text:
Christofer Toumazou

According to our database1, Christofer Toumazou authored at least 155 papers between 1993 and 2019.

Collaborative distances:
• Dijkstra number2 of four.
• Erdős number3 of four.

IEEE Fellow

IEEE Fellow 2001, "For contributions to the field of analog circuit design with particular emphasis on current-mode signal processing.".

Book
In proceedings
Article
PhD thesis
Other

Bibliography

2019
System on Chip for Closed Loop Neuromodulation Based on Dual Mode Biosignals.
Proceedings of the IEEE International Symposium on Circuits and Systems, 2019

A computational model for anti-cancer drug sensitivity prediction.
Proceedings of the 2019 IEEE Biomedical Circuits and Systems Conference, 2019

2018
Adapting ISFETs for Epigenetics: An Overview.
IEEE Trans. Biomed. Circuits and Systems, 2018

PERSON - Personalized Expert Recommendation System for Optimized Nutrition.
IEEE Trans. Biomed. Circuits and Systems, 2018

Influence of Cholecystokinin-8 on Compound Nerve Action Potentials from Ventral Gastric Vagus in Rats.
Int. J. Neural Syst., 2018

A Deep Autoencoder System for Differentiation of Cancer Types Based on DNA Methylation State.
CoRR, 2018

Live Demo: Reconfigurable Low-noise Multichannel Amplifier for Neurochemical Recording.
Proceedings of the IEEE International Symposium on Circuits and Systems, 2018

Reconfigurable Low-noise Multichannel Amplifier for Neurochemical Recording.
Proceedings of the IEEE International Symposium on Circuits and Systems, 2018

A trapped charge compensation scheme for ISFET based translinear circuits.
Proceedings of the IEEE International Symposium on Circuits and Systems, 2018

Links Between DNA-Based Diet and Salivary Leptin Hormone Concentration.
Proceedings of the 2018 IEEE Biomedical Circuits and Systems Conference, 2018

2017
Supervised learning for infection risk inference using pathology data.
BMC Med. Inf. & Decision Making, 2017

Enhancing automatic closed-loop glucose control in type 1 diabetes with an adaptive meal bolus calculator - in silico evaluation under intra-day variability.
Comput. Methods Programs Biomed., 2017

Live demonstration: A CMOS-based ISFET array for rapid diagnosis of the Zika virus.
Proceedings of the IEEE International Symposium on Circuits and Systems, 2017

Injection moulded microneedle sensor for real-time wireless pH monitoring.
Proceedings of the 2017 39th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC), 2017

Improving the pH sensitivity of ISFET arrays with reactive ion etching.
Proceedings of the IEEE Biomedical Circuits and Systems Conference, 2017

Live demo: Platform for closed loop neuromodulation based on dual mode biosignals.
Proceedings of the IEEE Biomedical Circuits and Systems Conference, 2017

A deep belief network system for prediction of DNA methylation.
Proceedings of the IEEE Biomedical Circuits and Systems Conference, 2017

2016
An Advanced Bolus Calculator for Type 1 Diabetes: System Architecture and Usability Results.
IEEE J. Biomedical and Health Informatics, 2016

Live demonstration: Smartwatch implementation of an advanced insulin bolus calculator for diabetes.
Proceedings of the IEEE International Symposium on Circuits and Systems, 2016

An ISFET-based switched current DNA integrator.
Proceedings of the IEEE International Symposium on Circuits and Systems, 2016

Epigenetic-IC: A fully integrated sensing platform for epigenetic reaction monitoring.
Proceedings of the IEEE International Symposium on Circuits and Systems, 2016

A weak inversion ISFET current mirror for differential bio-sensing.
Proceedings of the IEEE Biomedical Circuits and Systems Conference, 2016

2015
Advanced Insulin Bolus Advisor Based on Run-To-Run Control and Case-Based Reasoning.
IEEE J. Biomedical and Health Informatics, 2015

Method for automatic adjustment of an insulin bolus calculator: In silico robustness evaluation under intra-day variability.
Comput. Methods Programs Biomed., 2015

A low-noise instrumentation amplifier with DC suppression for recording ENG signals.
Proceedings of the 37th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, 2015

2014
Bio-Inspired Glucose Control in Diabetes Based on an Analogue Implementation of a $\beta$-Cell Model.
IEEE Trans. Biomed. Circuits and Systems, 2014

A Low Power Sub-µW Chemical Gilbert Cell for ISFET Differential Reaction Monitoring.
IEEE Trans. Biomed. Circuits and Systems, 2014

Parylene C-Based Flexible Electronics for pH Monitoring Applications.
Sensors, 2014

A lab-on-chip approach for monitoring the electrochemical activity of biorealistic cell cultures.
Proceedings of the IEEE International Symposium on Circuits and Systemss, 2014

A temperature insensitive continuous time ΔpH to digital converter.
Proceedings of the IEEE International Symposium on Circuits and Systemss, 2014

An ISFET based analogue ratiometric method for DNA methylation detection.
Proceedings of the IEEE International Symposium on Circuits and Systemss, 2014

Live demonstration: An advanced bolus calculator for diabetes management - A clinical and patient platform.
Proceedings of the IEEE Biomedical Circuits and Systems Conference, 2014

Live demonstration: A handheld Bio-inspired Artificial pancreas for treatment of diabetes.
Proceedings of the IEEE Biomedical Circuits and Systems Conference, 2014

Towards Ultra-low Power Bio-inspired Processing.
Proceedings of the Body Sensor Networks, 2014

2013
Empirical Mode Decomposition: Real-Time Implementation and Applications.
Signal Processing Systems, 2013

A Bionics Chemical Synapse.
IEEE Trans. Biomed. Circuits and Systems, 2013

The spatial pattern of light determines the kinetics and modulates backpropagation of optogenetic action potentials.
Journal of Computational Neuroscience, 2013

Improving prediction of exchange rates using Differential EMD.
Expert Syst. Appl., 2013

Noise Reduction for Nonlinear Nonstationary Time Series Data using Averaging Intrinsic Mode Function.
Algorithms, 2013

Prediction of exchange rates using averaging intrinsic mode function and multiclass support vector regression.
Artif. Intell. Research, 2013

REFET replication for ISFET-based SNP detection arrays.
Proceedings of the 2013 IEEE International Symposium on Circuits and Systems (ISCAS2013), 2013

Temporal processing with volatile memristors.
Proceedings of the 2013 IEEE International Symposium on Circuits and Systems (ISCAS2013), 2013

A piecewise linear approximating ISFET readout.
Proceedings of the 2013 IEEE Biomedical Circuits and Systems Conference (BioCAS), Rotterdam, The Netherlands, October 31, 2013

2012
A Simulation Study of the Combined Thermoelectric Extracellular Stimulation of the Sciatic Nerve of the Xenopus Laevis: The Localized Transient Heat Block.
IEEE Trans. Biomed. Engineering, 2012

Inductive and Ultrasonic Multi-Tier Interface for Low-Power, Deeply Implantable Medical Devices.
IEEE Trans. Biomed. Circuits and Systems, 2012

An Efficient Implementation of the SIVIA Algorithm in a High-Level Numerical Programming Language.
Reliable Computing, 2012

Frequency analysis of wireless accelerometer and EMG sensors data: Towards discrimination of normal and asymmetric walking pattern.
Proceedings of the 2012 IEEE International Symposium on Circuits and Systems, 2012

Measurement of cell and bacterial activity using array-based ISFET Chemical Current-Conveyor in weak-inversion.
Proceedings of the 2012 IEEE International Symposium on Circuits and Systems, 2012

A CMOS architecture allowing parallel DNA comparison for on-chip assembly.
Proceedings of the 2012 IEEE International Symposium on Circuits and Systems, 2012

A fully-programmable neural interface for multi-polar, multi-channel stimulation strategies.
Proceedings of the 2012 IEEE International Symposium on Circuits and Systems, 2012

Theoretical investigation of transcranial alternating current stimulation using laminar model.
Proceedings of the Annual International Conference of the IEEE Engineering in Medicine and Biology Society, 2012

2011
Modeling Study of the Light Stimulation of a Neuron Cell With Channelrhodopsin-2 Mutants.
IEEE Trans. Biomed. Engineering, 2011

A Biomimetic Model of the Outer Plexiform Layer by Incorporating Memristive Devices
CoRR, 2011

A bio-implantable platform for inductive data and power transfer with integrated battery charging.
Proceedings of the International Symposium on Circuits and Systems (ISCAS 2011), 2011

A 5s-time-constant temperature-stable integrator for a tuneable PID controller in LOC applications.
Proceedings of the International Symposium on Circuits and Systems (ISCAS 2011), 2011

Live demonstration: A CMOS-based lab-on-chip array for combined magnetic manipulation and opto-chemical sensing.
Proceedings of the International Symposium on Circuits and Systems (ISCAS 2011), 2011

"Capacitive" pulse shapes for platinum cuff electrodes.
Proceedings of the 33rd Annual International Conference of the IEEE Engineering in Medicine and Biology Society, 2011

A robust microfluidic in vitro cell perifusion system.
Proceedings of the 33rd Annual International Conference of the IEEE Engineering in Medicine and Biology Society, 2011

High-frequency limit of neural stimulation with ChR2.
Proceedings of the 33rd Annual International Conference of the IEEE Engineering in Medicine and Biology Society, 2011

Bio-inspired semiconductors for early detection and therapy.
Proceedings of the IEEE Asian Solid-State Circuits Conference, 2011

2010
Application of Maxwell-Wagner polarization in delay lines.
Microelectron. J., 2010

An Integrated ISFETs Instrumentation System in Standard CMOS Technology.
J. Solid-State Circuits, 2010

A multichannel DNA SoC for rapid point-of-care gene detection.
Proceedings of the IEEE International Solid-State Circuits Conference, 2010

A silicon pancreatic islet for the treatment of diabetes.
Proceedings of the International Symposium on Circuits and Systems (ISCAS 2010), May 30, 2010

RF inductive sensors for detection of change in the ionic strength and pH of liquid samples.
Proceedings of the International Symposium on Circuits and Systems (ISCAS 2010), May 30, 2010

Fabrication and electrical characteristics of memristors with TiO2/TiO2+x active layers.
Proceedings of the International Symposium on Circuits and Systems (ISCAS 2010), May 30, 2010

A bio-inspired ultrasensitive imaging chip - Phase one: Design paradigm.
Proceedings of the International Symposium on Circuits and Systems (ISCAS 2010), May 30, 2010

An ISFET based sensing array with sensor offset compensation and pH sensitivity enhancement.
Proceedings of the International Symposium on Circuits and Systems (ISCAS 2010), May 30, 2010

A review on memristive devices and applications.
Proceedings of the 17th IEEE International Conference on Electronics, 2010

2009
Nanopower Subthreshold MCML in Submicrometer CMOS Technology.
IEEE Trans. on Circuits and Systems, 2009

Subthreshold Parallel FM-to-Digital Delta- Sigma Converter With Output-Bit-Stream Addition by Interleaving.
IEEE Trans. on Circuits and Systems, 2009

A 30 pA/V-25µA/V linear CMOS channel-length-modulation OTA.
Microelectron. J., 2009

A CMOS image sensor with light-controlled oscillating pixels for an investigative optobionic retinal prosthesis system.
Microelectron. J., 2009

An Auto-offset-removal Circuit for Chemical Sensing based on the PG-ISFET.
Proceedings of the International Symposium on Circuits and Systems (ISCAS 2009), 2009

Towards a Bionic Chemical Synapse.
Proceedings of the International Symposium on Circuits and Systems (ISCAS 2009), 2009

Effect of Mobile Ionic-charge on CMOS based Ion-sensitive Field-effect Transistors (ISFETs).
Proceedings of the International Symposium on Circuits and Systems (ISCAS 2009), 2009

An Adaptive CMOS-based PG-ISFET for pH Sensing.
Proceedings of the International Symposium on Circuits and Systems (ISCAS 2009), 2009

A Neural Implant ASIC for the Restoration of Balance in Individuals with Vestibular Dysfunction.
Proceedings of the International Symposium on Circuits and Systems (ISCAS 2009), 2009

Health-care electronics The market, the challenges, the progress.
Proceedings of the Design, Automation and Test in Europe, 2009

2008
Energy Efficient Medium Access Protocol for Wireless Medical Body Area Sensor Networks.
IEEE Trans. Biomed. Circuits and Systems, 2008

A Partial-Current-Steering Biphasic Stimulation Driver for Vestibular Prostheses.
IEEE Trans. Biomed. Circuits and Systems, 2008

A 1 V Wireless Transceiver for an Ultra-Low-Power SoC for Biotelemetry Applications.
J. Solid-State Circuits, 2008

The chemical current-conveyor: a new microchip biosensor.
Proceedings of the International Symposium on Circuits and Systems (ISCAS 2008), 2008

A CMOS image sensor with spiking pixels for retinal stimulation.
Proceedings of the International Symposium on Circuits and Systems (ISCAS 2008), 2008

A bio-inspired closed-loop insulin delivery based on the silicon pancreatic beta-cell.
Proceedings of the International Symposium on Circuits and Systems (ISCAS 2008), 2008

An adaptive ISFET chemical imager chip.
Proceedings of the International Symposium on Circuits and Systems (ISCAS 2008), 2008

A partial-current-steering biphasic stimulation driver for neural prostheses.
Proceedings of the International Symposium on Circuits and Systems (ISCAS 2008), 2008

A micropower front-end interface for differential-capacitive sensor systems.
Proceedings of the International Symposium on Circuits and Systems (ISCAS 2008), 2008

A fully-integrated semicircular canal processor for an implantable vestibular prosthesis.
Proceedings of the 15th IEEE International Conference on Electronics, Circuits and Systems, 2008

2007
A Silicon Pancreatic Beta Cell for Diabetes.
IEEE Trans. Biomed. Circuits and Systems, 2007

An On-line, Multi-Parametric, Multi-Channel Physicochemical Monitoring Platform for Stem Cell Culture Bioprocessing.
Proceedings of the International Symposium on Circuits and Systems (ISCAS 2007), 2007

A novel voltage-clamped CMOS ISFET sensor interface.
Proceedings of the International Symposium on Circuits and Systems (ISCAS 2007), 2007

A Wide Tuning Range CMOS Oscillator for an Optoelectronic Retinal Prosthesis System.
Proceedings of the International Symposium on Circuits and Systems (ISCAS 2007), 2007

A Micropower Cochlear Prosthesis System Demonstrator.
Proceedings of the International Symposium on Circuits and Systems (ISCAS 2007), 2007

Fractional-Rate FM-to-Digital Delta-Sigma-Converters.
Proceedings of the International Symposium on Circuits and Systems (ISCAS 2007), 2007

A Bio-Inspired Adaptive Retinal Processing Neuron with Multiplexed Spiking Outputs.
Proceedings of the International Symposium on Circuits and Systems (ISCAS 2007), 2007

Embedded Real-Time Heart Variability Analysis.
Proceedings of the 4th International Workshop on Wearable and Implantable Body Sensor Networks, 2007

2006
Towards an ultra low power chemically inspired electronic beta cell for diabetes.
Proceedings of the International Symposium on Circuits and Systems (ISCAS 2006), 2006

A micropower vision processor for parallel object positioning and sizing.
Proceedings of the International Symposium on Circuits and Systems (ISCAS 2006), 2006

An adaptable foveating vision chip.
Proceedings of the International Symposium on Circuits and Systems (ISCAS 2006), 2006

Bit stream processing for Delta-Sigma FM-to-digital converters.
Proceedings of the International Symposium on Circuits and Systems (ISCAS 2006), 2006

2005
A biochemical translinear principle with weak inversion ISFETs.
IEEE Trans. on Circuits and Systems, 2005

A micropower CMOS continuous-time filter with on-chip automatic tuning.
IEEE Trans. on Circuits and Systems, 2005

Guest Editorial.
IEEE Trans. on Circuits and Systems, 2005

Towards an implantable ultra-low power biochemical signal processor for blood and tissue monitoring.
Proceedings of the International Symposium on Circuits and Systems (ISCAS 2005), 2005

Ultra-low power UWB for real time biomedical wireless sensing.
Proceedings of the International Symposium on Circuits and Systems (ISCAS 2005), 2005

2004
Power spectral density of Transmit Reference Doublet trains and Reference Sharing Doublet trains in ultra wideband systems.
Proceedings of the 2004 International Symposium on Circuits and Systems, 2004

Reference Sharing Ultra Wideband Communication System.
Proceedings of the 2004 International Symposium on Circuits and Systems, 2004

3-state pseudorandom noise (PN) sequence 3-pulse Reference Sharing Ultra Wideband System.
Proceedings of the 2004 International Symposium on Circuits and Systems, 2004

An ultra-low power analogue directionality system for digital hearing aids.
Proceedings of the 2004 International Symposium on Circuits and Systems, 2004

A nano-power tuneable edge-detection circuit.
Proceedings of the 2004 International Symposium on Circuits and Systems, 2004

Towards a bio-inspired mixed-signal retinal processor.
Proceedings of the 2004 International Symposium on Circuits and Systems, 2004

2003
Power efficient scalable precision rational digital to analogue converters.
Proceedings of the 2003 International Symposium on Circuits and Systems, 2003

A CMOS micro-power wideband data/power transfer system for biomedical implants.
Proceedings of the 2003 International Symposium on Circuits and Systems, 2003

A highly linear front-end based on a logarithmic multiplier-filter.
Proceedings of the 2003 International Symposium on Circuits and Systems, 2003

A micropower cochlear prosthesis system.
Proceedings of the 2003 International Symposium on Circuits and Systems, 2003

An auto-input-offset removing floating gate pseudo-differential transconductor.
Proceedings of the 2003 International Symposium on Circuits and Systems, 2003

2002
The invention of CMOS amplifiers using genetic programming and current-flow analysis.
IEEE Trans. on CAD of Integrated Circuits and Systems, 2002

Towards fast solid state DNA sequencing.
Proceedings of the 2002 International Symposium on Circuits and Systems, 2002

A resistorless low current reference circuit for implantable devices.
Proceedings of the 2002 International Symposium on Circuits and Systems, 2002

2001
A unified matrix method for systematic synthesis of log-domain ladder filters.
Proceedings of the 2001 International Symposium on Circuits and Systems, 2001

SiGe HMOSFET differential pair.
Proceedings of the 2001 International Symposium on Circuits and Systems, 2001

Understanding Wilson current mirror via the negative feedback approach.
Proceedings of the 2001 International Symposium on Circuits and Systems, 2001

An operating point elimination technique for weak-inversion log-domain filters with multiple operating points.
Proceedings of the 2001 International Symposium on Circuits and Systems, 2001

High-order lowpass and bandpass elliptic log-domain ladder filters.
Proceedings of the 2001 International Symposium on Circuits and Systems, 2001

Design of a class E power amplifier with non-linear transistor output capacitance and finite DC-feed inductance.
Proceedings of the 2001 International Symposium on Circuits and Systems, 2001

2000
Low-voltage class AB two-step sampling switched-currents.
Proceedings of the IEEE International Symposium on Circuits and Systems, 2000

A high-speed four-channel integrated optical receiver array using SiGe HBT technology.
Proceedings of the IEEE International Symposium on Circuits and Systems, 2000

Linearity enhancement techniques for MOSFET-only SC circuits.
Proceedings of the IEEE International Symposium on Circuits and Systems, 2000

Switched-capacitors versus switched-currents: a theoretical comparison [in CMOS].
Proceedings of the IEEE International Symposium on Circuits and Systems, 2000

1999
High-Frequency Amplifiers.
Proceedings of the VLSI Handbook., 1999

Error neutralised switched-current comparator.
Proceedings of the 1999 International Symposium on Circuits and Systems, ISCAS 1999, Orlando, Florida, USA, May 30, 1999

Class AB technique for high performance switched-current memory cells.
Proceedings of the 1999 International Symposium on Circuits and Systems, ISCAS 1999, Orlando, Florida, USA, May 30, 1999

Design of highly-efficient power-controllable CMOS class E RF power amplifiers.
Proceedings of the 1999 International Symposium on Circuits and Systems, ISCAS 1999, Orlando, Florida, USA, May 30, 1999

A low voltage bulk driven downconversion mixer core.
Proceedings of the 1999 International Symposium on Circuits and Systems, ISCAS 1999, Orlando, Florida, USA, May 30, 1999

An analogue micropower log-domain silicon circuit for the Hodgkin and Huxley nerve axon.
Proceedings of the 1999 International Symposium on Circuits and Systems, ISCAS 1999, Orlando, Florida, USA, May 30, 1999

1995
Analog IC design automation. I. Automated circuit generation: new concepts and methods.
IEEE Trans. on CAD of Integrated Circuits and Systems, 1995

Analog IC design automation. II. Automated circuit correction by qualitative reasoning.
IEEE Trans. on CAD of Integrated Circuits and Systems, 1995

A Novel High Speed Current Mirror Compensation Technique and Application.
Proceedings of the 1995 IEEE International Symposium on Circuits and Systems, ISCAS 1995, Seattle, Washington, USA, April 30, 1995

The Active-R Filter Technique Applied to Current-Feedback Op-Amps.
Proceedings of the 1995 IEEE International Symposium on Circuits and Systems, ISCAS 1995, Seattle, Washington, USA, April 30, 1995

A New BiCMOS Technique for Very Fast Discrete-Time Signal Processing.
Proceedings of the 1995 IEEE International Symposium on Circuits and Systems, ISCAS 1995, Seattle, Washington, USA, April 30, 1995

+/- 1V CMOS Rail to Rail Op Amp.
Proceedings of the 1995 IEEE International Symposium on Circuits and Systems, ISCAS 1995, Seattle, Washington, USA, April 30, 1995

Concurrent Self Test of Switched Current Circuits Based on the S2I-Technique.
Proceedings of the 1995 IEEE International Symposium on Circuits and Systems, ISCAS 1995, Seattle, Washington, USA, April 30, 1995

Delta-Sigma Converters Using Frequency-Modulated Intermediate Values.
Proceedings of the 1995 IEEE International Symposium on Circuits and Systems, ISCAS 1995, Seattle, Washington, USA, April 30, 1995

A Novel Architecture for Reducing the Sensitivity of Multibit Sigma-Delta ADCs To DAC Nonlinearity.
Proceedings of the 1995 IEEE International Symposium on Circuits and Systems, ISCAS 1995, Seattle, Washington, USA, April 30, 1995

1994
The Opto-Electronic Transconductor and Its Applications.
Proceedings of the 1994 IEEE International Symposium on Circuits and Systems, ISCAS 1994, London, England, UK, May 30, 1994

Part 2 - 101 Ways to Make a Circuit Fail.
Proceedings of the 1994 IEEE International Symposium on Circuits and Systems, ISCAS 1994, London, England, UK, May 30, 1994

Novel Self-Calibrated High-Speed D/A Converter using Trimmable Current Sources.
Proceedings of the 1994 IEEE International Symposium on Circuits and Systems, ISCAS 1994, London, England, UK, May 30, 1994

Trading Off Sspeed Versus Dynamic Range in Switched Current Circuits.
Proceedings of the 1994 IEEE International Symposium on Circuits and Systems, ISCAS 1994, London, England, UK, May 30, 1994

On the Feasibility of SI for low-Power VLSI Biomedical Signal Processing.
Proceedings of the 1994 IEEE International Symposium on Circuits and Systems, ISCAS 1994, London, England, UK, May 30, 1994

1993
Low-Noise Optimisation of Current-mode Transimpedance Optical Preamplifiers.
Proceedings of the 1993 IEEE International Symposium on Circuits and Systems, 1993

Current-feedback Versus Voltage Feedback Amplifiers: History, Insight and Relationships.
Proceedings of the 1993 IEEE International Symposium on Circuits and Systems, 1993

New Current-mode Precision Rectifiers.
Proceedings of the 1993 IEEE International Symposium on Circuits and Systems, 1993

Measurements of Linear Composite MOSFET Circuits and Further Applications.
Proceedings of the 1993 IEEE International Symposium on Circuits and Systems, 1993

Towards High Frequency Switched-Current Filters in CMOS and GaAs Technology.
Proceedings of the 1993 IEEE International Symposium on Circuits and Systems, 1993


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## raheen Group Title Find the holomorphic function f(x+iy) such that Re f(x+iy)= cosh(3y)sin(3x) and f(0)=0 3 years ago 3 years ago

1. hahd

ugh i havent taken calc yet so i cant do this

2. satellite73

cauchy reimann yes?

3. raheen

yes satellite

4. satellite73

so the derivative of this wrt x must be the derivative of the imaginary part wrt y right? the derivative is $3\cos(3x)\cosh(3y)$ integrate wrt y and get $\cos(3x)\sinh(3y)$ i think.

5. satellite73

it's been a while. am i on the right track?

6. satellite73

you also need the partial wrt y is minus the partial wrt x of the imaginary part. if we are lucky it already is oh and you also need that f(0)=0 i forgot the +C when i integrated

7. satellite73

how to you like that? i miracle! it works

8. satellite73

so i guess unless i totally screwed this up the answer is $f(x+iy)=\cosh(3y)\sin(3x)+\cos(3x)\sinh(3y)$

9. satellite73

think we lost raheen maybe he will be back

10. satellite73

rather $f(x+iy)=\cosh(3y)\sin(3x)+i\cos(3x)\sinh(3y)$

11. satellite73

i forgot the i part

12. satellite73

@raheen look ok?

13. satellite73

it does not come with a money guarantee because it has been several years but i think it looks good. you can check cauchy reimann equations for this and see if they work

14. raheen

satellite you are about to reach , great work I think you did how about using the 2 conditions of C-R then you need to integrate and don forget to find the constant

15. satellite73

well i integrated wrt y and got the answer. then i checked that the second equation and it worked. and by inspection you can see that $f(0)=0$

16. satellite73

i mean if the C-R equations are going to work, then after i take the derivative wrt x and integrate wrt y , then the second condition $\frac{\delta u}{\delta y}=-\frac{\delta v}{\delta x}$ had better work or else we are screwed. both conditions must hold. but in any case i checked and they do

17. raheen

that's so great satellite, thank you.

18. satellite73

yw

19. Zarkon

the only thing I would add is that when you integrated with respect to y you don't get C you get some function of x

20. raheen

Zarkon, thank you, you are right it's C(x)

21. Zarkon

It doesn't look like it will change the final answer though


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## LaTeX forum ⇒ Page Layout ⇒ Centering section titles in article class Topic is solved

Information and discussion about page layout specific issues (e.g. header and footer lines, page formats, page numbers).
Cham
Posts: 858
Joined: Sat Apr 02, 2011 4:06 pm

### Centering section titles in article class

I'm wondering if it's possible to do the following. Here's a MWE showing a very important paper to be published somewhere (content is highly classified! ). The section titles are horizontally centered with their number. I would like to center the title text itself, while the section number should have an offset to the left, keeping its constant space.
\RequirePackage[l2tabu,orthodox]{nag}\documentclass[12pt,letterpaper,twoside]{article}\usepackage{microtype}\usepackage[total={6.5in,10in},left=1in,top=0.5in,includehead,includefoot]{geometry}\usepackage{sectsty}\sectionfont{\centering}\subsectionfont{\sffamily}\subsubsectionfont{\sffamily}\raggedbottom\usepackage{lipsum} \begin{document} \section{Some not so hilarious introduction}\lipsum[1-2] \section{Fancy theory of absolutely everything}\lipsum[5-5] \section{General crap analysis} \subsection{Tables of useless data}\lipsum[1-2] \subsection{Funky graphics}\lipsum[3-3] \section{Painfull discussion and killer conclusion}\lipsum[4-4] \end{document}

Is it possible to center the title text, while keeping the section number (which would be pushed a bit to the left)?

Stefan Kottwitz
Posts: 8792
Joined: Mon Mar 10, 2008 9:44 pm
With titlesec instead of sectsty:

\usepackage{titlesec}\titleformat{\section}  [block]{\normalfont\bfseries\sffamily\Large}{\rlap{\thesection}}{0em}  {\hspace*{.05\textwidth}\begin{minipage}[t]{.9\textwidth}\centering}[\end{minipage}]

This centers the section title in a minipage, and keeps the number left aligned.

Stefan

Cham
Posts: 858
Joined: Sat Apr 02, 2011 4:06 pm
That's not what I meant. The section number should stay at the same location, relative to its title. I mean same constant space at the left part of the title, not completely flushed to the left side.

Is there a way to do this while keeping the sectsty package?

Stefan Kottwitz
Posts: 8792
Joined: Mon Mar 10, 2008 9:44 pm
Well, extremely uncommon... I guess nobody implemented such an asymmetric feature. It's like centering plus shifting. Or centering plus adding the numbers to the left. It's asymmetric, especially when numbers are of different width, such as 1 vs. 8 vs. 10.

I would reconsider doing that or not, before hacking it together.

Stefan

Cham
Posts: 858
Joined: Sat Apr 02, 2011 4:06 pm
Well, I agree. But when I look globally at the full text, I find it a bit weird that the section titles aren't centered, because of their number (it's a bit aesthetically unpleasing). Maybe that's why the default article class put all the titles flushed to the left instead. Maybe adding a dot after the numbers would fix the aesthetical glitch.

Cham
Posts: 858
Joined: Sat Apr 02, 2011 4:06 pm
What do you think of adding a point after the number, using the secdot package in the code above ?
\usepackage{secdot}

It looks good, but I have a doubt.

Stefan Kottwitz
Posts: 8792
Joined: Mon Mar 10, 2008 9:44 pm
I like the dot as a separator. "1 Introduction" looks like a bad "One Introduction" to me, while "1. Introduction" is clearly for me "First: Introduction".

I would use sans serif headings though:

\sectionfont{\sffamily\centering}

Serif bold big headings look fat to me, and remind me of stone age LaTeX. Specifically, serif section headings don't fit to sans serif subsection headings.

Also, I would not use left aligned subsection headings following centered section headings. If I would have centered headings, then no headings below them at all. And by the way, in some book styles it's considered to be bad if one heading follows another heading. Some prefer a bit intro text before the next sub heading comes.

Stefan

Cham
Posts: 858
Joined: Sat Apr 02, 2011 4:06 pm
I also feel that the default quad space is too large, between the number and its section/subsection title. These secdot options are working great, but I'm not sure this is good :
\usepackage{secdot}\sectionpunct{section}{. ~}\sectionpunct{subsection}{ ~}

What would you use as an elegant space ?

EDIT : \enskip appears to be perfect !
\sectionpunct{section}{.\enskip}\sectionpunct{subsection}{\enskip}


text:
# Aquila DSP C++ Library - Wave file FFT analog frequency off by factor of 4?

I'm working with the Aquila C++ DSP library. I'm computing the FFT of a wave file (16 bit depth, single channel, 44100 sample rate). I am using a window size of 16384 to calculate the FFT spectrum.

I'm having an issue converting the the digital frequency (0/N, 1/N, ... N/N) to the corresponding analog frequency. When I apply the sample rate multiplier S,

f = S*i/N; // Convert from digital frequency to analog frequency

I get analog frequencies that are 4 times greater than what I expect.

For example, I read in a pianos A1 note. I expect this to be ~55 Hz. Instead I'm getting ~220 Hz. Refer to the photo below.

Now I'm first wondering if I'm scaling my the wrong number. However, I'm pretty sure it's correct. So now I'm curious if somehow the time domain data I'm reading is compressed by a factor of 4, such that the frequencies appear to be 4 times greater. Does anyone know if there is a common .wav file 'gotch-ya' when reading from them?

I've posted the relevant part of my code if anyone is interested.

/* sample window */
int window_size = 16384;

/* Calculate the FFT */
std::shared_ptr<Aquila::Fft> p_fft_interface = Aquila::FftFactory::getFft(window_size);  // This returns a shared pointer to an FFT calculation object.
auto spectrum = p_fft_interface->fft(wave_object.toArray());

QVector<double> x(window_size);
QVector<double> y(window_size);

/* Prepare to plot & convert to analog frequency */
double max_value = 0;
for(int i = 0; i < window_size; i++)
{
x[i] = i*(sample_freq/window_size);
y[i] = abs(spectrum[i]);

if(abs(spectrum[i]) > max_value)
{
max_value = abs(spectrum[i]);
}
}

Not familiar with Aquila in particular, and I don't see how you're mapping the output spectrum samples to an X-axis that ends at 800 Hz, but remember that a real-only FFT mirrors its output data in the second half of the buffer. You may need to run your loop from 0 to window_size/2 if Aquila's FFT is implemented the usual way.

That could account for a factor of 2x.

Further to @user572's answer, the other 2x could be coming from the fact you are passing a real array to a complex FFT: p_fft_interface->fft(...). Check the documentation for p_fft_interface->fft to make sure it's not treating your samples as pairs of real/imaginary components rather than just real.

An alternative to other answers (that sugguest you're passing real-values to complex-fft).

One common mistake that results in exactly this error is an incorrect sampling rate parameter. It would sound like slow-motion if this is the case.

If the .wav file was actually sampled at 1/4 of the rate entered, your frequency spectrum would reflect this as well. It's possible your file was sampled at 11025 Hz. Try and verify the sampling rate both on your OS and within Aquila.

You didn't say how to obtained the signal, but another possibility is your mic filters out low frequencies, try putting another wav file in the function and see if you find any power below the 100 Hz range. This will confirm it's not just the signal.


text:
# Best query complexity of Goldreich-Levin / Kushilevitz-Mansour learning algorithm

What is the best known query complexity of Goldreich-Levin learning algorithm? Lecture notes from Luca Trevisan's blog, Lemma 3, states it as $O(1/\epsilon^4 n \log n)$. Is this the best known in terms of dependence on $n$? I will be particularly grateful for a reference to a citable source!

Related question: what is the best known query complexity of Kushilevitz-Mansour learning algorithm?

Prop 2.5.6 in the aforementioned section proves a much better bound: The algorithm runs in expected time $O(n \log^3(1/\epsilon))$ times the running time of the guessing procedure (see improvement from $n^2$ to $n$ in the comment right after the proof) and is correct w.p. $\Omega(\epsilon^2)$. Hence, correctness w.p. $2/3$ is obtained in time (factor) ${\tilde O}(n/\epsilon^2)$, which is optimal in some sense (see Exer 30).


text:
## Wednesday, April 04, 2007

### Causality issues

Yesterday, I was reading a paper by Ellis, Maartens and MacCallum on "Causality and the Speed of Sound" which made me rethink a few things about causality which I thought I new and now would like to share. See also an old post on faster than light communication.

First of all, there is the connection between causality and special relativity: It is a misconception that a relativistic theory is automatically causal. Just because you contracted all Lorentz indices properly does not mean that in your theory there is no propagation faster than light. There is an easy counter-example: Take the Lagrangian . where f is a smooth function (actually quadratic is enough for the effect) of the usual kinetic term of a scalar phi. I have already typed up a brief discussion of this theory but then I realised that this might actually be the basis of a nice exam problem (hey guys, are you reading this???) for the QFT course I am currently teaching. So just a sketch at this point: The equation of motion allows for solutions of the form and when you now expand small fluctuations around this solution you see that they propagate with an adjustable speed of sound depending on f and V.

Obviously, this theory is Lorentz invariant, it's only the solution which breaks this invariance (as most interesting solutions of field theories do).

The next thing is how you interpret this result: For suitably chosen V and f you can communicate with space-time points which are space-like to you. So is that really bad? If you think about it (or read the above mentioned paper) you find that this is not necessarily so: You really only get into trouble with causality if you have the possibility to call yourself in the past and tell you the lottery numbers of a drawing in the future of your past self.

If you can communicate with space-points, this can happen: If you send a signal faster than the speed of light to a point P which is space like to you, then from there it can be sent to your past, part of which is again space-like to P. If the sender at P (a mirror is enough) is moving the speed of communication (as measured by the respective sender) has to be only infinitesimally faster than the speed of light (if the whole set-up is Lorentz invariant).

In the theory above, however, this cannot happen: The communication using the fluctuations of the field phi is always to the future as defined by the flow of the vector field V (which we assume to be time-like and future directed). Thus you cannot send signals to points which are upstream in that flow and all of your past is. And using light (according to the usual light-cones) does not help either.

This only changes if you have two such field with superluminus fluctuations: Then you can use one field's fluctuations to send to P (which has to be downstream for that field) and the other field to send the signal from P to your past. So strictly speaking, only if you have two such fields, there is potential for sci-fi stories or get rich fast (or actually: in the past) schemes. But who stops you to have two such fields if one is already around?

At this point, it might be helpful to formalise the notion of "sending signals" a bit further. This also helps to better understand the various notions of velocity which are around when you have non-trivial dispersion relations: As an undergrad you learn that there is the phase velocity which is and that there is the group velocity but at least to me nobody really explained why the later one is important. It was only claimed that it is this velocity which is responsible for signal propagation.

Anyway, what you probably really want is the following: You have some hyperbolic field equation which you solve for some Cauchy data. Then you change the Cauchy data in a compact region K and solve again. Hopefully, the two solution differ only in the region causally connected to K. For this, it is the highest derivative term in the field equation (the leading symbol) which matters and if you Fourier transform you see this is actually the group velocity.

Formulating this "sending to P and back" procedure is a bit more complicated. My suspicion is that it's like the initial value problem when you have closed time-like loops: Then not all initial data is consistent: If my time fore example is periodic with a period of one year I should only give initial data which produces a solution with the same periodicity. But how exactly does this work for the two superluminal fields?

There is one further complication: If gravity is turned on and I have to give initial data for it as well, things get a lot more complicated as the question of a point with given coordinates is space-like to me depends on the metric. But my guess would be that also changes in the metric propagate only with maximally the speed of light in the reference metric.

And finally, there is the problem that the theory above (for non-linear f) is a higher derivative theory. Thus the initial value problem in that theory is likely to require more than phi and its time derivative to be given on the Cauchy surface.

Garbage said...

Hey, there is something even cooler to think about. For instance, the tachyonic mode (hint) in the KG equation. Check out Coleman lectures on Acausality, they are awesome, unfortunately I couldnt find them on the web.

If we have the wrong sign for the mass in the KG Lagrangian we will get causality from the fact that the kinetic piece didnt change (flipping the mass sign of hte mass term) and the characteristic surfaces are thus the same. Nevertheless, the theory is acausal from the simple observation that the group velocity is larger than 1.

Why isnt this a contradiction??? ;)

John Baez said...

It's actually neither the wave nor the group velocity that determines the speed at which signals can be sent! This is an old chestnut. Superluminal group velocities do occur in media with "anomalous dispersion"... but, despite misguided worries, what really matters is yet a third velocity: the signal velocity.

The best book on this stuff is Leon Brilloin's Wave Propagation and Group Velocity, Academic Press, 1960. He worked it all out very nicely. It's a really fun book.

In particular, tachyons have signal velocity equal to c.

John Baez said...

Actually, the technical term I should have used was not "signal velocity" but "propagation velocity".

Robert said...

John,

thanks for your explanation. Since I wrote this post I also heard the claim that it's the high frequency limit of the group velocity which determines the propagation velocity (with the hand-waving argument that it's the infinite frequency part of a step that one uses to send the information).

Well, I should better have a look at the book you recommend. What do you say about causality in these k-essence type models? At least if you have two such scalar fields (with different background solutions) this should lead to causality violation.

There is also another paper:
k-Essence, superluminal propagation, causality and emergent geometry.
Eugeny Babichev (Gran Sasso & Moscow, INR) , Viatcheslav Mukhanov, Alexander Vikman (ASC, Munich & Munich U.) . LMU-ASC-54-07, Aug 2007. 34pp.
e-Print: arXiv:0708.0561 [hep-th]

tercumenette said...
tercumenette said...


text:
## Introduction

Structural DNA nanotechnology using templating techniques for material construction, was first proposed in the early 1980s by Seeman1 and has rapidly developed since 20062. This development of DNA origami technology has shown great potential in a wide range of applications, including biomedicine3,4,5, biocomputing6, biochips and nano-circuits7,8, biomimicry9, masks for lithography10,11, and nano-mechanics12. All of these applications are based on the fact that a single DNA strand can be self-assembled into different two-dimensional (2D) and three-dimensional (3D) structures. In addition, spherical nanoparticles can be embedded in these structured DNA molecules as reported by Mirkin et al.13 and Alivisatos et al.14 and nanoparticle-capped DNA can be utilised as building blocks to build highly-ordered 3D lattice structures15,16, with a range of novel properties17,18,19. The physical properties of these are fundamentally determined by the relationship between the inorganic and biological components in the nano hybrid constructs which requires high-resolution 3D imaging of both the biological and non-biological components for characterisation.

Transmission electron microscopy (TEM), is a high resolution imaging technique, and is regarded as an essential tool for the characterisation of both biological and non-biological materials. Three dimensional imaging methods, such as single particle analysis (SPA)20 and electron tomography (ET)21,22, are widely used for 3D structural analysis of biological samples, and have recently been used in studies of DNA based structures23,24. SPA reconstruction, relies on computationally averaging thousands of images of identical particles (e.g., virus), and is more challenging to apply to heterogeneous samples with low symmetry. In contrast, ET, which is performed by recording a tilt series of projections of a single specimen, is more suitable for reconstructing the structure of non-identical biological samples such as 3D frameworks of DNA origami. Nevertheless, both of these approaches rely on the use of conventional phase contrast TEM images. It is well known that unstained biological samples, which are extremely radiation-sensitive and can be treated as pure phase objects. This offen results in images with low signal-to-noise ratio and low contrast, which can cause difficulties in the tomographic reconstruction. To enhance the contrast, samples of DNA origami frameworks in previous studies were prepared with staining25,26. However, the heavy metal ions used in the staining procedure can potentially damage the fine structure of native-state DNA27. An alternative to increase contrast at low spatial frequencies is to use high defocus values, but this leads to rapid oscillations in the phase contrast transfer function (CTF) at intermediate and high spatial frequencies if not corrected, for instance, by exit-wave restoration methods28. This poses a challenge to directly provide high-resolution 3D images of DNA frameworks, and to simultaneously visualise both the biological and non-biological components in their native state without staining.

Ptychography, as originally proposed by Hoppe29, is an alternative phase retrieval method related to coherent diffraction imaging30,31. The development of iterative algorithms32,33,34 has made ptychography capable of achieving superior spatial resolution compared to that obtained from conventional optics31, especially for extended non-crystalline samples32. Ptychography is now widely used in 2D imaging using both light35 and X-rays30,32 and in 3D imaging36,37,38,39,40. In TEM, it has also attracted considerable interest with a variety of potential applications in super-resolution imaging41,42,43,44,45, high-contrast light-element detection46,47, optical sectioning46,48, coupling to spectroscopic data acquisition49 and low-dose imaging50,51,52, using direct electron detectors53,54. Recent numerical simulations have shown that combining ptychography and electron tomography has the potential to reach atomic 3D reconstructions for inorganic materials55. Importantly, ptychography has a tunable and continuous wide-band information transfer, which can be adjusted using the probe-forming convergence angles which is important for biological applications. To transfer information from objects with larger length scales, the illumination can be further optimised to a smaller convergence angle56. This advantage has recently been demonstrated for organic matter (such as unstained virus particles), which were successfully reconstructed at a dose of 27 e2 in their native state56. We now propose that high-contrast 2D phase data reconstructed using ptychographic methods and recorded at different sample orientations can be aligned and used as an input to a tomographic reconstruction for unstained biological samples (such as DNA origami frameworks) with high resolution.

We demonstrate high-contrast 3D phase reconstructions to visualise unstained DNA origami with gold nanoparticles by combining electron ptychography and tomography. In comparison to conventional TEM, the enhancement of contrast was quantitatively evaluated under various electron dose conditions and accelerating voltages. Ptychography not only provides images with better contrast, but also simplifies the conventional tomographic workflow by reducing the electron dose and preventing radiation damage during tilting. Thus, electron ptychographic tomography (EPty-Tomo) developed as described here shows promise for revealing the relationship between 3D structures of hybrid nano-constructs fabricated with biomolecules and inorganic nanomaterials as used in aspects of nanotechnology.

## Results

### 3D ptychographic tomography (EPty-Tomo)

The schematic experimental setup used is illustrated in Fig. 1a. Samples of unstained DNA origami with gold nanoparticles were suspended on an ultrathin carbon film at room temperature for TEM studies (see Supplementary Note 1: Sample Preparation). A tilt series of ptychography-based tomography was acquired using a + /− 70° double tilt holder (Fischione Model 2040) on a double aberration-corrected FEI Titan Cubed G2 60–300 (S)TEM operated at 60 kV accelerating voltage to reduce beam damage. A defocused electron probe with a diameter of approximately 120 nm was incident on the sample with a convergence angle of 1.5 mrad and a nominal defocus of −40 μm. The choice of a small convergence angle was to enhance low spatial frequency transfer56 with a large depth of field, which is an advantage when using thick specimens57. At each tilt angle, ptychographic datasets were acquired by illuminating the sample with a scanning probe, recording 10 × 10 far-field diffraction patterns (as shown in Supplementary Fig. 1) as a function of probe position (see Supplementary Note 2: Tilt-series Ptychographic Data Acquisition). This gave rise to a total ptychographic dataset for 23 tilt angles of approximately 39 GB. The 2D complex wavefunction of the sample at each tilt was recovered using the extended ptychographic iterative engine (ePIE)33 (see Supplementary Note 3: 2D Ptychographic Reconstruction). The phases of the tilt-series complex functions (see Supplementary Fig. 2) were used as inputs for sequential tomography reconstruction implemented using the GENeralized Fourier Iterative Reconstruction (GENFIRE) algorithm58 to calculate a final 3D reconstruction (see Supplementary Note 4: 3D Tomographic Reconstruction).

The 3D phase reconstruction from ptychographic tomography is shown in Fig. 1b and Fig. 2. The 3D phase rendering of the unstained DNA origami structures with gold nanoparticles indicates that the DNA framework collapsed onto the carbon film due to the drop-cast sample preparation used. However, the side view and cross-section (Fig. 2a and Supplementary Fig. 3c) of the volume shows two adjacent gold nanoparticles spaced 5.5 nm apart along the z-axis. More importantly, the DNA strands together with the gold nanoparticles can both be resolved with high contrast in the 3D phase reconstruction. This is supported by the fact that the peaks of DNA strand and gold nanoparticles in the frequency histogram (Fig. 1c) are both separated from the background. A part of the reconstruction and its related video was also extracted, as shown in Fig. 2b and Supplementary Movie 1; Note that to reveal the gold particle core the signal of the DNA outer layer within the orange box is not rendered. An outer layer of signal surrounding the gold nanoparticles in the 3D phase reconstruction directly revealed the formation of core-shell structures in the scaffold. This outer layer of signal is attributed to a layer of DNA short strands formed from a spherical nucleic acid conjugate59. In contrast, ET, based on conventional defocused contrast TEM images (Supplementary Fig. 4), has difficulties in directly resolving the 3D structures of the biological and non-biological materials simultaneously. This is due to the low contrast of the biomolecules compared with that of gold nanoparticles, which will be discussed quantitatively in detail subsequently.

### Contrast quantification of DNA strands

In this study, EPty-Tomo exhibits two main advantages over conventional TEM based tomography. Firstly, reconstruction using ptychographic tomography shows an enhanced contrast from weakly scattering objects (unstained DNA strands), even though they are attached to strongly scattering material (gold nanoparticles). As a result, we could directly render the outer layer of the DNA short strands around the gold nanoparticles (Fig. 2b) which cannot be performed using conventional TEM tomography (Supplementary Fig. 4), unless the DNA strands are stained to boost contrast in the 2D TEM images that form the datasets used for tomographic reconstruction60. To quantify the contrast, the 3D phases were normalised with respect to the signals of the gold nanoparticles and the carbon film background (See Supplementary Note 5: Normalisation and Contrast Ratio). The signals of the carbon film background, DNA strands and gold nanoparticles were subsequently extracted from volumes with the equal number of the voxels as indicated with green, orange, and light blue frames in Fig. 1b and Supplementary Fig. 3, respectively. Finally, the normalised frequency histogram based on the extracted voxels was plotted as shown in Fig. 1c. The normalised phase of the DNA strands was localised within a narrow peak (orange) and was sufficiently high to be clearly distinguished from the carbon film background (green) by 0.17 (as a value of normalised intensity, this value is dimensionless. see Supplementary Note 6: Rendering and Histogram Analysis). This offset allows the contrast of the former to be directly separated from that of the latter in the 3D render. This result originates from the high-contrast 2D ptychographic phase reconstruction at each tilt (Supplementary Fig. 2), in which the contrast of DNA strands is higher than that of the conventional TEM images56. Figure 3a–c shows the normalised 2D ptychographic phase reconstructions at different electron doses of 88, 45 and 26 e2 varied by probe overlap ratios. As shown in the frequency histograms of the normalised data (Fig. 3f–h), the offset between the positions of the DNA and background peaks reduces from 0.24 to 0.15 with decreasing dose, confirming that the contrast in ptychographic reconstructions is dose-dependent51. As the data is normalised, the offset values can be considered as a contrast ratio (R), given by Eq. (1):

$${R}_{{DNA}/{gold}}=\frac{{P}_{{DNA}}-{P}_{{bkgd}}}{{P}_{{gold}}-{P}_{{bkgd}}}$$
(1)

where RDNA/gold stands is the contrast ratio of the DNA strands and gold nanoparticles; PDNA and Pbkgd is the intensity value (x-axis coordinate) at the peaks of the DNA strands and background in the frequency histograms, and Pgold is the mean value of the normalised intensity of a gold nanoparticle. Hence, larger RDNA/gold values indicate higher visibility of the DNA strands with respect to the background and gold nanoparticles.

For comparison, a defocus-series of TEM images were also obtained over a range of defocus values from −0.1 μm to −8.9 μm (Supplementary Fig. 5a). The histograms of the original images (Supplementary Fig. 5b) shows that the contrast of the standalone DNA strands could only be increased by few tens of counts with increasing defoci. whereas, the peak positions of the gold nanoparticles at frequency histograms (Supplementary Fig. 5b) were increased by a few hundred in intensity. As a result, the R values remain low around 0.07 in the histograms (i.e. defoci of −0.1 and −2.8 μm, as shown in Fig. 3i, j, with data for other defoci shown in Supplementary Fig. 5e). Hence, the visibility of the DNA strands with respect to the gold nanoparticles is not improved with increasing defocus. In addition, larger defoci (−8.9 μm) leads to visible Fresnel fringes around the gold nanoparticles (shown in Supplementary Fig. 5a), which completely suppresses the contrast of the DNA short strands at the surface of gold nanoparticles. Thus, it is clearly challenging to resolve biological molecules around inorganic nanoparticles with high contrast and resolution using defocused TEM images. However, for the 2D ptychographic phases (Fig. 3a–c), the R value (0.24 – 0.15 in Fig. 3f–h) was two-fold higher than any defocused TEM data, so that DNA samples were imaged with higher contrast as shown in the line profiles across the DNA strands (Fig. 3k).

The ptychographic phase can reflect the relative thickness of the sample61. In this work, the normalised phase at the intersection of two DNA strands (0.40) is approximately twice that of a single DNA strand (0.21), as shown in Fig. 3k suggesting that the phase signal is quantitative for this sample61,62.

### Resolution of 3D reconstructions

The second advantage of EPty-Tomo is the capability to achieve a optimised resolution, the bandwidth of which can be controlled by changing the convergence semi-angle of the probe. To evaluate the 3D resolution, Fourier shell correlation (FSC)63, as conventionally used in tomography, was employed to evaluate the degree of correlation between two tomographic reconstructions at different spatial frequencies. The FSC was calculated using the full dataset (90 diffraction patterns at each projection) split into two independent datasets (45 diffraction patterns at each projection, as shown schematically in Supplementary Fig. 6) which were used for independent reconstructions, one of which is shown in Supplementary Fig. 7a. Details of the FSC analysis can be found in Supplementary Note 7: FSC and FRC and the FSC as a function of spatial frequency is shown in Supplementary Fig. 7b. Using this approach, the 3D resolution was estimated as 2.08 nm for a 0.5-bit criterion. It is established that the resolution of 3D reconstruction is determined by both the number of tilt angles and the resolution of individual 2D projections64. The theoretical resolution for 2D ptychography (two-dimensional projections in this 3D reconstruction) can be expressed as λ/(α + β), where λ is the electron wavelength, α is the convergence angle and β is the collection angle65. Since the DNA strands used here were weakly scattering objects and almost transparent to the electron beam, the signal scattered outside of the bright field disc is negligible. Therefore, in this work only the signal within the bright field disc is used for the ptychographic reconstruction, such that the 2D theoretical resolution, evaluated as λ/(2α) was 1.62 nm, in agreement with the result of experimental 2D phase-contrast resolution (Fig. 3i) achieved. The resolution of conventional phase contrast TEM imaging was defined by the first zero crossing of the contrast transfer function. For the 60 kV TEM image at a dose of 27 e2 (Fig. 3e) with the best R value (0.07 in Fig. 3j) obtained with a defocus of −2.8 μm without using an objective aperture, the resolution was estimated as 3.69 nm, which is worse than that (1.83 nm in Fig. 3l) of the ptychographic phase (Fig. 3c) under the similar dose condition of 26 e2 with almost a two-fold increase in the R value (0.19 in Fig. 3h).

### Contrast enhancement at low voltage

As we have observed, both contrast and resolution were both strongly influenced by the accelerating voltage and the electron dose. Figure 4a–d shows comparisons between the normalised 2D ptychographic phases and TEM images taken at 60 kV and 300 kV accelerating voltages. From the same sample, the data at 60 kV showed a value of R approximately three times higher than that at 300 kV for both ptychography and TEM (Fig. 4e–h) consistent with increased contrast from weakly scattering objects at lower voltages66. Importantly R for the ptychographic reconstruction increased from 0.04 to 0.11, which was sufficient to distinguish the frequency peaks of the DNA strands from backgrounds at 60 kV, whereas for TEM data, it increased from 0.02 to 0.07, which did not meet the requirement for separation.

### Dose-dependent reconstructions

To study the dose-dependent ptychographic contrast of DNA, we reduced the total electron dose by reducing the overlap ratios (see Supplementary Note 8: Dose Reduction). As illustrated in Fig. 3a–c, the doses were 88 e2, 45 e2 and 26 e2 for each tilt angle, for overlap ratios of 83%, 76 and 66%. The resolution of 2D ptychographic reconstruction calculated by Fourier ring correlation (FRC) is shown in Fig. 3l (see details in Supplementary Note 7: FSC and FRC). Resolutions of 1.65 nm and 1.83 nm are calculated from two independent reconstructions with a dose of 45 e2 and 26 e2, respectively (Fig. 3l). Similarly, the contrast ratio R of the DNA strands was reduced from 0.24 (88 e2) to 0.19 (45 e2) and 0.15 (26 e2 as shown in Fig. 3f–h). By comparison, a series of TEM images with different doses (to over 250 e2) were also collected (Supplementary Fig. 8a). Using the same normalisation the contrast ratio (R) was maintained at around 0.065, when the dose was greater than 60 e2 (Supplementary Fig. 8c), suggesting that simply increasing the dose above this limit does not enhance the contrast of the DNA against the background of the amorphous carbon film in TEM imaging.

For 3D reconstruction, the total dose of the tilt series was reduced from 2024 e2 (Fig. 1b) to 1035 e2 (Supplementary Fig. 7a) and to 598 e2 (Supplementary Fig. 7d) using the dose-reduced 2D ptychographic phases (as shown in Fig. 3a–c). With reduced total dose (for details see Supplementary Note 8: Dose Reduction), the 3D structure of the DNA origami was still successfully reconstructed by ptychographic tomography. In a histogram analysis (shown in Supplementary Fig. 7c–f), the peaks were still separated although broadened. The 3D resolution calculated from a FSC was lowered from 2.08 nm at a dose of 1035 e2 (Supplementary Fig. 7c) to 3.74 nm at a dose of 598 e2 (Supplementary Fig. 7f) corresponding to the resolution degradation in the 2D phases (Fig. 3l). To further improve the quality of the reconstructed 2D phase data and at reduced dose, the use of a newly developed ultrafast detector53,54,67,68,69 shows promise. and recording data under cryogenic conditions will further limit radiation damage, as has been demonstrated by by Zhou et al.56.

## Discussion

To develop structural DNA nanotechnology, 3D TEM imaging is critical for precisely designing and characterising the programable inter-particle linkers, particularly at low electron dose. Generally, the 3D reconstruction methods that have been applied to DNA origami are either conventional tomography or SPA70 as summarised in Table 1. SPA is based on the assumption that the samples are homogeneous with many identical copies of the same structure. For example, the 3D reconstruction work by Shih et al.71 reported images of unstained DNA origami octahedral particles at 3.2 nm resolution, and assumed that many identical particles folded into the same structure23,72. However, DNA origami nanostructures are purposely designed and fabricated with multiple degrees of freedom and complex 2D/3D motion flexibility73,74 to diverse functionality and hence, SPA is unsuitable for reconstructing many different conformations. In contrast, TEM tomography is often chosen for 3D reconstruction of heterogeneous samples, as shown in Table 1. For example, Zhang et al.24 applied TEM tomography to study the structural dynamics of stained DNA-gold nanoparticle conjugates and achieved a 3D reconstruction with a resolution of 1.4 ~ 2.3 nm using a total dose of about 1500 ~ 2500 e2. However, the major problem of this approach is that the contrast of the DNA per se was not high enough to be distinguished from the support unless it was stained. This is consistent with our TEM observations of unstained DNA strands (Fig. 3d, e, Supplementary Fig. 4). However, taking advantage of the phase sensitivity of ptychography, we were able to achieve high contrast 3D reconstructions of unstained DNA origami at a resolution of 2.08 nm.

In general contrast and SNR in a tomogram of a biological sample are limited by the tolerance to total radiation dose during the entire acquisition of the entire tilt series. It is therefore worthwhile to compare the tomographic workflows that are used for conventional TEM with those for ptychography (shown respectively in Fig. 5a, b). For conventional TEM-based tomography, accurate defocus control is essential for high resolution image acquisition during tilting, as defoci need to be approximately constant for all tilt angles. However, in practice, the defocus value must be always tracked and adjusted before each image acquisition (Fig. 5a). This procedure can be time-consuming, but also adds electron dose that does not contribute to the final image dataset. In contrast, ptychography has the advantage of post-acquisition focusing48, and hence the defocus values can be compensated during the reconstruction after data collection (Fig. 5b). The defocus values for the current work were found to vary between −45 μm and −34 μm (Fig. 5c, Supplementary Table 1). Details of the post-acquisition focusing process are described in Supplementary Note 9: Post-focusing. As a result, defocus adjustment can be omitted during acquisition, saving exposure time and the dose budget.

As an alternative ptychographic retrival in STEM, phase-contrast methods including through focal series28 and tilt series22,75 have been used to increase resolution and improve image interpretation in TEM. Atomic resolution exitwave tomography has been theoretically demonstrated for an amorphous structure76. However, most of the experimental focus series exitwave reconstruction algorithms require small defocus changes relative to the dimensions of the sample77 in order to achieve high resolution78. To restore low spatial frequencies without compromising high spatial frequency transfer, the inclusion of a second focal series data set with a larger focal step has been suggested28. However, the large focal differences in the micrometre range required may lead to variations in magnification, image rotation, and possibly other distortions. In addition, the extent to which radiation damage may limit these alternative approaches remains to be explored experimentally, and the difficulties of image alignment at low dose may introduce further limitations.

In addition to computational methods, a physical phase plate such as Zernike79,80,81 and Volta82,83 that can be positioned at the back focal plane of objective lens to introduce a phase shift between the scattered and unscattered electron wave, leading to in-focus phase contrast without compromising low-resolution transfer. Tomography using phase plates is commonly used for the studies of biological objects in cryogenic TEM81,84. However, organic and inorganic hybrid structures such as the sample used here have not been studied. Furhermore these devices can suffer from signal attenuation at high frequencies, inconsistent fabrication, instability and a short usable life-span due to electrostatic charging85,86.

Recently, in STEM a pre-specimen phase plate was introduced in the probe-forming lens to acquire a 4D-STEM dataset with a focused probe, called MIDI-STEM87. This was further combined with non-iterative ptychography, giving enhancement of the contrast transfer at low spatial frequencies for 2D imaging88. Potentially this technique could further provide a 3D phase reconstruction when used in conjunction with tomography. Using MIDI-STEM also allows simultaneous annular dark field (ADF) imaging89, but it generally requires a fast detector. If raw data volumes in a dense representation are considered then there is also a substantial increase in data volume with field of view for this technique. However, we note that there have been reports of advanced data processing strategies to mitigate this68,90. In contrast, defocus-probe ptychography can be preformed with relatively simple detectors and requires less raw data volume for an object of the same size. Furthermore, removing the requirement to insert a condenser phase plate before each acquisition reduces the experimental complexity, particularly for low-dose experiments.

In summary, by combining electron ptychography and tomography, we have demonstrated 3D reconstruction of unstained DNA origami strands and gold nanoparticles with core-shell structures; a case of imaging biological and non-biological hybrid materials. In contrast to conventional TEM tomography, ptychography based tomography (EPty-Tomo) shows advantages of both high contrast and resolution at a low dose and can simultaneously visualise both weakly scattering materials (beam-sensitive biological materials) and strong scattering (inorganic, metal) materials. The post-focusing capability of ptychography simplifies the tomographic workflow, consequently reducing the total dose budget and radiation damage. With future developments of ultrafast detectors and improved cryogenic techniques, ptychographic tomography has great potential as an alternative to conventional electron cryo-tomography for high-resolution, large-volume visualisation of biological/non-biological hybrid structured materials. In turn this will assist the efficient development and refinement of fabrication processes and functional design.

## Methods

### Samples

DNA origami with a tetrahedral structure with gold nanoparticles inlayed was prepared using one-step self-assembly method. DNA origami was unstained and suspended on 50-mesh copper grid covered with an ultrathin carbon film in room temperature and air dried. Detailed information of sample preparation is described in Supplementary Note 1: Sample Preparation.

### Experimental measurements

Data for ptychographic tomography was acquired using a FEI Titan G2 Cubed with two aberration correctors at an accelerated voltage of 60 kV. A beam with a convergence angle of 1.5 mrad and defocus of −40 μm was formed giving a diameter of 120 nm at the sample. Diffraction patterns were recorded using Gatan Orius SC200 camera with 2048 × 2048 pixels for a dwell time of 0.2 s. At each tilt angle, the electron beam was scanned in a 10 × 10 array over the sample with a scanning step of 20 nm to fulfil the overlap ratio required by ptychography. The sample was tilted about two mutually perpendicular axes from −49.99 to 53.94 degree and from −53.42 to 46.40 degree, respectively. A Fischione Model 2040 tomographic holder was used which has a maximum tilt angle of +/− 70° degree. However, for higher tilting angles, the sample was blocked by the copper grid. The tilt angle increment was approximate 10 degree. Defocus values as a function of the tilt angles are listed in Supplementary Table 1 and typical diffraction patterns and 2D ptychographic phases are shown in Supplementary Fig. 1 and Supplementary Fig. 2.

### Ptychography and tomography reconstructions

The two-dimensional sample complex function at each tilt angle was reconstructed using the ePIE algorithm33. Detailed information of the ePIE algorithm used is described in Supplementary Note 3: 2D Ptychographic Reconstruction.

In the ptychographic reconstruction, amplitude of initial object guess is 1 (i.e. constant array), and initial phase is initialised with random low frequency information (from 0 to 0.035 nm−1). Initial probe function is calculated from the measured values of the convergence angle and defocus.

Diffraction patterns collected at each angle under different defocus conditions were processed by threshold and reconstructed using ePIE for 100 iterations with α = 0.5. Defocus values at each tilt angle are listed in Supplementary Table 1. The phases of the reconstructed complex functions (Supplementary Fig. 2) were then used as inputs for the subsequent tomographic reconstruction.

After ptychographic reconstructions, two datasets of the 2D ptychographic phase projections were generated from two tilt series as inputs for the tomographic reconstruction procedure. Tilt axes and image shifts were aligned manually using IMOD91 and tilt angles were subsequently calibrated (Supplementary Table 1). GENeralized Fourier Iterative Reconstruction (GENFIRE) algorithm58 was used for tomographyic reconstruction and the resultant 3D reconstructions is shown in Fig. 1b, Fig. 2, Supplementary Fig. 3a, Supplementary Fig. 7. Detailed information of tomographic reconstruction is described in Supplementary Note 4: 3D Tomographic Reconstruction.

### Reporting summary

Further information on research design is available in the Nature Research Reporting Summary linked to this article.


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Abstract| Volume 23, SUPPLEMENT 2, S496, December 2020

# PCV55 Cost-Effectiveness of Icosapent Ethyl (IPE) for the Reduction of the Risk of Ischemic Cardiovascular Events in Canada.

Open Archive

## Objectives

The recent REDUCE-IT clinical trial demonstrated that in statin-treated patients with hypertriglyceridemia with established CVD and/or diabetes plus 1 risk factor that the risk of ischemic events, including cardiovascular death, was significantly reduced in those treated with IPE vs. placebo. The objective of this study was to assess the economic impact of IPE in the reduction of ischemic cardiovascular events in Canada.

## Methods

A cost-utility analysis (CUA) was conducted to compare IPE to placebo for the reduction of ischemic cardiovascular events from a publicly funded Canadian healthcare payer perspective. The CUA is based on a time-dependent Markov transition model. In the CUA, patients cycled through the Markov model in one-year cycles. The Markov model is used to predict the long-term risk of major cardiovascular events through five different health states: cardiovascular event-free, non-fatal cardiovascular events composed of nonfatal MI, nonfatal stroke, coronary revascularization, or hospitalization for unstable angina, post-non-fatal cardiovascular event, death from fatal cardiovascular causes, and death from other causes for a 20-year time horizon. Costs for follow-up and monitoring, and utilities were obtained from provincial formularies and databases, manufacturer sources, and Canadian literature sources.

## Results

In the probabilistic base-case analyses, treatment with IPE was associated with an incremental cost of $12,523 (SD=$1,029) and an increment of 0.29 (SD=0.08) quality-adjusted life years (QALYs) (both discounted) compared to placebo, corresponding to an ICER of $42,797 per QALY gained (SD=$15,884).

## Conclusions

IPE represents an important new treatment for the reduction of ischemic cardiovascular events. Based on the clinical trial evidence, this CUA suggests that IPE is a cost-effective strategy in Canada based on the conventionally quoted thresholds of \$50,000 per QALY gained.