Michael Christopher Wendl

Last updated
Michael Wendl
Michael Wendl Headshot.png
Nationality American
Known for Phred base calling
Couette flow [1]
DNA sequencing theory
Scientific career
Fields Computational biology
Probability
Doctoral advisor Ramesh K. Agarwal [2]
Other academic advisors Bob Waterston (post-doctoral)
Website wendl.weebly.com

Michael Christopher Wendl is a mathematician and biomedical engineer who has worked on DNA sequencing theory, [3] covering and matching problems in probability, theoretical fluid mechanics, and co-wrote Phred. [4] He was a scientist on the Human Genome Project and has done bioinformatics and biostatistics work in cancer. Wendl is of ethnic German heritage and is the son of the aerospace engineer Michael J. Wendl. [5]

Contents

Research Work

Theoretical Fluid Mechanics

The problem of low Reynolds number flow in the gap between 2 infinite cylinders, so-called Couette flow, was solved in 1845 by Stokes. [6] Wendl reported the generalization of this solution for finite-length cylinders, [1] [7] which can actually be built for experimental work, in 1999, as a series of modified Bessel functions and . He also examined a variety of other low Reynolds number rotational devices and shear-driven devices, including a general form of the unsteady disk flow problem, for which the velocity profile is: [8]

where , , , and are physical parameters, are eigen-values, and are coordinates. This result united prior-published special cases for steady flow, infinite disks, etc. [8]

Covering and Matching Problems in Probability

Wendl examined a number of matching and covering problems in combinatorial probability, especially as these problems apply to molecular biology. He determined the distribution of match counts of pairs of integer multisets in terms of Bell polynomials, [9] a problem directly relevant to physical mapping of DNA. Prior to this, investigators had used a number of ad-hoc quantifiers, like the Sulston score, which idealized match trials as being independent. His result for the multiple-group birthday proposition [10] solves various related "collision problems", e.g. some types of P2P searching. [11] He has also examined a variety of 1-dimensional covering problems (see review by Cyril Domb [12] ), generalizing the basic configuration to forms relevant to molecular biology. [13] [14] His covering investigation of rare DNA variants with Richard K. Wilson [15] played a role in designing the 1000 Genomes Project. [16]

Bioinformatics and Biostatistics

Wendl co-wrote Phred, a widely used DNA trace analyzer that converted raw output stream of early DNA sequence machines to sequence strings. [17] [18] He has contributed extensively to biostatistical analysis of cancer studies [19] [20] and to the bioinformatics toolbase, [21] collaborating frequently with Li Ding, Elaine Mardis, and Richard K. Wilson.

Personal life

Wendl's heritage is ethnic German, originating from the Banat region of the old Austro-Hungarian Empire and he is the son of the aerospace engineer Michael J. Wendl. [5] He is married to the former Pamela Bjerkness of Chicago [22]

Related Research Articles

In physics, the cross section is a measure of the probability that a specific process will take place in a collision of two particles. For example, the Rutherford cross-section is a measure of probability that an alpha particle will be deflected by a given angle during an interaction with an atomic nucleus. Cross section is typically denoted σ (sigma) and is expressed in units of area, more specifically in barns. In a way, it can be thought of as the size of the object that the excitation must hit in order for the process to occur, but more exactly, it is a parameter of a stochastic process.

<span class="mw-page-title-main">Pauli matrices</span> Matrices important in quantum mechanics and the study of spin

In mathematical physics and mathematics, the Pauli matrices are a set of three 2 × 2 complex matrices that are Hermitian, involutory and unitary. Usually indicated by the Greek letter sigma, they are occasionally denoted by tau when used in connection with isospin symmetries.

In particle physics, the Dirac equation is a relativistic wave equation derived by British physicist Paul Dirac in 1928. In its free form, or including electromagnetic interactions, it describes all spin-12 massive particles, called "Dirac particles", such as electrons and quarks for which parity is a symmetry. It is consistent with both the principles of quantum mechanics and the theory of special relativity, and was the first theory to account fully for special relativity in the context of quantum mechanics. It was validated by accounting for the fine structure of the hydrogen spectrum in a completely rigorous way.

In the mathematical field of differential geometry, the Riemann curvature tensor or Riemann–Christoffel tensor is the most common way used to express the curvature of Riemannian manifolds. It assigns a tensor to each point of a Riemannian manifold. It is a local invariant of Riemannian metrics which measures the failure of the second covariant derivatives to commute. A Riemannian manifold has zero curvature if and only if it is flat, i.e. locally isometric to the Euclidean space. The curvature tensor can also be defined for any pseudo-Riemannian manifold, or indeed any manifold equipped with an affine connection.

<span class="mw-page-title-main">Lorentz group</span> Lie group of Lorentz transformations

In physics and mathematics, the Lorentz group is the group of all Lorentz transformations of Minkowski spacetime, the classical and quantum setting for all (non-gravitational) physical phenomena. The Lorentz group is named for the Dutch physicist Hendrik Lorentz.

In econometrics, the autoregressive conditional heteroskedasticity (ARCH) model is a statistical model for time series data that describes the variance of the current error term or innovation as a function of the actual sizes of the previous time periods' error terms; often the variance is related to the squares of the previous innovations. The ARCH model is appropriate when the error variance in a time series follows an autoregressive (AR) model; if an autoregressive moving average (ARMA) model is assumed for the error variance, the model is a generalized autoregressive conditional heteroskedasticity (GARCH) model.

In differential topology, the jet bundle is a certain construction that makes a new smooth fiber bundle out of a given smooth fiber bundle. It makes it possible to write differential equations on sections of a fiber bundle in an invariant form. Jets may also be seen as the coordinate free versions of Taylor expansions.

In abstract algebra, Hilbert's Theorem 90 (or Satz 90) is an important result on cyclic extensions of fields (or to one of its generalizations) that leads to Kummer theory. In its most basic form, it states that if L/K is an extension of fields with cyclic Galois group G = Gal(L/K) generated by an element and if is an element of L of relative norm 1, that is

In mathematics, the Fubini–Study metric is a Kähler metric on a complex projective space CPn endowed with a Hermitian form. This metric was originally described in 1904 and 1905 by Guido Fubini and Eduard Study.

In mathematics, Schubert calculus is a branch of algebraic geometry introduced in the nineteenth century by Hermann Schubert in order to solve various counting problems of projective geometry and, as such, is viewed as part of enumerative geometry. Giving it a more rigorous foundation was the aim of Hilbert's 15th problem. It is related to several more modern concepts, such as characteristic classes, and both its algorithmic aspects and applications remain of current interest. The term Schubert calculus is sometimes used to mean the enumerative geometry of linear subspaces of a vector space, which is roughly equivalent to describing the cohomology ring of Grassmannians. Sometimes it is used to mean the more general enumerative geometry of algebraic varieties that are homogenous spaces of simple Lie groups. Even more generally, Schubert calculus is sometimes understood as encompassing the study of analogous questions in generalized cohomology theories.

<span class="mw-page-title-main">Toroidal coordinates</span>

Toroidal coordinates are a three-dimensional orthogonal coordinate system that results from rotating the two-dimensional bipolar coordinate system about the axis that separates its two foci. Thus, the two foci and in bipolar coordinates become a ring of radius in the plane of the toroidal coordinate system; the -axis is the axis of rotation. The focal ring is also known as the reference circle.

Expected shortfall (ES) is a risk measure—a concept used in the field of financial risk measurement to evaluate the market risk or credit risk of a portfolio. The "expected shortfall at q% level" is the expected return on the portfolio in the worst of cases. ES is an alternative to value at risk that is more sensitive to the shape of the tail of the loss distribution.

A ratio distribution is a probability distribution constructed as the distribution of the ratio of random variables having two other known distributions. Given two random variables X and Y, the distribution of the random variable Z that is formed as the ratio Z = X/Y is a ratio distribution.

The Orr–Sommerfeld equation, in fluid dynamics, is an eigenvalue equation describing the linear two-dimensional modes of disturbance to a viscous parallel flow. The solution to the Navier–Stokes equations for a parallel, laminar flow can become unstable if certain conditions on the flow are satisfied, and the Orr–Sommerfeld equation determines precisely what the conditions for hydrodynamic stability are.

In applied mathematics, specifically in fuzzy logic, the ordered weighted averaging (OWA) operators provide a parameterized class of mean type aggregation operators. They were introduced by Ronald R. Yager. Many notable mean operators such as the max, arithmetic average, median and min, are members of this class. They have been widely used in computational intelligence because of their ability to model linguistically expressed aggregation instructions.

In probability and statistics, the Tweedie distributions are a family of probability distributions which include the purely continuous normal, gamma and inverse Gaussian distributions, the purely discrete scaled Poisson distribution, and the class of compound Poisson–gamma distributions which have positive mass at zero, but are otherwise continuous. Tweedie distributions are a special case of exponential dispersion models and are often used as distributions for generalized linear models.

DNA sequencing theory is the broad body of work that attempts to lay analytical foundations for determining the order of specific nucleotides in a sequence of DNA, otherwise known as DNA sequencing. The practical aspects revolve around designing and optimizing sequencing projects, predicting project performance, troubleshooting experimental results, characterizing factors such as sequence bias and the effects of software processing algorithms, and comparing various sequencing methods to one another. In this sense, it could be considered a branch of systems engineering or operations research. The permanent archive of work is primarily mathematical, although numerical calculations are often conducted for particular problems too. DNA sequencing theory addresses physical processes related to sequencing DNA and should not be confused with theories of analyzing resultant DNA sequences, e.g. sequence alignment. Publications sometimes do not make a careful distinction, but the latter are primarily concerned with algorithmic issues. Sequencing theory is based on elements of mathematics, biology, and systems engineering, so it is highly interdisciplinary. The subject may be studied within the context of computational biology.

In mathematics a translation surface is a surface obtained from identifying the sides of a polygon in the Euclidean plane by translations. An equivalent definition is a Riemann surface together with a holomorphic 1-form.

Type-1 OWA operators are a set of aggregation operators that generalise the Yager's OWA operators) in the interest of aggregating fuzzy sets rather than crisp values in soft decision making and data mining.

In mathematics, Ricci calculus constitutes the rules of index notation and manipulation for tensors and tensor fields on a differentiable manifold, with or without a metric tensor or connection. It is also the modern name for what used to be called the absolute differential calculus, developed by Gregorio Ricci-Curbastro in 1887–1896, and subsequently popularized in a paper written with his pupil Tullio Levi-Civita in 1900. Jan Arnoldus Schouten developed the modern notation and formalism for this mathematical framework, and made contributions to the theory, during its applications to general relativity and differential geometry in the early twentieth century.

References

  1. 1 2 Bordag LA et al. (2005) Interaction of a rotational motion and an axial flow in small geometries for a Taylor–Couette problem , J. Fluids and Structures 20(5), 621–641. The authors comment directly on Wendl's solution appearing so long after the classical problem discussed by Stokes in 1845: "It is also a bit astonishing that the exact analytical solution for the azimuthal component of the Taylor–Couette flow profile with boundary conditions on cylinder caps was obtained just recently in the work of Wendl (1999). His results expose the strong influence of caps on flow profiles."
  2. "Michael Wendl - the Mathematics Genealogy Project".
  3. Dorman, N (2006) The long and short of it, BioTechniques 41(4), pp 367.
  4. Ewing, B., Hillier, L., Wendl, M.C., and Green, P. (1998) Base-calling of automated sequencer traces using phred. I. Accuracy assessment. Genome Research 8(3), 175–185. PMID   9521921 full article
  5. 1 2 P Hummel and N Fuhry: "Sackelhausen im Banat" Volume 3, published by Heimatsortsgemeinschaft Sackelhausen, Reutlingen FRG, 2007, pages 2236-2237.
  6. G.G. Stokes(1845) ``On the theories of the internal friction of fluids in motion and of the equilibrium and motion of elastic solids, in Mathematical and Physical Papers, pp. 102-104, Cambridge, UK: Cambridge University Press, 1880.
  7. Wendl MC (1999) General Solution for the Couette Flow Profile , Physical Review E 60(5), 6192–6194.
  8. 1 2 Wendl MC (2001) Mathematical analysis of coaxial disk cellular shear loading devices, Review of Scientific Instruments 72(11), 4212-4217.
  9. Wendl MC (2005) Probabilistic assessment of clone overlaps in DNA fingerprint mapping via a priori models, J. Comp. Biol. 12(3), 283-297.
  10. Wendl MC (2003) Collision probability between sets of random variables, Stat. Prob. Lett. 64(3), 249–254.
  11. Hautakorpi, J and Schultz, G (2010) A Feasibility Study of an Arbitrary Search in Structured Peer-to-Peer Networks, IEEE Computer Communications and Networks, Proc ICCCN, pp 1–8.
  12. Cyril Domb (1989) Covering by random intervals and one-dimensional continuum percolation, J. Stat. Phys. 55, 441-460.
  13. Wendl MC (2008) Random covering of multiple one-dimensional finite domains with an application to DNA sequencing, SIAM J. Appl. Math. 68(3), 890-905.
  14. Wendl MC, Kota K, Weinstock GM, and Mitreva M (2013) Coverage theories for metagenomic DNA sequencing based on a generalization of Stevens' theorem, J. Math. Biol. 67(5), 1141-1161.
  15. Wendl MC and Wilson RK (2009) The theory of discovering rare variants via DNA sequencing, BMC Genomics 10 art. 485.
  16. Altshuler DM et al. (2010) A map of human genome variation from population-scale sequencing, Nature 467(7319), 1061-1073.
  17. Koboldt, D. C. and Miller, R. D. (2011) Identification of Polymorphic Markers for Genetic Mapping, chapter 2 in "Genomics: Essential Methods", John Wiley and Sons.
  18. Highsmith, W. E. (2006) Electrophoretic Methods for Mutation Detection and DNA Sequencing, chapter 9 in "Molecular Diagnostics for the Clinical Laboratorian", Humana Press
  19. Lu C, Xie M, Wendl MC et al. (2015) Patterns and functional implications of rare germline variants across 12 cancer types, Nature Comm. 6 art. 10086.
  20. Chen, F, Wendl MC, Wyczalkowski MA, Bailey MH, Li Y, and Ding, L (2015) Moving pan-cancer studies from basic research toward the clinic, Nature Cancer 2(9), 879-890.
  21. Wendl MC et al. (2011) PathScan: A tool for discerning mutational significance in groups of putative cancer genes, Bioinformatics 27(12), 1595-1602.
  22. Hochzeitsglocken lauteten fur Pamela Marie and Michael Christopher Wendl, Eintracht 74(13), page 6.