text:
Recursos de colección

1. Corrigendum On the class groups of pure function fields

Ichimura, Humio

2. Corrigendum On the class groups of pure function fields

Ichimura, Humio

Horie, Taro

Horie, Taro

5. A Thermodynamic formalism for one dimensional cellular automata

Namiki, Takao

6. A Thermodynamic formalism for one dimensional cellular automata

Namiki, Takao

7. The Bergman kernel on weakly pseudoconvex tube domains in $\mathbf {C}^2$

Kamimoto, Joe

8. The Bergman kernel on weakly pseudoconvex tube domains in $\mathbf {C}^2$

Kamimoto, Joe

9. Bernstein degree of singular unitary highest weight representations of the metaplectic group

Nishiyama, Kyo; Ochiai, Hiroyuki

10. Bernstein degree of singular unitary highest weight representations of the metaplectic group

Nishiyama, Kyo; Ochiai, Hiroyuki

11. On the homology of Torelli groups and Torelli spaces

Akita, Toshiyuki

12. On the homology of Torelli groups and Torelli spaces

Akita, Toshiyuki

13. On boundedness of a function on a Zalcman domain

Kobayashi, Yasuyuki
We consider boundedness of a function defined by an infinite product which is used to study a uniqueness theorem on a plane domain and the point separation problem of a two-sheeted covering Riemann surface. We show that there is such an infinite product that it converges but the function defined by it is not bounded on arbitrary Zalcman domain.

14. On boundedness of a function on a Zalcman domain

Kobayashi, Yasuyuki
We consider boundedness of a function defined by an infinite product which is used to study a uniqueness theorem on a plane domain and the point separation problem of a two-sheeted covering Riemann surface. We show that there is such an infinite product that it converges but the function defined by it is not bounded on arbitrary Zalcman domain.

15. On boundedness of a function on a Zalcman domain

Kobayashi, Yasuyuki
We consider boundedness of a function defined by an infinite product which is used to study a uniqueness theorem on a plane domain and the point separation problem of a two-sheeted covering Riemann surface. We show that there is such an infinite product that it converges but the function defined by it is not bounded on arbitrary Zalcman domain.

16. On an infinite convolution product of measures

Uchida, Motoo
We prove that infinite convolution products of complex probability measures with bounded total variation converge to a hyperfunction under a weak assumption on supports.

17. On an infinite convolution product of measures

Uchida, Motoo
We prove that infinite convolution products of complex probability measures with bounded total variation converge to a hyperfunction under a weak assumption on supports.

18. On an infinite convolution product of measures

Uchida, Motoo
We prove that infinite convolution products of complex probability measures with bounded total variation converge to a hyperfunction under a weak assumption on supports.

19. Homotopy groups of the homogeneous spaces $F_4/G_2$, $F_4/\mathrm {Spin}(9)$ and $E_6/F_4$

Hirato, Yoshihiro; Kachi, Hideyuki; Nimura, Mamoru
In this paper we calculate 2-primary components of homotopy groups of the homogeneous spaces $F_4/G_2$, $F_4/\mathrm{Spin}(9)$ and $E_6/F_4$.

20. Homotopy groups of the homogeneous spaces $F_4/G_2$, $F_4/\mathrm {Spin}(9)$ and $E_6/F_4$

Hirato, Yoshihiro; Kachi, Hideyuki; Nimura, Mamoru
In this paper we calculate 2-primary components of homotopy groups of the homogeneous spaces $F_4/G_2$, $F_4/\mathrm{Spin}(9)$ and $E_6/F_4$.

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location:  Publications → journals
Search results

 Restricted Radon Transforms and Projections of Planar Sets We establish a mixed norm estimate for the Radon transform in $\mathbb{R}^2$ when the set of directions has fractional dimension. This estimate is used to prove a result about an exceptional set of directions connected with projections of planar sets. That leads to a conjecture analogous to a well-known conjecture of Furstenberg. Categories:44A12, 28A78


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Vol. 4, No. 1, 2011

 Recent Issues
 The Journal About the Journal Editorial Board Subscriptions Editors’ Interests Scientific Advantages Submission Guidelines Submission Form Ethics Statement Editorial Login ISSN: 1944-4184 (e-only) ISSN: 1944-4176 (print) Author Index Coming Soon Other MSP Journals
On the maximum number of isosceles right triangles in a finite point set

Bernardo M. Ábrego, Silvia Fernández-Merchant and David B. Roberts

Vol. 4 (2011), No. 1, 27–42
Abstract

Let $Q$ be a finite set of points in the plane. For any set $P$ of points in the plane, ${S}_{Q}\left(P\right)$ denotes the number of similar copies of $Q$ contained in $P$. For a fixed $n$, Erdős and Purdy asked for the maximum possible value of ${S}_{Q}\left(P\right)$, denoted by ${S}_{Q}\left(n\right)$, over all sets $P$ of $n$ points in the plane. We consider this problem when $Q=△$ is the set of vertices of an isosceles right triangle. We give exact solutions when $n\le 9$, and provide new upper and lower bounds for ${S}_{△}\left(n\right)$.

Keywords
Erdős problems, similar triangles, isosceles right triangles
Primary: 52C10
Secondary: 05C35


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# Homework Help: Real analysis: Limit superior proof

1. Jan 16, 2010

### kingwinner

1. The problem statement, all variables and given/known data
Definition:
Let (an) be a sequence of real numbers. Then we define
lim [sup{an: n≥k}] = lim sup an
k->∞

(note: sup{an: n≥k} = sup{ak,ak+1,ak+2,...} = bk
(bk) is itself a sequence of real numbers, indexed by k)

Theorem:
Let a=lim sup an.
Then for all ε>0, there exists N such that if n≥N, then an<a+ε

2. Relevant equations
N/A

3. The attempt at a solution
I am trying to prove the theorem.
Proof:
Let bk=sup{an: n≥k}.
By the definition of "a" as a limit of supremums (bk->a), we have that
for all ε>0, there exists an integer N such that if k≥N, then
|sup{an: n≥k} - a| = |bk -a|< ε
=> sup{an: n≥k} < a + ε
By definition of an upper bound, sup{an: n≥k} ≥ an if n≥k.
So the above shows that if k≥N and n≥k, then an< a+ ε.

Now I am stuck...how should I continue? (I need to prove that: for all ε>0, there exists N such that if n≥N, then an<a+ε. But from my work so far, I'm really feeling hopeless)

There are so many different subscripts (e.g. n and k) to keep track of that I am really puzzled and frustrated now.


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## Making Unit Conversions in the U.S. System of Measurement

### Learning Outcomes

• Make conversions between U. S. units of length, volume, time, and weight
• Use mixed units of measurement in the U.S. system

There are two systems of measurement commonly used around the world. Most countries use the metric system. The United States uses a different system of measurement, usually called the U.S. system. We will look at the U.S. system first.

The U.S. system of measurement uses units of inch, foot, yard, and mile to measure length and pound and ton to measure weight. For capacity, the units used are cup, pint, quart and gallons. Both the U.S. system and the metric system measure time in seconds, minutes, or hours.

The equivalencies among the basic units of the U.S. system of measurement are listed in the table below. The table also shows, in parentheses, the common abbreviations for each measurement.

U.S. System Units
Length Volume
$1$ foot (ft) = $12$ inches (in)

$1$ yard (yd) = $3$ feet (ft)

$1$ mile (mi) = $5280$ feet (ft)

$3$ teaspoons (t) = $1$ tablespoon (T)

$16$ Tablespoons (T) = $1$ cup (C)

$1$ cup (C) = $8$ fluid ounces (fl oz)

$1$ pint (pt) = $2$ cups (C)

$1$ quart (qt) = $2$ pints (pt)

$1$ gallon (gal) = $4$ quarts (qt)

Weight Time
$1$ pound (lb) = $16$ ounces (oz)

$1$ ton = $2000$ pounds (lb)

$1$ minute (min) = $60$ seconds (s)

$1$ hour (h) = $60$ minutes (min)

$1$ day = $24$ hours (h)

$1$ week (wk) = $7$ days

$1$ year (yr) = $365$ days

In many real-life applications, we need to convert between units of measurement. We will use the identity property of multiplication to do these conversions. We’ll restate the Identity Property of Multiplication here for easy reference.

$\text{For any real number }a,a\cdot 1=a$    $1\cdot a=a$

To use the identity property of multiplication, we write $1$ in a form that will help us convert the units. For example, suppose we want to convert inches to feet. We know that $1$ foot is equal to $12$ inches, so we can write $1$ as the fraction $\Large\frac{\text{1 ft}}{\text{12 in}}$. When we multiply by this fraction, we do not change the value but just change the units.

But $\Large\frac{\text{12 in}}{\text{1 ft}}$ also equals $1$. How do we decide whether to multiply by $\Large\frac{\text{1 ft}}{\text{12 in}}$ or $\Large\frac{\text{12 in}}{\text{1 ft}}?$ We choose the fraction that will make the units we want to convert from divide out. For example, suppose we wanted to convert $60$ inches to feet. If we choose the fraction that has inches in the denominator, we can eliminate the inches.

$60\overline{)\text{in}}\cdot\Large\frac{\text{1 ft}}{12\overline{)\text{in}}}\normalsize=\text{5 ft}$

On the other hand, if we wanted to convert $5$ feet to inches, we would choose the fraction that has feet in the denominator.

$\text{5 ft}\cdot\Large\frac{\text{12 in}}{1\overline{)\text{ft}}}\normalsize=\text{60 in}$

We treat the unit words like factors and ‘divide out’ common units like we do common factors.

### Make unit conversions.

1. Multiply the measurement to be converted by $1$; write $1$ as a fraction relating the units given and the units needed.
2. Multiply.
3. Simplify the fraction, performing the indicated operations and removing the common units.

### example

Mary Anne is $66$ inches tall. What is her height in feet?

Solution

 Convert $66$ inches into feet. Multiply the measurement to be converted by $1$. $66$ inches $\cdot 1$ Write $1$ as a fraction relating the units given and the units needed. $\text{66 inches}\cdot \Large\frac{\text{1 foot}}{\text{12 inches}}$ Multiply. $\Large\frac{\text{66 inches}\cdot \text{1 foot}}{\text{12 inches}}$ Simplify the fraction. $\Large\frac{66\overline{)\text{inches}}\cdot \text{1 foot}}{12\overline{)\text{inches}}}$ $\Large\frac{\text{66 feet}}{12}$ $\text{5.5 feet}$

Notice that the when we simplified the fraction, we first divided out the inches.
Mary Anne is $5.5$ feet tall.

### try it

In the following video we show more examples of converting between units of length in the U.S. system of measurement.

When we use the Identity Property of Multiplication to convert units, we need to make sure the units we want to change from will divide out. Usually this means we want the conversion fraction to have those units in the denominator.

### example

Ndula, an elephant at the San Diego Safari Park, weighs almost $3.2$ tons. Convert her weight to pounds.

(credit: Guldo Da Rozze, Flickr)

### try it

How many teaspoons are in $1$ cup?

### Use Mixed Units of Measurement in the U.S. System

Performing arithmetic operations on measurements with mixed units of measures requires care. Be sure to add or subtract like units.

### example

Charlie bought three steaks for a barbecue. Their weights were $14$ ounces, $1$ pound $2$ ounces, and $1$ pound $6$ ounces. How many total pounds of steak did he buy?

(credit: Helen Penjam, Flickr)

### example

Anthony bought four planks of wood that were each $6$ feet $4$ inches long. If the four planks are placed end-to-end, what is the total length of the wood?


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# Gas station without pumps

## 2013 April 10

### Supplemental sheets, draft 3

This post updates and replaces the Supplemental sheets, draft 2. It reflects the redesign of the course based on running a prototype version of the course in as a group tutorial in Winter 2013.

### Lecture Course

Information to accompany Request for Course Approval
Course #:
101
Catalog Title: Applied Circuits for Bioengineers

1. Are you proposing a revision to an existing course? If so give the name, number, and GE designations (if applicable) currently held.

This is not a revision to any existing course.A prototype version of the course was run as BME 194 Group Tutorial in Winter 2013. Notes on the design and daily running of that prototype can be found at https://gasstationwithoutpumps.wordpress.com/circuits-course-table-of-contents

2. In concrete, substantive terms explain how the course will proceed. List the major topics to be covered, preferably by week.

The Applied Circuits course is centered around the labs in the accompanying lab course.  Concepts are taught as needed for the labs, with design and analysis exercises in the lecture course cementing the understanding. The recurring theme throughout the course is voltage dividers: for change of voltage, for current-to-voltage conversion, for high-pass and low-pass RC filters, in Wheatstone bridges, and as feedback circuits in op amp circuits.  The intent of this course is to provide substantial design experience for bioengineering students early in their studies, and to serve both as as bridge course to entice students into the bioelectronics concentration and as a terminal electronics course for those students focussing on other areas.

1. Basic DC circuit concept review: voltage current, resistance, Kirchhoff’s Laws, Ohm’s Law, voltage divider, notion of a transducer.
The first week should cover all the concepts needed to do the thermistor lab successfully.
2. Models of thermistor resistance as a function of temperature. Voltage and current sources, AC vs DC, DC blocking by capacitors, RC time constant, complex numbers, sine waves, RMS voltage, phasors. The second week should cover all the concepts needed to do the electret microphone lab successfully.
3. Low-pass and high-pass RC filters as voltage dividers, Bode plots. Concepts necessary for properly understanding digitized signals: quantized time, quantized voltage, sampling frequency, Nyquist frequency, aliasing.
4. Amplifier basics: op amps, AC coupling, gain computation, DC bias for single-power-supply offsets, bias source with unity-gain amplifier.  In the lab, students will design, build, and test a low-gain amplifier (around 5–10 V/V) for audio signals from an electret microphone. We’ll also include a simple current-amplifier model of a bipolar transistor, so that they can increase the current capability of their amplfier.
5. Op amps with feedback that has complex impedance (frequency-dependent feedback), RC time constants, parallel capacitors, hysteresis, square-wave oscillator using Schmitt triggers, capacitance-output sensors, capacitance-to-frequency conversion.   Topics are selected to support students designing a capacitive touch sensor in the accompanying lab.
6. Phototransistors and FETs for the tinkering lab and for the class-D amplifier lab. In preparation for the lab in which students model a pair of electrodes as R+(C||R), we will need a variety of both electronics and electrochemistry concepts: variation of parameters with frequency, impedance of capacitors, magnitude of impedance, series and parallel circuits, limitations of R+(C||R) model, and at least a vague understanding of half-cell potentials for the electrode reactions: Ag → Ag+ + e-, Ag+ + Cl- → AgCl, Fe + 2 Cl-→ FeCl2 + 2 e-.
7. Differential signals, twisted-pair wiring to reduce noise, strain gauge bridges, instrumentation amplifier, DC coupling, multi-stage amplifiers.
Topics are selected to support the design of a 2-stage amplifier for a piezoresistive pressure sensor in the lab.
8. System design, comparators, more on FETs. Students will design a class-D power amplifier to implement in the lab.
9. A little electrophysiology: action potentials, electromyograms, electrocardiograms. Topics are chosen so that students can design a simple 3-wire electrocardiogram (EKG) in the lab.There will also be a bit more development of simple (single-pole) filters.
10. The last week will be review and special topics requested by the students.

3. Systemwide Senate Regulation 760 specifies that 1 academic credit corresponds to 3 hours of work per week for the student in a 10-week quarter. Please briefly explain how the course will lead to sufficient work with reference to e.g., lectures, sections, amount of homework, field trips, etc. [Please note that if significant changes are proposed to the format of the course after its initial approval, you will need to submit new course approval paperwork to answer this question in light of the new course format.]

The combination of BME101 and BME101L is 7 units (21 hours per week).  The time will be spent approximately as follows:

• 3.5 hours lecture/discussion
• 3.5 hours reading background and circuits text
• 3 hours read lab handouts and doing pre-lab design activities
• 6 hours lab
• 5 hours writing design reports for lab

4. Include a complete reading list or its equivalent in other media.

No existing book covers all the material.  For the prototype run of the course, we relied heavily on Wikipedia articles, which turned out to be too dense for many of the students.  Other alternatives (such as Op amps for everyone by Ron Mancini http://www.e-booksdirectory.com/details.php?ebook=1469 Chapters 1–6 and Op Amp Applications Handbook by Analog Devices http://www.analog.com/library/analogDialogue/archives/39-05/op_amp_applications_handbook.html Sections 1-1 and 1-4) were also much too advanced.

In future we will most likely use the free on-line text All about Circuits as the primary text, with material not covered there (such as the various sensors) coming mainly from Wikipedia and the datasheets for the components.

5. State the basis on which evaluation of individual students’ achievements in this course will be made by the instructor (e.g., class participation, examinations, papers, projects).

Students will be evaluated primarily on design reports with some in-class or take-home quizzes to ensure that they do the needed reading on theoretical concepts.

6. List other UCSC courses covering similar material, if known.

EE 101 covers some of the same circuit material, but without the focus on sensors and without instrumentation amps.  It covers linear circuit theory in much more depth and focuses on mathematical analysis of complicated linear circuits, rather than on design with simple circuits.  The expectation for bioengineering students is that those in the bioelectronics track would take BME 101 before taking EE101, and that those in other tracks would take BME 101 as a terminal electronics course providing substantial engineering design.  The extra material in BME 101 would prepare the bioengineering students better for EE 101.

Physics 160 offers a similar level of practical electronics, but focuses on physics applications, rather than on bioengineering applications, and is only offered in alternate years.

7. List expected resource requirements including course support and specialized facilities or equipment for divisional review. (This information must also be reported to the scheduling office each quarter the course is offered.)

The lecture part of the course needs no special equipment—a standard media-equipped classroom with a whiteboard, screen, and data projector should suffice. Having a portable laptop-connected oscilloscope would make demos much easier to do, but is not essential.

The lecture course is not really separable from the associated lab course,whose equipment needs are described on the supplemental sheet for that course.

The course requires a faculty member (simultaneously teaching the co-requisite Applied Circuits lab course) and a teaching assistant or undergraduate group tutor for discussion sections and assistance in grading.  The same TA/group tutor should be used for both the lecture and the lab courses.

8. If applicable, justify any pre-requisites or enrollment restrictions proposed for this course. For pre-requisites sponsored by other departments/programs, please provide evidence of consultation.

Students will be required to have single-variable calculus and a physics electricity and magnetism course. Both are standard prerequisites for any circuits course. Although DC circuits can be analyzed without calculus, differentiation and integration are fundamental to AC analysis. Students should have already been introduced to the ideas of capacitors and inductors and to serial and parallel circuits.

The prerequisite courses are already required courses for biology majors and bioengineering majors, so no additional impact on the courses is expected.

9. Proposals for new or revised Disciplinary Communication courses will be considered within the context of the approved DC plan for the relevant major(s). If applicable, please complete and submit the new proposal form (http://reg.ucsc.edu/forms/DC_statement_form.doc or http://reg.ucsc.edu/forms/DC_statement_form.pdf) or the revisions to approved plans form (http://reg.ucsc.edu/forms/DC_approval_revision.doc or http://reg.ucsc.edu/forms/DC_approval_revision.pdf).

This course is not expected to contribute to any major’s disciplinary communication requirement, though students will get extensive writing practice in the design reports (writing between 50 and 100 pages during the quarter).

10. If you are requesting a GE designation for the proposed course, please justify your request making reference to the attached guidelines.

No General Education code is proposed for this course, as all relevant codes will have already been satisfied by the prerequisites.

11. If this is a new course and you requesting a new GE, do you think an old GE designation(s) is also appropriate? (CEP would like to maintain as many old GE offerings as is possible for the time being.)

No General Education code is proposed for this course, as all relevant codes (old or new) will have already been satisfied by the prerequisites.

### Lab course

Information to accompany Request for Course Approval
Course #
101L
Catalog Title
Applied Circuits Lab

1. Are you proposing a revision to an existing course? If so give the name, number, and GE designations (if applicable) currently held.

This is not a revision to any existing course. A prototype version of the course was run as BME 194F Group Tutorial in Winter 2013. Notes on the design and daily running of that prototype can be found at https://gasstationwithoutpumps.wordpress.com/circuits-course-table-of-contents

2. In concrete, substantive terms explain how the course will proceed. List the major topics to be covered, preferably by week.

The course is a lab course paired with BME 101, Applied Circuits for Bioengineers.  The labs have been designed to be relevant to bioengineers and to have as much design as is feasible in a first circuits course.  The labs are the core of the course, with lecture/discussion classes to support them. There will be six hours of lab a week, split into 2 3-hour sessions. Lab assignments will generally take two lab sessions, with data collection in the first lab session, and data analysis and design between lab sessions.   Some of the more straightforward labs will need only a single session.  Except for the first intro lab, these labs have been used in the prototype run of the class as 3-hour labs.  Most did not fit in one 3-hour lab session and would benefit from being split into two separate lab sessions with data analysis and design between the sessions.

1. Intro to parts, tools, and lab equipment (single session)
2. Thermistor
3. Microphone
4. Sampling and aliasing (single session)
5. Audio amp
6. Hysteresis oscillator and soldering lab
7. FET and phototransistor
8. Electrode modeling
9. Pressure sensor and instrumentation amp (soldered)
10. Class-D power amplifier
11. EKG (instrumentation amp with filters, soldered)
1. Intro to parts, tools, and lab equipment
Students will learn about the test equipment by having them use the multimeters to measure other multimeters. What is the resistance of a multimeter that is measuring voltage? of one that is measuring current? what current or voltage is used for the resistance measurement? Students will be  issued their parts and tool kits, learn to use the wire strippers and make twisted-wire cables for the power supplies to use all quarter.  They will learn to set the current limits on the power supplies and  measure voltages and currents for resistor loads around 500Ω.  This lab will not require a written lab report.
Lab skills developed: wire strippers, multimeter for measuring voltage and current, setting bench power supply
Equipment needed: multimeter, power supply
2. Thermistor lab
The thermistor lab will have two lab sessions involving the use of a Vishay BC Components NTCLE413E2103F520L thermistor or equivalent.
For the first lab session, the students will use a bench multimeter to measure the resistance of the thermistor, dunking it in various water baths (with thermometers in them to measure the temperature). They should fit a simple curve to this data based on standard thermistor models. A class period will be spent on learning both the model and how to do model fitting with gnuplot, and there will be a between-lab exercise where they derive the formula for maximizing | dV/dT | in a voltage divider that converts the resistance to a voltage.
For the scond lab session, they will add a series resistor to make a voltage divider. They have to choose a value to get as large and linear a voltage response as possible at some specified “most-interesting” temperature (perhaps body temperature, perhaps room temperature, perhaps DNA melting temperature).  They will then measure and plot the voltage output for another set of water baths. If they do it right, they should get a much more linear response than for their resistance measurements.
Finally, they will hook up the voltage divider to an Arduino analog input and record a time series of a water bath cooling off (perhaps adding an ice cube to warm water to get a fast temperature change), and plot temperature as a function of time.
Lab skills developed: use of multimeter for measuring resistance and voltage, use of Arduino with data-acquisition program to record a time series, fitting a model to data points, simple breadboarding.Equipment needed: multimeter, power supply, thermistor, selection of various resistors, breadboard, clip leads, thermoses for water baths, secondary containment tubs to avoid water spills in the electronics lab. Arduino boards will be part of the student-purchased lab kit. All uses of the Arduino board assume connection via USB cable to a desktop or laptop computer that has the data logger software that we will provide.
3. Electret microphone
First, we will have the students measure and plot the DC current vs. voltage for the microphone. The microphone is normally operated with a 3V drop across it, but can stand up to 10V, so they should be able to set the Agilent E3631A  bench power supply to various values from 0V to 10V and get the voltage and current readings directly from the bench supply, which has 4-place accuracy for both voltage and current. Ideally, they should see that the current is nearly constant as voltage is varied—nothing like a resistor.  They will follow up the hand measurements with automated measurements using the Arduino to measure the voltage across the mic and current through it for voltages up to about 4v.  The FET in the microphone shows a typical exponential I vs. V characteristic below threshold, and a gradually increasing current as voltage increases in the saturation region.  We’ll do plotting and model fitting in the data analysis class between the two labs.
Second, we will have them do current-to-voltage conversion with a 5v power supply and a resistor to get a 1.5v DC output from the microphone and hook up the output of the microphone to the input of the oscilloscope. Input can be whistling, talking, iPod earpiece, … . They should learn the difference between AC-coupled and DC-coupled inputs to the scope, and how to set the horizontal and vertical scales of the scope. They will also design and wire their own DC blocking RC filter (going down to about 1Hz), and confirm that it has a similar effect to the AC coupling on the scope. Fourth, they will play sine waves from the function generator through a loudspeaker next to the mic, observe the voltage output with the scope, and measure the AC voltage with a multimeter, perhaps plotting output voltage as a function of frequency. Note: the specs for the electret mic show a fairly flat response from 50Hz to 3kHz, so most of what the students will see here is the poor response of a cheap speaker at low frequencies.
EE concepts: current sources, AC vs DC, DC blocking by capacitors, RC time constant, sine waves, RMS voltage, properties varying with frequency.Lab skills: power supply, oscilloscope, function generator, RMS AC voltage measurement.Equipment needed: multimeter, oscilloscope, function generator, power supply, electret microphone, small loudspeaker, selection of various resistors, breadboard, clip leads.
4. Sampling and Aliasing
Students will use the data logger software on the Arduino to sample sine waves from a function generator at different sampling rates.  They will need to design a high-pass RC filter to shift the DC voltage from centered at 0 to centered at 2.5v in the middle of the Arduino A-to-D converter range.  They will also design a low-pass filter (with corner frequency below the Nyquist frequency) to see the effect of filtering on the aliasing.
EE concepts: quantized time, quantized voltage, sampling frequency, Nyquist frequency, aliasing, RC filters.
Equipment needed:  function generator, Arduino board, computer.
5. Audio amplifier
Students will use an op amp to build a simple non-inverting audio amplifier for an electret microphone, setting the gain to around 6 or 7. The amplifier will need a a high-pass filter to provide DC level shifting at the input to the amplifier. Note that we are using single-power-supply op amps, so they will have to design a bias voltage supply as well. The output of the amplifier will be recorded on the Arduino (providing another example of signal aliasing).
The second half of the lab will add a single bipolar transistor to increase the current and make a class A output stage for the amplifier, as the op amp does not provide enough current to drive the 8Ω loudspeaker loudly.
EE concepts: op amp, DC bias, bias source with unity-gain amplifier, AC coupling, gain computation.
Lab skills: complicated breadboarding (enough wires to have problems with messy wiring). If we add the Arduino recording, we could get into interesting problems with buffer overrun if their sampling rate is higher than the Arduino’s USB link can handle.
Equipment needed: breadboard, op amp chip, assorted resistors and capacitors, electret microphone, Arduino board, optional loudspeaker.
6. Hysteresis and capacitive touch sensor
For the first half of the lab, students will characterize a Schmitt trigger chip, determining VIL, VIH, VOL, and VOH. Using these properties, they will design an RC oscillator circuit with a specified period or pulse width (say 10μs), and measure the frequency and pulse width of the oscillator.
For the second half of the lab, the students will build a relaxation oscillator whose frequency is dependent on the parasitic capacitance of a touch plate, which the students can make from Al foil and plastic food wrap. In addition to breadboarding, students will wire this circuit by soldering wires and components on a PC board designed for the oscillator circuit. Students will have to measure the frequency of the oscillator with and without the plate being touched. We will provide a simple Arduino program that is sensitive to changes in the pulse width of the oscillator and that turns an LED on or off, to turn the frequency change into an on/off switch.  Students will treat the oscillator board as a 4-terminal component, and examine the effect of adding resistors or capacitors between different terminals.
EE concepts: frequency-dependent feedback, oscillator, RC time constants, parallel capacitors.
Lab skills: soldering, frequency measurement with digital scope.
Equipment needed: Power supply, multimeter, Arduino, clip leads, amplifier prototyping board, oscilloscope.
7. Phototransistor and FET
First half: characterize phototransistor in ambient light and shaded.  Characterize nFET and pFET.
Second half: students will “tinker” with the components they have to produce a light-sensitive, noise-making toy.
EE concepts: phototransistors, FETs.
Equipment needed: breadboard, phototransistor, power FETs, loudspeaker, hysteresis oscillator from previous lab, oscilloscope.
8. Electrode measurements
First, we will have the students attempt to measure the resistance of a saline solution using a pair of stainless steel electrodes and a multimeter. This should fail, as the multimeter gradually charges the capacitance of the electrode/electrolyte interface.Second, the students will use a function generator driving a voltage divider with a load resistor in the range 10–100Ω. The students will measure the RMS voltage across the resistor and across the electrodes for different frequencies from 3Hz to 300kHz (the range of the AC measurements for the Agilent 34401A Multimeter). They will plot the magnitude of the impedance of the electrodes as a function of frequency and fit an R2+(R1||C1) model to the data, most likely using gnuplot. There will be a prelab exercise to set up plotting of the model and do a little hand tweaking of parameters to help them understand what each parameter changes about the curve.Third, the students will repeat the measurements and fits for different concentrations of NaCl, from 0.01M to 1M. Seeing what parameters change a lot and what parameters change only slightly should help them understand the physical basis for the electrical model.Fourth, students will make Ag/AgCl electrodes from fine silver wire. The two standard methods for this involve either soaking in chlorine bleach or electroplating. To reduce chemical hazards, we will use the electroplating method. As a prelab exercise, students will calculate the area of their electrodes and the recommended electroplating current.  In the lab, they will adjust the voltage on the bench supplies until they get the desired plating current.Fifth, the students will measure and plot the resistance of a pair of Ag/AgCl electrodes as a function of frequency (as with the stainless steel electrodes).Sixth, if there is time, students will measure the potential between a stainless steel electrode and an Ag/AgCl electrode.EE concepts: magnitude of impedance, series and parallel circuits, variation of parameters with frequency, limitations of R+(C||R) model.Electrochemistry concepts: At least a vague understanding of half-cell potentials, current density, Ag → Ag+ + e-, Ag+ + Cl- → AgCl, Fe + 2 Cl-→ FeCl2 + 2 e-.Lab skills: bench power supply, function generator, multimeter, fitting functions of complex numbers, handling liquids in proximity of electronic equipment.Equipment needed: multimeter, function generator, power supply, stainless steel electrode pairs, silver wires, frame for mounting silver wire, resistors, breadboard, clip leads, NaCl solutions in different concentrations, beakers for salt water, secondary containment tubs to avoid salt water spills in the electronics lab.
9. Pressure sensor and instrumentation amplifier
Students will design an instrumentation amplifier with a gain of 300 or 500 to amplify the differential strain-gauge signal from a medical-grade pressure sensor (the Freescale MPX2300DT1), to make a signal large enough to be read with the Arduino A/D converter. The circuit will be soldered on the instrumentation amp/op amp protoboard. The sensor calibration will be checked with water depth in a small reservoir. Note: the pressure sensor comes in a package that exposes the wire bonds and is too delicate for student assembly by novice solderers. We will make a sensor module that protects the sensor and mounts the sensor side to a 3/4″ PVC male-threaded plug, so that it can be easily incorporated into a reservoir, and mounts the electronic side on a PC board with screw terminals for connecting to student circuits.  This sensor is currently being prototyped, and if it turns out to be too fragile, we will use a Freescale MPX2050GP, which has a sturdier package, but is slightly less sensitive and more expensive. (It also isn’t made of medical-grade plastics, but that is not important for this lab.) Note that we are deliberately notusing pressure sensors with integrated amplifiers, as the pedagogical point of this lab is to learn about instrumentation amplifiers.EE concepts: differential signals, twisted-pair wiring, strain gauge bridges, instrumentation amplifier, DC coupling, gain.Equipment needed: Power supply, amplifier prototyping board, oscilloscope, pressure sensor mounted in PVC plug with breakout board for easy connection, water reservoir made of PVC pipe, secondary containment tub to avoid water spills in electronics lab.
10. Class-D power amplifier
11. Electrocardiogram (EKG)
Students will design and solder an instrumentation amplifier with a gain of 2000 and bandpass of about 0.1Hz to 100Hz. The amplifier will be used with 3 disposable EKG electrodes to display EKG signals on the oscilloscope and record them on the Arduino.Equipment needed: Instrumentation amplifier protoboard, EKG electrodes, alligator clips, Arduino, oscilloscope.

3. Systemwide Senate Regulation 760 specifies that 1 academic credit corresponds to 3 hours of work per week for the student in a 10-week quarter. Please briefly explain how the course will lead to sufficient work with reference to e.g., lectures, sections, amount of homework, field trips, etc. [Please note that if significant changes are proposed to the format of the course after its initial approval, you will need to submit new course approval paperwork to answer this question in light of the new course format.]

The combination of BME101 and BME101L is 7 units (21 hours per week).  The time will be spent approximately as follows:

• 3.5 hours lecture/discussion
• 3.5 hours reading background and circuits text
• 3 hours read lab handouts and doing pre-lab design activities
• 6 hours lab
• 5 hours writing design reports for lab

4. Include a complete reading list or its equivalent in other media.

Lab handouts: there is a 5- to 10-page handout for each week’s labs, giving background material and design goals for the lab, usually with a pre-lab design exercise.  The handouts from the prototype run of the course can be found at http://users.soe.ucsc.edu/~karplus/bme194/w13/#labs
Data sheets: Students will be required to find and read data sheets for each of the components that they use in the lab.  All components are current commodity components, and so have data sheets easily found on the web.  Other readings are associated with the lecture course.

5. State the basis on which evaluation of individual students’ achievements in this course will be made by the instructor (e.g., class participation, examinations, papers, projects).

Students will be evaluated on in-lab demonstrations of skills (including functional designs) and on the weekly lab write-ups.

6. List other UCSC courses covering similar material, if known.

CMPE 167/L (sensors and sensing technologies) covers some of the same sensors and design methods, but at a more advanced level.  BME 101L would be excellent preparation for the CMPE 167/L course.

Physics 160 offers a similar level of practical electronics, but focuses on physics applications, rather than on bioengineering applications, and is only offered in alternate years.

7. List expected resource requirements including course support and specialized facilities or equipment for divisional review. (This information must also be reported to the scheduling office each quarter the course is offered.)

The course will need the equipment of a standard analog electronics teaching lab: power supply, multimeter, function generator,  oscilloscope,  computer, and soldering irons. The equipment in Baskin Engineering 150 (commonly used for EE 101L) is ideally suited for this lab. There are 12 stations in the lab, providing a capacity of 24 students since they work in pairs rather than as individuals.  The only things missing from the lab stations are soldering irons and circuit board holders (such as the Panavise Jr.), a cost of about $45 per station. Given that a cohort of bioengineering students is currently about 35–40 students, two lab sections would have to be offered each year. In addition, a few special-purpose setups will be needed for some of the labs, but all this equipment has already been constructed for the prototype run of the course. There are a number of consumable parts used for the labs (integrated circuits, resistors, capacitors, PC boards, wire, and so forth), but these are easily covered by standard School of Engineering lab fees. The currently approved lab fee is about$131, but may need some adjustment to change exactly what tools and parts are included, particularly if the students are required to buy their own soldering irons (a \$20 increase).

The course requires a faculty member (simultaneously teaching the co-requisite Applied Circuits course) and a teaching assistant (for providing help in the labs and for evaluating student lab demonstrations). Because the lab is such a core part of the combined course, it requires faculty presence in the lab, not just coverage by TAs or group tutors.

8. If applicable, justify any pre-requisites or enrollment restrictions proposed for this course. For pre-requisites sponsored by other departments/programs, please provide evidence of consultation.

Students will be required to have single-variable calculus and a physics electricity and magnetism course. Both are standard prerequisites for any circuits course. Most of the labs can be done without calculus, but it is essential for the accompanying lecture course.

9. Proposals for new or revised Disciplinary Communication courses will be considered within the context of the approved DC plan for the relevant major(s). If applicable, please complete and submit the new proposal form (http://reg.ucsc.edu/forms/DC_statement_form.doc or http://reg.ucsc.edu/forms/DC_statement_form.pdf) or the revisions to approved plans form (http://reg.ucsc.edu/forms/DC_approval_revision.doc or http://reg.ucsc.edu/forms/DC_approval_revision.pdf).

This course is not expected to contribute to any major’s disciplinary communication requirement, though students will get extensive writing practice in the design reports (writing between 50 and 100 pages during the quarter).

10. If you are requesting a GE designation for the proposed course, please justify your request making reference to the attached guidelines.

No General Education code is proposed for this course, as all relevant codes will have already been satisfied by the prerequisites.

11. If this is a new course and you requesting a new GE, do you think an old GE designation(s) is also appropriate? (CEP would like to maintain as many old GE offerings as is possible for the time being.)

No General Education code is proposed for this course, as all relevant codes (old or new) will have already been satisfied by the prerequisites.

## 2013 March 16

### Twenty-eighth day of circuits class

Filed under: Circuits course — gasstationwithoutpumps @ 12:29
Tags: , , ,

Yesterday’s lecture was a mish-mash of odds and ends that we hadn’t covered well previously, and questions that had come up.

I started with talking about where the EKG signal comes from.  The guest lecturer on Wednesday had done a good job of covering action potentials, but I pointed out that we were not sticking electrodes into their heart muscle cells: we had access to only the outside of the cells.  So where was the differential signal we were measuring coming from?  This had been one of my first puzzles in trying to understand how an EKG works, and they were mostly just as clueless about it as I had been.  The explanation that I settled on was looking at each of the cells as a little capacitor with a battery that charged it and a switch that discharged it, with one side accessible to us.  There is a resistance from each cell to each of the differential electrodes, and from the differential electrodes to the body reference electrode, so that the measurement electrodes act like they are in a voltage divider between the cell and the reference electrode.  The voltage difference between the differential electrodes depends on the difference in resistance from the cell to the electrodes, and the signal we see depends on the change in position of the discharge wave.  If everything depolarized at the same time, we’d see almost no difference voltage, but as the wave sweeps from left-to-right (or right-to left) we see difference voltages.    It’s not a perfect explanation of where the EKG signal comes from, but it is better than leaving them thinking that they are seeing the action potential directly.

After that a question came up about the 60Hz noise in the EKG signal, and where it came from.  I talked about the loop formed by the LA and RA wires and the body between them as an electromagnetic pickup, and how we could reduce the electromagnetic pickup by twisting the wires together more to reduce the area of the loop.  I also discussed capacitive coupling of 60Hz into the wires, reminding them of the capacitive touch sensor they had made earlier in the quarter.  We talked a bit about shielding cables and Faraday cages.  While on the subject of noise, I also mentioned the problem of microphonics in the nanopore equipment.  We have not discussed thermal noise or other problems of designing for very small signals.

Students asked where the 60Hz hum in their class-D power amplifiers came from, and I talked about ground loops and noise pickup in their power lines.  The op amps they were using had excellent power-supply noise rejection, but the voltage reference they were using (a pair of resistors as a voltage divider and a unity-gain buffer) provides an excellent path for noise in the power supply to be coupled into the amplifier.  I talked about two ways to reduce the hum: using twisted cables for the DC power, to reduce the electromagnetic pickup of 60Hz noise, and using a Zener diode reference instead of a simple voltage divider for the Vref signal.  I’m wondering whether I should add Zener diodes to the parts kit next year, or even whether I should get an adjustable voltage reference like the TL431ILP.  Either one is about 20¢ each in the small quantities that we would need.  The Zener diode is easier to explain, but the adjustable voltage reference is more versatile (the voltage is set by 2 external resistors as a voltage divider with the output of the voltage divider held at 2.5V) and has less variation in voltage with current (output impedance of 0.2Ω instead of 5–30Ω).  One minor problem with the TL431LP is that the lowest reference voltage it provides is 2.5V (using a wire from the “cathode” to the reference feedback input).  Since we are doing everything with power supplies of 5V or more, this shouldn’t be a problem for us.

After talking about noise, a question came up about the fat wires used for loudspeakers in stereo systems and whether they were shielded.  I managed to get the class to come up with the correct explanation: that the wires are fat to reduce resistance and avoid I2R power losses.  Currents to loudspeakers tend to be pretty big, since the resistance of the speaker itself is typically only 8Ω.  We talked about microphone cables being shielded (nowadays, I think that they are mostly twisted pairs inside a foil or metalized plastic shield, rather than coaxial cable) but that the tiny voltages and currents that speaker wires would pick up not mattering, since the signals were not amplified.  I also mentioned that solar panels were generally wired with fat wires also, to reduce the I2R power losses, since the voltages of the solar panels were fairly low (12V or 24V).

The students did not come up with any questions, so I pulled out one that had been asked weeks ago in lab: how sine-wave oscillators work.  The students had build square-wave oscillators with Schmitt triggers, and had used function generators, but had not seen any sine-wave oscillators.  I decided to do a classic oscillator: the Wien-bridge oscillator, since it uses the building blocks and concepts they are familiar with: a differential amplifier and two voltage dividers as a bridge circuit.  I started out with a generic bridge (just an impedance on each arm) and we got 3 formulas relating the nodes of the amplifier: $V_{out} = A(V_p - V_m)$, $V_m= V_{out} Z_1/(Z_1+Z_2)$, and $V_p = V_{out} Z_3/(Z_3+Z_4)$, from which we derived the stability condition $Z_1 Z_4 = Z_2 Z_3$.  This was all review for them, as they had had bridge nulling on a quiz.

The Wien bridge oscillator circuit. I initially gave it with just a resistor, not a light bulb, for R1, since the analysis is easier that way. The neat thing about the light bulb is that it provides an automatic gain control to set its resistance to  R2/2.

I then gave them the circuits for each arm of the bridge (just resistors on the negative feedback divider, and a series RC and a parallel RC for the arms of the positive feedback divider).  Rather than do complex impedance calculations, we just did Bode plots of the impedance of each of the RC arms, from which we could see that the voltage divider had zero output at DC and ∞ frequency, with a maximum at $1/(2\pi RC)$.  We were running out of time, so I did not derive with them that the gain of the positive voltage divider was 1/2 at that frequency, but jumped immediately to describing the use of an incandescent bulb in the negative feedback circuit to provide automatic gain adjustment (though I just waved my hands at it, not really showing how the thermal feedback mechanism worked).  I also managed to mention the historical importance of this oscillator design as the first product of Hewlett-Packard, and the start of “Silicon Valley”.

The range over which the automatic gain control with the light bulb works is determined by the range of resistance for the bulb filament. When the bulb is cold, its resistance must be less than R2/2. When the output is a sine wave with amplitude equal to the power supply, the resistance of the bulb filament must be larger than R2/2.  When the circuit is stable, the RMS voltage on the  bulb will be 1/3 the RMS voltage of the output, and the bulb filament resistance will be R2/2.  Nowadays other non-linear components are used rather than bulbs for the gain control, since bulbs suffer from microphonics and (for low frequencies) insufficient low-pass filtering (they are relying on the thermal mass of the filament to provide the low-pass filter of the automatic gain control).

On Monday, I plan to answer other questions students have, if they can come up with anything that confused them over the quarter.  If they can’t come up with any questions for me and send them to me this weekend, then maybe I’ll have to come up with some questions for them as an impromptu quiz.

## 2013 March 15

### Action potential lecture and EKG lab

Filed under: Circuits course — gasstationwithoutpumps @ 00:43
Tags: , , ,

I did not lecture on Wednesday, but had a guest lecturer from the biology department, who gave a lecture on action potentials, based on a similar lecture she gives in a neuropsychology course.  The lecture went a bit slow for the bioengineers, I think (with everything repeated 3 times), but there was some good information about the use of the Nernst equation to get resting and action potentials, the sodium and potassium channels, and the use of a voltage clamp to measure permeability of a squid axon to ions at different potentials.  If I were to give the lecture, I would probably pick up the pace a bit, but use a longer wait time when asking the class a question—the biology professor tended to answer her own questions as soon as she got any sound from the class.

The EKG lab this afternoon had mixed results—everyone finished with a working EKG board, but the last group to leave took 7 hours, so I was in the lab from 2 p.m. to 9 p.m.  I started the lab by demoing the board that I had build Tuesday morning, so that they could see that the project was possible.  It was a good thing that I did so, since several of the EKG boards the students designed and built worked fine with the electrodes I was wearing, but not with their electrodes on their bodies.  I’ve not figured out why this happened.  Had their electrodes dried out?  Was their skin prep or electrode placement poorer? Is my pulse larger than theirs, or my skin more conductive?  Some of the groups did manage to get their boards working with their own electrodes, and everyone’s worked with some set of electrodes.

One of the slowest debugging problems was a component value error: assembling the board with a 4.7µF capacitor, rather than the 4.7nF capacitor they had designed in their schematic, resulting in a low-pass corner frequency of 0.05Hz instead of 50Hz, eliminating their signal.  Another component value error by a different group was using an 8Ω gain resistor (giving a gain of 10,005) when a gain of 8 was desired—this resulted in saturating the amplifier.  There were other component errors that were less catastrophic (a 47nF capacitor where a 4.7nF capacitor was intended, eliminating the 60Hz ripple, but also eliminating a big chunk of the signal), but all were eventually found and fixed.

Almost everyone had a lot of 60Hz ripple in the output (as did I, though they generally had more with their electrodes).  I was confused on Tuesday about what I saw as a 40Hz ripple, but of course that was just aliasing of the 60Hz ripple with a 100Hz sampling frequency (with a Nyquist frequency of 50Hz, a component at 60Hz and a component at 40Hz are indistinguishable).  I think that most of the 60Hz ripple is coming from electromagnetic pickup in the loop from where the wires stop being twisted together and spread out to the three electrodes, but some may be capacitive also.  I may play around with better wiring to see if I can reduce the ripple.  I could also try sampling at 60Hz, so that the ripple is aliased to DC.  The only risk there is that it may not be exactly 60Hz, and aliasing to near DC could interfere with the meaningful part of the signal.  I believe that professional EKGs sample at a higher rate, then use a digital notch filter to remove the 60Hz ripple.

## 2013 March 12

### Tried EKG design on protoboard

Filed under: Circuits course — gasstationwithoutpumps @ 15:35
Tags: , ,

I built and tested an EKG circuit today using the protoboard that the students will use on Thursday, to make sure that there are no probems.

I decided to try out a circuit that uses active feedback for the common-mode signal.  It turned out to be a bust, having higher noise than just connecting Vref to the body electrode (I provided both options for wiring up the electrodes).  I’ve not yet figured out whether the problem is with the details of the design I used, or whether using active feedback to cancel the common-mode signal is a poor idea, despite its appearing in almost all the circuits I’ve found on-line. The instrumentation amp chip has a common-mode rejection ratio of 94dB (1/50,000), so the common-mode noise would have to be huge to be make any difference to the output.  As long as the two electrode signals stay well within the power rails of the instrumentation amp, there doesn’t seem to be much point to using feedback to cancel the common mode signal.

I’m also wondering now about some of the other circuit choices that I saw in almost all on-line circuits for EKGs, like putting the high-pass filters to eliminate the DC bias after the instrumentation amp.  Maybe after the quarter is over  I’ll try another EKG circuit with the high-pass filters before the instrumentation amp, to see if that causes any problems.

I’m glad that I did not recommend active feedback to cancel the common-mode signal to the students, so that they’ll be implementing simpler designs that are likely better.

I still have several things to do today:

• grading redone lab reports—I’d like to get half the stack done.
• trying to catch up in physics with my son.
• designing the T-shirt for the class.

I also have to check with tomorrow’s guest lecturer, to see if she plans to fill the full 70-minute period—if not, I should fill in with a demo of the EKG board I wired up today.

## 2013 March 11

### Twenty-sixth day of circuits class

Filed under: Circuits course — gasstationwithoutpumps @ 20:53
Tags: , , ,

I started today with feedback on the writing.  The students have been getting much better about the content and organization of their reports, and the writing is pretty good from at least half the class, but everyone is having trouble with not checking the details, particularly in the schematics.  I’d really like to give some A’s this quarter, but I can’t give an A to a lab report that has a power-ground short in a schematic or a missing connection.

After the writing feedback, I talked a bit about safety in biomedical equipment (battery operation, opto-isolators, isolation transformers, wireless, …).  I also talked about how skin was an excellent insulator at low frequencies and low voltages, but how at high frequencies the skin capacitance is no barrier, and that at high voltages, like with Automatic Electric Defibrillators (AEDs) the skin dielectric is broken down.  Even with EKGs, running at low voltages, they need to add series current-limiting resistors to all their electrode leads, to ensure that currents remain below 50µA, even if the leads are accidentally shorted to the highest voltage in the system.

After the safety discussion, I gave them some information about the AC signal they were trying to amplify (±0.5–1mV, with a DC offset of ±300mV, and a frequency range of 0.1Hz to 50Hz). Rather than covering the block diagram as a whole class, I had them split into 3 groups of 4 and try to design the block diagram for the EKG.  I circulated around the room and answered questions. I did tell the class that every design I’ve seen for an EKG puts the high-pass filter after the first-stage instrumentation amp.  I’m not sure why that is standard, but it certainly seems to be.

The main point (which some groups came to quickly and others slowly), is that the ±300mV offset constrains how much gain you can ask the first stage for, so that a second stage is essential.  One group asked if they could do a particular gain in one op amp, so I got a chance to remind them of gain-bandwidth product (the frequencies here are so low that the gain was easily feasible).

Over the weekend the whole class had gathered to work together (mainly on rewriting lab reports—I offered the class in the syllabus that they could rewrite any lab report whose grade they were not happy with).  They sent me a photo of the class working together—I think this is the first time I’ve seen a spontaneously formed study group consisting of an entire class.  Today I got 15 redone lab reports (about 2 weeks worth of grading, with more expected on Wednesday, not to mention the class-D amplifier reports that are due on Wednesday.

Since we are not having a final exam for the course (the quizzes and the 50 pages of design reports from the students is enough to evaluate them on), the students asked if we could meet during the exam period for beer (with the constraint that it must be a place that serves non-alcoholic beverages to those under 21, since not all the students are drinking age).  I agreed that we could, but I’ve not thought of an ideal location.  Perhaps Cafe Pergolesi would do—they serve beer and wine, but are primarily a café serving coffee, tea, and hot chocolate.  I don’t know how much of a hipster hangout it is on Tuesday afternoons, but I suspect that a dozen of us could occupy one of the “geek” rooms.  I had planned to make a detailed survey for the students to fill out about things that were good and bad about the course—they’ve been pretty good about giving me feedback as we go along, but I’m planning on redesigning the course somewhat and revising the course approval forms, so I’d like to know which aspects of the course worked best (and worst) from their perspective at the end of the course.  I’ll also be asking them to send me PDFs of all their lab reports, so that I can show them to the EE faculty to try to convince the faculty that this applied circuits course is acceptable preparation for the signals and systems course and the bioelectronics course.

I think I’ll be spending tomorrow on 3 things:

• trying out a different EKG circuit that uses active feedback of the common-mode signal.
• grading redone lab reports—if I can get half the stack done tomorrow I’ll probably be able to handle the load for the rest of the week.
• trying to catch up in physics with my son—it kind of slid for the past 2 weeks as both he and I were crazy-busy.

Wednesday I have a guest lecturer coming in to talk about action potentials and excitable cells, which should be good preparation for understanding the EKGs they will be making on Thursday—I’ve not really talked about where the voltages they’ll be measuring come from.

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(a)    If a Linear Programming problem is maximizing type, then its dual is minimizing type
(b)    Both primal and dual have same optimum value
(c)    Dual of dual of a linear programming problem is primal problem
(d)    If maximizing linear programming problem is with “less than” type constraints, the dual of this problem will have “more than” type constraints
Choose from the following options :

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Using statistical methods, the designs of multifraction experiments which are likely to give the most precise estimate of the α-β ratio in the linear-quadratic model are investigated. The aim of the investigation is to try to understand what features of an experimental design make it efficient for estimating α/β rather than to recommend a specific design. A plot of the design on an <tex-math>$nd^{2}$</tex-math> versus nd graph is suggested, and this graph is called the design plot. The best designs are those which have a large spread in the isoeffect direction in the design plot, which means that a wide range of doses per fraction should be used. For binary response assays, designs with expected response probabilities near to 0.5 are most efficient. Furthermore, dose points with expected response probabilities outside the range 0.1 to 0.9 contribute negligibly to the efficiency with which α/β can be estimated. For "top-up" experiments, the best designs are those which replace as small a portion as possible of the full experiment with the top-up scheme. In addition, from a statistical viewpoint, it makes no difference whether a single large top-up dose or several smaller top-up doses are used; however, other considerations suggest that two or more top-up doses may be preferable. The practical realities of designing experiments as well as the somewhat idealized statistical considerations are discussed.

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text:
# Tag Info

10

GPG's (or OpenPGP's) public-key file encryption uses multiple steps: Generate a random session key encrypt the file using this random session key encrypt the random session key using the public key of the receiver (or using multiple keys in parallel, if the file is meant to be decrypted by multiple receivers). store the encrypted file together with the ...

9

If there is a vulnerability in encrypting a RSA private key with the corresponding public key, when the private key is password-protected, then it mechanically implies a vulnerability in the password-based protection scheme: if an attacker gets a copy of the password-encrypted key (without the password), he can encrypt it with the public key himself; so an ...

9

There is at least one way in which compression can weaken security; it has to do with the fact that essentially all methods of encrypting arbitrarily long message will inevitably leak information about the length of the input. The only way to avoid this leak is to pad all messages to a constant length before encrypting them — but if the messages are ...

9

A PGP encrypted message can be hundreds or even thousands of bytes. Encrypting and decrypting large amounts of data using asymmetric algorithms is extremely slow. Encrypting only 32 to 16 bytes (the symmetric key) is much faster. Additionally, if you encrypt the same message twice with an asymmetric algorithm, you will get the exact same ciphertext. Using ...

9

I think you misunderstood a detail of PGP encryption. Only the random symmetric key is encrypted under the recipient's (asymmetric) public key. This way to encrypt stuff is quite common and is called KEM/DEM paradigm: Key Encapsulation Method/Data Encapsulation Method oy Hybrid Encryption. Some refs: en.wikipedia.org/wiki/Hybrid_cryptosystem and ...

8

OpenPGP's "Iterated and Salted S2K" is just a single hash instance over a very long input, which consists in the repeated concatenation of the salt and the password. This is extremely GPU-friendly, especially when using a hash function which is built over 32-bit elementary operations (this category includes MD5, SHA-1, SHA-256 and RIPEMD-160; GPU are not as ...

8

There are several kinds of asymmetric cryptographic algorithms. All use some sort of mathematical structure, but not the same, and not all involve prime integers. RSA is the most well-known asymmetric algorithm, which includes several variants (e.g. for asymmetric encryption or for digital signature). In a RSA public key, there is a big integer called the ...

8

Technically, if you use a cryptographically secure encryption algorithm with a fresh random key in a confidentiality mode such as (full block) CFB, you don't have to worry about the redundancy of the plain text, since the cipher + mode combination is supposed to be secure even if significant parts of the plain text are known to the adversary. If the cipher ...

8

This is hidden well in RFC 4880, the OpenPGP message format specification. Section 5.7 explains how message data is encrypted. (I'm using the values for a 16-byte block cipher like AES.) A random block of data is created: $p_{1} \dots p_{16}$ The last two bytes of this block are repeated: $(p_{17}, p_{18}) := (p_{15}, p_{16})$. These 18 bytes (in case ...

6

GnuPG follows the OpenPGP format, which is a protocol in its own right -- it uses AES (among other algorithms) but is more complex than "just AES with the right parameters". There is at least one OpenPGP implementation in Javascript (I have not tried it, though).

5

According to How PGP Works it uses a hybrid approach that generates a secret key for symmetric encryption. The wikipedia page for GPG then indicates that CAST5, Camellia, Triple DES, AES, Blowfish, and Twofish are the supported ciphers.

5

The "signed on date" field of any signature message format is only trustworthy if you trust the signer to not modify the software to include an arbitrary date (or use a software which allows setting the date) or change his computer's system date. So, if the signer wants to use this field to prove that this was signed at some time (specially, before some ...

5

This sounds like a fair exchange protocol where what is exchanged is a digital signature. Per this paper, these are impossible without trusted third parties. With a trusted third party, they are possible. Indeed people have proposed schemes that do what you describe again relying on a third party in the case of failure.

5

The basic explanation is that you need both keys to make a complete encryption/decryption cycle. Basically the encryption works with modulo arithmetic so that $$c=m^a \mod n$$ and $$m=c^b \mod n$$ where $a$ and $b$ are the public and private key of the algorithm. $m$ is the plain text message and $c$ s the ciphertext. The most important thing about the ...

5

"Secure" is not a binary, black-and-white thing. Instead, it's about risk management. Instead of asking whether something is secure, it's better to ask whether it is "secure enough for such-and-such purpose". On the one hand, 1024-bit keys are uncomfortably close to what can be cracked, given lots of computational resources. On the other hand, for casual ...

4

No. The passphrase you use creates a symmetric key that is used to encrypt the private key. You're not uploading the private key to the server, at least let's hope you aren't. But even if you are doing that, the password is salted and iterated in hashing, and that means that the visible encrypted private key is radically different even if the password is ...

4

Magic! Have a look at the wikipedia image from the PGP article. The magic behind how the whole thing works is using through the RSA algorithm. Let's say Alice wants to send an encrypted message to Bob. Bob generates a public and private key pair. How the key generation process works is through a whole bunch of mathematics. Essentially, this is how RSA ...

4

Use gpg --s2k-mode 3 --s2k-count N, where N is the number of iterations you want to use. The manual page says the default is 65536, and you can use any number between 1024 and 65011712. If you like to tweak the defaults, I suggest making this number as large as you can bear it, without introducing noticeable slowdown (e.g., ideal would be to make the ...

4

KEM/DEM hybrid encryption has another advantage. It enables a very efficient multi-recipient encryption. The payload is encrypted and transmitted only one time. Haven't you wondered yet why you are able to decrypt and read your own message although it was encrypted with the recipient's public key? Normally PGP encrypts the message key for symmetric ...

3

Let Alice have a key pair (PubKeyA, PrivKeyA), where the first is public, the second private, and similarly for Bob (PubKeyB, PrivKeyB). Alice and Bob know each other's public keys in a reliable way (from a key server, or because they received them in person etc.) If we use RSA keys, e.g., then they could use just one pair, so I'll assume this first. When ...

3

OpenPGP is a protocol that uses various encryption algorithms in it. For public keys, they're either RSA, DSA, or Elgamal. Note that DSA is signing-only and Elgamal is encryption-only. DSA and Elgamal are variants of Diffie-Hellman and thus their relationship to prime numbers is slightly tangential. RSA keys are made of (typically) two prime numbers ...

3

From my understanding no. If you look at the OpenPGP spec section 3.7 it covers the String-to-Key (S2K) Specifiers which convers a passphrase to a key. Assuming the Salted S2K or Iterated and Salted S2K method is used (which is recommended) then reusing your passphrase shouldn't be an issue. The larger key has a larger length, which means the passphrase ...

3

Short answer: “No”. The latest research shows that compression actually harms security. "Reducing redundancy" is an outdated concept from the late 20th century. The intuition was that if our ciphers turned out to be weak, we might avoid a practical loss of confidentiality by giving attackers less information to work with. For example, in the following ...

3

Compressing the data increases the security a number of ways. It reduces an attacker's ability to affect the decrypted output by flipping ciphertext bits. It removes regular patterns in plaintext (it might create other regular patterns, but they aren't directly the plaintext). There are a number of attacks on OpenPGP that are thwarted by compression. Most ...

3

Yes, your public key includes your UIDs. It may be possible to delete all before exporting though - for sure you could copy the key, add an "anonymous" UID and delete all others. As long as you're not signing the message, nobody will know who sent the message (but have a look at the mail or other headers!).

3

You cannot remove all UIDs, but you can create one which does not link to your identity and remove all others. Backup your .gnupg folder (for unix systems, for Windows wherever your key is stored)! Start editing your key: \$ gpg --edit-key 47AB515A Create an anonymous UID: gpg> adduid Real name: Anonymous Email address: Comment: You selected this ...

3

Since your problem seems to be with the principle of public key crypto rather than with the math itself, here is an analogy with a physical object that may help. Take a key lock padlock as below: To close the padlock, you don't need the key, just the padlock itself. To open you use the key. Now, if Bob has a copy of Alice's padlock, he can send her a ...

2

No, the user of the key does. A revocation issued by the key itself, or by a designated revoker, which is some different key. If I am going to encrypt to you, I look at the key before I do, and I look to see if your key is revoked. Similarly, if I am verifying a signature your key made, I look to see if the key is revoked.

2

I believe the answer can be found in section 5.2.4, "Computing Signatures". According to that section, what you actually need to hash is the concatenation of: the key packet (with an old-style packet header with a two-byte length — but your sample key packet has that header type already), for the first (certification) signature, the constant byte ...

2

It's a statement made by the signer, just like if I say that this message was written on 19 June 2012. Its value is context-dependent. Just like with a pen and paper, you can post-date or pre-date anything. In general, there's no such thing as verified time. Over the years, there are many people who have tried to create trusted time services, but they've ...

Only top voted, non community-wiki answers of a minimum length are eligible


text:
Table 3:
Statistics of Quadratic Fit to Correlation as a Function of Stimulus Filter ($k$) and Postspike Filter ($h$) Heterogeneity.
HeterogeneityNetwork Size234567
$k$ $R2$ 0.0018 0.0123 0.0076 0.0149 0.0212 0.0357
$p$-value for $F$-statistic versus Constant 0.003 $6.0×10-18$ $2.2×10-11$ $1.4×10-21$ $1.6×10-30$ $2.9×10-51$
$h$ $R2$ 0.0199 0.0159 0.0166 0.0156 0.0232 0.0356
$p$-value for $F$-statistic versus Constant $1.1×10-28$ $4.6×10-23$ $5.3×10-24$ $1.4×10-22$ $2.4×10-33$ $4.4×10-51$
HeterogeneityNetwork Size234567
$k$ $R2$ 0.0018 0.0123 0.0076 0.0149 0.0212 0.0357
$p$-value for $F$-statistic versus Constant 0.003 $6.0×10-18$ $2.2×10-11$ $1.4×10-21$ $1.6×10-30$ $2.9×10-51$
$h$ $R2$ 0.0199 0.0159 0.0166 0.0156 0.0232 0.0356
$p$-value for $F$-statistic versus Constant $1.1×10-28$ $4.6×10-23$ $5.3×10-24$ $1.4×10-22$ $2.4×10-33$ $4.4×10-51$

Notes: Correlations were prewhitened for the two time series to ensure unbiased estimates. Bold text corresponds to quadratic fits where the optimal level of heterogeneity is not in the interior.

Close Modal


text:
## Improved Confidence Bounds for the Linear Logistic Model and Applications to Bandits

### Kwang-Sung Jun, Lalit Jain, Blake Mason, Houssam Nassif

[ Abstract ] [ Livestream: Visit Bandits 1 ] [ Paper ]

We propose improved fixed-design confidence bounds for the linear logistic model. Our bounds significantly improve upon the state-of-the-art bound by Li et al. (2017) via recent developments of the self-concordant analysis of the logistic loss (Faury et al., 2020). Specifically, our confidence bound avoids a direct dependence on $1/\kappa$, where $\kappa$ is the minimal variance over all arms' reward distributions. In general, $1/\kappa$ scales exponentially with the norm of the unknown linear parameter $\theta^*$. Instead of relying on this worst case quantity, our confidence bound for the reward of any given arm depends directly on the variance of that arm's reward distribution. We present two applications of our novel bounds to pure exploration and regret minimization logistic bandits improving upon state-of-the-art performance guarantees. For pure exploration we also provide a lower bound highlighting a dependence on $1/\kappa$ for a family of instances.


text:
### The supersingular isogeny problem in genus 2 and beyond

Craig Costello and Benjamin Smith

##### Abstract

Let $A/\overline{\mathbb{F}}_p$ and $A'/\overline{\mathbb{F}}_p$ be supersingular principally polarized abelian varieties of dimension $g>1$. For any prime $\ell \ne p$, we give an algorithm that finds a path $\phi : A \rightarrow A'$ in the $(\ell, \dots , \ell)$-isogeny graph in $\widetilde{O}(p^{g-1})$ group operations on a classical computer, and $\widetilde{O}(\sqrt{p^{g-1}})$ calls to the Grover oracle on a quantum computer. The idea is to find paths from $A$ and $A'$ to nodes that correspond to products of lower dimensional abelian varieties, and to recurse down in dimension until an elliptic path-finding algorithm (such as Delfs--Galbraith) can be invoked to connect the paths in dimension $g=1$. In the general case where $A$ and $A'$ are any two nodes in the graph, this algorithm presents an asymptotic improvement over all of the algorithms in the current literature. In the special case where $A$ and $A'$ are a known and relatively small number of steps away from each other (as is the case in higher dimensional analogues of SIDH), it gives an asymptotic improvement over the quantum claw finding algorithms and an asymptotic improvement over the classical van Oorschot--Wiener algorithm.

Available format(s)
Category
Public-key cryptography
Publication info
Preprint. MINOR revision.
Keywords
Isogeniespost-quantum cryptographyabelian varietieselliptic-curve cryptography
Contact author(s)
smith @ lix polytechnique fr
History
2020-01-27: revised
See all versions
Short URL
https://ia.cr/2019/1387

CC BY

BibTeX

@misc{cryptoeprint:2019/1387,
author = {Craig Costello and Benjamin Smith},
title = {The supersingular isogeny problem in genus 2 and beyond},
howpublished = {Cryptology ePrint Archive, Paper 2019/1387},
year = {2019},
note = {\url{https://eprint.iacr.org/2019/1387}},
url = {https://eprint.iacr.org/2019/1387}
}

Note: In order to protect the privacy of readers, eprint.iacr.org does not use cookies or embedded third party content.


text:
# Solving an equation with parentheses

#### Differential Equations

46 Lectures 2.5 hours

#### Linear Equations in Two Variables

9 Lectures 2.5 hours

We come across problems about solutions of equations with parentheses.

In such cases, the parentheses are simplified by using the distributive property of multiplication over addition and subtraction. After simplification, the equations are solved as discussed in previous lesson by following the given rules in such cases.

Let us recall the distributive property of multiplication over addition and subtraction.

For any three numbers a, b, and c

1. a(b + c ) = ab + ac

2. a(b – c) = ab − ac

The example given below will make it easy to understand how to solve equations with parentheses.

Solve for w

7(w – 3) = 28

### Solution

Step 1:

Given 7(w – 3) = 28

Using the distributive property of multiplication

7w – (7 × 3) = 28; 7w – 21 = 28

Step 2:

The variable to be solved for is w.

7w – 21 + 21 = 28 + 21 = 49; 7w = 49

Step 3:

Dividing both sides by 7

$\frac{7w}{7} = \frac{49}{7}$

w = 7 is the solution

Step 4:

Checking the solution

Plugging in w = 7 in the original equation

7w – 21 = 28

7 × 7 – 21 = 28

49 – 21 = 28

28 = 28

So, the solution is verified to be correct.

Solve for w

4(z – 8) = 20

### Solution

Step 1:

Given 4(z – 8) = 20

Dividing both sides of the equation by 4

$\frac{4(z – 8)}{4} = \frac{20}{4}$

z – 8 = 5

Step 2:

The variable to be solved for is z.

z – 8 + 8 = 5 + 8 = 13

So, z = 13 is the solution

Step 3:

Checking the solution

Plugging in z = 13 in the original equation

4(z – 8) = 20

4(13 – 8) = 20

4(5) = 20

20 = 20

So, the solution is verified to be correct.