There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

https://www2.econ.iastate.edu/tesfatsi/DeepLearningInNeuralNetworksOverview.JSchmidhuber2015.pdf

Deep learning in neural networks

Deposits of clastic carbonate-dominated (calciclastic) sedimentary slope systems in the rock record have been identified mostly as linearly-consistent carbonate apron deposits, even though most ancient clastic carbonate slope deposits fit the submarine fan systems better. Calciclastic submarine fans are consequently rarely described and are poorly understood. Subsequently, very little is known especially in mud-dominated calciclastic submarine fan systems. Presented in this study are a sedimentological core and petrographic characterisation of samples from eleven boreholes from the Lower Carboniferous of Bowland Basin (Northwest England) that reveals a >250 m thick calciturbidite complex deposited in a calciclastic submarine fan setting. Seven facies are recognised from core and thin section characterisation and are grouped into three carbonate turbidite sequences. They include: 1) Calciturbidites, comprising mostly of highto low-density, wavy-laminated bioclast-rich facies; 2) low-density densite mudstones which are characterised by planar laminated and unlaminated muddominated facies; and 3) Calcidebrites which are muddy or hyper-concentrated debrisflow deposits occurring as poorly-sorted, chaotic, mud-supported floatstones. These

Phd by thesis

A comprehensive review of spatiotemporal pattern formation in systems driven away from equilibrium is presented, with emphasis on comparisons between theory and quantitative experiments. Examples include patterns in hydrodynamic systems such as thermal convection in pure fluids and binary mixtures, Taylor-Couette flow, parametric-wave instabilities, as well as patterns in solidification fronts, nonlinear optics, oscillatory chemical reactions and excitable biological media. The theoretical starting point is usually a set of deterministic equations of motion, typically in the form of nonlinear partial differential equations. These are sometimes supplemented by stochastic terms representing thermal or instrumental noise, but for macroscopic systems and carefully designed experiments the stochastic forces are often negligible. An aim of theory is to describe solutions of the deterministic equations that are likely to be reached starting from typical initial conditions and to persist at long times. A unified description is developed, based on the linear instabilities of a homogeneous state, which leads naturally to a classification of patterns in terms of the characteristic wave vector q0 and frequency ω0 of the instability. Type Is systems (ω0=0, q0≠0) are stationary in time and periodic in space; type IIIo systems (ω0≠0, q0=0) are periodic in time and uniform in space; and type Io systems (ω0≠0, q0≠0) are periodic in both space and time. Near a continuous (or supercritical) instability, the dynamics may be accurately described via "amplitude equations," whose form is universal for each type of instability. The specifics of each system enter only through the nonuniversal coefficients. Far from the instability threshold a different universal description known as the "phase equation" may be derived, but it is restricted to slow distortions of an ideal pattern. For many systems appropriate starting equations are either not known or too complicated to analyze conveniently. It is thus useful to introduce phenomenological order-parameter models, which lead to the correct amplitude equations near threshold, and which may be solved analytically or numerically in the nonlinear regime away from the instability. The above theoretical methods are useful in analyzing "real pattern effects" such as the influence of external boundaries, or the formation and dynamics of defects in ideal structures. An important element in nonequilibrium systems is the appearance of deterministic chaos. A greal deal is known about systems with a small number of degrees of freedom displaying "temporal chaos," where the structure of the phase space can be analyzed in detail. For spatially extended systems with many degrees of freedom, on the other hand, one is dealing with spatiotemporal chaos and appropriate methods of analysis need to be developed. In addition to the general features of nonequilibrium pattern formation discussed above, detailed reviews of theoretical and experimental work on many specific systems are presented. These include Rayleigh-Benard convection in a pure fluid, convection in binary-fluid mixtures, electrohydrodynamic convection in nematic liquid crystals, Taylor-Couette flow between rotating cylinders, parametric surface waves, patterns in certain open flow systems, oscillatory chemical reactions, static and dynamic patterns in biological media, crystallization fronts, and patterns in nonlinear optics. A concluding section summarizes what has and has not been accomplished, and attempts to assess the prospects for the future.

/pdf/pattern-formation-outside-of-equilibrium-1601b9znum.pdf

Pattern formation outside of equilibrium

Humans perceive the three-dimensional structure of the world with apparent ease. However, despite all of the recent advances in computer vision research, the dream of having a computer interpret an image at the same level as a two-year old remains elusive. Why is computer vision such a challenging problem and what is the current state of the art? Computer Vision: Algorithms and Applications explores the variety of techniques commonly used to analyze and interpret images. It also describes challenging real-world applications where vision is being successfully used, both for specialized applications such as medical imaging, and for fun, consumer-level tasks such as image editing and stitching, which students can apply to their own personal photos and videos. More than just a source of recipes, this exceptionally authoritative and comprehensive textbook/reference also takes a scientific approach to basic vision problems, formulating physical models of the imaging process before inverting them to produce descriptions of a scene. These problems are also analyzed using statistical models and solved using rigorous engineering techniques Topics and features: structured to support active curricula and project-oriented courses, with tips in the Introduction for using the book in a variety of customized courses; presents exercises at the end of each chapter with a heavy emphasis on testing algorithms and containing numerous suggestions for small mid-term projects; provides additional material and more detailed mathematical topics in the Appendices, which cover linear algebra, numerical techniques, and Bayesian estimation theory; suggests additional reading at the end of each chapter, including the latest research in each sub-field, in addition to a full Bibliography at the end of the book; supplies supplementary course material for students at the associated website, http://szeliski.org/Book/. Suitable for an upper-level undergraduate or graduate-level course in computer science or engineering, this textbook focuses on basic techniques that work under real-world conditions and encourages students to push their creative boundaries. Its design and exposition also make it eminently suitable as a unique reference to the fundamental techniques and current research literature in computer vision.

/pdf/computer-vision-algorithms-and-applications-25dn6wu83j.pdf

Computer Vision: Algorithms and Applications

Experiments on a slowly sheared 2D granular material show a continuous transition as the packing fraction $\ensuremath{\gamma}$ passes through ${\ensuremath{\gamma}}_{c}\ensuremath{\simeq}0.776$. The mean stress, $\overline{\ensuremath{\sigma}}$, plays the role of an order parameter. As $\ensuremath{\gamma}\ensuremath{\rightarrow}{\ensuremath{\gamma}}_{c}$ from above, (1) the compressibility becomes large, (2) a slowing down of the mean velocity occurs, (3) the force distributions change, and (4) the network of stress chains changes from intermittent long radial chains near ${\ensuremath{\gamma}}_{c}$ to a tangled dense network for larger $\ensuremath{\gamma}$.

Stress Fluctuations in a 2D Granular Couette Experiment: A Continuous Transition

Victor Hugo suggested the possibility that patterns created by the movement of grains of sand are in no small part responsible for the shape and feel of the natural world we live in. Certainly, granular materials, of which sand is but one example, are ubiquitous in our daily lives. They play an important role in industries, such as mining, agriculture and construction. They also are important in geological processes, such as landslides and erosion and, on a larger scale, plate tectonics, which determine much of Earth's morphology. Practically everything we eat started out in a granular form and the clutter on our desks is often so close to the angle of repose that a chance perturbation can create an avalanche onto the floor.

/pdf/the-physics-of-granular-materials-5d8t7k2ovj.pdf

The Physics of Granular Materials

Recent simulations have predicted that near jamming for collections of spherical particles, there will be a discontinuous increase in the mean contact number Z at a critical volume fraction ϕc. Above ϕc, Z and the pressure P are predicted to increase as power laws in ϕ-ϕc. In experiments using photoelastic disks we corroborate a rapid increase in Z at ϕc and power-law behavior above ϕc for Z and P. Specifically we find a power-law increase as a function of ϕ-ϕc for Z-Zc with an exponent β around 0.5, and for P with an exponent ψ around 1.1. These exponents are in good agreement with simulations. We also find reasonable agreement with a recent mean-field theory for frictionless particles.

/pdf/jamming-transition-in-granular-systems-5900tc2ifv.pdf

Jamming Transition in Granular Systems

Experiments on continuously sheared granular materials (glass spheres) with diameters $1.0\ensuremath{\le}d\ensuremath{\le}5\mathrm{mm}$ show large fluctuations in the normal stress, $\ensuremath{\sigma}(t)$. Experiments are carried out in an annular Couette geometry for rotation rates $0.003l\stackrel{\ifmmode \dot{}\else \.{}\fi{}}{\ensuremath{\theta}}l1\mathrm{rad}/\mathrm{s}$. Power spectra from $\ensuremath{\sigma}(t)$, $P(\ensuremath{\omega})$, show rate invariance in the fluctuations: $\stackrel{\ifmmode \dot{}\else \.{}\fi{}}{\ensuremath{\theta}}P(\ensuremath{\omega})$ is a function only of $\ensuremath{\omega}/\stackrel{\ifmmode \dot{}\else \.{}\fi{}}{\ensuremath{\theta}}$, independent of $\stackrel{\ifmmode \dot{}\else \.{}\fi{}}{\ensuremath{\theta}}$. $\stackrel{\ifmmode \dot{}\else \.{}\fi{}}{\ensuremath{\theta}}P(\ensuremath{\omega})$ depends relatively weakly on $d$. The distributions of stresses ${\ensuremath{\rho}}_{\ensuremath{\sigma}}$ are similar to recent predictions for static arrays, but the width of ${\ensuremath{\rho}}_{\ensuremath{\sigma}}$ varies only weakly with $d$, suggesting stronger spatial correlation effects than expected from theory.

/pdf/stress-fluctuations-for-continuously-sheared-granular-1hvavh8176.pdf

Stress Fluctuations for Continuously Sheared Granular Materials

A passenger car Mercedes 500 SEL has been equipped with vision in the framework of the EUREKA-project 'Pometheus III'. Road and object recognition is performed both in a look-ahead and in a look-back region; this allows an internal servo-maintained representation of the entire situation around the vehicle using the 4D approach to dynamic machine vision. Obstacles are detected and tracked both in the forward and in the backward viewing range up to about 100 meters distance; depending on the computing power available for this purpose up to 4 or 5 objects may be tracked in parallel in each hemisphere. A fixation type viewing direction control with the capability of saccadic shifts of viewing direction for attention focussing has been developed. The overall system comprises about 60 transputers of T-222 and T-800. Beside a PC as transputer host all other processors in VaMoRs-P are transputers. A description of the parallel processing architecture is given; the system integration follows the well proven paradigm of orientation towards 4D physical objects and expectations with prediction error feedback. This allows frequent data driven bottom-up and model driven top-down integration steps for efficient and robust object tracking.

Robert Behringer

Papers

Stress Fluctuations in a 2D Granular Couette Experiment: A Continuous Transition

The Physics of Granular Materials

Jamming Transition in Granular Systems

Stress Fluctuations for Continuously Sheared Granular Materials

The seeing passenger car 'VaMoRs-P'