I am a medical researcher and quantum systems engineer, whose research
interests focus upon quantum spin microscopy in service of regenerative
The primary objective of my research is SHOW: the Synthesis for Healing Our Warriors, and SHOW is the perennial focus of our UW/ISH Intent and Guidance Seminar.
A one-page math syllabus of the 2012 I&G Seminar is viewable here. By design, this syllabus focuses upon aspects of modern mathematical naturality that encompass and unify a broad swathe of STEM enterprises, focusing in particular upon the mathemtically natural elements of separatory transport (NEST).
The mathematical formalism of the 2012 NEST I&G Seminar will be geometric throughout, in fairly strict accord with the mathematical notation of Jack Lee's Introduction to Smooth Manifolds (2003), and encompassing the spin physics of Charles Slichter's Principles of Magnetic Resonance (1990), the quantum informatics of Michael Nielsen and Isaac Chuang's Quantum Computation and Quantum Information (2001), the quantum physics of Abhay Ashtekar and Troy Schilling's Geometrical formulation of quantum mechanics (1997), the geometric thermodynamics of John Krommes and Genze Hu's General theory of Onsager symmetries (1993) and George Ruppeiner's Riemannian geometry in thermodynamic fluctuation theory (1995), implemented within the practical computational framework of Daan Frenkel and Berend Smit's Understanding Molecular Simulation: from Algorithms to Applications, and applied within a reconsideration and extension of the survey by Bob Griffin and coauthors Dynamic nuclear polarization at high magnetic fields (2008).
The broad focus of the 2012 NEST I&G Seminar will accord with the enterprise-centric viewpoint of Calvin Gidding's textbook Unified Separation Science, as updated in light of the above-mentioned advances in geometric classical dynamics, geometric quantum mechanics, and geometric thermodynamics, and then as applied to clinical opportunities in dynamic nuclear polarization (DNP) and in hyperpolarized medical imaging generally.
The envisioned resolution of the 2012 NEST I&G Seminar is sustainment of the historical doubling cadence of magnetic resonance sensitivity in service of the SHOW enterprise, by an operational strategy of speeding the pace, retiring the risks, focusing the capabilities, and uniting the efforts, of the individual enterprises that are associated to SHOW.
An historical aside: Colleagues for whom the history of the STEM enterprise is substantially the history of geometric ideas and methods are referred to Joshiah Willard Gibbs' article A method of geometrical representation of the thermodynamic properties of substances by means of surfaces (1873), which anticipates many of the key physical ideas and geometric mathematical methods of the seminar.
Q: Synthesis for Healing Our
Warriors (SHOW)! What's that?
A: SHOW is an enterprise whose primary objective is the healing and restoration
to ordinary daily life of wounded warriors. DNP-ST is an enabling capability
for SHOW that, by imaging healing processes at atomic resolution, serves to
speed the pace, retire the risks, and focus the strategy of achieving the directed
regenerative healing of even the most severe and intractable battle wounds.
pace, retiring the risks, increasing the capabilities, and focusing
SHOW's strategy has been the primary motive for developing DNP-ST; this website
documents the resulting (and accelerating) progress toward SHOW's main objective:
the healing and restoration to daily life of wounded warriors.
SHOW can be
appreciated as an accelerated realization of the NIH Roadmap
along the imaging-centric lines of Elias Zerhouni's 2007 Pendergrass Lecture,
as augmented by transformational new capabilities in observational epigenomics
that are being enabled by the advances in DNP-ST reported here.
New for July 29, 2011
The meeting Black Forest Focus on Soft Matter 6: Magnetic Resonance at the Microscale is finished, and it was terrific!
Our UW QSE Group's presentation was titled. Transport Mechanisms for Inducing Dynamic Nuclear Polarization in Magnetic Resonance Microsystems: Dynamical Theory, Design Rules, and Experimental Protocols. The gist of it follow …
On average, magnetic resonance channel capacity has doubled every year for 65 years.
Q: Can this doubling pace be
A: Yes, via Dynamically Natural (hyper) Polarization
by (quantum) Separative Transport (DNP-ST).
We've been experimenting with various names and acronyms for this new mechanism for hyperpolarization and it looks like the final choice will be Dynamically Natural (hyper) Polarization by (quantum) Separative Transport (DNP-ST) (and version 1.3 of the slides now reflects this convention)
Q: What topics are
A: (1) Objectives and metrics for progress in quantum spin imaging and spectroscopy,
(2) Technical means for progress (from math, science, and engineering), and
(3) Global-scale enterprises arising from continued progress.
Q: What are the key objectives and technical metrics of this
A: The key objective is to sustain the historical cadence of advancement,
that is, the yearly doubling since 1946 of magnetic resonance sensitivity.
The key metric is the achieved Shannon channel capacity (per the lecture).
Natural (hyper) Polarization by (quantum)
(DNP-ST)! What's that?
A: Dynamically Natural Polarization-exchange interactions (in leading order) create
nuclear hyperpolarization by Separatively Transporting up-spins & down-spins.
DNP-ST is stronger, faster, and more power-efficient than traditional DNP,
because the older method is based upon non-leading transfer dynamics,
as contrasted with DNP-ST's leading-order separative transport.
Q: Separative Transport
(ST)! What's that?
A: Separative transport is a key enterprise technology that “just works”
in concentrating and purifing quantities such as (clockwise from top) quantum
states of laser gain media (as required for laser output), coherence in quantum
cryptography, chemical and petroleum feedstocks, desalinated water, photoelectric
and thermoelectric power, nuclear isotopes, and cell nutrients and electrolytes.
Microscopic details vary greatly among these processes, yet fundamentally
they all are alike in that (1) the dynamics is constrained by conservation laws
(for example, conservation of energy, chemical species, charge, or polarization),
(2) an entropy gradient is externally induced (via heat, sunlight, electric current,
chemical potential, or magnetic fields), and (3) the entropy gradient induces
coupled dynamical flows (for example, flows of 235U and 238U, thermal energy
and electric current, quantum correlations, sodium ions and glucose, quanta
in pumped laser gain media, dissolved salts in seawater, and chemical products
undergoing distillation) that all accomplish valuable separative purposes
(like sustained light-amplifying population inversions in laser gain media).
The importance of these separative purposes, and the richness of their physics,
is the reason why — for more than a century — the science and engineering
of separative transport processes has been among the most lively, dramatic,
strategically vital, and entrepreneurially job-creating, of all STEM disciplines.
Q: Natural mathematics! What's that?
A: Ideas that don't depend upon arbitrary conventions (like coordinates) are said
to be mathematically natural. DNP-ST is born of the union of natural dynamics
(both classical and quantum) with First and Second Laws of thermodynamics
(with is the foundation of the modern theory of separative transport).
mathematical foundations of transport theory arise in geometry,
and thus can be challenging to grasp:
own natural appreciation of mathematics and dynamics
is quite a lot of work, yet well-worth the effort (as Hermione knows):
“magic” that Hermione is painstakingly teaching to Ron and
is discussed below. Yes, you have to “mean it to learn it”.
Q: What is DNP-ST good for?
A: In spin biomicroscopy, DNP-ST boosts signal strength and reduces noise;
this key capability sustains the sensitivity-doubling cadence.
Q: Dirac's separative value function! What's that?
A: Dirac's separative value function is a well-known and and mathematically simple
measure of the work accomplished in isotope separation. It provides the
starting-point of Dirac's theory of optimized separative transport cascades,
which are cascades that maximize the value function's rate-of-increase.
DNP-ST is the first nuclear-spin hyperpolarization method that is naturally
compatible with Dirac's theory (in particular, the slide below derives Dirac's
function as the thermodynamically natural work accomplished in DNP-ST).
Physically speaking, DNP-ST separates up- from down-polarization
by processes that are physically analogous and mathematically isomorphic
to separating 12C from 13C (or U235 from U238) by gas centrifuge cascades.
In strategic terms, the isotope separation technologies of the 20th century
provided concentrated sources of energy; now in the 21st century,
DNP-ST technologies provide concentrated sources of Shannon channel capacity.
For both isotope separation and DNP-ST the concentration ratio (of specific
energy / channel capacity) is of order 105 to 107, such that both technologies
transformationally augment 20-21st century STEM enterprise capabilities.
Q: Shannon capacity! What's
A: Shannon capacity is the number of bits-per-second of information
that a sample can transmit to an observer (it is easy to calculate).
far can we push magnetic resonance imaging and spectroscopy?
A: Thanks to new methods for distilling spin coherence (DNP-ST in particular),
there is quantum headroom for ~27 more yearly doublings of channel capacity.
Q: What are some consequences
of sustainment via spin hyperpolarization?
A: Comprehensive surveys of epigenetic structural dynamics.
New for July 22, 2011 For an overvew of our math, science, engineering, and medical objectives, see our answer posted on MathOverflow to Gil Kalai's question "What is a book you would like to write?"
The image below is a link to the the first page of a (reasonably non-technical) 3-page PDF summary of my present research interests. These interests are presently focused upon the experimental demonstration of transport-driven nuclear spin hyperpolarization, for purposes of amplifying signal strength and reducing noise levels in quantum spin biomicroscopy.
For details, read on.
For a (relatively) non-technical overview of this work, see our PNAS Commentary Spin microscopy's heritage, achievements, and prospects
Synopsis: Chapter 4 is the sequel to Chapter 3: Magnetic Dipolar Broadening and Transport Dynamics of Rigid Lattices that we presented at Asilomar (as described below).
In essence, Chapter 4 describes how to turn these ideas into hardware that is useful (among other purposes) for transformationally accelerating the pace of research in regenerative medicine.
Here is our UW Quantum Systems Engineering (QSE) Group's poster "Quantum Spin Microscopy's Emerging Methods, Roadmaps, and Enterprises", as presented at the 52nd ENC, Asilomar, CA.
Our ENC poster is an imagined 21st century edition of Charlie Slichter's celebrated textbook Principles of Magnetic Resonance (1963), specifically an extended version of Slichter's Chapter 3 "Magnetic Dipolar Broadening of Rigid Lattices".
We color-coded the text of our imagined 21st century edition as follows:
We did have one very special visitor ...
... who was Charlie Slichter himself!
Building on the well-validated dipolar spin physics of Slichter's original text, three new topics are introduced:
The green box (below) states a key theorem. To assist non-specialists, the definitions associated to the theorem are stated in detail; thus the theorem can be read in two ways:
Option A Readers familiar with standard definitions in geometric dynamics can skip directly to the statement of the theorem.
Option B Readers familiar with vector-space quantum mechanics formalisms, but not geometric dynamical formalisms, can parse the definitions incrementally, as (effectively) encompassing the main dynamical elements of Nielsen and Chuang's Quantum Computation and Quantum Information (2000) in the mathematical language of four classic texts:
Here is a key theorem that draws upon the above "Yellow Book" math to obtain a result that is useful in large-scale spin simulations. To assist students (especially), mathematical elements associated to the Hilbert state-space appear in blue, while elements associated to the simulation state-space appear in red:
Pulled-back state-spaces are varieties Viewed as an algebraic variety, Kr belongs to the class of r'th secant varieties of n-factor Segre varieties; the many practical applications of this class of varieties are reviewed in Joseph Landsberg's Geometry and the complexity of matrix multiplication (2008).
Algebraic geometers call the simulation state-space Kr a variety (rather than a manifold) because dim Kr is non-constant in consequence of singular points at which the dimensionality of Kr drops and the Riemann curvature of K diverges; in consequence of these singularities Kr (formally speaking) is not a manifold, but rather has a more subtle geometric structure associated to the singularities.
Hilbert space is itself a ruled join As it happens, some joins are singularity-free; Hilbert space itself can be regarded as a linear join of exponentially many trivial (degree zero) algebraic varieties (one variety for each Hilbert space basis vector). From this catholic point of view, the n-particle Hilbert join Hn and the rank-r Kronecker join Kr both are projective algebraic varieties, both are members of a natural stratification of quantum state-spaces (as set forth in the definitions that are associated to quantum pullback theorem given above), and so the natural question "Does Hn pullback onto Kr or does Kr pullback onto Hn?" has the well-posed answer "yes" in both directions.
Pullback is robust A key feature of the quantum pullback theorem is that it holds at all points of Kr (including the singular points). The practical consequence is that as dynamical trajectories approach and pass through the singular points of Kr, simulation codes ``just keep running''... and yield sensible physical predictions that respect symmetries and conservation laws.
Quantum-to-classical transitions are smooth Physically the quantum pullback theorem ensures that quantum-to-classical transitions (and their associated reduction of state-space dimensionality) are dynamically smooth.
The ubiquitous Kronecker product A broader venue for appreciating the quantum pullback theorem is provided by Charles van Loan's terrific article "The ubiquitous Kronecker product". The figure below is van Loan's listing of the (many) natural algebraic properties that the Kronecker product possesses:
The quantum pullback theorem can be regarded as the algebraically natural extension of van Loan's list of natural Kronecker properties to the domain of quantum dynamical potentials and differential forms.
The present poster PDF files are Version 2.5 (April 15, 2011); and they include three extra pages of material relative to the original paper poster.
Here are three audio files:
The Slichter lecture was accompanied by these slides (apologies are extended for their marginal photographic quality):
Further material is presented in Prof. Slichter's recent Physical Chemistry Chemical Physics article "The discovery and demonstration of dynamic nuclear polarization: a personal and historical account"