the logarithm of the angle between $f(z_0)$ and certain critical values. Previous complexity results for related algorithms depend linearly on the reciprocals of these angles. Note that the complexity of the algorithm does not depend directly on the degree of $f$, but only on the geometry of the critical values. Furthermore, for any polynomial $f$ with distinct roots, the average number of steps required over all starting points taken on a circle containing all the roots is bounded by a constant times the average of $\log(1/\rho_\zeta)$. The average of $\log(1/\rho_\zeta)$ over all polynomials $f$ with $d$ roots in the unit disk is ${\mathcal{O}}({d})$. This algorithm readily generalizes to finding all roots of a polynomial (without deflation); doing so increases the complexity by a factor of at most $d$.Comment: 44 pages, 12 figure

Investigating the Atmospheric Mass Loss of the Kepler-105 Planets Straddling the Radius Gap

An intriguing pattern among exoplanets is the lack of detected planets between approximately $1.5$ R$_\oplus$ and $2.0$ R$_\oplus$. One proposed explanation for this "radius gap" is the photoevaporation of planetary atmospheres, a theory that can be tested by studying individual planetary systems. Kepler-105 is an ideal system for such testing due to the ordering and sizes of its planets. Kepler-105 is a sun-like star that hosts two planets straddling the radius gap in a rare architecture with the larger planet closer to the host star ($R_b = 2.53\pm0.07$ R$_\oplus$, $P_b = 5.41$ days, $R_c = 1.44\pm0.04$ R$_\oplus$, $P_c = 7.13$ days). If photoevaporation sculpted the atmospheres of these planets, then Kepler-105b would need to be much more massive than Kepler-105c to retain its atmosphere, given its closer proximity to the host star. To test this hypothesis, we simultaneously analyzed radial velocities (RVs) and transit timing variations (TTVs) of the Kepler-105 system, measuring disparate masses of $M_b = 10.8\pm2.3$ M$_\oplus$ ($\rho_b = 0.97\pm0.22$ g cm$^{-3}$) and $M_c = 5.6\pm1.2$ M$_\oplus$ ($\rho_c = 2.64\pm0.61$ g cm$^{-3}$). Based on these masses, the difference in gas envelope content of the Kepler-105 planets could be entirely due to photoevaporation (in 76\% of scenarios), although other mechanisms like core-powered mass loss could have played a role for some planet albedos.Comment: 14 pages, 3 figures, 2 table

Array algorithms for H^2 and H^∞ estimation

Currently, the preferred method for implementing H^2 estimation algorithms is what is called the array form, and includes two main families: square-root array algorithms, that are typically more stable than conventional ones, and fast array algorithms, which, when the system is time-invariant, typically offer an order of magnitude reduction in the computational effort. Using our recent observation that H^∞ filtering coincides with Kalman filtering in Krein space, in this chapter we develop array algorithms for H^∞ filtering. These can be regarded as natural generalizations of their H^2 counterparts, and involve propagating the indefinite square roots of the quantities of interest. The H^∞ square-root and fast array algorithms both have the interesting feature that one does not need to explicitly check for the positivity conditions required for the existence of H^∞ filters. These conditions are built into the algorithms themselves so that an H^∞ estimator of the desired level exists if, and only if, the algorithms can be executed. However, since H^∞ square-root algorithms predominantly use J-unitary transformations, rather than the unitary transformations required in the H^2 case, further investigation is needed to determine the numerical behavior of such algorithms

Low-Spin Heme b3 in the Catalytic Center of Nitric Oxide Reductase from Pseudomonas nautica

Biochemistry, 2011, 50 (20), pp 4251–4262 DOI: 10.1021/bi101605pRespiratory nitric oxide reductase (NOR) was purified from membrane extract of Pseudomonas (Ps.) nautica cells to homogeneity as judged by polyacrylamide gel electrophoresis. The purified protein is a heterodimer with subunits of molecular masses of 54 and 18 kDa. The gene encoding both subunits was cloned and sequenced. The amino acid sequence shows strong homology with enzymes of the cNOR class. Iron/heme determinations show that one heme c is present in the small subunit (NORC) and that approximately two heme b and one non-heme iron are associated with the large subunit (NORB), in agreement with the available data for enzymes of the cNOR class. Mössbauer characterization of the as-purified, ascorbate-reduced, and dithionite-reduced enzyme confirms the presence of three heme groups (the catalytic heme b(3) and the electron transfer heme b and heme c) and one redox-active non-heme Fe (Fe(B)). Consistent with results obtained for other cNORs, heme c and heme b in Ps. nautica cNOR were found to be low-spin while Fe(B) was found to be high-spin. Unexpectedly, as opposed to the presumed high-spin state for heme b(3), the Mössbauer data demonstrate unambiguously that heme b(3) is, in fact, low-spin in both ferric and ferrous states, suggesting that heme b(3) is six-coordinated regardless of its oxidation state. EPR spectroscopic measurements of the as-purified enzyme show resonances at the g ∼ 6 and g ∼ 2-3 regions very similar to those reported previously for other cNORs. The signals at g = 3.60, 2.99, 2.26, and 1.43 are attributed to the two charge-transfer low-spin ferric heme c and heme b. Previously, resonances at the g ∼ 6 region were assigned to a small quantity of uncoupled high-spin Fe(III) heme b(3). This assignment is now questionable because heme b(3) is low-spin. On the basis of our spectroscopic data, we argue that the g = 6.34 signal is likely arising from a spin-spin coupled binuclear center comprising the low-spin Fe(III) heme b(3) and the high-spin Fe(B)(III). Activity assays performed under various reducing conditions indicate that heme b(3) has to be reduced for the enzyme to be active. But, from an energetic point of view, the formation of a ferrous heme-NO as an initial reaction intermediate for NO reduction is disfavored because heme [FeNO](7) is a stable product. We suspect that the presence of a sixth ligand in the Fe(II)-heme b(3) may weaken its affinity for NO and thus promotes, in the first catalytic step, binding of NO at the Fe(B)(II) site. The function of heme b(3) would then be to orient the Fe(B)-bound NO molecules for the formation of the N-N bond and to provide reducing equivalents for NO reduction

Accelerated functional brain aging in pre-clinical familial Alzheimer’s disease

Resting state functional connectivity (rs-fMRI) is impaired early in persons who subsequently develop Alzheimer’s disease (AD) dementia. This impairment may be leveraged to aid investigation of the pre-clinical phase of AD. We developed a model that predicts brain age from resting state (rs)-fMRI data, and assessed whether genetic determinants of AD, as well as beta-amyloid (Aβ) pathology, can accelerate brain aging. Using data from 1340 cognitively unimpaired participants between 18–94 years of age from multiple sites, we showed that topological properties of graphs constructed from rs-fMRI can predict chronological age across the lifespan. Application of our predictive model to the context of pre-clinical AD revealed that the pre-symptomatic phase of autosomal dominant AD includes acceleration of functional brain aging. This association was stronger in individuals having significant Aβ pathology

The Behavioral Roots of Information Systems Security:Exploring Key Factors Related to Unethical IT Use

Unethical information technology (IT) use, related to activities such as hacking, software piracy, phishing, and spoofing, has become a major security concern for individuals, organizations, and society in terms of the threat to information systems (IS) security. While there is a growing body of work on this phenomenon, we notice several gaps, limitations, and inconsistencies in the literature. In order to further understand this complex phenomenon and reconcile past findings, we conduct an exploratory study to uncover the nomological network of key constructs salient to this phenomenon, and the nature of their interrelationships. Using a scenario-based study of young adult participants, and both linear and nonlinear analyses, we uncover key nuances of this phenomenon of unethical IT use. We find that unethical IT use is a complex phenomenon, often characterized by nonlinear and idiosyncratic relationships between the constructs that capture it. Overall, ethical beliefs held by the individuals, along with economic, social, and technological considerations are found to be relevant to this phenomenon. In terms of practical implications, these results suggest that multiple interventions at various levels may be required to combat this growing threat to IS security