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# Christofer Toumazou

Affiliations:
• Imperial College London, UK

According to our database1, Christofer Toumazou authored at least 176 papers between 1993 and 2021.

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

2021
Detection of Multiple Breast Cancer ESR1 Mutations on an ISFET Based Lab-on-Chip Platform.
IEEE Trans. Biomed. Circuits Syst., 2021

Signal Identification of DNA Amplification Curves in Custom-PCR Platforms.
Proceedings of the IEEE International Symposium on Circuits and Systems, 2021

A Point-of-Care Device for Sensitive Protein Quantification.
Proceedings of the IEEE International Symposium on Circuits and Systems, 2021

Personalised trainer recommendation based on physical activity and genetic profile.
Proceedings of the IEEE EMBS International Conference on Biomedical and Health Informatics, 2021

2020
A DNA-Based Intelligent Expert System for Personalised Skin-Health Recommendations.
IEEE J. Biomed. Health Informatics, 2020

A Convolutional Neural Network for Classification of Nerve Activity Based on Action Potential Induced Neurochemical Signatures.
Proceedings of the IEEE International Symposium on Circuits and Systems, 2020

In-Silico Automated Allele-Specific Primer Design for Loop-Mediated Isothermal Amplification.
Proceedings of the IEEE International Symposium on Circuits and Systems, 2020

Detection of Breast Cancer ESR1 p.E380Q Mutation on an ISFET Lab-on-Chip Platform.
Proceedings of the IEEE International Symposium on Circuits and Systems, 2020

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 Syst., 2018

PERSON - Personalized Expert Recommendation System for Optimized Nutrition.
IEEE Trans. Biomed. Circuits Syst., 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 Medical Informatics Decis. Mak., 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

Current feedback neural amplifier with real time electrode offset suppression.
Proceedings of the IEEE 60th International Midwest Symposium on Circuits and Systems, 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. Biomed. 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
IEEE J. Biomed. 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 Syst., 2014

A Low Power Sub-µW Chemical Gilbert Cell for ISFET Differential Reaction Monitoring.
IEEE Trans. Biomed. Circuits Syst., 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.
J. Signal Process. Syst., 2013

A Bionics Chemical Synapse.
IEEE Trans. Biomed. Circuits Syst., 2013

The spatial pattern of light determines the kinetics and modulates backpropagation of optogenetic action potentials.
J. Comput. Neurosci., 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. Res., 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. Eng., 2012

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

An Efficient Implementation of the SIVIA Algorithm in a High-Level Numerical Programming Language.
Reliab. Comput., 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

A TDC based ISFET readout for large-scale chemical sensing systems.
Proceedings of the 2012 IEEE Biomedical Circuits and Systems Conference, 2012

An ISFET design methodology incorporating CMOS passivation.
Proceedings of the 2012 IEEE Biomedical Circuits and Systems Conference, 2012

ISFET's threshold voltage control using bidirectional electron tunnelling.
Proceedings of the 2012 IEEE Biomedical Circuits and Systems Conference, 2012

2011
Modeling Study of the Light Stimulation of a Neuron Cell With Channelrhodopsin-2 Mutants.
IEEE Trans. Biomed. Eng., 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.
IEEE 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. Circuits Syst. I Regul. Pap., 2009

Subthreshold Parallel FM-to-Digital Delta- Sigma Converter With Output-Bit-Stream Addition by Interleaving.
IEEE Trans. Circuits Syst. I Regul. Pap., 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 Syst., 2008

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

A 1 V Wireless Transceiver for an Ultra-Low-Power SoC for Biotelemetry Applications.
IEEE 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 Syst., 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

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

Modeling and Engineering aspects of ChannelRhodopsin2 System for Neural Photostimulation.
Proceedings of the 28th International Conference of the IEEE Engineering in Medicine and Biology Society, 2006

2005
A biochemical translinear principle with weak inversion ISFETs.
IEEE Trans. Circuits Syst. I Regul. Pap., 2005

A micropower CMOS continuous-time filter with on-chip automatic tuning.
IEEE Trans. Circuits Syst. I Regul. Pap., 2005

Guest Editorial.
IEEE Trans. Circuits Syst. I Regul. Pap., 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
Low-power high-frequency class-AB two-step sampling switched-current techniques.
IEEE Trans. Circuits Syst. II Express Briefs, 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

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. Comput. Aided Des. Integr. Circuits Syst., 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

A micropower cochlear prosthesis system.
Proceedings of the 14th International Conference on Digital Signal Processing, 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

Double-regenerated switched-current comparator.
Proceedings of the 6th IEEE International Conference on Electronics, Circuits and Systems, 1999

Design of low-distortion CMOS Class E power amplifier for wireless communications.
Proceedings of the 6th IEEE International Conference on Electronics, Circuits and Systems, 1999

SC quadrature mixer for IF bandpass sampling.
Proceedings of the 6th IEEE International Conference on Electronics, Circuits and Systems, 1999

1998
An investigation of log domain current feedback amplifiers.
Proceedings of the 5th IEEE International Conference on Electronics, Circuits and Systems, 1998

A high Q RF CMOS differential active inductor.
Proceedings of the 5th IEEE International Conference on Electronics, Circuits and Systems, 1998

1996
On the design of micropower active resonators and oscillators using log-domain processing.
Proceedings of Third International Conference on Electronics, Circuits, and Systems, 1996

Wideband CMOS analog cells for video and wireless communications.
Proceedings of Third International Conference on Electronics, Circuits, and Systems, 1996

1995
Analog IC design automation. I. Automated circuit generation: new concepts and methods.
IEEE Trans. Comput. Aided Des. Integr. Circuits Syst., 1995

Analog IC design automation. II. Automated circuit correction by qualitative reasoning.
IEEE Trans. Comput. Aided Des. Integr. Circuits Syst., 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 S<sup>2</sup>I-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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Is the first differential Pontryagin class a morphism of stacks? - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-21T20:55:10Z http://mathoverflow.net/feeds/question/83147 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/83147/is-the-first-differential-pontryagin-class-a-morphism-of-stacks Is the first differential Pontryagin class a morphism of stacks? domenico fiorenza 2011-12-10T21:36:05Z 2011-12-14T12:24:09Z
In Cech Cocycles for Characteristic Classes, Jean-Luc Brylinski and Dennis McLaughlin provide explicit formulas for Cech cocycles for characteristic classes of real and complex vector bundles, and show how to refine these to Cech-Deligne cocycles for differential characteristic classes in differential cohomology.

When the compact Lie group $G$ involved is enough connected, e.g., if one is interested in the second Chern class of a principal $SU(n)$-bundle, the Brylinski-McLaughlin formula drastically simplifies, and it can be shown that in this case it actually gives a morphism of stacks from the classifying stack of principal $G$-bundles with connections to the (higher) stack of principal $U(1)$-$n$-gerbes with connections (here $n+2$ is the degree of the characteristic class involved).

This stacky interpretation is emphatised, e.g., in the follow-up Cech cocycles for differential characteristic classes - An $\infty$-Lie theoretic construction, by Urs Schreiber, Jim Stasheff and myself, where it is obtained (as the title suggests) via integration of $L_\infty$-algebras to higher Lie groups. For this approach, the connectivity of $G$ is essential. For instance one can see that the first fractional differential Pontryagin class $\frac{1}{2}\hat{p}_1$ is a morphism of stacks from the stack of princiapl Spin bundles with connection to the 3-stack of $U(1)$-2-gerbes with connection, and this precisely reproduces Brylinski-McLaughlin construction, the but one cannot see the Brylinski-McLaughlin cocycle for the first differential Pontryagin class $\hat{p}_1$ for princiapal $SO$-bundles with connections via Lie integration: $SO$ is not enough connected to allow this. This pheneomenon is in a sense not surprising: for instance the "identity" morphism from the Lie algebra of $O(2)$ to the Lie algebra of $SO(2)$ cannot be integrated to a morphism of Lie groups from $O(2)$ to $SO(2)$ due to "lack of connectivity" reasons.

Yet the fact that a particular technique fails does not mean that a statement is false. So here is my question: is there a natural interpretation of Brylinski-McLaughlin cocycle for the first differential Pontryagin class $\hat{p}_1$ as a morphism of stacks (from $SO$-bundles with connections to $U(1)$-2-gerbes with connections)? or is there a natural interpretation of Brylinski-McLaughlin cocycle for the second differential Chern class $\hat{c}_2$ as a morphism of stacks from $U$-bundles (not $SU$!) with connections to $U(1)$-2-gerbes with connections)?

My feeling is that once there are no topological obstruction (i.e., once the characteristic classes are defined at the non-very-conected level, as in these cases), the morphism of stacks (which surely exists at the highly connected level) descends from the higher connected cover of $G$ involved to the original $G$. So, for instance since $\frac{1}{2}p_1$ is not an integral class for $SO$-bundles one can not make $\frac{1}{2}\hat{p}_1$ descend from principal Spin-bundles with connections to princiapal $SO$-bundles with connections; but since $p_1$ is an integral class for $SO$-bundles, then it should be possible that $\hat{p}_1$ descends. But all my attemps towards a rigorous proof of this have failed so far, so I've begun thinking that I may be wrong, and that $\hat{p}_1$ can be given no natural interpretation as a morphism of stacks after all.

Any suggestion, reference or criticism concerning this problem is welcome.
 http://mathoverflow.net/questions/83147/is-the-first-differential-pontryagin-class-a-morphism-of-stacks/83369#83369 Answer by Konrad Waldorf for Is the first differential Pontryagin class a morphism of stacks? Konrad Waldorf 2011-12-13T21:49:41Z 2011-12-14T12:24:09Z
Yes, every differential characteristic class is a stack morphism.

The point is that there exist universal differential characteristic classes. These are not easy to describe since they involve a notion of differential cohomology of classifying spaces. One way is to use Urs Schreiber's approach. At least in the case of degree four classes one can alternatively use the theory of multiplicative bundle gerbes.

In this context, I'd use the following working definition:

Definition: A universal degree four differential characteristic class on a Lie group $G$ is a multiplicative $U(1)$-bundle gerbe over $G$ with (multiplicative) connection of curvature $H$.

Here, $H$ is the "canonical" 3-form on $G$, it is defined using a bilinear symmetric linear form on the Lie algebra of $G$ - I think any such form is fine.

Multiplicative bundle gerbes have been introduced in the paper (1); they represent classes in $H^4(BG,\mathbb{Z})$. The notion of a multiplicative connection is subtle, I'd refer to Definition 1.3 of my paper (2). The point is that the "naive" definition is too strict and leaves essentially no space for examples. In particular, while a multiplicative gerbe over $G$ can be seen as a 2-gerbe over $BG$, a multiplicative connection is NOT a connection (in the ordinary sense) on this 2-gerbe.

Example 1: If $G=Spin(n)$, the basic gerbe $\mathcal{G}$ over $G$ carries a canonical connection of curvature $H$ and a canonical multiplicative structure. It is the universal differential half first Pontryagin class, $\frac{1}{2}\widehat{p_1}$. It underlies the definition of string connections I have proposed in my paper (3).

Example 2: If $G = SO(n)$, the bundle gerbe $\mathcal{G}$ descends together with its connection along the projection $Spin(n) \to SO(n)$, but its multiplicative structure does not descend. Instead, only the multiplicative bundle gerbe $\mathcal{G}^2 := \mathcal{G} \times \mathcal{G}$ descends together with its connection and its multiplciative structure. The descended gerbe over $SO(n)$ is the universal differential first Pontryagin class, $\widehat{p_1}$. Descent theory for multiplicative gerbes, together with obstructions is discussed in (4), see Table 1 at the end of the paper.

Now suppose that $\mathcal{G}$ is a universal differential characteristic class, $X$ is a smooth manifold and $P$ is a principal $G$-bundle with connection $A$ over $X$. The Chern-Simons 2-gerbe $\mathbb{CS}_P(\mathcal{G})$ is a $U(1)$-bundle 2-gerbe over $X$, see (1). A connection on $\mathbb{CS}_P(\mathcal{G})$ is constructed from the Chern-Simons 3-form $CS(A)$ and the multiplicative connection on $\mathcal{G}$; here the condition that the curvature of $\mathcal{G}$ is $H$ is important. This construction is described in detail in Section 3.2 of (2). It has the following properties:

Theorem:

if $\xi_P: M \to BG$ is a classifying map for $P$, then $[\mathbb{CS}_P(\mathcal{G})] = \xi_P^*[\mathcal{G}] \in H^4(M,\mathbb{Z})$.

a connection-preserving bundle morphism $P_1 \to P_2$ (covering some smooth map $X_1 \to X_2$ between base manifolds) induces a morphism $$\mathbb{CS}_{P_1}(\mathcal{G}) \to \mathbb{CS}_{P_2}(\mathcal{G})$$ between bundle 2-gerbes.

The first statement is Theorem 3.2.3 in (2). It means that on the level of the underlying (non-differential) characteristic class the construction is just pullback. The second statement follows by inspection of the definition of $\mathbb{CS}_P(\mathcal{G})$. It means precisely that we have a stack morphism $$\mathbb{CS}(\mathcal{G}): Bun_G^{\nabla} \to 2\text{-}Grb_{U(1)}^{\nabla}.$$

References:

"Bundle gerbes for chern-simons and wess-zumino-witten theories"

"Multiplicative bundle gerbes with connection"

"String connections and Chern-Simons theory"

"Polyakov-Wiegmann formula and multiplicative gerbes"

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# Consequences of ortho effect on resonance

Consider any carboxylic acid with any group at ortho position. According to ortho effect, the resonance of the $$\ce{C=O}$$ with the ring is inhibited.

Is this resonance entirely lost? Or some little amount still exists?

Can resonance be present when the participating orbitals are not in the same plane?

• Well, the "extent of overlap" of the orbitals will decrease but it won't completely vanish, so yes, there will be some resonance stabilisation. – user79161 May 20 '19 at 7:59

If they are off the plane due to steric effect, then resonance wouldn't occur, hence the (-)R effect of - COOH group vanishes and hence "generally" acidity of the respective acid increases.

• Wouldn't occur at all? – user226375 May 20 '19 at 14:13
• Also it took me a minute to realize OFF is not oxygen difluoride. Please don't use CAPS for emphasis (italics or bold is much better). – andselisk May 20 '19 at 14:15


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## Council Statement on AMS Membership Dues for 2010

In light of the current economic downturn, at its meeting on January 4, 2009, the AMS Council approved posting the following explanatory paragraph about the dues process:

After extensive review and discussion, the Board of Trustees and the Council of the AMS have reluctantly voted to increase the dues of individual members in accordance with the guidelines adopted by  the Trustees in 2003.  Regular low dues will increase from $123 to$126, and regular high dues from $164 to$168. All segments of the mathematics community – individuals, institutions and professional societies – are facing difficult times, and this small increase appears to be the best compromise.  However, the AMS governing bodies will continue to monitor the impact of the economic crisis and will revisit options for the dues structure in 2010.


text:
[SciPy-user] Usage of fmin_tnc and fmin_l_bfgs_b

Nils Wagner nwagner at iam.uni-stuttgart.de
Fri Sep 15 03:45:44 CDT 2006

Nils Wagner wrote:
> Hi all,
>
> I would like to solve a constrained optimization problem with scipy.
> As far as I understand it there exists two possible functions for my
> problem in scipy - fmin_tnc and fmin_l_bfgs_b.
>
> The problem is given by
>
> min f(x)
>
> subjected to
>
> \theta_1 \le theta \le theta_2
>
>  and
>
>  r_1 \le r \le r_2
>
> where x is a vector \in \mathds{R}^{2n+1}.
>
> theta is the last entry in x.
>
> r = \| x[:2*n] \| = linalg.norm(x[:2*n])
>
>
> How do I specify the bounds for my problem ? I mean
> it's easy to define the bounds for the l a s t parameter (\theta) but
> I am at a loss how to formulate
> the bounds for x[0],...,x[2n-1] s e p a r a t e l y.
>
>     bounds  -- a list of (min, max) pairs for each element in x, defining
>                the bounds on that parameter. Use None for one of min or max
>                when there is no bound in that direction
>
> Any hint would be appreciated.
>
> Nils
>
> _______________________________________________
> SciPy-user mailing list
> SciPy-user at scipy.org
> http://projects.scipy.org/mailman/listinfo/scipy-user
>

I guess I can use fmin_cobyla with the following constraints

cons1= x[-1]-\theta_1
cons2=\theta_2-x[-1]
cons3=linalg.norm(x[:2*n])-r_1
cons4=r_2-linalg.norm(x[:2*n])

Is that correct ? Is there a better way to implement the problem ?

Nils


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# Thin film interference

## Homework Statement

Between two pieces of glass (##n_1=1.70##), there is a thin film of water (##n_2=1.33## and width ##d=1 \mu m##). If there is normal-incidence of white light on the water surface, find:
(a) which wavelenghts can be seen in the light transmitted (answer: 667 nm,533 nm,444 nm, 381 nm)
(b) which wavelenghts can be seen in the light reflected (answer: 593 nm,484 nm, 410 nm, (355 nm) )

## The Attempt at a Solution

(a) I don't know how to deal with light transmitted
(b) I set the ##2d= \left(m-\frac{1}{2} \right) \cdot \frac{\lambda}{n_2}## to find the lambdas for ##m=1,2...## but I obtain only ##\lambda_{m=1}=355 nm## (below the light that can be seen).

Any help?

TSny
Homework Helper
Gold Member
(a) I don't know how to deal with light transmitted
You can assume that none of the light is absorbed by the material. So, the total amount of incoming light energy must be conserved. As less light is reflected, more light must be transmitted. And vice versa.

(b) I set the ##2d= \left(m-\frac{1}{2} \right) \cdot \frac{\lambda}{n_2}## to find the lambdas for ##m=1,2...## but I obtain only ##\lambda_{m=1}=355 nm## (below the light that can be seen).
Your equation looks OK. But, in order to get a wavelength of 355 nm, I have to let m = 8. You will need to choose values of m that yield visible wavelengths.

You can assume that none of the light is absorbed by the material. So, the total amount of incoming light energy must be conserved. As less light is reflected, more light must be transmitted. And vice versa.

Thanks. But how can I set the equation for the constructive interference in the first case? There is no interference since the light is transmitted(?)

TSny
Homework Helper
Gold Member
Thanks. But how can I set the equation for the constructive interference in the first case? There is no interference since the light is transmitted(?)
There is always interference (constructive, destructive, or something in between) in the transmitted waves and in the reflected waves. Standard textbooks show how you get two reflected rays that interfere. See if you can show how to get two transmitted waves that interfere. Hint: One of the transmitted rays has no reflections. The other transmitted wave has more than one reflection.


text:
# Explain why organic reactions occur at a slower rate than inorganic reactions. What do chemists use to speed these reactions up? Why doesn't this change the products of the reaction?

###### Question:

Explain why organic reactions occur at a slower rate than inorganic reactions. What do chemists use to speed these reactions up? Why doesn't this change the products of the reaction?

### Explain which type of service delivery model this scenario represents. Situation: A shy teenage boy feared crowds and struggled when called upon in class. His social worker discovered the teen enjoyed and had a gift for computer math games. The social worker encouraged the teen to get involved in a small after-school math team that worked with elementary students who needed help in math. In the small group setting, using his gift for math, the teen began to overcome his fear of crowds.

Explain which type of service delivery model this scenario represents. Situation: A shy teenage boy feared crowds and struggled when called upon in class. His social worker discovered the teen enjoyed and had a gift for computer math games. The social worker encouraged the teen to get involved in a ...

### Whitch rock types tend to the weather in rounded shapes

Whitch rock types tend to the weather in rounded shapes...

### Solve for y 5y-(-2)<17 write you answer as an inequality , starting with y > or y

Solve for y 5y-(-2)<17 write you answer as an inequality , starting with y > or y...

### 1. 360 is divisible by which of the following numbers 2. 3. 4. 5. 6. 9. or 10 3. 4. 5. and 9 02.3. 5. and 10 02. 3. 4. 6. and 9 e. 3. 4. 5. 6. 9. and 10

1. 360 is divisible by which of the following numbers 2. 3. 4. 5. 6. 9. or 10 3. 4. 5. and 9 02.3. 5. and 10 02. 3. 4. 6. and 9 e. 3. 4. 5. 6. 9. and 10...

### Which of the following is not a way an author creates suspense in a story

Which of the following is not a way an author creates suspense in a story...

### In what industry do fertilizers and pesticides wash off and contaminate water supplies?Construction Oil Transportation Agriculture

In what industry do fertilizers and pesticides wash off and contaminate water supplies?Construction Oil Transportation Agriculture...

### Theа af forsimple Harmonic motion 2=cos (mt).period is

theа af forsimple Harmonic motion 2=cos (mt).period is...

### (3x + 5)(x2 + 6x +11) multiply

(3x + 5)(x2 + 6x +11) multiply...

### Nzinga always resisted the Portuguese colonizers. True or false

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### 9 - 3x +7y -Зу +3 Thx!!!

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### Alina has a spinner that has 5 equal sections: red, blue, green, purple, and orange. She spins the spinner 200 times. About how many times should Alina expect the spinner to land on either purple or orange?

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### What was the primary purpose of Wilson's Fourteen Points? •serve as the basis for peace negotiations •position the United States as a world power •punish the Central Powers for starting World War I

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### If ƒ(x ) = x 2 + 1 and g(x ) = 3x + 1, find g(20) + ƒ(6).

If ƒ(x ) = x 2 + 1 and g(x ) = 3x + 1, find g(20) + ƒ(6)....

### PLS HELP ASAP BIG PART OF MY GRADE TOPIC: Geography & the Survival of European Culture. TN STANDARD 7.14: Analyze the importance of regional geography and the location of Constantinople in maintaining European culture. Analyze the importance of the survival of the Eastern Roman Empire with its capital in Constantinople for the survival of European culture. SPECIFICALLY: In paragraph one analyze the importance of the regional geography of the Eastern Roman Empire to its survival and success.

PLS HELP ASAP BIG PART OF MY GRADE TOPIC: Geography & the Survival of European Culture. TN STANDARD 7.14: Analyze the importance of regional geography and the location of Constantinople in maintaining European culture. Analyze the importance of the survival of the Eastern Roman Empire with its c...

### Food gives animals energy. Which of the following could be an animal's food? Select all that apply. A. nectar B. a spider C. water D. a twig E. a mushroom

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### A garage door opener has a component that stop the door from coming down if something is in the way. This component is made up of a laser light on one side and a receiver on the other. Which best explains why this component works. A) The receiver collects the laser light indicating that something is in the way. B) Any object blocking the path of the laser will reflect the beam into the reciever. C) Any object in its path changes the color of the laser before it gets to the reciever. D)

A garage door opener has a component that stop the door from coming down if something is in the way. This component is made up of a laser light on one side and a receiver on the other. Which best explains why this component works. A) The receiver collects the laser light indicating that something ...


text:
## Differential Equations and Linear Algebra (4th Edition)

We know that the determinant of a matrix $\left[\begin{array}{rr} a & b \\ c &d \\ \end{array} \right]$ is $D=ad-bc$. Also, a matrix is non-invertible if $D=0$. here $D=x^2y-xy^2=xy(y-x)$. Thus if it is non-invertible then $x=0$, $y=0$ or $x=y$, thus the statement is false.


text:
# Atomic number of copper is 29, its atomic weight is 63.5 gm/mole. If two pieces of copper having weight 10 gm are taken and on one of the pieces 1 electron per 1000 atom is transferred to the other piece and there after this these pieces are placed 10 cm apart, then what will be the coulomb force between them.

In 1 mole copper (63.5 gm) there are $6 \times 10^{23}$ atoms (NA = Avogadro number $= 6 \times 10^{23}$ atoms)
Number of atoms $=\large\frac{6 \times 10^{25} \times 10}{63.5}$$=9.45 \times 10^{22} For every 1000 atoms, 1 electron is transferred therefore total number of transferred electron is =\large\frac{9.45 \times 10^{22}}{1000}$$=9.45 \times 10^{19}$
Therefore charge on one piece is $9.45 × 10^{19}\; e$ and on the other will be $(9.45 × 10^{19}e)$
$F= \large\frac{1}{4 \pi \in_0} \frac{(9.45 \times 10^{19})^2e^2}{(10 \times 10^{-2})^2}$
$\quad= \large\frac{9 \times 10^9 \times (9.45 \times 10^{19} )^2 \times (1.6 \times 10^{-19})^2}{(10 \times 10^{-2})^2}$
$\qquad= 2 \times 10^{14}\;N$


text:
# How do you solve the following system?: x +3y =8 , 6x +4y = -3

May 12, 2018

The values $x = - 2 \frac{13}{14}$ , $y = 3 \frac{9}{14}$ fulfills both equations.

#### Explanation:

It is always helpful to start with drawing the two equations as graphs in a diagram, not least as a check that our solution makes sense:

We want to find a value of x and y which fulfill both equations at the same time, i.e. it must be on both lines f and g on the figure above.

As $x + 3 y = 8$, it follows that
(1) $x = - 3 y + 8$

Insert this value for x in the second equation. To make the solution simpler to follow I will write it as $- 3 = 6 x + 4 y$, that is:
$- 3 = 6 x + 4 y = 6 \left(- 3 y + 8\right) + 4 y$
$- 3 = - 18 y + 48 + 4 y = - 14 y + 48$

The last expression can be written as
$14 y = 48 + 3 = 51$ or $y = \frac{51}{14} = 3 \frac{9}{14}$

Insert this in expression (1):
$x = - 3 y + 8 = \left(- 3\right) \frac{51}{14} + 8 = \frac{- 3 \cdot 51 \cdot 8 \cdot 14}{14}$
$x = \frac{- 153 + 112}{14} = - \frac{41}{14} = - 2 \frac{13}{14}$

Our solution, therefore, is
$x = - 2 \frac{13}{14}$ , $y = 3 \frac{9}{14}$

If we convert these two values to decimal numbers, we see that it agrees with our graph.


text:
Auxiliary Image Regularization for Deep CNNs with Noisy Labels

# Auxiliary Image Regularization for Deep CNNs with Noisy Labels

## Abstract

Precisely-labeled data sets with sufficient amount of samples are very important for training deep convolutional neural networks (CNNs). However, many of the available real-world data sets contain erroneously labeled samples and those errors substantially hinder the learning of very accurate CNN models. In this work, we consider the problem of training a deep CNN model for image classification with mislabeled training samples an issue that is common in real image data sets with tags supplied by amateur users. To solve this problem, we propose an auxiliary image regularization technique, optimized by the stochastic Alternating Direction Method of Multipliers (ADMM) algorithm, that automatically exploits the mutual context information among training images and encourages the model to select reliable images to robustify the learning process. Comprehensive experiments on benchmark data sets clearly demonstrate our proposed regularized CNN model is resistant to label noise in training data.

## 1Introduction

Deep Convolutional Neural Network (CNN) models have seen great success in solving general object recognition problems [14]. However, due to their extremely huge parameter space, the performance of deep models relies heavily on the availability of a sufficiently large number of training examples. In practice, collecting images as well as their accurate annotations at a large scale is usually tedious and expensive. On the other hand, there are millions of freely available images with user-supplied tags that can be easily collected from the web. Being able to exploit this rich resource seems promising for learning a deep classification model. The labels of these web images, however, tend to be much more noisy, and hence challenging to learn from.

In this work, we consider the problem of image classification in this challenging scenario where annotations of the training examples are noisy. In particular, we are interested in how to learn a deep CNN model that is able to produce robust image representations and classification results in presence of noisy supervision. Deep CNN models have been recognized to be sensitive to sample and label noise in recent works [20]. Thus, several methods [20] have been developed to alleviate the negative effect of noisy labels in learning the deep models. However, most of the existing methods only consider modeling a fixed category-level label confusion distribution and cannot alleviate the effect of noise in representation learning for each sample.

We propose a novel auxiliary image regularizer (AIR) to address this issue of deception of training annotations. Intuitively, the proposed regularizer exploits the structure of the data and automatically retrieves useful auxiliary examples to collaboratively facilitate training of the classification model. Here, structure of the data means the nonlinear manifold structure underlying images from multiple categories learned from a well-trained deep model on another data set . To some extent, the AIR regularizer can be deemed as seeking some “nearest neighbors” within the training examples to regularize the fitting of a deep CNN model to noisy samples and improve its classification performance in presence of noise.

Robustifying classification models via regularization is a common practice to enhance robustness of the models. Popular regularizers include Tikhonov regularization (-norm) and the -norm on the model parameters [22]. However, an effective regularizer for training a deep CNN model is still absent, especially for handling the above learning problem with faulty labels. To the best of our knowledge, this work is among the first to introduce an effective regularizer for deep CNN models to handle label noise.

Inspired by related work in natural language processing [26], we use a group sparse norm to automatically select auxiliary images. Figure 1 shows an exemplar overview of our model. In contrast to previous works imposing the regularization on the model parameter, we propose to construct groups of input image features and apply the group sparse regularizer on the response maps. Imposing such group sparsity regularization on the classifier response enables it to actively select the relevant and useful features, which gives higher learning weights to the informative groups in the classification task and forces the weights of irrelevant or noisy groups toward zero. The activated auxiliary images implicitly provide guiding information for training the deep models. We solve the associated optimization problem via ADMM [10], recently popularized by [4]. In particular, we use the stochastic ADMM method of [19] and [1] on this large-scale problem.

We demonstrate the effect of AIR on image classification via deep CNNs, where we synthetically corrupt the training annotations. We investigate how the proposed method identifies informative images and filters out noisy ones among the candidate auxiliary images. Going one step further, we then explore how the proposed method improves learning of image classification from user-supplied tags and handles the inherent noise in these tags. Comprehensive experiments on benchmark data sets, shown in Section 4, clearly demonstrate the effectiveness of our proposed method for the large-scale image classification task.

### 1.1Related Work

A large body of existing work proposes to employ sparsity-inducing [22] or group-sparsity inducing [8] norms for effective model regularization and better model selection, with applications to dictionary learning [17] and image representation learning [25], to name a few examples from the field of computer vision. However, most focus on imposing a structured prior on the model parameters. The idea of exploiting the group sparsity structure within raw data was recently proposed in [26], to solve text recognition problems, by exploiting the intrinsic structure among sentences in a document. However, as far as we know, none of existing works have investigated how to exploit the structural information among data for a deep model, as we address here, and we are among the first to propose such a regularized deep model based on auxiliary data.

In this work, we are particularly interested in learning from noisy labeled image data, where a limited number of training examples are supplied with clean labels. Among the most recent contributions, [21] solve this problem by learning the noise distribution through an extra noise layer added to the deep model,while [24] explore this problem from a probabilistic graphical model point of view and train a classifier in an end-to-end learning procedure. [11] introduce a robust logistic regression method for classification with user-supplied tags. [7] deal with arbitrary outliers in the data through a robust logistic regression method by estimating the parameters in a linear programming scheme. Different from those existing works, we automatically exploit the contextual information from useful auxiliary images via a new regularization on deep CNN models.

## 2Auxiliary Image Regularizer

### 2.1Problem Setup

Suppose we are given a set of training images . Some training samples in have noisy annotations. We do not assume any specific distribution on the noise in . Indeed, we only assume the number of noisy labels does not exceed the number of correct labels. This significantly relaxes the assumptions imposed in previous works [20]. For instance, [20] require the noise to follow a fixed confusion distribution. Our goal is to learn a deep CNN model for the data set while we have access to a deep network pre-trained on an independent set containing sufficiently many accurately annotated examples in categories . We use this pre-trained network to produce representations of images in the main set . We employ the popular AlexNet architecture [14] to build our CNN model. The top layer which accounts for classification is parameterized by , and we apply the usual empirical risk minimization method to learn such parameter:

where is the classification loss on an individual training example in set . Adding a regularizer to the loss function is a common approach in solving large-scale classification problems to prevent overfitting and train a more accurate and generalizable classifier:

Popular regularizers include , and .

### 2.2Auxiliary Image Regularizer

In this work, beyond imposing a prior structure of the model , we propose a novel regularizer to exploit the data structure within to handle the sample noise, which is defined as:

where denotes the group norm defined as . In the group norm, is an index set of all groups/partitions within the vector , are some positive weights, and denotes the sub-vector indexed by group . The norm induces a group sparsity that encourages the coefficients outside a small number of groups to be zero.

We do not impose the group norm on the parameter directly. Instead, we encourage the unlabeled response of the deep model on the learned representation of image data set to be group-wisely sparse, such that only a small number of images will contribute to learning of the model, while other non-relevant images are filtered out. These image representations are extracted from the model pre-trained on the well-labeled data set . Therefore, the regularization draws information from features trained on available data .

Each image is a “group” of active features. The regularizer enforces the features of the “good” and “stable” images to be used for model learning, while noisy additional activations will be disregarded. The active images are the ones that are categorized well in the feature space obtained from the deep model. For a new image, the subset of active features close to those stable images in the learned manifold will be weighted most highly (hence “neighbor regularization”).

Towards this target, the matrix is constructed as and . Here, is a diagonal matrix consisting of the features (such as the outputs of the fc-7 layer) of image representing the -th group in the group norm regularization setting. The group norm enforces the resulting response vector to be sparse, namely only a small number of images are active. These active images are auxiliary examples for learning that are automatically identified by the model. They contribute additional information to model learning. In multi-class classification, is a matrix and the group norm regularizer is defined as the sum of all group sparsity norms of each column.

Our proposed auxiliary image regularized (AIR) model is then defined as:

Our goal is to classify an independent target data set that has corrupted labels.

A deep Convolutional Neural Network (CNN) is parameterized layer-wisely by , and in this work we only impose the auxiliary regularizer on the top (last) layer of the CNN. The objective function we are going to work with for training a deep CNN model is

A popular loss function used for image classification with CNNs is the following cross-entropy loss with softmax:

with the output feature being a function of and the raw input image. Here, is an indicator function.

The standard backprogapation technique via stochastic gradient descent cannot handle the non-smooth regularization term well and presents slow convergence rate. We here demonstrate how the loss function in Section 2.2 can be optimized via ADMM. In this section, we use to denote the parameter of the top layer .

After introducing an auxiliary variable , our optimization problem becomes:

The matrix is a sparse matrix with only one non-zero entry in each row, which corresponds to an entry in the feature vector, and the first rows of correspond to the features of the first sample, indicated as in Section 2.2. In other words, the matrix gives a weight to the parameter value () within each group that is equal to the -th entry in the feature vector. Feature values indicate the activity of corresponding visual feature of an image in the network model. Each term in the group regularizer is normalized by the size of the group through weights such that all of the groups have the same overall effect in the regularizer.

The approximated Augmented Lagrangian [19] for the objective function in Eq. with being the Lagrange variable is:

where is replaced with its first order approximation at , with indicating the number of iteration. Here, is the gradient of at the -th iteration over a mini-batch of training samples. We set equal to according to [1]. Then applying Stochastic Alternating Direction Method of Multipliers (SADMM) [19] followed by a non-uniform averaging step to give higher weights to the recent updates, inspired by [1], gives the following alternative updates of the variables :

We use an adaptive by increasing its value by a factor of in each iteration up to a fixed maximum value . can be updated in a closed form solution as:

The update of has a closed-form solution as the proximal operator for the -norm (group soft-thresholding) [2]:

where soft-thresholding operator for group norm is defined as

Since the update of is independent of the update of any other when , all can be updated in parallel to further reduce computational cost.

Thereafter, we apply a non-uniform averaging step on as:

where ; similar updates apply for and .

## 4Experiments on Deep CNN Model

In this section, we explore the robustness added to the classifier by the proposed auxiliary regularizer and evaluate the performance of the regularized CNN model proposed in Section 2.2 on different benchmark data sets. First, we examine the effect of the auxiliary regularizer when noisy labels are added to clean data sets manually. Second, we investigate its influence on the robustness of the model trained on a freely-available user-tagged data set.

In all of our experiments, we use the AlexNet CNN model pre-trained on the ISLVRC2012 data set [12] and fine-tune its last layer on the target data set . Furthermore, we set in Eq. to a very small number, equal to over the length of each feature vector, and fine-tune the other set of hyper-parameters (batch size, , and ) in the SADMM updates of Eq. on the cross-validation set for each experiment. The initial value for is in all experiments. We cross-validate the regularization parameter for our SVM baseline from the set of . We define our loss function to be a softmax and apply the AIR regularizer on the top layer in the CNN model.

### 4.1Experiments with Synthetic Noisy Labels

First, we conduct image classification on a subset of the ImageNet7k data set [6]. We use a pre-trained AlexNet CNN model and fine-tune its last layer on randomly selected classes from ImageNet7k data set as the leaf categories of animal each of which contains samples. We randomly flipped half of the labels among all 50 categories. This is exactly the problem described in Section 2.1.

We perform similar experiment on the MNIST data with 10 categories of handwritten digits containing samples in total. We use a confusion matrix to define the distribution of noisy labels among the 10 categories. We followed the same settings as in [21] to determine the probability of changing label to label for all as . Different levels of noise are applied by setting the diagonal values of the matrix equal to the noise level and normalizing the distribution accordingly.

We empirically investigate the robustness gained from applying the proposed AIR regularize compared to a linear SVM classifier as well as Robust Logistic Regression (RoLR) [7] which assumes a constant fraction of outliers The SVM and RoLR classifiers are used on the last layer of a similar network. The results, shown in Table 1, demonstrate that AIR offers significant improvements over the performance of deep CNN plus SVM or RoLR. On the ImageNet7k data, the performance gain is as large as compared to the SVM.

We also trained the deep CNN with AIR on the CIFAR-10 data which contains 10 different categories each with training samples. We used the same confusion matrix as explained above and exactly the same as the matrix defined in [21] to randomly corrupt the labels. Since the size of images in CIFAR-10 and MNIST data sets is small ( and respectively), we re-sized images to , and then cropped them to and thereafter extracted their fc7 features from the pre-trained model explained above. We tested the robustness of the model on different batches of CIFAR-10 with various noise levels. In Figure 2, we compare the accuracy of the AIR model to that of an SVM with regularization, [21]’s deep model that adds a noise layer to the CudaConv network, and the CudaConv network. CudaConv refers to the network with three convolutional layers with similar model architecture and hyper-parameter settings used in [21] given by [13].

Figure 2 illustrates that the SVM model suffers as the number of incorrect labels grows, whereas AIR remains robust even with large amounts of corruption. Moreover, the performance of both CudaConv+learned-Q and CudaConv depends heavily on the number of training samples, while we can reach the same classification accuracy with significantly fewer number of data points and the same noise level.

To show the benefit of stochastic ADMM in solving our proposed regularized optimization problem in comparison with stochastic gradient descent (SGD), we re-run the same experiment on CIFAR-10 data set but train the model with SGD in the presence of label noise. This experiment results in an accuracy of compared to accuracy achieved by stochastic ADMM following the same settings discussed in Section 3.

We also trained AlexNet with regularizer in an end-to-end scheme on CIFAR-10 with incorrect labels where the weights of the last layer are initialized with the learned weights from AlexNet+ft-last-SVM and AlexNet+ft-last-AIR. Classification accuracy obtained from these different initializations is and , respectively. It shows that even implementing the proposed AIR regularizer in the last layer will improve the accuracy of the whole deep model that is trained end-to-end.

The AIR regularizer automatically incorporates inherent structure in the image data by forcing the weights of noisy groups to decrease toward zero and giving higher learning weights to the stable groups. We illustrate this characteristic of AIR in Figure 3 by comparing the distribution of activations of noisy-labeled images and the distribution of the activations of clean images in the Imagenet7k experiment along different learning iterations. Here “activation” refers to the -norm of the weights associated with each of the groups, i.e., in Eq. . The distributions of these two sets of activations highly overlap in the first iteration and they gradually get more and more distinct from each other revealing the ability of the auxiliary regularizer in finding the images with noisy annotations. We manually compute the same activation scores per image for SVM by setting and compare the corresponding distribution in the right plot of Figure 3. Activation scores for images with both clean and noisy labels, learned from SVM, overlap notably after equal number of epochs of training with AIR.

### 4.2Experiments with Real Noisy Labels

In this section, we examine the performance of deep image classifier on images with user-supplied tags from publicly available multi-label NUS-WIDE-LITE data set [5] as a subset of large Flickr data set. This data set contains 81 different tags with the total number of 55615 samples divided into two equal-sized train and test sets. After ignoring the subset of training samples which are not annotated by any tags, we have samples in the training set. We train the classifier on the user-tagged images of training data and evaluate the performance on the test set with ground-truth labels.

We followed the same experimental settings as explained in Section 4. We compare the performance of deep model with different classifiers applied to the last layer of AlexNet. In Figure 6, we plot averaged-per-image precision and recall values when we assign highest-ranked predictions to each image. As a secondary metric, we compare AIR’s performance with the baselines in terms of Mean Average Precision () [15] which does not depend on the top rankings, but on the full rankings for each image. We use to measure the quality of image ranking per label and to measure the quality of tag ranking per image. Robustness to noisy user-tags obtained from the auxiliary regularizer is significant as shown in Figure 6. A few sample images and their top-5 predictions by both AIR and SVM regularizers are represented in Figure 7.

### 4.3Visualization of Selected Auxiliary Images

Finally, we try to understand whether the model indeed has the expected ability of retrieving informative images during the training process. To this end, we visualize the automatically selected auxiliary images in Figure ?, left plot. The figure refers to the experiments on the Imagenet7k data set with noisy labels with the same settings explained in Section 4.1, and displays the images whose corresponding groups were active (selected during the optimization), and also the images that were filtered out (suppressed). The images in this figure are ranked based on their activation scores, expecting clean images to have higher ranks and appearing on the top rows of the plot. Similar to Section 4.1, we rank images based on their activation scores obtained from SVM learned weights on the right hand side of Figure ?. Indeed, the figure shows that AIR forces the weights of noisy or non-informative images to zero and encourages the model to select clear and informative images in the training procedure much more accurately than SVM. This also explains why our proposed model is robust to the noisy-labeled training examples, as shown in the previous experiments.

### 4.4Scalability of the Auxiliary Image Regularizer

To reduce memory requirement for matrix on large data sets, we can randomly select a small number of groups to be considered in AIR regularizer. When large number of data points are available, randomly ignoring the groups in regularization of the response will not substantially affect the learning process that is influenced by the distribution of informative images in the feature space. To verify this point, we repeat the experiment on CIFAR-10 data set with synthetic noise level but with only of the groups used in the regularization term. This significant memory reduction will only drop the accuracy by from to . This experiment shows sampling from the groups does not reduce the final classification accuracy considerably in the case of large data sets but saves the memory cost significantly.

## 5Summary and Future Work

We introduced a new regularizer that uses overlapping group norms for deep CNN models to improve image classification accuracy when training labels are noisy. This regularizer is adaptive, in that it automatically incorporates inherent structure in the image data. Our experiments demonstrated that the regularized model performs well for both synthetic and real noisy labels: it leads to a substantial enhancement in performance on the benchmark data sets when compared with standard models. In the future, we will explore the effect of AIR on robustifying the classifier in an end-to-end scheme where the error information from the auxiliary regularizer will back-propagate through the inner layers of deep model to produce robust image representations.

### References

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Bach, Francis, Jenatton, Rodolphe, Mairal, Julien, and Obozinski, Guillaume. Foundations and Trends in Machine Learning
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8. A note on the group lasso and a sparse group lasso.
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10. Sur l’approximation, par elements finis d’ordre un, et la resolution, par penalisation-dualite d’une classe de problemes de dirichlet non lineaires.
Glowinski, Roland and Marroco, A. ESAIM: Mathematical Modelling and Numerical Analysis-Modélisation Mathématique et Analyse Numérique
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Li, Xirong, Uricchio, Tiberio, Ballan, Lamberto, Bertini, Marco, Cees, Snoek, and Bimbo, Alberto Del. http://arxiv.org/pdf/1503.08248v2.pdf
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18. Deep neural networks are easily fooled: High confidence predictions for unrecognizable images.
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19. Stochastic alternating direction method of multipliers.
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20. Learning from noisy labels with deep neural networks.
Sukhbaatar, Sainbayar and Fergus, Rob. arXiv preprint arXiv:1406.2080
21. Training convolutional networks with noisy labels.
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22. Regression shrinkage and selection via the lasso.
Tibshirani, Robert. Journal of the Royal Statistical Society. Series B (Methodological)
23. Visualizing data using t-sne.
Van der Maaten, Laurens and Hinton, Geoffrey. Journal of Machine Learning Research
24. Learning from massive noisy labeled data for image classification.
Xiao, Tong, Xia, Tian, Yang, Yi, Huang, Chang, and Wang, Xiaogang. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 2691–2699, 2015.
25. Linear spatial pyramid matching using sparse coding for image classification.
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26. Making the most of bag of words: Sentence regularization with alternating direction method of multipliers.
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27. Regularization and variable selection via the elastic net.
Zou, Hui and Hastie, Trevor. Journal of the Royal Statistical Society: Series B (Statistical Methodology)
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text:
# Differences between Bit Rate and Baud Rate

Computer EngineeringComputer NetworkMCA

Both Bit rate and Baud rate are used in data communication. Bit rate and Baud rate are related using below formula.

Bit Rate = Baud rate x the number of bit per baud

Following are the important differences between Pure Aloha and Slotted Aloha.

Sr. No.KeyBit RateBaud Rate
1DefinitionBit rate is transmission of number of bits per second.Baud rate is number of signal units per second.
2DefinitionIt can be defined as per second travel number of bits.It can be defined as per second number of changes.
3FocusBit rate focusses on computer efficiency.Baud rate focusses on data transmission.
4FormulaBit Rate = Baud rate x the number of bit per baudBaud Rate = Bit rate / the number of bit per baud
Published on 26-Nov-2019 10:52:14


text:
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Using a Mac for B-School

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Using a Mac for B-School [#permalink]

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15 Apr 2007, 09:41
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Howdy,
Is anyone here planning on using a Mac for school? If so, what program will you use to take class notes?

I'm having trouble finding a good Mac equivalent to MS OneNote, which is giving me some pause about getting a Mac. (I don't want to use Parallels to switch over to OneNote all the time).

Most of the Mac note-taking programs I've found are either souped up stickies or more of a cataloguer intended for serious academic research.

I like OneNote because it's basically a word processor with extra flexibility in the page layout (ie multiple text boxes) and the tabs on the top and the side make it super easy to organize everything. Also, all your notes are one place, which makes it easy to search and navigate.
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16 Apr 2007, 02:11
I may well get a mac - the ability to dual boot it makes sense, and I am a sucker for the asthetics as well as its music capability (apparently my school says a 15" MacBook Pro is OK).

For notes? Software? I am obviously so retro.

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16 Apr 2007, 08:35
Ha! Nothing beats the reliability of the pen/paper option.

Did you see that Leopard got pushed back from June to October? If the new hardware is delayed I'm not sure what I'm going to do.

Have you ever used OneNote? It's so intuitive and easy to use that it doesn't even feel like you're on a PC. It's enough to make me reconsider getting a mac.
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16 Apr 2007, 09:37
Naturallight - What do you use OneNote for? Taking notes at work meetings?

I went to the Microsoft website and "test drove" the program, seems pretty cool, I could see how it would be handy in school but don't think I'd need it at work.
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16 Apr 2007, 09:51
I would just have the concern that it would be a nightmare for any calculus.

Which shows me up as the kind of maths bore that I am.
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16 Apr 2007, 10:01
There are other math specific packages out there that would work well for Calc. Maple comes to mind as a pretty inexpensive albiet good option.
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16 Apr 2007, 10:16
I still can't see how anyone thinks they could use a computer to quickly note down a PDE or somesuch. It doesn't make sense to me. If I need it in an essay, I will have the application to do it, but I have yet to see any formula software that is quick to use.

And the accuracy of these things is so important I would just stick with a pencil and paper.
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16 Apr 2007, 13:19
Johnnyx9--I used OneNote for my CFA studies. My wife (and many of her classmates) used it for law school.

It definitely is a better app for taking notes from a book or a lecture than taking notes in a math class.

However, if you have a tablet laptop, you can draw graphs and math equations directly into OneNote. I've done this on my friend's computer, and it seems to work ok.
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07 May 2007, 18:16
Using a mac at bschool should be fine, but you need to load bootcamp on your computer so that you can run non-mac programs. I've been running bootcamp for a while and, thus far, its been great.
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07 May 2007, 18:19
Using a mac at bschool should be fine, but you need to load bootcamp on your computer so that you can run non-mac programs. I've been running bootcamp for a while and, thus far, its been great.
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13 May 2007, 18:02
Are there any differences in performance between a Mac running on bootcamp and a Window machine with similar specs (say 2.0GHz Intel Core 2 Duo, 1GB ram)?
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26 May 2007, 22:22
I know I'm a little late adding to this thread, but I thought I would chime in. I actually decided to switch to a Mac for B-School because I couldn't find any PC laptops that I really liked.

I didn't want to run bootcamp because it requires a full reboot to switch between the different operating systems...instead I'm running Parallels with a WinXP image and Office 2007. The cool thing is you can run Parallels in Coherence mode which allows you to run native Windows applications directly from OS X. It works great for just running OneNote without requiring a reboot.

I have a Macbook Pro (2.16ghz dual core with 3gb ram) and the CPU barely budges when I have everything open.

-Steve
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26 May 2007, 23:29
3underscore wrote:
I still can't see how anyone thinks they could use a computer to quickly note down a PDE or somesuch. It doesn't make sense to me. If I need it in an essay, I will have the application to do it, but I have yet to see any formula software that is quick to use.

And the accuracy of these things is so important I would just stick with a pencil and paper.

I agree with the pencil and paper approach. Let me explain why:

I can type quite fast and without looking at the screen. I can even follow up with a conversation between different people and type what everyone says (I've been doing so for some time at a regular meeting at work). However, what I've learnt in the process is that this method would probably not be so useful for taking notes during classes. The main limitation I foresee is the impossibility of rapidly drawing arrows or other types of graphic aids or cross-referencing stuff in your notes. Yeah, you could scroll up and down and insert the drawing objects, but you'd need to look at the screen, thereby missing on the non verbal communication and probably getting lost. In particular, for case method classes, I may be writing notes in the case print itself or cross-referencing sections in the case with my own notes. Try doing that with a computer.

On the Macs, I love their style, but IMHO aren't worth the hassle (probably because I haven't used Macs aside from the occasional drop by at Apple stores). All systems at school (at least the one I'll attend) are Windows-centric. Why would I want to pay more for a Mac and then boot Windows in it? I'd rather save some money and use the Lenovo.

Cheers. L.

Last edited by lepium on 27 May 2007, 00:06, edited 1 time in total.
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26 May 2007, 23:58
As I see it, the main advantage of taking notes on a laptop is that you can search them quickly on the computer. It's not possible to do that with handwritten notes, and I can't imagine transcribing notes after taking them by hand (ahh how nice it was to have a secretary). Anyhow, I'll probably be doing both, typing notes into the laptop, and also taking notes by hand that I can reference.

With regards to using a Mac, I agree with Lepium. I don't know about other schools, but I know that Darden has specific requirements for integrating laptops with their system at school. For example, the required XP Pro or Vista Business - XP & Vista Home do not have the required security functionality and cannot be configured for use on their network. I can only speculate, but I don't believe that Macs running parallels could be so configured either. I think Bootcamp (as I understand it) might work because it basically boots up a copy of XP and you can utilize Pro. However, as Lepium said, why pay more, just so you can boot to Windows?

Another thing about Macs is that they get really really hot, uncomfortably so. I guess there are different opinions about this, but it seems that most people attribute this flaw to designing for looks over functionality. Whatever the reason, the heat is really annoying. The fans in Macs are also really loud - according to a friend loud enough to be very noticeable in a classroom or especially in a library. Some of the better designed business notebooks run 30-40 degrees cooler than Macs, and have whisper quiet fans that rarely come on.

I've voted with my pocketbook and selected a nice Lenovo. I was wondering what people view as the strengths of Macs in a business setting. Other than the looks (which are a matter of personal taste and completely meaningless to me), why would someone want the aggravation of trying to work with a Mac when everything is designed to work with Windows? Not a rhetorical question, I'd actually like to understand.
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27 May 2007, 04:06
For me I need to buy a new laptop and I want a mac because of the benefits of being able to run Reason, Ableton and a variety of other software that I want.

Because business school is a reason to buy a computer, and not the sole motivating factor.

There are several classes where they won't allow laptops at school, btw. And at most schools you should be able to configure a mac.
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27 May 2007, 04:35
Personally I like the size/mobility of Macs - but I am a PC guy so I don't think I could live with one. That black macbook would be sweet - but only if it was running windows

I think it would be too annoying in the business environment to have to work around the issues that would come up.
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29 May 2007, 08:19
I don't want to start a Mac vs Windows flame war, but in regards to the pricing, I thought that Macs had nearly closed the gap. I think they seem expensive because Apple doesn't offer a super low-end version--the cheapest Macbook has some pretty decent specs.

In some cases, however, the pricing is weirdly expensive. Going from a 80 gig HD to 160 is about $150 on a Mac,$70 on a PC. That seems pretty stupid, considering that HDs aren't unique.
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26 Jun 2007, 15:00
Finally pulled the trigger. Got the stock 15" MacBook Pro. Unfortunately they're out of stock, so it could be a couple weeks before it comes in.

I got a heck of a deal though: $200 off for my edu discount, a free nano (worth$200), $160 off Applecare, no tax (~$200), and only $8 in shipping cost. Can't wait! VP Joined: 11 Dec 2006 Posts: 1430 Location: New York, NY Schools: NYU Stern 2009 Followers: 42 Kudos [?]: 220 [0], given: 6 [#permalink] Show Tags 27 Jun 2007, 04:10 Ah - good work, Natural light. I am still deliberating (mainly as to how long it will take me to get my head around parallels), but will likely plump for the same model. I might call NYU Bookstore before I arrive to give them a leadtime on me buying it. Was that deal through yr school, or elsewhere? Current Student Joined: 24 Aug 2005 Posts: 260 Followers: 1 Kudos [?]: 4 [0], given: 0 [#permalink] Show Tags 27 Jun 2007, 07:50 3underscore - yeah, it was through the Berkeley computer store. It was buy far the best deal, since I have to pay tax on amazon and online apple store purchases. The online apple store was offering$100 of the printer, but not the apple care discount, so that part evens out.

Yeah, I have no idea how Parallels works either. Do you know when Office 2008 for macs will be out?

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text:
green s theorem template

green s theorem template is a green s theorem template sample that gives infomration on green s theorem template doc. When designing green s theorem template, it is important to consider different green s theorem template format such as green s theorem template word, green s theorem template pdf. You may add related information such as green’s theorem questions and answers pdf, green’s theorem statement, green’s theorem formula, green’s theorem proof.

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notice that both of the curves are oriented positively since the region $$d$$ is on the left side as we traverse the curve in the indicated direction. now, since this region has a hole in it we will apparently not be able to use green’s theorem on any line integral with the curve $$c = {c_1} \cup {c_2}$$. then, if we use green’s theorem in reverse we see that the area of the region $$d$$ can also be computed by evaluating any of the following line integrals.

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