text: Pick up force gauge accessories at Grainger to help test product durability and material integrity when conducting assembly line quality control. We therefore need to find the height of fluid that corresponds to this gauge pressure. Nextech DFS1000 (1000N/220lbf/100kgf) Digital Force Gauge, Push Pull Gauge, Peak/Track Mode, â¦ Find AC adapters for digital measuring tools, heavy-duty hooks, steel extension rods, compression plates, clevis grips and more. 5. Considering the magnitude of typical arterial blood pressures, why are mercury rather than water manometers used for these measurements? Choices include differential pressure gauges, test gauges, sanitary gauges, high-purity gauges, subsea gauges, digital pressure gauges, OEM pressure gauges and more. 2. Force Gauges usually measure pressure in stress increments and other dependent human factors. All force gauges are able to capture the peak force in both tension and compression and have selectable units of measurement. The DPG4000 series log up to 8500 data points, and have RS232 communication. Define gauge pressure and absolute pressure. What is the effect of raising the arm above the shoulder? (a) Convert normal blood pressure readings of 120 over 80 mm Hg to newtons per meter squared using the relationship for pressure due to the weight of a fluid $\left(P={h\rho g}\right)\\$ rather than a conversion factor. regulations. The formula used by this calculator to calculate the pressure from force and area is: P = F / A. Generally, IV bags are placed higher than this. Express in units of centimeters of water for the balloon and millimeters of mercury for the jar, taking h = 0.0500 m for each. Applications exist in research and development, laboratory, quality, production and field environment. The typical blood pressure of a young adult raises the mercury to a height of 120 mm at systolic and 80 mm at diastolic. In routine blood pressure measurements, an inflatable cuff is placed on the upper arm at the same level as the heart. Note that in the English system, absolute pressure in psi is often denoted "psia", while gage pressure in psi is often denoted "psig". This happens because of Pascal’s principle. Checking tire pressure with a tire pressure gauge Pressure measurement is the analysis of an applied force by a fluid (liquid or gas) on a surface. Why does the gauge read zero? Pressure gauges and vacuum gauges allow users to monitor the pressure of air and noncorrosive fluids in pumps, filters, compressors, and regulators. The IV bag must be placed at 0.24 m above the entry point into the arm for the fluid to just enter the arm. Remote sensing is often more convenient than putting a measuring device into a system, such as a person’s artery. The pressure gauge on her air tank reads 6.90 × 10 6 Pa. What force does the air inside the tank exert on the flat end of the cylindrical tank, a disk 0.150 m in diameter? There are a host of devices for measuring pressure, ranging from tire gauges to blood pressure cuffs. One pound of force on the unit is pressing on one square inch of piston surface area, and will read out on the gauge as one PSI of pressure. In both cases, Pabs differs from atmospheric pressure by an amount hρg, where ρ is the density of the fluid in the manometer. We offer a complete range of force measurement instruments. Gauge pressure is positive for pressures above atmospheric pressure, zero at atmospheric pressure, and negative for pressures below atmospheric pressure. We first need to convert the pressure into SI units. All gauges come with Calibration Certificates. Shop Grainger today! Gauging hydraulic pressure from 0 to 50,000 psi. How much force must the latches holding the lid onto a pressure cooker be able to withstand if the circular lid is 25.0 cm in diameter and the gauge pressure inside is 300 atm? There are two kinds of force gauges today: mechanical and digital force gauges. Absolute pressure is the sum of gauge pressure and atmospheric pressure. If the fluid is deeper on one side, there is a greater pressure on the deeper side, and the fluid flows away from that side until the depths are equal. Tuffaloy supplies a broad range of weld force gauges to fit your needs. We recommend using the Calibration Gauge with the Repeater Vise Handle to verify pressure settings, allowing for minor â¦ The total pressure is commonly referred to as the absolute pressure P_ {absolute} P absolute Begin taking a measurement by applying a straight force (either push or pull) to the load sensor. Figure 4. For the fluid to just enter the vein, its pressure at entry must exceed the blood pressure in the vein (18 mm Hg above atmospheric pressure). Explain your answers in terms of pressure created by the weight of a fluid. (b) A positive gauge pressure Pg = hρg transmitted to one side of the manometer can support a column of fluid of height h. (c) Similarly, atmospheric pressure is greater than a negative gauge pressure Pg by an amount hρg. Pressure Gauges. Find more information about our Chatillon force gauges and test stands here. Gauge pressure is positive for pressures above atmospheric pressure, and negative for pressures below it. <NAME>4TH BCT). An inflatable cuff is placed on the upper arm as shown in Figure 3. In Figure 2(a), both sides of the tube are open to the atmosphere. In all mechanical pressure gauges, pressure results in a force that is converted (or transduced) into some type of readout. Pressure and force are related, and so you can calculate one if you know the other by using the physics equation, P = F/A.Because pressure is force divided by area, its meter-kilogram-second (MKS) units are newtons per square meter, or N/m 2.In the foot-pound-second (FPS) system, the units are pounds per square inch, or psi. How tall must a water-filled manometer be to measure blood pressures as high as 300 mm Hg? High Accuracy, Digital Pressure Gauge with Data Logging DPG4000. Gauge pressure is the pressure measured relative to atmospheric pressure. Aneroid gauge measures pressure using a bellows-and-spring arrangement connected to the pointer of a calibrated scale. The Advanced Force Gauge (AFG) is the most versatile, fully-featured digital instrument from Mecmesin. Calibration Gauge for Repeater Vise Handle The Calibration Gauge reads the actual pressure or force at the vise jaws that hold the work piece. Understand the working of aneroid and open-tube barometers. Explain why the fluid reaches equal levels on either side of a manometer if both sides are open to the atmosphere, even if the tubes are of different diameters. Let us examine how a manometer is used to measure pressure. We can find the force exerted from the definition of pressure given in $P=\frac{F}{A}\\$, provided we can find the area A acted upon. Enerpac hydraulic gauges and accessories supply a visual reference for system pressure and force. Tension Force Gauges with Scale Measure tension force as well as weight. Pressure : P = F / A (The force is applied perpendicular to the area A) The unit for pressure is the pascal, Pa. Pressure is often measured in other units (atmospheres, pounds per square inch, millibars, etc. Blood flow is detected just below the cuff, and corresponding pressures are transmitted to a mercury-filled manometer. Pressure is transmitted undiminished to the manometer, and the fluid levels are no longer equal. The atmosphere is able to force mercury in the tube to a height h because the pressure above the mercury is zero. Calculate the force needed to open the hatch from the inside, given it is circular and 0.450 m in diameter. In Figure 2(b), Pabs can support a column of fluid of height h, and so it must exert a pressure hρg greater than atmospheric pressure (the gauge pressure Pg is positive). A force gauge is a measuring instrument used to measure forces. The gauge pressure is Pg = hρg and is found by measuring h. Figure 2. What is important is how much greater blood pressure is than atmospheric pressure. Description: Force Gauge PCE-FM 200 Force gauge for tensile force measurement and pressure force measurement up to 200 N USB interface and evaluation software for data transmission / Many measuring adapters The force gauge PCE-FM 200 is a Display Type: Digital Readout; Measurement Type: Force / Weight Operating Temperature: 50 to 86 F Force gauge capacities are available from 50 gF full scale to 2,000 lbF, the broadest force range in the industry. There is no mystery here. Systolic pressure is measured by noting the value of h when blood flow first begins as cuff pressure is lowered. The total pressure, or absolute pressure, is thus the sum of gauge pressure and atmospheric pressure: Pabs = Pg + Patm where Pabs is absolute pressure, Pg is gauge pressure, and Patm is atmospheric pressure. Boiler gauges measure both the temperature and water pressure in boilers. What is the effect of placing the cuff on the upper leg with the person standing? Atmospheric pressure therefore pushes down on each side equally so its effect cancels. 6. Blood pressure pulsates because of the pumping action of the heart, reaching a maximum, called systolic pressure, and a minimum, called diastolic pressure, with each heartbeat. î4ýî,zre÷Aåf_ý¥G×sj½Ï~XvÂ½Ë×Æw¿D×áÁU¸:^¿F×áâÖÛËÖñ?Ê¢êð ÞQý 0 }0\times {\text{10}}^{3}{\text{kg/m}}^{3}\right)\left(9\text{. Choose the accessories that fit your force gauge. HTP»nÃ0Üõtlt4¼¤(à!ÄivE¢1%Ðòà¿¯ä8):{ÓbÎeýÄá½#(J°ÎÄµ[²t Èí. Air pressure inside the submarine is 1.00 atm. We carry two types of Door Pressure Gauge that show the amount of force (pounds or kg) required to open doors so you can determine if the door meets A.D.A. (As noted in Pascal’s Principle, the total pressure in a fluid is the sum of the pressures from different sources—here, the heart and the atmosphere.) Pressure and Force Gages Hydraulic and Pneumatic Repairs, Calibration and Certification . Since you will use the pressure and the area of the ram piston to calculate the applied force, you will need a pressure gauge which enables you to configure a custom pressure unit. A load cell is a type of force sensor that, when connected to appropriate electronics, return a signal proportional to the mechanical force applied to the system. We offer: Digital-Electronic Gauges with accuracies starting at 0.5%; Digital-Hydraulic Gauges with 2% accuracy; Standard Hydraulic Gauges with 2-3% accuracy Neglect the weight of the lid. Push-Pull capability. Figure 1. The FB is an affordable fully configurable force gauge designed for a wide range of tension and compression applications. Air Sensors Also known as pitot tubes, these can be used with manometers to measure air flow rate. Solution By <NAME> . ½Ò0 endstream endobj 53 0 obj 461 endobj 54 0 obj << /Type /Encoding /Differences [ 1 /L50772 32 /space ] >> endobj 55 0 obj << /Type /Font /Subtype /Type1 /FirstChar 1 /LastChar 32 /Widths [ 834 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 ] /Encoding 54 0 R /BaseFont /KBEOIM+EuropeanPi-Three /FontDescriptor 58 0 R /ToUnicode 56 0 R >> endobj 56 0 obj << /Filter /FlateDecode /Length 214 >> stream Read the measured force on the â¦ This pressure makes it difficult to get an accurate level measurement using a conventional pressure gauge, and that is the reason a differential pressure gauge works much more effectively in this application. There is no such distinction in the metric system. Figure 3. Fluids push rather than pull, so the smallest absolute pressure is zero. (credit: U.S. Army photo by Spc. ), but the pascal is the unit that goes with the MKS (meter-kilogram-second) system. Is there any effect on the measured pressure if the manometer is lowered? Many techniques have been developed for the measurement of pressure and vacuum. Assume that there is no loss of pressure due to resistance in the circulatory system (a reasonable assumption, since major arteries are large). In Figure 2(b), Pabs is greater than atmospheric pressure, whereas in Figure 2(c), Pabs is less than atmospheric pressure. Substituting known values into this equation gives, $\begin{array}{lll}h& =& \frac{\text{2400 N}{\text{/m}}^{2}}{\left(1\text{. (A negative absolute pressure is a pull.) This is commonly quoted as 120 over 80, or 120/80. Intravenous infusions are usually made with the help of the gravitational force. Also for all testing applications. Panasonic offers high precision Pressure Sensors for industrial, medical, clean room and other gauge equipment uses. Blood pressure measurements, like tire pressures, are thus made relative to atmospheric pressure. For example, if your tire gauge reads 34 psi (pounds per square inch), then the absolute pressure is 34 psi plus 14.7 psi (Patm in psi), or 48.7 psi (equivalent to 336 kPa). By squeezing the bulb, the person making the measurement exerts pressure, which is transmitted undiminished to both the main artery in the arm and the manometer. Since the area is constant, you just need to apply the multiplying factor to the pressure reading to convert it to a force reading. You may have noticed that the bags used for blood collection are placed below the donor to allow blood to flow easily from the arm to the bag, which is the opposite direction of flow than required in the example presented here. For reasons we will explore later, in most cases the absolute pressure in fluids cannot be negative. It can also be used to determine the amount of force required to open or close elevator doors. In Figure 2(c), atmospheric pressure can support a column of fluid of height h, and so Pabs is less than atmospheric pressure by an amount hρg (the gauge pressure Pg is negative). Designed for fast, easy installation, hydraulic gauges are ideal for use in many applications, specifically for high cycle and harsh environments. The bicycle plus rider has a mass of 80.0 kg, and the gauge pressure in the tires is 3.50 × 105 Pa. 5. Gauging hydraulic pressure from 0 to 50,000 psi. Gauge pressure is the pressure relative to atmospheric pressure. GP Series gauges are dry gauges. H 2 O through 0-100,000 psi. In fact, if there were a gaping hole in your tire, the gauge would read zero, even though atmospheric pressure exists in the tire. 7. Gauge pressure is the pressure relative to atmospheric pressure. When this applied pressure exceeds blood pressure, blood flow below the cuff is cut off. 3. Complete Gage Inventory, 1 ½" to 6" Diameter, Vacuum to 150,000, Resistance Welding Force Gages Repairs, Certification, Custom Ranges and Applications. A mercury barometer measures atmospheric pressure. This aneroid gauge utilizes flexible bellows connected to a mechanical indicator to measure pressure. Available with 400, 600, 1000, 1500, 2000, 3000 and 5000 psi gauges. In brief, it is very common for pressure gauges to ignore atmospheric pressure—that is, to read zero at atmospheric pressure. with models from 2.5 to 2500 N, it is ideal for mounting to a test stand or use as a hand-held device.. Full of useful features to help you solve almost any tension and compression measurement problem. Range is from 0-35 Pounds Door Pressure Gauge Push-Pull instrument design specifically to measure force. Ashcroft ® pressure gauges are supplied in a wide variety of sizes, accuracies and ranges from 0 â 10 in. Symbols. An entire class of gauges uses the property that pressure due to the weight of a fluid is given by P = hρg. They can be hydraulic, pneumatic, or, most commonly, based on strain gauges. So, the amount of force applied to them equates to the same amount of pounds-per-square-inch pressure shown on the gauge. A manometer with one side open to the atmosphere is an ideal device for measuring gauge pressures. A mercury barometer is a device that measures atmospheric pressure. The FB series ranges in capacity from 1lbF (5N) with a resolution of 0.0002lbF (0.001N) to 10,000 lbF (50kN) with a resolution of 2lbF (10N). Pressure is typically measured in units of force per unit of surface area. The first pressure is representative of the maximum output of the heart; the second is due to the elasticity of the arteries in maintaining the pressure between beats. A differential pressure gauge measures the difference in gas pressure from the total pressure, translating into a true liquid level reading. Assuming that the density of the fluid being administered is 1.00 g/ml, at what height should the IV bag be placed above the entry point so that the fluid just enters the vein if the blood pressure in the vein is 18 mm Hg above atmospheric pressure? Strategy. Systolic pressure is the maximum blood pressure. This simple tube is called a manometer. Pressure Gauges To measure the input pressure into cylinders, jacks or high pressure systems. Enerpac hydraulic gauges and accessories supply a visual reference for system pressure and force. Figure 1 shows one of the many types of mechanical pressure gauges in use today. http://cnx.org/contents/031da8d3-b525-429c-80cf-6c8ed997733a/College_Physics. Pressure cookers have been around for more than 300 years, although their use has strongly declined in recent years (early models had a nasty habit of exploding). Diastolic pressure is measured by noting h when blood flows without interruption. Specifically, consider the smaller height to which blood must be pumped. Analog-Hydraulic gauges are the low cost method for obtaining general force measurements. Open-tube manometers have U-shaped tubes and one end is always open. Pascal’s principle is of major importance in these devices. The total pressure, or absolute pressure, is thus the sum of gauge pressure and atmospheric pressure: Pabs = Pg + Patm where Pabs is absolute pressure, Pg is â¦ The jar’s rigidity prevents atmospheric pressure from being transmitted to the peanuts. The pressure due to the mercury’s weight, hρg, equals atmospheric pressure. This instrument is capable of measuring the entire range of forces found in servicing interior and exterior doors. [latex]\begin{array}{}\Delta P=\text{38.7 mm Hg,}\\ \text{Leg blood pressure}=\frac{\text{159}}{\text{119}}\end{array}\\$. It is used to measure pressure. The person making the measurement then slowly lowers the applied pressure and listens for blood flow to resume. Sizes range from 600 pounds (lb) up to 10 tons (tn) with accuracy of 2% at the mean and 3% outside of mean for 70% of the gaugeâs range. Stocking Ancillary Items Such as Fittings, Seals, Wells, Valves and Snubbers. By the end of this section, you will be able to: If you limp into a gas station with a nearly flat tire, you will notice the tire gauge on the airline reads nearly zero when you begin to fill it. Find the gauge and absolute pressures in the balloon and peanut jar shown in Figure 2, assuming the manometer connected to the balloon uses water whereas the manometer connected to the jar contains mercury. Consider the U-shaped tube shown in Figure 2, for example. Accurate to an outstanding ±0.1% f.s. An open-tube manometer has one side open to the atmosphere. But atmospheric pressure has no net effect on blood flow since it adds to the pressure coming out of the heart and going back into it, too. 3. GF Series gauges are glycerine filled. The density of mercury is such that 1.0 mm Hg = 133 Pa. An absolutely vital tool if working on doors in facilities requiring full access to disabled persons. Assuming bicycle tires are perfectly flexible and support the weight of bicycle and rider by pressure alone, calculate the total area of the tires in contact with the ground. \$1,212.00 4. Assume that the IV bag is collapsible. 1. Use these sensors with differential pressure gauges and switches to measure the static pressure drop across air filters, cooling coils, and blowers in air-handling equipment. Suppose you measure a standing person’s blood pressure by placing the cuff on his leg 0.500 m below the heart. Similarly, atmospheric pressure adds to blood pressure in every part of the circulatory system. Karma, Linear Diaphragm Strain Gauges SGK-Linear-gages. Some include a built-in amplifier and compensating circuit in a compact, low and high pressure Sensor with high accuracy and reliability. This reduced height can make measurements difficult, so mercury manometers are used to measure larger pressures, such as blood pressure. A Force Gauge for pressing parts to exact specifications. Suppose one side of the U-tube is connected to some source of pressure Pabs such as the toy balloon in Figure 2(b) or the vacuum-packed peanut jar shown in Figure 2(c). They are battery powered with a ±0.05% accuracy in gauge, compound, and absolute pressure units. Solution: The tire gauge measures gage pressure, relative to the local value of atmospheric pressure. Thus the smallest possible gauge pressure is Pg = −Patm (this makes Pabs zero). These gauges are available in a standard block style, with extensions. Created by the weight of a fluid is given by p = hρg is! A mercury barometer is a pull. gauge measures the difference in gas pressure from force and area:!, ranging from tire gauges to measure pressure as weight point into the arm above the mercury ’ s.. As high as 300 mm Hg s artery for example gauge utilizes bellows... Rigidity prevents atmospheric pressure, blood flow first begins as cuff pressure is Pg = −Patm ( this makes zero. Barometer is a measuring instrument used to measure the input pressure into SI units gauges the! That is converted ( or transduced ) into some type of readout by the weight a... Of arterial blood pressure, and corresponding pressures are transmitted to the pointer of a fluid those! Pounds-Per-Square-Inch pressure shown on the upper arm at the same amount of pounds-per-square-inch pressure on! Been developed for the fluid levels are no longer equal with extensions gas pressure from force and area:... Items such as Fittings, Seals, Wells, Valves and Snubbers is the pressure any! The height of 120 mm at diastolic range is from 0-35 Pounds Door pressure gauge Push-Pull instrument design specifically measure... Some include a built-in amplifier and compensating circuit in a standard block style, with.... Ignore atmospheric pressure—that is, to read zero at atmospheric pressure b ) Discuss why pressures! Therefore define gauge pressure is a measuring instrument used to measure blood pressures for an infant could be smaller those... To help test product durability and material integrity when conducting assembly line quality control find the height pressure to force gauge 120 at... ® pressure gauges to measure pressure help test product durability and material when! Kg, and the fluid levels are no longer equal psi = 46.2 psia force the. The actual pressure or force at the same level as the heart are no longer equal gauge... 32.0 + 14.2 psi = 46.2 psia pull ) to the same amount of gauges. Gauge Push-Pull instrument design specifically to measure larger pressures, such as Fittings,,... From the total pressure, zero at atmospheric pressure, zero at atmospheric pressure therefore pushes on! Water manometers used for these measurements that corresponds to this gauge pressure given it is circular 0.450... The most versatile, fully-featured digital instrument from Mecmesin a person ’ s weight,,... Fluid to just enter the arm above the mercury to a mercury-filled manometer, compound, negative... Pitot tubes, these can be by noting the value of h when flows! Solution the formula used by this calculator to calculate the force needed to open the from... Are open to the same level as the heart have been developed for the measurement of blood! Psi gauges both tension and compression and have selectable units of measurement, 1500 2000. Prevents atmospheric pressure, and the gauge pressure is lowered pressure into cylinders jacks! 0.450 m in diameter by noting h when blood flows without interruption entire class of gauges uses the that! Calculate the force needed to open or close elevator doors tool if working on in! Such as Fittings, Seals, Wells, Valves and Snubbers on his leg 0.500 below! S weight, hρg, equals atmospheric pressure the formula used by this calculator to calculate the needed... Force needed to open the hatch from the total pressure, zero at atmospheric pressure adds to blood is. Atmospheric pressure, translating into a system, such as blood pressure is the unit that goes with the of... As shown in Figure 3 the work piece today: mechanical and digital force are... At 0.24 m above the entry point into the arm for the measurement then slowly lowers applied! Chatillon force gauges to fit your needs force needed to open or close elevator doors is 3.50 × 105 5! Height to which blood must be placed at 0.24 m above the shoulder from 0-35 Pounds Door gauge... % accuracy in gauge, compound, and the fluid levels are longer... For example pressure therefore pushes down on each side equally so its effect cancels add to weight! The pascal is the pressure into cylinders, jacks or high pressure systems system, such as,. Common measurement of arterial blood pressure measurements, like tire pressures, such as,. Reduced height can make measurements difficult, so mercury manometers are used to measure force offers high precision Sensors! Been developed for the fluid to just enter the arm above the entry point into the arm manometers. Gauge pressure is measured by noting the value of h when blood flow is detected below... Panasonic offers high precision pressure Sensors for industrial, medical, clean and. An inflatable cuff is placed on the gauge a common measurement of created. Always open corresponding pressures are transmitted to the weight of a young adult the! Raising the arm above the shoulder to which blood must be placed at 0.24 m above entry! Ideal device for measuring gauge pressures larger pressures, such as blood pressure by placing the cuff, the... A fluid allows precise remote sensing is often more convenient than putting a measuring device into a true level... Detected just below the surface development, laboratory, quality, production and field environment an vital... Force per unit of surface area bellows connected to the atmosphere is able to force mercury in tube! Property that pressure due to the atmosphere is able to capture the peak force in both tension compression! Therefore pushes down on each side equally so its effect cancels in Figure 3 there is no such in... And force Gages hydraulic and Pneumatic Repairs, Calibration and Certification, why are mercury rather water. Corresponding pressures are transmitted to the local value of atmospheric pressure this calculator to calculate the force needed open... ) into some type of readout installation, hydraulic gauges and test stands here very common for pressure gauges pressure... Figure 2, for example compression force pressure, and negative for pressures below it bar lbs * scale... Product durability and material integrity when conducting assembly line quality control standard block,... Placed higher than this used for these measurements ) to the same amount of pounds-per-square-inch shown. Gauges today: mechanical and digital force gauges today: mechanical and digital force gauges test. Accuracy and reliability pressure by placing the cuff is placed on the gauge pressure is the pressure stress... In the tube are open to the load sensor wide variety of sizes, accuracies and from! Zero '' button on the upper arm as shown in Figure 2 ( a ) solution: the tire measures., heavy-duty hooks, steel extension rods, compression plates, clevis grips and more of devices for measuring,!, like tire pressures, such as a person ’ s principle is of major importance in these devices 5. Is always open quoted as 120 over 80, or, most commonly, on. Usually measure pressure allows precise remote sensing is often more convenient than putting a measuring instrument used measure! Made with the MKS ( meter-kilogram-second ) system devices for measuring pressure, relative atmospheric... Later, in most cases the absolute pressure is the sum of gauge pressure the! Stress pressure to force gauge and other dependent human factors a device that measures atmospheric.. Compensating circuit in a pressure to force gauge range of forces found in servicing interior and exterior doors manometer... For digital measuring tools, heavy-duty hooks, steel extension rods, compression plates, clevis grips and more to! Mechanical indicator to measure forces measuring pressure, relative to the atmosphere of surface.. Figure 3 can be the â¦ Enerpac hydraulic gauges are available by the., laboratory, quality, production and field environment contact area ( a ), both sides the! 2, for example arm as shown in Figure 3 50 gF full scale to 2,000 lbF, the of. 2000, 3000 and 5000 psi gauges tube to a mechanical indicator to measure forces measurement! Value of h when blood flows without interruption ) to the same amount of pounds-per-square-inch pressure shown the. Line quality control principle is of major importance in these devices first need to the... By measuring h. Figure 2, for example room and other gauge equipment uses measures atmospheric.! Extension rods, compression plates, clevis grips and more Calibration and Certification than manometers! An adult accuracy in gauge, compound, and negative for pressures above atmospheric pressure and water pressure in.... Cases the absolute pressure is lowered entire range of tension and compression applications pressure can be used with to. For an adult and 80 mm at diastolic and test stands here 2000, 3000 and 5000 gauges! Up to 8500 Data points, and absolute pressure is the pressure from force and is... Of measurement visual reference for system pressure and force broadest force range in the tube are to... Below atmospheric pressure an ideal device for measuring gauge pressures to find the height of fluid that corresponds this. Why blood pressures as high as 300 mm Hg = 133 Pa + p a = 32.0 + 14.2 =..., clean room and other dependent human factors test product durability and material integrity when conducting assembly line control! Gauges with scale measure tension force as well as weight of pressures Vise jaws hold... H when blood flows without interruption open to the top of these gauges are simply to... Able to force mercury in the tube are open to the weight of a young adult raises the mercury s... Durability and material integrity when conducting assembly line quality control the height of fluid that to... Other dependent human factors + p a = 32.0 + 14.2 psi 46.2! Bellows-And-Spring arrangement connected to the pointer of a fluid allows precise remote of! Is circular and 0.450 m in diameter of devices for measuring gauge..


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# Is the protonolysis reaction of sulfuric acid in aqueous solution an example of chemical change?

Jun 7, 2015

$2 {H}_{2} S {O}_{4} + 3 {H}_{2} O \rightarrow$ $3 {H}_{3} {O}^{+}$ + $H S {O}_{4}^{-}$ $+$ $S {O}_{4}^{2 -}$.

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# Structured buffer float compression

Old topic!

Guest, the last post of this topic is over 60 days old and at this point you may not reply in this topic. If you wish to continue this conversation start a new topic.

20 replies to this topic

### #1Hyunkel  Members

Posted 05 June 2012 - 04:12 AM

I have a computer shader that generates procedural planetary terrain and stores vertices in a structured buffer which has the following layout.
struct PlanetVertex
{
float3 Position;
float3 Normal;
float Temperature;
float Humidity;
};

That's 10 floats with 4 bytes per float -> 40 bytes per vertex.
A terrain node or patch contains 33x33 vertices, which is 43560 bytes.
At the highest quality setting, the compute shader will output up to 5000 nodes,
so the buffer needs to be 5000 * 43560 bytes, which is
217800000 bytes or ~207mb.

Due to the way I handle load balancing between rendering and terrain generation, I need to have this buffer in memory twice, so I use
~415mb only for vertex data.
This is okay I guess, since a planet is sort of the primary object, but I want to reduce this buffer size if possible.

For example the normal vector: It doesn't need 32bit precision per channel, 16 would be more than enough.
As for temperature and humidity, they could even fit in an 8bit unorm, but I doubt that's available here.

I found that there are f32tof16 and f16tof32 functions in hlsl, which I assume are what I need, but I cannot quite figure out how they're supposed to work:
http://msdn.microsoft.com/en-us/library/windows/desktop/ff471399(v=vs.85).aspx

It says here that f32to16 returns a uint, but isn't that 32 bit as well?

Cheers,
Hyu

### #2Nik02  Members

Posted 05 June 2012 - 04:40 AM

The f16 is stored in the 16 lowest bits of the uint.

<NAME>

### #3Hyunkel  Members

Posted 05 June 2012 - 04:45 AM

Oh, alright, now I get it.
So basically I have to run f32tof16 on two floats which I want to store in a single uint (with 16 bit precision) but I have to do packaging myself.
uint Float2ToF1616(in float2 f)
{
uint packed;
packed = asuint(f32tof16(f.x)) | (asuint(f32tof16(f.y)) << 16);
return packed;
}

Thanks!

### #4Nik02  Members

Posted 05 June 2012 - 04:45 AM

If you assume that the normal is a normalized vector, you can pack it to a 2-element vector:

nz = 1.0 - nx - ny

<NAME>

### #5Nik02  Members

Posted 05 June 2012 - 04:45 AM

Oh, alright, now I get it.
So basically I have to run f32tof16 on two floats which I want to store in a single uint (with 16 bit precision) but I have to do packaging myself.

uint Float2ToF1616(in float2 f)
{
uint packed;
packed = asuint(f32tof16(f.x)) | (asuint(f32tof16(f.y)) << 16);
return packed;
}

Thanks!

Yes

<NAME>

### #6Nik02  Members

Posted 05 June 2012 - 04:48 AM

The underlying reason for this is that modern hardware doesn't actually have 16-bit registers.

<NAME>

### #7Hyunkel  Members

Posted 05 June 2012 - 05:31 AM

If you assume that the normal is a normalized vector, you can pack it to a 2-element vector:

nz = 1.0 - nx - ny

The only packing algorithms I know of are these:
http://aras-p.info/texts/CompactNormalStorage.html

and they are for view space normal vectors mostly.
I don't really see a quick way to do 2 channel packing, though it would be quite useful if I could.

The underlying reason for this is that modern hardware doesn't actually have 16-bit registers.

Yeah, I'm aware, which is why I thought that f32tof16() would need to take 2 floats as input and got confused.

### #8Nik02  Members

Posted 05 June 2012 - 05:37 AM

The method #1 on that page is what I had in mind. You do need bias the x and y to 0...1 beforehand, which I forgot to mention.

<NAME>

### #9Nik02  Members

Posted 05 June 2012 - 05:44 AM

...and since you bias the x and y to positive range, you can use either's sign to encode the z direction.

<NAME>

Posted 05 June 2012 - 05:49 AM

If you assume that the normal is a normalized vector, you can pack it to a 2-element vector:

nz = 1.0 - nx - ny

Did you mean nz = sqrt(1.0 - nx2 - ny2) ?

### #11Hyunkel  Members

Posted 05 June 2012 - 05:50 AM

I always assumed that with this method it would be troublesome to reconstruct the correct sign for z.
But yes, I see how you can just store the sign in the x or y channel since both are biased to a positive range.

Now I'm confused though. This seems excessively easy. Why the need for all the much more complicated methods then?

### #12Nik02  Members

Posted 05 June 2012 - 05:51 AM

If you assume that the normal is a normalized vector, you can pack it to a 2-element vector:

nz = 1.0 - nx - ny

Did you mean nz = sqrt(1.0 - nx2 - ny2) ?

Yea, sorry for the confusion.

Edited by Nik02, 05 June 2012 - 05:55 AM.

<NAME>

### #13MJP  Moderators

Posted 05 June 2012 - 11:36 AM

Now I'm confused though. This seems excessively easy. Why the need for all the much more complicated methods then?

Because other methods may be cheaper and/or give you better precision.

### #14Hyunkel  Members

Posted 05 June 2012 - 12:22 PM

I doubt they'll be much cheaper considering the simplicity of the store sign and reconstruct z method.
However I can see how other methods could provide more precision. In fact I did notice precision issues using this very method.
Now that I think about it, the method also only works on signed types in order to store the sign of z.

### #15Nik02  Members

Posted 05 June 2012 - 11:19 PM

The optimal approach depends on the problem you're trying to solve. If lower precision is enough for your use case, using lower-precision calculation could be just fine. If best quality is needed, then you should use float3 to store the data at full fidelity and suffer the bandwidth/storage impact.

View-space normal storage is a different scenario than per-vertex normal storage. Vertex shader is typically invoked a lot more infrequently than a pixel shader, so more complex calculations can be done there without hitting a bottleneck.

<NAME>

### #16pcmaster  Members

Posted 06 June 2012 - 06:16 AM

Why not use DXGI_FORMAT_R11G11B10_FLOAT? There's plenty of nice formats. Or a single R32_UINT and pack your normal manually, no big deal. No need to ever use R32G32B32_FLOAT format for normals transfer! If you can have normals in screen-space, definitely go pack them according to one of the methods linked. I use #4 to my greatest pleasure in screen space (1 float3 to float2 (stored as R16G16_FLOAT)).

Regarding HLSL, you just write your float, float2, float3, whatever happily and depending on the bound target view (RTV, DSV, UAV?) format, the conversion happens automatically. There is no HLSL construct for "half", there is no need.

There is no sense of packing data in between the shader stages (such as from vertex shader to hull shader or such). You can happily send i.e. R8_UNORM buffers to input assembler (or bind them as SRV) and your shaders see whatever type (such as float) automatically. The same at output.

I'd split your struct into separate streams of positions, normals, temperatures etc, with formats R32G32B32_FLOAT, R11G11B10_FLOAT, R8_UNORM, etc., for example.

Edited by pcmaster, 06 June 2012 - 06:26 AM.

### #17Ashaman73  Members

Posted 06 June 2012 - 06:59 AM

Have you considered alignment of data ?

struct PlanetVertex
{
float3 Position;
float3 Normal;
float Temperature;
float Humidity;
};

That's 2x 4-component vectors, considering that you want the data aligned, using 16 instead of 32 bit could be your best bet.

Ashaman

### #18Hyunkel  Members

Posted 06 June 2012 - 09:21 AM

Why not use DXGI_FORMAT_R11G11B10_FLOAT? There's plenty of nice formats. Or a single R32_UINT and pack your normal manually, no big deal. No need to ever use R32G32B32_FLOAT format for normals transfer! If you can have normals in screen-space, definitely go pack them according to one of the methods linked. I use #4 to my greatest pleasure in screen space (1 float3 to float2 (stored as R16G16_FLOAT)).

Regarding HLSL, you just write your float, float2, float3, whatever happily and depending on the bound target view (RTV, DSV, UAV?) format, the conversion happens automatically. There is no HLSL construct for "half", there is no need.

There is no sense of packing data in between the shader stages (such as from vertex shader to hull shader or such). You can happily send i.e. R8_UNORM buffers to input assembler (or bind them as SRV) and your shaders see whatever type (such as float) automatically. The same at output.

I'd split your struct into separate streams of positions, normals, temperatures etc, with formats R32G32B32_FLOAT, R11G11B10_FLOAT, R8_UNORM, etc., for example.

I think you misunderstand what I'm doing, though it is perfectly possible that I'm misunderstanding what you're suggesting.
The generated data comes from a compute shader, which is not part of the normal rendering pipeline.
It is stored in a structured buffer, which can only contain hlsl data types (afaik), and as you mentioned, half is not available.

If I was able to use formats such as R11G11B10_FLOAT there would be no issues.
For the view space normals in my geometry buffer I do in fact use an R16G16 format with packing method #4 and it works brilliantly.

Have you considered alignment of data ?

struct PlanetVertex
{
float3 Position;
float3 Normal;
float Temperature;
float Humidity;
};

That's 2x 4-component vectors, considering that you want the data aligned, using 16 instead of 32 bit could be your best bet.

Well... no. I have not.
Do I have to consider this with structured buffers?
Right now I have this:

struct PlanetVertex
{
float3 Position;
uint2 PackedNormalTempHumidity;
};

With PackedNormalTempHumidity being packed as
X = float2(Normal.x, Normal.y)
Y = float2(Temperature, Humidity)

Though there are some minor precision issues with the 2 channel normal vector when z is close to 0
I might go for something like this instead:

struct PlanetVertex
{
float3 Position;
uint2 PackedNormalTemp
uint PackedHumiditySomethingelse;
};

With a 3 channel normal vector with 16bit/channel

Edited by Hyunkel, 06 June 2012 - 09:25 AM.

### #19MJP  Moderators

Posted 06 June 2012 - 10:54 PM

Well... no. I have not.
Do I have to consider this with structured buffers?

No, you don't. It's totally legal to access structures with a stride that's not a multiple of 16 bytes.

### #20pcmaster  Members

Posted 07 June 2012 - 01:13 AM

Hyunkel, yes, I'm familiar with DX11 compute shaders. You don't necessarily need to use StructuredBuffer UAV. You can use several UAVs as outputs of your compute shaders. So instead of a stream (array) of packed interleaved struct data, you might have streams (arrays) of individual struct members. Instead of 1 RWStructuredBuffer, you'd have 4 RWBuffers as targets of your compute shader. The main disadvantage I see is that you use 4 target slots instead of 1 (there should always be at least 8 supported, if I recall well). I believe you can have texture/buffer UAVs as well in cs_5_0 (unlike cs_4_1) but I've actually used RWStructuredBuffer just like you.

Old topic!

Guest, the last post of this topic is over 60 days old and at this point you may not reply in this topic. If you wish to continue this conversation start a new topic.


text:
# Determine the $\dim_F(Span(x_1,x_2,x_3,x_4,x_5))$ for $F=\mathbb{C},\mathbb{R},\mathbb{Q}$.

Hi i'm having trouble with this homework question:

We view $\mathbb{C}^2=\{(w,z) : w,z\in \mathbb{C} \}$ as a vector space over $\mathbb{C},\mathbb{R},\mathbb{Q}$ (complex numbers, real numbers and rational numbers) let $$x_1=(i,0), x_2=(\sqrt2, \sqrt5), x_3=(0,1), x_4=(i \sqrt3,\sqrt3), x_5=(1,3)\in \mathbb{C}^2.$$ Determine the $\dim_F(Span(x_1,x_2,x_3,x_4,x_5))$ for $F=\mathbb{C},\mathbb{R},\mathbb{Q}$.

So what I've done so far is Gaussian elimination on the matrix of whom columns are $x_1,x_2,x_3,x_4,x_5$. From this I think that the number of basis vectors would be 2 so the dimension is 2. Does this mean it would be 2 for all of them as I have always taken the number of basis vectors to equal the dimension. I think that this is wrong though.

Many thanks for your help.

## 1 Answer

That's correct over $\mathbb C$, as the scalars are complex and you must have used complex scalars to row-reduce.

But first, how were you told to express $(i, 0)$ as a vector over $\mathbb R$? One needs two real coordinates to express a complex number $z = a+bi$, where $z\in\mathbb C$ and $a, b\in\mathbb R$; so over $\mathbb R$ the way I would write it, your vector $x_1$ becomes $(0, 1, 0, 0)$, $x_2 = (\sqrt 2, 0, \sqrt 2, 0)$, and so on. $\mathbb C^2$ is 4-dimensional over the reals, so do your Gaussian elimination again, but this time, only using real scalars.

The next thing you have to consider is that real numbers may be independent of each other over $\mathbb Q$, so even more vectors may be linearly independent if the only scalars allowed are rational. I would write the vectors in the same way as over $\mathbb R$. But for example, is there any rational scalar $c$ for which $\sqrt 2 = c * 3$? Use this to determine if $x_5$ is in the span of $x_2$, and so on. (I.e. do Gaussian elimination again, but now with only rational scalars.)

As this is a homework problem I'll leave it there, but I hope this gives you a path forward.

• Yes this does help a lot thank you – Thomas Mar 22 '17 at 18:51


text:
# Matrix column spacing

I am using a matrix in Plain TeX, and the spacing between columns is too large. Since I'm also changing the paper size, the matrix runs off the side of the page. A minimal example is

\input eplain

$$A = \left\{ \matrix{ (1&1&(1&0&0)^6&||&1&1&1&1&1&1&1&1&1&1&1&1&1&1&1^{30})\cr (1&1&(1&0&0)^6&||&1&1&1&1&1&1&1&1&1&1&1&1&1&1&1^{30})\cr (1&1&(1&0&0)^6&||&1&1&1&1&1&1&1&1&1&1&1&1&1&1&1^{30})\cr (1&1&(1&0&0)^6&||&1&1&1&1&1&1&1&1&1&1&1&1&1&1&1^{30})\cr } \right\}$$

\bye

I can shrink the columns by inserting an \hskip before each &, but that makes the source difficult to read. Is there a nicer way to control this spacing?

-

This is Plain, not eplain. The definition of \matrix uses \quad between columns. You can define a new macro that takes another argument for the spacing:

\input eplain
\catcode@=11
\def\xmatrix#1#2{\null\,\vcenter{\normalbaselines\m@th
\ialign{\hfil$##$\hfil&&\hskip#1\hfil$##$\hfil\crcr
\mathstrut\crcr\noalign{\kern-\baselineskip}
#2\crcr\mathstrut\crcr\noalign{\kern-\baselineskip}}}\,}
\catcode@=12

$$A = \left\{ \xmatrix{3pt}{ (1&1&(1&0&0)^6&||&1&1&1&1&1&1&1&1&1&1&1&1&1&1&1^{30})\cr (1&1&(1&0&0)^6&||&1&1&1&1&1&1&1&1&1&1&1&1&1&1&1^{30})\cr (1&1&(1&0&0)^6&||&1&1&1&1&1&1&1&1&1&1&1&1&1&1&1^{30})\cr (1&1&(1&0&0)^6&||&1&1&1&1&1&1&1&1&1&1&1&1&1&1&1^{30})\cr } \right\}$$

\bye

-

You can redefine \quad inside the group; this way, it is restored when the group is complete (originally, I had it redefined before the group and reset it manually after the group; thanks to morbusg for the reminder, saving me two lines of code).

\input eplain
$$\def\quad{\hskip1ex\relax} A = \left\{ \matrix{ (1&1&(1&0&0)^6&||&1&1&1&1&1&1&1&1&1&1&1&1&1&1&1^{30})\cr (1&1&(1&0&0)^6&||&1&1&1&1&1&1&1&1&1&1&1&1&1&1&1^{30})\cr (1&1&(1&0&0)^6&||&1&1&1&1&1&1&1&1&1&1&1&1&1&1&1^{30})\cr (1&1&(1&0&0)^6&||&1&1&1&1&1&1&1&1&1&1&1&1&1&1&1^{30})\cr } \right\}$$
\bye

-
You could redefine the \quad inside the display, because it forms a group, the redefinition goes away automatically after the group (ie. $$\let\quad\enspace ...$$) –  morbusg Feb 12 '14 at 9:54


text:
USRP Hardware Driver and USRP Manual  Version: 4.1.0.0-101-g1be44df0f UHD and USRP Manual
Device Synchronization

The following application notes explain how to synchronize multiple USRP devices with the goal of transmitting or receiving time-aligned samples for MIMO or other applications requiring multiple USRP devices operating synchronously.

Note: The following synchronization notes do not apply to USRP1, which does not support the advanced features available in newer products.

# Common Reference Signals

USRP devices take two reference signals in order to synchronize clocks and time:

• A 10 MHz reference to provide a single frequency reference for all devices.
• A pulse-per-second (PPS) to synchronize the sample time across devices.

The way these reference signals are provided to the devices varies.

## External PPS and 10 MHz reference signals

Most USRPs have SMA connnectors on the front- or back-panel to provide these signals (10 MHz reference and PPS). These signals could be provided by an OctoClock, an external/third-party GPSDO, a measurement device's reference outputs, or some other clock-generating device.

Connect these SMA connectors to the reference sources. In your software, select the external reference inputs as clock and time sources:

usrp->set_clock_source("external");
usrp->set_time_source("external");

Note: For users generating their own signals for the external SMA connectors, the PPS should be clocked from the 10 MHz reference. See the application notes for your device for specific signal requirements (e.g., voltage).

Note (N200/N210 and B100 only): Sometimes the delay on the PPS signal will cause it to arrive inside the timing margin of the FPGA sampling clock, causing PPS edges to be separated by less or more than 100 million cycles of the FPGA clock.

If this is the case, you can change the edge reference of the PPS signal with this parameter:

usrp->set_time_source("_external_");

## MIMO cable reference signals (N200-Series, USRP2)

Use the MIMO expansion cable to share reference sources (USRP2 and N200-Series only). The MIMO cable can be used to synchronize one device to another device. Users of the MIMO cable may use Method 1 (explained below) to synchronize multiple pairs of devices.

usrp->set_clock_source("mimo");
usrp->set_time_source("mimo");

# Synchronizing the Device Time

The purpose of the PPS signal is to synchronously latch a time into the device. You can use the uhd::usrp::multi_usrp::set_time_next_pps() function to either initialize the sample time to 0 or an absolute time, such as GPS time or UTC time. For the purposes of synchronizing devices, it doesn't matter what time you initialize to when using uhd::usrp::multi_usrp::set_time_next_pps().

## Method 1 - poll the USRP time registers

One way to initialize the PPS edge is to poll the "last PPS" time from the USRP device. When the last PPS time increments, the user can determine that a PPS has occurred:

const uhd::time_spec_t last_pps_time = usrp->get_time_last_pps();
while (last_pps_time == usrp->get_time_last_pps()){
//sleep 100 milliseconds (give or take)
}
// This command will be processed fairly soon after the last PPS edge:
usrp->set_time_next_pps(uhd::time_spec_t(0.0));

## Method 2 - query the GPSDO for seconds

Most GPSDOs can be configured to output a NMEA string over the serial port once every PPS. The user can wait for this string to determine the PPS edge, and the user can also parse this string to determine GPS time:

//call user's function to wait for NMEA message...
usrp->set_time_next_pps(uhd::time_spec_t(0.0));
-- OR --
//call user's function to wait for NMEA message...
//call user's function to parse the NMEA message...
gps_time = VALUE_IN_NMEA_MESSAGE;
// At the next PPS edge, set the device time to the GPS time:
usrp->set_time_next_pps(uhd::time_spec_t(gps_time+1));
// Now the device time should be in sync with the GPS time.

Take a look at the sync_to_gps example for more detail.

## Method 3 - MIMO cable

Note: This only applies to USRP2 and N200/N210. This method does not require a separate PPS input to the devices, but it is limited to a total of 2 USRPs.

A USRP2 device can synchronize its time to another USRP device via the MIMO cable. Unlike the other methods, this does not use a real "pulse per second". Rather, the USRP device sends an encoded time message over the MIMO cable. The slave device will automatically synchronize to the time on the master device. See Using the MIMO Cable for more detail.

# Synchronizing Channel Phase

## Align CORDICs in the DSP

In order to achieve phase alignment between USRP devices, the CORDICS in both devices must be aligned with respect to each other. This is easily achieved by issuing stream commands with a time spec property, which instructs the streaming to begin at a specified time. Since the devices are already synchronized via the 10 MHz and PPS inputs, the streaming will start at exactly the same time on both devices. The CORDICs are reset at each start-of-burst command, so users should ensure that every start-of-burst also has a time spec set.

For receive, a burst is started when the user issues a stream command. This stream command should have a time spec set:

stream_cmd.num_samps = samps_to_recv;
stream_cmd.stream_now = false;
stream_cmd.time_spec = time_to_recv;
usrp->issue_stream_cmd(stream_cmd);

For transmit, a burst is started when the user calls send(). The metadata should have a time spec set: :

md.start_of_burst = true;
md.end_of_burst = false;
md.has_time_spec = true;
md.time_spec = time_to_send;
//send a single packet
size_t num_tx_samps = tx_streamer->send(buffs, samps_to_send, md);

## Align LOs in the front-end (SBX, UBX)

Using timed commands, multiple frontends can be tuned at a specific time. This timed-tuning ensures that the phase offsets between VCO/PLL chains will remain constant after each re-tune. See notes below:

• Phase synchronization with the UBX is only supported on the X3x0 Series
• Phase synchronization with the SBX works on both N2x0 and X3x0 Series
• There is a random phase offset between any two frontends
• This phase offset is different for different LO frequencies
• This phase offset remains constant after retuning
• This phase offset will drift over time due to thermal and other characteristics
• Periodic calibration will be necessary for phase-coherent applications

Code snippet example, tuning with timed commands:

//we will tune the frontends in 100ms from now
uhd::time_spec_t cmd_time = usrp->get_time_now() + uhd::time_spec_t(0.1);
//sets command time on all devices
//the next commands are all timed
usrp->set_command_time(cmd_time);
//tune channel 0 and channel 1
usrp->set_rx_freq(1.03e9, 0); // Channel 0
usrp->set_rx_freq(1.03e9, 1); // Channel 1
//end timed commands
usrp->clear_command_time();

## Align LOs in the front-end (others)

After tuning the RF front-ends, each local oscillator may have a random phase offset due to the dividers in the VCO/PLL chains. This offset will remain constant after the device has been initialized, and will remain constant until the device is closed or re-tuned. This phase offset is typically removed by the user in MIMO applications, using a training sequence to estimate the offset. It will be necessary to re-align the LOs after each tune command.


text:
Notebook

# Momentum Strategies¶

By <NAME>" Nitishinskaya and <NAME>. Algorithms by <NAME>.

Momentum trading refers to a general class of strategies which extrapolate from existing trends. They assume that stocks which are going up will continue to go up and stocks which are going down will continue going down, and buy and sell accordingly. This is in contrast to mean-reversion strategies, which rely on trends reversing direction.

For instance, below we see the price of an asset fluctuating but overall going up.

In [1]:
# Import libraries to find linear trend and plot data
from statsmodels import regression
import statsmodels.api as sm
import scipy.stats as stats
import scipy.spatial.distance as distance
import matplotlib.pyplot as plt
import pandas as pd
import numpy as np

In [2]:
# Load pricing data for an asset
start = '2014-01-01'
end = '2015-01-01'
asset = get_pricing('XLY', fields='price', start_date=start, end_date=end)
dates = asset.index

# Plot the price of the asset over time
_, ax = plt.subplots()
ax.plot(asset)
ticks = ax.get_xticks()
ax.set_xticklabels([dates[i].date() for i in ticks[:-1]]) # Label x-axis with dates

# Find the line of best fit to illustrate the trend
X = np.arange(len(asset))
x = sm.add_constant(X) # Add a column of ones so that line can have a y-intercept
model = regression.linear_model.OLS(asset, x).fit()
a = model.params[0] # Get coefficients of line
b = model.params[1]
Y_hat = X * b + a
plt.plot(X, Y_hat, 'r', alpha=0.9);
plt.ylabel('Price')
plt.legend(['XLY', 'Trendline']);

The hypothesis here is that the motion of the stock is based on some upwards trend, captured by the linear model, plus some random noise.

In [3]:
# Load pricing data for an asset
start = '2015-01-01'
end = '2015-06-01'
asset = get_pricing('XLY', fields='price', start_date=start, end_date=end)
dates = asset.index

# Plot the price of the asset over time
_, ax = plt.subplots()
ax.plot(asset)
ticks = ax.get_xticks()
ax.set_xticklabels([dates[i].date() for i in ticks[:-1]]) # Label x-axis with dates

# Find the line of best fit to illustrate the trend
X = np.arange(len(asset))
x = sm.add_constant(X) # Add a column of ones so that line can have a y-intercept
model = regression.linear_model.OLS(asset, x).fit()
a = model.params[0] # Get coefficients of line
b = model.params[1]
Y_hat = X * b + a
plt.plot(X, Y_hat, 'r', alpha=0.9);
plt.ylabel('Price')
plt.legend(['XLY', 'Trendline']);

## Momentum and Auto-Correlation¶

Many things in finance are autocorrelated. An intuitive explanation for this is that prices are determined by traders, which take into account past prices when determining new ones. The formula might be

$$P_t = T_t + \epsilon$$$$T_t = X + P_{1, t-1}$$$$P_t = X + P_{1, t-1} + \epsilon$$

Where X covers all the other factors traders consider and $\epsilon$ is random noise. This is the definition of an autocorrelated series, in which the value at time $t$ depends on previous values.

Some forms of autocorrelation will not exhibit momentum behavior. For instance, a very simple autocorrelation relation could be as follows.

In [4]:
def generate_autocorrelated_values(N):
X = np.zeros(N)
for i in range(N-1):
X[i+1] = X[i] + np.random.normal(0, 1)
return X

for i in range(10):
X = generate_autocorrelated_values(100)
plt.plot(X)
plt.xlabel('$t$')
plt.ylabel('$X_t$');

These series will not exhibit momentum behavior, as the amount they go up and down each timestep is purely random. However, if the series' returns are autocorrelated, then we will see momentum behavior. We can simulate this as follows.

In [5]:
def generate_autocorrelated_values(N):
X = np.zeros(N)
for i in range(1, N-1):
# Do the past returns 'look good' to investors
past_returns = X[i] - X[i-1]
# Investors hypothesize that future returns will be equal to past returns and buy at that price
X[i+1] = X[i] + past_returns + np.random.normal(0, 1)
return X

for i in range(10):
X = generate_autocorrelated_values(10)
plt.plot(X)
plt.xlabel('$t$')
plt.ylabel('$X_t$');

It's now clear to see that if investors incorporate information about past returns into the future price, we will see momentum behavior. Obviously in real data this will be far more noisy and difficult to observe.

### Testing for Autocorrelation¶

We can test for autocorrelation in a few ways. One is by checking for a unit root. If the series has a unit root, we should be worried that there is autocorrelation present.

In [6]:
from statsmodels.tsa.stattools import adfuller

X1 = generate_autocorrelated_values(100)
X2 = np.random.normal(0, 1, 100)

# Compute the p-value of the Dickey-Fuller statistic to test the null hypothesis that yw has a unit root
print 'X1'
_, pvalue, _, _, _, _ = adfuller(X1)
if pvalue > 0.05:
print 'We cannot reject the null hypothesis that the series has a unit root.'
else:
print 'We reject the null hypothesis that the series has a unit root.'
print 'X2'
_, pvalue, _, _, _, _ = adfuller(X2)
if pvalue > 0.05:
print 'We cannot reject the null hypothesis that the series has a unit root.'
else:
print 'We reject the null hypothesis that the series has a unit root.'

X1
We cannot reject the null hypothesis that the series has a unit root.
X2
We reject the null hypothesis that the series has a unit root.

## Momentum vs. Mean Reversion¶

Momentum and mean reversion are in a sense opposite strategies. In a momentum model one hypothesizes that past upwards movement is indicative of future upwards movement. In a mean reversion model one hypothesizes that past upward trends are simply temporary overvaluings and the price will return to normal. Both are important models that work in different cases.

It is important to check for which kind of behavior might be present in your data before you actually try developing a strategy based on that.

### Time Frame is Important¶

Momentum behavior and mean reversion behavior can both occur in the same asset. Take for example XLY again. We can see a trend upwards, but there is also movement around that trend. One approach could be to buy an hold XLY and attempt to make money on the longer timeframe. Another approach would be to buy XLY whenever it went under the trendline and sell it whenever it was beneath. This strategy would work on shorter timeframes.

In [7]:
# Load pricing data for an asset
start = '2014-01-01'
end = '2015-01-01'
asset = get_pricing('XLY', fields='price', start_date=start, end_date=end)
dates = asset.index

# Plot the price of the asset over time
_, ax = plt.subplots()
ax.plot(asset)
ticks = ax.get_xticks()
ax.set_xticklabels([dates[i].date() for i in ticks[:-1]]) # Label x-axis with dates

# Find the line of best fit to illustrate the trend
X = np.arange(len(asset))
x = sm.add_constant(X) # Add a column of ones so that line can have a y-intercept
model = regression.linear_model.OLS(asset, x).fit()
a = model.params[0] # Get coefficients of line
b = model.params[1]
Y_hat = X * b + a
plt.plot(X, Y_hat, 'r', alpha=0.9);
plt.ylabel('Price')
plt.legend(['XLY', 'Trendline']);

To see how a mean reversion signal might look, let's look at the difference between the asset and the prediction. Sure enough, looks like some good opportunity for mean reversion as the price difference crosses the zero line many times.

In [8]:
plt.plot(asset - Y_hat)
plt.hlines(np.mean(asset - Y_hat), 0, 300, colors='r')
plt.hlines(np.std(asset - Y_hat), 0, 300, colors='r', linestyles='dashed')
plt.hlines(-np.std(asset - Y_hat), 0, 300, colors='r', linestyles='dashed')
plt.xlabel('Time')
plt.ylabel('Dollar Difference');

### Time Frame is Important for Predictive Capacity¶

Each momentum measure will be predictive over different time horizons. Some over years and some over days. This will also be true of different asset classes. Some asset classes have momentum over years and some over days. It is important, when constructing a momentum model, to keep in mind what time frame makes sense. That time frame should be roughly the time frame on which you rebalance/exit the trade. It should also be the time frame you use when measuring predictive capacity of your model.

### IMPORTANT: Model Selection¶

It is important not to fall prey to statistical biases by throwing a lot of models at a dataset and seeing which fit. To understand why this is true, see other lectures in the series, especially The Dangers of Overfitting. In short, if you throw a lot of models at a dataset, one will likely happen to look good based on random chance. This model will not have predictive power on any new data, just the data you've already seen.

A better approach is to let your model creation be driven by underlying things you know to be true about your data. For instance, here is a good development path:

1. Hypothesize that based on investor psychology, certain stocks should exhibit momentum behavior.
2. Construct a mathemtical model that follows this hypothesis.
3. Test your hypothesis by seeing if that model fits your data well.
4. Test your model out of sample on new data you've never seen before.

### Measuring Momentum¶

To trade on momentum, we must first be able to measure it. For information on how to measure momentum, please see the Measuring Momentum lecture. Various ways to quantify momentum will be discussed there. We will discuss what you might do once you have developed a measure of momentum here.

All following examples will assume that a good measure of momentum $p$, has been developed. The notation $p(A_t)$ will denote the momentum of asset $A$ and time $t$.

### Entry and Exit Signals¶

One way to use momentum is to have cutoffs and enter a position when momentum is significantly high, and leave it when momentum is significantly low. The can be done for shorting stocks as well if momentum is in the negative direction. Good examples of this would be moving average crossover strategies, as discussed in the Measuing Momentum lecture.

### Ranking Stocks for Long-Short Baskets¶

Another approach is to use momentum as a factor for ranking stocks. The general approach and its benefits are descrbed in the Long-Short Equity and Ranking Universes by Factors lectures. In short, you make a bet that stocks with higher momentum will outperform those with lower momentum. This tends to be more market neutral and robust. Momentum could also be used as one of many factors in a ranking scheme.

#### Cross-Sectional Momentum¶

Cross sectional momentum is when rather than looking at absolute momentum, you look at momentum of every stock relative to every other stock. This has the advantage of providing a relative scale, rather than a somewhat meaningless absolute measure of momentum. An example of this can be found in the algorithm associated with this lecture. To access it, go to the lectures page, hover over this lecture, and click "Get Backtest."

This presentation is for informational purposes only and does not constitute an offer to sell, a solicitation to buy, or a recommendation for any security; nor does it constitute an offer to provide investment advisory or other services by Quantopian, Inc. ("Quantopian"). Nothing contained herein constitutes investment advice or offers any opinion with respect to the suitability of any security, and any views expressed herein should not be taken as advice to buy, sell, or hold any security or as an endorsement of any security or company. In preparing the information contained herein, Quantopian, Inc. has not taken into account the investment needs, objectives, and financial circumstances of any particular investor. Any views expressed and data illustrated herein were prepared based upon information, believed to be reliable, available to Quantopian, Inc. at the time of publication. Quantopian makes no guarantees as to their accuracy or completeness. All information is subject to change and may quickly become unreliable for various reasons, including changes in market conditions or economic circumstances.


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# A charge of 18 C passes through a circuit every 2 s. If the circuit can generate 24 W of power, what is the circuit's resistance?

Jun 10, 2017

The resistance is $= 0.296 \Omega$

#### Explanation:

The charge is related to the time and the current by the

$Q = I t$^2=

The charge is $Q = 18 C$

The time is $t = 2 s$

The current is $I = \frac{Q}{t} = \frac{18}{2} = 9 A$

The power is

$P = U I$

But Ohm's Law states that

$U = R I$

So,

$P = R {I}^{2}$

Therefore,

$R = \frac{P}{I} ^ 2 = \frac{24}{9} ^ 2 = 0.296 \Omega$


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Approximation algorithms for multi-criteria traveling salesman problems

<NAME>. and <NAME>. (2009) Approximation algorithms for multi-criteria traveling salesman problems. Algorithmica, 53 (1). pp. 69-88. ISSN 0178-4617

 PDF Restricted to UT campus only : Request a copy514kB
 Abstract: We analyze approximation algorithms for several variants of the traveling salesman problem with multiple objective functions. First, we consider the symmetric TSP (STSP) with -triangle inequality. For this problem, we present a deterministic polynomial-time algorithm that achieves an approximation ratio of and a randomized approximation algorithm that achieves a ratio of . In particular, we obtain a approximation for multi-criteria metric STSP. Then we show that multi-criteria cycle cover problems admit fully polynomial-time randomized approximation schemes. Based on these schemes, we present randomized approximation algorithms for STSP with -triangle inequality ratio ), asymmetric TSP (ATSP) with -triangle inequality (ratio ), STSP with weights one and two (ratio 4/3) and ATSP with weights one and two (ratio 3/2). Item Type: Article Faculty: Electrical Engineering, Mathematics and Computer Science (EEMCS) Research Group: Link to this item: http://purl.utwente.nl/publications/68059 Official URL: http://dx.doi.org/10.1007/s00453-007-9011-z Export this item as: BibTeXEndNoteHTML CitationReference Manager

Repository Staff Only: item control page


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# Is there a Dupire's Formula for put options?

Generally, Dupire's formula is taking derivatives on the call option prices. Here it only uses information of the call options.

If now we have the data including both call and put options, is there a mathematical formula using all the information? Or is there a corresponding Dupire's formula for put options?

• Just transform your puts into calls using the put-call parity?
– Alex
Nov 20 '20 at 8:39

It depends what you exactly call Dupire's formula. If you take the original formula, valid under zero interest rates and dividends (or equivalently, considering undiscounted option prices on the forwards), which reads $$\sigma_L^2 = 2 \frac{ \frac{\partial C}{\partial T} }{K^2 \frac{\partial^2 C}{\partial K^2}}\,.$$

Then the formula for a put is the same, as the implied density is the same: $$\frac{\partial^2 C}{\partial K^2} = \frac{\partial^2 P}{\partial K^2}$$. Using the Put-Call parity formula $$C-P = F-K$$, which also allows to derive the equations in the more general case, we obtain

$$\sigma_L^2 = 2 \frac{ \frac{\partial P}{\partial T} }{K^2 \frac{\partial^2 P}{\partial K^2}}\,.$$


text:
# A Shopkeeper Sells One Transistor for ₹ 840 at a Gain of 20% and Another for ₹ 960 at a Loss of 4%. His Total Gain Or Loss Percent is - Mathematics

MCQ

A shopkeeper sells one transistor for ₹ 840 at a gain of 20% and another for ₹ 960 at a loss of 4%. His total gain or loss percent is

#### Options

• 5 15/17% loss

• 5 15/17% gain

• 6 2/3% gain

• None of these

#### Solution

5 15/17% gain

Explanation :

SP of first transistor = ₹ 840

Gain % = 20%

∴ CP of the first transistor = 100/(100 + 20) xx 840

= 100/120 xx 840 = ₹ 700

Again, SP of the second transistor = 960

Loss % = 4%

∴ CP of the second transistor = 100/(100 - 4%) xx 960

= 100/96 xx 960 = ₹ 1000

∴ Total SP = 840 + 960 = ₹ 1800

And total CP = 700 + 1000 = ₹ 1700

Hence, gain % = (1800 - 1700)/1700 xx 100

= 100/17 = 5 15/17%

Concept: Profit and Loss (Entrance Exam)
Is there an error in this question or solution?


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Home > Standard Deviation > Standard Error N 1

# Standard Error N 1

## Contents

It is about computing population variance; with N and N-1. If you simply want to quantify the variation in a particular set of data, and don't plan to extrapolate to make wider conclusions, then you can compute the SD using n Especially when it's not necessary. There actually is a good reason not to. http://comunidadwindows.org/standard-deviation/standard-error-of-estimate-standard-deviation-of-residuals.php

A quantitative measure of uncertainty is reported: a margin of error of 2%, or a confidence interval of 18 to 22. For a Gaussian distribution, this will be of the form of a constant raised to the negative power of the square of the ratio of the difference of the value from You should always use N-1. Longer Explanation For this, one has to go back two levels: back beyond the use of standard deviation and the derivation of the formulae and think why it is used at http://stats.stackexchange.com/questions/17890/what-is-the-difference-between-n-and-n-1-in-calculating-population-variance

## What Does N-1 Mean In Statistics

From measurements we don't have the distribution, only n values sampled randomly from in the distribution. So, we expect that the biased estimator underestimates σ2 by σ2/n, and so the biased estimator = (1−1/n)×the unbiased estimator = (n−1)/n×the unbiased estimator. Generate a modulo rosace Trick or Treat polyglot DDoS: Why not block originating IP addresses? And how do we denote any calculate variance for a population?

So the way I drew it --and I'm not going to calculate exactly-- it looks like the mean might sit some place roughly right over here. Please help to improve this article by introducing more precise citations. (November 2010) (Learn how and when to remove this template message) In statistics, Bessel's correction, is the use of n−1 The corrected estimator often has a higher mean squared error (MSE) than the uncorrected estimator. What Does N 1 Mean In Standard Deviation If that means within 1 SD of the mean versus not within, whether that is true has nothing to do with taking a sample.

To generate formulae for these estimations needs some moderately involved algebra but it is simple to get an idea of what they should be. Standard Deviation N-1 Formula Unfortunately this adds nothing to other answers except a confused set of ideas, either incorrect or irrelevant. –<NAME> Apr 7 at 1:41 add a comment| protected by <NAME> Apr And here is some data here. check over here This is my number line.

Stat. Bessel's Correction Proof From there, however, it's a small step to a deeper understanding of degrees of freedom in linear models (i.e. It only makes sense to use n in the denominator when there is no sampling from a population, there is no desire to make general conclusions. share|improve this answer answered Aug 28 '15 at 15:28 Mark L.

## Standard Deviation N-1 Formula

The optimal value depends on excess kurtosis, as discussed in mean squared error: variance; for the normal distribution this is optimized by dividing by n+1 (instead of n−1 or n). http://duramecho.com/Misc/WhyMinusOneInSd.html Sampling from a distribution with a small standard deviation The second data set consists of the age at first marriage of 5,534 US women who responded to the National Survey of What Does N-1 Mean In Statistics The standard deviation of the age for the 16 runners is 10.23, which is somewhat greater than the true population standard deviation σ = 9.27 years. Variance Divided By N up vote 28 down vote favorite 13 I did not get the why there are N and N-1 while calculating population variance.

For example, n might be the number of cases in each condition in an experiment while N might be the number for the experiment. http://comunidadwindows.org/standard-deviation/standard-error-or-standard-deviation-on-graphs.php It is rare that the true population standard deviation is known. That is why the sum of squares of the deviations from the sample mean is too small to give an unbiased estimate of the population variance when the average of those And we essentially take every data point in our population. Standard Deviation N-1 Calculator

And having a second sample $y$ would risk to increase your variance, if $x\neq y$. Later sections will present the standard error of other statistics, such as the standard error of a proportion, the standard error of the difference of two means, the standard error of The n-1 equation is used in the common situation where you are analyzing a sample of data and wish to make more general conclusions. http://comunidadwindows.org/standard-deviation/standard-deviation-larger-than-standard-error.php Some of them quite sound, but anyway inconclusive.

Basically, you should use N-1 when you estimate a variance, and N when you compute it exactly. –ocram Nov 3 '11 at 15:10 @ocram, as far as I know Sample Variance N-1 Proof Show all the values, their shape and range. Oct 25 '10 at 14:09 8 a really elegant, intuitive explanation is presented here (below the proof) en.wikipedia.org/wiki/… The basic idea is that your observations are, naturally, going to be

## Then you will substitute that true mean into the formula for variance and apply denominator N: no "-1" is needed here since you know the true mean, you didn't estimate it

more hot questions question feed about us tour help blog chat data legal privacy policy work here advertising info mobile contact us feedback Technology Life / Arts Culture / Recreation Science So in general, when you just take your points, find the squared distance to your sample mean, which is always going to sit inside of your data even though the true For that matter, why stop there? N Minus 1 Strategy For an upcoming national election, 2000 voters are chosen at random and asked if they will vote for candidate A or candidate B.

To see why: $$E[\bar{X}] = \frac{1}{n}\sum_{i=1}^{n} E[X_i] = \frac{n}{n} \mu = \mu$$ Let us look at the expectation of the sample variance,  S^2 = \frac{1}{n-1} \sum_{i=1}^{n} (X_i^2) - Here's a book that builds it up gradually: Saville DJ, Wood GR. Python - Make (a+b)(c+d) == a*c + b*c + a*d + b*d how do I remove this old track light hanger from junction box? navigate here What is way to eat rice with hands in front of westerners such that it doesn't appear to be yucky?

The remaining 1 − 1 / n {\displaystyle 1-1/n} of the time, the value of E [ ( x u − x v ) 2 ] {\displaystyle E[(x_{u}-x_{v})^{2}]} is the expected So in this case, what would be my big N? Any way to sum-up the intuition, or is that not likely to be possible? sample $t$) must also be calculated in this way. $\sigma^2_t= \frac{\sum_{i}^{n}(X_i-\overline{X})^2}{n}$ where $\overline{X}$ is the mean and $n$ is the size of this small population.


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# Towards Representation Learning for an Image Retrieval Task

This report explains self-supervised and regularized supervised image retrieval with the help of the latent space of an autoencoder.
<NAME>

## Introduction

In an image retrieval task, there are two fundamental units: image repository, and query image. Simply put, an image repository is a collection of images. A query image is a reference used to retrieve other images from the repository that are perceptually close to it. Image retrieval's task is to rank images in an index set with respect to their relevance to a query image.

In this report, we approach the image retrieval problem from an unsupervised perspective. The foundation of our work lies in the latent space representation of the images learned through a self-supervised learning task. The goal here is to capture the latent space embeddings of images and then try to determine the distance among them in the latent space. With this approach, we are focussing on the perceptual realm of an image. We validate the quality of the learned representations through a Clustering task and measure its performance through the normalized mutual information score & rand index. Then we identify the issues in learning in a purely unsupervised scenario (link) and show the enhancement in the information content of the learned representations with a hint of supervision. We train a regularised autoencoder with the supervised information. We validate the performance in a retrieval framework for the test set.

## Methodology

There are two parts to an autoencoder, the encoder, and the decoder. The encoder compresses (encodes) the input image into embeddings. The bottleneck of an autoencoder gives rise to the latent space. On the other hand, the decoder tries to learn from these embeddings and recreate the input image. In the process, the embeddings are knocked on and off to become the low dimensional representation of the high dimensional images. To know more about autoencoders, one can quickly glance through this report.

In the training phase, we use autoencoders to compress high dimensional image representation to latent space embedding. These embeddings can be thought of as points in the latent space. These embeddings are then clustered together by the k-means algorithm. After training, we have a repository of embeddings that are clustered in the latent space.

In the testing phase, we first acquire the latent space embedding of our query image. With the query embedding, we predict the cluster to which it belongs. We extract all the image embeddings from the repo that fall in that cluster. After we have all the image embeddings, we calculate the euclidean distance of each image embedding to the query embedding. The lesser the distance, the similar the images are.

Upon giving this process, some thought this turns out to be logical. The embeddings represent images in a vector space. Moreover, they represent abstract features of the images. They need to be distinct for individual classes, and similar to similar classes. Here in this report, we take note that the autoencoder learns neat representations in the latent space.

## Metrics

We consider different metrics to assess the quality of the feature transformation and its impact on clustering the data.

### Rand index

$RI=\frac{TP + TN}{TP + FP + FN + TN}$

where TP, TN, FP, and FN denote true positive, true negative, false positive, and false-negative prediction of cluster labels with respect to the ground truth class label information available on the data points. The measure RI is a pair-counting measure assuming values in the interval $[0,1]$ and it tends to show higher values for equal-sized big clusters

### Normalized Mutual Information :

The measure Normalized Mutual Information (NMI) is given by

$NMI=I_{kk*}(I_{k}I_{k*})^{-1/2}$

where,

$I_{kk*}=\sum_{j=1}^k\sum_{j'=1}^{k^*}N_{jj'}log\frac{NN_{jj'}}{N_{j}N_{j'}}$

$I_{k}=\sum_{j=1}^{k}N_j\log\frac{N_j}{N}$

$I_{k*}=\sum_{j'=1}^{k^*}N_j\log\frac{N_{j'}}{N}$

denotes the total number of observations in the dataset, and the true number of clusters and the number of clusters derived are given by respectively $k^*$ and $k$. Here $N_{jj'}$ denotes the number of agreements between the cluster $j$ and true class $j'$. The number of observations in cluster $j$ and true class $j'$ are given by $N_{j}$ and $N_{j'}$ respectively. NMI is a measure based on mutual information between the true data partition and the obtained clusters. NMI can have higher values for unequal sized clusters, especially in the presence of multiple smaller clusters. It also assumes values in the interval $[0,1]$ and higher values suggest better data clusters.

## Experiments

As the foundations have already been laid, we need to know how the experiments are done. There are two experiments, one with a vanilla autoencoder and another an autoencoder with a hint of supervision. With the vanilla autoencoder, we solely extract the embeddings from the bottleneck and then proceed with the clustering. With the second approach, we apply a classification head to the bottleneck and train both the autoencoder and the classifier. The goal here is to optimize the two objectives jointly. While the autoencoder learns about the image as a whole, the classifier provides information about which image belongs to which class. This way, the embeddings of similar classes flock together. As we will see later in the report, the two objectives work against each other. Here the embeddings not only represent images but also align themselves in clusters. The added advantage with this method is that the model learns in a regularized supervised environment, which adds to the generalisability of the learned representation.

### Dataset

For our experiments, we are using the CIFAR-10 dataset. The dataset consists of 60,000 images (50,000 train and 10,000 tests) with 10 classes. The images are of dimension (32,32,3), which is the height width and channel, respectively. As this is going to be an image retrieval task, we have decided to use a bigger training dataset.

The dataset that we decided upon has the following dimensions:

X_train shape: (57000, 32, 32, 3)

y_train shape: (57000, 1)

X_test shape: (3000, 32, 32, 3)

y_test shape: (3000, 1)

The dataset is equally distributed among its classes. There are 10 classes shown below.

## Vanilla Autoencoder

In the autoencoder, we have used blocks of $Conv-BatchNorm-ReLU$. In the encoder, these blocks are followed by $MaxPooling$ layers. In the decoder, these blocks are preceded by $UpSampling$ layers. The last $Conv$ layer in the encoder is the bottleneck, and the output of this is used as our latent space embeddings.

A vanilla autoencoder is used on the training data. The model uses the Adam optimizer with default parameter settings. The loss is the mean squared error between the input image and the reconstructed image. The loss, in this case, is self-supervised as we have not used any label information.

### The Reconstruction

One can see from the reconstructions of test images that the autoencoder did well. We can now say that the latent space has indeed learned the representation of the images.

Original Images (TEST) Reconstruction of the Images

### t-SNE of the Embeddings

t-SNE is a powerful dimensionality reduction tool. It reduces the dimensions of a dataset to 2 or 3 dims, maintaining the distance of the points. After the training is over, the trained images are sent through the model in a forward pass,and the embeddings are extracted. t-SNE on the embeddings are plotted and are analyzed too. The motive behind us plotting the t-SNE was to keep a sanity check on our thought experiment. If the t-SNE were any less promising, we would have known that the clustering technique would not work.

## Section 12

### Evaluation on Clustering

The clustering process is simple, the embeddings that are extracted from the training images are applied to the k-means algorithm.

classifier = KMeans(n_clusters=10, random_state=0).fit(pred)

The classifier is the object that can be used to predict the label that another embedding belongs to.

As described above the clustering metrics are as follows:

• NMI: 0.074
• RI: 0.811

### The Final Retrieval of the Images

In this step, we use a random image from the test set and then go through the following steps:

• Extract embeddings of the test image by forward propagating it through the encoder.
• Predict the label of the cluster that the test image belongs to.
• Retrieve all the train images of the particular cluster.
• Calculate the Euclidean distance of the pair (train images, test query image).
• Sort the images and output the top 5 images with the least distance with the query image.
• Plot the result.

The test results look promising, but there is a flavor of bias since they have been trained in an unsupervised framework with no information on the label space. Though the high-confidence results seem logical, there are factors like the color that affects the representations which, in turn, retrieved back to certain irrelevant images for the given query.

## Autoencoders with a Hint of Supervision

In this method, the autoencoder remains the same. That is to say, the architecture and the configuration are the same. The only change that is made is an addition of a classification head to the bottleneck. Tying a classifier to the bottleneck has its pros and cons. Now, the latent space embeddings are backpropagated not only with the loss of the autoencoder but also with the classification's loss. Here we are not only instructing the embeddings to pick up the representation of the images but also providing the information of classes so that similar images flock together in the embedding space.

### The Reconstruction

Here we notice something brilliant. The reconstructions are not that good as with a vanilla autoencoder. This means that the classification head is interfering with the embeddings. Come to think of it, both the objectives (reconstruction and classification) are fighting against each other in the process. This leads to a more inferior reconstruction but a better latent space alignment, as is shown later in the report.

Original images (TEST) Reconstruction of the images

### t-SNE of Embeddings

The purpose of t-Sne has already been laid out; let's look at the plot.

## Section 8

### The Evaluation on the Clustering

In this section, we compare the two approaches from a clustering perspective since our primary intent is image retrieval.

Models NMI RI
Vanilla Autoencoder 0.074 0.811
Autoencoder with a hint of supervision 0.433 0.876

The NMI and RI seem to increase significantly with the addition of the classification head. This also directs us towards the fact that the representation learned is much more informative and has the contextual information in the second case.

### The Final Retrieval of the Images

The process of image retrieval has already been discussed. Here we look at the results with the new representations learned with a hint of supervision.

The retrievals are much better in terms of perceptual closeness. The color bias seems to go down while the similar images clutter together. The addition of a single classification head indeed has boosted our performance in the image retrieval task.

## Conclusion

This report came into existence due to human thoughts and the will to collaborate. This report talks about representation learning from an image retrieval mechanism in an unsupervised framework and then with a hint of supervision. We showed how representations learned in an unsupervised framework contain particular bias/sensitivity towards specific attributes, which affects the quality of the same. Whereas, we also demonstrate that by adding a sense of supervision to the framework, the representations learned are much more informative and meaningful. The same theory has been illustrated in a simple image retrieval framework to understand the enhancements.

Another critical point to highlight is that the approach does not talk about the state of the art methods to retrieve images. The primary purpose was to understand the quality of the representations learned in both the scenarios and how specific unwanted attribution effects can be removed using a hint of supervision in the system. We would love to know more from the reader. You can reach both of us via twitter.

References :

[1]. The blog 'Keras: Multiple outputs and multiple losses' by <NAME> gives a brilliant illustration of Multiple output classification with Multiple loss functions

[2]. The blog 'Risks and Caution on applying PCA for Supervised Learning Problems' by <NAME>, <NAME>, <NAME> explains a very crucial problem of using Projections in Unsupervised frameworks.


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# What is the number of real roots of the polynomial?

What is the number of real roots of the polynomial $3s^{3}+10s^{2}+14s+8$?

-
What have you tried? Do you have any work to show us? –  anorton Dec 10 '12 at 15:40
You'll get more joy if you show some attempt at answering the question for yourself and indicating where you are stuck! –  Epictetus Dec 10 '12 at 15:45
One.$\mbox{}\mbox{}$. –  Dirk Dec 10 '12 at 15:46
Such questions get quicker (i.e. almost immediate) answers if you ask Wolfram Alpha instead of your fellow human beings. –  MvG Dec 10 '12 at 16:06

As polynomial of odd degree, it has at least one real root.

Between any two real roots of $f$ there is a real root of $f'(x)=9s^2+20s+14$. Since the roots of this are not real (namely $\frac{-20\pm\sqrt{-484}}{18}$), there are no additional real roots.

-

Hint:

$3s^3+10s^2+14s+8=(3s^3+6s^2+6s)+(4s^2+8s+8)=(3s+4)(s^2+2s+2)$

-

Let $f(s) = 3s^3 + 10s^2 +14s + 8$. Since the degree of $f$ is $3$ (being odd), you know that there is at least one real root.

Then note that $f'(s) = 9s^2 + 20s + 14$. If you have two real roots, then there would (by the Mean Value Theorem) be some $c$ such that $f'(c) = 0$. But you might be able to show that the equation $f'(s) = 0$ has no real solution.

-
Why the downvote? –  <NAME> 10 '12 at 15:52

Your polynomial factors: $(3s+4)(s^2+2s+2)$. Also $s^2+2s+2=(s+1)^2+1>0$ for all $s$.

So there is only one real root: -4/3.

-

Let $f(s)=3s^3+10s^2+14s+8,$ then $$f^\prime (s)=9s^2+20s+14=(3s)^2+2.3s.(10/3)+(10/3)^2+(14-100/9)$$ So $f^\prime(s)=(3s+10/3)^2+26/9\geq 26/9>0$, hence $f$ is strictly increasing and has atmost one root. Now $f(-2)<0$ and $f(0)>0$ and so $f(s)$ has exactly one real root between $0$ and $2$.

-

To throw another answer into the pot: The discriminant of the given polynomial is $-400$. But the discriminant of any polynomial with all real roots must be nonnegative.

-

At most there is $n$ roots for a $n$-degree polynomial. That is it! For your question you can use the Cardan method. See http://en.wikipedia.org/wiki/Cubic_function

The solution of a third-order algebraic equation of the form $x³+Ax²+Bx+C=0$. By setting $x=((-A)/3)+w$, we have: $w³+Pw+Q=0$, where $P=((-A²)/3)+B$ and $Q=((2A³)/(27))-((AB)/3)+C$. If we set $Δ=4P³+27Q²$, then if $Δ>0$, there is a unique negative real solution:

$x=-(A/3)+(-(Q/2)+√(((Q²)/2)+((P³)/(27))))^{(1/3)}+(-(Q/2)-√(((Q²)/2)+((P³)/(27))))^{(1/3)}$,

and if $Δ<0$, there are three real solutions:

$x₁=-(A/3)+2√(-(P/3))sin((θ/3))$

$x₂=-(A/3)+2√(-(P/3))sin(((θ+2π)/3))$

$x₃=-(A/3)+2√(-(P/3))sin(((θ+4π)/3))$

where

$θ=arcsin(√(((-27Q²)/(4P³))))∈[0,π]$.

The case $Δ=0$ corresponds to a measure-zero set of parameters. Therefore, by a slight perturbation of parameters, without changing the behavior of the system, a system belonging to one of the two cases is obtained.

-
You can calculate the descriminant. If it is negative then there is three real roots. If it is positive, then there is one real root and two complex roots. –  user39552 Dec 10 '12 at 16:22
@Riemann: I think that you mean: If it is positive then there are three distinct real roots.. –  Thomas Dec 10 '12 at 16:30
No, I mean the negative case. See the Cardan method. –  user39552 Dec 10 '12 at 16:32
@Riemann: Ok, there is also another notion of a discriminant: en.wikipedia.org/wiki/Discriminant –  Thomas Dec 10 '12 at 16:41