From the Publisher:
Pattern recognition has long been studied in relation to many different (and mainly unrelated) applications, such as remote sensing, computer vision, space research, and medical imaging. In this book Professor Ripley brings together two crucial ideas in pattern recognition; statistical methods and machine learning via neural networks. Unifying principles are brought to the fore, and the author gives an overview of the state of the subject. Many examples are included to illustrate real problems in pattern recognition and how to overcome them.This is a self-contained account, ideal both as an introduction for non-specialists readers, and also as a handbook for the more expert reader.

Pattern recognition and neural networks

Machine learning is one of the fastest growing areas of computer science, with far-reaching applications. The aim of this textbook is to introduce machine learning, and the algorithmic paradigms it offers, in a principled way. The book provides an extensive theoretical account of the fundamental ideas underlying machine learning and the mathematical derivations that transform these principles into practical algorithms. Following a presentation of the basics of the field, the book covers a wide array of central topics that have not been addressed by previous textbooks. These include a discussion of the computational complexity of learning and the concepts of convexity and stability; important algorithmic paradigms including stochastic gradient descent, neural networks, and structured output learning; and emerging theoretical concepts such as the PAC-Bayes approach and compression-based bounds. Designed for an advanced undergraduate or beginning graduate course, the text makes the fundamentals and algorithms of machine learning accessible to students and non-expert readers in statistics, computer science, mathematics, and engineering.

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Understanding Machine Learning: From Theory To Algorithms

We show that any language recognized by an NC 1 circuit (fan-in 2, depth O (log n )) can be recognized by a width-5 polynomial-size branching program. As any bounded-width polynomial-size branching program can be simulated by an NC 1 circuit, we have that the class of languages recognized by such programs is exactly nonuniform NC 1 . Further, following Ruzzo ( J. Comput. System Sci. 22 (1981), 365–383) and Cook ( Inform. and Control 64 (1985) 2–22) , if the branching programs are restricted to be ATIME(logn)-uniform, they recognize the same languages as do ATIME(log n )-uniform NC 1 circuits, that is, those languages in ATIME(log n ). We also extend the method of proof to investigate the complexity of the word problem for a fixed permutation group and show that polynomial size circuits of width 4 also recognize exactly nonuniform NC 1 .

Bounded-width polynomial-size branching programs recognize exactly those languages in NC1

Concrete mathematics, a foundation for computer science, by Ronald L. Graham, Donald E. Knuth and Oren Patashnik. Pp 625. £24·95. 1989. ISBN 0-201-14236-8 (Addison-Wesley)

Clinical question What is the role of drug interventions in the treatment of patients with covid-19? New recommendation Increased attention on ivermectin as a potential treatment for covid-19 triggered this recommendation. The panel made a recommendation against ivermectin in patients with covid-19 regardless of disease severity, except in the context of a clinical trial. Prior recommendations (a) a strong recommendation against the use of hydroxychloroquine in patients with covid-19, regardless of disease severity; (b) a strong recommendation against the use of lopinavir-ritonavir in patients with covid-19, regardless of disease severity; (c) a strong recommendation for systemic corticosteroids in patients with severe and critical covid-19; (d) a conditional recommendation against systemic corticosteroids in patients with non-severe covid-19, and (e) a conditional recommendation against remdesivir in hospitalised patients with covid-19. How this guideline was created This living guideline is from the World Health Organization (WHO) and provides up to date covid-19 guidance to inform policy and practice worldwide. Magic Evidence Ecosystem Foundation (MAGIC) provided methodological support. A living systematic review with network analysis informed the recommendations. An international guideline development group (GDG) of content experts, clinicians, patients, an ethicist and methodologists produced recommendations following standards for trustworthy guideline development using the Grading of Recommendations Assessment, Development and Evaluation (GRADE) approach. Understanding the new recommendation There is insufficient evidence to be clear to what extent, if any, ivermectin is helpful or harmful in treating covid-19. There was a large degree of uncertainty in the evidence about ivermectin on mortality, need for mechanical ventilation, need for hospital admission, time to clinical improvement, and other patient-important outcomes. There is potential for harm with an increased risk of adverse events leading to study drug discontinuation. Applying pre-determined values and preferences, the panel inferred that almost all well informed patients would want to receive ivermectin only in the context of a randomised trial, given that the evidence left a very high degree of uncertainty on important effects. Updates This is a living guideline. It replaces earlier versions (4 September, 20 November, and 17 December 2020) and supersedes the BMJ Rapid Recommendations on remdesivir published on 2 July 2020. The previous versions can be found as data supplements. New recommendations will be published as updates to this guideline. Readers note This is the fourth version (update 3) of the living guideline (BMJ 2020;370:m3379). When citing this article, please consider adding the update number and date of access for clarity.

https://www.bmj.com/content/bmj/370/bmj.m3379.full.pdf

A living WHO guideline on drugs for covid-19

Computers and computation the discrete neuron the Boolean neuron alternating circuits small, shallow alternating circuits threshold circuits cyclic networks probabilistic neural networks.

Circuit complexity and neural networks

Cartesian Coordinate Systems 1D Mathematics 2D Cartesian Space 3D Cartesian Space Odds and ends Vectors Vector - mathematical definition and other boring stuff Vector - a geometric definition Specifying vectors using Cartesian coordinates Vectors vs. points Negating a vector Vector multiplication by a scalar Vector addition and subtraction Vector magnitude (length) Unit vectors The distance formula Vector dot product Vector cross product Linear algebra identities Multiple Coordinate Spaces Why multiple coordinate spaces? Some useful coordinate spaces Coordinate space transformations Nested coordinate spaces In defense of upright space Introduction to Matrices Matrix - a mathematical definition Matrix - a geometric interpretation The bigger picture of linear algebra Matrices and Linear Transformations Rotation Scale Orthographic projection Reection Shearing Combining transformations Classes of transformations More on Matrices Determinant of a matrix Inverse of a matrix Orthogonal matrices 4 x 4 homogeneous matrices 4 x 4 matrices and perspective projection Polar Coordinate Systems 2D Polar Space Why would anybody use Polar coordinates? 3D Polar Space Using polar coordinates to specify vectors Rotation in Three Dimensions What exactly is "orientation?" Matrix form Euler angles Axis-angle and exponential map representations Quaternions Comparison of methods Converting between representations Geometric Primitives Representation techniques Lines and rays Spheres and circles Bounding boxes Planes Triangles Polygons Mathematical Topics from 3D Graphics How graphics works Viewing in 3D Coordinate spaces Polygon meshes Texture mapping The standard local lighting model Light sources Skeletal animation Bump mapping The real-time graphics pipeline Some HLSL examples Further reading Mechanics 1: Linear Kinematics and Calculus Overview and other expectation-reducing remarks Basic quantities and units Average velocity Instantaneous velocity and the derivative Acceleration Motion under constant acceleration Acceleration and the integral Uniform circular motion Mechanics 2: Linear and Rotational Dynamics Newton's three laws Some simple force laws Momentum Impulsive forces and collisions Rotational dynamics Real-time rigid body simulators Suggested reading Curves in 3D Parametric polynomial curves Polynomial interpolation Hermite curves Bezier curves Subdivision Splines Hermite and Bezier splines Continuity Automatic tangent control Afterword What next? Appendix A: Geometric Tests Appendix B: Answers to the Exercises Bibliography Index Exercises appear at the end of each chapter.

3D math primer for graphics and game development

We study two classes of unbounded fan-in parallel computation, the standard one, based on unbounded fan-in ANDs and ORs, and a new class based on unbounded fan-in threshold functions. The latter is motivated by a connectionist model of the brain used in Artificial Intelligence. We are interested in the resources of time and address complexity. Intuitively, the address complexity of a parallel machine is the number of bits needed to describe an individual piece of hardware. We demonstrate that (for WRAMs and uniform unbounded fan-in circuits) parallel time and address complexity is simultaneously equivalent to alternations and time on an alternating Turing machine (the former to within a constant multiple, and the latter a polynomial). In particular, for constant parallel time, the latter equivalence holds to within a constant multiple. Thus, for example, polynomial-processor, constant-time WRAMs recognize exactly the languages in the logarithmic time hierarchy, and polynomial-word-size, constant-time WRAMs recognize exactly the languages in the polynomial time hierarchy. As a corollary, we provide improved simulations of deterministic Turing machines by constant-time shared-memory machines. Furthermore, in the threshold model, the same results hold if we replace the alternating Turing machine with the analogous threshold Turing machine, and replace the resource of alternations with the corresponding resource of thresholds. Threshold parallel computers are much more powerful than the standard models (for example, with only polynomially many processors, they can compute the parity function and sort in constant time, and multiply two integers in O(log*n) time), and appear less amenable to known lower-bound proof techniques.

Parallel Computation with Threshold Functions

Some optimal path planning algorithms for navigating mobile rectangular robot among obstacles and weighted regions are presented. The approach is based on a higher geometry maze routing algorithm. Starting from a top view of a workspace with obstacles, the so-called free workspace is first obtained by virtually expanding the obstacles in the image. After that, an 8-geomerty maze routing algorithm is applied to obtain an optimal collision-free path with linear time and space complexities. The proposed methods cannot only search an optimal path among various terrains but also find an optimal path for the 2-D piano mover's problem with 3 DOF. Furthermore, the algorithm can be easily extended to the dynamic collision avoidance problem among multiple autonomous robots or path planning in the 3-D space.

Ian Parberry

Papers

Circuit complexity and neural networks

3D math primer for graphics and game development

Parallel Computation with Threshold Functions

Optimal Path Planning for Mobile Robot Navigation

On the construction of parallel computers from various bases of Boolean functions