Adiabatic Evolution for Systems with Infinitely many Eigenvalue Crossings

We formulate an adiabatic theorem adapted to models that present an instantaneous eigenvalue experiencing an infinite number of crossings with the rest of the spectrum. We give an upper bound on the leading correction terms with respect to the adiabatic limit. The result requires only differentiability of the considered spectral projector, and some geometric hypothesis on the local behaviour of the eigenvalues at the crossings

The Pribram-Bohm Hypothesis: A Topology of Consciousness

A holoflux theory of consciousness as modulated energy is hypothesized and shown to support both local and non-local properties. This thesis emerges from an integral evaluation of evidence drawn from: (1) the holonomic mind/brain theories of Karl Pribram, (2) the ontological interpretation of quantum theory by David Bohm. Applying an integral methodology to superimpose and correlate seemingly disparate concepts from among these sources and others, a composite theory emerges, a "holoflux" theory of consciousness, after the term favored by Karl Pribram to describe David Bohm's "holomovement" between an explicate order and an implicate order. This Pribram-Bohm composite holoflux theory is shown to be congruent with established principles of physics, mathematics, and electrical engineering. Extending the panpsychist paradigm that consciousness is inherent in the structure of the universe, the thesis describes a dynamic energy process bridging the explicate space-time domain with a transcendent flux domain located at the spatial center, everywhere. This center is hypothesized to be synonymous with Karl Pribram's "flux domain" and David Bohm's "implicate order." Extending the theories of Pribram and Bohm, the holoflux hypothesis maps reality as a nondual energy, cycling mathematically, lens-like, in a process of transformation manifesting in three modes: (1) electromagnetic energy in space-time, (2) holoflux energy in a transcendent order, and (3) vibrating isospheres at the boundary gap separating the implicate from the explicate orders

The Pribram – Bohm Hypothesis

A holoflux theory of consciousness as modulated energy is hypothesized and shown to support both local and non-local properties. This thesis emerges from an integral evaluation of evidence drawn from: (1) the holonomic mind/brain theories of Karl Pribram, (2) the ontological interpretation of quantum theory by David Bohm. Applying an integral methodology to superimpose and correlate seemingly disparate concepts from among these sources and others, a composite-theory emerges, a “holoflux” theory of consciousness, after the term favored by Karl Pribram to describe David Bohm’s “holomovement” between an explicate order andan implicate order. This Pribram–Bohm composite holoflux theory is shown to be congruent with established principles of physics, mathematics, and electrical engineering. Extending the panpsychist paradigm that consciousness is inherent in the structure of the universe, the thesis describes a dynamic energy process bridging the explicate space–time domain with a transcendent flux domain located at the spatial center, everywhere. This center is hypothesized to be synonymous with Karl Pribram’s “flux domain” and David Bohm’s “implicate order.” Extending the theories of Pribram and Bohm, the holoflux hypothesis maps reality as a nondual energy, cycling mathematically, lens-like, in a process of transformation manifesting in three modes: (1) electromagnetic energy in space–time, (2) holoflux energy in a transcendent order, and (3) vibrating isospheres at the boundary gap separating the implicate from the explicate orders

Tuning the Mind in the Frequency Domain: Karl Pribram's Holonomic Brain Theory and David Bohm's Implicate Order

It is proposed that consciousness manifests as modulated radiant electromagnetic energy resonating in and between two regions, an explicate space-time order and a nondual implicate order. In such a model, the range of human consciousness is a function of the bandwidth of mind in the frequency domain. The hypothesis emerges from an integration of two paradigms: (1) the holonomic mind/brain theory of Karl Pribram, and (2) the ontological interpretation of quantum theory by David Bohm. The composite model, known as the Pribram-Bohm holoflux hypothesis, addresses observed phenomena of non-locality, both spatially and temporally. Holoflux is a term suggested by Karl Pribram to describe David Bohm's "holomovement" of information-energy cycling between an outer explicate order and an interior implicate order. Bohm concluded that consciousness will eventually be found as primary within the actuality of the implicate order. Pribram's decades of laboratory data, collected over the course of decades, convinced him that memory storage and retrieval follows a holographic Fourier process of transformation between frequency and time domains (i.e., simultaneous resonance between frequency spectra observed within the implicate and explicate orders). This Pribram-Bohm composite holoflux theory is congruent with established principles of radio communication engineering. In Bohm's explicate space-time domain, the holoflux spectra manifest as electromagnetic shells of information, or isospheres. Each isosphere has a unique tunable wavelength equal to its diameter, and each isosphere is separated by one Planck length. Information imprinted on the holosphere resonates with the nonlocal holoflux within the implicate order. This is outside of space-time, located at the bottom of space, and beginning below 10-35 m. Extending the panpsychist paradigm that consciousness is inherent in the structure of the universe, the holoflux theory describes a single, dynamic, nondual but tunable energy. This energy cycles mathematically, in a lens-like process of transformation between the two domains, the explicate order and the implicate order

The Pribram – Bohm Hypothesis Part II: The Physiology of Consciousness

A physiology of consciousness is elaborated, based upon implications of the Pribram-Bohm hypothesis (developed in Part I of this series). The model presented here is in sharp contrast to the prevailing conviction among neuroscientists that consciousness will eventually be discovered to be a physiological epiphenomenon of neuronal electrical impulses firing in the brain. In contrast, the Pribram-Bohm theory holds that consciousness, inherent in what Bohm views cosmologically as “the Whole,” manifests as a dynamic conscious energy resonance bridging the explicate space-time domain with the nonlocal, transcendent flux domain termed the “implicate order.” Presented in Part I, the Pribram-Bohm hypothesis posits a relatively infinite ether-like ground of innumerable quantum black holes, or “holospheres,” centrally located at every point in cosmological space. Being nonlocal, the implicate order is clearly a singularity, yet topologically accessible at each and every point with in space, connected everywhere below the Planck length of 10-35m. Bohm suggests that within the implicate order, consciousness is the primary awareness as contrasted with human mental cognition, a derivative in the explicate order (space–time). It is into these centers of the implicate order that information from space–time flows, and within which this information is eternally (non-temporally) stored. In this topology, consciousness is looking out from the implicate order center, everywhere, while simultaneously projecting form into the explicate order, space–time universe. Within such a topology of consciousness, human physiology would have evolved with structural aspects that provide feasible wavelengths (frequency bands) within which modulated information might be processed and stored isospherically in resonance with holoflux consciousness in the implicate order. Physiological candidates discussed as carriers of human consciousness processing and information storage (memory) include infrared radiation among erythrocytes in the blood stream, and the waveguide potential of microtubules for ultraviolet radiation throughout the neuronal system

Localization for Random Unitary Operators

We consider unitary analogs of $1-$dimensional Anderson models on $l^2(\Z)$ defined by the product $U_\omega=D_\omega S$ where $S$ is a deterministic unitary and $D_\omega$ is a diagonal matrix of i.i.d. random phases. The operator $S$ is an absolutely continuous band matrix which depends on a parameter controlling the size of its off-diagonal elements. We prove that the spectrum of $U_\omega$ is pure point almost surely for all values of the parameter of $S$. We provide similar results for unitary operators defined on $l^2(\N)$ together with an application to orthogonal polynomials on the unit circle. We get almost sure localization for polynomials characterized by Verblunski coefficients of constant modulus and correlated random phases

Close to Uniform Prime Number Generation With Fewer Random Bits

In this paper, we analyze several variants of a simple method for generating prime numbers with fewer random bits. To generate a prime $p$ less than $x$, the basic idea is to fix a constant $q\propto x^{1-\varepsilon}$, pick a uniformly random $a<q$ coprime to $q$, and choose $p$ of the form $a+t\cdot q$, where only $t$ is updated if the primality test fails. We prove that variants of this approach provide prime generation algorithms requiring few random bits and whose output distribution is close to uniform, under less and less expensive assumptions: first a relatively strong conjecture by H.L. Montgomery, made precise by Friedlander and Granville; then the Extended Riemann Hypothesis; and finally fully unconditionally using the Barban-Davenport-Halberstam theorem. We argue that this approach has a number of desirable properties compared to previous algorithms.Comment: Full version of ICALP 2014 paper. Alternate version of IACR ePrint Report 2011/48

The prediction of macrophyte species occurrence in Swiss ponds

The study attempted to model the abundance of aquatic plant species recorded in a range of ponds in Switzerland. A stratified sample of 80 ponds, distributed all over the country, provided input data for model development. Of the 154 species recorded, 45 were selected for modelling. A total of 14 environmental parameters were preselected as candidate explanatory variables. Two types of statistical tools were used to explore the data and to develop the predictive models: linear regression (LR) and generalized additive models (GAMs). Six LR species models had a reasonable predictive ability (30-50% of variance explained by the selected predictors). There was a gradient in the quality of the 45 GAM models. Ten species models exhibited both a good fit and statistical robustness: Lemnaminor, Phragmitesaustralis, Lysimachiavulgaris, Galiumpalustre, Lysimachianummularia, Irispseudacorus, Lythrumsalicaria, Lycopuseuropaeus, Phalarisarundinacea, Alismaplantago-aquatica, Schoenoplectuslacustris, Carexnigra. Altitude appeared to be a key explanatory variable in most of the species models. In some cases, the degree to which the shore was shaded, connectivity between water bodies, pond area, mineral nitrogen levels, pond age, pond depth, and the extent of agriculture or pasture in the catchment were selected as additional explanatory variables. The species models demonstrated that it is possible to predict species abundance of aquatic macrophytes and that each species responded individually to distinct environmental variable

Geophysical and geochemical signatures of Gulf of Mexico seafloor brines

International audienceGeophysical, temperature, and discrete depth-stratified geochemical data illustrate differences between an actively venting mud volcano and a relatively quiescent brine pool in the Gulf of Mexico along the continental slope. Geophysical data, including laser-line scan mosaics and sub-bottom profiles, document the dynamic nature of both environments. Temperature profiles, obtained by lowering a CTD into the brine fluid, show that the venting brine was at least 10°C warmer than the bottom water. At the brine pool, thermal stratification was observed and only small differences in stratification were documented between three sampling times (1991, 1997 and 1998). In contrast, at the mud volcano, substantial temperature variability was observed, with the core brine temperature being slightly higher than bottom water (by 2°C) in 1997 but substantially higher than bottom water (by 19°C) in 1998. Detailed geochemical samples were obtained in 2002 using a device called the "brine trapper" and concentrations of dissolved gases, major ions and nutrients were determined. Both brines contained about four times as much salt as seawater and steep concentration gradients of dissolved ions and nutrients versus brine depth were apparent. Differences in the concentrations of calcium, magnesium and potassium between the two brine fluids suggest that the fluids are derived from different sources, have different dilution/mixing histories, or that brine-sediment reactions are more important at the mud volcano. Substantial concentrations of methane, ammonium, and silicate were observed in both brines, suggesting that fluids expelled from deep ocean brines are important sources of these constituents to the surrounding environment

Temporal Interferometry: A Mechanism for Controlling Qubit Transitions During Twisted Rapid Passage with Possible Application to Quantum Computing

In an adiabatic rapid passage experiment, the Bloch vector of a two-level system (qubit) is inverted by slowly inverting an external field to which it is coupled, and along which it is initially aligned. In twisted rapid passage, the external field is allowed to twist around its initial direction with azimuthal angle $\phi (t)$ at the same time that it is inverted. For polynomial twist: $\phi (t) \sim Bt^{n}$. We show that for $n \geq 3$, multiple avoided crossings can occur during the inversion of the external field, and that these crossings give rise to strong interference effects in the qubit transition probability. The transition probability is found to be a function of the twist strength $B$, which can be used to control the time-separation of the avoided crossings, and hence the character of the interference. Constructive and destructive interference are possible. The interference effects are a consequence of the temporal phase coherence of the wavefunction. The ability to vary this coherence by varying the temporal separation of the avoided crossings renders twisted rapid passage with adjustable twist strength into a temporal interferometer through which qubit transitions can be greatly enhanced or suppressed. Possible application of this interference mechanism to construction of fast fault-tolerant quantum CNOT and NOT gates is discussed.Comment: 29 pages, 16 figures, submitted to Phys. Rev.