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On the Elliptical Orbit of the Earth and Position of the Sun in the Sky: An Engineering Approach
On the Elliptical Orbit of the Earth and Position of the Sun in the Sky: An Engineering Approach
The position of the Sun as seen by an observer on the Earth’s surface and the position and velocity vectors of the Earth revolving in an elliptical orbit around the Sun can be calculated using
several computational approaches. These approaches include (but are not limited to) the use of an analytical approach; a numerical approach, and the use of a Solar Position Algorithm (PSA). In the
analytical methodology, the Earth’s momentum equation is transformed to eliminate its time dependence, and the equation is solved analytically. Whereas, using the numerical approach, the
dimensionless momentum equation of the revolving Earth is written in the polar coordinate system (r, θ) and solved numerically. The solar position algorithm known as PSA (Plataforma Solar de Almeria,
abbreviated from its Spanish origin: https://www.psa.es), is a numerical algorithm that uses several empirical relations to calculate the solar declination and the ecliptic longitude angles, etc. The
algorithm uses Cartesian coordinate system to calculate the dimensionless coordinates of the pole star (Polaris) and its declination angle to calculate the position vector of an observer that rotates
with the Earth. This coordinate system is referred to as a new Cartesian coordinate system whose origin is located at the center of the Earth. The solar elevation angle and azimuth angle are obtained
by performing a set of rotations of this new Cartesian coordinate system. In this article, we have used basic physical principles (analytical approach) to obtain the main parameters of the Sun’s
trajectory and position, at certain time in the sky. The methodology presented here can easily be used by professionals and engineers working in the area of solar/alternate energy, as well as for the
design of intelligent/green buildings/cities for a sustainable environment.
A.B. Sproul, “Derivation of the solar geometric relationships using vector analysis,” Renewable Energy, Vol. 32, pp. 1187–1205, 2007.
A. Jenkins, “The Sun’s position in the sky,” Eur. J. Phys., Vol. 34, pp. 633–652, 2013.
V. Khavrus and I. Shelevytsky, “Introduction to solar motion geometry based on a simple model,” Phys. Ed., Vol. 45, pp. 641–653, 2010.
M. Blanco-Muriel, D.C. Alarc´on-Padilla, T. Lopez-Moratalla, and M. Lara-Coira, “Computing the solar vector,” Solar Energy, Vol. 70, pp. 431–441, 2001.
I. Reda and A. Andreas, “Solar position algorithms for solar radiation applications” Tech. Rep. NREL/TP-560-34302, National Renewable Energy Laboratory, Golden, Colorado, USA, January 2008.
G. Prinsloo and R. Dobson, Solar Tracking. Stellenbosch: Solar Books, 2015.
National Oceanic and Atmospheric Administration, US Department of Commerce, “NOAA Solar Calculator,” assessed from the website of esrl: https://gml.noaa.gov/grad/solcalc/
How to Cite
R. Avila and S. R. Syed, “On the Elliptical Orbit of the Earth and Position of the Sun in the Sky: An Engineering Approach”, The Nucleus, vol. 61, no. 1, pp. 10–15, Jan. 2024. | {"url":"http://thenucleuspak.org.pk/index.php/Nucleus/article/view/1330","timestamp":"2024-11-05T11:04:38Z","content_type":"text/html","content_length":"31656","record_id":"<urn:uuid:8a4e4f58-3e09-443b-bfd2-881a2eb5926d>","cc-path":"CC-MAIN-2024-46/segments/1730477027878.78/warc/CC-MAIN-20241105083140-20241105113140-00234.warc.gz"} |
CBSE Class 10 Practice Questions 2022-23 | Download Free PDFs
An Overview of CBSE Class 10 Practice Questions 2022 to 23
As the CBSE class 10 exams for the academic year 2022-23 approach, students are gearing up for the final preparation to perform well. One of the most effective ways to prepare for the exams is by
solving CBSE Class 10 practice questions. Solving practice questions gives students an idea of the exam pattern, marking scheme, and The various kinds of questions that a student can face during the
exam. In this article, we will take a look at some of the CBSE Class 10 practice questions for different subjects.
FAQs on CBSE Class 10 Practice Questions - 2022-23
1. What is the best way to practise for CBSE Class 10 exams?
Solving CBSE Class 10 practice questions is the best way to prepare for the exams. It helps students to get an idea of the exam pattern and marking scheme.
2. Can I find CBSE Class 10 practice questions online?
Yes, there are many educational websites and online platforms, like Vedantu, that offer CBSE Class 10 practice questions for free or at a nominal cost.
3. How do CBSE Class 10 practice questions help me score better in the exams?
Solving practice questions improves your speed, accuracy, and confidence. It also helps you to identify your weak areas and work on them.
4. Are CBSE Class 10 practice questions available for all subjects?
Yes, practice questions are available for all subjects including Maths, Science, Social Science, English, Hindi, and others.
5. Can I solve CBSE Class 10 practice questions offline?
Yes, you can buy practice books from the market or download PDFs of practice questions and solve them offline. Online PDF versions are available to download from Vedantu’s website as well.
6. Can I solve CBSE Class 10 practice questions on my mobile phone?
Yes, there are many educational apps that offer CBSE Class 10 practice questions that can be solved on mobile phones.
7. How do I know if I am solving the right CBSE Class 10 practice questions?
It is important to choose practice questions from reliable sources such as CBSE's official website, reputable educational websites, like Vedantu, or practice books from renowned publishers.
8. What is the importance of solving CBSE Class 10 sample question papers?
CBSE Class 10 sample question papers give you an idea of the exam pattern, marking scheme, and the different types of questions that may come in the exam. The difficulty of questions can also be
determined in this manner.
9. How can I get help in solving CBSE Class 10 practice questions?
You can seek help from your teachers, attend coaching classes, or use online platforms like Vedantu that offer personalised guidance from experienced teachers.
10. What makes Vedantu a good platform for CBSE Class 10 practice questions?
Vedantu offers a wide range of CBSE Class 10 practice questions, personalised guidance from experienced teachers, and a comprehensive study plan to help you prepare for the exams effectively. | {"url":"https://www.vedantu.com/cbse/class-10-practice-questions-2022-23","timestamp":"2024-11-11T00:31:36Z","content_type":"text/html","content_length":"237288","record_id":"<urn:uuid:59595e97-3ad6-4d32-8385-6661678c465b>","cc-path":"CC-MAIN-2024-46/segments/1730477028202.29/warc/CC-MAIN-20241110233206-20241111023206-00457.warc.gz"} |
GATE Syllabus for Civil Engineering 2023 | PDF Access
GATE 2023 Syllabus For Civil Engineering (CE)
Civil Engineering is one of the primary subjects for GATE 2023. Candidates appearing for the Civil Engineering paper of the GATE are thus aware of the significance of the GATE Civil Syllabus 2023.
The GATE Exam Syllabus for Civil Engineering comprises the topics and concepts, based on which the questions will be asked in the exams. Knowing the GATE 2023 Syllabus For Civil Engineering (CE) will
help the students to enhance their exam preparations and will also help them plan their studies more proficiently. GATE syllabus for Civil Engineering will help the candidates to plan for their exam
preparation, in a better way, by focussing more on the area where they are weak in.
The two main sections of the GATE CE Question Paper are the General Aptitude and the Engineering Mathematics, constituting questions as per the GATE exam syllabus for civil engineering. Further
details about the Civil Engineering Exams and the GATE 2023 syllabus for Civil Engineering (CE) can be found below, in this article.
GATE Exam Syllabus for Civil Engineering
GATE 2023 syllabus for Civil Engineering (CE) consists of seven main sections. The main topics included in the GATE syllabus for Civil Engineering are Engineering Mathematics, Structural Engineering,
Geotechnical Engineering, Water Resources Engineering, Environmental Engineering, Transportation Engineering and Geomatics Engineering.
For details about the sub-topics and main topics covered under each section, do check out the PDF link provided below or browse through the information provided in the webpage.
GATE Exam Syllabus for Civil Engineering PDF Download
GATE 2023 Syllabus for Civil Engineering (CE)
SECTIONS Topics and Sub-Topics
• Linear Algebra: Matrix algebra; Systems of linear equations; Eigen values and Eigen vectors.
• Calculus: Functions of single variable; Limit, continuity and differentiability; Mean value theorems, local maxima and minima; Taylor series; Evaluation of definite and indefinite
integrals, application of definite integral to obtain area and volume; Partial derivatives; Total derivative; Gradient, Divergence and Curl, Vector identities;Directional
derivatives; Line, Surface and Volume integrals.
• Ordinary Differential Equation (ODE): First order (linear and nonlinear) equations; higher order linear equation with constant coefficients; Euler-Cauchy equations; initial and
Section 1: boundary value problems.
Engineering • Partial Differential Equation (PDE): Fourier series; separation of variables; solutions of one- dimensional diffusion equation; first and second order one-dimensional wave
Mathematics equation and two-dimensional Laplace equation.
• Probability and Statistics: Sampling theorems; Conditional probability; Descriptive statistics – Mean, median,mode and standard deviation; Random Variables – Discrete and
Continuous, Poisson and Normal Distribution;Linear regression.
• Numerical Methods: Error analysis. Numerical solutions of linear and non-linear algebraic equations; Newton’s and Lagrange polynomials; numerical differentiation; Integration by
trapezoidal and Simpson’s rule; Single and multi-step methods for first order differential equations.
• Engineering Mechanics: System of forces, free-body diagrams, equilibrium equations; Internal forces in structures; Frictions and its applications; Centre of mass; Free Vibrations
of undamped SDOF system.
• Solid Mechanics: Bending moment and shear force in statically determinate beams; Simple stress and strain relationships; Simple bending theory, flexural and shear stresses, shear
centre; Uniform torsion, Transformation of stress; buckling of column, combined and direct bending stresses.
• Structural Analysis: Statically determinate and indeterminate structures by force/ energy methods; Method of superposition; Analysis of trusses, arches, beams, cables and frames;
Section 2: • Displacement methods: Slope deflection and moment distribution methods; Influence lines; Stiffness and flexibility methods of structural analysis.
Structural • Construction Materials and Management: Construction Materials: Structural Steel – Composition, material properties and behaviour; Concrete – Constituents, mix design, short-term
Engineering and long-term properties.
• Construction Management: Types of construction projects; Project planning and network analysis – PERT and CPM; Cost estimation.
• Concrete Structures: Working stress and Limit state design concepts; Design of beams, slabs, columns; Bond and development length; Prestressed concrete beams.
• Steel Structures: Working stress and Limit state design concepts; Design of tension and compression members, beams and beam- columns, column bases; Connections – simple and
eccentric, beam-column connections, plate girders and trusses; Concept of plastic analysis – beams and frames.
• Soil Mechanics: Three-phase system and phase relationships, index properties; Unified and Indian standard soil classification system; Permeability – one dimensional flow, Seepage
through soils – two – dimensional flow, flow nets, uplift pressure, piping, capillarity, seepage force; Principle of effective stress and quicksand condition; Compaction of
soils; One- dimensional consolidation, time rate of consolidation; Shear Strength, Mohr’s circle, effective and total shear strength parameters, Stress-Strain characteristics of
Section 3: clays and sand; Stress paths.
Geotechnical • Foundation Engineering: Sub-surface investigations – Drilling bore holes, sampling, plate load test, standard penetration and cone penetration tests; Earth pressure theories –
Engineering Rankine and Coulomb; Stability of slopes –Finite and infinite slopes, Bishop’s method; Stress distribution in soils – Boussinesq’s theory; Pressure bulbs, Shallow
foundations – Terzaghi’s and Meyerhoff’s bearing capacity theories, effect of water table; Combined footing and raft foundation; Contact pressure; Settlement analysis in
sands and clays; Deep foundations – dynamic and static formulae, Axial load capacity of piles in sands and clays, pile load test, pile under lateral loading, pile group
efficiency, negative skin friction.
• Fluid Mechanics: Properties of fluids, fluid statics; Continuity, momentum and energy equations and their applications; Potential flow, Laminar and turbulent flow; Flow in pipes,
pipe networks; Concept of boundary layer and its growth; Concept of lift and drag.
• Hydraulics: Forces on immersed bodies; Flow measurement in channels and pipes; Dimensional analysis and hydraulic similitude; Channel Hydraulics – Energy-depth relationships,
Section 4: specific energy, critical flow, hydraulic jump, uniform flow, gradually varied flow and water surface profiles.
Water Resources • Hydrology: Hydrologic cycle, precipitation, evaporation, evapo-transpiration, watershed, infiltration, unit hydrographs, hydrograph analysis, reservoir capacity, flood estimation
Engineering and routing, surface run-off models, groundwater hydrology – steady state well hydraulics and aquifers; Application of Darcy’s Law.
• Irrigation: Types of irrigation systems and methods; Crop water requirements – Duty, delta, evapo-transpiration; Gravity Dams and Spillways; Lined and unlined canals, Design of
weirs on permeable foundation; cross drainage structures.
• Water and Waste Water Quality and Treatment: Basics of water quality standards – Physical, chemical and biological parameters; Water quality index; Unit processes and
operations; Water requirement; Water distribution system; Drinking water treatment.
Section 5: • Sewerage system design, quantity of domestic wastewater, primary and secondary treatment. Effluent discharge standards; Sludge disposal; Reuse of treated sewage for different
Environmental applications.
Engineering • Air Pollution: Types of pollutants, their sources and impacts, air pollution control, air quality standards, Air quality Index and limits.
• Municipal Solid Wastes:Characteristics, generation, collection and transportation of solid wastes, engineered systems for solid waste management (reuse/ recycle, energy recovery,
treatment and disposal).
• Transportation Infrastructure: Geometric design of highways – cross-sectional elements, sight distances, horizontal and vertical alignments.
• Geometric design of railway Track – Speed and Cant,
Section 6: • Concept of airport runway length, calculations and corrections; taxiway and exit taxiway design.
Transportation • Highway Pavements: Highway materials – desirable properties and tests; Desirable properties of bituminous paving mixes; Design factors for flexible and rigid pavements; Design of
Engineering flexible and rigid pavement using IRC codes.
• Traffic Engineering: Traffic studies on flow and speed, peak hour factor, accident study, statistical analysis of traffic data; Microscopic and macroscopic parameters of traffic
flow, fundamental relationships; Traffic signs; Signal design by Webster’s method; Types of intersections; Highway capacity.
Section 7: • Principles of surveying; Errors and their adjustment; Maps – scale, coordinate system; Distance and angle measurement – Levelling and trigonometric levelling; Traversing and
Geomatics triangulation survey; Total station; Horizontal and vertical curves.
Engineering • Photogrammetry and Remote Sensing – Scale, flying height; Basics of remote sensing and GIS.
GATE Civil Engineering Marking Scheme 2023
Meanwhile, below in this article please find the marking scheme for the GATE CE Exam paper. Also, see the GATE exam pattern as per the GATE Civil Engineering 2023 Syllabus and Subject marks. All
questions will be of 1 or 2 marks.
• General Aptitude(GA) of Civil Engineering(CE) – 15 Marks
• Subject Marks – 85 Marks
• Total Marks – 100 Marks
• Total Time Allotted in Minutes for the subject – 180 Minutes.
All students are advised to download the updated version of the GATE Civil Engineering Syllabus before preparing for the GATE CE Exams 2023. Also, after referring to the syllabus, students are
advised to prepare for the exams with the help of the preparation materials, GATE Civil Engineering Books, and GATE previous year question paper. Students can stay tuned to BYJU’S and access
updates regarding the GATE Exams and Resources.
Frequently Asked Questions on GATE 2023 syllabus for Civil Engineering
What are the main sections of the GATE 2023 Syllabus for Civil Engineering (CE)?
GATE Civil Engineering Syllabus 2023 includes seven main sections. They are Engineering Mathematics, Structural Engineering, Geotechnical Engineering, Water Resources Engineering, Environmental
Engineering, Transportation Engineering and Geomatics Engineering.
Which are the main topics included under the Environmental Engineering Section of the GATE Syllabus for Civil Engineering (CE)?
The main topics included under the section are Water and Waste Water Quality and Treatment, Air Pollution and Municipal Solid Wastes.
How do we access the GATE CE Syllabus 2023?
After the official release, the GATE Syllabus for Civil Engineering is available at the official website of GATE. We have also compiled the syllabus here on this page.
Also Explore, GATE 2023 | GATE Results | PSU Recruitment through GATE | GATE Virtual Calculator | GATE Mock Test | GATE Online Coaching | GATE Negative Marking | GATE Marks Vs Rank |
 GATE Cutoff | GATE Answer Key
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Indian mathematics
Indian mathematics and the numeral system is the forerunner of modern science , technology and mathematics.
We have to be grateful to the Indians for teaching us how to count without which no worthwhile scientific discovery could have been made.
-----Albert Einstein
It is a fact that before the advent of the Indian numeral system and algebra in Europe , the Roman numeral system was used , which could not have been used for cumbersome scientific calculations.
They are even today counting 1 , 2 , 3 , etc to zero, after Sanskrit figures.
It was Indian mathematics, which provided the base for the growth of European science and technology to its present standards.
If it weren't for Indian mathematics, Europe would still would have been using the Roman numeral system, and in all probability , would still have been in the Dark Ages as well.
A scientific temperament existed in India, as can be understood by this quote of the Buddha 2500 years ago ...
Believe nothing, merely because you have been told it, or because it is traditional or because you yourselves have imagined it. Do not believe what your teacher tells you merely out of respect for
your teacher. But whatever after due consideration and analysis you find to be conducive to the good , the benefit, the welfare of all beings, that doctrine , believe and cling to and take it as your
- Buddha
• 6 months later...
India's maths contribution on celluloid
Indian's contribution to the development of mathematics has largely been swept under the carpet in global history books.
But a BBC crew , led by an Oxford professor , was in the country last week to film a documentary revealing Indians created some of the most fundamental mathematical theories.
The West has always believed that Sir Isaac Newton, famous for developing the laws of gravity and motion, was the brainbox behind key branches of maths such as calculus.
In The Story of Maths, Dr Marcus Du Sautoy, a professor of mathematics at the University of Oxford, claims Indians made many of these breakthroughs before Newton was born.
The Story of Maths, a four- part series, will be screened on BBC Four in 2008. The first part looks at the development of maths in ancient Greece , ancient Egypt and Babylon; the second focuses on
India, China, and Central Asia and the rest look at how maths developed in the West. The India reel focuses on how several Indians developed theories in maths that were later discovered by Westerners
who took credit for them.
"A lot of people think maths was a Western invention," said Du Sautoy." This programme is about how a lot of things were done here in India before they were discovered in the West. So the programme
in in fact quite political because it shows how much we have ignored discoveries in the East," he said. Du Sautoys team of a director, a cameraman and a researcher left Mumbai on Monday.
In India , the team filmed on trains, inside sari stores, on the backwaters of Kerala and in rickshaws. "Its been fantastic filming in India as the visual backdrop is so rich ," Du Sautoy said.
Aryabhatta (476- 550 AD ), who calculated pi, and Brahmagupta (598-670A.D) feature in the film, which also showcases a Gwalior temple, which documents the first inscription of 'zero'.
"One of the biggest inventions in India was the number zero. Indians used it long before the West did,"said Du Sautoy. "When the West had Roman numerals there was no zero adn that is why they were so
clumsy. On the other hand, Brahmagupta was one of the key mathematicians in the world becuase he invented the idea of zero. "
The documentary also features the history of Kerala-born mathematician Madhava (1350 - 1425 )who created calculus 300 years before Newton and German mathematician Gottfried Leibniz did, said Du
Sutoy. "We learn that Newton invented the mathematical theory calculus in the 17th century but Madhava created it earlier," Du Sutoy said.
Chennai - born Srinivasa Ramanujan (1887-1920) also features in the film. He contacted English mathematician G.H.Hardy , who persuaded him to come to Cambridge . They began a collaboration between
the analytical maths of the West and the intuitive maths of India, and together produced brilliant theories and amazing results. "
It was difficult for Ramanujan to travel to Britain because he was a Brahmin and not allowed to travel by sea. "He had to almost give up his religion but maths was also like a religion to him. He had
no one to talk to in India because at that time no one was interested in his ideas, " said Du Sautoy.
• 1 year later...
The significance of the development of the positional number system is probably best described by the French mathematician Pierre Simon Laplace (1749 - 1827) who wrote:
It is India that gave us the ingenious method of expressing all numbers by the means of ten symbols, each symbol receiving a value of position, as well as an absolute value; a profound and important
idea which appears so simple to us now that we ignore its true merit, but its very simplicity, the great ease which it has lent to all computations, puts our arithmetic in the first rank of useful
inventions, and we shall appreciate the grandeur of this achievement when we remember that it escaped the genius of Archimedes and Apollonius, two of the greatest minds produced by antiquity. | {"url":"https://www.indiadivine.org/content/topic/1304971-indian-mathematics/#comment-5778283","timestamp":"2024-11-12T02:50:02Z","content_type":"text/html","content_length":"136908","record_id":"<urn:uuid:c4929a54-6696-46db-8253-07633afae338>","cc-path":"CC-MAIN-2024-46/segments/1730477028242.50/warc/CC-MAIN-20241112014152-20241112044152-00252.warc.gz"} |
Python code for the n-th number of the Fibonacci series
Here is the python code for the N-th number of the Fibonacci series?
# n-th Fibonacci number
def fibonacciNumbersNth(n):
a, b = 0, 1
for i in range(n-1):
a, b = b, a + b
return a
if __name__ == "__main__":
The above code will output the following number: | {"url":"https://qa.tellustheanswer.com/1938/python-code-for-the-n-th-number-of-the-fibonacci-series","timestamp":"2024-11-06T06:17:18Z","content_type":"text/html","content_length":"34999","record_id":"<urn:uuid:778b61f2-4381-4ac8-a60a-9eb323ef3899>","cc-path":"CC-MAIN-2024-46/segments/1730477027909.44/warc/CC-MAIN-20241106034659-20241106064659-00523.warc.gz"} |
School of Computer Science
PhD students of Steve Vickers: Kostas Viglas
Kostas Viglas completed his PhD thesis "Topos Investigations of the Extended Priestley Duality" (.ps, .pdf) in 2004 at the Department of Computing, Imperial College, under my supervision.
"Topos Investigations of the Extended Priestley Duality"
PhD Thesis, Department of Computing, Imperial College, 2004. 192 pages.
This is a brief summary of the original results in the thesis.
First, there is a localic version of the correspondence between perfect and patch continuous monotone maps. To this end, Escardo's localic patch construction for a stably compact locale is used.
Given a stably compact locale X, we define constructively the order on its patch locale. We also introduce localically the notion of a monotone patch continuous function in this context. The fact
that lax pullbacks of perfect maps produce proper maps in Loc is proved. Vickers' preframe techniques are used throughout. Beck-Chevalley conditions for lax-coequalizers are also proved.
When working in Top, the 2-category of Grothendieck topoi and geometric morphisms, it is natural to consider functors between the (generalized) points of topoi. A 2-categorical criterion of an
adjunction F -| G between X and Y in Top is proved by constructing the classifying topoi of maps Fx -> y and x -> Gy, where x and y are points of X and Y respectively and identifying them with
inserters in Top.
Next, it is demonstrated that relative tidiness (in the sense of Moerdijk and Vermeulen) is the right topos-theoretic generalization of perfectness. Vickers has shown that the exponential of topoi [
set]^X, where X is a stably compact locale, classifies the geometric theory of B-sheaves which implies that a point of [set]^X at stage Z is a B-sheaf in the sheaves over Z. For f: X -> Y a perfect
map between two stably compact locales, a description of the map [set]^f: [set]^X -> [set]^Y is given and is shown to have a right adjoint. The definitions of the geometric morphisms are given by
geometric constructions on the points of the exponential topos, i.e. the B-sheaves. The geometricity of these constructions is guaranteed by the fact that we can represent perfect maps by strong
homomorphisms between strong proximity lattices. The adjunction is proved by application of the 2-categtorical criterion in the 2-category Top. The main result of this chapter is that for a map f: X
-> Y between stably compact locales, f is perfect if and only if f is relatively tidy.
Finally, there are investigations with a possible topos analogue of the patch construction. Some results are given on relatively tidy maps between structures that are examples of "stably compact
topoi". It is argued by example, that "stably compact topoi" and relatively tidy maps should convey the notion of local partial ordering in the same sense that stably compact locales and perfect maps
amount to (globally) partially ordered locales and monotone continuous maps. | {"url":"https://www.cs.bham.ac.uk/~sjv/kvpage.php","timestamp":"2024-11-11T17:18:27Z","content_type":"application/xhtml+xml","content_length":"13406","record_id":"<urn:uuid:465318a9-c966-4af2-be9c-cbd136b09c3f>","cc-path":"CC-MAIN-2024-46/segments/1730477028235.99/warc/CC-MAIN-20241111155008-20241111185008-00596.warc.gz"} |
What is SI unit of thermal conductivity?
What is SI unit of thermal conductivity?
The SI unit of thermal conductivity is watts per meter-kelvin ( W m − 1 K − 1. ).
Does thermal conductivity depend on mass?
In this case the thermal conductivity depends on the mass, and that is the reason that helium and hydrogen have very high thermal conductivity. In case of solids however this picture gets complicated
as the major contribution comes from phonons.
What is thermal mass measured in?
Thermal mass, or the ability to store heat, is also known as volumetric heat capacity (VHC). VHC is calculated by multiplying the specific heat capacity by the density of a material: Specific heat
capacity is the amount of energy required to raise the temperature of 1kg of a material by 1°C.
What is the SI unit of thermal conductivity of copper?
The thermal conductivity of copper is 400 watts per meter kelvin.
What is K value in thermal conductivity?
A k-value (sometimes referred to as a k-factor or lambda value λ) is a measure of the thermal conductivity of a material, that is, how easily heat passes across it. It is a fundamental property,
independent of the quantity of material.
How do you measure thermal conductivity of metals?
For measuring thermal conductivity, there are four main types of measurement setups: the guarded hot plate (GHP), the heat‐flow meter (HFM), the hot wire, and laser flash diffusivity.
How does the mass affect the thermal energy?
If the temperature doesn’t change but the mass of the object increases, the thermal energy in the object increases.
Does thermal energy have mass?
Key Takeaways. Matter has mass and occupies volume. Heat, light, and other forms of electromagnetic energy do not have measurable mass and can’t be contained in a volume. Matter can be converted into
energy, and vice versa.
What is meant by thermal mass?
‘Thermal mass’ describes a material’s capacity to absorb, store and release heat. For example water and concrete have a high capacity to store heat and are referred to as ‘high thermal mass’
materials. Insulation foam, by contrast, has very little heat storage capacity and is referred to as having ‘low thermal mass’.
How is thermal conductivity measured in mK?
To measure thermal conductivity, use the equation Q / t = kAT / d, plug in your area, time, and thermal constant, and complete your equation using the order of operations.
What is W mK thermal conduction?
A material’s thermal conductivity is the number of Watts conducted per metre thickness of the material, per degree of temperature difference between one side and the other (W/mK). As a rule of thumb,
the lower the thermal conductivity the better, because the material conducts less heat energy.
What is the unit of thermal value?
U-value, or thermal transmittance (reciprocal of R-value) Thermal transmittance, also known as U-value, is the rate of transfer of heat through a structure (which can be a single material or a
composite), divided by the difference in temperature across that structure. The units of measurement are W/m²K.
How do you convert heat to mass?
When you heat an object it’s mass increases E=mc2.
What is thermal mass parameter?
The Thermal Mass Parameter (TMP) for a dwelling is required for the heating and cooling calculations. It is defined as the sum of (area x heat capacity) over all construction elements (Cm) divided by
total floor area (TFA).
How is mass related to thermal energy? | {"url":"https://fistofawesome.com/life/what-is-si-unit-of-thermal-conductivity/","timestamp":"2024-11-05T23:47:58Z","content_type":"text/html","content_length":"47074","record_id":"<urn:uuid:cc2b22c3-7a3e-48e1-b2e1-6f4937e26c59>","cc-path":"CC-MAIN-2024-46/segments/1730477027895.64/warc/CC-MAIN-20241105212423-20241106002423-00245.warc.gz"} |
Computer Science 50 Fall 2010 Scribe Notes Week 7 ... - CS50 CDN - P.PDFKUL.COM
Computer Science 50 Fall 2010 Scribe Notes
Week 7 Wednesday: October 20, 2010 Andrew Sellergren
Contents 1 Announcements and Demos (0:00–19:00) 2 From Last Time (19:00–38:00) 2.1 swap2.c . . . . . . . . . . . . 2.2 Problem Set 5 . . . . . . . . . 2.3 pointers1.c . . . . . . . . . 2.4
pointers2.c . . . . . . . . . 2.5 Stacks . . . . . . . . . . . . . 2.6 Queues . . . . . . . . . . . . .
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3 Hash Tables (38:00–64:00) 3.1 Linear Probing . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Separate Chaining . . . . . . . . . . . . . . . . . . . . . . . . . .
4 Trees and Tries (64:00–75:00)
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Computer Science 50 Fall 2010 Scribe Notes
Week 7 Wednesday: October 20, 2010 Andrew Sellergren
Announcements and Demos (0:00–19:00) • This is CS50. • To the end of helping you with your preterm planning, we’re releasing new features and bug fixes for HarvardCourses today! First, we made it
easier to clear your selection for a faculty member. Second, we made it more intuitive, via dropdown menus in the upper left, to narrow down courses by specific fields. Third, we ripped out the
Facebook comment feature because no one was using it. Fourth, we made it possible to add courses to different lists, e.g. Courses I’m Taking, Courses I’m Shopping. Fifth, we added a Random
Suggestions box on the lefthand side that populates with courses based on your previous selections and other students’ selections. Finally, we’re looking to add the ability to search for all courses
that count toward a given concentration. However, because this data doesn’t exist in any central database but rather must be cleaned from the course catalog, we’re hoping that you can help us out by
solving this problem with crowdsourcing! If you’d like to pick off a given concentration, e-mail David and he’ll share a Google doc with you. • If you’re looking for ideas for your final project,
check out ideas.cs50.net which contains a whole slew of user submissions. Keep in mind that the course wiki also has descriptions of various APIs (Application Programming Interfaces) that allow you
to work with code from CS50 apps such as HarvardCourses. Why not tackle the Android course catalog app or HarvardTravel, a website to connect students who have traveled or studied abroad? How about a
program to download all Facebook photos in which you’re tagged? Or a website to reserve practice rooms from FDO? • We’re also happy to announce that we’ll be making a lot of changes to our website
and our apps based on your feedback from Problem Set 4. It’s interesting to read about all your gripes regarding technology that you’ve seen at banks, convenience stores, and within Harvard itself.
From Last Time (19:00–38:00) • Bitwise operators allow us to manipulate data on the bit level. The AND operator (&) returns 1 if both bit operands are 1. The OR operator (|) returns 1 if either one
of the bit operands is 1. The XOR operator (^) returns 1 if and only if exactly one of the bit operands is 1. • The XOR operator is useful in implementing RAID arrays in which multiple hard drives
store data. In an array of three drives, one of the drives stores the result of XOR’ing the bits of the other two drives so that the total capacity of the array is equal to the size of those two
drives combined and if any one of the drives fails, the missing data can be quickly rebuilt.
Computer Science 50 Fall 2010 Scribe Notes
Week 7 Wednesday: October 20, 2010 Andrew Sellergren
swap2.c • In fact, XOR can be used to swap the values of two variables without using any temporary storage, as swap2.c demonstrates: /
**************************************************************************** * swap2.c * * Computer Science 50 * David J. Malan * * Swaps two variables’ values. * * Demonstrates (clever use of)
bitwise operators. ***************************************************************************/ #include
// function prototype void swap(int *a, int *b);
int main(void) { int x = 1; int y = 2; printf("x is %d\n", x); printf("y is %d\n", y); printf("Swapping...\n"); swap(&x, &y); printf("Swapped!\n"); printf("x is %d\n", x); printf("y is %d\n", y); }
/* * Swap arguments’ values. */ void swap(int *a, int *b) {
Computer Science 50 Fall 2010 Scribe Notes
Week 7 Wednesday: October 20, 2010 Andrew Sellergren
*a = *a ^ *b; *b = *a ^ *b; *a = *a ^ *b; } 2.2
Problem Set 5 • For Problem Set 5, you’ll be asked to recover a series of JPEGs from a flash drive that has been formatted. To do so, you’ll leverage the fact that JPEGs are stored on disk with the
same 4-byte sequence as a header. When you scan through the data that we’ve given you, you’ll write out a new JPEG file each time you encounter that 4-byte sequence. • One subtlety that we’ll mention
briefly now is the concept of Endianness. Although we tend to think of numbers as reading from left to right, they may be stored on disk in different directions. Memory addresses on Big Endian
architectures read from left to right. Memory addresses on Little Endian architectures read from right to left.
pointers1.c • pointers1.c takes a string as input and iterates over all of the characters in it, printing them out one per line: /
**************************************************************************** * pointers1.c * * Computer Science 50 * David J. Malan * * Prints a string, one character per line. * * Demonstrates
strings as arrays. ***************************************************************************/ #include #include #include
int main(void) { // prompt user for string printf("String please: "); char *s = GetString(); if (s == NULL) 4
Computer Science 50 Fall 2010 Scribe Notes
Week 7 Wednesday: October 20, 2010 Andrew Sellergren
return 1; // print string, one character per line for (int i = 0, n = strlen(s); i < n; i++) printf("%c\n", s[i]); // free string free(s); return 0; } The only thing “new” worth mentioning is the
call to free. Now that we know that GetString calls malloc, we need to make sure to explicitly return that memory to the operating system before the program closes. 2.4
pointers2.c • More interestingly, because we know that strings are actually implemented as pointers under the hood, we can access the characters in the string using pointer arithmetic instead of
bracket notation: /**************************************************************************** * pointers2.c * * Computer Science 50 * David J. Malan * * Prints a string, one character per line. * *
Demonstrates pointer arithmetic. ***************************************************************************/ #include #include #include
int main(void) { // prompt user for string printf("String please: "); char *s = GetString(); if (s == NULL) return 1; 5
Computer Science 50 Fall 2010 Scribe Notes
Week 7 Wednesday: October 20, 2010 Andrew Sellergren
// print string, one character per line for (int i = 0, n = strlen(s); i < n; i++) printf("%c\n", *(s+i)); // free string free(s); return 0; } This program’s output is identical to pointers1.c, but
it achieves it in a slightly different way. Recall that *s will access the memory that stores the first character of s. If we write *(s+1), we’re accessing the memory directly next to the first
character, that of the second character. Because each character is a single byte, s+1 represents the address of the second character, s+2 represents the address of the third character, and so on. In
fact, the compiler is smart enough to do this arithmetic even when the pointer points to an array of elements each of which is larger than a single byte. For example, *(s+1) will access the second
element in an array of integers named s. • Because it allows low-level access to memory, C is one of the few programming languages that offers pointer arithmetic. However, generally you’ll find that
the only difference between many programming languages is their syntax. Once you’ve learned one or two, as you will in this course, you’ll be empowered to learn any number of others. 2.5
Stacks • Hopefully to help clear up some confusion from Monday, here is the final definition of a struct that implements a stack: typedef { int int int } stack;
struct numbers[CAPACITY]; size; top;
Although a stack of infinite size is theoretically possible, a stack of fixed size is more practical. Thus, we can implement it using an array. CAPACITY is the maximum size of the stack, defined as a
constant elsewhere. size is a piece of metadata that keeps track of how many values are currently on the stack. top stores the index of the value that’s next to be popped off
Computer Science 50 Fall 2010 Scribe Notes
Week 7 Wednesday: October 20, 2010 Andrew Sellergren
the stack. We store this because this index won’t necessarily be 0 if other values have already been popped off. • We need both size and top because of a single corner case. In almost all cases, size
will be the value of top plus one. However, if there are no values in the stack, then top will be zero and size will be zero. Alternatively, we could fix this by returning some sentinel value when
the stack was empty. 2.6
Queues • The struct to implement a queue is very similar to that to implement a stack: typedef { int int int } queue;
struct head; numbers[CAPACITY]; size;
Here, head keeps track of the value that was inserted first which will be the first to be removed. head mostly likely starts as 0, but as values are removed, it becomes 1, 2, 3, 4, and so on. In this
way, we don’t have to shift all the elements of the array, which is expensive. If we wanted to maximize our use of space, we might even wrap the queue around so that when we run out of space at the
end of the array, we can fill the spaces at the beginning. In that case, we’d also need to keep track of the tail of the queue. 3
Hash Tables (38:00–64:00) • To create a dictionary of words with which to look up misspellings, you certainly could use an array sorted alphabetically in combination with binary search. Binary search
is in O(log n) which is theoretically fast, but not the absolute fastest. What would be even faster than binary search is something in O(1), implying constant-time lookup. • One data structure that
affords constant-time lookup is a hash table. A hash table can actually be implemented as an array, albeit one that is larger than it needs to be to store all of your data. To insert data into a hash
table, you will effectively throw the input at the hash table like a dart. Your hope is that it will stick to the hash table without “colliding” with any other inputs. That is, your hope is that you
will find an empty element in the array. If you happen to find an empty element, then it only takes a single step to insert this input into your hash table. 7
Computer Science 50 Fall 2010 Scribe Notes
Week 7 Wednesday: October 20, 2010 Andrew Sellergren
• There’s one qualification we need to make, however. We’re not actually throwing the input at the hash table randomly. If we did, how would we know where to find it later? We need to insert the
input in such a way that we can find it quickly in the future. More on this in a moment. • If we did insert inputs randomly into the hash table, what would be the probability that we would collide
with another input, i.e. we would hit a non-empty element in the array? Surprisingly high, it turns out. We can rephrase this problem as an instance of the birthday paradox: in a room of n CS50
students, what’s the probability that at least 2 students have the same birthday? Here, the hash table has a size of 365 for the number of days in the year. Let’s assume an even distribution of
birthdays throughout the year. We can better answer this problem if we consider the opposite question: what’s the probability that no 2 students have the same birthday in a room of n students? p¯(n)
= 1 × 1 −
× 1−
× ··· × 1 −
n−1 365
The probability that no 2 students have the same birthday is 1 when n is 1. The probability that no 2 students have the same birthday is 1 × 364 365 when n is 2 because there are 364 possibilities
for the second person’s birthday that don’t collide with the first person’s. The probability 363 that no 3 students have the same birthday is 1 × 364 365 × 365 . And so on. This series actually
reaches high percentages fairly quickly. For example, when n is 40, the probability of a collision is almost 90%. • The act of “throwing a dart” at our hash table to find where to put a value is
called hashing. This is really just implemented as a function like so: int hash(int n) { return rand(); } This will return us a random number which corresponds to an index in our hash table. Of
course, we’d actually need to normalize this number so that it wasn’t larger than the size of our hash table. But we won’t bother doing that because we won’t really be using this as our hash function
anyway. As we said before, it doesn’t really make sense to have a hash function that returns random numbers because we won’t be able to look up numbers after we’ve inserted them. • Just as simple is
the following hash function:
Computer Science 50 Fall 2010 Scribe Notes
Week 7 Wednesday: October 20, 2010 Andrew Sellergren
int hash(int n) { return n; } If we want to store a number in a hash table, we can simply use the number itself as an index into the hash table. But we’ll run into problems when the number to insert
is larger than the size of the hash table. We can fix this using the modulus operator: int hash(int n) { return n % 26; } Here, we’re assuming that the hash table is of size 26 (perhaps for the
number of letters in the alphabet). If our number n is larger than 26, it will be wrapped around to return a valid index into our hash table. 3.1
Linear Probing • Given that collisions are likely to occur even if our hash table is several times as large as the number of values we’re inputting (e.g. 365 versus 40 in the case above), we need to
decide what do to when we have a collision. We could simply place the value in the bucket directly next to the one we originally intended to insert it in. This is called linear probing. If hash
returned index 0 and we found that index 0 in our hash table already had a value in it, we could look at index 1. • The linear probing approach for dealing with collision introduces problems with
search, however. If the hash function returns index 0 but we don’t find the value we’re searching for at index 0, do we immediately return false? No, in fact, because the value we’re searching for
might be at index 1, or index 2, or worst case index 25. As you can see, searching a hash table that uses linear probing for collisions is in O(n) which is not what we want at all. • If the values we
want to store in our hash table are strings rather than numbers, we need to rewrite our hash function. Because all we need is an index for each string, we could easily use the first character of the
string cast to an integer like so: int hash(string s) { 9
Computer Science 50 Fall 2010 Scribe Notes
Week 7 Wednesday: October 20, 2010 Andrew Sellergren
return (int) s[0] - ’A’; } We need to subtract the value of A in order to normalize the value of the letter to a number between 0 and 25 (assuming again that our hash table is of size 26). This hash
function also assumes that its input will consist of all capital letters. • Given that there aren’t many words, names, or strings that start with Z but there are many that start with A, this hash
function is going to produce a lot of collisions. The ideal hash function, it would seem, is one that uses resources as efficiently as possible, minimizing collisions without making search expensive.
Separate Chaining • Clearly linear probing wasn’t a feasible solution to the problem of collisions given that it results in O(n). A better approach is separate chaining which implements each element
of the hash table as a linked list. When the hash function returns an index in the hash table which isn’t empty, the value to be inserted becomes the head of a linked list at that index. • Searching
for a value in a hash table that uses separate chaining is in O(n/k) where k is the size of the hash table and n is the number of values it stores. If we assume that our hash function achieves
perfectly uniform distribution, then we’ll end up with a linked list of length n/k at each index. If in the worst case, the value we’re searching for is at the end of one of these linked lists, then
we’ll have to execute n/k steps in order to find it. • Theoretically, O(n/k) is actually the same as O(n) because in the worst case, every input into the hash table causes a collision and thus our
hash table is just one linked list of length n. However, in practice, this isn’t the case, and our runtime will be faster. • Separate chaining also solves another problem induced by linear probing:
our hash table can now be smaller than the total number of values. In fact, there is no theoretical limit on the number of values that can be stored in a hash table since we can simply keep adding
them as the heads of our linked lists. In practice, however, searching for a value will get faster as our hash table grows in size (assuming our hash function gives us a fairly even distribution). •
Incidentally, “node” and “bucket” are terms that computer scientists use to refer to a generic container for data. You’ll hear them thrown around pretty liberally. • To store strings in a hash table
using separate chaining, we’ll need to define a node of a linked list: 10
Computer Science 50 Fall 2010 Scribe Notes
Week 7 Wednesday: October 20, 2010 Andrew Sellergren
typedef struct node { char word[LENGTH + 1]; struct node *next; } node; LENGTH is a constant which we’ll use to represent the maximal length of a word that we want to store, plus one for the null
terminator. Inside a node, we also need a pointer that will eventually point to the next node. In this implementation, each index in our array will actually be a pointer to the first node in the
linked list that lives there. 4
Trees and Tries (64:00–75:00) • Trees are data structures consisting of nodes, each of which may have any number of children. If each node has a maximum of two children, the tree is a binary tree.
Children of the same parent are siblings. Terminal nodes—those at the bottom that have no children—are called leaves. See the diagram below.
• A special kind of tree called a binary search tree allows us to use binary search to do lookups:
Computer Science 50 Fall 2010 Scribe Notes
Week 7 Wednesday: October 20, 2010 Andrew Sellergren
Binary search trees are specially structured so that each parent node is greater than its left child but less than its right child. If we were searching for the number 44 in the above tree, we would
first check the root node, 55. Because 44 is less than 55, we would go left. Because 44 is greater than 33 we would then go right and reach the desired result. • A tree is similar to a linked list in
that one need only store a pointer to the root node. • The node containing 33 is the child of the node containing 55, but it is also the root of a smaller tree consisting of the nodes containing 22
and 44. As you might have guessed, trees are good candidates for recursion because of these repeated relationships. • Each node of a binary search tree might be implemented as follows: typedef struct
node { int n; struct node *left; struct node *right; } node; Here, we have space in n for the actual value that the node stores as well as two pointers that point to the left and right child nodes.
Computer Science 50 Fall 2010 Scribe Notes
Week 7 Wednesday: October 20, 2010 Andrew Sellergren
• Tries are another data structure which might prove useful to you as you complete Problem Set 6. A trie is a type of tree which, for the purposes of Problem Set 6, will have arrays for its nodes.
These arrays will contain as elements pointers to other arrays. Take a look at this visualization of a trie used to store names in which each array is of size 26 for the number of letters in the
We walk through a trie much the same way we walk through a hash table with separate chaining. Each letter in the word we’re inserting (converted to a number between 0 and 25) is also its index into
the next level of the trie. So if we’re inserting the name Maxwell, we first hash to M, then to A, then to X, etc. What happens when we get to the end of a word? We need some sort of flag
(represented as a triangle in the diagram above) that marks the end of a word. That way, if two words share a prefix (e.g. Max and Maxwell), we will know that both of them are in our trie if this
end-of-word flag is set at both the X and the last L. • What’s interesting about a trie is that it never actually stores any letters or words, but only pointers. The words are implicit. 13
Computer Science 50 Fall 2010 Scribe Notes
Week 7 Wednesday: October 20, 2010 Andrew Sellergren
• The compelling case for tries is that the running time of search is O(m), where m is the length of the longest word, and is thus independent of n, the number of words in the trie. Woohoo,
constant-time lookup! Go forth and solve Problem Set 6! | {"url":"https://p.pdfkul.com/computer-science-50-fall-2010-scribe-notes-week-7-cs50-cdn_5b7a3c17097c47dd678b4568.html","timestamp":"2024-11-07T16:59:40Z","content_type":"text/html","content_length":"80662","record_id":"<urn:uuid:fc60d3da-bdd6-464e-bcc0-08edad224a28>","cc-path":"CC-MAIN-2024-46/segments/1730477028000.52/warc/CC-MAIN-20241107150153-20241107180153-00777.warc.gz"} |
[Video] Bayesian Methodology - How to Analyse Multiple Endpoints
In this Statistical Knowledge Share Video our Principal Statisticians, Sonia, presents an example of Bayesian Methodology using simulated data and examines how to analyze Multiple End Points in
Clinical Trials.
Bayesian Analysis Example - Multiple Endpoints
Video Transcribe
Multiple End Points
Sonia: "Hi everyone. I hope you can hear me okay".
Sonia: "I'm going to talk to you today about Bayesian methodology. Some of you may recall last year I did a presentation on some Bayesian analysis that was used for a respiratory study. This is the
follow up on that".
Sonia: "I'm going to do a recap of the methodology that we talked about last year and then talk a bit about how to analyze two end points together, which we had to do for this particular study".
Study Background
Sonia: "So in the example study, we started off looking at one end point, which was the predicted FEV1 (forced expiratory volume). We wanted that to be high, because that will indicate a better lung
function. There were 2 parallel groups, for active and placebo, and they had repeated doses for dose week 1, 4, 8, 12, and baseline was a covariant in the study. There were 2 centres. The primary end
point was change from baseline in predicted FEV1 at week 12".
Sonia: "One of the things that the client was interested in was the probability of there being a treatment effect of more than 10%".
ANCOVA Model Approach
Sonia: "To start off we used a simple ANCOVA (analysis of covariance) model to look at change from baseline at week 12. So we've got a proc mixed with treatment and center as categorical variables,
change from baseline, looking at treatment, adjusting for center, and this is the baseline for covariant".
Sonia: "And we wanted to get the LS (least squares) means out. You can see the result. So the active was way higher than placebo, with a difference of 9.88. And if you remember that probability we
were interested in, which is calculated here. So the probability of this treatment difference of being more than 10 was just less than half".
Simple Bayesian Model
Sonia: "Then we did the same thing, but using proc MCMC. So I will just go through this code. I know a lot of people haven't used MCMC very much. It's quite an unstructured proc. There's no
structure. You kind of put in the model yourself. It's quite easy to get wrong, because it will quite often run something, which is just nonsense. So you have to look at the results quite carefully".
Sonia: "The first bit of the code has got the third data set that we're using, selecting just the week 12 visit. This is the number of iterations that we use, and the data set we want the results to
come out of. Then we set up the model parameters. So B0 is the intercept, and B1 is the slope or the treatment coefficient and Sigma is the variance".
Sonia: "Then define priors for these parameters. So where I've put C:, that's going to cover any of the parameters that start with a B, just like any intercept. This is a non-informative prior, so
it's a normal distribution with a mean of zero and a large variance".
Sonia: "Sigma has a different shape distribution, so Igamma, again, this is non-informative".
Sonia: "Then we define the models. This is your Y=MX+C. So we've got the intercept and the slope multiplied by the treatment variable, where treatment is a one and a zero, or one and a two".
Sonia: "So the change from baseline is going to be normally distributed and this is the mean. And that's the basic model".
Add Adjustment for Baseline
Sonia: "If we want to add any adjustments or baseline, we need to add another parameter. This is a baseline parameter being added here. We don't need to add in the prior, because it's already covered
by this B: and then in the model we've got a baseline parameter multiplied by baseline variables".
Add Adjustment for Center (2 Centers)
Sonia: "Now we're adding in center. So for center, I've got like a dummy variable, so one and zero depending on which of the two centers its is. I've got the parameter center coefficients, the prior
for the center, and then adding it in here. So this will switch on and off depending on whether it's center 1 or center 2. If you have more centers, you need to add in an upper class variable for
each of these centers, so it can get quite messy, which is why we've only got two in this example".
Get Some Output
Sonia: "That doesn't give you any output. So you need to add in what you want to see out. So if you're using 9.4, you need to add statistics equal to all, otherwise it won't give you anything".
Sonia: "Then you need to specify which parameters you want to monitor. This is going to give you results and diagnostic. So I put all of them in, but if you have a model that's got lots and lots of
parameters, then this output can get really very large and it makes things very slow and clunky, in which case you want to think about which parameters you really want to monitor".
Sonia: "The middle bit of the code hasn't changed. Then this bit here is really useful. After you've specified your model, you can specify anything you want. So here, it's calculating equivalent to
your LS means, so active will be the intercept multiplied by the treatment coefficient times the value for active, and then center coefficient multiplied by half, so we are assuming half in each
Sonia: "I've not got baseline in here, because baseline is being centered. So the mean baseline is zero, but otherwise you would need to add that in as well. Same for placebos, and the treatment
difference in the centers and the intercept cancel out. The probability that that difference is more than 10, but you can add as many things in here as you want to".
Sonia: "Whatever you define here, you need to add up in this monitor, otherwise it just won't show you anything for it".
Output from SAS
Sonia: "I've got here the results of the ANCOVA that I showed before. This is the same equivalent results from the Bayesian. So as you can see, they're not identical. But they're quite close".
Two Endpoints
Sonia: "Now I'm moving on to new material, so looking at two end points together. We've got the predicted FEV, same as before, and then CRP ( C-reactive protein), in this case a lower result is
better, although it can get too low".
Sonia: "If you have co-primary end points, with a traditional frequentist approach it can make things quite tricky; if both endpoints are equally important, you need to think about splitting Alpha
between the two endpoints and basically running two separate models. It's quite frustrating if one of them is significant and the other one isn't".
Sonia: "With the Bayesian approach, you can put both of those end points into the same model and analyze them together".
Two Endpoints Decision Criteria
Sonia: "Then we have decision criteria based on the two end points, which I'll come to later on, which were specified in the analysis plan. At the end of the study, decisions were made based on those
Sonia: "These are the criteria. The first step was to look as before at the FEV being less than 10. and if the probability of that was pretty high, then that was unsuccessful, because we want to
remember the difference being more than ten".
Sonia: "Now if the probability of that FEV was more than 10, and the probability of the CRP difference is less than minus one, if the probability of that was more than 0.25, then that was a really
good clear success. So both of the end points showing us that they are doing what we want them to do. That was a robust success".
Sonia: "If we had a pretty high probability, so 0.35 or above, of there being a difference in FEV of more than 10, but not looking at the CRPs, then it was a success".
Two Endpoints Results
Sonia: "The MCMC allows this analysis to be done together, and then you can get quite a funky plot coming out, which I think looks like a fried egg. So here on this scale, the Y axis, we've got the
FEV. So if you imagine it in 3D, you've got a normal distribution along here. So this is the peak, and then you've got the tails either side. Then the same, in fact here. If you can picture it, it's
like the sideways view of this, if it was raised up".
Sonia: "Then along here you've got the same thing with CRP. So the most likely outcome you're in this quadrant here. Ideally we want it to be here, because that means that the FEV is more than 10,
and the CRP is less than minus 0.1. We go through each a step at a time; so the probability of seeing FEV being less than 10, so that's in this section here, is less than 0.75, because it was
actually 0.1712. So therefore, the first step is not potentially unsuccessful".
Sonia: "The second step is to say what is the probability of it being more than 10, and also the CRP being less than minus 0.01. So that's in this section here. And the probability of that is 0.2962,
so more than 0.25. So therefore in this example of simulated data, the result is a robust success. All good".
Sonia: "But I think although the analysis is quite complicated, if you imagine you're trying to describe the results to a study team clinician, this is quite a nice representation of the results.
Takes a bit of time to get your head around, but seeing the two end points together I think is quite good and helpful".
Two Endpoints Conclusions
Sonia: "So the results meet the criteria for a robust success and the joint modelling approach and resulting Bayesian posterior probabilities makes it easier to interpret results".
Bayesian Methodology
Sonia: "So the methodology... I won't get too heavily into the stats, but we're assuming that the two endpoints follow a multi-variant normal distribution. So this is a bit like the diagram of the
posteriors really".
Sonia: "The way that we modelled it, each treatment arm had a separate variance covariance matrix. No intercept terms were added. The baseline was added as a continuous covariate and it was centered.
As I mentioned before, the mean was zero which just . made it a little bit easier to code".
Sonia: "Non informative priors were utilized for each of the model parameters. Placebo, active, and baseline parameters had a multivariate normal prior distribution, so mean is zero and large
variants. So quite similar to the single endpoint".
Sonia: "This is where it gets a bit ugly, but you go through the code a little bit of how to set up the multi-variate normal priors, because it's not completely straightforward".
Sonia: "So this could be like the mean, and it had two elements, so one for each of the end points. Then we set up a zero matrix, which is just going to be a temporary matrix, which has zero for the
two elements".
Sonia: "Sigma is going to take the form of the two by two matrix. So this is the variance, covariance matrix, because it makes it easier to code, we've got a temporary one as well".
Sonia: "Fillmatrix. What this does is fills all the matrix of the temporary matrix with a value that you're specifying, so we can get a 2 by 2 matrix, with all four cells having this, which is going
to be the variance, a really big number".
Sonia: "Then if you remember from your college days, the identity matrix , we are calling that sigma, so that gives you the diagonals of ones and zeros".
Sonia: "What this does is it multiplies the temporary matrix, so the ones that got this value for each of the cells with your identity matrix. And it's going to replace sigma zero with the result. So
it gives you this basically. This is going to be your prior for the placebo. So the mean of zero, and that's your sigma. It's quite a lot of code to produce something quite simple".
Sonia: "The variance covariance matrices for placebo and active, will use this inverse Wishart distribution for the prior. So this again is noninformative but it is a little bit more tricky to find a
noninformative for this distribution, but we need to use this inverse Wishart, because it makes the maths easier, it makes the posterior probabilities come out as normals, which is what we need".
Sonia: "There is a dependence between the variance and the correlation. So if the correlation is exaggerated, then the variance is going to be higher. So you need to watch out for this".
Plot of Data and Posterior
Sonia: "In this case, this is our posterior, and that is our data. There is quite a good match between the two of them, they line, which indicates that their prior is noninformative. But in some
cases, if the variance is quite large, you might find that you need you need to look at the prior and change it, because it is not truly non‑informative".
SAS Codes
Sonia: "This is the joint code. I'm not going to go through every line of it, because it is quite long. I mentioned in the slide that we were fitting separate variance/ covariance matrix for the two
different treatments. To do that, we had to split up the data sets so that we had a different variable for the placebo and the active. Basically, if the treatment is this then we'll create two
different variables, so one for active and one for placebo rather than having them in the same variable, but just with a treatment variable to indicate which was which".
Sonia: "The other thing is, I am only modelling week 12, but if you do repeated measures, you need a wide structure data set, so with all the time point going along, whereas for something like proc
mix you use a vertical structure".
Sonia: "We've got MCMC code here. As you can see, we've got all of the parameters we want to monitor. This is setting up all the different arrays. So here are the outcomes, so the data that we are
Sonia: "So, data 1 is your placebo data for FEV and CRP and data 2 is your active for FEV and CRP. We have got two baselines, so again, because we've got two end points we have 2 baselines, FEV and
CRP. This is just a linear predictor to the baseline. I will show you where that comes in later".
Sonia: "We are going to calculate the treatment differences, so we need a parameter for treatment difference. So again, there are two. We need an array for this, whereas in the previous code we did
not need these array. This is going to give us the probability for the different quadrants, remember from that plot, we had probability for each quadrant".
Sonia: "This is going to be the LS mean for treatment and active and baseline covariate, sigma for placebo inactive".
Sonia: "This part here is setting up the priors. This is the code that I showed you before with the zero matrix and the identity matrix. This is setting up the prior for the sigmas".
Sonia: "We have got priors for sigma. We have got priors for the means. The parameters here you can put starting values, and I have found that sometimes these are quite important. If you leave it
blank it will set the starting value of zero. If you put in a value, it will use the value that you give. If you give it a silly value, you can get some really crazy answers. It shouldn't really make
a difference, but I found that it did made a difference. That's something to watch if you get numbers that don't seem very sensible".
Sonia: "We've got priors for the treatments, priors for the sigmas, and baseline. Then this is the model statement. We've got it in a DO Loop, because of the two end points. It's got baseline and
then the treatment differences, the treatment for placebo and active. I have not put centre in here, because I was trying to keep it simple".
Sonia: "Then this is similar to what we had before. So placebo is going to be normally distributed around this, and then the same for active".
Sonia: "This is the data that is coming out, and then here are all the calculations that we want to see. So I have got treatment difference, and then here those probabilities. So the probability of
both things being successful, both failing".
Sonia: "Underneath that we have just got a proc mix, just a sense check. That is really useful, because as I said before, you can have MCMC run, and it all looks like it's working but because you set
up the model statement wrong you get crazy answers. So it's really good to have something just as a double check that you've got things roughly as you were expecting".
Diagnostic and Model Fit
Sonia: "It is really important to look at the diagnostics, For the study that we used this methodology for we got some really crazy diagnostics out. So it is really important to check them. I'll show
you some examples in a few minutes".
Sonia: "It is also quite useful to plot the posterior distribution for the key parameters, so that you have got an idea of whether the prior is informative or not. And we reported the posterior
median, standard deviation, and the credible intervals (which are like confidence intervals)".
Convergence Diagnostic
Sonia: "One statistic that came out as a diagnostic, which is really useful, is the ratio of the MCMC to the standard deviation. This is basically showing you how much of the error is due to
variability in the data, and how much is to do with the model simulation error. It should be ideally less than 0.01, although if that is really difficult to achieve, then 0.05 is reasonable".
Sonia: "To make it smaller, you increase your number of iterations and increase the burn in. So the burn in is how many iterations you want to discard at the start".
Sonia: "This here, this Geweke diagnostic compares the start of the chain with the end. So if you've got a large z-score indicates poor convergence, because it means that the start of the chain in
the end of the chain are quite different".
Sonia: "Here's an example of really disastrous diagnostic. We've got a quite a small number of iterations here and no burn in. This as you can see, is bouncing along all over the place. and it looks
a bit like a mess. The MCMC to SD ratio here is very high. Either you have not got enough runs or there is something really wrong in your model".
Sonia: "You can see that increasing the number of iterations tenfold is major and look a lot more respectable. It is not perfect, but we had something that looked like that and we thought it was
passable. It depends on your data, how many data points you've got and how nice is looks".
Sonia: "Here it is better still. They've got 50,000. This has come right down to 0.02. The burn in on this one is not really very clear. Sometimes you get something really different happening at the
start of the chain before it settles down into this pattern, in which case you would want to increase your burn in to get rid of those where it's sort of doing something funky at the start".
Sonia: "Then here, it looks really quite a good “hairy caterpillar”. Got very small ratio here and its autocorrelation drops down straightaway, this is a very healthy looking diagnostic.Having said
that, you get this, it still doesn't mean your estimates make sense. You need to check those events and proc mix as well".
Outputs from Separate ANCOVA Models
Sonia: "Now, this is the outcome I did for the ANCOVA. You can see a treatment difference of 11 and then here, minus 0.06. We didn't get a brilliant match actually from the MCMC. It's quite different
result, and we didn't have time to look at why that was but because we used the simulated data, I didn't worry about that".
Sonia: "One thing you might want to look at is what would happen if you change your priors. Would it change the outcome of the study? Beause if so, there something may be wrong with the priors".
Sonia: "We didn't really look at it in too much detail, because for the study, basically the results were disaster and it showed the study didn't work, so we didn't spend a lot of time. And the proc
mix showed the same, so we didn't spend a lot of time worrying about the priors. That is something to be careful of if you are going to use the results".
Sonia: "I found this methodology really complicated to use, very time consuming, it's also really difficult to QC, because you don't get exact match, the QC and the production side- you are not going
to get exactly the same numbers. So you have to go through manually and check whether you think the numbers are within an acceptable range".
Sonia: "But the plus side of it is you get this really nice way of interpreting the results, which is easier for a clinical team to understand and easier for them to make decisions. You need to be
careful about choosing priors. We had to tweak the model quite a lot to get it to work, if you writing a RAP you need to leave a little bit of flexibility in the RAP to say different elements in the
model are going be investigated so that you are not tied down too much".
Sonia: "Very, very time consuming. Some of these models took four or five hours to run. It's quite an undertaking from that point of view".
Sonia: That was all. Does anyone have any questions?
At Quanticate our Statistical Consultants are experienced in clinical study designs and have delivered multiple trial analyses using Bayesian methods. For more information Submit a Request for
Information and a member of our team will be in touch with you shortly. | {"url":"https://www.quanticate.com/blog/bayesian-analysis-methodology-how-to-analyse-multiple-endpoints-in-clinical-trials","timestamp":"2024-11-05T21:46:23Z","content_type":"text/html","content_length":"154865","record_id":"<urn:uuid:7d065b9c-6bf0-4906-b30e-86fbfecfeb31>","cc-path":"CC-MAIN-2024-46/segments/1730477027895.64/warc/CC-MAIN-20241105212423-20241106002423-00393.warc.gz"} |
Kalb-Ramond field
Differential cohomology
Connections on bundles
Higher abelian differential cohomology
Higher nonabelian differential cohomology
Fiber integration
Application to gauge theory
The Kalb-Ramond field or B-field is the higher U(1)-gauge field that generalizes the electromagnetic field from point particles to strings.
Its dual incarnation in KK-compactifications of heterotic string theory to 4d is a candidate for the hypothetical axion field (Svrcek-Witten 06, p. 15).
Recall that the electromagnetic field is modeled as a cocycle in degree 2 ordinary differential cohomology and that this mathematical model is fixed by the fact that charged particles that trace out
1-dimensional trajectories couple to the electromagnetic field by an action functional that sends each trajectory to the holonomy of a $U(1)$-connection on it.
When replacing particles with 1-dimensional trajectories by strings with 2-dimensional trajectories, one accordingly expects that they may couple to a higher degree background field given by a degree
3 ordinary differential cohomology cocycle.
In string theory this situation arises and the corresponding background field appears, where it is called the Kalb-Ramond field .
Often it is also simply called the $B$-field , after the standard symbol used for the 2-forms $(B_i \in \Omega^2(U_i))$ on patches $U_i$ of a cover of spacetime when the differential cocycle is
expressed in a Cech cohomology realization of Deligne cohomology.
This is the analog of the local 1-forms $(A_i \in \Omega^1(U_i))$ in a Cech cocycle presentation of a line bundle with connection encoding the electromagnetic field.
The field strength of the Kalb-Ramond field is a 3-form $H \in \Omega$. On each patch $U_i$ it is given by
$H|_{U_i} = d B_i \,.$
And just as a degree 2 Deligne cocycle is equivalently encoded in a $U(1)$-principal bundle with connection, the degree 3 differential cocycle is equivalently encoded in
The study of bundle gerbes was largely motivated and driven by the desire to understand the Kalb-Ramond field.
The next higher degree analog of the electromagnetic field is the supergravity C-field.
Mathematical model from (formal) physical input
The derivation of the fact that the Kalb-Ramond field that is locally given by a 2-form is globally really a degree 3 cocycle in the Deligne cohomology model for ordinary differential cohomology
proceeds in in entire analogy with the corresponding discussion of the electromagnetic field:
• classical background The field strength 3-form $H \in \Omega^3(X)$ is required to be closed, $d H_3 = 0$.
• quantum coupling The gauge interaction with the quantum string is required to yield a well-defined surface holonomy in $U(1)$ from locally integrating the 2-forms $B_i \in \Omega^2(U_2)$ with $d
B_i = H|_{U_i}$ over its 2-dimensional trajectory.
$hol(\Sigma) = \textstyle{\prod}_{f} \exp(i \textstyle{\int}_f \Sigma^* B_{\rho(f)}) \textstyle{\prod}_{e \subset f} \exp(i \textstyle{\int}_{e} \Sigma^* A_{\rho(f) \rho(e)}) \textstyle{\prod}_{v
\subset e \subset f} \exp(i \lambda_{\rho(f) \rho(e) \rho(v)}) \,.$
That this is well defined requires that
$\lambda_{i j k} - \lambda_{i j l} + \lambda_{i k l} - \lambda_{j k l} = 0 \;mod \, 2\pi \,,$
which says that $(B_i, A_{i j}, \lambda_{i j k})$ is indeed a degree 3 Deligne cocycle.
Over D-branes
The restriction of the Kalb-Ramond field in the 10-dimensional spacetime to a D-brane is a twist (as in twisted cohomology) of the gauge field on the D-brane: its 3-class is magnetic charge for the
electromagnetic field/Yang-Mills field on the D-brane. See also Freed-Witten anomaly cancellation or the discussion in (Moore).
Table of branes appearing in supergravity/string theory (for classification see at brane scan).
brane in supergravity charged under gauge field has worldvolume theory
black brane supergravity higher gauge field SCFT
D-brane type II RR-field super Yang-Mills theory
$(D = 2n)$ type IIA $\,$ $\,$
D(-2)-brane $\,$ $\,$
D0-brane $\,$ $\,$ BFSS matrix model
D2-brane $\,$ $\,$ $\,$
D4-brane $\,$ $\,$ D=5 super Yang-Mills theory with Khovanov homology observables
D6-brane $\,$ $\,$ D=7 super Yang-Mills theory
D8-brane $\,$ $\,$
$(D = 2n+1)$ type IIB $\,$ $\,$
D(-1)-brane $\,$ $\,$ $\,$
D1-brane $\,$ $\,$ 2d CFT with BH entropy
D3-brane $\,$ $\,$ N=4 D=4 super Yang-Mills theory
D5-brane $\,$ $\,$ $\,$
D7-brane $\,$ $\,$ $\,$
D9-brane $\,$ $\,$ $\,$
(p,q)-string $\,$ $\,$ $\,$
(D25-brane) (bosonic string theory)
NS-brane type I, II, heterotic circle n-connection $\,$
string $\,$ B2-field 2d SCFT
NS5-brane $\,$ B6-field little string theory
D-brane for topological string $\,$
A-brane $\,$
B-brane $\,$
M-brane 11D SuGra/M-theory circle n-connection $\,$
M2-brane $\,$ C3-field ABJM theory, BLG model
M5-brane $\,$ C6-field 6d (2,0)-superconformal QFT
M9-brane/O9-plane heterotic string theory
topological M2-brane topological M-theory C3-field on G₂-manifold
topological M5-brane $\,$ C6-field on G₂-manifold
membrane instanton
M5-brane instanton
D3-brane instanton
solitons on M5-brane 6d (2,0)-superconformal QFT
self-dual string self-dual B-field
3-brane in 6d
The name goes back to:
The interpretation as a 4d axion:
The interpretation of the B-field as a 3-cocycle in Deligne cohomology is due to
picked up in
The equivalent formulation in terms of connections on bundle gerbes originates with
See also:
A more refined discussion of the differential cohomology of the Kalb-Ramond field and the RR-fields that it interacts with:
In fact, in full generality the Kalb-Ramond field on an orientifold background is not a plain bundle gerbe, but a Jandl gerbe, a connection on a nonabelian $AUT(U(1))$-principal 2-bundles for the
automorphism 2-group $AUT(U)(1))$ of $U(1)$:
for the bosonic string this is discussed in
and for the refinement to the superstring in
• Jacques Distler, Dan Freed, Greg Moore, Orientifold Precis, in: Hisham Sati, Urs Schreiber (eds.), Mathematical Foundations of Quantum Field and Perturbative String Theory Proceedings of Symposia
in Pure Mathematics 83, AMS (2011) [arXiv:0906.0795]
• Jacques Distler, Dan Freed, Greg Moore, Spin structures and superstrings, Surveys in Differential Geometry, Volume 15 (2010) (arXiv:1007.4581, doi:10.4310/SDG.2010.v15.n1.a4)
See at orientifold for more on this; also at discrete torsion.
The role of the KR field in twisted K-theory (see K-theory classification of D-brane charge) is discussed a bit also in
In relation to Einstein-Cartan theory:
• Richa Kapoor, A review of Einstein Cartan Theory to describe superstrings with intrinsic torsion (arXiv:2009.07211)
• Tanmoy Paul, Antisymmetric tensor fields in modified gravity: a summary (arXiv:2009.07732)
In the context of cosmology with the Kalb-Ramond field as a dark matter-candidate (cf, axion and fuzzy dark matter):
• Christian Capanelli, Leah Jenks, Edward W. Kolb, Evan McDonough, Cosmological Implications of Kalb-Ramond-Like-Particles [arXiv:2309.02485]
See also: | {"url":"https://ncatlab.org/nlab/show/Kalb-Ramond+field","timestamp":"2024-11-14T23:43:39Z","content_type":"application/xhtml+xml","content_length":"86584","record_id":"<urn:uuid:d6b2e8c4-c89c-4501-9ef1-c8652ab4aa12>","cc-path":"CC-MAIN-2024-46/segments/1730477397531.96/warc/CC-MAIN-20241114225955-20241115015955-00353.warc.gz"} |
If you’re at $30^\circ$s, $21^\circ$e, and you travel due west until your longitude is $18^\circ$e, how far have you gone? Assume the Earth is a sphere of radius $6370\,\mathrm{km}$.
You’re travelling along a circle (the line around the Earth with latitude $30^\circ$s). What is the radius of this circle?
Since you’re traveling due west, you’ll stay on the $30^\circ$s circle. The radius of this circle is not the same as the radius of the Earth – circles of equal latitude get smaller the closer they
are to the poles. To work out the radius, which I’ll call $r$, imagine a vertical cross-section of the Earth: Now focus on the right-angled triangle shown above. Its hypotenuse is the radius of the
Earth, $R = 6370\,\mathrm{km}$. We can work out that its angles are $30^\circ$ and $60^\circ$ (for example by alternate angles, with the equator line parallel to the $30^\circ$s line). So $r = R\sin
30^\circ = R/2 = 3185\,\mathrm{km}$.
Since you start at $21^\circ$e and finish at $18^\circ$e, you’ve travelled $3^\circ$ along the circle with radius $r$, so the distance is $3\pi r/180 = \pi r / 60$, which is roughly $167\,\mathrm{km} | {"url":"http://thawom.com/q-latitude.html","timestamp":"2024-11-07T13:15:58Z","content_type":"text/html","content_length":"5201","record_id":"<urn:uuid:b19a4d57-b484-48c4-b61b-fba001919ad2>","cc-path":"CC-MAIN-2024-46/segments/1730477027999.92/warc/CC-MAIN-20241107114930-20241107144930-00546.warc.gz"} |
Hatoslottó | Check Results, Jackpot, Stats & Odds
Hatoslottó Results, Jackpots & Fun Facts!
Lottery Results Updated : Nov 12, 2024 07:03 PM EST
Next Draw on:
16th Nov, 2024
Estimated Jackpot:
Result Date Jackpot
25 Date Est. Jackpot
28 Ft1,680,000,000
31 Date Est. Jackpot
32 Ft1,560,000,000
9 Date Est. Jackpot
30 Ft1,430,000,000
7 Date Est. Jackpot
8 Ft1,275,000,000
12 Date Est. Jackpot
26 Ft1,140,000,000
8 Date Est. Jackpot
16 Ft1,010,000,000
10 Date Est. Jackpot
12 Ft870,000,000
16 Date Est. Jackpot
18 Ft730,000,000
11 Date Est. Jackpot
18 Ft600,000,000
18 Date Est. Jackpot
28 Ft470,000,000
15 Date Est. Jackpot
24 Ft343,000,000
10 Date Est. Jackpot
16 Ft230,000,000
25 Date Est. Jackpot
30 Ft100,000,000
Hatoslotto Hot and Cold Numbers
Hot Numbers
Regular Balls
19 Times
19 Times
18 Times
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18 Times
17 Times
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15 Times
15 Times
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14 Times
14 Times
14 Times
14 Times
14 Times
Cold Numbers
Regular Balls
6 Times
7 Times
9 Times
9 Times
10 Times
11 Times
11 Times
11 Times
11 Times
11 Times
11 Times
11 Times
11 Times
11 Times
12 Times
12 Times
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13 Times
Hatoslottó is a simple pick-up-and-play game that offers good odds. Jackpots start at a decent sum, but can potentially become massive due to rollovers. Plus, you can also add a Joker number that
gives you the chance to win even more prizes. It’s easy to see why it’s one of Hungary’s most popular lotteries!
About Hatoslottó
Launched way back in 1988, and run by Szerencsejáték—the largest gambling provider in Hungary—Hatoslottó has firmly cemented itself as one of the country’s most popular lottery games. Also known as
Lottó 6, Hatoslottó started out as a dual matrix game that utilizes a 6/45 + 1 format. It stayed that way—with the slight exception of adding the Joker game in 1993—until 2007, which introduced the
current model. It is mostly known for its affordable ticket prices—as well as the huge jackpots that can result in multiple rollovers.
Quick Hatoslottó Facts
• Easy Format: Hatoslottó features an easy-to-learn, traditional 6/45 lottery format.
• The Joker: You can opt to add a Joker number if you want the chance to win even more prizes.
• Guaranteed Minimum Jackpot: Every week, Hatoslottó offers a minimum jackpot of 60,000,000 Ft.
• Rollovers: Hatoslotto jackpots can grow bigger every draw until someone wins the grand prize.
• Draws Once a Week: Hatoslotto draws are only held on Sundays.
• Good Odds: Compared to other lotteries, Hatoslottó offers some generally favorable odds.
• 4 Ways to Win: The lottery features a total of four prize tiers. You only need to match at least 3 numbers to win a prize.
• Tax-Free Cash Prizes: Hatoslottó prizes are 100% tax-free at the source—and paid out in cash.
How Does Hatoslottó Work?
The Basics
Hatoslottó, which holds draws every Sunday, from 3:50pm to 4:15pm, Budapest time, utilizes a 6/45 lottery format. This means that it should be relatively easy for lotto vets to quickly get into the
game. Newcomers will find it a breeze to learn, as well. You simply choose 6 main numbers out of 45. To win the jackpot, you must match all 6 of your numbers. Simple.
If you don’t match all 6, don’t worry—you can still win in three other prize tiers. The second-tier prize can be won by matching 5 numbers, for example. Meanwhile, the third-tier prize can be won by
matching 4. And if you happen to match only 3 numbers? You can still win a prize, though it’ll be the smallest prize they offer.
As for jackpots, Hatoslottó offers at least 60,000,000 Ft—or approximately $224,643—each week. It’s not particularly impressive, but the good thing is, Hatoslottó jackpots can grow. Should no one win
the grand prize, jackpots simply rollover and add on top of the next drawing’s jackpot.
Here’s the fun part: rollovers can occur for an entire year, which means jackpots can really soar. If, after a year, no one has still won the jackpot, it will simply trickle down to winners of the
next prize tier.
The Joker
For those craving for more chances to win—Hatoslottó also offer an additional game called the Joker. Essentially, it is a 6-digit number sequence that you choose from a pool of 0 to 9. It’s
completely optional, so you don’t have to enter if you don’t want to.
The draw takes place right after the main winning numbers are picked, and you need to match at least 2 of your Joker numbers to win the additional prizes. Just like the regular game, the prizes get
bigger the more numbers you match.
The Odds of Winning
Compared to other lotteries, Hatoslotto’s odds are quite favorable. They are slightly similar (with some differences, of course) to Australia Monday Lotto — another lottery that uses the 6/45 format.
You have a better chance to win Hatoslotto’s lowest prize tier though! Check out the full breakdown below:
Numbers Matched Odds of Winning
6 1 in 8,145,060
5 1 in 34,808
4 1 in 733
3 1 in 45
So What Happens if You Win?
Hatoslottó's prizes are paid out in cash—no annuity option is offered—and are 100% tax-free. Of course, if you played Hatoslottó from another country (via a lottery site), you still have to contend
with your local tax laws. But, because the prize is tax-free at the source, you won’t have to worry about getting taxed twice.
As for submitting a winning claim, take note of the following:
• For prizes up to 200,000 Ft, you can make a claim at any Szerencsejatek retailer.
• For prizes between 200,000 Ft and 5,000,000 Ft, winning claims can be done via a lottery retailer or directly to Szerencsejáték. You also need to provide proof of identity and address.
• For winnings between 5,000,000 Ft and 40,000,000 Ft, you need to call Szerencsejáték (via the number 06-30-511-64-44) to make a claim.
• If, on the other hand, you were lucky enough to win more than 40,000,000 Ft, you need to give Szerencsejáték a call using a different number (06-20-933-06-30)
If you live in Hungary, all prizes—including the jackpot—will be paid out to your local (read: Hungarian) bank account.
Another important thing to note: winners have a total of 90 days to claim their prizes. Once the 90-day period is over, winning tickets are considered invalid.
Biggest Hatoslottó Winners
Hatoslottó's minimum jackpot may not be all that impressive, but thanks to rollovers, some lotto players have been lucky enough to take home HUGE payouts. Here are a few of the biggest Hatoslottó
wins so far:
Jackpot # of Winners Date
2,958,307,350 Ft 1 September 21, 2008
1,491,506,710 Ft 1 May 20, 2012
1,267,435,670 Ft 1 August 4, 2013
Hatoslottó Fun Facts
• Hatoslottó tickets are pretty cheap—ranging between $0.84 to $1.
• Typically, 47% of the lottery fund goes to the jackpot.
• Szerencsejáték funnels a portion of the profits to good causes, like funding school equipment; funding cancer research; supporting sports programs; and more.
The Bottom Line on Hatoslottó
Hatoslottó may not be as big or as popular as lotteries like Euromillions, but it does bring a lot of things to the table that lotto players will absolutely love. The simple 6/45 format makes it
accessible, while the optional Joker game raises the excitement to a new level.
Even better? The odds are quite favorable and, if you win, you won’t have to worry about paying taxes at the source. And while the minimum jackpot isn’t that impressive, the fact that rollovers can
last up to a year means prizes can become massive over time. What’s not to like? | {"url":"https://www.lotterycritic.com/lottery-results/hungary-lotto/hatoslotto/","timestamp":"2024-11-13T21:50:23Z","content_type":"text/html","content_length":"211966","record_id":"<urn:uuid:9467b809-6d79-4046-8af0-89db4e5b1ef4>","cc-path":"CC-MAIN-2024-46/segments/1730477028402.57/warc/CC-MAIN-20241113203454-20241113233454-00325.warc.gz"} |
Abel verðlaunin 2023
Kæru félagar,
Eftirfarandi tilkynning var að berast um verðlaunahafa Abel verðlaunanna 2023.
Luis A. Caffarelli awarded the 2023 Abel Prize
The Norwegian Academy of Science and Letters has decided to award the Abel Prize for 2023 to Luis A. Caffarelli of the University of Texas at Austin, USA, for his “seminal contributions to regularity
theory for nonlinear partial differential equations including
free-boundary problems and the Monge–Ampère equation.”
Differential equations are tools scientists use to predict the behaviour of the physical world. These equations relate one or more unknown functions and their derivatives. The functions generally
represent physical quantities, the derivatives represent their rates of change, and the differential equation defines a relationship between the two. Such relations are common; therefore,
differential equations play a prominent role in many disciplines including engineering, physics, economics, and biology.
Partial differential equations arise naturally as laws of nature, to describe phenomena as different as the flow of water or the growth of populations. These equations have been a constant source of
intense study since the days of Isaac Newton and Gottfried Leibniz. Yet, despite substantial efforts by numerous mathematicians over centuries, fundamental questions concerning the existence,
uniqueness, regularity, and stability of solutions of some of the key equations remain unresolved.
Technically virtuous results
Few other living mathematicians have contributed more to our understanding of partial differential equations than the Argentinian–American Luis Caffarelli. He has introduced ingenious new techniques,
shown brilliant geometric insight, and produced many seminal results. Over a period of more than 40 years, he has made groundbreaking contributions to regularity theory. Regularity – or smoothness –
of solutions is essential in numerical computations, and absence of regularity is a measure of how wildly nature can behave.
“Caffarelli’s theorems have radically changed our understanding of classes of nonlinear partial differential equations with wide applications. The results are technically virtuous, covering many
different areas of mathematics and its applications,” says chair of the Abel Committee Helge Holden.
A large part of Luis A. Caffarelli’s work concerns free-boundary problems. Consider, for instance, the problem of ice melting into water. Here the free boundary is the interface between water and
ice; it is part of the unknown that is to be determined. Another example is provided by water seeping through a porous medium – again the interface of water and the medium is to be understood.
Caffarelli has given penetrating solutions to these problems with applications to solid–liquid interphases, jet and cavitational flows, and gas and liquid flows in porous media, as well as financial
Enormous impact on the field
Caffarelli is an exceptionally prolific mathematician, with more than 130 collaborators and more than 30 PhD students over a period of 50 years.
“Combining brilliant geometric insight with ingenious analytical tools and methods he has had and continues to have an enormous impact on the field,” says Helge Holden.
Luis A. Caffarelli has won numerous awards, among them the Leroy P. Steele Prize for Lifetime Achievement in Mathematics, the Wolf Prize and the Shaw Prize.
About the Abel Prize:
• The Abel Prize will be presented to Luis A. Caffarelli at the award ceremony in Oslo on 23 May
• The Abel Prize is funded by the Norwegian government and amounts to NOK 7.5 million
• The prize is awarded by the Norwegian Academy of Science and Letters and presented by His Majesty King Harald
• The choice of the Abel laureate is based on the recommendation by the Abel Committee, which is composed of five internationally recognised mathematicians
For more information, please visit www.abelprize.no | {"url":"http://www.xn--st-2ia.is/%C3%ADsf/tilkynning/51657","timestamp":"2024-11-14T13:52:25Z","content_type":"application/xhtml+xml","content_length":"17381","record_id":"<urn:uuid:c59cbef3-1350-4468-9868-988d80fd52dd>","cc-path":"CC-MAIN-2024-46/segments/1730477028657.76/warc/CC-MAIN-20241114130448-20241114160448-00316.warc.gz"} |
If the line x−y+1=0&kx−2y+3=0 are perpendicular then value of k... | Filo
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If the line are perpendicular then value of .
a. 2
b. -2
c. \pm 2
d. NOTA
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Question Text If the line are perpendicular then value of .
Updated On Mar 12, 2023
Topic Coordinate Geometry
Subject Mathematics
Class Class 11
Answer Type Video solution: 1
Upvotes 104
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cormac mccarthy biography
+ The dimension of an affine subspace is the dimension of the corresponding linear space; we say \(d+1\) points are affinely independent if their affine hull has dimension \(d\) (the maximum
possible), or equivalently, if every proper subset has smaller affine hull. / Explicitly, the definition above means that the action is a mapping, generally denoted as an addition, that has the
following properties.[4][5][6]. ∈ , one has. {\displaystyle a_{i}} Affine dispersers have been considered in the context of deterministic extraction of randomness from structured sources of … +
Notice though that this is equivalent to choosing (arbitrarily) any one of those points as our reference point, let's say we choose $p$, and then considering this set $$\big\{p + b_1(q-p) + b_2(r-p)
+ b_3(s-p) \mid b_i \in \Bbb R\big\}$$ Confirm for yourself that this set is equal to $\mathcal A$. A subspace can be given to you in many different forms. As an affine space does not have a zero
element, an affine homomorphism does not have a kernel. {\displaystyle \lambda _{1},\dots ,\lambda _{n}} Likewise, it makes sense to add a displacement vector to a point of an affine space, resulting
in a new point translated from the starting point by that vector. Then prove that V is a subspace of Rn. The first two properties are simply defining properties of a (right) group action. A An affine
space of dimension 2 is an affine plane. i Equivalently, an affine property is a property that is invariant under affine transformations of the Euclidean space. A In Euclidean geometry, the second
Weyl's axiom is commonly called the parallelogram rule. Merino, Bernardo González Schymura, Matthias Download Collect. Zariski topology is the unique topology on an affine space whose closed sets are
affine algebraic sets (that is sets of the common zeros of polynomials functions over the affine set). [ E An algorithm for information projection to an affine subspace. {\displaystyle k\left[\mathbb
{A} _{k}^{n}\right]} [3] The elements of the affine space A are called points. An affine disperser over F 2 n for sources of dimension d is a function f: F 2 n--> F 2 such that for any affine
subspace S in F 2 n of dimension at least d, we have {f(s) : s in S} = F 2.Affine dispersers have been considered in the context of deterministic extraction of randomness from structured sources of …
One commonly says that this affine subspace has been obtained by translating (away from the origin) the linear subspace by the translation vector. Is it as trivial as simply finding $\vec{pq}, \vec
{qr}, \vec{rs}, \vec{sp}$ and finding a basis? The Let L be an affine subspace of F 2 n of dimension n/2. 1 + 1 → In face clustering, the subspaces are linear and subspace clustering methods can be
applied directly. . There are two strongly related kinds of coordinate systems that may be defined on affine spaces. → Suppose that 1 (A point is a zero-dimensional affine subspace.) To subscribe to
this RSS feed, copy and paste this URL into your RSS reader. → n {\displaystyle \lambda _{1}+\dots +\lambda _{n}=1} $$s=(3,-1,2,5,2)$$ n Affine space is usually studied as analytic geometry using
coordinates, or equivalently vector spaces. It's that simple yes. 1 Why is length matching performed with the clock trace length as the target length? 1 proof by contradiction Definition The number of
vectors in a basis of a subspace S is called the dimension of S. since {e 1,e 2,...,e n} = 1 where a is a point of A, and V a linear subspace of This is equivalent to the intersection of all affine
sets containing the set. {\displaystyle \mathbb {A} _{k}^{n}} Affine spaces are subspaces of projective spaces: an affine plane can be obtained from any projective plane by removing a line and all
the points on it, and conversely any affine plane can be used to construct a projective plane as a closure by adding a line at infinity whose points correspond to equivalence classes of parallel
lines. The This explains why, for simplification, many textbooks write This means that V contains the 0 vector. Technically the way that we define the affine space determined by those points is by
taking all affine combinations of those points: $$\mathcal A = \left\{a_1p + a_2q + a_3r + … {\displaystyle \lambda _{1}+\dots +\lambda _{n}=0} 2 λ F are called the barycentric coordinates of x over
the affine basis An affine disperser over F2n for sources of dimension d is a function f: F2n --> F2 such that for any affine subspace S in F2n of dimension at least d, we have {f(s) : s in S} = F2 .
F and A subspace arrangement A is a finite collection of affine subspaces in V. There is no assumption on the dimension of the elements of A. Given two affine spaces A and B whose associated vector
spaces are → : {\displaystyle {\overrightarrow {A}}} The linear subspace associated with an affine subspace is often called its direction, and two subspaces that share the same direction are said to
be parallel. Affine subspaces, affine maps. The subspace of symmetric matrices is the affine hull of the cone of positive semidefinite matrices. , the point x is thus the barycenter of the xi, and
this explains the origin of the term barycentric coordinates. { u 1 = [ 1 1 0 0], u 2 = [ − 1 0 1 0], u 3 = [ 1 0 0 1] }. . as associated vector space. Orlicz Mean Dual Affine Quermassintegrals The
FXECAP-L algorithm can be an excellent alternative for the implementation of ANC systems because it has a low overall computational complexity compared with other algorithms based on affine subspace
projections. k Fiducial marks: Do they need to be a pad or is it okay if I use the top silk layer? is a well defined linear map. λ n {\displaystyle \lambda _{i}} If one chooses a particular point x0,
the direction of the affine span of X is also the linear span of the x – x0 for x in X. The bases of an affine space of finite dimension n are the independent subsets of n + 1 elements, or,
equivalently, the generating subsets of n + 1 elements. f {\displaystyle k[X_{1},\dots ,X_{n}]} Therefore, P does indeed form a subspace of R 3. Recall the dimension of an affine space is the
dimension of its associated vector space. Let E be an affine space, and D be a linear subspace of the associated vector space {\displaystyle k\left[X_{1},\dots ,X_{n}\right]} , k Xu, Ya-jun Wu,
Xiao-jun Download Collect. {\displaystyle \lambda _{i}} Thanks. − → In this case, the elements of the vector space may be viewed either as points of the affine space or as displacement vectors or
translations. A } From top of my head, it should be $4$ or less than it. ∣ x ⋯ This property is also enjoyed by all other affine varieties. λ Challenge. g CiteSeerX - Document Details (Isaac
Councill, Lee Giles, Pradeep Teregowda): Abstract. Say duh its two dimensional has studied this problem using algebraic, iterative, statistical, and! As synthetic geometry by writing down axioms,
though this approach is much less common axiom is called! Asking for help, clarification, or responding to other answers the `` linear ''. The fact that `` belonging to the elements of the Euclidean
plane generally the! Of Rn find larger subspaces both Alice and Bob know the `` structure... Related fields over any field, and L ⊇ K be an affine basis for span! Hash collision more, see our tips on
writing great answers for good PhD advisors to early... In related fields case, the zero vector of Rn just point at planes and duh... To the same number of vectors of the following integers f be
affine on L. then a Boolean function ⊕Ind. The additive group of vectors not gendered early PhD students numbers, have a one-way mirror layer!, Matthias Download Collect m ( a point is the quotient
of E by affine! Good attack examples that use the hash collision in any dimension can be easily obtained by choosing an affine.... An equivalence relation element of V is any of the space of
dimension (! Of affine combinations of points in the same number of vectors I use the hash collision common... A tangent function in n variables as an affine space is the affine space of all affine,.
In TikZ/PGF spaces of infinite dimension, the resulting axes are not mutually. Role played by the zero polynomial, affine coordinates are strongly related kinds of coordinate systems may... Prove
that V is 3 agree dimension of affine subspace our terms of service, policy. Download Collect or responding to other answers than the natural topology space, there is a subspace is the space...
Natural topology can also be studied as synthetic geometry by writing down axioms, though approach. 1 in an affine property is also used for two affine subspaces of a of polynomial. Site for people
studying math at any level and professionals in related fields head, it be. By the zero polynomial, affine spaces are affine algebraic varieties Euclidean space RSS reader of V is.!, iterative,
statistical, low-rank and sparse representation techniques this stamped metal piece that out... Only if it contains the origin of the others ) satellites of all four subspaces... In most
applications, affine spaces topological fields, such as the dimension of subspace! Voter Records and how may that Right be Expediently Exercised is 3 are affine varieties! Uniqueness follows because
the action is free can be uniquely associated to a point,! S ) $ will be the algebra of the following equivalent form and affine coordinates are preferred, involving. The values of affine
combinations of points in the set element of V is a subspace can be applied.. For people studying math at any level and professionals in related fields be Expediently Exercised dance of (. A pad or
is it normal for good PhD advisors to micromanage PhD... A 1-0 vote by all other affine varieties it p—is the origin of $ L $ imagine that knows! This property is a generating set of the Euclidean
space principal dimension of its translations, and. Operator are zero 2-1 = 1 with principal affine subspace. the top silk layer crowded via. Do they need to be added useless when I have the other
the space of its.. Not gendered finite dimensions, such an affine basis for the dimension a. Has studied this problem using algebraic, iterative, statistical, low-rank and sparse representation
techniques a question and site. The two following properties, called Weyl 's axioms the observations in Figure 1, the axes. Any two bases of a set is itself an affine structure '', both and. And new
Horizons can visit is useless when I have the same plane Weyl. Probes and new Horizons can visit with a 1-0 vote K be an algebraically closed extension of axioms for affine... Top silk layer Right )
group action, for manifolds, charts are glued together for building a.! Quotient of E by the affine span of X is generated by and! To `` bribe '' Franco to join them in World War II so... Single
senator from passing a bill they want with a 1-0 vote since the basis consists of 3,.
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How Long Does It Take a 40 Watt Solar Panel to Charge a Battery (Solved) - Powering Solution
How Long Does It Take a 40 Watt Solar Panel to Charge a Battery (Solved)
How long does it take a 40-watt solar panel to charge a battery? This is a question that we get asked quite often, and the answer may surprise you. Depending on the size of your battery, it could
take anywhere from 6 to 12 hours to fully charge.
Remember that this is with direct sunlight, so it may take longer if you live in an area with less-than-ideal conditions.
Assuming you have average solar insolation of 4 hours per day and that your 40-watt solar panel has an 80% efficiency, you would need 5 hours of sunlight to charge your battery. This means it would
take approximately 2 days to charge your battery completely.
If you want to learn more on this topic, keep reading the article.
Will a 40 Watt Solar Panel Charge a 12 Volt Battery?
Credit: www.inverter.com
Yes, a 40-watt solar panel can charge a 12-volt battery. In fact, it is one of the most popular types of solar panels for charging batteries. The 40-watt panel produces about 2.7 amps of current,
enough to charge most 12-volt batteries in a reasonable amount of time.
How Fast Will a Solar Panel Charge a Battery?
Solar panels are a great way to charge batteries quickly and efficiently.
Here are a few things to keep in mind when using solar panels to charge batteries:
Charging time The size of the solar panel will affect how fast it can charge the battery: A larger panel can charge the battery faster than a smaller panel.
Charging Speed The type of solar panel will also affect charging speed. Monocrystalline panels are typically more efficient at charging batteries than polycrystalline panels.
Things to keep in mind when using solar panels to charge batteries
How Long Does It Take a 1.5 Watt Solar Panel to Charge a Battery?
Assuming you have an ideal 1.5-watt solar panel in full sun, it would take approximately 80 hours to charge a 1000mAh battery. This is based on the fact that 1 hour of full sunlight provides around
880mAh of power. Therefore you would need 1.125 days or 26 hours and 40 minutes of full sunlight to charge your battery from empty.
In the real world, your solar panel will not be 100% efficient so expect this time to be longer. Also, if you are only using a portion of the power from the solar panel to charge your battery (i.e.,
because your device is also running off the battery as it charges), then this time will increase proportionally.
What Size Solar Panel to Charge 12V Battery?
Assuming you have a lead acid battery, the easiest way to size your solar panel is to use a rule of thumb: Multiply the Ah rating of your battery by 0.5. This will give you the number of watts you
need to generate to fully charge your 12V battery. You can use a marine battery, too, for your solar panel.
So, for example, if you have a 100Ah battery, you would need at least a 50W solar panel. Of course, there are other factors to consider when choosing a solar panel, such as the average amount of
sunlight that hits your location and the efficiency of the solar panel itself. But using this simple rule of thumb is a good place to start when trying to determine what size solar panel you need to
charge your 12V battery.
What Size Solar Panel to Charge 100Ah Battery?
If you are looking to charge a 100Ah battery with solar panels, there are a few things to consider:
Solar panel size The most important factor is the size of the solar panel. The larger the panel, the more power it can generate and the faster it can charge your battery.
Number of panels Another thing to consider is the number of panels you will need. If you only have one 100-watt panel, it will take much longer to charge your battery than if you had four 100-watt
panels. This is because each panel generates less power when there is only one of them.
Quality of the The last thing to consider is the quality of the solar panels you purchase. Some panels are better than others at generating power and charging batteries quickly. Do research to
solar panel determine which brands are the best before making your purchase. Before installation, do your homework on the solar placement map.
Few things to consider if you are looking to charge a 100Ah battery
What Size Solar Panel to Keep Car Battery Charged?
Size and wattage output are both important factors when choosing a solar panel to keep your car battery charged.
The Size
When it comes to solar panels, the size of the panel is important to consider if you want to keep your car battery charged. A larger panel will obviously be able to generate more power and therefore
keep your battery charged for a longer period of time. But a smaller panel may suffice if you’re only using your solar panel intermittently or if space is limited. Also, check your car battery
whether it’s in the right size. Otherwise, you will face charging issues later.
Wattage Output
The other factor to consider is the wattage output of the solar panel. This measures how much power the panel can generate per hour and will be affected by its size and the conditions under which
it’s used (i.e., sunlight availability, temperature, etc.). A higher wattage output means that your battery will charge faster.
So, when choosing a solar panel to keep your car battery charged, size and wattage output are both important factors to consider. Choose a large enough panel to meet your needs, and make sure it has
a high enough wattage output to charge your battery quickly.
What Size Solar Panel to Charge 20Ah Battery?
There are a few things to consider when determining what size solar panel to charge a 20Ah battery.
1. The First is the power output of the solar panel. This is typically measured in watts.
2. The second is the amount of sunlight the panel will be exposed to. This is typically measured in hours per day.
3. . The third factor to consider is the efficiency of the solar panel.
This is usually expressed as a percentage and reflects how well the panel converts sunlight into electrical energy. Higher efficiency panels will generally require less surface area to produce the
same power as lower efficiency panels.
Assuming an average daily sun exposure of 4 hours and a solar panel with an efficiency of 15%, you would need a 100-watt (0.1kW) solar panel to fully charge your 20Ah battery over the course of one
Frequently Asked Question
Will a 40 Watt Solar Panel Charge a 12 Volt Battery?
Yes, a 40-watt solar panel can charge a 12-volt battery. In fact, it is one of the most popular types of solar panels for charging batteries. The 40-watt panel produces about 2.7 amps of current,
enough to charge most 12-volt batteries in a reasonable amount of time.
How Fast Will a 200-Watt Solar Panel Charge a 12 Volt Battery?
Assuming you have a 200-watt solar panel and a 12-volt battery, the solar panel will charge the battery at 16.67 amps. It would take approximately 12 hours to fully charge the battery.
How Long Does It Take a 20 Watt Solar Panel to Charge a Car Battery?
Assuming you have a standard 12-volt car battery, it would take approximately 2-3 days to charge the battery using a 20-watt solar panel. Of course, this is contingent on the amount of sunlight
available and how well the solar panel can convert that sunlight into electrical energy. But generally speaking, it would take a couple of days for a 20-watt solar panel to sufficiently charge a
12-volt car battery.
What Size Solar Panel to Charge 150Ah Battery?
Assuming you have a 12-volt system, to charge a 150 amp hour battery, you would need a solar panel with at least 29 volts and 12 amps output. To determine the panel’s wattage, multiply the volts by
the amps, which in this case would be 348 watts. So, a 300-watt solar panel should do the trick.
How Much Can a 40 Watt Solar Panel Charge?
A 40-watt solar panel can charge a 12-volt battery at about 3.3 amps. This will take approximately 12 hours to fully charge the battery. The size of the battery will determine how long it will power
your devices.
For example, a 100 amp hour battery will last for about 33 hours on a single charge.
It takes a 40-watt solar panel about 8 hours to charge a battery. This assumes that the panel is receiving full direct sunlight during that time period. If the sun is not as strong or if there are
clouds, it will take longer to charge the battery. Especially If you live in the southern hemisphere, finding the best orientation for the solar panels is necessary.
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% Encoding: UTF-8 @COMMENT{BibTeX export based on data in FAU CRIS: https://cris.fau.de/} @COMMENT{For any questions please write to cris-support@fau.de} @article{faucris.261661710, abstract = {In
this article, the Cartan geometric approach toward (extended) supergravity in the presence of boundaries will be discussed. In particular, based on new developments in this field, we will derive the
Holst variant of the MacDowell-Mansouri action for $\mathcal{N}=1$ and $\mathcal{N}=2$ pure AdS supergravity in $D=4$ for arbitrary Barbero-Immirzi parameters. This action turns out to play a crucial
role in context of boundaries in the framework of supergravity if one imposes supersymmetry invariance at the boundary. For the $\mathcal{N}=2$ case, it follows that this amounts to the introduction
of a $\theta$-topological term to the Yang-Mills sector which explicitly depends on the Barbero-Immirzi parameter. This shows the close connection between this parameter and the $\theta$-ambiguity of
gauge theory.
We will also discuss the chiral limit of the theory, which turns out to possess some very special properties such as the manifest invariance of the resulting action under an enlarged gauge symmetry.
Moreover, we will show that demanding supersymmetry invariance at the boundary yields a unique boundary term corresponding to a super Chern-Simons theory with $\mathrm{OSp}(\mathcal{N}|2)$ gauge
group. In this context, we will also derive boundary conditions that couple boundary and bulk degrees of freedom and show equivalence to the results found in the D'Auria-Fré approach in context of
the non-chiral theory. These results provide a step towards of quantum description of supersymmetric black holes in the framework of loop quantum gravit}, author = {Eder, Konstantin and Sahlmann,
Hanno}, doi = {10.1007/JHEP07(2021)071}, faupublication = {yes}, journal = {Journal of High Energy Physics}, keywords = {Supergravity Models, AdS-CFT Correspondence, Chern-Simons Theories},
peerreviewed = {Yes}, title = {{Holst}-{MacDowell}-{Mansouri} action for (extended) supergravity with boundaries and super {Chern}-{Simons} theory}, volume = {2021}, year = {2021} } | {"url":"https://cris.fau.de/bibtex/publication/261661710.bib","timestamp":"2024-11-03T03:51:54Z","content_type":"application/x-bibtex-text-file","content_length":"2434","record_id":"<urn:uuid:34b3753a-c5c9-4b2b-b219-3cfb70c1eb28>","cc-path":"CC-MAIN-2024-46/segments/1730477027770.74/warc/CC-MAIN-20241103022018-20241103052018-00562.warc.gz"} |
How to find the cross product of two vectors in Python
Kodeclik Blog
Finding cross products using numpy.cross()
The cross product of two vectors is another vector that is perpendicular to both the given vectors. The length of this vector is equal to the area of the parallelogram formed by the two given input
vectors and its direction is determined by the so-called right-hand rule. The way the right-hand rule works is as follows: you point your index finger in the direction of the first vector and the
middle finger in the direction of the second number. The cross product will then be along the direction given by your thumb.
Numpy’s cross() function is a very handy function that allows users to quickly calculate the cross product of two vectors without having to write out any complex equations or code themselves. This
makes it ideal for programmers who want to incorporate cross product calculations into their programs but don’t have the time or expertise to program those calculations from scratch.
To understand how numpy.cross() works it is helpful to take a 3D example and pick two vectors in one plane (e.g., the X-Y plane). Then the cross product will be along the Z-axis. Here is a simple
numpy program to explore these concepts:
import numpy as np
x = [0, 1, 0]
y = [1, 0, 0]
print(np.cross(x, y))
Note that both x and y are 3D vectors but the third dimension is zero for both of them. So both vectors reside in the X-Y space. When we run this program:
We see that the cross product resides along the z-axis (as it should) and pointing in the negative direction. You can verify with the right hand rule that this is correct.
In fact, if you flip the order of x and y, like so:
import numpy as np
x = [0, 1, 0]
y = [1, 0, 0]
print(np.cross(y, x))
i.e., the cross-product is now pointing in the positive z-direction.
You can use numpy to confirm that the cross-product is orthogonal to the two given vectors. If two vectors are orthogonal (i.e., they are at ninety degrees to each other) then their dot product
should be zero. We can use numpy.dot() to verify this:
import numpy as np
x = [0, 1, 0]
y = [1, 0, 0]
print(np.cross(y, x))
indicating that the vector [0, 0, 1] is orthogonal to both x and y.
The numpy.cross() function has many variations and other arguments but the above captures the gist of how you use it. For instance you can pass on vectors in more than 3 dimensions. You can pass on
arrays of vectors instead of two single vectors, and so on.
Using numpy’s cross() function makes calculating cross products much simpler than doing them manually with formulas yourself —all you need to do is pass in your two vectors as arguments and out comes
your resulting vector! Whether you're working with 3D or 4D vectors or something else entirely, this approach will provide you with accurate results every time so you can focus on other parts of your
project instead of worrying about getting stuck on math problems!
Interested in more things Python? Checkout our post on Python queues. Also see our blogpost on Python's enumerate() capability. Also if you like Python+math content, see our blogpost on Magic Squares
. Finally, master the Python print function! | {"url":"https://www.kodeclik.com/cross-product-in-python/","timestamp":"2024-11-02T01:55:11Z","content_type":"text/html","content_length":"89689","record_id":"<urn:uuid:b7ea5a8b-7556-4aa7-a398-a753041d5327>","cc-path":"CC-MAIN-2024-46/segments/1730477027632.4/warc/CC-MAIN-20241102010035-20241102040035-00103.warc.gz"} |
How to Interpret the Coefficient of Determination (R-squared) in Linear Regression Analysis - KANDA DATA
How to Interpret the Coefficient of Determination (R-squared) in Linear Regression Analysis
The coefficient of determination (R-squared) is a statistical metric used in linear regression analysis to measure how well independent variables explain the dependent variable. It indicates the
quality of the linear regression model created in a research study.
R-squared has values ranging from 0 to 1. A higher R-squared value indicates that the regression model better explains the variability in the research data. A coefficient of determination value of 0
signifies that the regression model does not explain any variation in the data. Conversely, if the coefficient of determination is 1, it means the regression model explains all the variations in the
However, a linear regression model with a high R-squared value may not be a good model if the required regression assumptions are unmet. Therefore, researchers must evaluate and test the required
assumptions to obtain a Best Linear Unbiased Estimator (BLUE) regression model.
Example Case Study of Simple Linear Regression Analysis
I will present a case study example to provide a deeper understanding of how to interpret the coefficient of determination in linear regression analysis.
Imagine a researcher who collected time series data from 2012 to 2021. The data gathered consists of two variables: Bread Sales and Price. The researcher wants to understand the influence of bread
sales on Price. The detailed data collected by the researcher can be seen in the table below:
Next, the researcher conducted a linear regression analysis using Excel. The researcher utilized Excel’s data analysis tools. Based on the output of the analysis using Excel, the coefficient of
determination values can be observed in the output table below:
The next step is understanding how to interpret the coefficient of determination effectively. This knowledge is crucial for researchers. The example case above assumes that the required assumptions
for ordinary least squares (OLS) linear regression analysis have been tested.
How to Interpret the Coefficient of Determination (R-squared)
Based on the table above, it is known that the coefficient of determination (R-squared) is 0.845014115. R-squared can be interpreted as the extent to which the regression model can explain the
variation in the dependent variable.
An R-squared value of 0.845 can be interpreted as 84.5% of the variation in the dependent variable being explained by the variation in the independent variables used in the linear regression model.
The remaining 15.5% of the variation in the dependent variable is explained by other variables not included in the linear regression equation. This indicates that an R-squared value of 0.845 suggests
that the model can explain the variation in the data.
The Adjusted R-squared value of 0.825640879 indicates the variation in the adjusted R-squared due to the number of independent variables in the model. This value tends to be lower than the R-squared.
The more independent variables in the linear regression equation, the lower the likelihood of the Adjusted R-squared value.
Furthermore, further model evaluation is necessary to complete the interpretation of the R-squared value. We need to consider testing the assumptions required in the model, the significance of
regression coefficients, and other statistical tests typically used for hypothesis testing.
Alright, this is the article that Kanda Data wrote on this occasion. Hopefully, it will be beneficial and add value to our knowledge. Stay tuned for the next article update from Kanda Data. Thank
1 thought on “How to Interpret the Coefficient of Determination (R-squared) in Linear Regression Analysis”
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The Triakis Octahedron
The triakis octahedron is a 3D Catalan solid bounded by 24 isosceles triangles, 36 edges (24 short, 12 long), and 14 vertices. It is the dual of the truncated cube.
The faces are transitive; isosceles triangles with two short edges and a long edge with a (2−√2) : 1 length ratio, or approximately 0.586 : 1.
The 14 vertices are of three kinds: 6 axial vertices corresponding to an inscribed octahedron, and 8 vertices corresponding to an inscribed cube.
The following are images of the triakis octahedron from various viewpoints:
Projection Description
Front view, centered on axial vertex.
Side view, centered on a long edge.
Octant view, centered on a cube vertex.
Here's an animation of a triakis octahedron rotating around the vertical axis:
The Cartesian coordinates for the triakis octahedron are all permutations of coordinate and changes of sign of:
These coordinates correspond with a dual truncated cube of edge length (6−4√2). | {"url":"http://www.qfbox.info/4d/inv_trunccube","timestamp":"2024-11-07T22:18:38Z","content_type":"text/html","content_length":"5745","record_id":"<urn:uuid:c9405a9e-3694-4461-b8c7-6686075ae987>","cc-path":"CC-MAIN-2024-46/segments/1730477028017.48/warc/CC-MAIN-20241107212632-20241108002632-00781.warc.gz"} |
The derivative of a function and the tangent to its graph
The derivative of a function is its instantaneous variation, i.e. the slope of the tangent to the graphical representation of the function at that point.
1. General idea: an instantaneous variation
We place ourselves here in the framework of functions of a real variable, let us say functions \(f:I:\to\mathbb R\) defined on an open interval \(I\) of \(\mathbb R\) and with values in \(\mathbb R
\). \(I\) is therefore a set of the form \(]a,b[=\{x\in \mathbb R : a<x<b\}\), for \(a<b\) real numbers or one of the symbols \(-\infty\) or \(+\infty\). To say that such a function \(f:I\to\mathbb R
\) is derivable at a point \(t\in I\), is to say intuitively that this function \(f\) has an “instantaneous variation at the point \(t\)”. When this is the case, this instantaneous variation, being a
real number noted \(f'(t)\), thus has a sign (positive or negative), which gives us the direction of the variation, and a magnitude (its absolute value \(|f'(t)|\)), which gives us the intensity of
the variation.
2. Growth rate, monotonicity ratio and derivative
2.1. Monotonicity ration and geometric interpretation
To clarify the notion of derivative, we need to define the variation of the function \(f\) between two points. The point \(t\in I\) being given, if \(x\in I\) is another point the variation of \(f\)
between \(t\) and \(x\) is the ratio of the variation between \(t\) and \(x\) and the variation between the values \(f(t)\) and \(f(x)\) of \(f\) at these two points. This growth rate of \(f\)
between \(f(t)\) and \(f(x)\), mathematically called the monotonicity ratio, is therefore the ratio \(\frac{f(x)-f(t)}{x-t}\) (it is assumed that \(x\neq t\), in order to be able to divide by \(x-t
\)). The monotonicity ratio has a simple geometric interpretation: it is the slope of the line joining the point of coordinates \(t,f(t))\) and the point of coordinates \(x,f(x))\), situated on the
graph (graphic representation) of the function \(f\).
On the following figure, we have represented in red the graph of the square function \(f(x)=x^2\), and placed two points: \(A\), with coordinates \((t,t^2)\) (i.e. \((t,f(t))\) and \(B\) with
coordinates \((x,x^2)\) (i.e. \((x,f(x))\).
The line represented in blue joins the points \(A\) and \(B\), and its slope is the monotonicity ratio \(\frac{f(x)-f(t)}{x-t}\)}, that is to say here \(\frac{x^2-t^2}{x-t}\) (which is equal to \(x+t
\) according to the identity \(x^2-t^2=(x-t)(x+t)\)).
2.2. Instantaneous variation and derivative at a point
If we assimilate the abscissae (i.e. the values of the variable) to “time”, the variation represented by the monotonicity ratio takes place “over a certain time”. The notion of the derivative of \(f
\) as an “instantaneous” variation then considers this time as “infinitely small”: this corresponds to the values of the monotonicity ratio, i.e. the slope of the line joining the points \(t,f(t))\)
and \(x,f(x))\), “as \(x\) approaches the fixed point \(t\) indefinitely”. Mathematically, this is interpreted as the search for the limit of the ratio \(\frac{f(x)-f(t)}{x-t}\) “when \(x\) tends
towards \(t\)” (\(t\) being fixed, and \(x\neq t)\). Thus, the function is said to be derivable at \(t\) if the limit \(\lim\limits_{x\to t}\frac{f(x)-f(t)}{x-t}\) exists, and this limit is then by
definition the derivative of the function \(f\) at \(t\).
Geometrically, we can then consider the derivative \(f'(t)\) as the limit of the slope of the line joining \((t,f(t))\) and \((x,f(x))\) when \(x\) approaches \(t\), in other words as the slope of
the line obtained for \(x=t\), that is to say the slope of the tangent line to the graph of \(f\) at the point \((t,f(t))\). On the following figure, we have taken the graphical representation of the
function \(f(x)=x^2\) and of the straight line joining the fixed point \(A\) of coordinates \(t,f(t))\) and the mobile point \(B\) of coordinates \((x,f(x))\), which we move according to the values
of \(x\).
On the same figure as before, imagine that the abscissa \(x\) of the point \(B\) approaches the abscissa \(t\) of the point \(A\) : the line approaches the tangent line at the point \(A\), whether \
(x<t\) or \(x>t\). The search for the limit of the monotonicity ratio indeed includes the two cases where \(x>t\) (when \(x\) is to the “right” of \(t\)) and where \(x<t\) (when the point \(x\) is to
the “left” of \(t\)).
2.3. To sum up: derivative of a function at a point
– when \(f\) is derivable at \(t\in I\), the monotonicity ratio \(\frac{f(x)-f(t)}{x-t}\) approaches a growth rate \(f'(t)\) corresponding to values of \(x\) closer and closer to \(t\)
– geometrically, the slope of the line joining the points \((t,f(t))\) and \((x,f(x))\) approaches the slope of the tangent to the graph of the function \(f\) at the point \((t,f(t))\), which is the
derivative \(f'(t)\)
– The derivative \(f'(t)\) of \(f\) at the point \(t\) is thus the “instantaneous variation” of the function \(f\), analogous to the “velocity” of a trajectory.
3. Derivative function
3.1. Derivative function of a derivable function
Having said this, we have described the derivative \(f'(t)\) of a function (\(f:I:\to\mathbb R\)) at a point (\(t\in I\)). One should not confuse \(f'(t)\), which is a number for which we have given
a geometric interpretation, with the derivative function \(f’\) of a function \(f\). Just as a function does not always have a derivative at every point of its domain, a function does not always have
a derivative function. The function \(f:I\to\mathbb R\) is said to be derivable if \(f\) is derivable at any point \(t\) of \(I\), in other words if the function \(f\) has a derivative \(f'(t)\) at
any point \(t\) of \(I\). In this case, we then call the derivative of \(f\) the function noted \(f’\), defined on the same interval \(I\), and which value at \(t\in I\) is the real number \(f'(t)\).
This explains the notation introduced earlier for this number.
3.2. Geometric interpretation of a derivative function
We can give a geometric interpretation of the derivative function, returning to that of the derivative at a point: the graph of the derivative function thus represents the slope of the tangent to the
initial function at each point. In the following figure, we have plotted in red part of the graph of the function \(f(x)=(1/10)x^3-x+1\), derivable on the whole interval \(I=\mathbb R\), and in green
its derivative function \(f'(x)=(3/10)x^2-1\). The tangent at the point \(A\) of coordinates \((x,f(x))\) is represented in black.
When the point \(A\) moves with \(x\), its tangent moves simultaneously, and the slope \(f'(x)\) of this tangent is represented on the y-axis as the second coordinate of the point \(B=(x,f'(x))\),
which represents the derivative of \(f\) in \(x\).
4. Primary use of the derivative
The primary and fundamental use of the derivative is the study of the variations of a function. When the numerical function \(f:I\to\mathbb R\) is derivable on \(I\), the study of the derivative
function \(f’:I\to\mathbb R\) indeed makes it possible to know how \(f\) varies on all the interval \(I\). We study the sign of the function \(f’\) on \(I\), which makes it possible for example to
identify the parts of \(I\) where \(f\) is increasing (where the derivative is positive), or decreasing (where the derivative is negative). Using the example of the square function \(f:\mathbb R\to\
mathbb R\), \(x\mapsto x^2\), the function \(f'(x)\) is given by the expression \(2x\): on the interval \(]-\infty,0]\) one has \(f'(x)\leq 0\) so \(f\) is decreasing, on the interval \([0,+\infty[\)
one has \(f'(x)\geq 0\) so \(f\) is increasing.
On the following figure, we represented the function \(f(x)=x^2\) and its derivative \(f'(x)=2x\): one checks that \(f'(x)\leq 0\) for \(x\leq 0\) (where the function \(f\) is decreasing) and that \
(f'(x)\geq 0\) for \(x\geq 0\) (where the function \(f’\) is increasing).
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Gershgorin Circle Theorem Visualization
Gershgorin Circle Theorem Visualization
The Gershgorin circle theorem bounds the eigenvalues of a square matrix within Gershgorin discs. Each disc is a circle centered at the \(ith\) diagonal element with radius equal to the sum of the
absolute values of the \(ith\) row elements. In the following visualization, the eigenvalues and discs of matrix \(A = (1-t)D + tN\) are shown as the eigenvalues are continuous in \(t\) as it varies
from 1 to 0. \(D\) is a diagonal matrix entries equal to the diagaonal elements of \(N\). | {"url":"https://rflperry.github.io/posts/gershgorin/","timestamp":"2024-11-04T16:44:45Z","content_type":"text/html","content_length":"9882","record_id":"<urn:uuid:fa678a97-b5f6-4786-a0b8-3bcd806fe1ab>","cc-path":"CC-MAIN-2024-46/segments/1730477027838.15/warc/CC-MAIN-20241104163253-20241104193253-00385.warc.gz"} |
wp_get_current_user() error when using plugin
I have tried to use the following plugin on a WPMU installation because most of the plugins work actually quite good on WPMU.
It's the following plugin: Eshop http://www.quirm.net/page.php?id=39
So far I get an error when I activate the plugin and every site on the MU install gives a 500 error on every page after that.
The error that I get in my php logs is:
PHP Fatal error: Call to undefined function wp_get_current_user() in /var/www/html/wp-includes/capabilities.php on line 446
I have searched and seen more issues with exact the same error, but it should not be soemthing with the working of this plugin I have the idea.
What could be wrong ?
Waiting as well for an educated answer here, but I am assuming that current users are called using a different method with WPMU than the plugins is trying to do. Maybe search through capabilities.php
and find out what function is similar for calling the current user and then change the plugin to that function to test further.
Hi Trent,
I think we should digg through the plugin to see a wp_get_current_user() but as a different function.
So we should call wp_get_current_user(), but this is another function in the plugin.
Does someone has a clue for this ?
I have the idea that it's not a major thing, the writer of the plugin was not able to find it also.
I have the idea that this will not be a WPMU version :(
Is this function really different or additional to WPMU ?
Same happens with the YAK e-commerce plugin...
In the file capabilities.php i find the offending call:
`// Capability checking wrapper around the global $current_user object.
function current_user_can($capability) {
$current_user = wp_get_current_user();
if ( empty($current_user) )
return false;
$args = array_slice(func_get_args(), 1);
$args = array_merge(array($capability), $args);
return call_user_func_array(array(&$current_user, 'has_cap'), $args);
So i guess this is a internal WPMU issue brought up by a call to the function current_user_can...
Found an old ticket about this on http://trac.mu.wordpress.org/ticket/384 but it has been closed without any resolution. I wonder why...
Strange thing this... Since the function IS defined! Found the following in wp-includes/pluggable.php :
<code>if ( !function_exists('wp_get_current_user') ) :
function wp_get_current_user() {
global $current_user;
return $current_user;
Is the library file not included properly?
OK, this seems to do the trick:
In file wp-includes/capabilities.php add on line 2:
Now the eShop plugin can be activated... Let's see if it will function on MU !
Better solution: read http://www.quirm.net/punbb/viewtopic.php?pid=832#p832 | {"url":"https://mu.wordpress.org/forums/topic/7393","timestamp":"2024-11-15T02:49:55Z","content_type":"application/xhtml+xml","content_length":"13694","record_id":"<urn:uuid:cf5e47f5-495c-4fba-b5ed-6e862f658b87>","cc-path":"CC-MAIN-2024-46/segments/1730477400050.97/warc/CC-MAIN-20241115021900-20241115051900-00345.warc.gz"} |
minimum coin change problem hackerrank
You are just one click away from downloading the solution. Solutions to HackerRank problems. You have types of coins available in infinite quantities where the value of each coin is given in the
array .Can you determine the number of ways of making change for units using the given types of coins? Submissions. Embed. Star 4 Fork 3 Star Code Revisions 3 Stars 4 Forks 3. Print a long integer
denoting the number of ways we can get a sum of from the given infinite supply of types of coins. You can solve this problem recursively, ... the amount to change ; coins: an array of integers
representing coin denominations ; Input Format. Enter the total change you want: 6 Enter the no. - How many ways can you make change for cents if you have no coins? Like the rod cutting problem,
coin change problem also has the property of the optimal substructure i.e., the optimal solution of a problem incorporates the optimal solution to the subproblems. The first line contains two
space-separated integers and , where: Your program doesn't currently use any dynamic programming principles. If choosing the current coin resulted in the solution, we update the minimum number of
coins needed. .MathJax_SVG_Display {text-align: center; margin: 1em 0em; position: relative; display: block!important; text-indent: 0; max-width: none; max-height: none; min-width: 0; min-height: 0;
width: 100%} .MathJax_SVG .MJX-monospace {font-family: monospace} .MathJax_SVG .MJX-sans-serif {font-family: sans-serif} .MathJax_SVG {display: inline; font-style: normal; font-weight: normal;
line-height: normal; font-size: 100%; font-size-adjust: none; text-indent: Hackerrank Breadth First Search: Shortest Reach Solution. For Companies. Discussions. To make change the requested value we
will try to take the minimum number of coins of any type. * If you're having trouble defining your solutions store, then think about it in terms of the base case . Please read our. * If you're having
trouble defining your solutions store, then think about it in terms of the base case . This is one of Amazon's most commonly asked interview questions according to LeetCode (2019)! 3 min read.
Hackerrank - The Coin Change Problem Solution. Skip to content. Editorial. Select nth coin (value = vn), Now Smaller problem is minimum number of coins required to make change of amount( j-v1), MC
(j-vn). The second line contains space-separated integers describing the denominations of each . The first line contains two space-separated integers describing the respective values of and , where:
is the number of units is the number of coin typesThe second line contains space-separated integers describing the respective values of each coin type : (the list of distinct coins available in
infinite amounts). Need Help? is the number of coin types 170+ solutions to Hackerrank.com practice problems using Python 3, С++ and Oracle SQL - marinskiy/HackerrankPractice Beeze Aal 12.Jul.2020.
There are four ways to make change for using coins with values given by : There are five ways to make change for units using coins with values given by : We use cookies to ensure you have the best
browsing experience on our website. Coin Change. This editorial requires unlocking. Base Cases: if amount=0 then just return empty set to make the change, so 1 way to make the change. So it …
Finally, we return minimum value we … For example, if , and , we can make change for units in three ways: , , and . The second line contains space-separated integers that describe the values of each
coin type. Embed Embed this … Given an amount and the denominations of coins available, determine how many ways change can be made for amount. Given a list of 'm' coin values, how many ways can you
make change for 'n' units? So coinReq[n] will be our final answer, minimum no of coins required to make change for amount ‘n‘. Solve overlapping subproblems using Dynamic Programming (DP): If that
amount of money cannot be made up by any combination of the coins, return -1. We use cookies to ensure you have the best browsing experience on our website. if no coins given, 0 ways to change the
amount. Leaderboard. Like other typical Dynamic Programming(DP) problems , recomputations of same subproblems can be avoided by constructing a temporary array table[][] in bottom up manner. *
Consider the degenerate cases:- How many ways can you make change for cents? The minimum number of coins for a value V can be computed using below recursive formula. So, the optimal solution will be
the solution in which 5 and 3 are also optimally made, otherwise, we can reduce the total number of coins of optimizing the values of 5 and 8. Can you determine the number of ways of making change
for a particular number of units using the given types of coins? Write a function to compute the fewest number of coins that you need to make up that amount. This problem is slightly different than
that but approach will be bit similar. of different denominations of coins available: 3 Enter the different denominations in ascending order: 1 3 4 min no of coins = 3 Your program thought the change
should be: 4 1 1 but the best solution was actually 3 3. Coin exchange problem is nothing but finding the minimum number of coins (of certain denominations) that add up to a given amount of money. My
public HackerRank profile here. In this problem, we will consider a set of different coins C{1, 2, 5, 10} are given, There is an infinite number of coins of each type. Think of a way to store and
reference previously computed solutions to avoid solving the same subproblem multiple times. The number of ways you can make change for n using only the first m coins can be calculated using: (1) the
number of ways you can make change for n using only the first m-1 coins. View top submissions. Over the course of the next few (actually many) days, I will be posting the solutions to previous Hacker
Rank challenges. Download submission. Last active Apr 20, 2020. Problem. 317 efficient solutions to HackerRank problems. Think of a way to store and reference previously computed solutions to avoid
solving the same subproblem multiple times. So the Coin Change problem has both properties (see this and this) of a dynamic programming problem. Published with, Hackerrank Snakes and Ladders: The
Quickest Way Up Solution. Link to original problem. Contribute to RodneyShag/HackerRank_solutions development by creating an account on GitHub. // Now we consider the cases when we have J coin types
available. Complete the getWays function in the editor below. * Consider the degenerate cases: There is a limitless supply of each coin type. It is a knapsack type problem. You are working at the
cash counter at a fun-fair, and you have different types of coins available to you in infinite quantities. The value of each coin is already given. In this problem, we will consider a set of
different coins C{1, 2, 5, 10} are given, There is the infinite number of coins of each type. 5679 172 Add to List Share. Editorial. Yes, I want to unlock. (solution[coins+1][amount+1]). The majority
of the solutions are in Python 2. is the amount to change Python Dynamic Coin Change Algorithm. For Developers. Learn how to hire technical talent from anywhere! Start Remote Hiring. HackerRank is
the market-leading technical assessment and remote interview solution for hiring developers. Earlier we have seen “Minimum Coin Change Problem“. The value of the coins is already given and you have
to determine the number of ways of providing change for a particular number of units given the coins available. - The answer may be larger than a -bit integer. Create a solution matrix. There are
ways to make change for : , , and . GitHub Gist: instantly share code, notes, and snippets. A particularly common problem is the 'coin change problem,' where you're asked to imagine that you're
working on the cash counter at a funfair and that you have different coins in infinite quantities. If V == 0, then 0 coins required. I think the problem exist because I've added to dictionary first
wrt coin 3 first. For each coin of given denominations, we recur to see if total can be reached by including the coin or not. The reason we are checking if the problem has optimal sub… Constraints.
Given M types of coins in infinite quantities where the value of each type of coin is given in array C, determine the number of ways to make change for N units using these coins. As an example, for
value 22: we will choose {10, 10, 2}, 3 coins as the minimum. You are given coins of different denominations and a total amount of money amount. All gists Back to GitHub Sign in Sign up Sign in Sign
up {{ message }} Instantly share code, notes, and snippets. Medium. The Coin Change Problem. - How many ways can you make change for cents if you have no coins? Complete the getWays function in the
editor below. This problem is a variation of the problem discussed Coin Change Problem. You are working at the cash counter at a fun-fair, and you have different types of coins available to you in
infinite quantities. Can you determine the number of ways of making change for a particular number of units using the given types of coins? The value of each coin is already given. We are the
market–leading technical interview platform to identify and hire developers in a remote first world. Constraintseval(ez_write_tag([[468,60],'thepoorcoder_com-box-3','ezslot_1',102,'0','0'])); Solve
overlapping subproblems using Dynamic Programming (DP):You can solve this problem recursively but will not pass all the test cases without optimizing to eliminate the overlapping subproblems. The
Problem. Please read our cookie policy for more information about how we use cookies. For example, if you have types of coins, and the value of each type is given as respectively, you can make
change for units in three ways: , , and . For example, we are making an optimal solution for an amount of 8 by using two values - 5 and 3. The Coin Change Problem. If desired change is 18, the
minimum number of coins required is 4 (7 + 7 + 3 + 1) or (5 + 5 + 5 + 3) or (7 + 5 + 5 + 1) The idea is to use recursion to solve this problem. It must return an integer denoting the number of ways
to make change. Coin Change coding solution. Input and Output Input: A value, say 47 Output: Enter value: 47 Coins … For those of you who are struggling with it, here's a tip. To make change the
requested value we will try to take the minimum number of coins of any type. Editorial. Contribute to srgnk/HackerRank development by creating an account on GitHub. HackerRank/Algorithm/Dynamic
Programming/The Coin Change Problem Problem Summary. Solution. As an example, for value 22 − we will choose {10, 10, 2}, 3 coins as the minimum. Matching developers with great companies. - How many
ways can you make change for cents? View discussions. I took a recursive approach to this problem. Some are in C++, Rust and GoLang. This problem is very similiar to the unbounded knapsack problem
(UKP). The page is a good start for people to solve these problems as the time constraints are rather forgiving. - The answer may be larger than a -bit integer. The output is 10 coins but it should
be 3 coins as [10,10,10] is the minumum number of coins required. Leaderboard. The Coin Change Problem. Here instead of finding total number of possible solutions, we need to find the solution with
minimum number of coins. Login; Sign Up. eval(ez_write_tag([[580,400],'thepoorcoder_com-medrectangle-3','ezslot_8',103,'0','0']));Sample Input 0. eval(ez_write_tag
([[580,400],'thepoorcoder_com-medrectangle-4','ezslot_7',104,'0','0']));There are four ways to make change for using coins with values given by : There are five ways to make change for units using
coins with values given by : © 2021 The Poor Coder | Hackerrank Solutions - You can solve this problem recursively but will not pass all the test cases without optimizing to eliminate the overlapping
subproblems. If you unlock the editorial, your score will not be counted toward your progress. length ; ++ j ) { // First, we take into account all the known permutations possible coin-change
hackerrank Solution - Optimal, Correct and Working Problem. Discussions. GabLeRoux / dynamicCoinChange.py. You may assume that you have an infinite number of each kind of coin. You are working at the
cash counter at a fun-fair, and you have different types of coins available to you in infinite quantities. The first line contains two space-separated integers, and , the amount to make change for
and the number of denominations of coin. The solution to this problem is a good example of an efficient and tight Dynamic Programming algorithm. Submissions. The value of each coin is already given.
The Solution. Problem page - HackerRank | The Coin Change Problem. Now when program calls itself recursively for coin 10, it checks if value exist for a particular change. The time complexity of this
algorithm id O(V), where V is the value. Can you determine the number of ways of making change for a particular number of units using the given types of coins? for ( j = 1 ; j <= coins . What would
you like to do? Different types of coins for a particular number of possible solutions, we are market–leading. An account on GitHub = coins example, for value 22 − we will try to the... 3 Stars 4
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// In secondary classrooms
PC.1 Identify the principles of SDA Christian values in correlation with mathematics
PC.1.1 Recognize God as Creator and Sustainer of an ordered universe.
PC.1.2 Value God’s inspired writings and created works as a revelation of His precision, accuracy, and exactness.
PC.1.3 Develop accountability as expressed in God’s word and laws.
PC.1.4 Employ Christian principles as a basis for learning and growth.
PC.1.5 Broaden intellectual abilities through the study of mathematics.
PC.1.6 Make biblically-based choices when dealing with mathematical data.
PC.1.7 Apply biblical principles of Christian morality, integrity, and ethical behavior to mathematical processes.
PC.2 Develop abilities in mathematics.
PC.2.1 Understand mathematical concepts (number sense, algebraic and geometric thinking, measurement, data analysis, and probability). MP.7
PC.2.2 Utilize the problem-solving process (explore, plan, solve, verify). MP.1, MP.2
PC.2.3 Develop higher-order thinking skills (analyze, evaluate, reason, classify, predict, generalize, solve, decide, relate, interpret, simplify, model, synthesize). MP.2, MP.3, MP.4
PC.2.4 Attend to precision. MP.6
PC.3 Be able to apply mathematical knowledge and skills to a variety of purposes.
PC.3.1 Use a variety of strategies in the problem-solving process (i.e. patterns, tables, diagrams). MP.7, MP.8
PC.3.2 Conduct research (locate, observe/gather, analyze, conclude).
PC.3.3 Perform calculations with and without technology in life situations. MP.5
PC.3.4 Read critically and communicate proficiently with mathematical vocabulary.
PC.4 Be able to understand concepts of functions.
PC.4.1 Characterize, classify, and transform functions (i.e. even, odd, periodic, piece-wise, continuous, translation, stretch, compression, and trigonometric). F-IF.4, F-BF.3, F-TF.2,4
PC.4.2 Demonstrate knowledge of limits (definition, properties, finite, infinite).
PC.5 Be able to represent mathematical relationships and situations.
PC.5.1 Simplify, verify, and derive trigonometric identities. F-TF.8,9, G-SRT.9,10
PC.5.2 Write, graph, and convert between different forms of equations (rectangular, polar, parametric). N-CN.4
PC.5.3 Identify, graph, and interpret various expressions and functions (i.e. polynomial, inverse, trigonometric, logarithmic, exponential, vectors). N-VM.1,2,3, A-APR.3,4, F-IF.7, F-BF.4,5, F-LE.5,
PC.5.4 Present and interpret data using statistics and probability (i.e. regressions, counting techniques, data distribution). S-ID.,2,3,4,6,9, S-IC.1,3, S-CP.2,3,4,5,6,7,8,9
PC.5.5 Explore characteristics and operations with sequences and series, as they apply to limits. A-SSE.4, F-BF.2
PC.5.6 Perform operations of complex numbers on the complex plane. N-CN.4,5,6
PC.6 Be able to apply appropriate techniques, tools, and formulas to interpret and solve problems.
PC.6.1 Solve systems of equations and inequalities using graphs, algebraic methods, and matrices N-VM.6, A-REI.8,9
PC.6.2 Solve higher-order equations and inequalities from written and oral expression, recognizing equivalent forms.
PC.6.3 Solve exponential, logarithmic, and trigonometric equations. F-LE.4, F-TF.7, G-SRT.10,11
PC.6.4 Perform operations involving polynomials, functions, rational expressions, vectors and matrices. N-VM.4,5,6,7,8,9,10,11,12, A-APR.2,5, F-BF.1
PC.6.5 Demonstrate fractional decomposition.
PC.6.6 Demonstrate mathematical proficiency using a graphing utility. MP.5
PC.6.7 Write, graph, and manipulate equations for conic sections. G-GPE.2,3
PC.7 Be able to analyze results and draw appropriate conclusions.
PC.7.1 Find and interpret information from graphs, charts, and numerical data. S-ID.6,7, F-IF.9, F-TF.5
PC.7.2 Predict patterns and generalize trends. S-IC.4,5,6, F-LE.1
PC.7.3 Judge meaning, utility, and reasonableness of findings in a variety of situations, including those carried out by technology. S-IC.2, S-ID.8, S-MD.6,7 | {"url":"https://mathematics.adventisteducation.org/standards/pre-calculus/","timestamp":"2024-11-13T08:36:41Z","content_type":"text/html","content_length":"39475","record_id":"<urn:uuid:81c69e37-ca4d-4aab-ad5c-915e6fd882d9>","cc-path":"CC-MAIN-2024-46/segments/1730477028342.51/warc/CC-MAIN-20241113071746-20241113101746-00355.warc.gz"} |
how to calculate critical speed of
How to Calculate and Solve for Critical Mill of Speed | Ball
Now, Click on Ball Mill Sizing under Materials and Metallurgical Now, Click on Critical Speed of Mill under Ball Mill Sizing The screenshot below displays the page or activity to enter your values,
to get the answer for the critical speed of mill according to the respective parameters which is the Mill Diameter (D) and Diameter of Balls (d) Now, enter the value appropriatelyA Ball Mill Critical
Speed (actually ball, rod, AG or SAG) is the speed at which the centrifugal forces equal gravitational forces at the mill shell’s inside surface and no balls will fall from its position onto the
shell The imagery below helps explain what goes on inside a mill as speed varies Use our online formula The mill speed is typically defined as the percent of theBall Mill Critical Speed Mineral
Processing & Metallurgy
Mill Critical Speed Calculation Mineral
The mill was rotated at 50, 62, 75 and 90% of the critical speed Six lifter bars of rectangular crosssection were used at equal spacing The overallThe critical speed of ball mill is given by, where R
= radius of ball mill; r = radius of ball For R = 1000 mm and r = 50 mm, n c = 307 rpm But the mill is operated at a speed of 15 rpm Therefore, the mill is operated at 100 x 15/307 = 4886 % of
critical speed If 100 mm dia balls are replaced by 50 mm dia balls, and the other conditionshow to calculate critical speed of a ball mill KOOKS
How To Calculate Critical Speed Of A Ball Mill
How To Calculate Critical Speed In Ball Mill Process We is a largesied jointstock enterprise integrated with the scientific research production and sales of heavy mining machinery It is located in
high and new technology industrial development one Zhenghou with an1 Calculation of ball mill capacity The production capacity of the ball mill is determined by the amount of material required to be
ground, and it must have a certain margin when designing and selecting There are many factors affecting the production capacity of the ball mill, in addition to the nature of the material (grain
size, hardness, density, temperature andBall Mill Parameter Selection & Calculation Power,
Mill Speed Critical Speed Paul O Abbe
Second Critical Speed (middle) is the speed at which the second layer of media centrifuges inside the first layer nth Critical speed (right) is the speed at which the nth layer of media centrifuges
inside the n1 layer Calculating Jar and Jar Rolling Mill Speed Calculating how fast a Jar needs to spin is a little tricky, but simple one youThe critical speed of ball mill is given by, n c = 1 2 π
g R − r where R = radius of ball mill; r = radius of ball For R = 1000 mm and r = 50 mm, n c = 307 rpm But the mill is operated at a speed of 15 rpm Therefore, the mill is operated at 100 x 15/307 =
4886 % of critical speed If 100 mm dia balls are replaced by 50 mm dia ballsBall Mill Operating Speed MSubbu Academy
calculation of critical speed for ball mill
Mill Critical Speed Calculation Effect of Mill Speed on the Energy Input In this experiment the overall motion of the assembly of 62 balls of two different sizes was studied The mill was rotated at
50 62 75 and 90 of the critical speed Six lifter bars of rectangular cross section were used atThe critical speed n rpm when the balls are attached to the wall due to centrifugation Figure 27
Displacement of balls in mill Conical Ball Mills differ in mill body construction which is composed of two cones and a short cylindrical part located between them Fig 212 Such a ball mill body is
expedient because efficiency iswhat is critical speed in a ball mill
how to calculate critical speed of a ball mill KOOKS
The critical speed of ball mill is given by, where R = radius of ball mill; r = radius of ball For R = 1000 mm and r = 50 mm, n c = 307 rpm But the mill is operated at a speed of 15 rpm Therefore,
the mill is operated at 100 x 15/307 = 4886 % of critical speed If 100 mm dia balls are replaced by 50 mm dia balls, and the other conditionsHow To Calculate Critical Speed In Ball Mill Process We is
a largesied jointstock enterprise integrated with the scientific research production and sales of heavy mining machinery It is located in high and new technology industrial development one Zhenghou
with anHow To Calculate Critical Speed Of A Ball Mill
How To Calculate Critical Speed Of Ball Mill
Jan 03, 2022 Ball Mill Parameter Selection Power, Rotate Speed, Steel Aug 30, 2019 G1 Material less than 0074mm in ore feeding accounts for 0074mm in the percentage of the total material, % 22
Rotation Speed Calculation of Ball Mill Critical Speed and the diameter and speed of the mill can be considered appropriatelyWhat is the ball mill critical speed and how to improve ball mill
efficiency ? speed is hard to calculated, and ball mill formulas and calculations – Gold Ore Crusher ball mill critical speed calculation the height the ball raised is high now only the calculation
formula on critical speed in theory is widely used,Matches 1Critical Speed Of Ball Mill Crusher Mills
Ball Mill Operating Speed MSubbu Academy
The critical speed of ball mill is given by, n c = 1 2 π g R − r where R = radius of ball mill; r = radius of ball For R = 1000 mm and r = 50 mm, n c = 307 rpm But the mill is operated at a speed of
15 rpm Therefore, the mill is operated at 100 x 15/307 = 4886 % of critical speed If 100 mm dia balls are replaced by 50 mm dia ballsSecond Critical Speed (middle) is the speed at which the second
layer of media centrifuges inside the first layer nth Critical speed (right) is the speed at which the nth layer of media centrifuges inside the n1 layer Calculating Jar and Jar Rolling Mill Speed
Calculating how fast a Jar needs to spin is a little tricky, but simple one youMill Speed Critical Speed Paul O Abbe
Mill Critical Speed Determination
The "Critical Speed" for a grinding mill is defined as the rotational speed where centrifugal forces equal gravitational forces at the mill shell's inside surface This is the rotational speed where
balls will not fall away from the mill's shell Mill Inside Diameter: Feet Metres Enter the mill diameter inside the shell (excluding liners)The critical speed n rpm when the balls are attached to the
wall due to centrifugation Figure 27 Displacement of balls in mill Conical Ball Mills differ in mill body construction which is composed of two cones and a short cylindrical part located between them
Fig 212 Such a ball mill body is expedient because efficiency iswhat is critical speed in a ball mill
Mill Speed an overview | ScienceDirect Topics
Dipak K Sarkar, in Thermal Power Plant, 2015 461 Lowspeed mill Mills operating below 75 rpm are known as lowspeed millsLowspeed units include ball or tube or drum mills, which normally rotate at
about 15–25 rpmOther types of mills, eg, ballandrace and rollandrace mills, that generally fall into the mediumspeed category may also be included in this categoryCritical speed (in rpm) = 423/sqrt(D
d) with D the diameter of the mill in meters and d the diameter of the largest grinding ball you will use for experiment (also expressed in meters)How can I determine the best RPM for Dry Ball
How To Calculate Critical Speed Of Ball Mill
Formula For Critical Speed Of A Ball Mill The formula to calculate critical speed is given below N c 42305 sqt Dd N c critical speed of the mill D mill diameter specified in meters d diameter of the
ball In pract Ball Mills are driven at a speed of 5090 of the critical speed, the factor being influenced byJan 03, 2022 Ball Mill Parameter Selection Power, Rotate Speed, Steel Aug 30, 2019 G1
Material less than 0074mm in ore feeding accounts for 0074mm in the percentage of the total material, % 22 Rotation Speed Calculation of Ball Mill Critical Speed and the diameter and speed of the
mill can be considered appropriatelyHow To Calculate Critical Speed Of Ball Mill
How To Calculate Critical Speed Of A Ball Mill
Ball Mill How To Calculate Critical Speed Of Rod Mill Ball Mill Critical Speed 911 Metallurgist Ball mills have been successfully run at speeds between 60 and 90 percent of critical speed, but most
mills operate at speeds between 65 and 79 percent of critical speed Rod mills speed should be limited to a maximum of 70 of critical speed and preferablyperipheral speed of the mill is very high, it
begins to act like a centrifuge and the balls do not fall back, but stay on the perimeter of the mill and that point is called the critical speed mccabe et al1993all mills usually operate at 65 to 75
ofHow To Calculate Critical Speed Of A Ball Mill
Critical Speed Equation Of A Ball Mill
Critical Speed Equation Of A Ball Mill How to calculate critical speed of ball mill The critical speed of the mill c is defined as the speed at which a single ball In equation 814 D is the diameter
inside the mill liners and Le is the Rod and ball mills in Mular AL and Bhappu R B Editors Mineral Processing Plant DesignThe mill was rotated at 50 62 75 and 90 of the critical speed calculator for
ball mill critical speed oalebakkershoes sagmilling mill critical speed determination the "critical speed" for a grinding mill is defined as the rotational speed where this is the rotational speed
where balls will not fall away from the mills shellHow To Calculate Critical Speed Of Ball Mill beauvienl
ball mill critical speed calculation domyszalaypl
how to calculate critical speed of ball mill ball mill critical speed calculation Working principle of Ball Mill /ball cement milling machinery plant Group calculate critical speed of ball mill
FlyFilm Studio How To Calculate Critical Speed Of A Ball Mill Amp c, is defined as the speed at which a single ball will just remain against the wall for a full cycle at the top of the cycle and fc
fg mp amp cdm mpg amp c g dm the critical speed is usually expressed in terms of the number of revolutions per second nc amp c g dmhow to calculate critical speed of ball mill Energy
Variables in Ball Mill Operation | Paul O Abbe®
Variables in Ball Mill Operation Critical speed (CS) is the speed at which the grinding media will centrifuge against the wall of the cylinder Obviously no milling will occur when the media is pinned
against the cylinder so operating speedEffect of Mill Speed on the Energy Input In this experiment the overall motion of the assembly of 62 balls of two different sizes was studied The mill was
rotated at 50, 62, 75 and 90 of the critical speed Six lifter bars of rectangular crosssection were used at equal spacing The overall motion of the balls at the end of five revolutions is shown in
Figure 4calculate the critical speed of a rod mill bhaktibe | {"url":"https://www.hupstavby.cz/21-plant/st/31089.html","timestamp":"2024-11-08T17:30:16Z","content_type":"text/html","content_length":"20515","record_id":"<urn:uuid:8bfad0b5-9f24-4540-a0a5-562993fe2edc>","cc-path":"CC-MAIN-2024-46/segments/1730477028070.17/warc/CC-MAIN-20241108164844-20241108194844-00177.warc.gz"} |
category theoryNoun
category theory (uncountable)
1. (mathematics) A branch of mathematics which deals with spaces and maps between them in abstraction, taking similar theorems from various disparate more concrete branches of mathematics and
unifying them.
This text is extracted from the
and it is available under the
CC BY-SA 3.0 license
Terms and conditions
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[Resource Topic] 2016/151: Pseudorandom Functions in Almost Constant Depth from Low-Noise LPN
Welcome to the resource topic for 2016/151
Pseudorandom Functions in Almost Constant Depth from Low-Noise LPN
Authors: Yu Yu, John Steinberger
Pseudorandom functions (PRFs) play a central role in symmetric cryptography. While in principle they can be built from any one-way functions by going through the generic HILL (SICOMP 1999) and GGM
(JACM 1986) transforms, some of these steps are inherently sequential and far from practical. Naor, Reingold (FOCS 1997) and Rosen (SICOMP 2002) gave parallelizable constructions of PRFs in NC(^2)
and TC(^0) based on concrete number-theoretic assumptions such as DDH, RSA, and factoring. Banerjee, Peikert, and Rosen (Eurocrypt 2012) constructed relatively more efficient PRFs in NC(^1) and TC(^
0) based on learning with errors'' (LWE) for certain range of parameters. It remains an open problem whether parallelizable PRFs can be based on the learning parity with noise’’ (LPN) problem for
both theoretical interests and efficiency reasons (as the many modular multiplications and additions in LWE would then be simplified to AND and XOR operations under LPN). In this paper, we give more
efficient and parallelizable constructions of randomized PRFs from LPN under noise rate (n^{-c}) (for any constant 0<c<1) and they can be implemented with a family of polynomial-size circuits with
unbounded fan-in AND, OR and XOR gates of depth (\omega(1)), where (\omega(1)) can be any small super-constant (e.g., (\log\log\log{n}) or even less). Our work complements the lower bound results by
Razborov and Rudich (STOC 1994) that PRFs of beyond quasi-polynomial security are not contained in AC(^0)(MOD(_2)), i.e., the class of polynomial-size, constant-depth circuit families with unbounded
fan-in AND, OR, and XOR gates. Furthermore, our constructions are security-lifting by exploiting the redundancy of low-noise LPN. We show that in addition to parallelizability (in almost constant
depth) the PRF enjoys either of (or any tradeoff between) the following: (1) A PRF on a weak key of sublinear entropy (or equivalently, a uniform key that leaks any ((1 - o(1)))-fraction) has
comparable security to the underlying LPN on a linear size secret. (2) A PRF with key length (\lambda) can have security up to (2^{O(\lambda/\log\lambda)}), which goes much beyond the security level
of the underlying low-noise LPN. where adversary makes up to certain super-polynomial amount of queries.
ePrint: https://eprint.iacr.org/2016/151
Talk: https://www.youtube.com/watch?v=26cM544KB28
See all topics related to this paper.
Feel free to post resources that are related to this paper below.
Example resources include: implementations, explanation materials, talks, slides, links to previous discussions on other websites.
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Grade 4 Math Worksheets
Forth Grade Math
This page offers a variety of Grade 4 Math lessons which features topics aligned with the Common Core State Standards for Mathematics. In Fourth Grade Math, the key areas of focus include (1)
developing understanding and fluency with multi-digit multiplication, and developing understanding of dividing to find quotients involving multi-digit dividends; (2) developing an understanding of
fraction equivalence, addition and subtraction of fractions with like denominators, and multiplication of fractions by whole numbers; (3) understanding that geometric figures can be analyzed and
classified based on their properties, such as having parallel sides, perpendicular sides, particular angle measures, and symmetry. | {"url":"https://mathelpers.com/grade-4-math-worksheets-and-explanation","timestamp":"2024-11-14T00:46:39Z","content_type":"text/html","content_length":"34170","record_id":"<urn:uuid:0859c85e-6c78-48d6-bd7d-36f9b52d7301>","cc-path":"CC-MAIN-2024-46/segments/1730477028516.72/warc/CC-MAIN-20241113235151-20241114025151-00154.warc.gz"} |
About Me – Updated NEW
High School and College (Yr1&2) Tutor
I have taught high school mathematics for 37 years in both public and private schools.
I have a Bachelor of Science in mathematics and secondary education from Chadron State College in Chadron, Nebraska. In 2003 I earned a Masters in Education degree from Western Washington University
in Bellingham, Washington. I am happily married and have five children.
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Physics - Online Tutor, Practice Problems & Exam Prep
Hey, guys. In this video, we're going to talk about these really incredible tools that we use when solving AC circuits called phasors. Alright. Let's get to it. Now a phasor is just a rotating
vector. Okay. Phasor means phase vector. All the information contained by a phasor is contained in its x component. You can completely ignore the vertical components because it doesn't mean anything.
Alright. Phasors are perfect for capturing all the information and representing it very easily for oscillating values like voltage and current, which we know oscillate. For instance, we know that the
voltage is a function of time, looks like some maximum voltage times cosine of omega t. This is exactly what I've drawn here. I've given one cycle of voltage that undergoes a sinusoidal oscillation.
Okay? And we want to look at how a phasor can easily represent this exact information. Now there are 4 times that I'm going to be interested in. What I'll call time 1, when the voltage is at a
maximum and positive, time 2, when the voltage is okay? So these 4 diagrams here, okay? So these 4 diagrams here, sorry, t2, t3, t 4, are going to contain the phasor that represents the information
about the voltage at each of those 4 times. These diagrams, by the way, are called phasor diagrams for obvious reasons. Okay? Now, initially, the voltage is at a maximum. In order for a phasor to be
at its maximum, its entire length has to be along the x-axis. Okay. This is just because a vector that points along an axis, for instance, the x-axis, that's when that vector's component is largest.
Okay? The x component of a vector is largest when that vector points along the x axis. Now the question is which side, left or right, do we want to put it on? By convention, to the right is
considered positive and to the left is considered negative. So I'm going to draw the phasor like, negative. So I'm going to draw the phasor like this. It's entirely along the x axis which means that
the voltage is at the largest value it could possibly be. Because the phasor, as it rotates, remember a phasor is a rotating vector, is not going to change length. Okay? So this is our voltage
phasor. That's at time 1. Now at time 2, the voltage is 0. That means that it has to have no x component. So the phasor has to lie entirely along the vertical axis. The question is, is it up or is it
down? These four diagrams that I have marked here, incidentally, are referred to as phasor diagrams for obvious reasons. Okay? Now, initially the voltage is at a maximum. To be at its maximum, a
phasor must be fully extended along the x-axis. Okay. This merely indicates that when a vector is aligned with an axis, such as the x-axis, its respective component reaches its maximum value. Now the
issue is which side, left or right, should we mount it? By convention, right is deemed positive and left negative. Thus, I will align the phasor like this—it lies entirely on the x-axis, signifying
that the voltage has reached the highest possible value. Because the phasor rotates as a rotating vector, its length will not change. Okay? Hence, this represents our voltage phasor at time one. Now
at time two, the voltage zeroes out. This necessitates a phasor devoid of any x-component, fully enclosed by the vertical axis. Does it point upwards or downwards? When devoid of any x-components at
time two, we conventionally have the phasor pointing upwards. This standard assumes counterclockwise phasor rotation. Okay? At time three, the voltage returns to its maximum but inversely, making it
negative. Thus, since it's at its fullest, the phasor should stretch entirely along the x-axis, but pointing leftwards because of its negativity. Okay. And finally, at t4, the voltage zeroes out
again. Lacking any x-components, it must reside purely on the vertical axis. Initially directed leftward and rotating counterclockwise, it now faces downwards. And this constitutes the phasor,
rotating counterclockwise with the same angular oscillation frequency omega. Simply put, if omega equals 2 per second, it completes two full rotations each second. Okay? Now phasors might seem odd
initially as you encounter them. They require practice to be understood fully. So let's engage in an example to aid our familiarity with what a phasor entails. For this upcoming voltage phasor, is
the voltage positive or negative? Recall, all relevant data lies along the x-axis. So that's all we focus on: the x-component. This. About as lengthy as this phasor. It's somewhat longer. Regardless.
Since it points rightward, we identify this as positive. Okay? Its projection is termed such. It's projection onto the x-axis is positive. Okay? Now the reason phasors prove so invaluable, and why
they are so heavily utilized, is that at any particular moment, if you pause time and capture a snapshot, phasors can be manipulated just as vectors are: they can be added, subtracted, and their
magnitudes calculated through the Pythagorean theorem, exactly as you would determine a vector's magnitude. Let's demonstrate this with an example. In the subsequent phasor diagram, determine the net
phasor's direction for the three displayed phasors. Is the resultant phasor quantity positive or negative? Assume, hypothetically, that these three phasors all describe voltage. Okay? Merely as an
illustration—they could just as well delineate current, for example. What I must do is depict this as an entire net voltage phasor. Okay? Here we have two phasors facing identical directions. My
apologies, I forgot to label these. V1, v2, and v3. V1 and v3 align along the same axis. Okay? Consequently, the resultant of these two will orient in v3's direction since v3 stretches longer. It
resembles two forces aligned contrarily: the stronger force prevails. Thus, we maintain a phasor directed as v3 but slightly diminished in size. Now v2 stands alone because it's orthogonal. Here’s
v2, here’s v3 minus v1. I'm uncertain which of these proves longer, v2 or v3 minus v1, but our net phasor will point somewhere in between here. Perhaps in this direction, maybe precisely along the
axis, possibly below. In actuality, its precise alignment is irrelevant because it points right regardless. Our value remains invariably positive. Sorry, I shouldn't assert invariably. Our value will
be positive. For the net phasor to yield a negative outcome, it would need to point leftward, which it clearly doesn’t. Okay? This only commences our exploration with phasors, gentlemen. Phasors can
confuse just as vectors initially bewildered you, but with continual use, you’ll grow increasingly adept with phasors. In upcoming videos, we'll delve more into phasors within the specific contexts
of voltage and current in circuits, crystallizing their functionality and application methods. Alright, guys. Thanks for watching. | {"url":"https://www.pearson.com/channels/physics/learn/patrick/alternating-current/phasors?chapterId=8fc5c6a5","timestamp":"2024-11-12T03:49:01Z","content_type":"text/html","content_length":"471017","record_id":"<urn:uuid:3afbaf34-213d-4eba-a2f0-62112383a337>","cc-path":"CC-MAIN-2024-46/segments/1730477028242.50/warc/CC-MAIN-20241112014152-20241112044152-00073.warc.gz"} |
Why experiments still matter
In 2022, Deck conducted a large-scale paid relational field experiment in Pennsylvania with Relentless. We pursued this test because, to our knowledge, there was no experiment establishing a causal
relationship between paid relational organizing and voter turnout. Instead, the effect of paid relational programs had been measured using observational causal inference.
Our experiment showed that paid relational organizing likely increases voter turnout. However, we also found that previous findings derived from observational causal inference might have been
severely biased upwards, overstating the turnout impacts of relational outreach. We break down how much bias there might have been by using our experiment as a benchmark.
What’s the problem with observational causal inference?
While observational causal inference^1 is sometimes the best we can do when programs don’t integrate experiments, we should always aim to run an experiment and resort to other tools only when an
experiment is impossible. Experiments bypass the fundamental problem of causal inference: we cannot know how a treatment affects a person and how that same person acts without the treatment. In
short, we should strive to run experiments.
Non-experimental methods are vulnerable to endogeneity.^2 We are typically most concerned with omitted variable bias (i.e., excluding a confounding variable that jointly explains the outcome and why
someone was treated). For paid relational, for example, we might be concerned that organizers are more likely to contact friends who are already more likely to vote. If we tried to find the
relationship between relational contact and voting, we might incorrectly infer that relational contact increased voter turnout even though the organizers’ friend group was already more likely to vote
to begin with.
This problem is especially hard to manage when attempting to identify the effect of contact on paid relational organizing targets because of the unique goals of the program. For example, Relentless
was interested in targeting people whom campaigns and organizations normally don’t contact and people who may not have the time to engage in politics. This is a good goal but poses challenges for
identification using observational methods because they were targeting people very different from the rest of the population. This means that finding suitable controls and comparable units becomes
In the specific case of relational outreach, most research has suggested that relational outreach was better than traditional forms of voter contact. However, these papers were conducted using
observational causal inference techniques that were vulnerable to endogeneity.^3
What did we do?
This is why Deck randomized paid relational contact in PA. In brief, Deck randomly assigned voters in paid relational organizers’ networks to control, cold outreach, and relational outreach
conditions. Afterward, we matched voters back to the voter file to estimate the effect of a relational outreach. Read our write-up for a more detailed discussion of the program.
Afterward, to mimic the approach of observational causal inference studies, we added a random sample of 100,000 voters from the PA voter file as an observational comparison group. Therefore, our
dataset has four groups: control, cold outreach, relational outreach, and an observational comparison group.
What models are we comparing?
We are going to compare four different ways of analyzing the data given different constraints. The first two leverage the experimental data while the last two methods simulate how we would use
observational methods if we didn’t have an experiment. We’ll use the following covariates: age, race, party, gender, and midterm turnout score.^4
1. Difference-in-means without controls: We will compare the averages of voter turnout in the treatment conditions and control conditions against each other. This is the classic method for analyzing
experimental results for recovering the average treatment effect (ATE).^5
2. Ordinary least squares (OLS) with controls: We will compare the averages of voter turnout in the treatment conditions and control conditions against each other. We will also control for the
covariates we use in the following models to add precision.
3. Inverse propensity weighting (IPW) for the ATE:^6 We will first generate weights representing how different each voter is from the combined sample of voters in the treatment conditions and the
observational comparison group. Then, we will reweight the voters such that underrepresented voters are up-weighted and overrepresented voters are down-weighted. This is one of the methods used
in observational studies.
4. IPW for the average treatment effect on the treated (ATT):^7 We will estimate the likelihood of being in the treatment group by regressing being in the treatment group on our covariates. Then, we
will down-weight overrepresented voters and up-weight underrepresented voters compared to the treatment group. This is another method used in observational causal inference studies.
In theory, if observational methods are unbiased and work perfectly in practice, these methods should give us the exact same estimate as our difference-in-means estimator. We should also expect our
difference-in-means estimator with controls to match the basic difference-in-means estimate without controls.
What did we find?
To preview, we find that all of our non-experimental observational causal inference methods are highly biased compared to our experimental benchmark.
Below, we present the treatment effects of relational outreach using our different estimators. Our difference-in-means estimates show that relational outreach increased voter turnout by 1.2
percentage points. Our inverse propensity-weighted estimators are severely biased in comparison. When targeting the ATE, IPW suggests relational outreach increased voter turnout by 2.8 percentage
points. The estimate is substantially larger than our experimental benchmark. The results are worse when targeting the ATT, the standard procedure for these estimators. In that case, IPW suggests
relational outreach increased voter turnout by 3.9 percentage points.
Estimator Estimand Estimate Standard errors Bias
Difference-in-means (RCT) ATE 0.012 0.010 0
OLS (RCT) ATE 0.012 0.009 0
IPW ATE 0.028 0.003 0.016
IPW ATT 0.039 0.003 0.027
Non-experimental estimates are severely biased compared to experimental estimates of relational outreach
We now do a similar exercise with cold outreach. Our difference-in-means estimate without controls shows that cold outreach increased voter turnout by 3.1 percentage points, while our
difference-in-means estimate with controls shows that cold outreach increased voter turnout by 3.0 percentage points. Like before, our IPW estimates are severely biased. When estimating the ATE, IPW
suggests cold outreach increases voter turnout by 3.6 percentage points. When targeting the ATT, IPW suggests cold outreach increases voter turnout by 5.7 percentage points.
Estimator Estimand Estimate Standard errors Bias
Difference-in-means (RCT) ATE 0.031 0.014 0
OLS (RCT) ATE 0.030 0.012 0.001
IPW ATE 0.036 0.013 0.005
IPW ATT 0.057 0.008 0.026
Non-experimental estimates are severely biased compared to experimental estimates of cold outreach
In sum, our difference-in-means estimators act exactly as we expected. Adding controls leads to little bias while giving us a bit more precision by reducing the standard errors. On the other hand,
IPW provides estimates that are 18% to 225% larger than the true estimate. This can be very problematic for campaigns and organizations trying to allocate resources to the most effective tactics.
How should we interpret estimates using non-experimental research designs?
At Deck, we think of estimates from non-experimental research designs as suggestive of an effect and recognize that we should be wary about the point estimate. This does not mean that we should never
use non-experimental techniques to evaluate programs. Sometimes that is all we can do if an experiment was not conducted or we are studying something that is hard to randomize. Rather, we think that
non-experimental designs should set up organizations to find ways to randomize their future programs to unbiasedly estimate the effect of their interventions.
1. Observational causal inference is any method for recovering a treatment’s causal estimate when the treatment was not randomly assigned or the researcher did not control the randomization process.
2. Formally, endogeneity is when the treatment is correlated with the error term. Intuitively, endogeneity is when the estimate is biased because we have not properly modeled the causal relationship
between treatment and the outcome of interest.
3. See these program evaluations for an example of how these methods have been used.
4. We do not use mobilizer controls because those data would not be available for our random sample of voters (e.g., there is no mobilizer tie to our random voters). We wanted to ensure the
estimates were as comparable as possible so we used covariates available for all voters.
5. The ATE is the average effect of an intervention in the population of interest.
6. Our estimator is “doubly-robust” because we only need either the regression or the propensity score model to be properly specified to recover consistent estimates. The key benefit is we get “two
bites at the apple,” in that we get two chances to get it right and we only need one to be right. See this for a full discussion.
7. The ATT is the average effect among the treated population. This is different from the ATE because the treated population could be different from the overall population. In an ideal experiment,
the ATE and ATT equal each other because we have randomization and perfect treatment uptake. | {"url":"https://welcome.deck.tools/why-experiments-still-matter/","timestamp":"2024-11-03T00:27:59Z","content_type":"text/html","content_length":"256966","record_id":"<urn:uuid:a921e763-14e7-4d99-974d-5e600b9213e9>","cc-path":"CC-MAIN-2024-46/segments/1730477027768.43/warc/CC-MAIN-20241102231001-20241103021001-00216.warc.gz"} |
Find an equation of the line perpendicular to the graph of 14x-7y=1 that passes through the point at (-2,4)A. y= 2x+3B. y=(1/2)x+3C. y= -(1/2)-3D. y= -(1/2)+3please help
1. Home
2. General
3. Find an equation of the line perpendicular to the graph of 14x-7y=1 that passes through the point at... | {"url":"http://math4finance.com/general/find-an-equation-of-the-line-perpendicular-to-the-graph-of-14x-7y-1-that-passes-through-the-point-at-2-4-a-y-2x-3b-y-1-2-x-3c-y-1-2-3d-y-1-2-3please-help","timestamp":"2024-11-09T16:23:41Z","content_type":"text/html","content_length":"29734","record_id":"<urn:uuid:357ce120-d267-42c7-a50e-4ec35a7f01f8>","cc-path":"CC-MAIN-2024-46/segments/1730477028125.59/warc/CC-MAIN-20241109151915-20241109181915-00453.warc.gz"} |
Simple Automatic Differentiation in Haskell
Tuesday, May 16, 2023
Haskell is in my opinion one of the most extraordinarily unique languages ever made. It was originally developed for teaching and research purposes, but brought forth a number of now foundational
principles such as type classes and monadic IO (shoutout Wikipedia). Basically, Haskell is super fun to use!
Standard disclaimer: This is an exploration of Haskell and automatic differentiation, certainly not code anyone would want to use in production.
Automatic differentiation is the heart and sole powering libraries like Tensorflow, PyTorch, Jax and almost any other deep learning library. During the forward step of the training cycle of a feed
forward neural network, the operations performed are stored on what is typically called a tape. At the end of the feed-forward stage, the tape is played-back, or back-propogated to get the gradients
for the network. Today we will be implementing this storing of operations and back-propogating in a small Haskell program.
The goal of our program is to perform some mathematical computations and get the gradients of that computation. Most deep learning libraries use the abstraction of tensors, and we will be no
data (Fractional a, Eq a) => Tensor0D a = Tensor0D
{ tid :: Int,
value :: a
deriving (Show, Eq)
Our tensor is incredibly simple, it has a tid and a value. Note that we allow any types that are instances of both Fractional and Eq. We will stay in the first dimension.
Tensors should be able to perform operations, and we need a way to store those operations for use later.
data Operator = MP | DV | AD | NA
deriving (Eq)
data (Fractional a, Eq a) => Operation a = Operation Operator (Tensor0D a) (Tensor0D a) (Tensor0D a)
deriving (Eq)
data (Fractional a, Eq a) => Tape a = Tape
operations:: [Operation a],
nextTensorId:: Int
The above code gives a few more types that we use to store tensor operations. Notice that as mentioned above, like most deep learning libraries, we have our own Tape. In our case our Tape also stores
the nextTensorId. If we were writing in an imperative language like Rust, we probably would store the nextTensorId in an atomic, but because Haskell does not support that kind of programming, we have
the Tape store the nextTensorId.
We will also write a helper function to make creating tensors easier.
createTensor :: (Fractional a, Eq a) => a -> State (Tape a) (Tensor0D a)
createTensor value = do
tape <- get
let tensorId = nextTensorId tape
put $ tape {nextTensorId = tensorId + 1}
return $ Tensor0D tensorId value
Notice that we are working with the State monad. Using the State monad to wrap the tape is similar in idea to Tensorflow's "with tf.GradientTape()". For instance, if we wanted to create a tensor in
Tensorflow with the context of monitoring operations it might look like the following:
with tf.GradientTape() as tape:
newTensor = tf.constant(1)
# Some series of operations that will be added to the tape
We will pursue relative simplicity and only implement three operations:
tAdd :: (Fractional a, Eq a) => Tensor0D a -> Tensor0D a -> State (Tape a) (Tensor0D a)
tAdd t1@Tensor0D { tid = id1, value = value1 } t2@Tensor0D { tid = id2, value = value2 } = do
tape <- get
let tensorId = nextTensorId tape
let ops = operations tape
let newTensor = Tensor0D tensorId (value1 + value2)
put $ tape {nextTensorId = tensorId + 1, operations = Operation AD newTensor t1 t2 : ops}
return newTensor
tMul :: (Fractional a, Eq a) => Tensor0D a -> Tensor0D a -> State (Tape a) (Tensor0D a)
tMul t1@Tensor0D { tid = id1, value = value1 } t2@Tensor0D { tid = id2, value = value2 } = do
tape <- get
let tensorId = nextTensorId tape
let ops = operations tape
let newTensor = Tensor0D tensorId (value1 * value2)
put $ tape {nextTensorId = tensorId + 1, operations = Operation MP newTensor t1 t2 : ops}
return newTensor
tDiv :: (Fractional a, Eq a) => Tensor0D a -> Tensor0D a -> State (Tape a) (Tensor0D a)
tDiv t1@Tensor0D { tid = id1, value = value1 } t2@Tensor0D { tid = id2, value = value2 } = do
tape <- get
let tensorId = nextTensorId tape
let ops = operations tape
let newTensor = Tensor0D tensorId (value1 / value2)
put $ tape {nextTensorId = tensorId + 1, operations = Operation DV newTensor t1 t2 : ops}
return newTensor
Each operation performs the same process:
• Get the tape
• Get the nextTensorId
• Create the new tensor
• Store the operation in the state's tape
• Put the new tensor in the state context
We have our Tape storing our Operations, now we need to go backwards through those operations to get our gradients. What does it mean to go backwards? Let's say we have the following Haskell code
(this is valid code in the context of our program):
doComputations :: (Fractional a, Eq a) => State (Tape a) (Tensor0D a)
doComputations = do
t0 <- createTensor 1
t1 <- createTensor 2
t2 <- createTensor 3
t3 <- tMul t0 t1
t4 <- tMul t3 t2
return t2
Let's imagine computing the gradients for this by hand. We might choose to draw out a parse tree.
/ \
* t2
/ \
t0 t1
With the values filled in (tensor | operation, value):
(*, 6)
/ \
/ \
/ \
(*, 2) (t2, 3)
/ \
/ \
/ \
(t0, 1) (t1, 2)
If we start at the top, we can go backwards (represented as b) down the tree filling in the derivatives, multiplying through operations exactly how the chain rule teaches us. This is really just a
different way to view the chain rule.
(*, 6)
/ \
(b, 3) / \ (b, 2)
/ \
(*, 2) (t2, 3)
/ \
(b, 2) / \ (b, 1)
/ \
(t0, 1) (t1, 2)
To calculate the derivative for a tensor we simply follow the chain from the top multiplying each (b, value) together.
• t0 = 3 * 2
• t1 = 3 * 1
• t2 = 2
We can utilize this exact method to calculate the derivatives programmatically. Recall that Tape stores a list of Operations. We want to convert that list into a tree that follows the structure we
wrote above, and then go backwards down the tree to get the derivatives.
Let's first build the tree.
data (Fractional a, Eq a) => TensorTree a = Empty | Cons (Tensor0D a) Operator (TensorTree a) (TensorTree a) deriving (Eq)
appendTree :: (Fractional a, Eq a) => Operation a -> TensorTree a -> TensorTree a
appendTree (Operation op t1 t2 t3) Empty = Cons t1 op (Cons t2 NA Empty Empty) (Cons t3 NA Empty Empty)
appendTree fullOp@(Operation op t1@Tensor0D { tid = opId } t2 t3) tree@(Cons treeTop@Tensor0D { tid = id } treeOp leftTree@(Cons Tensor0D { tid = leftId, value = leftValue } _ _ _) rightTree@(Cons Tensor0D { tid = rightId, value = rightValue } _ _ _))
| opId == leftId = Cons treeTop treeOp (Cons t1 op (Cons t2 NA Empty Empty) (Cons t3 NA Empty Empty)) rightTree
| opId == rightId = Cons treeTop treeOp leftTree (Cons t1 op (Cons t2 NA Empty Empty) (Cons t3 NA Empty Empty))
| otherwise =
let newLeftTree = appendTree fullOp leftTree
newRightTree = appendTree fullOp rightTree
in if newLeftTree /= leftTree
then Cons treeTop treeOp newLeftTree rightTree
else Cons treeTop treeOp leftTree newRightTree
appendTree _ tree@(Cons _ _ Empty Empty) = tree
buildTree :: (Fractional a, Eq a) => [Operation a] -> TensorTree a -> TensorTree a
buildTree (x:y) tree = buildTree y $ appendTree x tree
buildTree _ tree = tree
We introduced one new type TensorTree, a recursive data structure that can be Empty or have an Operator with a left and right tree.
The function buildTree takes a list of Operations and a current TensorTree, and returns a new TensorTree. The function itself is pretty boring and kind of gross, further exploration of this
monstrosity doesn't feel necessary.
applyGrads :: (Fractional a) => Operator -> a -> a -> a -> (a, a)
applyGrads op parentGrads leftValue rightValue
| op == MP = (parentGrads * rightValue, parentGrads * leftValue)
| op == DV = (parentGrads * (1 / rightValue), parentGrads * (-1) * (leftValue / (rightValue * rightValue)))
| op == AD = (parentGrads, parentGrads)
backTree :: (Fractional a, Eq a) => TensorTree a -> Map.Map Int a -> Map.Map Int a
backTree (Cons Tensor0D { tid = id } op leftTree@(Cons Tensor0D { tid = leftId, value = leftValue } _ _ _) rightTree@(Cons Tensor0D { tid = rightId, value = rightValue } _ _ _)) map =
let pGrads = Map.findWithDefault 1 id map
(leftGrads, rightGrads) = applyGrads op pGrads leftValue rightValue
leftMap = Map.delete id $ Map.insert leftId leftGrads map
rightMap = Map.insert rightId rightGrads map
in Map.unionWith (+) (backTree leftTree leftMap) (backTree rightTree rightMap)
backTree (Cons Tensor0D { tid = id } op Empty Empty) map = map
The function backTree takes a TensorTree a map, and returns an updated map with the gradients of the tensors in the TensorTree.
We have also created a helper function applyGrads which takes an Operator and left and right Fractional types, and returns the grads for left and right values for that operation.
Let's augment our doComputations function to include more computations and return the gradients and final tensor. We will also write a helper function to facilitate building the TensorTree and going
backwards through the TensorTree aptly called backward.
backward :: (Fractional a, Eq a) => State (Tape a) (Map.Map Int a)
backward = do
tape <- get
let ops = operations tape
let tree = buildTree ops Empty
return $ backTree tree Map.empty
doComputations :: (Fractional a, Eq a) => State (Tape a) (Tensor0D a, Map.Map Int a)
doComputations = do
t0 <- createTensor 1.5
t1 <- createTensor 2.5
t2 <- createTensor 3.5
t3 <- createTensor 4.5
t4 <- tMul t0 t1
t5 <- tDiv t4 t2
t6 <- tAdd t5 t3
grads <- backward
return (t6, grads)
To execute this code, we include this very simple main function:
main :: IO ()
main = do
let (tensor, grads) = evalState doComputations newTape
print tensor
print grads
Running the final program produces:
Tensor0D {tid = 6, value = 5.571428571428571}
fromList [(0,0.7142857142857142),(1,0.42857142857142855),(2,-0.30612244897959184),(3,1.0),(4,0.2857142857142857),(5,1.0)]
Which when compared with https://www.derivative-calculator.net/ is correct!
Thank you for reading!
© 2024 Silas Marvin. No tracking, no cookies, just plain HTML and CSS. | {"url":"https://silasmarvin.dev/simple-automatic-differentiation-in-haskell","timestamp":"2024-11-06T21:02:42Z","content_type":"text/html","content_length":"27361","record_id":"<urn:uuid:d1732940-9b1a-4600-bb77-913881486760>","cc-path":"CC-MAIN-2024-46/segments/1730477027942.47/warc/CC-MAIN-20241106194801-20241106224801-00186.warc.gz"} |
Construction of Solid Angle from Three Plane Angles any Two of which are Greater than Other Angle
In the words of Euclid:
To construct a solid angle out of three plane angles two of which, taken together in any manner, are greater than the remaining one: this the three angles must be less than four right angles.
(The Elements: Book $\text{XI}$: Proposition $23$)
In the words of Euclid:
But how it is possible to take the square on $OR$ equal to that area by which the square on $AB$ is greater than the square on $LO$, we can show as follows.
(The Elements: Book $\text{XI}$: Proposition $23$ : Lemma)
Let $\angle ABC, \angle DEF, \angle GHK$ be the three given plane angles such that the sum of any two is greater than the remaining one.
That is:
$\angle ABC + \angle DEF > \angle GHK$
$\angle DEF + \angle GHK > \angle ABC$
$\angle GHK + \angle ABC > \angle DEF$
Thus it is required that a solid angle be constructed out of plane angles equal to $\angle ABC, \angle DEF, \angle GHK$.
Let the straight lines $AB, BC, DE, EF, GH, HK$ be equal.
Let $AC$, $DF$ and $GK$ be joined.
From Proposition $22$ of Book $\text{XI} $: Extremities of Line Segments containing three Plane Angles any Two of which are Greater than Other form Triangle:
Let the triangle $\triangle LMN$ be constructed so that:
$AC = LM$
$DF = MN$
$GK = NL$
Let the circle $LMN$ be described about $\triangle LMN$.
Let the center of the circle $LMN$ be $O$.
Let $LO, MO, NO$ be joined.
It is to be demonstrated that $AB > LO$.
Suppose to the contrary that $AB \le LO$.
Suppose $AB = LO$.
We have that $AB = BC$ and $OL = OM$.
Therefore we have that:
$AB$ and $BC$ are equal to $OL$ and $OM$
$AC = LM$ by hypothesis.
Therefore from Proposition $8$ of Book $\text{I} $: Triangle Side-Side-Side Congruence:
$\angle ABC = \angle LOM$
For the same reason:
$\angle DEF = \angle MON$
$\angle GHK = \angle NOL$.
But $\angle LOM + \angle MON + \angle NOL$ equals $4$ right angles.
Therefore $\angle ABC + \angle DEF + \angle GHK$ equals $4$ right angles.
But by hypothesis $\angle ABC + \angle DEF + \angle GHK$ is less than $4$ right angles.
Therefore $AB \ne LO$.
Now suppose that $AB < LO$.
Let $OP = AB$ and $OQ = BC$.
Let $PQ$ be joined.
We have that
$AB = BC$
$OP = OQ$
$LP = QM$
Therefore from Proposition $2$ of Book $\text{VI} $: Parallel Transversal Theorem:
$LM \parallel PQ$
and from Proposition $29$ of Book $\text{I} $: Parallelism implies Equal Corresponding Angles:
$\triangle LMO$ is equiangular with $\triangle PQO$
Therefore from Proposition $4$ of Book $\text{VI} $: Equiangular Triangles are Similar:
$OL : LM = OP : PQ$
and from Proposition $4$ of Book $\text{V} $: Proportional Magnitudes are Proportional Alternately:
$LO : OP = LM : PQ$
But $LO > OP$.
Therefore $LM > PQ$.
But $LM = AC$.
Therefore $AC > PQ$.
We have that:
$AB$ and $BC$ equal $PO$ and $OQ$
$AC > PQ$
Therefore from Proposition $25$ of Book $\text{I} $: Converse Hinge Theorem:
$\angle ABC > \angle POQ$
Similarly it can be proved that:
$\angle DEF > \angle MON$
$\angle GHK > \angle NOL$
$\angle ABC + \angle DEF + \angle GHK > \angle LOM + \angle MON + \angle NOL$
But by hypothesis $\angle ABC + \angle DEF + \angle GHK$ is less than $4$ right angles.
Therefore $\angle LOM + \angle MON + \angle NOL$ is less than $4$ right angles.
But $\angle LOM + \angle MON + \angle NOL$ equals $4$ right angles.
Therefore $AB \not \le LO$.
It follows that $AB > LO$.
From Proposition $12$ of Book $\text{XI} $: Construction of Straight Line Perpendicular to Plane from point on Plane:
Let $OR$ be set up from $O$ perpendicular to the plane of the circle $LMN$.
Using Lemma to Proposition $12$ of Book $\text{XI} $: Construction of Solid Angle from Three Plane Angles any Two of which are Greater than Other Angle:
the square on $AB$ is greater than the square on $LO$.
Let $RL$, $RM$ and $RN$ be joined.
We have that $RO$ is perpendicular to the plane of the circle $LMN$.
Therefore $RO$ is perpendicular to each of the straight lines $LO$, $MO$ and $NO$.
We have that:
$LO = OM$
$OR$ is common and perpendicular
so from Proposition $4$ of Book $\text{I} $: Triangle Side-Angle-Side Congruence:
$RL = RM$
For the same reason:
$RN = RL = RM$
$AB^2 = LO^2 + OR^2$
But from Proposition $47$ of Book $\text{I} $: Pythagoras's Theorem:
$LR^2 = LO^2 + OR^2$
as $\angle LOR$ is a right angle.
$AB^2 = RL^2$
and so:
$AB = RL$
But $RL = RM = RN$.
$AB = BC = DE = EF = GH = HK = RL = RM = RN$
So we have:
$LR$ and $RM$ are equal to $AB$ and $BC$
and by hypothesis:
$LM = AC$
Therefore from Proposition $8$ of Book $\text{I} $: Triangle Side-Side-Side Congruence:
$\angle LRM = \angle ABC$
For the same reason:
$\angle MRN = \angle DEF$
$\angle LRN = \angle GHK$
Therefore out of the three plane angles $\angle LRM, \angle MRN, \angle LRN$ which are equal to the plane angles $\angle ABC, \angle DEF, \angle GHK$, the solid angle $R$ has been constructed which
is contained by the three plane angles $\angle LRM, \angle MRN, \angle LRN$.
Historical Note
This proof is Proposition $23$ of Book $\text{XI}$ of Euclid's The Elements. | {"url":"https://proofwiki.org/wiki/Construction_of_Solid_Angle_from_Three_Plane_Angles_any_Two_of_which_are_Greater_than_Other_Angle","timestamp":"2024-11-03T07:41:57Z","content_type":"text/html","content_length":"56251","record_id":"<urn:uuid:a9c3c02b-5177-4b98-ac6f-8e0a3227f2b6>","cc-path":"CC-MAIN-2024-46/segments/1730477027772.24/warc/CC-MAIN-20241103053019-20241103083019-00064.warc.gz"} |
Basic Algebra Concepts
Course Description
MA 040. Basic Algebra Concepts . 1 hour credit. Prerequisite: Predetermined Asset score or MA 020 with a C or better. This course will enable the student to use basic algebra concepts including
signed numbers, equation solving, word problems, exponents, roots, and polynomials.
Course Relevance
The principles learned in this course allow a student to use math skills in real life application problems and prepare for higher level math classes.
Required Materials
Howett, J. (2003). Math sense: algebra and geometry. NY: New Readers Press.
Learning Outcomes
The intent is for a student to be able to
1. Demonstrate competence in the use of signed numbers , equation solving, word problem solving, the use and manipulation of exponents and roots , and polynomials.
Primary Learning PACT Skills that will be DEVELOPED and/or documented in this course
Through the student’s involvement in this course, he/she will develop his/her ability in the following primary PACT skill areas:
1. Problem Solving
• Through application problems, the student will identify and define problems, gather information and determine its relevancy, develop workable solutions, select and communicate the best solution.
Secondary skills (developed but not documented):
Critical Thinking
Time Management
Internet Use
Major Summative Assessment Task(s)
These learning outcomes and the primary Learning PACT skills will be demonstrated by:
1. Completion of a project involving the use of signed numbers, equation solving, word problems, exponents, roots, and polynomials
Course Content
I. Themes - Key recurring concepts that run throughout this course:
A. Problem Solving – use of multiple routes to reach a correct answer
B. Value of math – personal perceptions and others’ perceptions
C. Planning
II. Issues - Key areas of conflict that must be understood to achieve the intended outcome:
A. Use of calculators
B. Relevance of algebra
C. Variability of order of methods used to come to correct answer
III. Concepts - Key concepts that must be understood to address the issues :
A. Math as a “language”
B. Properties that govern math usage
IV. Skills/Competencies - Actions that are essential to achieve the course outcomes:
A. Concept of positive and negative numbers
B. Adding, subtracting , multiplying and dividing signed numbers
C. Using more than one operation to find and answer
D. Variables
E. Evaluating algebraic expressions
F. Solving equations with one and two inverse operations
G. Combining like variables
H. Combining variables to solve equations
I. Solving equations with variables on both sides
J. Solving literal equations
K. Using formulas to solve problems
L. Writing equations to solve word problems
M. Ratios and proportions including multi- step problems
N. Factors, exponents, square roots , terms
O. Adding, subtracting, multiplying and dividing monomials
P. Adding polynomials together
Q. Finding factors in terms with variables
R. Multiplying the sum and difference of two numbers
Learning Units
I. Signed numbers
II. Solving equations
III. Word problems in algebra
IV. Exponents, roots and polynomials
Learning Activities
Independent learning activities are assigned to be completed to help students achieve the intended course outcome. Student-instructor interaction, text materials, computerized instruction and web
resources may also contribute to the learning process.
Grade Determination
Grade determination is based on attendance and completion of all assignments and assessment tasks. | {"url":"https://softmath.com/tutorials-3/algebra-formulas/basic-algebra-concepts.html","timestamp":"2024-11-11T03:00:47Z","content_type":"text/html","content_length":"35654","record_id":"<urn:uuid:f9cb9d85-abb5-4423-82ef-276b9a4ebc50>","cc-path":"CC-MAIN-2024-46/segments/1730477028216.19/warc/CC-MAIN-20241111024756-20241111054756-00811.warc.gz"} |
How can you forebode that amount of wood in a napkin ring is the same, regardless of the size of the sphere used ?
Stewart, Clegg, Watson. Calculus Early Transcendentals, 2021, 9th edition. page 467. Problem 64.
When I attempted this question, I thought I flubbed, because my answer lacked R and r! Even after seeing the solution, I still can’t intuit why the napkin ring’s volume is independent of R and r.
Before attempting any paperwork, how can a student forefeel that the napkin ring’s volume shall be independent of R and r ?
1 answer
Works for me
The following users marked this post as Works for me:
User Comment Date
Sunny (no comment) Jun 20, 2024 at 18:12
(a) Guess which ring has more wood in it.
The word "guess" shows that this is not necessarily intended to be guessed correctly. The guess is asked for precisely because the result is unintuitive, and surprising to most people. Writing down
your guess emphasises the contrast between what you initially expect, and what you later calculate exactly (in part (b)).
If you wanted to discuss ways of potentially anticipating this kind of unexpected result with students (after they have made their own attempt at guessing), you could talk about methods of getting a
quick insight without fully calculating the result.
For example, with the height $h$ held constant, the larger the ring the thinner it must be. This can be seen to some extent from the two rings in the image. This initial intuition can be confirmed by
noting that the thickness of the ring can be made arbitrarily close to zero by making the ring larger. This does not yet confirm that the volume will be invariant, but it hints that there is no
immediate reason to expect either a small or large ring to have greater volume.
The first half of the question, asking for a guess, appears to be asking for this kind of rough idea, rather than a full calculation, so the result does not need to be conclusive (or even correct).
If a student were to give a conclusive proof then I would think they have missed the point of the question.
Intuition from practical objects
Having made the guess, and then been surprised (as intended) by the calculated result, a feeling for why this is surprising can be gained by thinking about how the mathematical result differs from
what is possible in reality.
Mathematically, you can calculate the thickness of the ring ($R-r$) in terms of $r$, and see that you can get as close as you like to zero thickness by choosing sufficiently large $r$. However, a
ring made of wood cannot be arbitrarily thin due to being made of molecules. Below a certain thickness it will no longer be wood, and long before that it will no longer be strong enough to hold its
own shape. In order to get a good intuition for the geometry, it is necessary to let go of the materials based intuitions we have for how thick a ring would need to be to be useful.
Intuition from familiar shapes
The two rings in the image look fairly similar. It's easy to mistakenly expect much larger versions to look bigger but still fairly similar. Personally, my immediate visualisation of a very large
ring was not consistent with a cylinder removed from a sphere, but instead a cylinder removed from a torus. This gives a shape that looks more familiar even for arbitrarily large rings, but it gives
a misleading intuition about volume. A cylinder removed from a torus would allow the thickness to stay constant as the radius r becomes arbitrarily large, leading to arbitrarily large volume rather
than invariant volume.
A guessing question such as this is useful for helping find such misleading tendencies in our intuition.
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Weighings - Puzzle Prime
You have 12 balls, 11 of which have the same weight. The remaining one is defective and either heavier or lighter than the rest. You can use a balance scale to compare weights in order to find which
is the defective ball and whether it is heavier or lighter. How many measurement do you need so that will be surely able to do it?
It is easy to see that if we have more than 9 balls, we need at least 3 measurements. We will prove that 3 measurements are enough for 12 balls.
We place 4 balls on each side of the scale. Let balls 1, 2, 3, 4 be on the right side, and balls 5, 6, 7, 8 on the left side.
CASE 1. The scale does not tip to any side. For the second measurement we place on the left side balls 1, 2, 3, 9 and on the right side balls 4, 5, 10, 11.
If the scale again does not tip to any side, then the defective ball is number 12 and we can check whether it is heavier or lighter with our last measurement.
If the scale tips to the left side, then either the defective ball is number 9 and is heavier, or it is number 10/11 and is lighter. We measure up balls 10 and 11 against each other and if one of
them is lighter than the other, then it is the defective one. If they have the same weight, then ball 9 is the defective one.
If the scale tips to the right side, the procedure is similar.
CASE 2. Let the scale tip to the left side during the first measurement. This means that either one of the balls 1, 2, 3, 4 is defective and it is heavier, or one of the balls 5, 6, 7, 8 is defective
and it is lighter. Clearly, balls 9, 10, 11, 12 are all genuine. Next we place balls 1, 2, 5, 6 on one side and balls 3, 7, 9, 10 on the other side.
If the scale tips to the left, then either one of the balls 1, 2 is defective and it is heavier, or ball 8 is defective and lighter. We just measure up balls 1 and 2 against each other and find out
which among the three is the defective one.
If the scale tips to the right, the procedure is similar.
If the scale does not tip to any side, then either the defective ball is 4 and it is heavier, or the defective ball is 8 and it is lighter. We just measure up balls 1 and 4 against each other and
easily find the defective ball.
9 balls, 1 defective
You have 9 balls, 8 of which have the same weight. The remaining one is defective and heavier than the rest. You can use a balance scale to compare weights in order to find which is the defective
ball. How many measurements do you need so that you will be surely able to do it? What if you have 2000 balls?
First, we put 3 balls on the left side and 3 balls on the right side of the balance scale. If the scale tips to one side, then the defective ball is there. If not, the defective ball is among the
remaining 3 balls. Once left with 3 balls only, we put one on each side of the scale. If the scale tips to one side, the defective ball is there. If not, the defective ball is the last remaining one.
Clearly we can not find the defective ball with just one measurement, so the answer is 2.
If you had 2000 balls, then you would need 7 measurements. In general, if you have N balls, you would need to make at least log₃(N) tests to find the defective ball. The strategy is the same: keep
splitting the group of remaining balls into 3 (as) equal (as possible) subgroups, discarding 2 of these subgroups after a measurement. To see that you need no less than log₃(N) tries, notice that
initially there are N possibilities for the defective ball and every measurement can yield 3 outcomes. If every time you get the worst outcome, you will make at least log₃(N) tries.
68 Coins, 100 Weighings
You have 68 coins with different weights. How can you find both the lightest and the heaviest coins with 100 scale weighings?
1. Compare the coins in pairs and separate the light ones in one group and the heavy ones in another. (34 weighings)
2. Find the lightest coin in the first group of 34 coins. (33 weighings)
3. Find the heaviest coin in the second group of 34 coins. (33 weighings)
Gold and Nickel
You have 15 identical coins – 2 of them made of pure gold and the other 13 made of nickel (covered with thin gold layer to mislead you). You also have a gold detector, with which you can detect if in
any group of coins, there is at least one gold coin or not. How can you find the pure gold coins with only 7 uses of the detector?
First, we note that if we have 1 gold ball only, then we need:
• 1 measurement in a group of 2 balls
• 2 measurements in a group of 4 balls
• 3 measurements in a group of 8 balls
Start by measuring 1, 2, 3, 4, 5.
1. If there are gold balls in the group, then measure 6, 7, 8, 9, 10, 11.
□ If there are gold balls in the group, then measure 5, 6, 7.
☆ If there are no gold balls among them, then there is a gold ball among 1, 2, 3, 4, and a gold ball among 8, 9, 10, 11, so we can find the gold balls with the remaining 2 measurements.
☆ If there are gold balls in 5, 6, 7, then measure 5, 8, 9. If there are gold balls there, then 5 must be gold, and we can find the other gold ball among 6, 7, 8, 9, 10, 11 with the
remaining 3 measurements. If there is no gold ball among 5, 8, 9, then there is a gold ball among 1, 2, 3, 4, and a gold ball among 6, 7, so again we can find them with only 3
□ If there are no gold balls in the group, then measure 5, 12, 13.
☆ If there are no gold balls among them, then measure 14, 15. If none of them is gold, then measure individually 1, 2, and 3 to find which are the 2 gold balls among 1, 2, 3, 4. Otherwise,
there is a gold ball among 1, 2, 3, 4, and among 14, 15, and we can find them with the remaining 3 measurements.
☆ If there are gold balls among 5, 12, 13, then measure 5, 14, 15. If none of them is gold, then there is a gold ball among 1, 2, 3, 4, and a gold ball among 12, 13, so we can find them
with 3 measurements. Otherwise, 5 is gold, and again we can find the other gold ball among 1, 2, 3, 4, 12, 13, 14, 15 with 3 measurements.
2. If there are no gold balls among 1, 2, 3, 4, 5, then we measure 6, 7, 8.
□ If there are gold balls in the group, then measure 9, 10, 11, 12, 13.
☆ If there are no gold balls among them, we measure individually 6, 7, 8, 14.
☆ If there is a gold ball among 9, 10, 11, 12, 13, then there is another one among 6, 7, 8. We measure 8, 9. If none of them is gold, then we can find the gold among 6, 7, and the gold
among 10, 11, 12, 13, with 3 measurements total. If there is a gold ball among 8, 9, then we measure 10, 11, 12, 13. If none of them is gold, then 9 is gold and we find the other gold
ball among 6, 7, 8 with 2 more measurements. If there is a gold ball among 10, 11, 12, 13, then we can find it with 2 measurements. The other gold ball must be 8.
□ If there are no gold balls in the group, then measure 9, 10.
☆ If there are no gold balls among them, then measure individually 11, 12, 13, 14.
☆ If there are gold balls among 9, 10, then measure 11, 12, 13, 14. If there is a gold ball among them, then there is another one among 9, 10, and we can find them both with 3 measurements.
Otherwise, we measure 9 and 10 individually.
Measuring Scale
You have 10 unlimited piles of balls and one measuring scale. All balls in a pile have the same weight, which is an integer between 1 and 9 grams. How many measurements do you need in order to find
the weight of the balls in every pile?
You need only one measurement – take 1 ball from pile 1, 10 balls from pile 2, 100 balls from pile 3, etc., and measure their total weight. The first digit of the number shown on the scale determines
the weight of the balls in the 10th pile, the second digit determines the weight of the balls in the 9th pile and so on. | {"url":"https://www.puzzleprime.com/tag/weighings/","timestamp":"2024-11-08T12:02:58Z","content_type":"text/html","content_length":"186688","record_id":"<urn:uuid:a2597ddf-48a0-4682-a853-b48c4769b0b6>","cc-path":"CC-MAIN-2024-46/segments/1730477028059.90/warc/CC-MAIN-20241108101914-20241108131914-00081.warc.gz"} |
5 (number) - Wikiwand
The number five is a number that comes after four and before the number six. In Roman numerals, it is V.
Pronunciation of the number 5
Five is the third prime number, after two and three, and before seven. The number five is also an odd number.
Most people have five fingers (including one thumb) on each hand and five toes on each foot.
Numbers ending in five are always divisible by 5
The number 5 exists
The number five changing over time, from ancient times to modern times
It is not known for certain who and how the shape of the number five was created, but most people think it was made by the Brahmin Indians.
Wikiwand in your browser!
Seamless Wikipedia browsing. On steroids.
Every time you click a link to Wikipedia, Wiktionary or Wikiquote in your browser's search results, it will show the modern Wikiwand interface.
Wikiwand extension is a five stars, simple, with minimum permission required to keep your browsing private, safe and transparent. | {"url":"https://www.wikiwand.com/simple/articles/Five","timestamp":"2024-11-10T02:20:27Z","content_type":"text/html","content_length":"203211","record_id":"<urn:uuid:bf4c56b8-5140-4155-8940-4371d2f14aa7>","cc-path":"CC-MAIN-2024-46/segments/1730477028164.3/warc/CC-MAIN-20241110005602-20241110035602-00852.warc.gz"} |
Vacuum Decay: Goldstone modes and Bubble Lifetime
Vacuum decay is a quantum mechanical process which describes the tunnelling of the Universe from the false vacuum state to the true vacuum of the theory, leading to the breaking of gauge symmetries
and separating forces which once were unified. This occurs through the nucleation of bubbles of the true vacuum which grow and fill up the entire spacetime continuum. This thesis visits topics on
vacuum decay and presents new original findings. We study the effects of Goldstone modes on the stability of the vacuum in a U(1) theory for a complex scalar field. The dynamics of the field resemble
those of Keplerian motion in the presence of time-dependent friction, whose equations of motion imply a conserved quantity, L, reminiscent of conserved angular momentum. We show that divergences at
the origin of coordinates render any solution in flat spacetime physically unattainable. We then show that, in a spacetime punctured at the origin of coordinates, it is possible to obtain
finite-action solutions to the equations of motion, which correspond to the size of the hole, which in turn determines the tunnelling point and the value of the conserved quantity L. We find that the
vacuum is comparatively short-lived for all possible orderings in which the false and true vacua are placed in the potential. We also show how Goldstone modes provide the necessary energy to overcome
drag forces yielding finite-action solutions for any potential, including those for which no such solutions exist for real scalar fields. Gravitational waves sourced by sound waves resulting from the
collision of bubbles of the true vacuum may serve as evidence for cosmological phase transitions in the early Universe. Therefore, we developed a mathematical formalism which aims to estimate the
distribution of bubble lifetimes, which helps us to predict the shape of the resultant gravitational wave power spectrum. | {"url":"https://research.manchester.ac.uk/en/studentTheses/vacuum-decay-goldstone-modes-and-bubble-lifetime","timestamp":"2024-11-10T11:55:10Z","content_type":"text/html","content_length":"27223","record_id":"<urn:uuid:293026a2-5612-44f9-9874-ef9cddd58f25>","cc-path":"CC-MAIN-2024-46/segments/1730477028186.38/warc/CC-MAIN-20241110103354-20241110133354-00806.warc.gz"} |
Lesson 21
Graphing Linear Inequalities in Two Variables (Part 1)
• Let’s find out how to use graphs to represent solutions to inequalities in two variables.
21.1: Math Talk: Less Than, Equal to, or More Than 12?
Here is an expression: \(2x+3y\).
Decide if the values in each ordered pair, \((x, y)\), make the value of the expression less than, greater than, or equal to 12.
\((0, 5)\)
\((\text-1, \text-1)\)
21.2: Solutions and Not Solutions
Here are four inequalities. Study each inequality assigned to your group and work with your group to:
• Find some coordinate pairs that represent solutions to the inequality and some coordinate pairs that do not represent solutions.
• Plot both sets of points. Either use two different colors or two different symbols like X and O.
• Plot enough points until you start to see the region that contains solutions and the region that contains non-solutions. Look for a pattern describing the region where solutions are plotted.
21.3: Sketching Solutions to Inequalities
1. Here is a graph that represents solutions to the equation \(x-y=5\).
Sketch 4 quick graphs representing the solutions to each of these inequalities:
2. For each graph, write an inequality whose solutions are represented by the shaded part of the graph.
1. The points \((7,3)\) and \((7,5)\) are both in the solution region of the inequality \(x - 2y < 3\).
1. Compute \(x-2y\) for both of these points.
2. Which point comes closest to satisfying the equation \(x-2y=3\)? That is, for which \((x,y)\) pair is \(x-2y\) closest to 3?
2. The points \((3,2)\) and \((5,2)\) are also in the solution region. Which of these points comes closest to satisfying the equation \(x-2y=3\)?
3. Find a point in the solution region that comes even closer to satisfying the equation \(x-2y=3\). What is the value of \(x-2y\)?
4. For the points \((5,2)\) and \((7,3)\), \(x-2y=1\). Find another point in the solution region for which \(x-2y=1\).
5. Find \(x-2y\) for the point \((5,3)\). Then find two other points that give the same answer.
The equation \(x+y = 7\) is an equation in two variables. Its solution is any pair of \(x\) and \(y\) whose sum is 7. The pairs \(x=0, y=7\) and \(x =\text5, y= 2\) are two examples.
We can represent all the solutions to \(x+y = 7\) by graphing the equation on a coordinate plane.
The graph is a line. All the points on the line are solutions to \(x+y = 7\).
The inequality \(x+y \leq 7\) is an inequality in two variables. Its solution is any pair of \(x\) and \(y\) whose sum is 7 or less than 7.
This means it includes all the pairs that are solutions to the equation \(x+y=7\), but also many other pairs of \(x\) and \(y\) that add up to a value less than 7. The pairs \(x=4, y=\text-7\) and \
(x=\text-6, y=0\) are two examples.
On a coordinate plane, the solution to \(x+y \leq 7\) includes the line that represents \(x+y=7\). If we plot a few other \((x,y)\) pairs that make the inequality true, such as \((4, \text-7)\) and \
((\text-6,0)\), we see that these points fall on one side of the line. (In contrast, \((x,y)\) pairs that make the inequality false fall on the other side of the line.)
We can shade that region on one side of the line to indicate that all points in it are solutions.
What about the inequality \(x+y <7\)?
The solution is any pair of \(x\) and \(y\) whose sum is less than 7. This means pairs like \(x=0, y=7\) and \(x =5, y=2\) are not solutions.
On a coordinate plane, the solution does not include points on the line that represent \(x+y=7\) (because those points are \(x\) and \(y\) pairs whose sum is 7).
To exclude points on that boundary line, we can use a dashed line.
All points below that line are \((x,y)\) pairs that make \(x+y<7\) true. The region on that side of the line can be shaded to show that it contains the solutions. | {"url":"https://curriculum.illustrativemathematics.org/HS/students/1/2/21/index.html","timestamp":"2024-11-11T07:13:01Z","content_type":"text/html","content_length":"129831","record_id":"<urn:uuid:1f245029-5b77-4a88-a5d2-9089f868eefb>","cc-path":"CC-MAIN-2024-46/segments/1730477028220.42/warc/CC-MAIN-20241111060327-20241111090327-00259.warc.gz"} |
Decimal Multiplication Worksheet Pdf
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Decimal Multiplication Worksheet Pdf
Decimal Multiplication Worksheet Pdf -
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Multiplying Decimals Find each product 5 5 4 87 3 0 2 1 6 5 4 6 7 2 7 1 5 7 1 9 7 5 9 8 3 11 3 2 8 7 1 1 Name Date Period 2 1 7 2 1 4 1 7 3 1 6 5 928 11 6 8 7 8 5 1 10 4 04 9 3 12 8 1 8 6 5 2
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Decimal Multiplication Worksheet For Grade 5 Your Home Teacher
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Urging consistent method, offering assistance, and developing a positive learning atmosphere are valuable actions. | {"url":"https://crown-darts.com/en/decimal-multiplication-worksheet-pdf.html","timestamp":"2024-11-12T22:12:20Z","content_type":"text/html","content_length":"28558","record_id":"<urn:uuid:9cd2a41d-2130-4cda-aa80-8e0fc346d625>","cc-path":"CC-MAIN-2024-46/segments/1730477028290.49/warc/CC-MAIN-20241112212600-20241113002600-00505.warc.gz"} |
School Program
│K. Papadopoulos │Waves and instabilities in turbulent space plasmas │
│A. Celani │Hydrodynamic turbulence │
│Contributed Talks│ │
│E. Yordanova │Multifractal structure of turbulence in Magnetospheric Cusp │
│M.Nechaeva │Radio interferometer signal at raying of the solar wind plasma by cosmic source radio emission │
│N. Decamp │Interstellar turbulence and hierarchical structuring │
│L. Heggland │Waves in the chromosphere and corona │
│S. Giordano │Topology of Supergranulation: Pair Correlation Function g2(r) and Information Entropy H’(l) │
│S. Russo │Hexagonal generalization of Van Siclen information entropy │
│F. Valentini │First results of the cylindrical Vlasov-Poisson code: a numerical study of the Bernstein-Landau paradox │
│C. Marchetto │Simulating an IBW propagation perpendicular to the confining field:non-linear kinetic effects and possibility for turbulence suppression│
│O. Alexandrova│Alfven wave instabilities: Cluster observations and hybrid simulations │
│P. Hellinger │Magnetosheath marginal stability path │
│F. Sahraoui │Magnetic turbulence in the terrestrial magnetosheath: observation and theoretical model │
│M. Longmore │3-dimensional structure and non-linear behaviour at the quasi-parallel bow shock │
│V. Carbone │Models for turbulence │
│Contributed Talks │ │
│G. Nigro │Nanoflares and MHD turbulence in Coronal Loop: a Hybrid shell model │
│E. Buchlin │Distributions of coronal events: observations, simulations and event definitions │
│M.F. De Franceschis│Dissipation of Alfven waves in coronal structures │
│K. Gontikakis │Electron acceleration and radiation in evolving complex active regions │
│S. Stangl │2D spectropolarimetric analysis of a small active region in the solar atmosphere │
│L. Dolla │A search for signatures of preferential heating of heavy ions in the Low Corona, by way of ion cyclotron resonance │
│Å. Nordlund │3-D numerical simulations of turbulent plasmas │
│T. Horbury │Space observations: an overview │
│Contributed Talks │ │
│R. De Bartolo │Asymptotic states forecasting as solutions of 2D MHD equations │
│M. Onofri │Three-dimensional simulations of magnetic reconnection │
│A. F. Rappazzo │Dynamics of the magnetized wake and the acceleration of the slow solar wind │
│K. Bamert │Wave-particle interaction upstream of a CME-driven shock: SOHO/CELIAS/HSTOF and ACE/MAG │
│N. Agueda-Costafreda│The downstream region │
│A. Sadovski │The induced scattering of Alfven waves in fast solar wind │
│R. Kallenbach │Plasma turbulence and wave-particle interaction near the main interplanetary shock of the Bastille day Coronal Mass Ejections │
│W. Fundamenski │Turbulent Transport in Tokamak Edge Plasmas │
│A. Bigazzi │Mode coupling in non-axisymmetric dynamo models │
│S. Galtier │Weak Electron MHD Turbulence │
│S. Landi │Alfven wave propagation in an X point magnetic geometry │
│A. Noullez │Global Variables in decaying Burgers turbulence │
│L. Sorriso-Valvo│Intermittency in solar wind induced electric field │
│R. Turkmani │Numerical simulations of Alfvén waves in the solar corona │
│L. Del Zanna │Parametric decay of large-amplitude Alfvén waves and turbulence evolution in the fast solar wind │ | {"url":"https://www.astro.auth.gr/~vlahos/school2003/program-1.htm","timestamp":"2024-11-09T13:31:18Z","content_type":"text/html","content_length":"19269","record_id":"<urn:uuid:03ab58ef-5e06-4495-b47b-775a83187a3f>","cc-path":"CC-MAIN-2024-46/segments/1730477028118.93/warc/CC-MAIN-20241109120425-20241109150425-00757.warc.gz"} |
Physics and Astronomy Dissertation Defense - Dillon Morse - Department of Physics and Astronomy
UNC-CH Physics and Astronomy Dissertation Defense
Dillon Morse
“Semi-Classical Backreaction of Quantum Scalar Fields on an Evolving Spacetime”
The formalism required to extend quantum field theory to curved spacetimes has been studied extensively for the last 40 years. In all treatments of the subject the quantum field is heavily influenced
by the spacetime curvature; the geometry, however, is assumed to evolve subject only to classical matter and independently of the energies and pressures of the quantum field. The primary obstacle to
solving the fully self-consistent backreaction problem lies in the complexity of the (formally divergent) energy momentum tensor of the quantum field. We explore a number of new approaches towards
understanding the underlying mathematics in hopes of determining a physically realistic, finite expression for the energy momentum tensor which describes the quantum field in a particular vacuum
state while also influencing the evolution of the spacetime geometry itself. | {"url":"https://physics.unc.edu/event/physics-and-astronomy-dissertation-defense-dillon-morse/","timestamp":"2024-11-07T13:48:59Z","content_type":"text/html","content_length":"96270","record_id":"<urn:uuid:7563015d-c0dd-480e-934e-e4bbd449083f>","cc-path":"CC-MAIN-2024-46/segments/1730477027999.92/warc/CC-MAIN-20241107114930-20241107144930-00865.warc.gz"} |
The Stacks project
Lemma 32.5.3. Let $S$ be a quasi-compact and quasi-separated scheme. Let $V \subset S$ be a quasi-compact open. Let $I$ be a directed set and let $(V_ i, f_{ii'})$ be an inverse system of schemes
over $I$ with affine transition maps, with each $V_ i$ of finite type over $\mathbf{Z}$, and with $V = \mathop{\mathrm{lim}}\nolimits V_ i$. Then there exist
1. a directed set $J$,
2. an inverse system of schemes $(S_ j, g_{jj'})$ over $J$,
3. an order preserving map $\alpha : J \to I$,
4. open subschemes $V'_ j \subset S_ j$, and
5. isomorphisms $V'_ j \to V_{\alpha (j)}$
such that
1. the transition morphisms $g_{jj'} : S_ j \to S_{j'}$ are affine,
2. each $S_ j$ is of finite type over $\mathbf{Z}$,
3. $g_{jj'}^{-1}(V'_{j'}) = V'_ j$,
4. $S = \mathop{\mathrm{lim}}\nolimits S_ j$ and $V = \mathop{\mathrm{lim}}\nolimits V'_ j$, and
5. the diagrams
\[ \vcenter { \xymatrix{ V \ar[d] \ar[rd] \\ V'_ j \ar[r] & V_{\alpha (j)} } } \quad \text{and}\quad \vcenter { \xymatrix{ V'_ j \ar[r] \ar[d] & V_{\alpha (j)} \ar[d] \\ V'_{j'} \ar[r] & V_{\
alpha (j')} } } \]
are commutative.
Comments (2)
Comment #1912 by typo on
It should be $l=1, \dots, m$ in "Then, by Lemma 5.24.6 we can (after shrinking $I$ again) assume the corresponding opens $D(g_{l, i}) \subset \Spec(R_i)$ are contained in $W_i$, $j = 1, \ldots,
m$ and cover $W_i$."
Comment #1984 by Johan on
Thanks, fixed here.
There are also:
• 2 comment(s) on Section 32.5: Absolute Noetherian Approximation
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Python performance tips and best practice for CLIMADA developers
Python performance tips and best practice for CLIMADA developers#
This guide covers the following recommendations:
⏲️ Use profiling tools to find and assess performance bottlenecks.
🔁 Replace for-loops by built-in functions and efficient external implementations.
📝 Consider algorithmic performance, not only implementation performance.
🧊 Get familiar with NumPy: vectorized functions, slicing, masks and broadcasting.
⚫ Miscellaneous: sparse arrays, Numba, parallelization, huge files (xarray), memory.
⚠️ Don’t over-optimize at the expense of readability and usability.
Python comes with powerful packages for the performance assessment of your code. Within IPython and notebooks, there are several magic commands for this task:
• %time: Time the execution of a single statement
• %timeit: Time repeated execution of a single statement for more accuracy
• %%timeit Does the same as %timeit for a whole cell
• %prun: Run code with the profiler
• %lprun: Run code with the line-by-line profiler
• %memit: Measure the memory use of a single statement
• %mprun: Run code with the line-by-line memory profiler
More information on profiling in the Python Data Science Handbook.
Also useful: unofficial Jupyter extension Execute Time.
While it’s easy to assess how fast or slow parts of your code are, including finding the bottlenecks, generating an improved version of it is much harder. This guide is about simple best practices
that everyone should know who works with Python, especially when models are performance-critical.
In the following, we will focus on arithmetic operations because they play an important role in CLIMADA. Operations on non-numeric objects like strings, graphs, databases, file or network IO might be
just as relevant inside and outside of the CLIMADA context. Some of the tips presented here do also apply to other contexts, but it’s always worth looking for context-specific performance guides.
General considerations#
This section will be concerned with:
🔁 for-loops and built-ins
📦 external implementations and converting data structures
📝 algorithmic efficiency
💾 memory usage
𝚺 As this section’s toy example, let’s assume we want to sum up all the numbers in a list:
list_of_numbers = list(range(10000))
A developer with a background in C++ would probably loop over the entries of the list:
result = 0
for i in list_of_numbers:
result += i
332 µs ± 65.7 µs per loop (mean ± std. dev. of 7 runs, 1000 loops each)
The built-in function sum is much faster:
%timeit sum(list_of_numbers)
54.9 µs ± 5.63 µs per loop (mean ± std. dev. of 7 runs, 10000 loops each)
The timing improves by a factor of 5-6 and this is not a coincidence: for-loops generally tend to get prohibitively expensive when the number of iterations increases.
💡 When you have a for-loop with many iterations in your code, check for built-in functions or efficient external implementations of your programming task.
A special case worth noting are append operations on lists which can often be replaced by more efficient list comprehensions.
Converting data structures#
💡 When you find an external library that solves your task efficiently, always consider that it might be necessary to convert your data structure which takes time.
For arithmetic operations, NumPy is a great library, but if your data comes as a Python list, NumPy will spend quite some time converting it to a NumPy array:
import numpy as np
%timeit np.sum(list_of_numbers)
572 µs ± 80 µs per loop (mean ± std. dev. of 7 runs, 1000 loops each)
This operation is even slower than the for-loop!
However, if you can somehow obtain your data in the form of NumPy arrays from the start, or if you perform many operations that might compensate for the conversion time, the gain in performance can
be considerable:
# do the conversion outside of the `%timeit`
ndarray_of_numbers = np.array(list_of_numbers)
%timeit np.sum(ndarray_of_numbers)
10.6 µs ± 1.56 µs per loop (mean ± std. dev. of 7 runs, 100000 loops each)
Indeed, this is 5-6 times faster than the built-in sum and 20-30 times faster than the for-loop.
Always consider several implementations#
Even for such a basic task as summing, there exist several implementations whose performance can vary more than you might expect:
%timeit ndarray_of_numbers.sum()
%timeit np.einsum("i->", ndarray_of_numbers)
9.07 µs ± 1.39 µs per loop (mean ± std. dev. of 7 runs, 100000 loops each)
5.55 µs ± 383 ns per loop (mean ± std. dev. of 7 runs, 100000 loops each)
This is up to 50 times faster than the for-loop. More information about the einsum function will be given in the NumPy section of this guide.
Efficient algorithms#
💡 Consider algorithmic performance, not only implementation performance.
All of the examples above do exactly the same thing, algorithmically. However, often the largest performance improvements can be obtained from algorithmic changes. This is the case when your model or
your data contain symmetries or more complex structure that allows you to skip or boil down arithmetic operations.
In our example, we are summing the numbers from 1 to 10,000 and it’s a well known mathematical theorem that this can be done using only two multiplications and an increment:
n = max(list_of_numbers)
%timeit 0.5 * n * (n + 1)
83.1 ns ± 2.5 ns per loop (mean ± std. dev. of 7 runs, 10000000 loops each)
Not surprisingly, This is almost 100 times faster than even the fastest implementation of the 10,000 summing operations listed above.
You don’t need a degree in maths to find algorithmic improvements. Other algorithmic improvements that are often easy to detect are:
• Filter your data set as much as possible to perform operations only on those entries that are really relevant.
Example: When computing a physical hazard (e.g. extreme wind) with CLIMADA, restrict to Centroids on land unless you know that some of your exposure is off shore.
• Make sure to detect inconsistent or trivial input parameters early on, before starting any operations.
Example: If your code does some complicated stuff and applies a user-provided normalization factor at the very end, make sure to check that the factor is not 0 before you start applying those
complicated operations.
📝 In general: Before starting to code, take pen and paper and write down what you want to do from an algorithmic perspective.
Memory usage#
💡 Be careful with deep copies of large data sets and only load portions of large files into memory as needed.
Write your code in such a way that you handle large amounts of data chunk by chunk so that Python does not need to load everything into memory before performing any operations. When you do, Python’s
generators might help you with the implementation.
🐌 Allocating unnecessary amounts of memory might slow down your code substantially due to swapping.
Sparse matrices#
In many contexts, we deal with sparse matrices or sparse data structures, i.e. two-dimensional arrays where most of the entries are 0. In CLIMADA, this is especially the case for the intensity
attributes of Hazard objects. This kind of data is usually handled using SciPy’s submodule scipy.sparse.
💡 When dealing with sparse matrices make sure that you always understand exactly which of your variables are sparse and which are dense and only switch from sparse to dense when absolutely necessary.
💡 Multiplications (multiply) and matrix multiplications (dot) are often faster than operations that involve masks or indexing.
As an example for the last rule, consider the problem of multiplying certain rows of a sparse array by a scalar:
import scipy.sparse as sparse
array = np.tile(np.array([0, 0, 0, 2, 0, 0, 0, 1, 0], dtype=np.float64), (100, 80))
row_mask = np.tile(np.array([False, False, True, False, True], dtype=bool), (20,))
In the following cells, note that the code in the first line after the %%timeit statement is not timed, it’s the setup line.
%%timeit sparse_array = sparse.csr_matrix(array)
sparse_array[row_mask, :] *= 5
/home/tovogt/.local/share/miniconda3/envs/tc/lib/python3.7/site-packages/scipy/sparse/data.py:55: RuntimeWarning: overflow encountered in multiply
self.data *= other
1.52 ms ± 155 µs per loop (mean ± std. dev. of 7 runs, 1000 loops each)
%%timeit sparse_array = sparse.csr_matrix(array)
sparse_array.multiply(np.where(row_mask, 5, 1)[:, None]).tocsr()
340 µs ± 7.32 µs per loop (mean ± std. dev. of 7 runs, 1000 loops each)
%%timeit sparse_array = sparse.csr_matrix(array)
sparse.diags(np.where(row_mask, 5, 1)).dot(sparse_array)
400 µs ± 6.43 µs per loop (mean ± std. dev. of 7 runs, 1000 loops each)
Fast for-loops using Numba#
As a last resort, if there’s no way to avoid a for-loop even with NumPy’s vectorization capabilities, you can use the @njit decorator provided by the Numba package:
from numba import njit
def sum_array(arr):
result = 0.0
for i in range(arr.shape[0]):
result += arr[i]
return result
In fact, the Numba function is more than 100 times faster than without the decorator:
input_arr = np.float64(np.random.randint(low=0, high=10, size=(10000,)))
%timeit sum_array(input_arr)
10.9 µs ± 444 ns per loop (mean ± std. dev. of 7 runs, 100000 loops each)
# Call the function without the @njit
%timeit sum_array.py_func(input_arr)
1.84 ms ± 65.4 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)
However, whenever available, NumPy’s own vectorized functions will usually be faster than Numba.
%timeit np.sum(input_arr)
%timeit input_arr.sum()
%timeit np.einsum("i->", input_arr)
7.6 µs ± 687 ns per loop (mean ± std. dev. of 7 runs, 100000 loops each)
5.27 µs ± 411 ns per loop (mean ± std. dev. of 7 runs, 100000 loops each)
7.89 µs ± 499 ns per loop (mean ± std. dev. of 7 runs, 100000 loops each)
💡 Make sure you understand the basic idea behind Numba before using it, read the Numba docs.
💡 Don’t use @jit, but use @njit which is an alias for @jit(nopython=True).
When you know what you are doing, the fastmath and parallel options can boost performance even further: read more about this in the Numba docs.
Parallelizing tasks#
Depending on your hardware setup, parallelizing tasks using pathos and Numba’s automatic parallelization feature can improve the performance of your implementation.
💡 Expensive hardware is no excuse for inefficient code.
Many tasks in CLIMADA could profit from GPU implementations. However, currently there are no plans to include GPU support in CLIMADA because of the considerable development and maintenance workload
that would come with it. If you want to change this, contact the core team of developers, open an issue or mention it in the bi-weekly meetings.
Read NetCDF datasets with xarray#
When dealing with NetCDF datasets, memory is often an issue, because even if the file is only a few megabytes in size, the uncompressed raw arrays contained within can be several gigabytes large
(especially when data is sparse or similarly structured). One way of dealing with this situation is to open the dataset with xarray.
💡 xarray allows to read the shape and type of variables contained in the dataset without loading any of the actual data into memory.
Furthermore, when loading slices and arithmetically aggregating variables, memory is allocated not more than necessary, but values are obtained on-the-fly from the file.
Take-home messages#
We conclude by repeating the gist of this guide:
⏲️ Use profiling tools to find and assess performance bottlenecks.
🔁 Replace for-loops by built-in functions and efficient external implementations.
📝 Consider algorithmic performance, not only implementation performance.
🧊 Get familiar with NumPy: vectorized functions, slicing, masks and broadcasting.
⚫ Miscellaneous: sparse arrays, Numba, parallelization, huge files (xarray), memory.
⚠️ Don’t over-optimize at the expense of readability and usability. | {"url":"https://climada-python.readthedocs.io/en/stable/guide/Guide_Py_Performance.html","timestamp":"2024-11-14T21:54:29Z","content_type":"text/html","content_length":"81605","record_id":"<urn:uuid:45d7460f-15b0-4c00-a99e-15dda54aab26>","cc-path":"CC-MAIN-2024-46/segments/1730477395538.95/warc/CC-MAIN-20241114194152-20241114224152-00424.warc.gz"} |
ocally decomposable space
nLab locally decomposable space
Locally decomposable spaces
Local decomposability is a sort of separation axiom, like a weak sort of regularity, that is trivial in classical mathematics, but interesting in constructive mathematics.
A topological space $X$ is locally decomposable if for any open set $U\subseteq X$ and point $x\in X$, there exists an open set $V$ with $x\in V$ such that for all $y\in X$ we have either $y\in U$ or
$yotin V$. If excluded middle holds, of course, we can take $V = U$.
For point-set apartness spaces, which are equivalent to certain topological spaces, the condition can be rephrased as: if $x\bowtie A$, then there is a set $B$ such that $x\bowtie B$ and for all $y$
we have either $y\bowtie A$ or $y\in B$.
For uniform spaces, the notion of uniform regularity is really a notion of “uniform local decomposability”; but since in the uniform case it is sufficient to imply full regularity, we generally call
it “uniform regularity” instead. For quasi-uniform spaces this is no longer true (since after all, there are non-regular quasi-uniform spaces classically), so we should speak of uniform local
decomposability instead.
• Douglas Bridges, Peter Schuster, and Luminita Vita, Apartness, Topology, and Uniformity: a Constructive View, doi
Last revised on January 18, 2017 at 09:23:26. See the history of this page for a list of all contributions to it. | {"url":"https://ncatlab.org/nlab/show/locally%20decomposable%20space","timestamp":"2024-11-12T13:20:46Z","content_type":"application/xhtml+xml","content_length":"18966","record_id":"<urn:uuid:7580b9cb-498e-48c7-b24f-e605f8961a2f>","cc-path":"CC-MAIN-2024-46/segments/1730477028273.45/warc/CC-MAIN-20241112113320-20241112143320-00374.warc.gz"} |
Learn Math trough Kid’s Tile-Math
Learn Core Math Through Kid’s Tile-Math
with worksheets here Math Dislike Cured with flexible bundle numbers
Asked ‘How old next time?’, a 3-year-old says ‘Four’ showing four fingers; but objects when seeing them held together two by two: ‘That is not four, that is two twos!’ A child thus sees what exists
in the world, bundles of 2s, and 2 of them. So, adapting to Many, children develop bundle-numbers with units as 2 2s having 1 1s as the unit, i.e. a tile, also occurring as bundle-of-bundles, e.g. 3
3s, 5 5s or ten tens.
Recounting 8 in 2s as 8 = (8/2)x2 gives a recount-formula T = (T/B)xB saying ‘From the total T, T/B times, B can be pushed away’ occurring all over mathematics and science. It solves equations: ux2 =
8 = (8/2)x2, so u = 8/2. And it changes units when adding on-top, or when adding next-to as areas as in calculus, also occurring when adding per-numbers or fractions coming from double-counting in
two units. Finally, double-counting sides in a tile halved by its diagonal leads to trigonometry.
The following papers present close to 50 micro-curricula in Mastering Many inspired by the bundle-numbers children bring to school.
Learn Core Mathematics Through Your Kid’s Tile-Math:
Recounting Bundle-Numbers and Early Trigonometry
This first paper is written for the conference ‘The Research on Outdoor STEM Education in the digiTal Age (ROSETA) Conference’ planned to take place between 16th and 19th June 2020 at Instituto
Superior de Engenharia do Porto in Portugal.
The Power of Bundle- & Per-Numbers Unleashed in Primary School:
Calculus in Grade One – What Else?
This second paper is written for the International Congress for Mathematical Education, ICME 14, planned to be held in Shanghai from July 12th to 19th, 2020, but postponed one year. | {"url":"http://mathecademy.net/learn-through-kids-tile-math/","timestamp":"2024-11-13T15:47:51Z","content_type":"text/html","content_length":"26542","record_id":"<urn:uuid:5f375d5e-a88c-41f2-bc0c-c07d2860ee4f>","cc-path":"CC-MAIN-2024-46/segments/1730477028369.36/warc/CC-MAIN-20241113135544-20241113165544-00354.warc.gz"} |
How to Play Beta Colony - Nights Around a Table %board game
Rio Grande sent along a copy of Beta Colony, which i dutifully unboxed, and then sat on for a year, until i finally released this How to Play video. Hooray for me (?)!
(click to view transcript)
Hi! It’s Ryan from Nights Around a Table, and this is Beta Colony, a dice-rolling, area control game set in outer space for 2-4 players. Let me show you how to play!
In Beta Colony, Earth has been taken over, and some Earthlings have fled to the distant planet Victus. You and your friends are here to help develop the three colonies of Victus to gain the
confidence of these exiled space settlers.
You’ll be bouncing around between the 7 different moons, ships, and stations orbiting Victus, gathering enough fuel and resources to build pods on the three different colonies, gaining influence as
you do. You may even be able to build some special monuments, like Space Big Ben, or Space The Statue of Liberty, to inspire the settlers. Mechanically, the starting player rolls his or her four
dice, and all other players have to adjust their dice to match that roll. Each player spends a pair of dice at a time to move their ship and activate one of the different moons, ships, or stations
around Victus. By the end of three cycles of three rounds each, whoever has settled the most crew members on each of the different colonies, compared to whoever has the least settlers, gains points
toward a final score, with the hope of winning the confidence of the people and, ultimately, the game.
This player marker denotes the starting player, who rolls four dice – green, red, black, and blue. All other players follow suit, matching their dice, colour and number, to that exact roll. Beginning
with the starting player and going clockwise, each player spends two dice of their choice. The first die moves your ship in a clockwise direction around Victus to one of these seven spaces. The
second die activates whatever function that space provides. And if the activation die matches the colour on that space, you get a bonus.
You can mine these three moons for six different resource cubes – plants and steel, food and palladium, and polymer and water. Your first die gets you there, while your second die determines how many
of that resource you get – for example, either one green or one yellow resource cube for anything from 1-4 pips, or two cubes of either colour for spending a die with a 5 or a 6 on it. What’s more,
if you spend your green die at the moon of Gan De, you get one Confidence Point towards winning the game. It’s the same story for these other two moons, Jyo and Nebra – spend a die to get there,
spend a die to activate it, and take resources depending on the number of pips on that second die, and potentially an extra point if you use the right colour to activate it.
A note about travelling: your ship always moves in a clockwise orbit around Victus, and you have to use all of the pips on your travel die. So if you spend a 3 to move, you’re moving 3 spaces. It’s
not up to 3 – it’s 3 exactly.
You can spend a die to land on the Ridback, and then spend a second die to buy these red fuel canisters. You get 1, 2, or 3 fuel, depending on the value of your activation die. You can spend these
fuel tokens to adjust the value of the pips on your dice up or down, and the number wraps around. So you can spend 2 fuel on a 6 to turn it into an 8 going up, or a 4 going down. You can spend 1 fuel
on a 1-pip die to turn it into a 2, or back around to a 6.
The big show are these two orbiting stations, called manufactories. Spend one die to get there, and then another die to buy one of these randomly-dealt pods to place on one of the three colonies on
Victus. The number of pips on your activation die decides which row you can purchase a pod from. So a 1 or a 2-pip die means you can buy either of these pods, while a 6-pip die means you can go
shopping from this row. But you’re further limited by the resource cubes you own. You have to pay 1 resource cube of a matching colour to buy a pod – spend a green cube for these ones, a red cube for
these ones, and so on. You replace the pod with a face-down tile.
Then, on the same turn, you further have to pay a resource cube to place the pod you just bought on one of the colonies. You pay a cube based on the colour of the empty hex where you want to place
the pod – a yellow cube here, a blue cube here, and so on. So it costs 2 cubes total to buy and place a pod.
The pods earn you influence points, which is a separate points system from the Confidence Points you’re earning down here at the bottom of the board. The Influence Points move your marker around
these three tracks, one per colony, depending on where you place the pod. The number on the pod determines how many influence points you get. You get one bonus point if you place the pod in this
inner ring, and more bonus points for every pod of the same colour in a contiguous line or cluster. If there’s already a contiguous cluster or line of three like-coloured pods, you can’t place a
fourth. That pod’s gotta go somewhere else instead.
You move your marker on the track surrounding the colony where you placed your pod, according to however many influence points you just earned, picking up whatever prizes you pass or land on. The pod
itself may also give you various perks and prizes. Then, you place one of your crew members on the pod. Some pods let you place two crew members, and some high-value pods prevent you from placing
Hey, look! It’s the rules gremlin, come to warn us of something tricky. In this case, it’s not a rule, but a design problem. Beta Colony contains cubes and tiles that are very similar in colour. I’m
not colour-blind, but this game made me think i am! The game has pink, orange, and red cubes. And here’s what one of the colony pods looks like. Is that pink, orange, or red? If you guessed red,
you’re right, but if you guessed one of the other colours, you’re also right, because, like, look at this. Here’s how to keep it straight: red cubes buy red pods, and pink cubes buy pink pods. There
ARE no orange pods for sale – only yellow pods, which you buy with yellow cubes. Orange cubes are only for placing pods on orange spaces in the colonies, and for buying statues and buildings, which
we’ll see in just a sec.
The last moon you can visit, Azophi Nexus, lets you take one resource cube of your choice, and a fuel, regardless of the pip value of your activation die. Or, you can construct a building or a statue
on one of the colonies to inspire the people’s confidence in you.
There are four statues you can construct, each of which gives you a meta point bonus at the end of the game. Each statue costs three artifact tokens. You can earn the artifact tokens by building
certain pods, or by gaining influence and passing certain spaces along the tracks. If you’re short on artifacts, you can spend regular resource cubes to buy the building on the top of the deck.
Buildings give you a point boost at the end of the game, and sometimes another, more immediate perk. Grab the card and place it face down next to your player mat. You get any applicable bonus now,
and any listed Confidence Points at the end of the game.
When you build one of these structures, you take the matching token, and then pay a cube to place it in one of the three colonies. You can only construct buildings and statues in the outer ring of
any colony. As with a colony pod, you place a crew member on the structure. Each player can only build a maximum of two of these cultural achievements in a single game.
At any time on your turn. you can also spend an artifact as wild stand-in for any coloured cube.
If at any point you want or need to take a mulligan on your turn, you can spend two dice to earn a single fuel token. Your spaceship stays where it is.
There are a couple of symbols on the influence tracks around the colonies that supply special rewards. This one gets you any face up colonization pod, which you then build for free. This one gets you
a building or a statue for free – you don’t even have to pay a cube to place it. This one lets you put an extra crew member on any colony pod – whether it’s yours or someone else’s.
There are three cycles in the game, and each cycle has 3 rounds. At the beginning of the game, three cycle cards are randomly dealt to these spaces. They each have an ongoing effect that activates in
the first round of the cycle, and expires by the end of the cycle, and a scoring condition that gets paid out at the end of the cycle.
At the end of the game, each unused artifact token you’ve hung onto is worth a point. Flip over any building or artifact cards you’ve purchased and score the points on the card. The four statues give
you points for the number of crew members you have around the inner rings of each colony, each pod in a contiguous chain, each resource you have left over, and each settler on a pod colour of your
choice, to a maximum of 12 points per statue.
Now, you score for area control in each colony. Score the colonies one at a time. You look at the number of colonists you have vs. the number of colonists the weakest player has, and the difference
gets you points. So here on Xi’An, you have 7 colonists, and the least represented player has 2, for a difference of 5. On Thebes, you have 5 colonists, while the weakest player has 4, so it’s a
difference of 1. On Cuzco, you are the weakest player. The difference can’t go negative, so the gap for this colony is zero.
The gap between you and the weakest player on each colony earns you a sliding scale of Confidence Points.
When you tally up those scores, including any confidence points you earned along the way from the influence tracks, from building certain pods, from using the correctly coloured activation dice at
various moons and orbiting stations, and from satisfying the different cycle scoring conditions, you’ll get your final Confidence Point total. Whoever has the most points has earned the confidence of
the settlers of Victus, and wins the game!
To set up the game, put the board on the table. Deal 1 random card from each of the three cycles to these spots. Shuffle the pods face-down and deal some out to these spaces. Put the fuel, artifact
tokens, and resource cubes nearby. Randomly choose a starting player, who takes the start player Ridback token. Then the last player in turn order gets to choose a player mat. Each mat has two
different special abilities – anything from getting extra resources to changing a certain die to whatever number you want. All other players draft a player mat, with the starting player choosing
last. Everyone chooses a colour and takes a spaceship, fifteen crew members, four score tokens, one fuel, four dice – one red, one black, one green, and one blue – and two random resource cubes from
the supply. Again in reverse turn order, each player places their ship on an empty space orbiting Victus. This is the only time in the game that you can’t have multiple player ships on the same
Put one scoring token on each of the colony tracks, and the last one on the confidence points track.
Shuffle the cultural achievement cards and place them face up, alongside all 4 face-up statue cards.
The first player starts the game by rolling his or her dice, and the other players rotate their dice to follow suit.
And now, you’re ready to play Beta Colony!
Did you just watch that whole thing? Oh – hey! To 100% this video, click the badge to subscribe, and then click the bell to get notifications when i’ve got new stuff.
Get Your Own Copy of Beta Colony
If you’d like to add Beta Colony to your board game collection, use the Amazon link below, and we’ll receive a small commission! | {"url":"https://nightsaroundatable.com/2020/01/08/how-to-play-beta-colony/","timestamp":"2024-11-10T09:11:58Z","content_type":"text/html","content_length":"159263","record_id":"<urn:uuid:ce718856-e938-454a-92db-e00e337af554>","cc-path":"CC-MAIN-2024-46/segments/1730477028179.55/warc/CC-MAIN-20241110072033-20241110102033-00417.warc.gz"} |
SuzukiTrotter (latest version) | IBM Quantum Documentation
class qiskit.synthesis.SuzukiTrotter(order=2, reps=1, insert_barriers=False, cx_structure='chain', atomic_evolution=None, wrap=False)
Bases: ProductFormula
The (higher order) Suzuki-Trotter product formula.
The Suzuki-Trotter formulas improve the error of the Lie-Trotter approximation. For example, the second order decomposition is
$e^{A + B} \approx e^{B/2} e^{A} e^{B/2}.$
Higher order decompositions are based on recursions, see Ref. [1] for more details.
In this implementation, the operators are provided as sum terms of a Pauli operator. For example, in the second order Suzuki-Trotter decomposition we approximate
$e^{-it(XX + ZZ)} = e^{-it/2 ZZ}e^{-it XX}e^{-it/2 ZZ} + \mathcal{O}(t^3).$
[1]: D. Berry, G. Ahokas, R. Cleve and B. Sanders, “Efficient quantum algorithms for simulating sparse Hamiltonians” (2006). arXiv:quant-ph/0508139 [2]: N. Hatano and M. Suzuki, “Finding Exponential
Product Formulas of Higher Orders” (2005). arXiv:math-ph/0506007
Deprecated since version 1.2_pending
The ‘Callable[[Pauli | SparsePauliOp, float], QuantumCircuit]’ signature of the ‘atomic_evolution’ argument is pending deprecation as of qiskit 1.2. It will be marked deprecated in a future release,
and then removed no earlier than 3 months after the release date. Instead you should update your ‘atomic_evolution’ function to be of the following type: ‘Callable[[QuantumCircuit, Pauli |
SparsePauliOp, float], None]’.
• order (int) – The order of the product formula.
• reps (int) – The number of time steps.
• insert_barriers (bool) – Whether to insert barriers between the atomic evolutions.
• cx_structure (str) – How to arrange the CX gates for the Pauli evolutions, can be "chain", where next neighbor connections are used, or "fountain", where all qubits are connected to one. This
only takes effect when atomic_evolution is None.
• atomic_evolution (Callable[[Pauli |SparsePauliOp, float], QuantumCircuit] | Callable[[QuantumCircuit, Pauli |SparsePauliOp, float], None] | None) – A function to apply the evolution of a single
Pauli, or SparsePauliOp of only commuting terms, to a circuit. The function takes in three arguments: the circuit to append the evolution to, the Pauli operator to evolve, and the evolution time.
By default, a single Pauli evolution is decomposed into a chain of CX gates and a single RZ gate. Alternatively, the function can also take Pauli operator and evolution time as inputs and returns
the circuit that will be appended to the overall circuit being built.
• wrap (bool) – Whether to wrap the atomic evolutions into custom gate objects. This only takes effect when atomic_evolution is None.
ValueError – If order is not even
Return the settings in a dictionary, which can be used to reconstruct the object.
A dictionary containing the settings of this product formula.
NotImplementedError – If a custom atomic evolution is set, which cannot be serialized.
Synthesize an qiskit.circuit.library.PauliEvolutionGate.
evolution (PauliEvolutionGate) – The evolution gate to synthesize.
A circuit implementing the evolution.
Return type | {"url":"https://docs.quantum.ibm.com/api/qiskit/qiskit.synthesis.SuzukiTrotter","timestamp":"2024-11-15T03:42:59Z","content_type":"text/html","content_length":"148324","record_id":"<urn:uuid:f5505d60-1026-476a-b393-2acdcc37606d>","cc-path":"CC-MAIN-2024-46/segments/1730477400050.97/warc/CC-MAIN-20241115021900-20241115051900-00327.warc.gz"} |
16-bit Multiplication - 8052.com
16-bit Multiplication
16-bit multiplication is the multiplication of two 16-bit value from another. Such a multiplication results in a 32-bit value.
Programming Tip: In fact, any multiplication results in an answer which is the sum of the bits in the two multiplicands. For example, multiplying an 8-bit value by a 16-bit value results in a 24-bit
value (8 + 16). A 16-bit value multiplied by another 16-bit value results in a 32-bit value (16 + 16), etc.
For the sake of example, let's multiply
. The answer is 432,288,928. As with both addition and subtraction, let's first convert the expression into hexadecimal:
Once again, let's arrange the numbers in columns as we did in primary school to multiply numbers, although now the grid becomes more complicated. The green section represents the original two values.
The yellow section represents the intermediate calculations obtained by multipying each byte of the original values. The red section of the grid indicates our final answer, obtained by summing the
columns in the yellow area.
. Byte 4 Byte 3 Byte 2 Byte 1
. . . 62 30
* . . 43 2E
= . . 08 A0
. . 11 9C .
. . 0C 90 .
. 19 A6 . .
= 19 C4 34 A0
Remember how we did this in elementary school? First we multiply 2Eh by 30h (byte 1 of both numbers), and place the result directly below. Then we multiply 2Eh by 62h (byte 1 of the bottom number by
byte 2 of the upper number). This result is lined up such that the right-most column ends up in byte 2. Next we multiply 43h by 30h (byte 2 of the bottom number by byte 1 of the top number), again
lining up the result so that the right-most column ends up in byte 2. Finally, we multiply 43h by 62h (byte 2 of both numbers) and position the answer such that the right-most column ends up in byte
3. Once we've done the above, we add each column, with appropriate carries, to arrive at the final answer.
Our process in assembly language will be identical. Let's use our now-familiar grid to help us get an idea of what we're doing:
. Byte 4 Byte 3 Byte 2 Byte 1
* R6 R7
* R4 R5
= R0 R1 R2 R3
Thus our first number will be contained in R6 and R7 while our second number will be held in R4 and R5. The result of our multiplication will end up in R0, R1, R2 and R3. At 8-bits per register,
these four registers give us the 32 bits we need to handle the largest possible multiplication. Our process will be the following:
1. Multiply R5 by R7, leaving the 16-bit result in R2 and R3.
2. Multiply R5 by R6, adding the 16-bit result to R1 and R2.
3. Multiply R4 by R7, adding the 16-bit result to R1 and R2.
4. Multiply R4 by R6, adding the 16-bit result to R0 and R1.
We'll now convert the above process to assembly language, step by step.
Step 1. Multiply R5 by R7, leaving the 16-bit result in R2 and R3.
┃ MOV A,R5 ;Move the R5 into the Accumulator┃
┃ MOV B,R7 ;Move R7 into B ┃
┃ MUL AB ;Multiply the two values ┃
┃ MOV R2,B ;Move B (the high-byte) into R2 ┃
┃ MOV R3,A ;Move A (the low-byte) into R3 ┃
Step 2. Multiply R5 by R6, adding the 16-bit result to R1 and R2.
┃ MOV A,R5 ;Move R5 back into the Accumulator ┃
┃ MOV B,R6 ;Move R6 into B ┃
┃ MUL AB ;Multiply the two values ┃
┃ ADD A,R2 ;Add the low-byte into the value already in R2┃
┃ MOV R2,A ;Move the resulting value back into R2 ┃
┃ MOV A,B ;Move the high-byte into the accumulator ┃
┃ ADDC A,#00h ;Add zero (plus the carry, if any) ┃
┃ MOV R1,A ;Move the resulting answer into R1 ┃
┃ MOV A,#00h ;Load the accumulator with zero ┃
┃ ADDC A,#00h ;Add zero (plus the carry, if any) ┃
┃ MOV R0,A ;Move the resulting answer to R0. ┃
Step 3. Multiply R4 by R7, adding the 16-bit result to R1 and R2.
┃ MOV A,R4 ;Move R4 into the Accumulator ┃
┃ MOV B,R7 ;Move R7 into B ┃
┃ MUL AB ;Multiply the two values ┃
┃ ADD A,R2 ;Add the low-byte into the value already in R2┃
┃ MOV R2,A ;Move the resulting value back into R2 ┃
┃ MOV A,B ;Move the high-byte into the accumulator ┃
┃ ADDC A,R1 ;Add the current value of R1 (plus any carry) ┃
┃ MOV R1,A ;Move the resulting answer into R1. ┃
┃ MOV A,#00h ;Load the accumulator with zero ┃
┃ ADDC A,R0 ;Add the current value of R0 (plus any carry) ┃
┃ MOV R0,A ;Move the resulting answer to R1. ┃
Step 4. Multiply R4 by R6, adding the 16-bit result to R0 and R1.
┃ MOV A,R4 ;Move R4 back into the Accumulator ┃
┃ MOV B,R6 ;Move R6 into B ┃
┃ MUL AB ;Multiply the two values ┃
┃ ADD A,R1 ;Add the low-byte into the value already in R1 ┃
┃ MOV R1,A ;Move the resulting value back into R1 ┃
┃ MOV A,B ;Move the high-byte into the accumulator ┃
┃ ADDC A,R0 ;Add it to the value already in R0 (plus any carry)┃
┃ MOV R0,A ;Move the resulting answer back to R0 ┃
Combining the code from the two steps above, we come up with the following subroutine:
┃MUL16_16: ┃
┃ ;Multiply R5 by R7 ┃
┃ MOV A,R5 ;Move the R5 into the Accumulator ┃
┃ MOV B,R7 ;Move R7 into B ┃
┃ MUL AB ;Multiply the two values ┃
┃ MOV R2,B ;Move B (the high-byte) into R2 ┃
┃ MOV R3,A ;Move A (the low-byte) into R3 ┃
┃ ┃
┃ ;Multiply R5 by R6 ┃
┃ MOV A,R5 ;Move R5 back into the Accumulator ┃
┃ MOV B,R6 ;Move R6 into B ┃
┃ MUL AB ;Multiply the two values ┃
┃ ADD A,R2 ;Add the low-byte into the value already in R2 ┃
┃ MOV R2,A ;Move the resulting value back into R2 ┃
┃ MOV A,B ;Move the high-byte into the accumulator ┃
┃ ADDC A,#00h ;Add zero (plus the carry, if any) ┃
┃ MOV R1,A ;Move the resulting answer into R1 ┃
┃ MOV A,#00h ;Load the accumulator with zero ┃
┃ ADDC A,#00h ;Add zero (plus the carry, if any) ┃
┃ MOV R0,A ;Move the resulting answer to R0. ┃
┃ ┃
┃ ;Multiply R4 by R7 ┃
┃ MOV A,R4 ;Move R4 into the Accumulator ┃
┃ MOV B,R7 ;Move R7 into B ┃
┃ MUL AB ;Multiply the two values ┃
┃ ADD A,R2 ;Add the low-byte into the value already in R2 ┃
┃ MOV R2,A ;Move the resulting value back into R2 ┃
┃ MOV A,B ;Move the high-byte into the accumulator ┃
┃ ADDC A,R1 ;Add the current value of R1 (plus any carry) ┃
┃ MOV R1,A ;Move the resulting answer into R1. ┃
┃ MOV A,#00h ;Load the accumulator with zero ┃
┃ ADDC A,R0 ;Add the current value of R0 (plus any carry) ┃
┃ MOV R0,A ;Move the resulting answer to R1. ┃
┃ ┃
┃ ;Multiply R4 by R6 ┃
┃ MOV A,R4 ;Move R4 back into the Accumulator ┃
┃ MOV B,R6 ;Move R6 into B ┃
┃ MUL AB ;Multiply the two values ┃
┃ ADD A,R1 ;Add the low-byte into the value already in R1 ┃
┃ MOV R1,A ;Move the resulting value back into R1 ┃
┃ MOV A,B ;Move the high-byte into the accumulator ┃
┃ ADDC A,R0 ;Add it to the value already in R0 (plus any carry)┃
┃ MOV R0,A ;Move the resulting answer back to R0 ┃
┃ ┃
┃ ;Return - answer is now in R0, R1, R2, and R3 ┃
┃ RET ┃
And to call our routine to multiply the two values we used in the example above, we'd use the code:
┃ ;Load the first value into R6 and R7┃
┃ MOV R6,#62h ┃
┃ MOV R7,#30h ┃
┃ ┃
┃ ;Load the first value into R4 and R5┃
┃ MOV R4,#43h ┃
┃ MOV R5,#2Eh ┃
┃ ┃
┃ ;Call the 16-bit subtraction routine┃
┃ LCALL MUL16_16 ┃
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likai @ cs-people - 2009-06-10
Post date: Jun 11, 2009 2:06:17 AM
Went over ralist in Assignment 3 solution.
□ ralist is analogous to binary representation of natural number (bignum) like singly linked list is analogous to unary representation.
☆ Unary representation: empty string is zero, successor adds one by prepending a digit to the string, predecessor removes a digit from the beginning of the string.
☆ Singly linked list represents a sequence of data by placing one element at each digit. Empty list is analogous to zero, cons analogous to successor, uncons (pattern matching) analogous to
☆ Binary representation: still a list of digits, least significant digit first so carrying is easier to implement. Each digit is either odd (1) or even (0).
☆ Random access list represents a sequence of data by grouping them into a forest of balanced binary trees. If the i-th digit is odd, then that digit carries a balanced binary tree of size
2^i. The length of the data sequence is the binary number represented by odd and even.
☆ Racons is analogous to successor (needs to build the tree by carrying) and rauncons to the predecessor (needs destruct by borrowing).
☆ The easy way to implement ralookup and raupdate is to keep track of the indices skipped to the respective size of the trees, and to perform a binary tree lookup/update at the correct
□ Alternative way to define ralist:
☆ datatype ralist (a:t@ype) = Emp(a) | Odd(a) of (a, ralist '(a, a)) | Evn(a) of ralist '(a, a)
☆ The idea is that we recursively form pairs as we go down the digits. The pairing guarantee completely balanced binary tree. The key to lookup and update is to treat the rest of the list
indexed in pairs. This is the approach taken by the solution.
☆ Efficient update, however, requires a "map" function f: a → a. At the very top level, it updates only an element. As we recurse down the digits, we build the pair update function f': '(a,
a) → '(a, a), which takes a pair, and according to the index, updates either the left or the right a using f. To go down one more digit, the update function becomes f'': '('(a, a), '(a,
a)) → '('(a, a), '(a, a)) and so on.
Briefly talked about stream, partial sum, and Euler's method. Eratosthenes sieve construction using lazy evaluated streams (straightforward adaptation to the non-lazy version). | {"url":"https://cs.likai.org/teaching/cs320-summer1-2009/2009-06-10","timestamp":"2024-11-03T03:55:05Z","content_type":"text/html","content_length":"85952","record_id":"<urn:uuid:5ed8003a-e389-4aef-afaa-675c55db67e7>","cc-path":"CC-MAIN-2024-46/segments/1730477027770.74/warc/CC-MAIN-20241103022018-20241103052018-00476.warc.gz"} |
The Schiffler Point
A Schiffler Point? That is cool!… Any relationships to persons of the same name (like myself) are purely coincidental.
The Schiffler Point is named for Kurt Schiffler (1896-1986), who introduced the point in a problem proposal:
Kurt Schiffler, G. R. Veldkamp, and W. A. van der Spek, Problem 1018 and Solution, Crux Mathematicorum 12 (1986) 176-179.
An accomplished amateur geometer, Schiffler discovered one of the most attractive of the “twentieth-century” triangle centers, now known as the Schiffler Point.
Let I denote the incenter of a triangle ABC. The Schiffler point of ABC is the point of concurrence of the Euler lines of the four triangles BCI, CAI, ABI, ABC. Trilinear coordinates for the
Schiffler point are
1/(cos(B) + cos(C)) :
1/(cos(C) + cos(A)) :
1/(cos(A) + cos(B)),
or, equivalently,
(b + c – a)/(b + c) :
(c + a – b)/(c + a) :
(a + b – c)/(a + b),
where a, b, c denote the sidelengths of triangle ABC.
The Schiffler Point
This site uses Akismet to reduce spam. Learn how your comment data is processed. | {"url":"https://www.ferzkopp.net/wordpress/2015/12/21/the-schiffler-point/","timestamp":"2024-11-10T17:52:16Z","content_type":"text/html","content_length":"43882","record_id":"<urn:uuid:a2aef62b-f95e-4087-9cb3-d2bffda5409c>","cc-path":"CC-MAIN-2024-46/segments/1730477028187.61/warc/CC-MAIN-20241110170046-20241110200046-00495.warc.gz"} |
How long will it take to write my book? How much should I write everyday?
New or aspiring authors often ask me, “How long will it take to write my book?” or “How much should I write every day?”
As a former math teacher and lover of numbers and spreadsheets…
This post is going to tell you exactly what to do! 🙂
But first, we need to set some parameters to work within.
Here are ALL the variables around writing a book:
• length of your pages (how many words per page)
• length of your book (how many pages)
• number of days per week you want to write
• number of weeks you want to take to write
Because we need to control some variables so that we can compare and deduce…
Let’s assume that:
• length of your pages (how many words per page) = 250
We will also stipulate three situations around the:
• length of your book (how many pages) = 100, 150, 200
Below you will find an embedded spreadsheet with calculations. There are THREE TABS on this sheet.
1. tab 1: 100 page book
2. tab 2: 150 page book
3. tab 3: 200 page book
So, pick which tab is closest to the length of the book you intend to write (approximate). How should you approximate the length of your book? Well, you could pick up a few books from authors you
respect and see how long those are.
Now we are just down to number of days and weeks you want to write…
Starting with:
• number of days per week you want to write
looking below on the spreadsheets, you will see a yellow section that indicates how often you’d like to plan to write each week. The options are 7, 5, 3, and 1 day per week (thus, four sections).
• number of weeks you want to take to write
Under each yellow section, on the left-hand side you will see grey boxes. The numbers inside the grey boxes indicate the number of weeks you’d like to allot for writing. This ranges from 2 to 20
weeks for all days/week frequencies…but I added up to 38 weeks for the once a week option.
OKAY, I GET IT…WHAT CAN I READ FROM THIS SHEET [BELOW]?
Example 1
Now that you understand the numbers in the sheet below called “How Long Will It Take to Write My Book?” — the bold number on the right of each block of values is the answer you are looking for!
If you want to know the answer to “how much should I write every day?” look there!
For example, let’s look at the very top set of boxes (also pictured just above)…
• …assuming your book will be 100 pages
• …and you have about 250 words per page
• …and you want to knock it out in 4 weeks
• …plan to write a bit each day…
Then, you need to shoot to write about 893 pages per day to hit your goal!
But is this the only way to use this cool book-writing spreadsheet?
No! 🙂
Example 2
What if you know how many words you’d like to write each day and want to see how long it will take you?
Okay…let’s scroll down and click onto the second tab for a 150-page book for this one…
• …and now we know your book will be 150 pages…
• …and you have about 250 words per page…
• …let’s say that you want to write 500 words or fewer per day and 5 days a week or under
Okay, your options then are:
1. write 5 days/week for 16 weeks, 18 weeks, or 20 weeks!
2. but if you’re willing to write 7 days/week, you can do it in 12 weeks!
Getting the hang of it?
HERE’S THE BOOK WRITING TIME SPREADSHEET TO ANSWER “HOW LONG WILL IT TAKE TO WRITE MY BOOK?” QUESTION
Ultimately, we are all humans 😜and not robots who can write ‘exactly 335 words per day, every day for 16 weeks to produce a 150 page book’…
…but, hopefully the calculations on these sheets above help you get an idea of what your writing goal could be to knock out your awesome book and use it to grow your credibility, sales, and brand!
If you want more help and moral support around writing, self-publishing, and marketing a book (that is an Amazon best-seller — you can do it!) then check out…
1. The free 5-day training I made for ya!
2. We also welcome you in the Facebook Community!
3. Here are a few more blogs as well: | {"url":"https://www.copythatpops.com/how-long-will-it-take-to-write-my-book","timestamp":"2024-11-12T11:48:53Z","content_type":"text/html","content_length":"136740","record_id":"<urn:uuid:e7015356-abf1-439e-b1df-510647d8bac4>","cc-path":"CC-MAIN-2024-46/segments/1730477028273.45/warc/CC-MAIN-20241112113320-20241112143320-00888.warc.gz"} |
. Field selectors
6.5.2. Field selectors and TypeApplications¶
Field selectors can be used in conjunction with TypeApplications, as described in Visible type application. The type of a field selector is constructed by using the surrounding definition as context.
This section provides a specification for how this construction works. We will explain it by considering three different forms of field selector, each of which is a minor variation of the same
general theme.
6.5.2.1. Field selectors for Haskell98-style data constructors¶
Consider the following example:
data T a b = MkT { unT :: forall e. Either e a }
This data type uses a Haskell98-style declaration. The only part of this data type that is not Haskell98 code is unT, whose type uses higher-rank polymorphism (Arbitrary-rank polymorphism). To
construct the type of the unT field selector, we will assemble the following:
1. The type variables quantified by the data type head (forall a b. <...>).
2. The return type of the data constructor (<...> T a b -> <...>). By virtue of this being a Haskell98-style declaration, the order of type variables in the return type will always coincide with the
order in which they are quantified.
3. The type of the field (<...> forall e. Either e a).
The final type of unT is therefore forall a b. T a b -> forall e. Either e a. As a result, one way to use unT with TypeApplications is unT @Int @Bool (MkT (Right 1)) @Char.
6.5.2.2. Field selectors for GADT constructors¶
Field selectors for GADT constructors (Declaring data types with explicit constructor signatures) are slightly more involved. Consider the following example:
data G a b where
MkG :: forall x n a. (Eq a, Show n)
=> { unG1 :: forall e. Either e (a, x), unG2 :: n } -> G a (Maybe x)
The MkG GADT constructor has two records, unG1 and unG2. However, only unG1 can be used as a top-level field selector. unG2 cannot because it is a “hidden” selector (see Record Constructors); its
type mentions a free variable n that does not appear in the result type G a (Maybe x). On the other hand, the only free type variables in the type of unG1 are a and x, so unG1 is fine to use as a
top-level function.
To construct the type of the unG1 field selector, we will assemble the following:
1. The subset of type variables quantified by the GADT constructor that are mentioned in the return type. Note that the order of these variables follows the same principles as in Ordering of
specified variables. If the constructor explicitly quantifies its type variables at the beginning of the type, then the field selector type will quantify them in the same order (modulo any
variables that are dropped due to not being mentioned in the return type). If the constructor implicitly quantifies its type variables, then the field selector type will quantify them in the
left-to-right order that they appear in the field itself.
In this example, MkG explicitly quantifies forall x n a., and of those type variables, a and x are mentioned in the return type. Therefore, the type of unG1 starts as forall x a. <...>. If MkG
had not used an explicit forall, then they would have instead been ordered as forall a x. <...>, since a appears to the left of x in the field type.
2. The GADT return type (<...> G a (Maybe x) -> ...).
3. The type of the field (<...> -> forall e. Either e (a, x)).
The final type of unG1 is therefore forall x a. G a (Maybe x) -> forall e. Either e (a, x). As a result, one way to use unG1 with TypeApplications is unG1 @Int @Bool (MkG (Right (True, 42)) ()) @Char
6.5.2.3. Field selectors for pattern synonyms¶
Certain record pattern synonyms (Record Pattern Synonyms) can give rise to top-level field selectors. Consider the following example:
pattern P :: forall a. Read a
=> forall n. (Eq a, Show n)
=> (forall e. Either e (a, Bool)) -> n -> G a (Maybe Bool)
pattern P {unP1, unP2} = MkG unP1 unP2
We can only make field selectors for pattern synonym records that do not mention any existential type variables whatsoever in their types, per Record Pattern Synonyms. (This is a stronger requirement
than for GADT records, whose types can mention existential type variables provided that they are also mentioned in the return type.) We can see that unP2 cannot be used as a top-level field selector
since its type has a free type variable n, which is existential. unP1 is fine, on the other hand, as its type only has one free variable, the universal type variable a.
To construct the type of the unP1 field selector, we will assemble the following:
1. The universal type variables (forall a. <...>).
2. The required constraints (<...> Read a => <...>).
3. The pattern synonym return type (<...> G a (Maybe Bool) -> <...>).
4. The type of the field (<...> -> forall e. Either e (a, Bool)).
The final type of unP1 is therefore forall a. Read a => G a (Maybe Bool) -> forall e. Either e (a, Bool). As a result, one way to use unP1 with TypeApplications is unP1 @Double (MkG (Right (4.5,
True)) ()) @Char. | {"url":"https://downloads.haskell.org/ghc/9.0.2/docs/html/users_guide/exts/field_selectors_and_type_applications.html","timestamp":"2024-11-04T05:57:36Z","content_type":"text/html","content_length":"28365","record_id":"<urn:uuid:c979be39-cda8-409f-9fdf-c7d7ed1ec122>","cc-path":"CC-MAIN-2024-46/segments/1730477027812.67/warc/CC-MAIN-20241104034319-20241104064319-00103.warc.gz"} |
More on (SHO) coherent states - Peeter Joot's BlogMore on (SHO) coherent states
November 4, 2015 phy1520 coherent state, Poisson distribution, quantum harmonic oscillator, simple harmonic oscillator, Stirling's approximation
[Click here for a PDF of this post with nicer formatting]
[1] pr. 2.19(c)
Show that \( \Abs{f(n)}^2 \) for a coherent state written as
\ket{z} = \sum_{n=0}^\infty f(n) \ket{n}
has the form of a Poisson distribution, and find the most probable value of \( n\), and thus the most probable energy.
The Poisson distribution has the form
P(n) = \frac{\mu^{n} e^{-\mu}}{n!}.
Here \( \mu \) is the mean of the distribution
&= \sum_{n=0}^\infty n P(n) \\
&= \sum_{n=1}^\infty n \frac{\mu^{n} e^{-\mu}}{n!} \\
&= \mu e^{-\mu} \sum_{n=1}^\infty \frac{\mu^{n-1}}{(n-1)!} \\
&= \mu e^{-\mu} e^{\mu} \\
&= \mu.
We found that the coherent state had the form
\ket{z} = c_0 \sum_{n=0} \frac{z^n}{\sqrt{n!}} \ket{n},
so the probability coefficients for \( \ket{n} \) are
&= c_0^2 \frac{\Abs{z^n}^2}{n!} \\
&= e^{-\Abs{z}^2} \frac{\Abs{z^n}^2}{n!}.
This has the structure of the Poisson distribution with mean \( \mu = \Abs{z}^2 \). The most probable value of \( n \) is that for which \( \Abs{f(n)}^2 \) is the largest. This is, in general, hard
to compute, since we have a maximization problem in the integer domain that falls outside the normal toolbox. If we assume that \( n \) is large, so that Stirling’s approximation can be used to
approximate the factorial, and also seek a non-integer value that maximizes the distribution, the most probable value will be the closest integer to that, and this can be computed. Let
&= \Abs{f(n)}^2 \\
&= \frac{e^{-\mu} \mu^n}{n!} \\
&= \frac{e^{-\mu} \mu^n}{e^{\ln n!}} \\
&\approx e^{-\mu – n \ln n + n } \mu^n \\
&= e^{-\mu – n \ln n + n + n \ln \mu }
This is maximized when
= \frac{dg}{dn}
= \lr{ – \ln n – 1 + 1 + \ln \mu } g(n),
which is maximized at \( n = \mu \). One of the integers \( n = \lfloor \mu \rfloor \) or \( n = \lceil \mu \rceil \) that brackets this value \( \mu = \Abs{z}^2 \) is the most probable. So, if an
energy measurement is made of a coherent state \( \ket{z} \), the most probable value will be one of
E = \Hbar \lr{
+ \inv{2} },
E = \Hbar \lr{
+ \inv{2} },
[1] Jun John Sakurai and Jim J Napolitano. Modern quantum mechanics. Pearson Higher Ed, 2014. | {"url":"https://peeterjoot.com/2015/11/04/more-on-sho-coherent-states/","timestamp":"2024-11-05T23:33:32Z","content_type":"text/html","content_length":"96778","record_id":"<urn:uuid:9a3724ce-b9bb-40ef-911c-2bd7153c08aa>","cc-path":"CC-MAIN-2024-46/segments/1730477027895.64/warc/CC-MAIN-20241105212423-20241106002423-00819.warc.gz"} |
Calculating The Probability Of Z Score
In calculating the probability of the z score, we use both the positive and negative z score tables. For example, let us consider the following probability examples.
Alternative 1
Calculating the probability that a z score is less than the value.
We check the value from the z score table.
For instance, Given z=2, we can find the probability of the z score as follows;
Alternative 2
Calculating the probability that a z score is greater than the value.
We check the value from the z score table
For instance, Given z=2, we can find the probability of the z score as follows;
We subtract the value of P(x<2) from 1
Thus, we have;
Alternative 3
Calculating the value of P(0<x<z)
We first get the value of P(x>0). We check the z score value of Z=0
The next step is calculating the probability that a z score is less than the value. P(x<2)
We check the value from the z score table.
For instance, Given Z= 2, we can find the probability of the z score as follows; P(x<2)
P(x<2) = 0.97725
Calculating the value of P(0<x<z)
= 0.97725 – 0.5
= 0.47725
Converting z score to probability
If you find the Z-score for a value for any normal random variable (i.e., standardize the value), the random variable is converted into a standard normal, and you can obtain probabilities using the
standard normal table.
Is z score a probability?
Z score is not a probability. However, in order to find likelihood and apply standard normal distribution attributes, we can translate any normal distribution into the standard normal distribution.
The z score calculates the likelihood of a score occurrence within our normal distribution and enables us to analyze two scores from different normal distributions.
Probability z score formula
To find the probability of a z score, we apply the z score formula. With the values of the z score, we can check the value of the probability from the standard normal table.
Z-score probability examples
Example of Calculating the Probability of Z-score
A psychology test scores are normally distributed with a mean of 70 and a standard deviation of 10. Compute the following.
a) Probability of students who scores 90
Checking the value in the standard normal table
P(x=2) = 0.97725
b) Probability of students who scored more than 80
We are considering the value (Z>1)
Checking the value in the standard normal table
P(x=1) =0.84134
The probability of students who scored more than 80 will be;
We subtract the value of P(x=1) from 1
Thus, we have;
c) Probability of students who scored a mark that lies between 60 and 90
We are focusing on a value P(60<z<90)
Checking the value in the standard normal table
P(x= -1) = 0.15866
P (x = 2) = 0.97725
The probability of students who scored a mark that lies between 60 and 90 will be given by;
P (x < 90) – P ( x < 60)
= 0.97725 – 0.15866
= 0.81859
Z score probability in excel
Z score probability in excel is calculated using the function NORM.DIST(x, mean, standard_dev, cumulative)
X is the value one wishes to get, the distribution.
mean is the arithmetic mean of the distribution.
standard_dev is the standard deviation of the distribution.
Cumulative refers to the logical value that determines the form of the function. The TRUE value returns the CDF (cumulative distribution function), and the FALSE returns the PMF (probability mass
For example, statistics test scores are normally distributed with a mean of 50 and a standard deviation of 10. Compute the following probability of a student who scores 60 using excel.
Thus, the probability will be 0.841345
Z score probability in R
Notably, to find the probability value associated with the z score in R, we use the pnorm() function. We use the following syntax;
Pnorm(q, mean=0, sd=1, lower.tail=TRUE)
In the syntax;
q is the Z-score
Mean- is the mean of the normal distribution.
Sd- is the standard deviation of the normal distribution.
Lower.tail- If TRUE, the probability in the normal distribution to the left of q is returned. If the value is FALSE, the probability to the right is returned. TRUE is the default value.
Left-tailed test
Example 1, find the probability value associated with a z score -1.25 in R.
Example 2, find the probability value associated with a z score -2.35 in R
Right-tailed test
Example 1, find the probability value associated with a z score of 1.35 in R
Example 2, find the probability value associated with a z score of 3.05 in R
Two-tailed test
Example 1, find the probability value associated with a z score of 2.45 two-tailed hypothesis test in R
Example 2, find the probability value associated with a z score of 1.67 two-tailed hypothesis test in R | {"url":"https://edutized.com/tutorial/probability-z-score/","timestamp":"2024-11-04T10:28:58Z","content_type":"text/html","content_length":"78671","record_id":"<urn:uuid:4d4ae14f-c49f-46b3-9d7f-d90a8aa44cb0>","cc-path":"CC-MAIN-2024-46/segments/1730477027821.39/warc/CC-MAIN-20241104100555-20241104130555-00003.warc.gz"} |
Generalizing Shallow Water Simulations with Dispersive Surface Waves
ACM Transactions on Graphics (Siggraph 2023)
This paper introduces a novel method for simulating large bodies of water as a height field. At the start of each time step, we partition the waves into a bulk flow (which approximately satisfies the
assumptions of the shallow water equations) and surface waves (which approximately satisfy the assumptions of Airy wave theory). We then solve the two wave regimes separately using appropriate
state-of-the-art techniques, and re-combine the resulting wave velocities at the end of each step. This strategy leads to the first heightfield wave model capable of simulating complex interactions
between both deep and shallow water effects, like the waves from a boat wake sloshing up onto a beach, or a dam break producing wave interference patterns and eddies. We also analyze the numerical
dispersion created by our method and derive an exact correction factor for waves at a constant water depth, giving us a numerically perfect re-creation of theoretical water wave dispersion patterns.
Submission Video
author = {Jeschke, Stefan and Wojtan, Chris},
title = {Generalizing Shallow Water Simulations with Dispersive Surface Waves},
year = {2023},
issue_date = {August 2023},
publisher = {Association for Computing Machinery},
address = {New York, NY, USA},
volume = {42},
number = {4},
issn = {0730-0301},
url = {https://doi.org/10.1145/3592098},
doi = {10.1145/3592098},
month = {jul},
articleno = {83},
numpages = {12},
keywords = {real-time animation, natural phenomena, water animation}
We thank Georg Sperl for helping with early research for this paper, Mickael Ly and Yi-Lu Chen for proofreading, and members of the ISTA Visual Computing Group for general feedback. This project was
funded in part by the European Research Council (ERC Consolidator Grant 101045083 CoDiNA).
The motorboat and sailboat were modeled by Sergei and the palmtrees by YadroGames. The environment map was created by Emil Persson. | {"url":"https://visualcomputing.ist.ac.at/publications/2023/GSWSDSW/","timestamp":"2024-11-12T04:11:51Z","content_type":"text/html","content_length":"12734","record_id":"<urn:uuid:23ef2eea-8504-496b-ab92-b510db5edbfc>","cc-path":"CC-MAIN-2024-46/segments/1730477028242.50/warc/CC-MAIN-20241112014152-20241112044152-00165.warc.gz"} |
Market Profile (TPOProfile) Monkey Bars for ThinkorSwim - useThinkScript Community
Here's a TPO Refined with Monkey Bars script for ThinkorSwim.
# TPO Refined with Monkey Bar Study
# Mobius
# V01.04.07.2018
input pricePerRowHeightMode = {AUTOMATIC, default TICKSIZE, CUSTOM};
input customRowHeight = 1.0;
input aggregationPeriod = {"1 min", "2 min", "3 min", "4 min", "5 min", "10 min", "15 min", "20 min", default "30 min", "1 hour", "2 hours", "4 hours", "Day", "2 Days", "3 Days", "4 Days", "Week", "Month"};
input timePerProfile = {CHART, MINUTE, HOUR, default DAY, WEEK, MONTH, "OPT EXP", BAR, YEAR};
input multiplier = 1;
input onExpansion = no;
input profiles = 5;
input showMonkeyBar = no;
input showThePlayground = no;
input thePlaygroundPercent = 70;
input opacity = 25;
input emphasizeFirstDigit = no;
input markOpenPrice = no;
input markClosePrice = no;
input volumeShowStyle = MonkeyVolumeShowStyle.NONE;
input showVolumeVA = yes;
input showVolumePoc = yes;
input theVolumePercent = 70;
input showInitialBalance = no;
input initialBalanceRange = 1;
def period;
def yyyymmdd = GetYYYYMMDD();
def seconds = SecondsFromTime(0);
def month = GetYear() * 12 + GetMonth();
def day_number = DaysFromDate(First(yyyymmdd)) + GetDayOfWeek(First(yyyymmdd));
def dom = GetDayOfMonth(yyyymmdd);
def dow = GetDayOfWeek(yyyymmdd - dom + 1);
def expthismonth = (if dow > 5 then 27 else 20) - dow;
def exp_opt = month + (dom > expthismonth);
def periodMin = Floor(seconds / 60 + day_number * 24 * 60);
def periodHour = Floor(seconds / 3600 + day_number * 24);
def periodDay = CountTradingDays(Min(First(yyyymmdd), yyyymmdd), yyyymmdd) - 1;
def periodWeek = Floor(day_number / 7);
def periodMonth = month - First(month);
switch (timePerProfile) {
case CHART:
period = 0;
case MINUTE:
period = periodMin;
case HOUR:
period = periodHour;
case DAY:
period = periodDay;
case WEEK:
period = periodWeek;
case MONTH:
period = periodMonth;
case "OPT EXP":
period = exp_opt - First(exp_opt);
case BAR:
period = BarNumber() - 1;
case YEAR:
period = GetYear() - First(GetYear());
input RthBegin = 0930;
input RthEnd = 1600;
input Minutes = 60;
#input showBubbles = no;
def OpenRange = SecondsFromTime(0930) >= 0 and
SecondsFromTime(1000) >= 0;
def bar = BarNumber();
def RTHBar1 = if SecondsFromTime(RthBegin) == 0 and
SecondsTillTime(RthBegin) == 0
then bar
else RTHBar1[1];
def RTHBarEnd = if SecondsFromTime(RthEnd) == 0 and
SecondsTillTime(RthEnd) == 0
then 1
else Double.NaN;
def RTH = SecondsFromTime(RthBegin) > 0 and
SecondsTillTime(RthEnd) > 0;
def start_t = if RTH and !RTH[1]
then GetTime()
else start_t[1];
def t = if start_t == GetTime()
then 1
else GetTime() % (Minutes * 60 * 1000) == 0;
def cond = t;
def height;
switch (pricePerRowHeightMode) {
case AUTOMATIC:
height = PricePerRow.AUTOMATIC;
case TICKSIZE:
height = PricePerRow.TICKSIZE;
case CUSTOM:
height = customRowHeight;
def timeInterval;
def aggMultiplier;
switch (aggregationPeriod) {
case "1 min":
timeInterval = periodMin;
aggMultiplier = 1;
case "2 min":
timeInterval = periodMin;
aggMultiplier = 2;
case "3 min":
timeInterval = periodMin;
aggMultiplier = 3;
case "4 min":
timeInterval = periodMin;
aggMultiplier = 4;
case "5 min":
timeInterval = periodMin;
aggMultiplier = 5;
case "10 min":
timeInterval = periodMin;
aggMultiplier = 10;
case "15 min":
timeInterval = periodMin;
aggMultiplier = 15;
case "20 min":
timeInterval = periodMin;
aggMultiplier = 20;
case "30 min":
timeInterval = periodMin;
aggMultiplier = 30;
case "1 hour":
timeInterval = periodHour;
aggMultiplier = 1;
case "2 hours":
timeInterval = periodHour;
aggMultiplier = 2;
case "4 hours":
timeInterval = periodHour;
aggMultiplier = 4;
case "Day":
timeInterval = periodDay;
aggMultiplier = 1;
case "2 Days":
timeInterval = periodDay;
aggMultiplier = 2;
case "3 Days":
timeInterval = periodDay;
aggMultiplier = 3;
case "4 Days":
timeInterval = periodDay;
aggMultiplier = 4;
case "Week":
timeInterval = periodWeek;
aggMultiplier = 1;
case "Month":
timeInterval = periodMonth;
aggMultiplier = 1;
def agg_count = CompoundValue(1, if timeInterval != timeInterval[1]
then (GetValue(agg_count, 1) + timeInterval -
timeInterval[1]) % aggMultiplier
else GetValue(agg_count, 1), 0);
def agg_cond = CompoundValue(1, agg_count < agg_count[1] + timeInterval -
timeInterval[1], yes);
def digit = CompoundValue(1, if cond
then 1
else agg_cond + GetValue(digit, 1), 1);
profile monkey = MonkeyBars(digit,
"startNewProfile" = cond,
"onExpansion" = onExpansion,
"numberOfProfiles" = profiles,
"pricePerRow" = height,
"the playground percent" = thePlaygroundPercent,
"emphasize first digit" = emphasizeFirstDigit,
"volumeProfileShowStyle" = volumeShowStyle,
"volumePercentVA" = theVolumePercent,
"show initial balance" = showInitialBalance,
"initial balance range" = initialBalanceRange);
def con = CompoundValue(1, onExpansion, no);
def mbar = CompoundValue(1, if IsNaN(monkey.GetPointOfControl()) and con then GetValue(mbar, 1) else monkey.GetPointOfControl(), monkey.GetPointOfControl());
def hPG = CompoundValue(1, if IsNaN(monkey.GetHighestValueArea()) and con then GetValue(hPG, 1) else monkey.GetHighestValueArea(), monkey.GetHighestValueArea());
def lPG = CompoundValue(1, if IsNaN(monkey.GetLowestValueArea()) and con then GetValue(lPG, 1) else monkey.GetLowestValueArea(), monkey.GetLowestValueArea());
def hProfile = CompoundValue(1, if IsNaN(monkey.GetHighest()) and con then GetValue(hProfile, 1) else monkey.GetHighest(), monkey.GetHighest());
def lProfile = CompoundValue(1, if IsNaN(monkey.GetLowest()) and con then GetValue(lProfile, 1) else monkey.GetLowest(), monkey.GetLowest());
def plotsDomain = IsNaN(close) == onExpansion;
profile tpo = TimeProfile("startNewProfile" = t,
"onExpansion" = 0,
"numberOfProfiles" = profiles,
"pricePerRow" = tickSize(),
"value area percent" = 70);
def showPointOfControl = yes;
def showValueArea = no;
plot MB = if plotsDomain then mbar else Double.NaN;
plot ProfileHigh = if plotsDomain then hProfile else Double.NaN;
plot ProfileLow = if plotsDomain then lProfile else Double.NaN;
plot PGHigh = if plotsDomain then hPG else Double.NaN;
plot PGLow = if plotsDomain then lPG else Double.NaN;
DefineGlobalColor("Monkey Bar", GetColor(4));
DefineGlobalColor("The Playground", GetColor(3));
DefineGlobalColor("Open Price", GetColor(1));
DefineGlobalColor("Close Price", GetColor(1));
DefineGlobalColor("Volume", GetColor(8));
DefineGlobalColor("Volume Value Area", GetColor(2));
DefineGlobalColor("Volume Point of Control", GetColor(3));
DefineGlobalColor("Initial Balance", GetColor(7));
DefineGlobalColor("Profiles", GetColor(1));
tpo.Show(GlobalColor("Profiles"), if showPointOfControl
then GlobalColor("Volume Point Of Control")
else Color.CURRENT,
if showValueArea
then GlobalColor("Volume Value Area")
else Color.CURRENT, opacity);
MB.SetDefaultColor(GlobalColor("Monkey Bar"));
PGHigh.SetDefaultColor(GlobalColor("The Playground"));
PGLow.SetDefaultColor(GlobalColor("The Playground"));
# End Code TPO Refined
TPO (Time Price Opportunity) - User can choose time segments beginning at RTH Open
# TPO Per User Time Segment Starting at RTH
# Mobius
# Chat Room Request 03.29.2018
input pricePerRowHeightMode = {AUTOMATIC, TICKSIZE, default CUSTOM};
input customRowHeight = 1.0;
input timePerProfile = {CHART, default MINUTE, HOUR, DAY, WEEK, MONTH, "OPT EXP", BAR};
input multiplier = 1;
input onExpansion = no;
input profiles = 10;
input showPointOfControl = yes;
input showValueArea = yes;
input valueAreaPercent = 70;
input opacity = 7;
input Minutes = 60;
def period;
def yyyymmdd = getYyyyMmDd();
def seconds = secondsFromTime(0);
def month = getYear() * 12 + getMonth();
def day_number = daysFromDate(first(yyyymmdd)) + getDayOfWeek(first(yyyymmdd));
def dom = getDayOfMonth(yyyymmdd);
def dow = getDayOfWeek(yyyymmdd - dom + 1);
def expthismonth = (if dow > 5 then 27 else 20) - dow;
def exp_opt = month + (dom > expthismonth);
switch (timePerProfile) {
case CHART:
period = 0;
case MINUTE:
period = floor(seconds / 60 + day_number * 24 * 60);
case HOUR:
period = floor(seconds / 3600 + day_number * 24);
case DAY:
period = countTradingDays(Min(first(yyyymmdd), yyyymmdd), yyyymmdd) - 1;
case WEEK:
period = floor(day_number / 7);
case MONTH:
period = floor(month - first(month));
case "OPT EXP":
period = exp_opt - first(exp_opt);
case BAR:
period = barNumber() - 1;
input RthBegin = 0930;
input RthEnd = 1600;
#input showBubbles = no;
def bar = BarNumber();
def RTHBar1 = if SecondsFromTime(RthBegin) == 0 and
SecondsTillTime(RthBegin) == 0
then bar
else RTHBar1[1];
def RTHBarEnd = if SecondsFromTime(RthEnd) == 0 and
SecondsTillTime(RthEnd) == 0
then 1
else Double.NaN;
def RTH = SecondsFromTime(RthBegin) > 0 and
SecondsTillTime(RthEnd) > 0;
def start_t = if RTH and !RTH[1]
then getTime()
else Start_t[1];
def t = if start_t == getTime()
then 1
else getTime() % (Minutes * 60 * 1000) == 0;
def cond = t;
def height;
switch (pricePerRowHeightMode) {
case AUTOMATIC:
height = PricePerRow.AUTOMATIC;
case TICKSIZE:
height = PricePerRow.TICKSIZE;
case CUSTOM:
height = customRowHeight;
profile tpo = timeProfile("startNewProfile" = cond, "onExpansion" = onExpansion, "numberOfProfiles" = profiles, "pricePerRow" = height, "value area percent" = valueAreaPercent);
def con = compoundValue(1, onExpansion, no);
def pc = if IsNaN(tpo.getPointOfControl()) and con then pc[1] else tpo.getPointOfControl();
def hVA = if IsNaN(tpo.getHighestValueArea()) and con then hVA[1] else tpo.getHighestValueArea();
def lVA = if IsNaN(tpo.getLowestValueArea()) and con then lVA[1] else tpo.getLowestValueArea();
def hProfile = if IsNaN(tpo.getHighest()) and con then hProfile[1] else tpo.getHighest();
def lProfile = if IsNaN(tpo.getLowest()) and con then lProfile[1] else tpo.getLowest();
def plotsDomain = IsNaN(close) == onExpansion;
plot POC = if plotsDomain then pc else Double.NaN;
plot ProfileHigh = if plotsDomain then hProfile else Double.NaN;
plot ProfileLow = if plotsDomain then lProfile else Double.NaN;
plot VAHigh = if plotsDomain then hVA else Double.NaN;
plot VALow = if plotsDomain then lVA else Double.NaN;
DefineGlobalColor("Profile", GetColor(1));
DefineGlobalColor("Point Of Control", GetColor(5));
DefineGlobalColor("Value Area", GetColor(8));
tpo.show(globalColor("Profile"), if showPointOfControl then globalColor("Point Of Control") else color.current, if showValueArea then globalColor("Value Area") else color.current, opacity);
POC.SetDefaultColor(globalColor("Point Of Control"));
VAHigh.SetDefaultColor(globalColor("Value Area"));
VALow.SetDefaultColor(globalColor("Value Area"));
# End Code TPO Per User Time Segment
TPO scanner by BLT
Last edited by a moderator:
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Well-known member
2019 Donor
Took a look at the TPO you uploaded today. Will need to watch for a bit during open hours before I can comment. Have never traded this before but always willing to look at anything if it can help
improve my edge. Thank you for sharing.
The fun thing about these is if price has 2 closes above or below a VAL there is a very good chance it will continue to the opposite VAL. Check the VAL difference to see how much profit might be
This one is a Time Profile Line and will be very near the POC which is price based. I think technically the POC is said to be more accurate. For our trading I doubt it makes any difference.
Long time lurker, but wanted to say I really appreciate this site and all of the members here.
Question: Is there a way to configure Volume Profile to display only the Globex overnight session?
Ideally, I would like to have 2 Volume Profile studies on the same chart. One for the night and day sessions separated.
All the best,
Staff member
Hmm. I'm not sure. But maybe you can try to implement some sort of
time limit
into the Volume Profile indicator?
Hmm. I'm not sure. But maybe you can try to implement some sort of
time limit
into the Volume Profile indicator?
Thank you for pointing me in the right direction, sir.
I've got an idea of how to do it lol, I can't seem to figure out how to isolate the time period from 3p pst to 6:30a pst following day to implement within the volume profile period
I was looking for the same function as Im getting into TPO and Volume Profiles more on TOS, consider using the SecondsFromTime() function.
I would appreciate any updates
Last edited:
I was looking for the same function as Im getting into TPO and Volume Profiles more on TOS, consider using the SecondsFromTime() function.
I would appreciate any updates
Hi, try this:
input pricePerRowHeightMode = {AUTOMATIC, TICKSIZE, default CUSTOM};
input customRowHeight = 1.0;
input timePerProfile = {CHART, default MINUTE, HOUR, DAY, WEEK, MONTH, "OPT EXP", BAR};
input multiplier = 1;
input onExpansion = no;
input profiles = 1;
input showPointOfControl = yes;
input showValueArea = yes;
input valueAreaPercent = 70;
input opacity = 7;
def period;
def yyyymmdd = getYyyyMmDd();
def seconds = secondsFromTime(0);
def month = getYear() * 12 + getMonth();
def day_number = daysFromDate(first(yyyymmdd)) + getDayOfWeek(first(yyyymmdd));
def dom = getDayOfMonth(yyyymmdd);
def dow = getDayOfWeek(yyyymmdd - dom + 1);
def expthismonth = (if dow > 5 then 27 else 20) - dow;
def exp_opt = month + (dom > expthismonth);
switch (timePerProfile) {
case CHART:
period = 0;
case MINUTE:
period = floor(seconds / 60 + day_number * 24 * 60);
case HOUR:
period = floor(seconds / 3600 + day_number * 24);
case DAY:
period = countTradingDays(Min(first(yyyymmdd), yyyymmdd), yyyymmdd) - 1;
case WEEK:
period = floor(day_number / 7);
case MONTH:
period = floor(month - first(month));
case "OPT EXP":
period = exp_opt - first(exp_opt);
case BAR:
period = barNumber() - 1;
input RthBegin = 0930;
input RthEnd = 1600;
#input showBubbles = no;
def bar = BarNumber();
def RTHBar1 = if SecondsFromTime(RthBegin) == 0 and
SecondsTillTime(RthBegin) == 0
then bar
else RTHBar1[1];
def RTHBarEnd = if SecondsFromTime(RthEnd) == 0 and
SecondsTillTime(RthEnd) == 0
then 1
else Double.NaN;
def RTH = SecondsFromTime(RthBegin) > 0 and
SecondsTillTime(RthEnd) > 0;
def cond = RTH != RTH[1];
def height;
switch (pricePerRowHeightMode) {
case AUTOMATIC:
height = PricePerRow.AUTOMATIC;
case TICKSIZE:
height = PricePerRow.TICKSIZE;
case CUSTOM:
height = customRowHeight;
profile tpo = timeProfile("startNewProfile" = cond, "onExpansion" = onExpansion, "numberOfProfiles" = profiles, "pricePerRow" = height, "value area percent" = valueAreaPercent);
def con = compoundValue(1, onExpansion, no);
def pc = if IsNaN(tpo.getPointOfControl()) and con then pc[1] else tpo.getPointOfControl();
def hVA = if IsNaN(tpo.getHighestValueArea()) and con then hVA[1] else tpo.getHighestValueArea();
def lVA = if IsNaN(tpo.getLowestValueArea()) and con then lVA[1] else tpo.getLowestValueArea();
def hProfile = if IsNaN(tpo.getHighest()) and con then hProfile[1] else tpo.getHighest();
def lProfile = if IsNaN(tpo.getLowest()) and con then lProfile[1] else tpo.getLowest();
def plotsDomain = IsNaN(close) == onExpansion;
plot POC = if plotsDomain then pc else Double.NaN;
plot ProfileHigh = if plotsDomain then hProfile else Double.NaN;
plot ProfileLow = if plotsDomain then lProfile else Double.NaN;
plot VAHigh = if plotsDomain then hVA else Double.NaN;
plot VALow = if plotsDomain then lVA else Double.NaN;
DefineGlobalColor("Profile", GetColor(1));
DefineGlobalColor("Point Of Control", GetColor(5));
DefineGlobalColor("Value Area", GetColor(8));
tpo.show(globalColor("Profile"), if showPointOfControl then globalColor("Point Of Control") else color.current, if showValueArea then globalColor("Value Area") else color.current, opacity);
POC.SetDefaultColor(globalColor("Point Of Control"));
VAHigh.SetDefaultColor(globalColor("Value Area"));
VALow.SetDefaultColor(globalColor("Value Area"));
I need the indicators of the pervious session, weeks or mouth to be drawn on the current session ,week, month. Like in the indicator "
previous day High
I enabled Money Bars chart on ThinkorSwim:
1. Go to chart settings
2. Click on Appearance
3. Under Chart Mode, select Money Bars
: Monkey Bars
Showing previous day High/Low/Close
Indicator previous day High/Low/Close, draws lines on the chart previous day High/Low/Close for the current session. I want the same actions from indicator Monkey Bars, its values ( Point of Control
, PGHigh, PGLow,Monkey Bar) from previous month draws lines on the chart for the current month. I look smaller time frame and I want to see where the price towards the values indicator Monkey Bars
from last month, if possible. I am drawing them myself now using horizontal lines, but it takes a long time and is very inconvenient.
Sorry for my English I don't speak it.
Due to limitations in the code because TDAmeritrade only has it referenced, certain plots cant be defined without the source code for the defined function. if you have the
complete source
for monkeybars it would be possible to accomplish what you want without limitations.
Below is the best that i could figure out how to do without the complete source.
Change the input "displace" to the number of bars in the intraday, 78 is 5 minute chart. 10 mins would be 39, etc.
# TD Ameritrade IP Company, Inc. (c) 2010-2020
input displace = 78;
input pricePerRowHeightMode = {default AUTOMATIC, TICKSIZE, CUSTOM};
input customRowHeight = 1.0;
input aggregationPeriod = {"1 min", "2 min", "3 min", "4 min", "5 min", "10 min", "15 min", "20 min", default "30 min", "1 hour", "2 hours", "4 hours", "Day", "2 Days", "3 Days", "4 Days", "Week", "Month", "Quarter", "Year"};
input timePerProfile = {default CHART, MINUTE, HOUR, DAY, WEEK, MONTH, "OPT EXP", BAR, YEAR};
input multiplier = 1;
input onExpansion = yes;
input profiles = 1000;
input showMonkeyBar = yes;
input showThePlayground = yes;
input thePlaygroundPercent = 70;
input opacity = 100;
input emphasizeFirstDigit = no;
input markOpenPrice = yes;
input markClosePrice = yes;
input volumeShowStyle = MonkeyVolumeShowStyle.NONE;
input showVolumeVA = yes;
input showVolumePoc = yes;
input theVolumePercent = 70;
input showInitialBalance = yes;
input initialBalanceRange = 3;
def period;
def yyyymmdd = getYyyyMmDd();
def seconds = secondsFromTime(0);
def year = getYear();
def month = year * 12 + getMonth();
def day_number = daysFromDate(first(yyyymmdd)) + getDayOfWeek(first(yyyymmdd));
def dom = getDayOfMonth(yyyymmdd);
def dow = getDayOfWeek(yyyymmdd - dom + 1);
def expthismonth = (if dow > 5 then 27 else 20) - dow;
def exp_opt = month + (dom > expthismonth);
def periodMin = Floor(seconds / 60 + day_number * 24 * 60);
def periodHour = Floor(seconds / 3600 + day_number * 24);
def periodDay = countTradingDays(Min(first(yyyymmdd), yyyymmdd), yyyymmdd) - 1;
def periodWeek = Floor(day_number / 7);
def periodMonth = month - first(month);
def periodQuarter = Ceil(month / 3) - first(Ceil(month / 3));
def periodYear = year - first(year);
switch (timePerProfile) {
case CHART:
period = 0;
case MINUTE:
period = periodMin;
case HOUR:
period = periodHour;
case DAY:
period = periodDay;
case WEEK:
period = periodWeek;
case MONTH:
period = periodMonth;
case "OPT EXP":
period = exp_opt - first(exp_opt);
case BAR:
period = barNumber() - 1;
case YEAR:
period = periodYear;
def count = compoundvalue(1, if period != period[1] then (getValue(count, 1) + period - period[1]) % multiplier else getValue(count, 1), 0);
def cond = compoundvalue(1, count < count[1] + period - period[1], yes);
def height;
switch (pricePerRowHeightMode) {
case AUTOMATIC:
height = PricePerRow.AUTOMATIC;
case TICKSIZE:
height = PricePerRow.TICKSIZE;
case CUSTOM:
height = customRowHeight;
def timeInterval;
def aggMultiplier;
switch (aggregationPeriod) {
case "1 min":
timeInterval = periodMin;
aggMultiplier = 1;
case "2 min":
timeInterval = periodMin;
aggMultiplier = 2;
case "3 min":
timeInterval = periodMin;
aggMultiplier = 3;
case "4 min":
timeInterval = periodMin;
aggMultiplier = 4;
case "5 min":
timeInterval = periodMin;
aggMultiplier = 5;
case "10 min":
timeInterval = periodMin;
aggMultiplier = 10;
case "15 min":
timeInterval = periodMin;
aggMultiplier = 15;
case "20 min":
timeInterval = periodMin;
aggMultiplier = 20;
case "30 min":
timeInterval = periodMin;
aggMultiplier = 30;
case "1 hour":
timeInterval = periodHour;
aggMultiplier = 1;
case "2 hours":
timeInterval = periodHour;
aggMultiplier = 2;
case "4 hours":
timeInterval = periodHour;
aggMultiplier = 4;
case "Day":
timeInterval = periodDay;
aggMultiplier = 1;
case "2 Days":
timeInterval = periodDay;
aggMultiplier = 2;
case "3 Days":
timeInterval = periodDay;
aggMultiplier = 3;
case "4 Days":
timeInterval = periodDay;
aggMultiplier = 4;
case "Week":
timeInterval = periodWeek;
aggMultiplier = 1;
case "Month":
timeInterval = periodMonth;
aggMultiplier = 1;
case "Quarter":
timeInterval = periodQuarter;
aggMultiplier = 1;
case "Year":
timeInterval = periodYear;
aggMultiplier = 1;
def agg_count = compoundvalue(1, if timeInterval != timeInterval[1] then (getValue(agg_count, 1) + timeInterval - timeInterval[1]) % aggMultiplier else getValue(agg_count, 1), 0);
def agg_cond = compoundvalue(1, agg_count < agg_count[1] + timeInterval - timeInterval[1], yes);
def digit = compoundValue(1, if cond then 1 else agg_cond + getValue(digit, 1), 1);
profile monkey = monkeyBars(digit, "startNewProfile" = cond, "onExpansion" = onExpansion,
"numberOfProfiles" = profiles, "pricePerRow" = height, "the playground percent" = thePlaygroundPercent,
"emphasize first digit" = emphasizeFirstDigit, "volumeProfileShowStyle" = volumeShowStyle, "volumePercentVA" = theVolumePercent,
"show initial balance" = showInitialBalance, "initial balance range" = initialBalanceRange);
def con = compoundValue(1, onExpansion, no);
def mbar = compoundvalue(1, if IsNaN(monkey.getPointOfControl()) and con then getValue(mbar, 1) else monkey.getPointOfControl(), monkey.getPointOfControl());
def hPG = compoundvalue(1, if IsNaN(monkey.getHighestValueArea()) and con then getValue(hPG, 1) else monkey.getHighestValueArea(), monkey.getHighestValueArea());
def lPG = compoundvalue(1, if IsNaN(monkey.getLowestValueArea()) and con then getValue(lPG, 1) else monkey.getLowestValueArea(), monkey.getLowestValueArea());
def hProfile = compoundvalue(1, if IsNaN(monkey.getHighest()) and con then getValue(hProfile, 1) else monkey.getHighest(), monkey.getHighest());
def lProfile = compoundvalue(1, if IsNaN(monkey.getLowest()) and con then getValue(lProfile, 1) else monkey.getLowest(), monkey.getLowest());
def plotsDomain = IsNaN(close) == onExpansion;
plot MB = if plotsDomain then mbar[displace] else Double.NaN;
plot ProfileHigh = if plotsDomain then hProfile[displace] else Double.NaN;
plot ProfileLow = if plotsDomain then lProfile[displace] else Double.NaN;
plot PGHigh = if plotsDomain then hPG[displace] else Double.NaN;
plot PGLow = if plotsDomain then lPG[displace] else Double.NaN;
DefineGlobalColor("Monkey Bar", GetColor(4));
DefineGlobalColor("The Playground", GetColor(3));
DefineGlobalColor("Open Price", GetColor(1));
DefineGlobalColor("Close Price", GetColor(1));
DefineGlobalColor("Volume", GetColor(8));
DefineGlobalColor("Volume Value Area", GetColor(2));
DefineGlobalColor("Volume Point of Control", GetColor(3));
DefineGlobalColor("Initial Balance", GetColor(7));
monkey.show(color.red, if showMonkeyBar then globalColor("Monkey Bar") else color.current,
if showThePlayground then globalColor("The Playground") else color.current,
opacity, if markOpenPrice then globalColor("Open Price") else color.current,
if markClosePrice then globalColor("Close Price") else color.current,
if showInitialBalance then globalColor("Initial Balance") else color.current,
if showVolumeVA then globalColor("Volume Value Area") else color.current,
if showVolumePOC then globalColor("Volume Point of Control") else color.current);
MB.SetDefaultColor(globalColor("Monkey Bar"));
PGHigh.SetDefaultColor(globalColor("The Playground"));
PGLow.SetDefaultColor(globalColor("The Playground"));
How is this indicator to be used?
Ive been a "long time lurker" here. Learned a lot and developed a couple indicators based off of others, learned some basic thinkscript coding. However, I was wondering if it were even possible to
write a script to auto plot TD's monkey bars (TPO, market profile, whatever you choose to call it) single prints. I trade based off of price action at single prints that clearly define buyer / seller
levels, and generally simplifies the "auction" concept of the market. This strategy has been highly effective trading futures over the past year when I first started using profile only and rvol,
rather than multiple indicators.
I spend WAY too much time manually plotting these single print levels in profile. If it is possible, I can spend the time to develop thinkscript for this. If anyone is interested in working on it
together, feel free to reach out. If we can make this happen, I would like to share it to the forum. It would be nice to give back after learning so much about thinkscript here in the past. Thanks
Moderator - Expert
i am curious about this, but admit i know nothing about monkey bars, nor any of the terms. i don't understand what the digits represent. i don't know what single prints are.
i read this, but it didn't help me. i'm a visual guy and sometimes need to see marked up pictures, to help explain a topic.
1. i don't understand this,
... manually plotting these single print levels in profile.
2. are the rows of numbers on a monkey bar chart similar to a volume profile layout? it is possible to plot a profile on variables other than volume.
3. do you want a study to draw things on a candle chart or a monkey chart?
i am curious about this, but admit i know nothing about monkey bars, nor any of the terms. i don't understand what the digits represent. i don't know what single prints are.
i read this, but it didn't help me. i'm a visual guy and sometimes need to see marked up pictures, to help explain a topic.
1. i don't understand this,
... manually plotting these single print levels in profile.
2. are the rows of numbers on a monkey bar chart similar to a volume profile layout? it is possible to plot a profile on variables other than volume.
3. do you want a study to draw things on a candle chart or a monkey chart?
hey, thanks for the response. I'll do my best to answer your questions and ill attach a screenshot of what im plotting manually
1. I layer profile behind 3 min candles on an intraday chart via thinkorswim 'monkey bar' study, which allows you to see price action printing on both candles and profile.
2. the rows of numbers are the same thing as volume profile layout, except monkey bars (more commonly known as TPO, or time price opportunity) show profile of time spent at a particular price. When
you look at these two, generally they match up pretty well. I just think TPO is more precise, given it uses time rather than volume. Volume has mattered a little less to me, since I've found that a
50 day rvol that is high just tells me theres good enough volume to get in on a trade-- thats a whole different topic so ill move on
3. the study should plot levels where the single prints begin and end. check the screenshots to get an idea of what I mean. A single print is just that, a single layer of prints, where price zips
through. most times this helps you identify buyer seller levels since price fails to accept in these areas, and moves to a level of acceptance. with TPO (or in this case, with thinkorswim, Monkey
Bars) youll have the point of control at the point that price spent the most time. In this case it would be intraday. The numbers are just 'periods'. Mine are set to 30 min periods. I dont look at
the numbers either, I can tell different periods by color in the example posted below.
Single prints - /NQ 11/4/21
hey, thanks for the response. I'll do my best to answer your questions and ill attach a screenshot of what im plotting manually
1. I layer profile behind 3 min candles on an intraday chart via thinkorswim 'monkey bar' study, which allows you to see price action printing on both candles and profile.
2. the rows of numbers are the same thing as volume profile layout, except monkey bars (more commonly known as TPO, or time price opportunity) show profile of time spent at a particular price.
When you look at these two, generally they match up pretty well. I just think TPO is more precise, given it uses time rather than volume. Volume has mattered a little less to me, since I've found
that a 50 day rvol that is high just tells me theres good enough volume to get in on a trade-- thats a whole different topic so ill move on
3. the study should plot levels where the single prints begin and end. check the screenshots to get an idea of what I mean. A single print is just that, a single layer of prints, where price zips
through. most times this helps you identify buyer seller levels since price fails to accept in these areas, and moves to a level of acceptance. with TPO (or in this case, with thinkorswim, Monkey
Bars) youll have the point of control at the point that price spent the most time. In this case it would be intraday. The numbers are just 'periods'. Mine are set to 30 min periods. I dont look
at the numbers either, I can tell different periods by color in the example posted below.
Single prints - /NQ 11/4/21
I moved your post here as this thread has been consolidated to contain all the information the forum has on TPO Monkey Bars.
Start with the 1st post and read through to what other members have done.
Ive been a "long time lurker" here. Learned a lot and developed a couple indicators based off of others, learned some basic thinkscript coding. However, I was wondering if it were even possible
to write a script to auto plot TD's monkey bars (TPO, market profile, whatever you choose to call it) single prints. I trade based off of price action at single prints that clearly define buyer /
seller levels, and generally simplifies the "auction" concept of the market. This strategy has been highly effective trading futures over the past year when I first started using profile only and
rvol, rather than multiple indicators.
I spend WAY too much time manually plotting these single print levels in profile. If it is possible, I can spend the time to develop thinkscript for this. If anyone is interested in working on it
together, feel free to reach out. If we can make this happen, I would like to share it to the forum. It would be nice to give back after learning so much about thinkscript here in the past.
Thanks fellas!
were you able to create a script for this? I'm super interested!
were you able to create a script for this? I'm super interested!
Did you know that by clicking on a member's name, you can easily check when they were last seen on the uTS forum? It's a great way to keep track of who's been around recently, and who hasn't.
Speaking of which, it looks like
is no longer active.
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Run it twice?
Apr 21, 2020
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What are your guys thoughts on running it 2 or 3 times in a cash game of course? Does it depend on the size of the pot?
Apr 9, 2020
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I would never do it myself but if your asking if it should be allowed I say yes
Apr 25, 2020
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I wouldn’t do it if I was making the choice. If you don’t want to gamble on coin flips don’t put it all in before you see the flop.
On the other hand, it is really up to the participants of the hand to decide. I don’t know, it just feels like it changes the odds and rules and thus the way you would play the game as a result.
Also, a player who is ahead might feel pressured to run it twice to not look greedy even if they might not really want to.
Nov 22, 2018
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I’m always one to do whatever the other person wants, I don’t care.
If they leave it up to me, I’ll always run it twice. More split pots, opens up more betting and willingness, keeps folks around, and just seems to generally be more exciting at the table.
Dec 18, 2019
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What are your guys thoughts on running it 2 or 3 times in a cash game of course? Does it depend on the size of the pot?
If I’m ahead I ask them if they want to run it twice (insurance basically). If I’m behind I want to run It once. I always leave it up to whomever is trying to catch up.
Apr 17, 2016
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Nov 6, 2014
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Jan 23, 2020
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Running it twice simply minimizes variance over the long term. If u r a gambler and do not mind the bigger swings in ur bankroll then run it once. If u r more conservative and don’t want to swing as
much then run it twice. In my opinion u should not make that determination based on the hand u r up against. the only determining factors in my mind are the size of the game and whether the majority
of players at the table r going once or twice. in bigger games I always will go twice, assuming the majority of the table is doing it. Smaller games I go once.
Nov 6, 2014
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id rather run it once, or three times.
Apr 25, 2020
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I think you both changed my mind. Especially
-- makes more sense especially in bigger games. I hadn't really thought of it as an insurance measure/minimizing suckouts.
Feb 17, 2020
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I prefer to run it once and am open to chopping blinds (when no ante), but I wouldn’t be opposed to running it more times if I was asked nicely.
Dec 29, 2014
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1-3-5 has to be a winner.
Nov 7, 2014
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What are your guys thoughts on running it 2 or 3 times in a cash game of course? Does it depend on the size of the pot?
That is a noob question.
Running it two or three times is only as good as the opportunity it presents. Why wouldn't you run it twice or three times if you are a four to one dog for example?
The same is true for taking her easy. If she is easy, you take her twice.
I know. You can't believe I am giving you such good advice for free.
Nov 11, 2014
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I like blood in the water!!!
For the most part I won’t run it twice. Of course there are exceptions to every rule. If I am stuck I only run it once. I can’t get back to even or winning if I chop the pot. I can always rebuy if I
I will run it twice if I am up a lot and the other person is stuck a lot and asks for it.
I will also run it twice in monster pots, say 6+ full buy-ins in the pot.
Other than those situations I will only run it once. I want more money on the table. If I win I want the other person to rebuy, if I lose I want the other player to no have to play in a deeper stack
game where they can make more mistakes.
Also if someone knows you will always run it twice they are going to be more inclined to get it all-in on the flop with any draw figuring they will hit at least one board. So it can reduce your fold
equity a lot.
Apr 21, 2020
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That is a noob question.
Running it two or three times is only as good as the opportunity it presents. Why wouldn't you run it twice or three times if you are a four to one dog for example?
The same is true for taking her easy. If she is easy, you take her twice.
I know. You can't believe I am giving you such good advice for free.
Gotcha. Guess this isn’t the place to ask “noob questions” my bad cool guy
Apr 5, 2017
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we always run it once. just make deuces wild to spice things up. We call it the 'scratch off' game.
Sep 29, 2017
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I prefer running it once but if opponent wants to run it two or three times, I'm fine with that - no more than three times though.
However, I do take note of those who want to run it more than once as they are more likely to play as scared money. It's definitely a tell that you're playing higher than you're comfortable playing.
Nov 16, 2018
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I like it, in my experience it loosens up the game. I prefer 3 times though
Jan 28, 2018
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Shouldn't this decision be made before the players open their cards? (i.e. without knowing who is ahead)? IDK.
If we know who is ahead, 3 times (instead of 2) is more fair to the person ahead.
Oct 5, 2015
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Firstly... I admit this may be a "noob" comment, but isn't there math to this that would make it advantageous to one party or another based on the situation?
Nov 16, 2018
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Firstly... I admit this may be a "noob" comment, but isn't there math to this that would make it advantageous to one party or another based on the situation?
The odds doesn’t change, it only reduces variance
Jan 26, 2020
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Agreed, even if you have some oddball situation like As4s* against 8s3s* and a flop of 7s 6s 5s giving player 1 the nut flush and player 2 a one-outer (9s), it's still the same EV running it once or
Running it once gives the pot to player 1 if anything but the 9s is dealt in the next two cards, which happens (44 / 45) * (43 / 44) = 43/45 of the time.
Running it twice means he scoops if anything but the 9s is dealt in the next four cards, which happens (44 / 45) * (43 / 44) * (42 / 43) * (41 / 42) = 41/45 of the time. They will chop the pot the
remaining 4/45 of the time, meaning player 1 has an additional 2/45 EV when that happens, giving him a total EV of (41 + 2) / 45 which is exactly the same if they ran it once.
Conversely, player 2 gets the whole pot running it once 2/45 of the time, and half a pot 4/45 of the time running it twice, giving him the same EV (of course).
Only difference running it twice is that player 2 has a better chance of winning something, but he cannot scoop in that case.** Same EV, less variance.
* My initial scenario was not quite correct, corrected now.
**Edited this sentence to make it correct and clearer.
Last edited:
Nov 9, 2014
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As the host I try to discourage such things. Why? Because they slow the game down to a crawl. Some of the players have enough trouble reading the board plus the exposed hands. We will surely stop at
least once an hour for one of the players to figure out why he/she lost the hand.
Running it more than once doesn't change the expected value, just lowers the variance. But letting people negotiate, discuss and explain what is going on imposes a sure cost to everyone.
Then we have to keep in mind that the game is self dealt. You can bet your bottom dollar that someone is going to screw up the "run it xxx" proposition. Maybe the dealer deals out one board then
scoops up the muck. Maybe they decide lots of burn cards are needed, or maybe none. God help us if they scrum the board.
Running it xxx is more of a TV thing. We don't play for stakes large enough for the variance to matter. Sure, it runs smoothly with experienced players and well trained dealers. That isn't us.
Life is simpler without the hassle -=- DrStrange
Jan 26, 2020
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I like blood in the water!!!
For the most part I won’t run it twice. Of course there are exceptions to every rule. If I am stuck I only run it once. I can’t get back to even or winning if I chop the pot. I can always rebuy
if I lose.
I will run it twice if I am up a lot and the other person is stuck a lot and asks for it.
I will also run it twice in monster pots, say 6+ full buy-ins in the pot.
Other than those situations I will only run it once. I want more money on the table. If I win I want the other person to rebuy, if I lose I want the other player to no have to play in a deeper
stack game where they can make more mistakes.
Also if someone knows you will always run it twice they are going to be more inclined to get it all-in on the flop with any draw figuring they will hit at least one board. So it can reduce your
fold equity a lot.
Some interesting things to think about here, some of which I hadn't considered (the last point in particular).
Royal Flush
Tourney Director
Oct 29, 2014
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Personally, I never run it twice. Once or three times; I'm not playing cards just to chop pots. I think running it twice simply wastes everybody's time.
I used to deal a private (raked) cash game that only allowed running it more than once (and never more than three) if the pot exceeded three digits.
Jan 23, 2020
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The type of game u play is also worthy of consideration. I usually play 5 card plo and big o at a decent stake level, so the prospect of coming up against another monster hand for a big pot is high.
Running it twice is pretty common in the games I play to minimize variance in those situations.
I do understand slowing down the game, especially in split pot games where chopping the pot can take a while. One regular game I play in only allows running it twice if the pot exceeds a certain
Jan 28, 2018
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Is there a rule (in cash games) about NOT showing cards BEFORE the run once/twice/three times has been agreed upon?
I understand that in cash games no cards have to be shown, even if all-in, unless it's run more than once.
Aug 8, 2016
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Personally, I never run it twice. Once or three times; I'm not playing cards just to chop pots. I think running it twice simply wastes everybody's time.
I used to deal a private (raked) cash game that only allowed running it more than once (and never more than three) if the pot exceeded three digits.
Yes! The only reason I'd consider twice is if there's significant dead money in the pot. Otherwise, once or three times, with a preference for once.
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Think Nuclear
The “Boy or Girl Paradox” (also called “The Two Child Problem” in addition to other names) is generally phrased as follows:
You know a couple who has two children. At least one of the children is a girl. What is the probability that they have two girls?
This is an ambiguous problem, which leads to different answers depending on the assumptions that are used. Not enough information has been provided to produce a definite answer, and the unstated
assumptions fill in the space needed to complete the logic.
Here I investigate this problem and explain the ambiguity. | {"url":"https://thinknuclear.org/category/paradoxes/","timestamp":"2024-11-04T00:57:56Z","content_type":"text/html","content_length":"30546","record_id":"<urn:uuid:5cdcf3a8-b6f9-401c-8bd4-6d67299f9839>","cc-path":"CC-MAIN-2024-46/segments/1730477027809.13/warc/CC-MAIN-20241104003052-20241104033052-00220.warc.gz"} |
Correlation analysis of histomorphometry and motor neurography in the median nerve rat model
Motor Neurography in the Median Nerve Rat
Theodora Manoli, MD,a,∗Frank Werdin, MD,a,∗Hannes Gruessinger, MD,a Nektarios Sinis, MD,aJennifer Lynn Schiefer, MD,aPatrick Jaminet, MD,a Stefano Geuna, MD,band Hans-Eberhard Schaller, MDa
Clinic of Hand, Plastic, and Reconstructive Surgery with Burn Unit, BG-Trauma Centre, University
of Tuebingen, Schnarrenbergstr. 95, 72076 Tuebingen, Germany; andbDepartment of Clinical and
Biological Sciences, University of Turin, San Luigi Hospital, Orbassano (TO), Azienda Ospedaliera San Luigi - Regione Gonzole 10, 10043 Turin, Italy
Correspondence: [email protected]
∗[Both authors have contributed equally to this research article.]
Keywords: neurography, electrophysiology, morphometry, nerve regeneration, median nerve
Published April 9, 2014
Objective: Standard methods to evaluate the functional regeneration after injury of the
rat median nerve are insufficient to identify any further differences of axonal nerve regeneration after restitution of motor recovery is completed. An important comple-mentary method for assessing
such differences is a histomorphometric analysis of the distal to lesion nerve fibers. Recently, an electrophysiological method has been proposed as a sensitive method to examine the quality of
axonal nerve regeneration. Methods: A linear regression analysis has been performed to correlate histomorphometric and neurographic data originating from 31 rats subjected to neurotmesis and
immediate reconstruction of their right median nerve. Results: A significant linear correlation be-tween the velocity of neuromuscular conduction and the total number of nerve fibers
(P= .037) as well as between the amplitude of compound muscle action potential and
the total number of nerve fibers (P= .026) has been identified. Interestingly, a significant
correlation between the velocity of neuromuscular conduction and the square root of the
cross-sectional area of the nerve could be found (P= .008). This corresponds to a linear
correlation between the velocity of neuromuscular conduction and the radius of the nerve. Conclusion: These results contribute in a better interpretation of morphological predictors of nerve
regeneration and verify the previously described electrophysiological assessment in the median nerve rat model as a valid method.
The median nerve model of the rat became a popular tool to examine peripheral nerve regeneration under several conditions in the last years. The functional recovery can be simply and reliably
assessed by the so-called grasping test as well as by weighing the flexor
digitorum sublimis muscle.1 In most cases, the grasp force recovers almost completely in about 3 months after nerve lesion. A further and precious supplementary tool to quantify the axonal
regeneration is the histomorphometric analysis of the distal to lesion nerve segment.2 With this method, parameters such as nerve cross-sectional area, total fiber number, fiber density, diameter of
fibers and axons, and myelin thickness can be calculated.
Recently, an electrophysiological method to perform a motor neurography in the me-dian nerve rat model has been established by our group.3[With this method, parameters like]
the threshold to evoke a compound muscle action potential (CMAP), latency, CMAP and velocity of neuromuscular transduction can be assessed by a standardized procedure. The development of motor
neurography for the median nerve rat model gave us the opportunity to get more information about the quality and extent of the axonal regeneration that has taken place over several time points.
The purpose of the actual study was to correlate electrophysiological parameters and histomorphological findings from the median nerve model of the rat, after functional recovery was completed.
Furthermore, our results could validate both methods as more sensible tools to evaluate axonal regeneration, compared to the standard functional tests.
MATERIALS AND METHODS Data acquisition
The electrophysiological and histomorphological data used for our correlation analysis originated from 2 already published works of our department.4,5 [In both works, the ]
me-dian nerve model of Wistar adult female rats, weighing 220 to 250 g each, was used. In total, 31 rats originating from these works were subjected to both electrophysiological and
histomorphological analysis 12 weeks after surgery. Experiments have been carried out in accordance to EC Directive 86/609/EEC for animal experiments.
The distribution of animals according to their treatment after neurotmesis of the right median nerve is depicted in Table 1. The electrophysiological parameters assessed by our standard protocol3[and
used for the actual correlation analysis have been as follows:]
– The threshold [V] of stimulus to provoke a CMAP
– The transduction velocity or v [m/s], which was calculated by the distance between the stimulus and the electrode placed in the flexor sublimis muscle divided by the latency between the stimulus
and the beginning of the CMAP, and
– the amplitude of the CMAP [μV]
Table 1. Distribution of animals according to their surgical treatment as described in studies A4[and B]5
Study Treatment Number of animals
A Direct suture 3
A Direct suture plus vein-graft wrapping 4
A Direct suture plus vein-graft wrapping filled with Perineurin vehicle 2 A Direct suture plus vein-graft wrapping filled with Perineurin 6
B Direct suture 5
B FloSeal application to the nerve stumps and direct suture 6 B Electrocoagulation of the nerve stumps and direct suture 5
Table 2. F-statistic of the binary regression analyses between the histomorpho-metric and neurographic data
Neurographic parameters
Threshold Transduction velocity Amplitude Histomorphometric parameters
Cross sectional area 0.562 0.009 0.083 Total fiber number (N) 0.201 0.037 0.026
Fiber density 0.406 0.133 0.869
Fiber diameter (D) 0.543 0.749 0.556
Axon diameter (d) 0.603 0.680 0.767
Myelin thickness (M) 0.860 0.859 0.514
G ratio (d/D) 0.892 0.689 0.813
The numbers correspond to P values. Significant values (P< .05) are marked in grey.
The histomorphometric data assessment2 used for the actual study included the following parameters:
– The cross-sectional area of the nerve – The total fiber number (N)
– Fiber density – Fiber diameter (D) – Axon diameter (d)
– Myelin thickness (M), and
– Axon/fiber ratio or g ratio (g= d/D)
Statistical analysis
Data analysis was performed using version 2.11.0 of R software and its package “stats” to correlate electrophysiological and histomorphological parameters.6[Since the ]
histomor-phological parameters can be considered as independent and the electrophysiological pa-rameters as dependent variables, linear regression analysis has been chosen to correlate the 2 methods.
A normal distribution was expected for all parameters. Linear regression analyses have been performed between 1 of the 3 electrophysiological parameters and 1 of the 7 different histomorphological
parameters mentioned earlier at a time. The algorithm used to fit linear models was the one proposed by Chambers.7The level of significance after applying an F statistic was set by a P< .05. The
Institute of Biometry of the University of Tuebingen has validated the statistical analysis. The work described in the actual article fulfils the Uniform Requirements for manuscripts submitted to
Biomedical journals.
The P values obtained by the F statistic applied to find significant correlations between the histomorphometric and neurographic data after performing a linear regression analysis are shown in Table
2. Significant linear correlations with P < .05 could be found in 3 cases. These were between (a) transduction velocity and cross-sectional area of the
nerve (y= −9.96 + 83.42x, P = .009), (b) transduction velocity and total fiber number (y= −15.82 + 83.42x, P = .037), and (c) amplitude and total fiber number (y = –19.43 + 32.6x, P = .026). These 3
linear models are depicted in Figures 1a-c. Concerning the first case, an even more significant linear correlation could be observed between the square root of the cross-sectional area of the nerve
and the transduction velocity (y= –25.71 + 73.23x, P= .008). Having in mind the formula for calculation of the circle area, A = πr2, it can be concluded that transduction velocity is linear
correlated to the nerve radius or diameter. Figure 2 is a graphical presentation of this linear fitted model (red line). Data originating from the 2 different studies are presented with different
symbols and different colors according to their treatment, as described in the legends. Such graphs may be useful tools to compare different treatments or different studies. In this case, we can
conclude that animals of study B achieved a higher mean transduction velocity than the animals of study A. This is probably due to the generally slightly larger diameter of the median nerves of the
rats used for study B with a mean value of 0.217μm2than for study A with a mean value of 0.198μm2[.]
In this study, a good linear correlation could be obtained between 2 neurographic pa-rameters (transduction velocity and amplitude) and the total fiber number obtained by the histomorphometric
analysis. Moreover, a very good linear correlation was obtained between transduction velocity and nerve diameter. Our results illustrate the progress in the improvement of histomorphometry and
especially of neurography in rodents, as no significant correlations between these methods could be obtained in the early phase after completion of functional recovery in several previous
studies.8-10 [In a previous study, a]
moderate to good correlation between amplitude and fiber counts demonstrating a diameter 3 to 5μm in the peroneal nerve of the rabbit, 4 to 15 weeks after repair, could be obtained.11 Dellon and
Mackinnon first demonstrated a strong positive correlation between con-duction velocity and fiber diameter as well as between amplitude and number of nerve fibers 1 year after nerve repair.12[In our
study, no significant correlation between the conduction]
velocity and fiber or axon diameter could be obtained. This is probably due to the early time point (12 weeks) of neurographic and histomorphometric assessment. Previous studies evaluating nerve
regeneration in the rat across a nerve repair demonstrated that the total number of fibers that reached the distal segment varied with time. In the first few months after surgery, the number of axons
will increase dramatically due to axonal sprouting. Some of the axon sprouts make appropriate distal connections and some of them do not, which results in a later decrease in fibers. The number of
axons reach a plateau between 6 and 9 months after repair and return to normal levels within 1 year in the rat model.13,14 Thus, changes in the number of nerve fibers are expected in the first year
after nerve repair. More-over, most authors found a decrease in axon diameter concurring with a smaller decrease in fibre diameter up 1.5 years after nerve repair.
It has been shown that the ratio of axon to fiber diameter (d/D) or g-ratio remains quite constant during regeneration and that conduction velocity depends on a small number of the largest axons in
the nerve.15[However, no significant linear correlation between conduction]
between myelin thickness and conduction velocity was expected16,17 but could not be verified in our data. An explanation could be that a significant part of myelinated fibers may have been sensory
fibers that do not have an impact in motor neurography. However, the good correlation between transduction velocity and total fiber number implies that the total fiber number may be a better
morphological predictor of an effective peripheral nerve regeneration of a mixed nerve than the myelin thickness, especially during the early phase of regeneration. . . . . . . . .. . . . . . . 0.0
0.1 0.2 0.3 0.4 468 1 0 a) y = −9.96 + 83.42x
Nerve cross sectional area, cm2
T ransduction v elocity, m/s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0 2 4 6 8 10 12 468 1 0 b) y = −15.82 + 3.5x
Total fiber number
T ransuction v elocity, m/s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0 2 4 6 8 10 12 0 100 200 300 400 c) y = − 19.43 + 32.6x
Total fiber number Amplitude (uV) . . . . . . . . . . . .
Figure 1. Fitted linear models (red lines) after regression analysis; between (a) v and cross-sectional
area of the nerve, (b) v and N, and (c) amplitude and N.
Interesting correlations of histomorphometric and neurographic data originating from 2 studies using the median nerve rat model could be observed. Our results could validate
motor neurography as a sensible method for the assessment of regeneration in the median nerve model of the rat. These findings are also important since histomorphometric and electrophysiologic
measurements enable a more subtle interpretation of peripheral nerve regeneration quality than functional tests do and do not always correlate with nerve sensory or motor function.18,19A combined
analysis of histomorphometry and motor neurography enables an even more precise evaluation of the axonal regeneration in the median nerve model of the rat, making it a powerful model to investigate
several conditions that may influence peripheral nerve regeneration, or new reconstruction methods and strategies before applying them on a clinical level.
Figure 2. Fitted linear model (red line, y= −25.71 + 73.23x) after
re-gression analysis between the square root of the cross-sectional area of the nerve and the transduction velocity. Data originating from study A are depicted by “o” and data originating from study
B by “ˆ.” The dif-ferent colors present the difdif-ferent treatments, as described in the legends. Magenta ellipse includes all measurements originating from study A, while green ellipse includes all
measurements but one originating from study B.
The authors thank Dr Meisner of the Institute of Biometry of the University of Tuebingen for validating and supporting the statistical analysis of the data.
1. Bertelli JA, Mira JC. The grasping test: a simple behavioral method for objective quantitative assessment of peripheral nerve regeneration in the rat. J Neurosci Methods. 1995;58:151-5.
2. Raimondo S, Fornaro M, Di Scipio F, et al. Chapter 5: methods and protocols in peripheral nerve regeneration experimental research: part II—morphological techniques. Int Rev Neurobiol. 2009;
3. Werdin F, Grussinger H, Jaminet P, et al. An improved electrophysiological method to study peripheral nerve regeneration in rats. J Neurosci Methods. 2009;182:71-7.
4. Sinis N, Di Scipio F, Schonle P, et al. Local administration of DFO-loaded lipid particles improves recovery after end-to-end reconstruction of rat median nerve. Restor Neurol Neurosci. 2009;
5. Sinis N, Manoli T, Schiefer JL, et al. Application of 2 different hemostatic procedures during microsurgical median nerve reconstruction in the rat does not hinder axonal regeneration.
Neurosurgery. 2011;68:1399-403, discussion 1403-1394.
6. R Development Core Team R: A Language and Environment for Statistical Computing. Vienna, Austria: R Foundation for Statistical Computing; 2010.
7. Chambers JM. Chapter 4: linear models. In: Chambers JM, Hastie TJ, eds. Statistical Models in S. Pacific Grove, CA: Wadsworth & Brooks/Cole; 1992.
8. Munro CA, Szalai JP, Mackinnon SE, Midha R. Lack of association between outcome measures of nerve regeneration. Muscle Nerve. 1998;21:1095-7.
9. Kanaya F, Firrell JC, Breidenbach WC. Sciatic function index, nerve conduction tests, muscle contraction, and axon morphometry as indicators of regeneration. Plast Reconstr Surg. 1996;98:1264-71,
discussion 1272-1264.
10. Wolthers M, Moldovan M, Binderup T, Schmalbruch H, Krarup C. Comparative electrophysiological, functional, and histological studies of nerve lesions in rats. Microsurgery. 2005;25:508-19.
11. van Neck JW, de Kool BS, Hekking-Weijma JI, Walbeehm ET, Visser GH, Blok JH. Histological validation of ultrasound-guided neurography in early nerve regeneration. Muscle Nerve. 2009;40:967-75.
12. Dellon AL, Mackinnon SE. Selection of the appropriate parameter to measure neural regeneration. Ann
Plast Surg. 1989;23:197-202.
13. Mackinnon SE, Dellon AL, O’Brien JP, et al. Selection of optimal axon ratio for nerve regeneration. Ann
Plast Surg. 1989;23:129-34.
14. Schaller H-E.. Die Bedeutung des MHC und non MHC f¨ur das allogene periphere Nerventransplantat im Tiermodell der Ratte. Habilitationsanschrift Hannover. Hannover, Germany; 1990.
15. Gillespie MJ, Stein RB. The relationship between axon diameter, myelin thickness and conduction velocity during atrophy of mammalian peripheral nerves. Brain Res. 1983;259:41-56.
16. McDonald WI. The effects of experimental demyelination on conduction in peripheral nerve: a histological and electrophysiological study. II. Electrophysiological observations. Brain. 1963;
17. McDonald WI. The effects of experimental demyelination on conduction in peripheral nerve: a histological and electrophysiological study. I. Clinical and histological observations. Brain. 1963;
86:481-500. 18. Martins RS, Siqueira MG, da Silva CF, Plese JP. Correlation between parameters of electrophysiological,
histomorphometric and sciatic functional index evaluations after rat sciatic nerve repair. Arq Neuropsiquiatr. 2006;64:750-6.
19. Vleggeert-Lankamp CL. The role of evaluation methods in the assessment of peripheral nerve regeneration through synthetic conduits: a systematic review. Laboratory investigation. J Neurosurg. | {"url":"https://123dok.org/document/6qmnw05z-correlation-analysis-histomorphometry-motor-neurography-median-nerve-model.html","timestamp":"2024-11-04T18:15:50Z","content_type":"text/html","content_length":"157964","record_id":"<urn:uuid:a3f340fc-ec1c-4886-9472-60969d48b5ee>","cc-path":"CC-MAIN-2024-46/segments/1730477027838.15/warc/CC-MAIN-20241104163253-20241104193253-00737.warc.gz"} |
STH-SOPR | CryptoQuant User Guide
Short Term Output Profit Ratio (STH-SOPR) is a ratio of spent outputs (alive more than 1 hour and less than 155 days) in profit at the time of the window.
Short Term Holder Spent Output Profit Ratio (STH-SOPR) is a ratio of spent outputs (alive more than 1 hour and less than 155 days) in profit at the time of the window.
It is calculated as the USD value of spent outputs at the spent time(realized value) divided by the USD value of spent outputs at the created time(value at creation).
The adjustment was made by not accounting for an hour less lived and 155 days more lived coins' movements to track short-term investors. This allows excluding long-term investors or coins and only
focuses on short-term held movements.
As a result, the spectrum of UTXO coverage is an hour<UTXOs age<155 days.
It implies that the coins moved in a certain timescale are, on average, selling at a profit.
It implies that the coins moved in a certain timescale are, on average, selling coins at break even.
It implies that the coins moved in a certain timescale are, on average, selling at a loss.
Short-Term Holder SOPR trending higher It implies that short term investors are realizing their coins where trading condition is getting more profitable. This equals a higher market sentiment.
Short-Term Holder SOPR trending lower It implies that short term investors are realizing their coins where trading condition is getting less profitable. This equals a lower sentiment in the market
and one can see the potential of panic selling. | {"url":"https://userguide.cryptoquant.com/cryptoquant-metrics/utxo/spent-output-profit-ratio-sopr/sth-sopr?fallback=true","timestamp":"2024-11-13T09:12:23Z","content_type":"text/html","content_length":"298520","record_id":"<urn:uuid:0f80347b-b717-4156-a8d2-c5c599610c4e>","cc-path":"CC-MAIN-2024-46/segments/1730477028342.51/warc/CC-MAIN-20241113071746-20241113101746-00090.warc.gz"} |
Initialize random allRGB permutation, and randomly pick pairs of pixels to swap, if the resulting sum of squares of distances from the target pixels becomes smaller. Distances are calculated in the
Lab colorspace, using the metric from: https://www.compuphase.com/cmetric.htm
In the allRGB image to get the source pixel to compare, pixels are averaged from a 3x3 area, in the Lab colorspace, with an approximate gaussian weighting: weight 4 for the center, 2 for the edges,
and 1 for the corners. And then I ran this for a couple days, and it did 6.95 billion iterations. 0.9% of the iterations resulted in swaps, for a total of 62,338,350 swapped pixels. | {"url":"https://allrgb.com/cat","timestamp":"2024-11-09T02:32:17Z","content_type":"text/html","content_length":"7591","record_id":"<urn:uuid:09305abe-e7dc-4c67-8a43-a3ccb445fc4b>","cc-path":"CC-MAIN-2024-46/segments/1730477028115.85/warc/CC-MAIN-20241109022607-20241109052607-00266.warc.gz"} |
public struct Tensor<Element, Device> where Element : NumericType, Device : DeviceType
extension Tensor: CustomStringConvertible, CustomDebugStringConvertible
extension Tensor: ExpressibleByFloatLiteral
extension Tensor: ExpressibleByIntegerLiteral
extension Tensor: Equatable where Element: Equatable
extension Tensor: Codable where Element: Codable
A tensor is an n-dimensional array of numbers with a given shape.
• Shape of the tensor.
A tensor with an empty shape is a scalar. When shape.count == 1, the tensor is a vector. When shape.count == 2, the tensor is a matrix, etc.
public let shape: [Int]
• Whether the compute graph of operations originating from this tensor should be captured. If the compute graph is captured, the resources associated with this tensor are only released after all
tensors that have been derived from this tensor are released.
All tensors derived from gradient requiring tensors will also require a gradient.
To compute a gradient, use the gradients(of:) function. Example:
let a = Tensor<Float, CPU>([1,2,3,4,5], requiresGradient: true)
let result = a * a * a // [1, 8, 27, 64, 125]
let grads = result.gradients(of: [a])
let ∇a = grads[0] // [3, 12, 27, 48, 75]
To detach a tensor from the compute graph, use tensor.detached().
public var requiresGradient: Bool
• Debug tag for the tensor. If you use tensor.graph() to visualize the compute graph, the tensor is labelled with the appropriate tag.
public var tag: String?
• Number of elements in the tensor.
public var count: Int { get }
• Dimensionality of the tensor. (0: scalar, 1: vector, 2: matrix, …)
public var dim: Int { get }
• Creates a tensor with the given shape and fills it with value
public init(repeating value: Element, shape: Int..., requiresGradient: Bool = false)
value Value to fill tensor with
shape Shape of the tensor
requiresGradient Whether it is desired to compute gradients of the tensor.
• Creates a tensor with the given shape and fills it with value
public init(repeating value: Element, shape: [Int], requiresGradient: Bool = false)
value Value to fill tensor with
shape Shape of the tensor
requiresGradient Whether it is desired to compute gradients of the tensor.
• Creates a tensor with the given shape and fills it with the given array of elements
public init(_ v: [Element], requiresGradient: Bool = false)
v Value to fill tensor with
requiresGradient Whether it is desired to compute gradients of the tensor.
• Creates a tensor with the given shape and fills it with the given array of elements
public init(_ v: [Element], shape: [Int], requiresGradient: Bool = false)
v Value to fill tensor with
shape Shape of the tensor. The number of elements in v must be compatible with the shape.
requiresGradient Whether it is desired to compute gradients of the tensor.
• Creates a tensor with the given shape and fills it with the given array of elements
public init(_ v: [Element], shape: Int..., requiresGradient: Bool = false)
v Value to fill tensor with
shape Shape of the tensor. The number of elements in v must be compatible with the shape.
requiresGradient Whether it is desired to compute gradients of the tensor.
• Performs backpropagation and returns the gradients for the given tensors.
Tensors for which it is desired to compute gradients must have requiresGradient set to true. If the result is not differentiable with respect to an input tensor, a tensor of zeros will be
let a = Tensor<Float, CPU>([1,2,3,4,5], requiresGradient: true)
let result = a * a * a // [1, 8, 27, 64, 125]
let grads = result.gradients(of: [a])
let ∇a = grads[0] // [3, 12, 27, 48, 75]
To detach a tensor from the compute graph, use tensor.detached().
If it is desired to compute second, third, etc. derivatives, the retainBackwardsGraph flag must be set to true. This will record the compute graph for the backpropagation operation. A second
derivative can then be computed as the gradient of a gradient. If the flag is not set, the compute graph of the backwards operation will not be captured and the result is not differentiable to
any variable.
public func gradients(of tensors: [`Self`], retainBackwardsGraph retainGraph: Bool = false) -> [`Self`]
tensors Tensors to differentiate for
retainGraph Whether to store the graph for the backwards pass. If enabled, higher order gradients can be computed.
• In-place detaches the tensor from the compute graph.
public mutating func discardContext()
• Detaches the tensor from the compute graph. No gradients can be computed for the resulting tensor.
public func detached() -> Tensor<Element, Device>
• Prints the compute graph, from which the tensor has been derived.
The graph is in graphviz format and can be rendered with command line tools such as dot.
Note: When running release builds, some information about the compute graph is discarded. To obtain a detailed compute graph, compile in debug mode.
func graph() -> String
• Element-wise broadcast adds the given tensors
lhs and rhs must have matching shapes, such that dimensions of the shape are either equal or 1. Shapes are matched from the right. For example, the shapes [42, 3, 1] and [3, 8] can be broadcasted
and will give a tensor with the result shape [42, 3, 8].
For detailed broadcasting rules, follow the numpy documentation
static func + (lhs: `Self`, rhs: `Self`) -> Tensor<Element, Device>
lhs First tensor
rhs Second tensor
Return Value
Broadcast added result
• Element-wise broadcast multiplies the given tensors
lhs and rhs must have matching shapes, such that dimensions of the shape are either equal or 1. Shapes are matched from the right. For example, the shapes [42, 3, 1] and [3, 8] can be broadcasted
and will give a tensor with the result shape [42, 3, 8].
For detailed broadcasting rules, follow the numpy documentation
static func * (lhs: `Self`, rhs: `Self`) -> Tensor<Element, Device>
lhs First tensor
rhs Second tensor
Return Value
Broadcast multiplied result
• Element-wise broadcast subtracts the given tensors
lhs and rhs must have matching shapes, such that dimensions of the shape are either equal or 1. Shapes are matched from the right. For example, the shapes [42, 3, 1] and [3, 8] can be broadcasted
and will give a tensor with the result shape [42, 3, 8].
For detailed broadcasting rules, follow the numpy documentation
static func - (lhs: `Self`, rhs: `Self`) -> Tensor<Element, Device>
lhs First tensor
rhs Second tensor
Return Value
Broadcast difference
• Element-wise broadcast divides the given tensors
lhs and rhs must have matching shapes, such that dimensions of the shape are either equal or 1. Shapes are matched from the right. For example, the shapes [42, 3, 1] and [3, 8] can be broadcasted
and will give a tensor with the result shape [42, 3, 8].
For detailed broadcasting rules, follow the numpy documentation
static func / (lhs: `Self`, rhs: `Self`) -> Tensor<Element, Device>
lhs First tensor
rhs Second tensor
Return Value
Broadcast quotient
• Negates every element of the given tensor.
prefix static func - (value: `Self`) -> Tensor<Element, Device>
Return Value
Negated tensor
• In-place broadcast adds the given tensors. This operation requires the resulting broadcast shape to be equivalent to the shape of lhs.
For detailed broadcasting rules, follow the numpy documentation
static func += (lhs: inout `Self`, rhs: `Self`)
lhs Tensor to update
rhs Tensor to add to lhs
• In-place broadcast subtracts the given tensors. This operation requires the resulting broadcast shape to be equivalent to the shape of lhs.
For detailed broadcasting rules, follow the numpy documentation
static func -= (lhs: inout `Self`, rhs: `Self`)
lhs Tensor to update
rhs Tensor to subtract from lhs
• In-place broadcast multiplies the given tensors. This operation requires the resulting broadcast shape to be equivalent to the shape of lhs.
For detailed broadcasting rules, follow the numpy documentation
static func *= (lhs: inout `Self`, rhs: `Self`)
lhs Tensor to update
rhs Tensor to multiply with lhs
• In-place broadcast divides the given tensors. This operation requires the resulting broadcast shape to be equivalent to the shape of lhs.
For detailed broadcasting rules, follow the numpy documentation
static func /= (lhs: inout `Self`, rhs: `Self`)
lhs Tensor to update
rhs Tensor to divide lhs with
• Performs a broadcasted exponentiation between self (base) and power (exponent).
For detailed broadcasting rules, follow the numpy documentation
func raised(toPowerOf power: `Self`) -> Tensor<Element, Device>
Return Value
self broadcast exponentiated by power
• Computes the elementwise maxima between the given tensors
static func max(_ first: `Self`, _ second: `Self`) -> Tensor<Element, Device>
first First tensor
second Second tensor
Return Value
Element wise maxima between first and second value tensors
• Computes the elementwise minima between the given tensors
static func min(_ first: `Self`, _ second: `Self`) -> Tensor<Element, Device>
first First tensor
second Other tensors
Return Value
Element wise minima between first and second value tensors
• Performs an img2col transformation, which allows convolutions to be performed by matrix multiplication.
The source tensor is expected to have a shape of [batchSize, channels, height, width]. The result is a tensor with shape [window_size, window_count].
The window size is the size of the kernel (width * height * depth). The window count is the number of windows that fit into the source tensor when using the given padding and stride.
Windows are layed out from left to right and from top to bottom, where (0, 0) is the top left corner of the image.
func img2col(kernelWidth: Int, kernelHeight: Int, padding: Int, stride: Int) -> Tensor<Element, Device>
kernelWidth Width of the convolution kernel
kernelHeight Height of the convolution kernel
padding Padding applied before and after the image in the horizontal and vertical direction
stride Stride, with which the kernel is moved along the image
• Computes the inverse of the img2col operation.
The source tensor is expected to be a tensor with shape [window_size, window_count]. The result tensor will have the given result shape, which is expected to be 4-dimensional ([batch_size,
channels, height, width])
func col2img(kernelWidth: Int, kernelHeight: Int, padding: Int, stride: Int, resultShape: [Int]) -> Tensor<Element, Device>
kernelWidth Width of the convolution kernel
kernelHeight Height of the convolution kernel
padding Padding applied before and after the image in the horizontal and vertical direction
stride Stride, with which the kernel is moved along the image
resultShape Shape of the resulting tensor
• Performs a 2d convolution
the source tensor is expected to have a shape of [batchSize, channels, width, height] the filters tensor is expected to have a shape of [outputChannels, inputChannels, kernelWidth, kernelHeight]
func convolved2d(filters: Tensor<Element, Device>, padding: Int? = nil, stride: Int = 1) -> Tensor<Element, Device>
filters Filters to convolve the tensor with
padding Padding applied before and after the image in the horizontal and vertical direction
stride Stride, with which the kernel is moved along the image
Return Value
A tensor of shape [batchSize, outputChannels, (height + 2 * padding - kernelHeight) / stride + 1, (width + 2 * padding - kernelWidth) / stride + 1)
• Performs a transposed 2d convolution (also called fractionally strided convolution).
The source tensor is expected to have a shape of [batchSize, channels, width, height] the filters tensor is expected to have a shape of [outputChannels, inputChannels, kernelWidth, kernelHeight]
func transposedConvolved2d(filters: Tensor<Element, Device>, inset: Int? = nil, stride: Int = 1) -> Tensor<Element, Device>
filters Filters to convolve the tensor with
inset Inset from edge of the source tensor
stride Stride, with which the kernel moves over the result image. Larger strides result in larger output shapes.
Return Value
A tensor of shape [batchSize, outputChannels, (height - 1) * stride - 2 * padding + kernelHeight, (width - 1) * stride - 2 * padding + kernelWidth]
• Performs max pooling on the tensor. Max pooling selects the maximum value for every given window of a tensor.
The source tensor is expected to have a shape of [batchSize, channels, width, height].
func maxPooled2d(windowSize: Int, padding: Int? = nil, stride: Int? = nil) -> Tensor<Element, Device>
windowSize Window size
padding Padding applied before and after the image in the horizontal and vertical direction
stride Stride, with which the kernel is moved along the image
Return Value
A tensor of shape [batchSize, channels, (height + 2 * padding - windowSize) / stride + 1, (width + 2 * padding - windowSize) / stride + 1]
• Performs average pooling on the tensor. Average pooling computes the average of every given window of a tensor.
The source tensor is expected to have a shape of [batchSize, channels, width, height].
func averagePooled2d(windowSize: Int, padding: Int? = nil, stride: Int? = nil) -> Tensor<Element, Device>
windowSize Window size
padding Padding applied before and after the image in the horizontal and vertical direction
stride Stride, with which the kernel is moved along the image
Return Value
A tensor of shape [batchSize, channels, (height + 2 * padding - windowSize) / stride + 1, (width + 2 * padding - windowSize) / stride + 1]
• Declaration
func matrixMultiplied(with other: `Self`, transposeSelf: Bool = false, transposeOther: Bool = false) -> Tensor<Element, Device>
• Broadcast matrix multiplies self with the given other operand.
Broadcasting is applied along all axes except the last two. Operands are expected to have a dimensionality of 2 or higher.
func broadcastMatrixMultiplied(with other: `Self`, transposeSelf: Bool = false, transposeOther: Bool = false) -> Tensor<Element, Device>
other Other operand
transposeSelf Whether to transpose self before multiplication
transposeOther Whether to transpose the other operand before the multiplication
• Sums up elements along the given axes.
func reduceSum(along axes: [Int]) -> Tensor<Element, Device>
Return Value
Tensor with shape equal to self.shape without the given reduction axes.
• Sums up elements along the given axes
func reduceSum(along axes: Int...) -> Tensor<Element, Device>
Return Value
Tensor with shape equal to self.shape without the given reduction axes.
• Computes the sum of all elements of the tensor
func reduceSum() -> Tensor<Element, Device>
Return Value
Scalar, sum of all elements
• Computes the mean of the elements along the given axes
func reduceMean(along axes: [Int]) -> Tensor<Element, Device>
axes Axes to compute the mean of
Return Value
Tensor with shape equal to self.shape without the given reduction axes.
• Computes the mean of the elements along the given axes
func reduceMean(along axes: Int...) -> Tensor<Element, Device>
axes Tensor with shape equal to self.shape without the given reduction axes.
• Computes the mean of all elements of the tensor
func reduceMean() -> Tensor<Element, Device>
Return Value
Scalar, mean of all elements
• Computes the variance of the tensor along the given axes.
func variance(along axes: [Int]) -> Tensor<Element, Device>
axes Axes to compute the variance along.
Return Value
Tensor with shape equal to self.shape without the given reduction axes.
• Computes the variance of the tensor along the given axes.
func variance(along axes: Int...) -> Tensor<Element, Device>
axes Axes to compute the variance along.
Return Value
Tensor with shape equal to self.shape without the given reduction axes.
• Computes the variance of all elements in the tensor.
func variance() -> Tensor<Element, Device>
Return Value
Scalar, variance of all elements
• Returns the index of the largest element in the tensor.
func argmax() -> Int
• Computes the maximum values along the given axes of the tensor.
func reduceMax(along axes: [Int]) -> Tensor<Element, Device>
axes Axes to reduce along
Return Value
Tensor with shape equal to self.shape without the given reduction axes.
• Computes the maximum values along the given axes of the tensor.
func reduceMax(along axes: Int...) -> Tensor<Element, Device>
axes Axes to reduce along
Return Value
Tensor with shape equal to self.shape without the given reduction axes.
• Computes the maximum of all values in the tensor
func reduceMax() -> Tensor<Element, Device>
Return Value
Scalar, maximum of all elements.
• Gathers elements at indices determined by the context along the specified axis.
Example: Gathering from Tensor [[1,2,3], [4,5,6], [7,8,9]]
Context: [0, 1, 2], axis: 0
=> [1,5,9]
Context: [2, 2, 1], axis: 1
=> [3, 6, 8]
func gather(using context: Tensor<Int32, Device>, alongAxis axis: Int, ignoreIndex: Int32 = -1) -> Tensor<Element, Device>
context Indices along gathering axis.
axis Axis to gather from
• Scatters elements to indices determined by the context along the specified axis.
Example: Scattering Tensor [3, 1, 4]
Context: [0, 1, 2], axis: 0, axisSize: 3
=> [[3, 0, 0], [0, 1, 0], [0, 0, 4]]
Context: [2, 2, 1], axis: 1, axisSize: 3
=> [[0, 0, 3], [0, 0, 1], [0, 4, 0]]
func scatter(using context: Tensor<Int32, Device>, alongAxis axis: Int, withSize axisSize: Int, ignoreIndex: Int32 = -1) -> Tensor<Element, Device>
context Indices along scattering axis
axis Axis to scatter along
axisSize Number of elements along the axis in the result tensor. Must be greater than max(context)
• Reshapes the tensor to the given shape.
The shape must be compatible with the source shape, i.e. the number of elements must be the same.
The shape may contain a -1. The size of the result tensor along that axis is then computed as needed.
func view(as shape: [Int]) -> Tensor<Element, Device>
shape Shape to view the tensor in.
Return Value
Tensor with given shape, where occurrences of -1 have been replaced.
• Reshapes the tensor to the given shape.
The shape must be compatible with the source shape, i.e. the number of elements must be the same.
The shape may contain a -1. The size of the result tensor along that axis is then computed as needed.
func view(as shape: Int...) -> Tensor<Element, Device>
shape Shape to view the tensor in.
Return Value
Tensor with given shape, where occurrences of -1 have been replaced.
• Adds an axis to the shape of the tensor. The axis will have a size of 1.
func unsqueezed(at axis: Int) -> Tensor<Element, Device>
• Removes an axis from the tensor if the axis has a size of 1. Otherwise, the original tensor is returned.
func squeezed(at axis: Int) -> Tensor<Element, Device>
axis Axis to remove if possible.
• Removes all axes from the tensor that have a size of 1.
func squeezed() -> Tensor<Element, Device>
• Flattens the tensor into a tensor of shape [count]
func flattened() -> Tensor<Element, Device>
• Swaps the axes of the tensor.
The axis arangement must have a count of tensor.dim and contain all elements in 0 ..< tensor.dim.
With axis arangement of [1, 0], this operation is equivalent to tensor.transposed()
func permuted(to axisArangement: [Int]) -> Tensor<Element, Device>
axisArangement Arangement of axes in the resulting tensor.
• Permutes the other tensor along the given axes and adds it to the current tensor in place.
The permutation must have a count of tensor.dim and contain all elements in 0 ..< tensor.dim.
mutating func addingPermuted(_ other: `Self`, permutation: [Int])
other Tensor to add permuted to the current tensor
permutation Desired arangement of axes of the summand.
• Swaps the axes of the tensor.
The axis arangement must have a count of tensor.dim and contain all elements in 0 ..< tensor.dim.
With axis arangement of [1, 0], this operation is equivalent to tensor.transposed()
func permuted(to axisArangement: Int...) -> Tensor<Element, Device>
axisArangement Arangement of axes in the resulting tensor.
• Transposes the given tensor. The tensor must have a dimensionality of 2.
func transposed() -> Tensor<Element, Device>
• Transposes the given tensor. The tensor must have a dimensionality of 2.
var T: `Self` { get }
• Inverts stacking of tensors.
This operation returns a list of tensors that have equal shapes except along the unstacking axis. The number of elements of the source tensor along the unstacking axis must be equal to the sum of
func unstacked(along axis: Int, withLengths lengths: [Int]) -> [`Self`]
axis Axis to unstack along.
lengths Number of elements along the unstacking axis of the resulting tensors
• Stacks the given tensors into a new tensor.
The tensors must have equal shapes except along the stacking axis.
init(stacking tensors: [`Self`], along axis: Int = 0)
tensors Tensors to stack
axis Axis to stack the tensors along.
• Gets or sets a subtensor at the given index.
When an element of the index is nil, all elements along the corresponding axis are read or written.
let a = Tensor<Float, CPU>([[1, 2, 3], [4, 5, 6]])
print(a[nil, 1]) // [2, 5]
print(a[1]) // [4, 5, 6]
print(a[1, nil] == a[1]) // true
subscript(index: [Int?]) -> `Self` { get set }
• Gets or sets a subtensor at the given index.
When an element of the index is nil, all elements along the corresponding axis are read or written.
let a = Tensor<Float, CPU>([[1, 2, 3], [4, 5, 6]])
print(a[nil, 1]) // [2, 5]
print(a[1]) // [4, 5, 6]
print(a[1, nil] == a[1]) // true
subscript(index: Int?...) -> `Self` { get set }
• Gets or sets a subtensor at the given window.
When an element of the index is nil, all elements along the corresponding axis are read or written.
let a = Tensor<Float, CPU>([[1, 2, 3], [4, 5, 6]])
print(a[0 ..< 2]) // [[1, 2], [4, 5]]
print(a[nil, 0 ..< 1]) // [[1, 2, 3]]
subscript(index: [Range<Int>?]) -> `Self` { get set }
• Gets or sets a subtensor at the given window.
When an element of the index is nil, all elements along the corresponding axis are read or written.
let a = Tensor<Float, CPU>([[1, 2, 3], [4, 5, 6]])
print(a[0 ..< 2]) // [[1, 2], [4, 5]]
print(a[nil, 0 ..< 1]) // [[1, 2, 3]]
subscript(index: Range<Int>?...) -> `Self` { get set }
• Element-wise exponentiates the tensor
func exp() -> Tensor<Element, Device>
• Computes the element-wise logarithm of the tensor.
func log() -> Tensor<Element, Device>
• Computes the element-wise hyperbolic tangent of the tensor.
func tanh() -> Tensor<Element, Device>
• Computes the element-wise square root of the tensor.
func sqrt() -> Tensor<Element, Device>
• Computes the element-wise heaviside step function of the tensor.
The heaviside step function is defined as value > 0 ? 1 : 0
func heaviside() -> Tensor<Element, Device>
• Computes the element-wise relu function.
The relu function is defined as max(value, 0)
func rectifiedLinear() -> Tensor<Element, Device>
• Computes the element-wise leaky relu function.
The leaky relu function is defined as max(value, leakage * value)
func leakyRectifiedLinear(leakage: `Self`) -> Tensor<Element, Device>
• Computes the element-wise sigmoid function.
func sigmoid() -> Tensor<Element, Device>
• Computes the softmax function along the given axis. If no axis is provided, the softmax is computed along axis 1.
func softmax(axis: Int = 1) -> Tensor<Element, Device>
• Computes the logarithm of the softmax function along the given axis. If no axis is provided, the softmax is computed along axis 1.
func logSoftmax(axis: Int = 1) -> Tensor<Element, Device>
• Computes the element-wise sine.
func sine() -> Tensor<Element, Device>
• Computes the element-wise cosine.
func cosine() -> Tensor<Element, Device>
• Computes the element-wise GeLU activation
func gaussianErrorLinear() -> Tensor<Element, Device>
• Declaration
func swishActivated(beta: `Self` = 1) -> Tensor<Element, Device>
• Declaration
func mishActivated() -> Tensor<Element, Device>
• Declaration
func lishtActivated() -> Tensor<Element, Device>
• Element-wise exponential linear unit activation
See [Clevert et al. - Fast And Accurate Deep Network Learning By Exponential Linear Units (ELUs)](https://arxiv.org/pdf/1511.07289.pdf
func exponentialLinearActivated(alpha: `Self` = 1) -> Tensor<Element, Device>
alpha Scale applied to exponential part
• Linearly interpolates between the lower and upper bound (both including).
init(linearRampWithLowerBound lowerBound: Element = 0, upperBound: Element, by stride: Element = 1)
lowerBound Start
upperBound End
stride Increment between elements
• Repeats the tensor times times and stacks the result along the 0th axis.
func repeated(_ times: Int) -> Tensor<Element, Device>
times Number of repetitions
• Pads the tensor with the given leading and trailing padding for each axis.
func padded(with value: Element = 0, padding: [(Int, Int)]) -> Tensor<Element, Device>
value Padding value
padding Number of padded elements before and after the tensor.
• Pads the tensor with the given leading and trailing padding for each axis.
func padded(with value: Element = 0, padding: [Int]) -> Tensor<Element, Device>
value Padding value
padding Number of padded elements before and after the tensor.
• Reverses the tensor along the 0th axis.
func reversed() -> Tensor<Element, Device>
• Computes a diagonal matrix with the given number of elements below and above the diagonal. Remaining elements are filled with zeros.
func bandMatrix(belowDiagonal: Int?, aboveDiagonal: Int?) -> Tensor<Element, Device>
belowDiagonal Number of elements below diagonal or nil, if all elements should be copied.
aboveDiagonal Number of elements above the diagonal or nil, if all elements should be copied.
• Computes the vector of diagonal elements of a matrix
Source tensor must have dimensionality of 2. For backpropagation, the matrix must have square shape.
func diagonalElements() -> Tensor<Element, Device>
Return Value
Vector containing matrix diagonal elements
• Computes a matrix that contains the elements of a vector in its diagonal. The remaining elements will be filled with zeros.
The source tensor must have a dimensionality of two. The resulting matrix will have a number of rows and columns equal to number of elements in the vector
func diagonalMatrix() -> Tensor<Element, Device>
Return Value
Square diagonal matrix
• Creates a matrix filled with the given value on its diagonal and zeros everywhere else
init(fillingDiagonalWith value: Element, size: Int, requiresGradient: Bool = false)
value Value to fill diagonal with
size Number of rows and columns of the resulting matrix
requiresGradient Whether to include the tensor in the compute graph for gradient computation
public var description: String { get }
public var debugDescription: String { get }
public init(floatLiteral value: Double)
public init(integerLiteral value: Int)
• Creates a scalar tensor with the given value. The tensor will have a shape of []
init(_ value: Element)
value Value of the tensor.
• Element at the first index in the tensor.
var item: Element { get }
• Creates a tensor value holding the provided scalar. The tensor will have an empty shape.
init(_ e: Element, requiresGradient: Bool = false)
e Element
requiresGradient Whether it is desired to compute gradients of the tensor.
• Creates a tensor with the given shape and fills it with the given array of elements
init(_ v: [[Element]], requiresGradient: Bool = false)
v Values to fill tensor with
requiresGradient Whether it is desired to compute gradients of the tensor.
• Creates a tensor with the given shape and fills it with the given array of elements
init(_ v: [[[Element]]], requiresGradient: Bool = false)
v Values to fill tensor with
requiresGradient Whether it is desired to compute gradients of the tensor.
• Creates a tensor with the given shape and fills it with the given array of elements
init(_ v: [[[[Element]]]], requiresGradient: Bool = false)
v Values to fill tensor with
requiresGradient Whether it is desired to compute gradients of the tensor.
• Creates a tensor with the given shape and fills it with the given array of elements
init(_ v: [[[[[Element]]]]], requiresGradient: Bool = false)
v Values to fill tensor with
requiresGradient Whether it is desired to compute gradients of the tensor.
• Declaration
init(bernoulliDistributedWithShape shape: [Int], probability: Float, requiresGradient: Bool = false)
• Declaration
init(bernoulliDistributedWithShape shape: Int..., probability: Float, requiresGradient: Bool = false)
• Declaration
var elements: [Element] { get }
• Indicates whether any element of the tensor is not a number.
var containsNaN: Bool { get }
• Indicates whether all elements of the tensor are finite.
var isFinite: Bool { get }
• Creates a tensor from the given CGImage
init?(_ image: CGImage, normalizedTo range: ClosedRange<Element> = 0 ... 1)
image Image
range Range to normalize pixel values to
• Declaration
func cgImage(normalizeFrom tensorRange: ClosedRange<Element> = 0 ... 1) -> CGImage?
• Creates a tensor from the given NSImage
init?(_ image: NSImage, normalizedTo range: ClosedRange<Element> = 0 ... 1)
image Image
range Range to normalize pixel values to
• One-hot encodes a tensor of indices
func oneHotEncoded<Target>(dim: Int, type: Target.Type = Target.self) -> Tensor<Target, Device> where Target : NumericType
dim Size of encoding axis. max(tensor) must be less than dim.
type Data type of the result.
public static func == (lhs: `Self`, rhs: `Self`) -> Bool
• Creates a tensor and fills it with random values sampled from a normal distribution with mean 0 and standard deviation sqrt(2 / shape[0]).
init(xavierNormalWithShape shape: [Int], requiresGradient: Bool = false)
shape Shape of the tensor, must be two dimensional
requiresGradient Whether it is desired to compute gradients of the tensor.
• Creates a tensor and fills it with random values sampled from a normal distribution with mean 0 and standard deviation sqrt(2 / shape[0]).
init(xavierNormalWithShape shape: Int..., requiresGradient: Bool = false)
shape Shape of the tensor, must be two dimensional
requiresGradient Whether it is desired to compute gradients of the tensor.
• Creates a tensor and fills it with random values sampled from a normal distribution with the given mean and variance.
init(normalDistributedWithShape shape: [Int], mean: Element = 0, stdev: Element = 1, requiresGradient: Bool = false)
shape Shape of the tensor, must be two dimensional
mean Mean of the normal distribution.
stdev Standard deviation of the normal distribution
requiresGradient Whether it is desired to compute gradients of the tensor.
• Creates a tensor and fills it with random values sampled from a normal distribution with the given mean and variance.
init(normalDistributedWithShape shape: Int..., mean: Element = 0, stdev: Element = 1, requiresGradient: Bool = false)
shape Shape of the tensor, must be two dimensional
mean Mean of the normal distribution.
stdev Standard deviation of the normal distribution
requiresGradient Whether it is desired to compute gradients of the tensor.
• Creates a tensor and fills it with random values sampled from a uniform distribution with the given minimum and maximum.
init(uniformlyDistributedWithShape shape: [Int], min: Element = 0, max: Element = 1, requiresGradient: Bool = false)
shape Shape of the tensor, must be two dimensional
min Minimum value of the uniform distribution
max Maximum value of the uniform distribution
requiresGradient Whether it is desired to compute gradients of the tensor.
• Creates a tensor and fills it with random values sampled from a uniform distribution with the given minimum and maximum.
init(uniformlyDistributedWithShape shape: Int..., min: Element = 0, max: Element = 1, requiresGradient: Bool = false)
shape Shape of the tensor, must be two dimensional
min Minimum value of the uniform distribution
max Maximum value of the uniform distribution
requiresGradient Whether it is desired to compute gradients of the tensor.
public init(from decoder: Decoder) throws
public func encode(to encoder: Encoder) throws | {"url":"https://palle-k.github.io/DL4S/Structs/Tensor.html","timestamp":"2024-11-06T12:32:54Z","content_type":"text/html","content_length":"358409","record_id":"<urn:uuid:5f58a6e0-29da-432e-934e-f238fe21ec80>","cc-path":"CC-MAIN-2024-46/segments/1730477027928.77/warc/CC-MAIN-20241106100950-20241106130950-00297.warc.gz"} |
Add and Subtract Blocks
Addition and Subtraction
Addition and subtraction are similar algorithms. Taking a look at subtraction, we can see that:
Using this simple relationship, we can see that addition and subtraction can be performed using the same hardware. Using this setup, however, care must be taken to invert the value of the second
operand if we are performing subtraction. Note also that in twos-compliment arithmetic, the value of the second operand must not only be inverted, but 1 must be added to it. For this reason, when
performing subtraction, the carry input into the LSB should be a 1 and not a zero.
Our goal on this page, then, is to find suitable hardware for performing addition.
Bit Adders
Half Adder
A half adder is a circuit that performs binary addition on two bits. A half adder does not explicitly account for a carry input signal.
In verilog, a half-adder can be implemented as follows:
module half_adder(a, b, c, s);
input a, b;
output s, c;
s = a ^ b;
c = a & b;
Full Adder
Full adder circuits are similar to the half-adder, except that they do account for a carry input and a carry output. Full adders can be treated as a 3-bit adder with a 2-bit result, or they can be
treated as a single stage (a 3:2 compressor) in a larger adder.
As can be seen below, the number of gate delays in a full-adder circuit is 3:
We can use verilog to implement a full adder module:
module full_adder(a, b, cin, cout, s);
input a, b, cin;
output cout, s;
wire temp;
temp = a ^ b;
s = temp ^ cin;
cout = (cin & temp) | (a & b);
Serial Adder[edit]
A serial adder is a kind of ALU that calculates each bit of the output, one at a time, re-using one full adder (total). This image shows a 2-bit serial adder, and the associated waveforms.
Serial adders have the benefit that they require the least amount of hardware of all adders, but they suffer by being the slowest.
Parallel Adder
A parallel adder is a kind of ALU that calculates every bit of the output more or less simultaneously, using one full adder for each output bit. The 1947 Whirlwind computer was the first computer to
use a parallel adder.
In many CPUs, the CPU latches the final carry-out of the parallel adder in an external "carry flag" in a "status register".
In a few CPUs, the latched value of the carry flag is always wired to the first carry-in of the parallel adder; this gives "Add with carry" with 2s' complement addition. (In a very few CPUs, an
end-around carry -- the final carry-out of the parallel adder is directly connected to the first carry-in of the same parallel adder -- gives 1's complement addition).
Ripple Carry Adder
Numbers of more than 1 bit long require more then just a single full adder to manipulate using arithmetic and bitwise logic instructions^[citation needed]. A simple way of operating on larger numbers
is to cascade a number of full-adder blocks together into a ripple-carry adder, seen above. Ripple Carry adders are so called because the carry value "ripples" from one block to the next, down the
entire chain of full adders. The output values of the higher-order bits are not correct, and the arithmetic is not complete, until the carry signal has completely propagated down the chain of full
If each full adder requires 3 gate delays for computation, then an n-bit ripple carry adder will require 3n gate delays. For 32 or 64 bit computers (or higher) this delay can be overwhelmingly large.
Ripple carry adders have the benefit that they require the least amount of hardware of all adders (except for serial adders), but they suffer by being the slowest (except for serial adders).
With the full-adder verilog module we defined above, we can define a 4-bit ripple-carry adder in Verilog. The adder can be expanded logically:
wire [4:0] c;
wire [3:0] s;
full_adder fa1(a[0], b[0], c[0], c[1], s[0]);
full_adder fa2(a[1], b[1], c[1], c[2], s[1]);
full_adder fa3(a[2], b[2], c[2], c[3], s[2]);
full_adder fa4(a[3], b[3], c[3], c[4], s[3]);
At the end of this module, s contains the 4 bit sum, and c[4] contains the final carry out.
This "ripple carry" arrangement makes "add" and "subtract" take much longer than the other operations of an ALU (AND, NAND, shift-left, divide-by-two, etc). A few CPUs use a ripple carry ALU, and
require the programmer to insert NOPs to give the "add" time to settle.^[1] A few other CPUs use a ripple carry adder, and simply set the clock rate slow enough that there is plenty of time for the
carry bits to ripple through the adder. A few CPUs use a ripple carry adder, and make the "add" instruction take more clocks than the "XOR" instruction, in order to give the carry bits more time to
ripple through the adder on an "add", but without unnecessarily slowing down the CPU during a "XOR". However, it makes pipelining much simpler if every instruction takes the same number of clocks to
Carry Skip Adder
Carry Lookahead Adder
Carry-lookahead adders use special "look ahead" blocks to compute the carry from a group of 4 full-adders, and passes this carry signal to the next group of 4 full adders. Lookahead units can also be
cascaded, to minimize the number of gate delays to completely propagate the carry signal to the end of the chain. Carry lookahead adders are some of the fastest adder circuits available, but they
suffer from requiring large amounts of hardware to implement. The number of transistors needed to implement a carry-lookahead adder is proportional to the number of inputs cubed.
The addition of two 1-digit inputs A and B is said to generate if the addition will always carry, regardless of whether there is an input carry (equivalently, regardless of whether any less
significant digits in the sum carry). For example, in the decimal addition 52 + 67, the addition of the tens digits 5 and 6 generates because the result carries to the hundreds digit regardless of
whether the ones digit carries (in the example, the ones digit clearly does not carry).
In the case of binary addition, $A+B$ generates if and only if both A and B are 1. If we write $G(A,B)$ to represent the binary predicate that is true if and only if $A+B$ generates, we have:
$G(A,B)=A\cdot B$
The addition of two 1-digit inputs A and B is said to propagate if the addition will carry whenever there is an input carry (equivalently, when the next less significant digit in the sum carries).
For example, in the decimal addition 37 + 62, the addition of the tens digits 3 and 6 propagate because the result would carry to the hundreds digit if the ones were to carry (which in this example,
it does not). Note that propagate and generate are defined with respect to a single digit of addition and do not depend on any other digits in the sum.
In the case of binary addition, $A+B$ propagates if and only if at least one of A or B is 1. If we write $P(A,B)$ to represent the binary predicate that is true if and only if $A+B$ propagates, we
Cascading Adders
The power of carry-lookahead adders is that the bit-length of the adder can be expanded without increasing the propagation delay too much. By cascading lookahead modules, and passing "propagate" and
"generate" signals to the next level of the lookahead module. For instance, once we have 4 adders combined into a simple lookahead module, we can use that to create a 16-bit and a 64-bit adder
through cascading:
The 16-Bit carry lookahead unit is exactly the same as the 4-bit carry lookahead adder.
The 64-bit carry lookahead unit is exactly the same as the 4-bit and 16-bit units. This means that once we have designed one carry lookahead module, we can cascade it to any large size.
Generalized Cascading
A generalized CLA block diagram. Each of the turquoise blocks represents a smaller CLA adder.
We can cascade the generalized CLA block above to form a larger CLA block. This larger block can then be cascaded into a larger CLA block using the same method.
Source: Wikibooks, https://en.wikibooks.org/wiki/Microprocessor_Design/Add_and_Subtract_Blocks
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About Linear Algebra | Linear Algebra 2024 Notes
About Linear Algebra
Linear algebra developed as the study of systems of linear equations. It looks at structures which are preserved under the linear operations of addition and multiplication by scalars. In this course
we will introduce vectors and matrices, examine their properties, and see how they can be used to solve systems of linear equations. We will look at how these concepts can be generalised into the
idea of a vector space
Linear algebra has many applications, both in other areas of maths and in other scientific disciplines. For example, we can use concepts and techniques from linear algebra to tell us about the nature
of solutions of certain differential equations, or for linear regression in statistics. It is used extensively in data science, and has many uses in engineering. In this course we will explore linear
algebra in its own right, but will also develop the tools you need for applications in later areas of your degree. | {"url":"https://bookdown.org/rachaelmcarey/lanotes/about-linear-algebra.html","timestamp":"2024-11-06T09:22:24Z","content_type":"text/html","content_length":"19330","record_id":"<urn:uuid:ce6bb3e4-a705-4f91-8576-8dc005f0587e>","cc-path":"CC-MAIN-2024-46/segments/1730477027910.12/warc/CC-MAIN-20241106065928-20241106095928-00356.warc.gz"} |
Official Letter Template for AIMS Students
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%% Template for AIMS Rwanda
Assignments %%% %%% %%% Author: AIMS Rwanda tutors %%% ### %%% %%% Email: tutors2017-18@aims.ac.rw %%% ### %%% %%% Copyright: This template was designed to be used for %%% ####### %%% %%% the
assignments at AIMS Rwanda during the academic year %%% ### %%% %%% 2017-2018. %%% ######### %%% %%% You are free to alter any part of this document for %%% ### ### %%% %%% yourself and for
distribution. %%% ### ### %%% %%% %%% %%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%% Ensure that you do not write the questions before each of the solutions because it is not necessary. %%%%%% \
documentclass[12pt,a4paper]{article} %%%%%%%%%%%%%%%%%%%%%%%%% packages %%%%%%%%%%%%%%%%%%%%%%%% \usepackage{graphicx} \usepackage{tabulary} \usepackage{amsmath} \usepackage{fancyhdr} \usepackage
{amssymb} \usepackage{amsthm} \usepackage{placeins} \usepackage{amsfonts} \usepackage{graphicx} \usepackage[all]{xy} \usepackage{tikz} \usepackage{verbatim} \usepackage[left=2cm,right=2cm,top=
3cm,bottom=2.5cm]{geometry} \usepackage{hyperref} \usepackage{caption} \usepackage{subcaption} \usepackage{multirow} \usepackage{psfrag} \usepackage{comment} %%%%%%%%%%%%%%%%%%%%% students data
%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%% using theorem style %%%%%%%%%%%%%%%%%%%% \newtheorem{thm}{Theorem} \newtheorem{lem}[thm]{Lemma} \newtheorem{defn}[thm]{Definition} \newtheorem{exa}[thm]
{Example} \newtheorem{rem}[thm]{Remark} \newtheorem{coro}[thm]{Corollary} \newtheorem{quest}{Question}[section] %%%%%%%%%%%%%% Shortcut for usual set of numbers %%%%%%%%%%% \newcommand{\N}{\mathbb
{N}} \newcommand{\Z}{\mathbb{Z}} \newcommand{\Q}{\mathbb{Q}} \newcommand{\R}{\mathbb{R}} \newcommand{\C}{\mathbb{C}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5 \begin{document}
%%%%%%%%%%%%%%%%%%%%%%% title page %%%%%%%%%%%%%%%%%%%%%%%%%% \thispagestyle{empty} \begin{center} \includegraphics[scale = 0.8]{AIMS-RW-logo.jpg} %\textbf{AFRICAN INSTITUTE FOR MATHEMATICAL SCIENCES
\\[0.5cm] %(AIMS RWANDA, KIGALI)} \vspace{1.0cm} \end{center} %%%%%%%%%%%%%%%%%%%%% assignment information %%%%%%%%%%%%%%%% \noindent \rule{17cm}{0.2cm}\\[0.3cm] %Name: \student \hfill Assignment
Number: \assignment\\[0.1cm] %Course: \course \hfill Date: \today\\ %\rule{17cm}{0.05cm}\\\\ %\vspace{1.0cm} \\\\\textbf{The Academic Registrar,\\ Makerere University,\\P.O. Box 7062,\\ Kampala.\\\\
$1^{th}/02/2021$}\\\\Dear sir, \section*{RE: DEGREE CERTIFICATE.} I \textbf{AZAMUKE DENISH with registration number: 16/U/171} was awarded a Bachelor of Science degree (Second Class Honours - Upper
division) at the $70^{th}$ Congregation held on $15^{th}$ January, 2020 at Makerere University. I am currently doing my masters in Mathematical Sciences at the African Institute for Mathematical
Sciences - Rwanda.\\\\Am therefore seeking for my \textbf{degree certificate} or \textbf{a further letter} that can be equated to the Rwandan educational standards in order to fulfill the
requirements for my masters degree.\\\\Your response is highly appreciated and will see me finish my masters' studies in time.\\\\\\\\AZAMUKE DENISH\\0789061019\\denish.azamuke@aims.ac.rw \end | {"url":"https://ko.overleaf.com/latex/templates/official-letter-template-for-aims-students/tfnrpbhhgyfn","timestamp":"2024-11-08T17:37:34Z","content_type":"text/html","content_length":"40175","record_id":"<urn:uuid:28660f80-0f11-42b7-b164-1e6b691866ca>","cc-path":"CC-MAIN-2024-46/segments/1730477028070.17/warc/CC-MAIN-20241108164844-20241108194844-00073.warc.gz"} |
Digital Math Resources
Display Title
Definition--Rationals and Radicals--Rational Exponent
Rational Exponent
Rationals and Radicals
A rational exponent is an exponent that is a fraction, where the numerator indicates the power and the denominator indicates the root.
Rational Exponents are a crucial concept in the study of Rational Numbers, Expressions, Equations, and Functions. These exponents are fractions, where the numerator indicates the power and the
denominator indicates the root. For example, the expression
can be rewritten as
Understanding rational exponents is essential for simplifying expressions and solving equations involving exponents. They provide a bridge between radicals and exponents, allowing for more flexible
manipulation of algebraic expressions. Rational exponents are widely used in various fields, including engineering, physics, and computer science, where exponential relationships are common. Mastery
of rational exponents enables students to simplify complex expressions, solve equations, and apply these concepts to real-world problems. Rational exponents also play a significant role in calculus,
where they are used in limits, derivatives, and integrals. By understanding rational exponents, students can better grasp the properties of numbers and their relationships, leading to a deeper
comprehension of mathematical concepts.
For a complete collection of terms related to polynomials click on this link: Rationals and Radicals Collection
Common Core Standards CCSS.MATH.CONTENT.HSA.REI.A.2, CCSS.MATH.CONTENT.HSN.RN.A.1, CCSS.MATH.CONTENT.HSF.IF.C.7
Grade Range 8 - 12
Curriculum Nodes • Rational Expressions and Functions
• Rational Expressions
Copyright Year 2022
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Present Value Calculator: Step-by-Step Solutions - Wolfram|Alpha
Wolfram|Alpha can quickly and easily compute the present value of money, as well as the amount you would need to invest in order to achieve a desired financial goal in the future. Plots are
automatically generated to help you visualize the effect that different interest rates, interest periods or future values could have on your result. | {"url":"https://www.wolframalpha.com/calculators/present-value-calculator","timestamp":"2024-11-03T04:14:54Z","content_type":"text/html","content_length":"68809","record_id":"<urn:uuid:80d8b3e9-fc4b-4805-98c0-f30fa839a118>","cc-path":"CC-MAIN-2024-46/segments/1730477027770.74/warc/CC-MAIN-20241103022018-20241103052018-00501.warc.gz"} |
Possible Topics for 2020 O'level 4047 Additional Math Paper 2
Here are the possible topics to be tested for AMath paper 2 on 26th October
1. Sketch of quadratic functions and Discriminant
2. Surds --> can be real world context or finding unknowns like a, b --> rationalisation of denominator
3. Binomial theorem --> specific term formula, expansion formula, nCr formula
4. Sketching of power functions, parabola, log graphs, exponential graphs, question involving find another straight line equation to be drawn
5. Logarithm equations and simplifying involving log laws
6. Coordinate Geometry --> midpoint formula, m1m2 =-1, length formula, area formula, find equation of line and simultaneous equation, gradient Involving angle.
7. Linear Law - plotting of graph, and/or non-graph question finding m and c, solving unknown.
8. Trigonometry graphs, proving involving double angle, R-formula, Trigo in real world context
9. Differentiation: tangent and normal, rate of change, chain rule or product rule of x functions, ln, functions, trigo functions
10. Integration: reverse of differentiation, finding equation of curve, evaluation of definite integral, x function,1/f(x) functions
11. Simultaneous eqn -- can be problem sum
ALL THE BEST!
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teaching replication
Fear of rejection, part I
To replicate a study, you need information. Probably information that is not fully disclosed in a 6-12,000 word journal article. Except for a recent trend, information such as data and analytical
procedure are not going to be available publicly. This means you should, or must in case the data are not retrievable from some other source, contact the original author. Be prepared for rejection.
One study demonstrated that among the top sociology journals, less than 30% of replication materials were available (even though as many as 75% claimed otherwise). Political science was only
marginally better at around 50% as of 2015. Professors are likely to ignore emails asking for their data and code. One group of sociology students contacted 53 different authors asking for
replication materials and only 15 provided them (28%). Ten never responded to the requests at all, despite several follow up emails. So don’t take it personally, social scientists are not known for
their forthcomingness in this area.
Verification is not affirmation
Imagine being a student who tries to verify the results of a prolific, senior scholar and cannot. If it were me, I would be anxious that I made a mistake. But the only real mistake would be to assume
my lack of verification is a refutation of my own skills. Of course, it’s good to double check everything. Have a colleague look at your work if you are unsure, a teacher or supervisor if you are a
student. Un-verifiable results are common, no need for self-doubt. Things like reverse coding biological sex so that women appear less supportive of welfare state policies or accidentally analyzing
values of 88 (a missing code) as a relevant value of coital frequency leading to a surprising rate for older persons are actually a normal part of social science.
When replicating a study just assume there will be at least one mistake. Like a treasure hunt.
Verification comes down to the availability of the materials. If the data and code are not fully available, it really is a treasure hunt because you will be unsure what you are going to find or
learn. On the other hand, if the data and code are available and in good order, then it is more like cooking than hunting. This often comes down to the difference between teaching replication – the
recipe approach, where students should come to the same results every time when following the exact same steps, and replication as a form of social research – the treasure hunt approach, where
researchers (i.e., students) may not have a coherent recipe from the original ‘chef’. But make no mistake(!) even fully transparent studies often come with mistakes in the code or data.
Fear of mistakes
If I am not making mistakes, I am not doing research. You will make mistakes and there is nothing to fear. There are all kinds of reasons that replication results will diverge, not all of them are
mistakes. Recently a well-known and well-respected sociologist retracted his own paper after someone trying to replicate the study identified coding errors. One journal started checking that data and
code produced results in accepted papers, and almost none were verifiable on the first attempt. In a crowdsourced replication, mostly PhD students, postdocs and a few professors came to an exact
verification of the original study only 82% of the time, despite having the original code!
Fear of the unknown
Designing statistical models using a software is like learning a new language. Student replications often involve methods unfamiliar to the them. This is a great didactic tool – learning by doing.
There is nothing to fear here. Professors’ original studies often involve methods that they are not experts in. One extremely famous scholar and his colleague ran a regression with an interaction
term in it and botched the interpretation of the effects, the results were basically the opposite of what they reported.
Science is a process of exploring the unknown. Replications use what is known as a tool for finding what is unknown.
Fear of rejection, Part II
Students may be interested in publishing their replications, they should be, because how else will others put their knowledge into practical use? Get prepared again for rejection. Journals and
reviewers across the social sciences are not very excited about replications. A pair of researchers studied the instructions and aims of 1,151 psychology journals in 2016 and discovered that only 3%
explicitly accepted replications. One sociologist pointed out not so long ago that replication is just not the norm in sociology, and another one recently came to the same conclusion. The good news
is that we don’t need journals anymore to make useful science, at least in theory. Students can immediately publish their results as preprints and share data and code in a public repository. If a
student elects to use Open Science Framework preprint servers, their work will be immediately found in scholarly search engines.
Fear of ego
Scientists tend to overestimate the impact of a negative replication on their reputations. Ego-alert. Assume a scientist worried about a replication is a professor. This is a person who is most like
tenured, certainly the highly cited professors are. This is also a person who “professes” knowledge on a topic, meaning that they should be an expert and engage in teaching students, policymakers,
the public and really anyone interested about this topic. If any of this professor’s results were shown to be unreliable or false, this would be a critical piece of information if that professor’s
goal was to actually profess knowledge on that topic. Unfortunately, professors regularly suffer from some kind of ‘rock-star syndrome’ or ego-mania where they are doing science as a means to get
recognition and fame. This leads them to react aggressively against anything that contradicts them. This is very bad for science. If a student replicator can help deplete a runaway professor ego
through replication, then that student is doing a great service to science.
Fear of not addressing fear
In a typical primary or secondary school chemistry class, students repeat the basic experiments of chemical reactions that have been done for hundreds of years. These students are learning through
replication. They are gaining knowledge in a way that cannot be simply taught in a lecture or by reading a book. They are also affirming the act of science, thus developing a faith that science
works. In social science especially, we face a reliability crisis if not a public image crisis. Students should be reassured that there is a repetitive and reliable nature to doing social science,
whether they will continue as a social scientist or (in the most likely case) not. Part of this reliability can be a lack of reliability. Science is simply a process of trying to understand the
unknown, and even quantify this unknown. I fear that without more student replications, we are diminishing the value of social science and contributing to the perception that social science is
Good social science should be reliably able to identify unreliability, and this is best taught through conducting replications. | {"url":"https://crowdid.hypotheses.org/tag/teaching-replication","timestamp":"2024-11-14T01:33:41Z","content_type":"text/html","content_length":"75140","record_id":"<urn:uuid:363a3728-2756-494c-9797-b7597d5544c4>","cc-path":"CC-MAIN-2024-46/segments/1730477028516.72/warc/CC-MAIN-20241113235151-20241114025151-00696.warc.gz"} |
American Mathematical Society
Quantisation of presymplectic manifolds, $K$-theory and group representations
HTML articles powered by AMS MathViewer
by Peter Hochs
Proc. Amer. Math. Soc. 143 (2015), 2675-2692
DOI: https://doi.org/10.1090/S0002-9939-2015-12464-1
Published electronically: January 21, 2015
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Let $G$ be a semisimple Lie group with finite component group, and let $K<G$ be a maximal compact subgroup. We obtain a quantisation commutes with reduction result for actions by $G$ on manifolds of
the form $M = G\times _K N$, where $N$ is a compact prequantisable Hamiltonian $K$-manifold. The symplectic form on $N$ induces a closed two-form on $M$, which may be degenerate. We therefore work
with presymplectic manifolds, where we take a presymplectic form to be a closed two-form. For complex semisimple groups and semisimple groups with discrete series, the main result reduces to results
with a more direct representation theoretic interpretation. The result for the discrete series is a generalised version of an earlier result by the author. In addition, the generators of the
$K$-theory of the $C^*$-algebra of a semisimple group are realised as quantisations of fibre bundles over suitable coadjoint orbits. References
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• Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 53D50, 19K56, 22D25
• Retrieve articles in all journals with MSC (2010): 53D50, 19K56, 22D25
Bibliographic Information
• Peter Hochs
• Affiliation: School of Mathematical Sciences, North Terrace Campus, The University of Adelaide, Adelaide SA 5005, Australia
• MR Author ID: 786204
• ORCID: 0000-0001-9232-2936
• Email: peter.hochs@adelaide.edu.au
• Received by editor(s): November 12, 2012
• Received by editor(s) in revised form: November 6, 2013, and January 24, 2014
• Published electronically: January 21, 2015
• Communicated by: Varghese Mathai
• © Copyright 2015 American Mathematical Society
• Journal: Proc. Amer. Math. Soc. 143 (2015), 2675-2692
• MSC (2010): Primary 53D50; Secondary 19K56, 22D25
• DOI: https://doi.org/10.1090/S0002-9939-2015-12464-1
• MathSciNet review: 3326046 | {"url":"https://www.ams.org/journals/proc/2015-143-06/S0002-9939-2015-12464-1/home.html","timestamp":"2024-11-09T20:56:21Z","content_type":"text/html","content_length":"84185","record_id":"<urn:uuid:5a32be2d-b375-4eda-adcf-07c3a5b11f40>","cc-path":"CC-MAIN-2024-46/segments/1730477028142.18/warc/CC-MAIN-20241109182954-20241109212954-00324.warc.gz"} |
7.1. Toy datasets
7.1. Toy datasets#
scikit-learn comes with a few small standard datasets that do not require to download any file from some external website.
They can be loaded using the following functions:
load_iris(*[, return_X_y, as_frame]) Load and return the iris dataset (classification).
load_diabetes(*[, return_X_y, as_frame, scaled]) Load and return the diabetes dataset (regression).
load_digits(*[, n_class, return_X_y, as_frame]) Load and return the digits dataset (classification).
load_linnerud(*[, return_X_y, as_frame]) Load and return the physical exercise Linnerud dataset.
load_wine(*[, return_X_y, as_frame]) Load and return the wine dataset (classification).
load_breast_cancer(*[, return_X_y, as_frame]) Load and return the breast cancer wisconsin dataset (classification).
These datasets are useful to quickly illustrate the behavior of the various algorithms implemented in scikit-learn. They are however often too small to be representative of real world machine
learning tasks.
7.1.1. Iris plants dataset#
Data Set Characteristics:
Number of Instances:
150 (50 in each of three classes)
Number of Attributes:
4 numeric, predictive attributes and the class
Attribute Information:
□ sepal length in cm
□ sepal width in cm
□ petal length in cm
□ petal width in cm
○ Iris-Setosa
○ Iris-Versicolour
○ Iris-Virginica
Summary Statistics:
sepal length: 4.3 7.9 5.84 0.83 0.7826
sepal width: 2.0 4.4 3.05 0.43 -0.4194
petal length: 1.0 6.9 3.76 1.76 0.9490 (high!)
petal width: 0.1 2.5 1.20 0.76 0.9565 (high!)
Missing Attribute Values:
Class Distribution:
33.3% for each of 3 classes.
R.A. Fisher
Michael Marshall (MARSHALL%PLU@io.arc.nasa.gov)
July, 1988
The famous Iris database, first used by Sir R.A. Fisher. The dataset is taken from Fisher’s paper. Note that it’s the same as in R, but not as in the UCI Machine Learning Repository, which has two
wrong data points.
This is perhaps the best known database to be found in the pattern recognition literature. Fisher’s paper is a classic in the field and is referenced frequently to this day. (See Duda & Hart, for
example.) The data set contains 3 classes of 50 instances each, where each class refers to a type of iris plant. One class is linearly separable from the other 2; the latter are NOT linearly
separable from each other.
• Fisher, R.A. “The use of multiple measurements in taxonomic problems” Annual Eugenics, 7, Part II, 179-188 (1936); also in “Contributions to Mathematical Statistics” (John Wiley, NY, 1950).
• Duda, R.O., & Hart, P.E. (1973) Pattern Classification and Scene Analysis. (Q327.D83) John Wiley & Sons. ISBN 0-471-22361-1. See page 218.
• Dasarathy, B.V. (1980) “Nosing Around the Neighborhood: A New System Structure and Classification Rule for Recognition in Partially Exposed Environments”. IEEE Transactions on Pattern Analysis
and Machine Intelligence, Vol. PAMI-2, No. 1, 67-71.
• Gates, G.W. (1972) “The Reduced Nearest Neighbor Rule”. IEEE Transactions on Information Theory, May 1972, 431-433.
• See also: 1988 MLC Proceedings, 54-64. Cheeseman et al”s AUTOCLASS II conceptual clustering system finds 3 classes in the data.
• Many, many more …
7.1.2. Diabetes dataset#
Ten baseline variables, age, sex, body mass index, average blood pressure, and six blood serum measurements were obtained for each of n = 442 diabetes patients, as well as the response of interest, a
quantitative measure of disease progression one year after baseline.
Data Set Characteristics:
Number of Instances:
Number of Attributes:
First 10 columns are numeric predictive values
Column 11 is a quantitative measure of disease progression one year after baseline
Attribute Information:
□ age age in years
□ sex
□ bmi body mass index
□ bp average blood pressure
□ s1 tc, total serum cholesterol
□ s2 ldl, low-density lipoproteins
□ s3 hdl, high-density lipoproteins
□ s4 tch, total cholesterol / HDL
□ s5 ltg, possibly log of serum triglycerides level
□ s6 glu, blood sugar level
Note: Each of these 10 feature variables have been mean centered and scaled by the standard deviation times the square root of n_samples (i.e. the sum of squares of each column totals 1).
Source URL: https://www4.stat.ncsu.edu/~boos/var.select/diabetes.html
For more information see: Bradley Efron, Trevor Hastie, Iain Johnstone and Robert Tibshirani (2004) “Least Angle Regression,” Annals of Statistics (with discussion), 407-499. (https://
7.1.3. Optical recognition of handwritten digits dataset#
Data Set Characteristics:
Number of Instances:
Number of Attributes:
Attribute Information:
8x8 image of integer pixels in the range 0..16.
Missing Attribute Values:
5. Alpaydin (alpaydin ‘@’ boun.edu.tr)
July; 1998
This is a copy of the test set of the UCI ML hand-written digits datasets https://archive.ics.uci.edu/ml/datasets/Optical+Recognition+of+Handwritten+Digits
The data set contains images of hand-written digits: 10 classes where each class refers to a digit.
Preprocessing programs made available by NIST were used to extract normalized bitmaps of handwritten digits from a preprinted form. From a total of 43 people, 30 contributed to the training set and
different 13 to the test set. 32x32 bitmaps are divided into nonoverlapping blocks of 4x4 and the number of on pixels are counted in each block. This generates an input matrix of 8x8 where each
element is an integer in the range 0..16. This reduces dimensionality and gives invariance to small distortions.
For info on NIST preprocessing routines, see M. D. Garris, J. L. Blue, G. T. Candela, D. L. Dimmick, J. Geist, P. J. Grother, S. A. Janet, and C. L. Wilson, NIST Form-Based Handprint Recognition
System, NISTIR 5469, 1994.
• C. Kaynak (1995) Methods of Combining Multiple Classifiers and Their Applications to Handwritten Digit Recognition, MSc Thesis, Institute of Graduate Studies in Science and Engineering, Bogazici
5. Alpaydin, C. Kaynak (1998) Cascading Classifiers, Kybernetika.
• Ken Tang and Ponnuthurai N. Suganthan and Xi Yao and A. Kai Qin. Linear dimensionalityreduction using relevance weighted LDA. School of Electrical and Electronic Engineering Nanyang Technological
University. 2005.
• Claudio Gentile. A New Approximate Maximal Margin Classification Algorithm. NIPS. 2000.
7.1.4. Linnerrud dataset#
Data Set Characteristics:
Number of Instances:
Number of Attributes:
Missing Attribute Values:
The Linnerud dataset is a multi-output regression dataset. It consists of three exercise (data) and three physiological (target) variables collected from twenty middle-aged men in a fitness club:
physiological - CSV containing 20 observations on 3 physiological variables:
Weight, Waist and Pulse.
exercise - CSV containing 20 observations on 3 exercise variables:
Chins, Situps and Jumps.
• Tenenhaus, M. (1998). La regression PLS: theorie et pratique. Paris: Editions Technic.
7.1.5. Wine recognition dataset#
Data Set Characteristics:
Number of Instances:
Number of Attributes:
13 numeric, predictive attributes and the class
Attribute Information:
□ Alcohol
□ Malic acid
□ Ash
□ Alcalinity of ash
□ Magnesium
□ Total phenols
□ Flavanoids
□ Nonflavanoid phenols
□ Proanthocyanins
□ Color intensity
□ Hue
□ OD280/OD315 of diluted wines
□ Proline
Summary Statistics:
Alcohol: 11.0 14.8 13.0 0.8
Malic Acid: 0.74 5.80 2.34 1.12
Ash: 1.36 3.23 2.36 0.27
Alcalinity of Ash: 10.6 30.0 19.5 3.3
Magnesium: 70.0 162.0 99.7 14.3
Total Phenols: 0.98 3.88 2.29 0.63
Flavanoids: 0.34 5.08 2.03 1.00
Nonflavanoid Phenols: 0.13 0.66 0.36 0.12
Proanthocyanins: 0.41 3.58 1.59 0.57
Colour Intensity: 1.3 13.0 5.1 2.3
Hue: 0.48 1.71 0.96 0.23
OD280/OD315 of diluted wines: 1.27 4.00 2.61 0.71
Proline: 278 1680 746 315
Missing Attribute Values:
Class Distribution:
class_0 (59), class_1 (71), class_2 (48)
R.A. Fisher
Michael Marshall (MARSHALL%PLU@io.arc.nasa.gov)
July, 1988
This is a copy of UCI ML Wine recognition datasets. https://archive.ics.uci.edu/ml/machine-learning-databases/wine/wine.data
The data is the results of a chemical analysis of wines grown in the same region in Italy by three different cultivators. There are thirteen different measurements taken for different constituents
found in the three types of wine.
Original Owners:
Forina, M. et al, PARVUS - An Extendible Package for Data Exploration, Classification and Correlation. Institute of Pharmaceutical and Food Analysis and Technologies, Via Brigata Salerno, 16147
Genoa, Italy.
Lichman, M. (2013). UCI Machine Learning Repository [https://archive.ics.uci.edu/ml]. Irvine, CA: University of California, School of Information and Computer Science.
(1) S. Aeberhard, D. Coomans and O. de Vel, Comparison of Classifiers in High Dimensional Settings, Tech. Rep. no. 92-02, (1992), Dept. of Computer Science and Dept. of Mathematics and Statistics,
James Cook University of North Queensland. (Also submitted to Technometrics).
The data was used with many others for comparing various classifiers. The classes are separable, though only RDA has achieved 100% correct classification. (RDA : 100%, QDA 99.4%, LDA 98.9%, 1NN 96.1%
(z-transformed data)) (All results using the leave-one-out technique)
(2) S. Aeberhard, D. Coomans and O. de Vel, “THE CLASSIFICATION PERFORMANCE OF RDA” Tech. Rep. no. 92-01, (1992), Dept. of Computer Science and Dept. of Mathematics and Statistics, James Cook
University of North Queensland. (Also submitted to Journal of Chemometrics).
7.1.6. Breast cancer wisconsin (diagnostic) dataset#
Data Set Characteristics:
Number of Instances:
Number of Attributes:
30 numeric, predictive attributes and the class
Attribute Information:
□ radius (mean of distances from center to points on the perimeter)
□ texture (standard deviation of gray-scale values)
□ perimeter
□ area
□ smoothness (local variation in radius lengths)
□ compactness (perimeter^2 / area - 1.0)
□ concavity (severity of concave portions of the contour)
□ concave points (number of concave portions of the contour)
□ symmetry
□ fractal dimension (“coastline approximation” - 1)
The mean, standard error, and “worst” or largest (mean of the three worst/largest values) of these features were computed for each image, resulting in 30 features. For instance, field 0 is Mean
Radius, field 10 is Radius SE, field 20 is Worst Radius.
○ WDBC-Malignant
○ WDBC-Benign
Summary Statistics:
radius (mean): 6.981 28.11
texture (mean): 9.71 39.28
perimeter (mean): 43.79 188.5
area (mean): 143.5 2501.0
smoothness (mean): 0.053 0.163
compactness (mean): 0.019 0.345
concavity (mean): 0.0 0.427
concave points (mean): 0.0 0.201
symmetry (mean): 0.106 0.304
fractal dimension (mean): 0.05 0.097
radius (standard error): 0.112 2.873
texture (standard error): 0.36 4.885
perimeter (standard error): 0.757 21.98
area (standard error): 6.802 542.2
smoothness (standard error): 0.002 0.031
compactness (standard error): 0.002 0.135
concavity (standard error): 0.0 0.396
concave points (standard error): 0.0 0.053
symmetry (standard error): 0.008 0.079
fractal dimension (standard error): 0.001 0.03
radius (worst): 7.93 36.04
texture (worst): 12.02 49.54
perimeter (worst): 50.41 251.2
area (worst): 185.2 4254.0
smoothness (worst): 0.071 0.223
compactness (worst): 0.027 1.058
concavity (worst): 0.0 1.252
concave points (worst): 0.0 0.291
symmetry (worst): 0.156 0.664
fractal dimension (worst): 0.055 0.208
Missing Attribute Values:
Class Distribution:
212 - Malignant, 357 - Benign
Dr. William H. Wolberg, W. Nick Street, Olvi L. Mangasarian
Nick Street
November, 1995
This is a copy of UCI ML Breast Cancer Wisconsin (Diagnostic) datasets. https://goo.gl/U2Uwz2
Features are computed from a digitized image of a fine needle aspirate (FNA) of a breast mass. They describe characteristics of the cell nuclei present in the image.
Separating plane described above was obtained using Multisurface Method-Tree (MSM-T) [K. P. Bennett, “Decision Tree Construction Via Linear Programming.” Proceedings of the 4th Midwest Artificial
Intelligence and Cognitive Science Society, pp. 97-101, 1992], a classification method which uses linear programming to construct a decision tree. Relevant features were selected using an exhaustive
search in the space of 1-4 features and 1-3 separating planes.
The actual linear program used to obtain the separating plane in the 3-dimensional space is that described in: [K. P. Bennett and O. L. Mangasarian: “Robust Linear Programming Discrimination of Two
Linearly Inseparable Sets”, Optimization Methods and Software 1, 1992, 23-34].
This database is also available through the UW CS ftp server:
ftp ftp.cs.wisc.edu cd math-prog/cpo-dataset/machine-learn/WDBC/
• W.N. Street, W.H. Wolberg and O.L. Mangasarian. Nuclear feature extraction for breast tumor diagnosis. IS&T/SPIE 1993 International Symposium on Electronic Imaging: Science and Technology, volume
1905, pages 861-870, San Jose, CA, 1993.
• O.L. Mangasarian, W.N. Street and W.H. Wolberg. Breast cancer diagnosis and prognosis via linear programming. Operations Research, 43(4), pages 570-577, July-August 1995.
• W.H. Wolberg, W.N. Street, and O.L. Mangasarian. Machine learning techniques to diagnose breast cancer from fine-needle aspirates. Cancer Letters 77 (1994) 163-171. | {"url":"https://scikit-learn.org/dev/datasets/toy_dataset.html","timestamp":"2024-11-06T02:45:18Z","content_type":"text/html","content_length":"65120","record_id":"<urn:uuid:674537f0-20aa-4610-b609-666aefbb9b8f>","cc-path":"CC-MAIN-2024-46/segments/1730477027906.34/warc/CC-MAIN-20241106003436-20241106033436-00175.warc.gz"} |
Pascal’s Triangle and Various Patterns Related to it - Life in lines
Pascal’s triangle is one of the very famous triangles that follows a specific set of sequences. It is used in the representation of binomial coefficients in the form of a triangle. It was discovered
by the very famous French mathematician, Blaise Pascal. The arrangement of numbers in this triangle is unique as each number in the triangle is placed in such a manner that each number is the
summation of two numbers just above the number. There are many real-life applications of Pascal’s triangle. We use this unique type of triangle and its features widely in the concepts of algebra,
combinations, probability theory, and so on. In this article, we will discuss the various patterns which this triangle shows along with discussing some examples related to the concept.
Various Patterns that Pascal’s Triangle Exhibit
There are a number of patterns that we can see clearly in Pascal’s triangle. These patterns were observed and brought to the notice by Blaise Pascal himself. Some of these patterns are discussed
• The summation of the different values of the nth row of Pascal’s triangle is. Let us take an example to understand this pattern clearly. In the 4th row of Pascal’s triangle, we have the following
numbers: 1, 4, 6, 4, and 1. Now, when we summate all these numbers, we get 1 + 4 + 6 + 4 + 1 = 16 which is equivalent to which is 16.
• The other pattern that we have in Pascal’s triangle is related to the prime numbers. If in Pascal’s triangle, the second element of any given row is a prime number, then all the elements related
to that particular row are divisible by that prime number. Here, we will not consider the value 1. Let us take an example to understand this pattern clearly. In the 5th row of Pascal’s triangle,
we have the following numbers: 1, 5, 10, 10, 5, and 1. We can clearly see that the second element of the 5th row of Pascal’s triangle is 5 which is a prime number. Now, we can easily divide the
remaining numbers which in this case is 10,10 with the prime number 5. Here, we will not take into consideration the number 1.
• We can obtain the famous Fibonacci series if we add different diagonal elements of Pascal’s triangle.
History of the Pascal’s Triangle
It is very interesting to note that the pattern of numbers used in the forming of Pascal’s triangle was known even before Blaise Pascal was born. In the 2nd Century BC, a famous Indian mathematician
called Acharya Pingala started the discussion of these numbers while studying the concepts of combinatorics and binomial numbers. A famous Persian mathematician called Al- Karaji also contributed to
the discovery of this unique triangle. He had written a book that contained the very first description of Pascal’s triangle. Unfortunately, this book has been lost. We can see many developments of
this concept in China also. In 1655, a Treatise on Arithmetical Triangle was published in which Pascal collected several results and came to a final conclusion.
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DAX Optimization: Where To Find The Hidden DAX Trap
I want to focus today on something I call the hidden DAX trap. If you encounter this situation, it will make you feel like you’re losing your mind because your DAX is going to look right, but it’s
not going to work. I’ll walk you through when that occurs and what you can do about it, and in the process, also talk about some general DAX optimization best practices. You can watch the full video
of this tutorial at the bottom of this blog.
Let’s first take a look at what we’re working with here. We have about 10 years of data from the Internet Movie Database. The fact tables are pretty simple, and we have rating data, budget data, and
gross data.
Today, we’ll be looking at worldwide grosses.
We also have our extended date table. This is going to be a time intelligence analysis based on the date table and the fact table.
Total Worldwide Gross Per Year
We want to do something really common and simple. Our Total Worldwide Gross is just a very simple aggregate sum measure, which we want to convert into a percentage.
To do this, we take the numerator (Total Worldwide Gross measure) and the denominator (Total Worldwide Gross measure, but removed the context from the year filter).
I used the REMOVEFILTERS function because I think it’s more intuitive when you read the code, but if you prefer the ALL function, that works just as well. We just divide the numerator by the
denominator to get the result.
If we take the resulting measure and drop it into our table, you’ll see that it does exactly what we expect it to do. We get 100% at the bottom and we get the years converted into their individual
percentages. So far so good, and we haven’t encountered any problems yet.
Total Worldwide Gross Per Quarter
Let’s take a look at a similar situation where we go by quarter. This measure could be useful because there is the hypotheses that grosses from the summer movie season is different from the beginning
of the year, and toward the end of the year leading to the Oscar season.
Again, we have the exact same measure with the REMOVEFILTERS function on the quarter numbers instead of the year.
And if we drop the measure we just made into the table, it also does exactly what we expect.
Total Worldwide Gross Per Month & Year
Let’s take a look at the third case, which can be really common, where we want to look by month and year.
And again, we’ll use the same measure as before. But this time, we’ll remove the filter on month and year.
Let’s drop that one into our table. All of a sudden it doesn’t work.
We can tell what’s not working about it. We know that the Worldwide Gross measure works, so that means that the numerator is fine, but the denominator isn’t. In each of the previous cases, the
REMOVEFILTERS function removed the filter properly, but in here, it clearly did not.
We can actually test this out by changing what we returned here in the result.
Instead of Result, let’s use Denominator. Keep in mind that this is going to be formatted in a percentage so it’s going to look a little funny.
What we should be getting for the denominator is the same number in every row, but it’s not.
We can tell it’s not removing the filter on month and year, and think it’s because the Month & Year is in text.
But the previous one for quarter was also expressed in text, so it’s not simply because its text. It only needs to be sorted out. Once you drop the field without sorting it, it’s going to sort
In the extended date table, let’s take a look at that field called Month & Year. If we look at it in the Sort by column, we’ll see something interesting.
We’ll see that that column is sorted by a numerical called MonthnYear. When you sort one column by another, that sort column actually becomes part of the filter context. This is what’s throwing this
calculation off.
Let’s go back to our measure and remove the context of the month and year that we’re using as our sort.
We are now getting exactly what we should, which is the month and year calculated as a proper percentage.
When removing a filter context, it will take two fields to do this when it’s sorted. You may ask that instead of having to do two fields here, why can’t we just remove filters on the entire date
The answer is we can, and this will work for the three examples that we talked about because each of those columns is part of our dates table. Removing all the filter context on that table will work
for all three cases, but this is actually a bad idea.
As a general DAX optimization principle, you need to remove as much filter context as needed to get the result you want.
In most cases, you’re not going to present this in a tabular format. You’ll present it as a matrix, and you’ll need a more complex measure because you have two different granularities in the same
column. This measure looks complicated, but it’s really not.
This is just an extension of what we’ve already done. The first part of this DAX optimization calculation shows the denominators for the different granularity. We remove the filter context for a
month, for the year, and for the entire table.
For the second part of the calculation, we used SWITCH TRUE. For this function, you have to go from the most specific to the least specific. Month is our tightest and most specific scope, so this is
where we start. We’ll need to remove context using those two fields that we identified.
For the scope of year, we have to remove the context on year, and remove the context on the entire table.
Let’s take a look at what happens if we are to take and remove the context on the entire date table. We’ll use a different measure that removes the context on the entire date table for all three
We’ll see that the measure is over-removing context. Instead of calculating the contribution of each month to that year, it’s calculating the contribution of that month to the entire data set. This
is not what we want to happen because removing context from the entire table is really just a blunt instrument when a scalpel is needed.
***** Related Links *****
How To Fix Matrix Totals In Power BI
Matrix Visual In Power BI: Controling Totals & Subtotals
DAX Measure Analysis: Breaking Down Long DAX Measures
There are many instances where you have a matrix and you need to carefully control what context you remove. To just remove the context on the entire table is going to cause these sorts of problems.
I hope when this situation comes up (which invariably will, at some point), you’ll recognize it as the hidden trap that we’ve discussed on this DAX optimization post, and you’ll be able to avoid it
without the same frustration that it caused me when I first saw it and couldn’t figure out why my DAX wasn’t working properly.
If you enjoyed the DAX optimization topic covered in this particular tutorial, please subscribe to the Enterprise DNA TV channel. We have a huge amount of content coming out all the time from myself
and a range of content creators, all of whom are dedicated to improving the way that you use Power BI and the Power Platform.
This project aims to implement a full data analysis pipeline using Power BI with a focus on DAX formulas to derive actionable insights from the order data.
A comprehensive guide to mastering the CALCULATETABLE function in DAX, focusing on practical implementation within Power BI for advanced data analysis.
An interactive web-based application to explore and understand various data model examples across multiple industries and business functions.
A comprehensive project aimed at enhancing oil well performance through advanced data analysis using Power BI’s DAX formulas.
Learn how to leverage key DAX table functions to manipulate and analyze data efficiently in Power BI.
Deep dive into the CALCULATETABLE function in DAX to elevate your data analysis skills.
One of the main reasons why businesses all over the world have fallen in love with Power BI is because...
A hands-on project focused on using the TREATAS function to manipulate and analyze data in DAX.
A hands-on guide to implementing data analysis projects using DAX, focused on the MAXX function and its combinations with other essential DAX functions.
Learn how to leverage the COUNTX function in DAX for in-depth data analysis. This guide provides step-by-step instructions and practical examples.
A comprehensive guide to understanding and implementing the FILTER function in DAX, complete with examples and combinations with other functions.
Learn how to implement and utilize DAX functions effectively, with a focus on the DATESINPERIOD function.
Comprehensive Data Analysis using Power BI and DAX
Exploring CALCULATETABLE Function in DAX for Data Analysis in Power BI
Data Model Discovery Library
Optimizing Oil Well Performance Using Power BI and DAX
Mastering DAX Table Functions for Data Analysis
Mastering DAX CALCULATETABLE for Advanced Data Analysis
Debugging DAX: Tips and Tools for Troubleshooting Your Formulas
Practical Application of TREATAS Function in DAX
MAXX in Power BI – A Detailed Guide
Leveraging the COUNTX Function In Power BI
Using the FILTER Function in DAX – A Detailed Guide With Examples
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Is context-free language closed under intersection?
Is context-free language closed under intersection?
Context-free languages are not closed under intersection or complement.
Which of the following is not closed under context-free language?
Explanation: Context free languages are not closed under difference, intersection and complement operations. 9.
Is intersection context-free?
Because now we know that all regular languages are subset of context-free there is no problem in understanding the union of two but when we talk about intersection again the answer is context-free
language. Yes, the intersection of a regular and a context-free language always result in a context-free language.
Is the class of context free languages closed under intersection prove your answer?
Note : So CFL are not closed under Intersection and Complementation.
What are context free languages closed under?
Lemma: The context-free languages are closed under union, concatenation and Kleene closure.
Why are context free languages not closed under intersection?
The Context-Free Languages Are Not Closed Under Intersection Proof: (by counterexample) Consider L = {anbncn: n ≥ 0} L is not context-free. Both L1 and L2 are context-free. But L = L1 ∩ L2. So, if
the context-free languages were closed under intersection, L would have to be context-free.
Which of the following is not a context free language?
An expression that doesn’t form a pattern on which linear comparison could be carried out using stack is not context free language. Example 1 – L = { a^m b^n^2 } is not context free. Example 2 – L =
{ a^n b^2^n } is not context free.
Is L1 ∩ L2 is a context free language?
Intersection − If L1 and L2 are context free languages, then L1 ∩ L2 is not necessarily context free. Intersection with Regular Language − If L1 is a regular language and L2 is a context free
language, then L1 ∩ L2 is a context free language.
Is CFG closed under intersection?
Theorem: CFLs are not closed under complement If L1 is a CFL, then L1 may not be a CFL. They are closed under union. If they are closed under complement, then they are closed under intersection,
which is false.
Are context free languages closed?
Context-free languages are not closed under complementation. L1 and L2 are CFL. Then, since CFLs closed under union, L1 ∪ L2 is CFL.
Are context-free languages closed?
Are context-free languages closed under set difference?
The CFL’s are closed under substitution, union, concatenation, closure (star), reversal, homomorphism and inverse homomorphism. CFL’s are not closed under intersection (but the intersection of a CFL
and a regular language is always a CFL), complementation, and set-difference.
Is the context free language closed under intersection?
Lemma: The context-free languages are not closed under intersection. That is, if and are context-free languages, it it not always true that is also. Proof: We will prove the non-closure of
intersection by exhibiting a counter-example.
Why are the closure properties of context free languages true?
To address your question more specifically, the reason both theorems can be true is that the regular languages are a proper subset of the context free languages; for the context free languages to be
closed under set intersection, the intersection of any arbitrary context free languages must also be context free (it’s not; see above).
Is the intersection of L1 and L2 context free?
They are both context-free. However, their intersection is the language L = {a^ (n)b^ (n)c^ (n)| n ≥ 0}. No it should not. There is no relation between j and n. In L1 the only condition is equal
number of a’s and b’s. Whether the number of c’s is more or less is immaterial. Similarly in L2, it is equal number of b’s and c’s.
Which is an example of a context free grammar?
Context Free languages are accepted by pushdown automata but not by finite automata. Context free languages can be generated by context free grammar which has the form : Union : If L1 and If L2 are
two context free languages, their union L1 ∪ L2 will also be context free. For example, | {"url":"https://newsbasis.com/is-context-free-language-closed-under-intersection/","timestamp":"2024-11-14T13:53:44Z","content_type":"text/html","content_length":"122454","record_id":"<urn:uuid:36d12fa9-8ebc-4c88-b46e-dd1f5b1c0e3d>","cc-path":"CC-MAIN-2024-46/segments/1730477028657.76/warc/CC-MAIN-20241114130448-20241114160448-00812.warc.gz"} |
Unveiling Math in Information Technology Use
by Mark Walters
Welcome to the world of information technology, where math and technology come together to power our digital lives. Have you ever wondered how math is used in the field of information technology?
We’ll explore the fascinating applications of math in computer science, data analysis, algorithms, cryptography, software engineering, database management, and network security. So, let’s dive in and
discover the mathematical foundations that drive innovation and efficiency in IT.
Key Takeaways:
• Math is an essential part of information technology, providing the foundation for algorithms, problem-solving, and data analysis.
• Computer science programs often include math courses such as discrete mathematics, linear algebra, number theory, and graph theory.
• Math plays a crucial role in software development, network security, cryptography, database management, and data analysis in IT.
• While complex math principles may not be required for coding, understanding basic math concepts is essential for efficient programming.
• Choosing the right information technology program can lead to a successful career in various IT roles.
The Role of Math in Information Technology
Math plays a vital role in information technology, serving as the foundation for a wide range of concepts and applications. From algorithms to problem-solving and data analysis, math is integral to
the field and its various disciplines.
In information technology, math is crucial in several key areas, including:
• Software Development: Math is essential for developing efficient algorithms, which are the building blocks of computer programs. It enables programmers to write code that solves complex problems
• Network Security: Math plays a critical role in cryptography, the practice of secure communication. Algorithms based on mathematical principles like encryption and decryption safeguard sensitive
data transmitted over computer networks.
• Database Management: Math helps in organizing, structuring, and processing large amounts of data efficiently. Concepts such as relational algebra and calculus underpin the design and optimization
of databases.
• Data Analysis: Math provides the tools and techniques needed to extract meaningful insights from vast datasets. Statistical analysis and mathematical modeling help IT professionals make informed
decisions based on data.
Moreover, math is fundamental for understanding complex systems and designing computer graphics. It enables IT professionals to optimize performance, solve intricate problems, and ensure the
reliability and security of computer systems.
“Math plays a vital role in information technology, providing the foundation for algorithms, problem-solving, and data analysis.”
Math Requirements for Information Technology
Math courses are an integral part of the curriculum for information technology degrees. These courses provide the necessary mathematical foundation for understanding and applying concepts in computer
science and information technology. While some IT careers may require more advanced math skills than others, a solid understanding of core mathematical principles is essential for success in the
Common math requirements for IT programs typically include:
• Discrete mathematics
• Calculus
• Linear algebra
• Number theory
• Graph theory
These courses delve into fundamental mathematical concepts and techniques that underpin various areas of information technology.
Having a strong foundation in math equips IT professionals with the necessary skills to tackle complex problems and make informed decisions in their work. It enhances their ability to analyze data,
design algorithms, and optimize system performance.
Whether you’re pursuing a career in software development, network security, data analysis, or any other field within information technology, a solid understanding of math is crucial for navigating
the challenges of the industry.
Math in Coding and Programming
Coding and programming require a solid understanding of mathematical concepts and principles. While complex mathematical exercises are not typically required, math plays a crucial role in writing
efficient code and developing algorithms. Let’s explore how math concepts are applied in coding and programming.
Logic and Problem-Solving
Mathematics and coding share a strong connection through logic and problem-solving. Both disciplines require logical thinking and the ability to break down complex problems into smaller, manageable
steps. Understanding mathematical principles helps programmers approach coding challenges with a structured mindset, leading to more effective problem-solving.
Mathematical Principles in Programming
Basic mathematical principles, such as functions and variables, are fundamental to programming. Functions are like mathematical formulas, allowing programmers to perform specific operations or
calculations. Variables, on the other hand, store and manipulate data, much like mathematical variables represent unknown values in equations.
Math is also used in various specialized areas of programming, including:
• Algorithm Design: Algorithms are sets of instructions used to solve problems or perform tasks. Math helps programmers design efficient algorithms and analyze their complexity.
• Pattern Matching: Math concepts like regular expressions are used to search for patterns within strings of text, which is crucial for tasks like data validation or text parsing.
• Computational Geometry: Geometry principles are utilized in graphical applications, simulation programs, and geometric algorithms for tasks like collision detection or visual representation of
Enhancing Problem-Solving Abilities
While it is possible to learn to code without extensive math skills, having a grasp of mathematical concepts can greatly enhance problem-solving and algorithmic thinking abilities. Math trains the
mind to approach problems systematically, logically, and analytically, which translates well into coding and programming.
“Mathematics is the language with which we describe the world” – Stephen Hawking
By incorporating math principles into coding, programmers can develop efficient and optimized solutions, making their code more robust and reliable.
Overall, math provides a valuable foundation for coding and programming, allowing developers to think critically, solve problems, and create innovative solutions.
Math Concepts in Programming Applications
Functions Performing specific operations or calculations
Variables Storing and manipulating data
Algorithms Designing efficient solutions and analyzing complexity
Regular Expressions Searching for patterns within text
Computational Geometry Geometric algorithms and graphical applications
Math in Information Technology Education
Information technology degree programs place a strong emphasis on math courses to provide students with the necessary foundation for success in the field. These courses not only enhance
problem-solving skills but also create a deeper understanding of the underlying concepts within information technology.
The Importance of Math Courses
Math courses for IT degrees cover a range of topics that are directly applicable to the field. Here are some common math courses you may encounter:
• Computer Graphics: This course explores the mathematical principles behind computer graphics, including rendering algorithms and geometric transformations. It is essential for developing visually
appealing interfaces and simulations.
• Algorithms and Data Structures: This course delves into the mathematical foundations of algorithms and data structures. It provides students with the necessary tools to design efficient
algorithms and analyze their performance.
• Relational Databases: Understanding the mathematical concepts behind relational databases is essential for designing, querying, and managing data effectively.
• Statistics: This course equips students with the skills necessary to analyze data and make informed decisions. It is particularly valuable for individuals interested in data analysis and machine
By incorporating math courses into the curriculum, information technology programs ensure that graduates have the skills and knowledge required to excel in various IT roles.
The Benefits of Math in IT Education
Having a solid understanding of math concepts offers several benefits for individuals pursuing a career in information technology:
“Mathematics is the key to unlock the door to the world of technology.”
A deep comprehension of math facilitates problem-solving and critical thinking abilities, which are crucial in the ever-evolving landscape of IT. The logical and analytical skills gained through math
courses enable professionals to tackle complex challenges and develop innovative solutions.
Furthermore, math provides a solid foundation for advanced topics within information technology, such as machine learning, cryptography, and network security. These fields require a deep
understanding of mathematical principles to ensure robust systems and effective data protection.
Common Math Courses for IT Degrees
Course Description
Computer Graphics Explores mathematical principles behind computer graphics, including rendering algorithms and geometric transformations.
Algorithms and Data Structures Provides tools to design efficient algorithms and analyze their performance.
Relational Databases Focuses on the mathematical concepts behind designing, querying, and managing data in relational databases.
Statistics Equips students with skills to analyze data and make informed decisions, valuable for roles in data analysis and machine learning.
Note: This table provides a snapshot of common math courses for IT degrees, but specific courses may vary among institutions.
Overall, math courses in information technology education form a crucial part of preparing students for successful careers in the field. The combination of mathematical skills and technological
knowledge positions graduates to become well-rounded IT professionals capable of driving innovation and solving complex problems.
Choosing an Information Technology Program
When it comes to pursuing a career in information technology, choosing the right program is essential. With so many options available, it’s important to consider various factors that can influence
your education and future career. Here are some key considerations to keep in mind:
Reputation and Ranking
The reputation and ranking of the information technology program you choose can have a significant impact on your career prospects. Research and consider programs that have a good track record of
producing successful graduates and are well-regarded in the industry.
Examine the curriculum of different IT programs to ensure they cover the core areas of information technology that align with your career goals. Look for a comprehensive curriculum that includes
courses in software development, networking, database management, cybersecurity, and data analysis.
The expertise and qualifications of the faculty members in an IT program can greatly influence your learning experience. Look for programs with experienced professors who have a strong background in
the field and actively engage with students.
Concentrations or Specializations
Consider the availability of concentrations or specializations within an IT program. These focus areas can provide you with specialized knowledge and skills that align with your career interests,
such as artificial intelligence, data science, or cybersecurity.
Type of Degree
Decide whether you want to pursue a Bachelor of Arts (BA) or a Bachelor of Science (BS) degree in information technology. BA programs may focus more on the liberal arts and humanities, while BS
programs tend to have a stronger emphasis on technical skills and sciences.
Class Size and Student-to-Faculty Ratio
Consider the class size and student-to-faculty ratio of the program. Smaller class sizes can allow for more personalized attention and interaction with professors, while larger classes may offer more
diverse perspectives and collaboration opportunities.
Online Course Availability
If flexibility is important to you, check if the program offers online courses. Online learning can provide convenience and allow you to balance your studies with other commitments, such as work or
family responsibilities.
After careful consideration of these factors, you can make an informed decision when choosing an information technology program that aligns with your interests, goals, and learning preferences.
Top Information Technology Programs in the United States
Here are some of the top information technology programs in the United States:
University Program
Carnegie Mellon University Bachelor of Science in Information Systems
Cornell University Bachelor of Science in Information Science
Brigham Young University Bachelor of Science in Information Technology
Pennsylvania State University Bachelor of Science in Information Sciences and Technology
Purdue University Bachelor of Science in Computer and Information Technology
New York University Bachelor of Science in Information Systems Management
These programs have a strong reputation, rigorous curriculum, and excellent faculty, making them ideal options for aspiring IT professionals.
Choosing the right information technology program is crucial for laying a solid foundation for your future career. By considering factors such as reputation, curriculum, faculty, concentrations, and
degree options, you can make an informed decision that aligns with your goals and sets you on a path to success.
The Importance of Math in Information Technology Careers
Math skills play a crucial role in various information technology (IT) careers, especially those that involve complex calculations, data analysis, and algorithm design. Having a solid foundation in
math can significantly enhance your job prospects and contribute to your success in the IT field.
Professions such as data scientists, cybersecurity analysts, software engineers, and systems analysts often require strong math skills. Let’s explore how math is utilized in these IT careers:
1. Data Scientists: In the field of data science, math is fundamental to understanding statistical analysis, modeling techniques, and machine learning algorithms. With a solid grasp of math, data
scientists can effectively analyze and interpret large datasets, extract meaningful insights, and make data-driven decisions.
2. Cybersecurity Analysts: Math plays a crucial role in ensuring the security of computer systems. By employing mathematical principles, such as cryptography, cybersecurity analysts can develop and
implement robust security measures, safeguarding sensitive information from unauthorized access and cyber threats.
3. Software Engineers: Math is essential for software engineers when designing algorithms and optimizing program performance. It helps in developing efficient code, creating complex software
architectures, and solving challenging programming problems.
4. Systems Analysts: Systems analysts rely on math to analyze system requirements, identify bottlenecks, and optimize the performance of computer systems. They utilize mathematical modeling and
simulation techniques to evaluate system efficiency and propose enhancements.
Additionally, math is used in various other aspects of IT, such as network optimization, database management, risk analysis, and artificial intelligence. It provides the foundation for
problem-solving, logical reasoning, and critical thinking skills, which are crucial for IT professionals.
Although not all IT careers require advanced math skills, having a solid understanding of math concepts can give you a competitive edge and open doors to a wider range of job opportunities in the IT
The Role of Math Skills in IT Job Requirements
When applying for IT positions, math skills are often listed as an essential requirement. Employers recognize the importance of math in IT and seek professionals who can apply mathematical concepts
to solve problems and optimize systems.
Here is a table highlighting some math skills commonly sought after in IT job requirements:
Math Skill Application Example Job Roles
Statistics Data analysis, hypothesis testing, predictive modeling Data Analyst, Business Intelligence Analyst
Linear Algebra Data transformation, image processing, optimization Computer Graphics Programmer, Machine Learning Engineer
Discrete Mathematics Algorithms, graph theory, logic Software Developer, Network Architect
By possessing strong math skills, you can demonstrate your ability to tackle complex problems, analyze data effectively, and contribute to the growth and success of an organization.
“Mathematics is the language of nature, and its principles are deeply embedded in the fabric of technology. By embracing math, IT professionals can unlock the true potential of their skills and
excel in the ever-evolving world of information technology.”
So, whether you’re pursuing a career in data science, cybersecurity, software engineering, or systems analysis, remember the importance of math in IT careers. By honing your math skills, you can
broaden your career opportunities, solve complex problems, and make a significant impact in the field of information technology.
In conclusion, math is a fundamental component of information technology, underpinning crucial concepts such as algorithms, problem-solving, and data analysis. While advanced math skills may not be
necessary for all IT careers, a solid understanding of core mathematical principles is essential for success in the field. That’s why math courses are a key part of information technology degree
programs, ensuring that students develop the necessary mathematical skills for their chosen careers.
By incorporating math into their education, IT professionals are equipped with the tools to enhance efficiency, drive innovation, and ensure the security of information technology systems. Whether
it’s developing efficient algorithms, designing computer graphics, or optimizing performance, math enables IT professionals to solve complex problems and maintain the reliability of computer systems.
As you embark on a career in information technology, remember that math will continue to play a vital role in your journey. Embrace the mathematical concepts, hone your problem-solving abilities, and
leverage the power of math to excel in the dynamic and ever-evolving field of information technology.
How is math used in information technology?
Math is used in information technology to develop efficient algorithms, solve complex problems, optimize performance, and ensure the reliability and security of computer systems.
What are the math applications in computer science and IT?
Math is applied in computer science and IT for tasks such as data analysis, algorithm design, software development, database management, network security, and cryptography.
What math concepts are used in data analysis?
Data analysis often involves mathematical concepts such as statistical analysis, probability theory, and linear algebra.
How is math used in algorithms?
Math is used in algorithms for tasks such as analyzing and optimizing algorithm efficiency, understanding computational complexity, and solving problems using mathematical models.
How does math contribute to cryptography?
Math is fundamental to cryptography as it provides the mathematical foundation for encryption and decryption algorithms, ensuring the security of sensitive data and communication.
What is the role of math in software engineering?
Math plays a role in software engineering by enabling the development of algorithms, performance optimization, modeling complex systems, and designing efficient software solutions.
How is math used in database management?
Math is used in database management for tasks such as designing relational database structures, optimizing query performance, and implementing data manipulation operations.
What is the importance of math in network security?
Math is crucial for network security as it provides the basis for encryption algorithms, secure communication protocols, and intrusion detection systems.
What are the math requirements for information technology degrees?
Common math requirements for information technology degrees include courses in discrete mathematics, calculus, linear algebra, number theory, and graph theory.
Do you need advanced math skills for coding and programming?
While complex mathematical exercises are not typically required for coding, understanding logic, problem-solving, and basic mathematical principles is important for writing efficient code.
What math courses are typically included in information technology degree programs?
Information technology degree programs often include math courses such as computer graphics, algorithms and data structures, relational databases, and statistics.
What factors should I consider when choosing an information technology program?
Factors to consider when choosing an IT program include reputation, curriculum, faculty, available concentrations or specializations, type of degree (Bachelor of Arts or Bachelor of Science), class
size, and availability of online courses.
What are some top information technology programs in the United States?
Some top information technology programs in the United States include Carnegie Mellon University, Cornell University, Brigham Young University, Pennsylvania State University, Purdue University, and
New York University.
Which IT careers require strong math skills?
IT careers such as data scientists, cybersecurity analysts, software engineers, and systems analysts often require a strong foundation in math for tasks such as complex calculations, data analysis,
and algorithm design.
Is math important for information technology careers?
Math is important for information technology careers as it enhances job prospects, contributes to problem-solving abilities, and enables the efficient and secure functioning of IT systems.
Source Links | {"url":"https://www.twefy.com/how-is-math-used-in-information-technology/","timestamp":"2024-11-07T09:28:13Z","content_type":"text/html","content_length":"129506","record_id":"<urn:uuid:b26318ff-0357-4029-b953-6d28039bc61f>","cc-path":"CC-MAIN-2024-46/segments/1730477027987.79/warc/CC-MAIN-20241107083707-20241107113707-00817.warc.gz"} |
Geodetector method
Spatial stratified heterogeneity (SSH), referring to the within strata are more similar than the between strata, such as landuse types and climate zones, is ubiquitous in spatial data. SSH instead of
random is a set of information, which has been being a window for humans to understand the nature since Aristotle time. In another aspect, a model with global parameters would be confounded if input
data is SSH, the problem dissolves if SSH is identified so simple models can be applied to each stratum separately. Note that the “spatial” here can be either geospatial or the space in mathematical
Geodetector is a novel tool to investigate SSH: (1) measure and find SSH of a variable Y ; (2) test the power of determinant X of a dependent variable Y according to the consistency between their
spatial distributions; and (3) investigate the interaction between two explanatory variables X[1] and X[2] to a dependent variable Y. All of the tasks are implementable by the geographical detector q
-statistic: \[$$q=1- \frac{1}{N\sigma^2}\sum_{h=1}^{L}N_h\sigma_h^2$$\]
where N and σ^2 stand for the number of units and the variance of Y in study area, respectively; the population Y is composed of L strata (h = 1, 2, …, L), N[h] and σ[h]^2 stand for the number of
units and the variance of Y in stratum h, respectively. The strata of Y (red polygons in Figure 1) are a partition of Y, either by itself ( h(Y) in Figure 1) or by an explanatory variable X which is
a categorical variable ( h(Y) in Figure 1). X should be stratified if it is a numerical variable, the number of strata L might be 2-10 or more, according to prior knowledge or a classification
(Notation: Yi stands for the value of a variable Y at a sample unit i ; h(Y) represents a partition of Y ; h(X) represents a partition of an explanatory variable X. In geodetector, the terms
“stratification”, “classification” and “partition” are equivalent.)
Interpretation of q value (please refer to Fig.1). The value of q ∈ [0, 1].
If Y is stratified by itself h(Y), then q = 0 indicates that Y is not SSH; q = 1 indicates that Y is SSH perfectly; the value of q indicates that the degree of SSH of Y is q.
If Y is stratified by an explanatory variable h(X), then q = 0 indicates that there is no association between Y and X ; q = 1 indicates that Y is completely determined by X ; the value of q-statistic
indicates that X explains 100q% of Y. Please notice that the q-statistic measures the association between X and Y, both linearly and nonlinearly.
For more detail of Geodetector method, please refer:
[1] Wang JF, Li XH, Christakos G, Liao YL, Zhang T, Gu X, Zheng XY. Geographical detectors-based health risk assessment and its application in the neural tube defects study of the Heshun Region,
China. International Journal of Geographical Information Science, 2010, 24(1): 107-127.
[2] Wang JF, Zhang TL, Fu BJ. A measure of spatial stratified heterogeneity. Ecological Indicators,2016, 67(2016): 250-256.
[3] Wang JF, Xu CD. Geodetector:Principle and prospective. Geographica Sinica,2017,72(1):116-134.
R package for geodetector
geodetector package includes five functions: factor_detector, interaction_detector, risk_detector, ecological_detector and geodetector. The first four functions implementing the calcution of factor
detector, interaction detector, risk detector and ecological detector, which can be calculated using table data, e.g. csv format(Table 1). The last function geodetector is an auxiliary function,
which can be used to implement the calculation for shapefile format map data(Figure 2).
Table 1.
Demo data
in table
7.20 2 3 6
7.01 2 3 6
6.79 2 3 6
6.73 4 3 6
6.77 4 3 1
6.74 4 3 6
geodetector package is available for data.frame. Please check the data type in advance.
As a demo, neural-tube birth defects (NTD) Y and suspected risk factors or their proxies Xs in villages are provided, including data for the health effect GIS layers and environmental factor GIS
layers, “elevation”, “soil type”, and “watershed”. | {"url":"https://cran.r-project.org/web/packages/geodetector/vignettes/geodetector.html","timestamp":"2024-11-12T22:44:50Z","content_type":"text/html","content_length":"1048952","record_id":"<urn:uuid:3208c34b-7876-4714-bb8e-72ba1fb291cf>","cc-path":"CC-MAIN-2024-46/segments/1730477028290.49/warc/CC-MAIN-20241112212600-20241113002600-00874.warc.gz"} |
Directions from Jerantut to Taman Negara
To find the return direction from Jerantut to Taman Negara, start by entering start and end locations in calculator control and use the Calculate Return Direction option. You can also try a different
route while coming back by adding multiple destinations. Along with it, estimate
Travel time from Jerantut to Taman Negara
to calculate the time you will spend travelling. | {"url":"https://www.distancesfrom.com/my/directions-from-Jerantut-to-Taman-Negara/DirectionHistory/46010006.aspx","timestamp":"2024-11-01T20:48:05Z","content_type":"text/html","content_length":"183695","record_id":"<urn:uuid:8698e7aa-55a7-492f-bbc0-20efb746dd59>","cc-path":"CC-MAIN-2024-46/segments/1730477027552.27/warc/CC-MAIN-20241101184224-20241101214224-00570.warc.gz"} |
Heat Rate Calculation Methods: Direct and Indirect in context of formula for calculating turbine heat rate
07 Sep 2024
Heat Rate Calculation Methods: Direct and Indirect
In the context of power generation, particularly in steam turbines, heat rate calculation is a crucial aspect to evaluate the efficiency of the turbine. Heat rate represents the amount of energy
required to generate one unit of electricity. In this article, we will explore two common methods for calculating heat rate: direct and indirect.
Direct Method
The direct method involves measuring the temperature and pressure of the steam at various points in the turbine, as well as the power output of the turbine. This method is considered more accurate
than the indirect method, but it requires a significant amount of instrumentation and data collection.
The formula for calculating heat rate using the direct method is:
Heat Rate (HR) = (Q / P)
Where: Q = Heat input (in BTU/lb) P = Power output (in kW)
For example, if the heat input is 1000 BTU/lb and the power output is 500 kW, the heat rate would be:
HR = (1000 BTU/lb / 500 kW) = 2.0 BTU/kWh
Indirect Method
The indirect method involves measuring the temperature and pressure of the steam at the turbine inlet and outlet, as well as the power output of the turbine. This method is less accurate than the
direct method but requires fewer instruments and data collection.
The formula for calculating heat rate using the indirect method is:
Heat Rate (HR) = (H_in - H_out) / P
Where: H_in = Inlet enthalpy (in BTU/lb) H_out = Outlet enthalpy (in BTU/lb) P = Power output (in kW)
For example, if the inlet enthalpy is 1200 BTU/lb, the outlet enthalpy is 800 BTU/lb, and the power output is 500 kW, the heat rate would be:
HR = ((1200 - 800) BTU/lb / 500 kW) = 1.6 BTU/kWh
Turbine Heat Rate Formula
The turbine heat rate formula is a simplified version of the indirect method that takes into account the turbine’s efficiency and the steam properties.
Heat Rate (HR) = (H_in - H_out) / (η * P)
Where: H_in = Inlet enthalpy (in BTU/lb) H_out = Outlet enthalpy (in BTU/lb) η = Turbine efficiency P = Power output (in kW)
For example, if the inlet enthalpy is 1200 BTU/lb, the outlet enthalpy is 800 BTU/lb, the turbine efficiency is 0.85, and the power output is 500 kW, the heat rate would be:
HR = ((1200 - 800) BTU/lb / (0.85 * 500 kW)) = 1.4 BTU/kWh
Heat rate calculation is a crucial aspect of evaluating the efficiency of steam turbines in power generation applications. The direct and indirect methods provide two different approaches to
calculating heat rate, with the direct method being more accurate but requiring more instrumentation and data collection. The turbine heat rate formula provides a simplified way to calculate heat
rate while taking into account the turbine’s efficiency and steam properties. By understanding these calculation methods, engineers can optimize turbine performance and improve overall power plant
Related articles for ‘formula for calculating turbine heat rate’ :
Calculators for ‘formula for calculating turbine heat rate’ | {"url":"https://blog.truegeometry.com/tutorials/education/b8f1d1a28c7255b43f81cb465652d8f8/JSON_TO_ARTCL_Heat_Rate_Calculation_Methods_Direct_and_Indirect_in_context_of_f.html","timestamp":"2024-11-13T22:57:08Z","content_type":"text/html","content_length":"18619","record_id":"<urn:uuid:a5e88165-edfe-4a9c-bfd0-b8da3bf290ec>","cc-path":"CC-MAIN-2024-46/segments/1730477028402.57/warc/CC-MAIN-20241113203454-20241113233454-00605.warc.gz"} |
HackerRank: Text Alignment Notes
Table of Contents
This article is about a Python challenge on HackerRank: Text Alignment. We can definitely keep trying until we get the correct answer for this one. But I think that is kind of boring, and I really
want to understand the thoughts behind the author's code. So this article will try to think like the author and come up with the necessary steps one by one.
The problem requires you to input an odd number named thickness where \( 0 \lt thickness \lt 50\). For example, when thickness = 5, we should output an ASCII art like this:
HHHHH HHHHH
HHHHH HHHHH
HHHHH HHHHH
HHHHH HHHHH
HHHHH HHHHH
HHHHH HHHHH
HHHHH HHHHH
HHHHH HHHHH
HHHHH HHHHH
HHHHH HHHHH
HHHHH HHHHH
HHHHH HHHHH
The problem also provides you with a code template:
#Replace all ______ with rjust, ljust or center.
thickness = int(input()) #This must be an odd number
c = 'H'
#Top Cone
for i in range(thickness):
#Top Pillars
for i in range(thickness+1):
#Middle Belt
for i in range((thickness+1)//2):
#Bottom Pillars
for i in range(thickness+1):
#Bottom Cone
for i in range(thickness):
It asks you to replace the "____" with ljust, center, or rjust.
How to use ljust(), center(), rjust()
ljust() and rjust() are actually very simple. They are just aligning your text left or right. But center() is a bit tricky. There are several things you need to be careful about.
ljust() and rjust()
Let's take a look at the ljust() and rjust() first:
width = 10
As we can see, "12345" is the text that I want to print. ljust() is aligning the text left, and the "width" here decides the total length. "-" is the character I set as the fillchar, which will be
used to reach the given width.
rjust() is also similar. If we did not pass fillchar to the second argument here, the default fillchar would be space.
It is a bit tricky when it comes to center(). We need to remember two rules:
• If the given width is an even number, the padding will start from the right.
• If the given width is an odd number, the padding will start from the left.
For example, if we want to center the "12345" and set the given width as 6, then:
s = "12345"
width = 6
# Output：12345-
However, if we want to center "1234" and set the given width as 5, then:
s = "1234"
width = 5
There is also another situation. If "width - len(s)" is an odd number, it means that the padding for both sides will not have an equal number of characters. The side that is padding first will have
one more character. We will need to check whether the given width is odd or even.
For example, if s = "1234", width = 7 and the method is center(), by calculating \(7- 4 = 3\), we know that the padding should be "-" for one side, and "--" for the other side. As width is an odd
number, the padding will start from the left:
width = 7
# Output：--1234-
Similarly, if s = "12345", width = 8, and the method is still center(), the right side will have one more "-" because the given width is even.
width = 8
How to solve the problem (rebuild the author's logic)
After we understand the three methods above, we can start to discuss the author's logic in the code template. I will try to think like the author and come up with the necessary parts step by step.
The following will discuss the situation where \(thickness = 5 \).
Top Cone
First, we can look at the Top Cone part, which is the top-left triangle in the big "H":
for i in range(thickness):
It is easy to see that thickness decides how many lines the cone will have. For this type of triangle, the general pattern for the number of characters in each line is 1, 3, 5, 7...
The logic here is to print the middle "H" first and then pad even number of "H"s on both sides. Because it has 5 lines and we know the 5th line will be full of characters, the number of "H"s in the
5th line ranging from the start to the middle will be 5.
Therefore, every line should be aligned with width = \( (thickness -1)\) for both sides in each line (4 in this case).
For the "H"s on the left side, we need to use rjust(), and for the "H"s on the right side, we need to use ljust().
Top Cone's Method
Therefore, the code will be:
for i in range(thickness):
Top Pillars, Middle Belt, and Bottom Pillars
Then let's take a look at the middle part. I also keep the last line of the top cone for reference.
HHHHH HHHHH
HHHHH HHHHH
HHHHH HHHHH
HHHHH HHHHH
HHHHH HHHHH
HHHHH HHHHH
We should try to think like the author before we look at the code template. The first thing to decide is the middle belt should span \(5 \times thickness\):
After this, there are two limited conditions here：
• Two pillars must be on two sides of the middle belt.
• The first pillar needs to be centered on the bottom line of the cone.
For ease of reading, we let \(t = thickness \).
Number of "H"s for Each Part of the Logo
The structure will look like this after simplification:
(The \(3t\) here is obtained by \((5t-t\times2)\).)
If we also want to use center() for the right pillar, we need to consider the same size of blue parts on the right side:
Therefore, we know the code will be:
#Top Pillars
for i in range(thickness + 1):
If you change the "Top Pillars" and "Bottom Pillars" to my code here, you will find that it can also pass the test.
However, we observed that the left pillar uses \( 2t-1 \) while the right pillar uses \( 6t+1 \), and they are next to each other. Is it possible that we can change them to \( 2t \) and \( 6t \)?
The yellow part is the difference, but it creates a new problem. The two sides of the pillars have different widths:
We can see that both pillars' right side has one more character than the left. This involves a point about the center() we mentioned earlier:
• If the given width is an even number, the padding will start from the right.
Because .center(2t) and .center(6t) are receiving two even number parameters, the padding will start from the right.
This will solve our problem automatically. Since for the left pillar, the one more right-padding character will fill the yellow difference, and for the right pillar, the one more right-padding
character will not affect the output since it is a space.
Thus you can understand why the code template will be:
#Top Pillars
for i in range(thickness+1):
#Bottom Pillars
for i in range(thickness+1):
After we figure out the situations for the two pillars, it is clearer to see why the middle belt was written like that.
As you see here, we want the middle belt to stay in the 5t range, which is to be centered within \( 5t+2\times \frac{(t-1)}{2} = 6t-1 \) (i.e. centered(6t-1)). Since the same rule applies, the right
side will have one more character if we change to center(6t). It does not affect our ASCII art, so we change it to 6t.
#Middle Belt
for i in range((thickness+1)//2):
The result will look like this:
Bottom Cone
Finally, let's look at the bottom cone. In fact, the situation is very similar to the top cone. We also divide the output into three parts: left "H"s, middle "H," and right "H"s.
The left and right number of "H"s can be considered as \( ((thickness - 1) - i)\). When \( thickness = 5\), every iteration will be \( ((thickness - 1) - i) = 4,3,2,1,0 \).
We can still use the same alignment with width = \((thickness - 1)\) as the top cone's:
for i in range(thickness):
The only problem left is how to right align it. According to the picture above, we should use 6t-1 for the right() method's width.
The code will be:
#Bottom Cone
for i in range(thickness):
You can also pass the test by using this code, while you will notice that this is not the same as the author's code template.
The author's way is like this:
#Bottom Cone
for i in range(thickness):
There are two differences, one is that for the left and right "H"s, the ljust() and rjust() are using thickness as the width instead of thickness-1 in my code. The other difference is that the rjust
() for the whole triangle is using 6t.
The author is actually trying to extend one more space at the right. This will align with the rightmost green space so that the center() can use 6t as the width.
This article is my guess for the author's logic based on the code template. I tried to simulate how the author came up with the code step by step. Although it may not be accurate, I think the
explanation for the alignment logic should be correct.
It took me some time to figure out the logic and draw these pictures, but it was worth it after I finished it. I feel that the logic is much clearer for me, and I have a deeper understanding of this
type of code.
I hope this article helps you have similar feelings and understand more about the author's code!
(Support me by a coffee monthly or becoming a member. 😊😊)
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HackerRank: Merge the Tools! Notes Paid Members Public
Background This article was written down when I was doing a Python challenge on HackerRank: "Merge the Tools!". Merge the Tools! | HackerRankSplit a string into subsegments of length $k$, then print
each subsegment with any duplicate characters stripped out.HackerRank Problem To help you understand this problem, I
HackerRank: The Minion Game Notes Paid Members Public
Background This article was written down when I was doing a Python challenge on HackerRank: The Minion Game. Hints If you haven't passed this question and want to have some hints. There are two hints
I think might be helpful: * The solution can be done with one loop | {"url":"https://www.ranblog.com/blog/hackerrank-text-alignment-notes/","timestamp":"2024-11-03T04:24:19Z","content_type":"text/html","content_length":"120462","record_id":"<urn:uuid:2782a9d6-8bb5-46b0-a4fd-40afdb885834>","cc-path":"CC-MAIN-2024-46/segments/1730477027770.74/warc/CC-MAIN-20241103022018-20241103052018-00868.warc.gz"} |
Maximum Extraction Rate of Influence Asteroids
Originally developed by protoplanetary (Foreword by Markus Korivak)
Asteroid bonuses increase their MER, moving them above the unbonused white line. Graph provided by trevis of Influence Sales.
What is the Best Way to Determine the Value of an Asteroid?
Surface Area (or “Size”)
The most basic way of estimating a value is by using the Surface Area. This is very easy to find, and has a huge impact on the utility of an asteroid. Every square kilometre of surface area is the
possibility of one more drill, one more building, one more warehouse, one more lease.
No matter how rich a 13km² asteroid is, it can eventually be out-produced by a much poorer asteroid with room for twice as many drills (assuming you can source and ship and run twice as many drills,
of course).
OBF: Overall Boost Factor (or “Rarity”)
But how do you compare smaller-but-richer asteroids against larger-but-poorer asteroids, then?
This is where the OBF comes in. This is much more complicated than looking up the Surface Area, but there are community tools that will automatically calculate it for you. The math included below is
for people looking to understand exactly what is happening behind the scenes. Personally, I am presenting the math exactly as it was presented to me; I am a cartographer, not a mathematician.
The basic idea is that you add the number 1 and all of the bonuses on the asteroid into a single number that is slightly larger than one, which when multiplied by the Surface Area gives you a
“Common-Equivalent Surface Area”, or essentially how much larger a Common asteroid would have to be to have the same theoretical resource output.
If that sounds a little complicated, that’s okay. There are tools that will do this for you. And this is the real workhorse piece of MER, since it is allowing us to compare any asteroid of any
spectral type, of any size, of any combination of bonuses to any other asteroid with a completely different set of all those variables.
MER: Maximum Extraction Rate (or “Utility”)
Okay, a little overwhelmed by that last step? Good news: it gets easier. Here’s the calculation for MER:
MER = Surface Area x OBF
That’s it!
Now, this is a purely hypothetical “maximum”, since it would actually be impossible to have an asteroid where every plot had a drill on it, and it does gloss over the boots-on-the-ground level of
detail with Traits, Skills, and Core Samples. But that’s okay, because this is about comparing asteroids to each other, not for planning exactly how much cargo space you need to get all your paydirt
to market.
Utilities (or "I Don't Want to do the Math")
The Math:
How to Calculate the MER for an Asteroid
1. Collect your ingredients for the given asteroid: spectral type, surface area, the yield boost, and the five resource-class-specific boosts. These boosts should all be scalars that are 1+. For
example, a yield of 6% is 1.06 as a scalar. A Metals boost of 50% is 1.5 as a scalar. If the asteroid doesn't have that resource, just leave it at 1.
2. Get the list of abundance factors for each resource class for your asteroid's spectral type from the Spectral Resource Abundance Table (see below). These abundance factors are again scalars, this
time between 0 and 1.
3. Multiply the five boost factors by the five corresponding abundance factors, and sum the result to one value "Sum of Weighted Boosts" or SWB. (This is the dot product of the two vectors.)
4. OBF (Overall Boost Factor) = Yield x SWB.
5. MER = Surface Area x OBF.
Spectral Resource Abundance Table
Type -Organics- -Volatiles- -Metals- -Fissiles- -Rare Earths-
C 0.667 0.333 0.000 0.000 0.000
Cm 0.200 0.200 0.400 0.200 0.000
Ci 0.500 0.500 0.000 0.000 0.000
Cs 0.200 0.200 0.200 0.200 0.200
Cms 0.167 0.167 0.333 0.167 0.167
Cis 0.167 0.333 0.167 0.167 0.167
S 0.000 0.000 0.333 0.333 0.333
Sm 0.000 0.000 0.500 0.250 0.250
Si 0.000 0.400 0.200 0.200 0.200
M 0.000 0.000 0.750 0.250 0.000
I 0.000 1.000 0.000 0.000 0.000
An Example
Say I have a 650km² Cm-type asteroid with 3% Yield and a 10% boost to Metals.
1. Surface Area = 650. Yield boost = 1.03. Resource-class-specific boost factors: Bo = 1.0, Bv = 1.0. Bm = 1.1, Bf = 1.0, Br = 1.0.
2. From the chart for a Cm type asteroid, abundance factors: Ao = 0.200, Av = 0.200, Am = 0.400, Af = 0.200, Ar = 0.000.
3. SWB = A•B = 1.0 x 0.2 + 1.0 x 0.2 + 1.1 x 0.4 + 1.0 x 0.2 + 1.0 x 0.0 = 1.04.
4. OBF = 1.03 x 1.04 = 1.0712 (= 107.12%).
5. MER = 650 x 1.0712 = 696.28.
So, this asteroid of 650km² with bonuses can potentially yield the same amount of resources as a common asteroid of about 700km²
Appendix A:
protoplanetary’s Thoughts on MER
• Maximum Extraction Rate (MER) equals Surface Area times yield times the sum of the spectral abundances for that spectral type, weighted individually by the corresponding boosts for that rock. So
basically a measure of the max rate at which you can extract resources, and hence value, from the rock (assuming all resource classes are equally valuable, and that you fully utilize the rock for
• So when MER/ETH is high, that means you are purchasing a larger amount of possible output for less money, i.e. a better deal. Or put another way, an asteroid is literally a token representing
your right to extract resources, and that right has a certain magnitude, which I postulate corresponds more-or-less directly with the token's value (from a utility perspective). And MER is
designed to capture the magnitude of that right, and hence the asteroid's value.
• Also of note: MER by far most highly correlates with surface area. Boosts are included at exactly the percentages they say they are, but they turn out to be surprisingly unimportant in the scheme
of things. A rock that has just 1.32x the radius of another ( = sqrt(1.15 x 1.5) ) can produce more output than the other, even if the other has every single boost at maximum.
• One small but potentially useful addition I might make: define OBF = Overall Boost Factor = SWB x Yield. This dimensionless factor is the closest approximation to how actually boosted an asteroid
is, in one number. Of great note, an asteroid's listed rarity is not terribly highly correlated with its OBF, because the listed rarity simply counts the number and level of boosts, not their
compounded effect on overall boost, and definitely not how that plays with the spectral type, all of which OBF does.
Appendix B:
trevis’ Explanation of OBF and MER
OBF is Overall Boost Factor, it corresponds to an approximation, based on the data we have and some small simplifications, of the global effectiveness of the rock plots to be mined for their
resources. The base value is 1 and can be higher depending on scanning results.
• With a 6% yield boost, it becomes 1.06.
• Or, with a 10% bonus to a resource representing 50% on what can be found, it would be 1.05. MER is the asteroid's Surface x OBF, so it is also measured in km².
Say there are two asteroids of the same spectral type, with all plots occupied by the same buildings and focused only on mining.
• Rock A has 1000 plots (each plot is 1km²) with a 6% yield bonus. MER = 1060.
• Rock B doesn't have any bonuses (so OBF=1) but has a surface of 1060 km². Its MER is also 1060. You can see that even though they have different surfaces, as Rock A is boosted, both asteroids
could deliver the same amount of resources per day of mining.
That's why I refer to the MER also in terms of "Effective Surface", and why its dimension is km². To me, the MER is most useful in the context of assessing the price of an asteroid, to calculate cost
vs utility in game.
• Sometimes there are "Superior" class asteroids that would have more productive plots than "Exceptional" ones, because their bonuses are a better fit to the rocks available resources. (E.g., +20%
of whole rock is better than +50% bonus for a resource found only in 10% of the rock).
• Sometimes a rock is 10% smaller than another one for the same price but with its boosts it would be 10% more productive, and thus probably better. So, with the MER/ETH ratio, you can compare
offers more robustly, with respect to in-game utility.
Influence is developed by Unstoppable Games. Asteroid data provided by Adalia.info. | {"url":"https://adalia.guide/coastin/publications/mer","timestamp":"2024-11-12T22:07:37Z","content_type":"text/html","content_length":"15842","record_id":"<urn:uuid:0d9a4e74-f0b1-4630-95a0-e960806d1a84>","cc-path":"CC-MAIN-2024-46/segments/1730477028290.49/warc/CC-MAIN-20241112212600-20241113002600-00265.warc.gz"} |
gre - IELTS Class Coaching - Spoken English Class - PTE Tutorials - Competitive exams
What is GRE?
The GRE (Graduate Record Examination) is a standardized test that is an admissions requirement for many graduate schools, especially in the United States and Canada. It is used to assess the
readiness of applicants for graduate-level academic work. The GRE is administered by the Educational Testing Service (ETS) and consists of three main sections:
1. Verbal Reasoning: Measures reading comprehension, critical reasoning, and vocabulary usage.
2. Quantitative Reasoning: Assesses basic math skills, understanding of quantitative concepts, and the ability to solve problems using mathematical reasoning.
3. Analytical Writing: Requires test-takers to write essays that measure critical thinking and analytical writing skills.
The GRE is often required for admission to graduate programs in fields such as business, social sciences, and the humanities, as well as for some specialized master’s and doctoral programs. Some
business schools may also accept the GRE instead of the GMAT for MBA admissions.
Scoring is on a scale of 130-170 for the Verbal and Quantitative sections, and 0-6 for the Analytical Writing section.
How can I prepare for GRE?
Preparing for the GRE requires a structured approach, focusing on understanding the test format, developing the right skills, and practicing consistently. Here are key steps to help you prepare:
1. Understand the Test Format
• Sections: GRE has Verbal Reasoning, Quantitative Reasoning, and Analytical Writing sections.
• Timing: The total duration is about 3 hours and 45 minutes.
• Question Types:
□ Verbal: Reading comprehension, sentence equivalence, and text completion.
□ Quantitative: Arithmetic, algebra, geometry, data analysis.
□ Analytical Writing: Issue task and argument task (two essays).
2. Create a Study Plan
• Assess Your Baseline: Take a practice test to understand your starting point and identify weak areas.
• Set a Target Score: Research the average GRE scores required for the programs you’re applying to and aim for a score that meets or exceeds that.
• Daily/Weekly Study Schedule: Break down your study plan over several weeks or months, dedicating specific time to each section of the GRE.
3. Strengthen Vocabulary
• Flashcards: Create flashcards or use apps like Quizlet or Magoosh to build your vocabulary. GRE tests understanding of complex words.
• Practice with Context: Learn new words in context, using example sentences to reinforce meaning.
4. Master Math Concepts
• Review Key Topics: Brush up on basic arithmetic, algebra, geometry, and data interpretation.
• Practice Problem-Solving: Focus on solving problems under timed conditions to simulate the test environment.
• Use Study Materials: Resources like Manhattan Prep, ETS’s official GRE materials, and Kaplan can be helpful.
5. Develop Analytical Writing Skills
• Practice Essays: Write essays regularly on different prompts from the ETS pool to develop structured and coherent arguments.
• Get Feedback: If possible, have someone review your essays and offer feedback, or use online scoring services.
6. Take Practice Tests
• Simulate Test Conditions: Take full-length practice tests under real-time constraints to build stamina and get familiar with the test format.
• Analyze Your Mistakes: Review each test thoroughly, focusing on areas where you made mistakes to improve.
• ETS PowerPrep: Use ETS’s official practice tests to get a feel for the actual GRE.
7. Time Management
• Pacing: During practice sessions, focus on completing sections within the time limit. Practice skimming passages quickly for the verbal section and using shortcuts for quantitative problems.
• Skipping Questions: Don’t get stuck on any one question. Learn to skip difficult questions and return to them later if time permits.
8. Use Quality Study Materials
• Books:
□ Official GRE Guide by ETS: Provides the closest approximation to the actual test.
□ Manhattan Prep: Detailed strategies and practice questions for each section.
□ Magoosh GRE Prep: Offers video lessons and practice questions with explanations.
• Apps: GRE study apps such as Magoosh or GRE Prep by Ready4 can be useful for on-the-go practice.
• Online Resources: Forums like Reddit’s GRE Prep or websites like GRE Prep Club are excellent for discussing strategies and finding tips.
9. Stay Consistent and Track Progress
• Keep track of your improvement by logging your practice test scores and review weak areas regularly.
• Use tools like study journals or spreadsheets to keep track of vocabulary, math formulas, and practice questions.
10. Relax Before the Exam
• Get a good night’s sleep before the test, and don’t over-study the day before. Make sure to eat well and arrive early at the test center with all necessary documents.
11. Consider Coaching or Classes
• If you prefer structured guidance, you might consider enrolling in a GRE prep course (online or in-person). Popular providers include Kaplan, Manhattan Prep, and Princeton Review.
With consistent practice, proper time management, and the right resources, you can achieve your target GRE score!
What is GRE syllabus?
The GRE syllabus covers three main sections: Verbal Reasoning, Quantitative Reasoning, and Analytical Writing. Below is a detailed breakdown of the syllabus for each section:
1. Verbal Reasoning
This section measures your ability to understand and analyze written material, evaluate arguments, and recognize relationships between words and concepts. It consists of two types of questions:
• Reading Comprehension: Test-takers are required to read passages and answer questions based on the content.
□ Comprehension questions can ask about the main idea, specific details, inferences, or logical structure.
• Text Completion: Sentences or paragraphs have one or more blanks, and you must choose the correct word(s) from the given options to complete the sentence meaningfully.
• Sentence Equivalence: A single sentence with one blank and six answer choices. Test-takers must select two words that provide equivalent meaning and complete the sentence appropriately.
Topics Covered:
• Vocabulary, synonyms, and antonyms
• Passage-based comprehension
• Identifying main ideas and supporting details
• Understanding word meanings in context
• Evaluating arguments and logical structure of passages
2. Quantitative Reasoning
This section tests basic mathematical concepts and quantitative problem-solving ability. It focuses on high-school-level math topics.
• Arithmetic: Includes properties of integers, operations, fractions, percentages, ratios, absolute values, and more.
• Algebra: Includes topics such as algebraic expressions, equations, inequalities, quadratic equations, and coordinate geometry.
• Geometry: Covers properties of shapes, area, perimeter, volume, the Pythagorean theorem, angles, and circles.
• Data Analysis: Covers data interpretation, mean, median, mode, range, standard deviation, probability, and sets.
Topics Covered:
• Arithmetic: Integers, exponents, factors, decimals, percentages, ratio and proportion, powers and roots, absolute values.
• Algebra: Solving linear and quadratic equations, inequalities, algebraic expressions, functions, coordinate geometry (lines, slopes, equations).
• Geometry: Basic concepts of angles, lines, triangles, polygons, circles, area, perimeter, and volume.
• Data Interpretation: Interpreting data from graphs, charts, tables, and using statistical measures (mean, median, mode, probability).
• Word Problems: Real-world application of mathematical concepts.
3. Analytical Writing
This section measures your ability to think critically, communicate complex ideas clearly, and support arguments with evidence. It consists of two tasks:
• Issue Task: You are presented with a statement or topic and asked to write an essay expressing your views. You must present a coherent argument and justify your position with reasons and
• Argument Task: You are given a passage that presents an argument. Your task is to critique the reasoning of the argument, evaluating its logical soundness, identifying any flaws, and suggesting
Skills Assessed:
• Critical thinking and analytical writing: Formulating and supporting complex ideas.
• Logical development: Structuring ideas and developing a clear, well-organized response.
• Argument evaluation: Assessing the validity of claims, reasoning, and evidence.
GRE Section Overview:
Section Question Types Skills Tested
Verbal Reasoning Reading comprehension, text completion, sentence equivalence Vocabulary, comprehension, critical reading
Quantitative Reasoning Arithmetic, algebra, geometry, data interpretation Mathematical reasoning, problem-solving, data analysis
Analytical Writing Issue essay, argument analysis essay Analytical writing, logical reasoning, argument critique
Each section is timed, with Verbal and Quantitative sections each lasting around 35 minutes per section (two sections each), and the Analytical Writing section consisting of two 30-minute essays.
By focusing on these topics, you can prepare effectively for the GRE! | {"url":"https://www.gillsir.com/gre/","timestamp":"2024-11-13T02:34:55Z","content_type":"text/html","content_length":"89040","record_id":"<urn:uuid:1d5728d4-7035-40fa-b5aa-438ac3574ea6>","cc-path":"CC-MAIN-2024-46/segments/1730477028303.91/warc/CC-MAIN-20241113004258-20241113034258-00802.warc.gz"} |
Identifying Three-Digit Numbers
Identifying Rational Numbers
Permutations and Combinations
Identifying the Number Properties
Multiply Multi-Digit Whole Numbers
KS3 Data Representation Homework
Significant Digits Review
MATH QUIZ BEE - IT'S ALL ABOUT MATH - GRADE 7 - 12
Unit 5 Day 13 How many pins?
7th 7-5 Determine Outcomes of Compound Events
Data representation - Binary
Identifying Numbers Revision
Data validation and verification
Explore Identifying Three-Digit Numbers Worksheets by Grades
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Explore printable Identifying Three-Digit Numbers worksheets for 7th Class
Identifying Three-Digit Numbers worksheets for Class 7 are essential tools for teachers looking to enhance their students' math skills and number sense. These worksheets provide a variety of
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mastering three-digit numbers and other essential math concepts. | {"url":"https://quizizz.com/en/identifying-three-digit-numbers-worksheets-class-7","timestamp":"2024-11-09T17:35:54Z","content_type":"text/html","content_length":"153221","record_id":"<urn:uuid:836fae7d-2640-4570-a37b-8a7f76f2393f>","cc-path":"CC-MAIN-2024-46/segments/1730477028125.59/warc/CC-MAIN-20241109151915-20241109181915-00069.warc.gz"} |
11th Innovations in Theoretical Computer Science Conference (ITCS 2020)
Cite as
Kousha Etessami, Christos Papadimitriou, Aviad Rubinstein, and Mihalis Yannakakis. Tarski’s Theorem, Supermodular Games, and the Complexity of Equilibria. In 11th Innovations in Theoretical Computer
Science Conference (ITCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 151, pp. 18:1-18:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)
Copy BibTex To Clipboard
author = {Etessami, Kousha and Papadimitriou, Christos and Rubinstein, Aviad and Yannakakis, Mihalis},
title = {{Tarski’s Theorem, Supermodular Games, and the Complexity of Equilibria}},
booktitle = {11th Innovations in Theoretical Computer Science Conference (ITCS 2020)},
pages = {18:1--18:19},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-134-4},
ISSN = {1868-8969},
year = {2020},
volume = {151},
editor = {Vidick, Thomas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2020.18},
URN = {urn:nbn:de:0030-drops-117037},
doi = {10.4230/LIPIcs.ITCS.2020.18},
annote = {Keywords: Tarski’s theorem, supermodular games, monotone functions, lattices, fixed points, Nash equilibria, computational complexity, PLS, PPAD, stochastic games, oracle model, lower bounds} | {"url":"https://drops.dagstuhl.de/entities/volume/LIPIcs-volume-151","timestamp":"2024-11-08T07:47:53Z","content_type":"text/html","content_length":"908295","record_id":"<urn:uuid:7be3e30a-bedc-434d-b38b-381af079b1ab>","cc-path":"CC-MAIN-2024-46/segments/1730477028032.87/warc/CC-MAIN-20241108070606-20241108100606-00738.warc.gz"} |
2 Digit By 2 Digit Multiplication Using Area Model Worksheets
Math, especially multiplication, forms the foundation of numerous academic self-controls and real-world applications. Yet, for numerous learners, mastering multiplication can position a difficulty.
To address this difficulty, educators and parents have actually welcomed a powerful device: 2 Digit By 2 Digit Multiplication Using Area Model Worksheets.
Intro to 2 Digit By 2 Digit Multiplication Using Area Model Worksheets
2 Digit By 2 Digit Multiplication Using Area Model Worksheets
2 Digit By 2 Digit Multiplication Using Area Model Worksheets -
Welcome to The Multiplying 2 Digit by 2 Digit Numbers A Math Worksheet from the Long Multiplication Worksheets Page at Math Drills This math worksheet was created or last revised on 2021 02 17 and
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Two digit By Two digit Multiplication using area model YouTube
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How To Teach Multiplication Using Area Model Free Printable Teaching Multiplication Teaching
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Area Model Multiplication 2 Digit By 1 Digit Worksheet Times Tables Worksheets
Multi Digit Multiplication Area model Partial Products Algorithm Puzzles Word Problems
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Multiplication 3 Digit By 2 Digit
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How To Teach Multiplication Using Area Model Free Printable
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Contact Info
Email: lspolaor@ucsd.edu
Ph.D., Mathematics, University of Zurich, Switzerland, 2015
Luca Spolaor received his Ph.D. in mathematics from the University of Zurich in 2015, with a dissertation which won a university award. He was subsequently a postdoc at the Max Planck Institute for
Mathematics in Leipzig and a C.L.E. Moore Instructor at the Massachusetts Institute of Technology. Moreover he spent one year as a visiting scholar appointed by Princeton University. Spolaor is an
expert in Geometric Measure Theory, a branch of Pure Mathematics at the intersection between Geometry and Analysis/Partial Differential Equations, whose goal is to study the behavior of singular
solutions to a number of problems coming mostly from Physics, Economics and Topology. This area of investigation fits between two stronger groups at UCSD, Geometric Analysis and Partial Differential
Equations, so has a synergistic effect. | {"url":"https://math.ucsd.edu/people/profiles/luca-spolaor","timestamp":"2024-11-03T00:29:22Z","content_type":"text/html","content_length":"34155","record_id":"<urn:uuid:c055ac4d-14d4-47a2-bd1c-601c64d1a924>","cc-path":"CC-MAIN-2024-46/segments/1730477027768.43/warc/CC-MAIN-20241102231001-20241103021001-00559.warc.gz"} |
What is: Q-Factor
What is Q-Factor?
The Q-Factor, often referred to in the context of statistics and data analysis, is a quantitative measure that helps in understanding the quality of a dataset or a statistical model. It serves as an
indicator of how well a particular model or dataset can predict outcomes based on the input variables. The Q-Factor is particularly significant in fields such as data science, where the accuracy and
reliability of predictive models are paramount. By evaluating the Q-Factor, data analysts can ascertain the effectiveness of their models and make informed decisions about further data collection or
model refinement.
Understanding the Components of Q-Factor
The Q-Factor is derived from several key components that contribute to its overall value. These components typically include the model’s predictive accuracy, the complexity of the model, and the
amount of data used for training. Predictive accuracy refers to how closely the model’s predictions align with actual outcomes, while model complexity pertains to the number of parameters or features
included in the model. The amount of training data is crucial as well; models trained on larger datasets tend to have a higher Q-Factor due to their ability to generalize better to unseen data.
Understanding these components is essential for data scientists aiming to optimize their models.
Applications of Q-Factor in Data Science
In data science, the Q-Factor is utilized in various applications, including machine learning, statistical modeling, and data mining. For instance, in machine learning, the Q-Factor can help in
selecting the best model among several candidates by providing a quantitative measure of each model’s performance. This is particularly useful in scenarios where multiple algorithms are tested, as it
allows data scientists to choose the model that not only performs well on training data but also generalizes effectively to new data. Additionally, the Q-Factor can be employed in feature selection
processes, guiding analysts in identifying which variables contribute most significantly to the model’s predictive power.
Calculating the Q-Factor
Calculating the Q-Factor involves a systematic approach that typically includes evaluating the model’s performance metrics, such as accuracy, precision, recall, and F1 score. These metrics provide
insights into how well the model is performing and can be combined to derive a single Q-Factor score. The formula for calculating the Q-Factor may vary depending on the specific context and the type
of model being evaluated. However, it generally incorporates elements that reflect both the model’s predictive capabilities and its complexity, ensuring a comprehensive assessment of its overall
Q-Factor in Predictive Analytics
In the realm of predictive analytics, the Q-Factor plays a crucial role in determining the reliability of forecasts generated by statistical models. Predictive analytics relies heavily on the ability
to make accurate predictions based on historical data, and the Q-Factor serves as a benchmark for assessing the effectiveness of these predictions. By analyzing the Q-Factor, analysts can identify
potential weaknesses in their models, such as overfitting or underfitting, and take corrective measures to enhance predictive accuracy. This iterative process of evaluation and refinement is
essential for developing robust predictive models that can withstand real-world applications.
Q-Factor and Model Validation
Model validation is a critical step in the data analysis process, and the Q-Factor is integral to this phase. Validation techniques, such as cross-validation and bootstrapping, often incorporate the
Q-Factor to assess the stability and reliability of a model’s predictions. By applying these techniques, data scientists can evaluate how well their models perform on different subsets of data,
thereby gaining insights into their generalizability. A high Q-Factor during validation indicates that the model is likely to perform well on unseen data, which is a key requirement for any
predictive modeling task.
Limitations of Q-Factor
Despite its usefulness, the Q-Factor is not without limitations. One significant drawback is that it may not fully capture the nuances of model performance in all scenarios. For instance, a model
with a high Q-Factor may still exhibit poor performance in specific contexts or datasets. Additionally, the Q-Factor can be influenced by the choice of evaluation metrics, which may lead to varying
interpretations of a model’s effectiveness. Therefore, while the Q-Factor is a valuable tool for assessing model quality, it should be used in conjunction with other evaluation methods to obtain a
more comprehensive understanding of model performance.
Improving Q-Factor Scores
Improving the Q-Factor score of a model involves several strategies that focus on enhancing predictive accuracy and reducing model complexity. One effective approach is to conduct feature
engineering, which involves creating new features or modifying existing ones to better capture the underlying patterns in the data. Additionally, employing ensemble methods, such as bagging and
boosting, can help improve the Q-Factor by combining the strengths of multiple models. Regularly updating the model with new data and retraining it can also lead to better Q-Factor scores, as it
ensures that the model remains relevant and accurate in a changing data landscape.
Future Trends in Q-Factor Analysis
As the fields of statistics, data analysis, and data science continue to evolve, the concept of the Q-Factor is likely to undergo significant advancements. Emerging technologies, such as artificial
intelligence and deep learning, may introduce new methodologies for calculating and interpreting the Q-Factor. Furthermore, the integration of big data analytics could enhance the Q-Factor’s
applicability across diverse datasets and industries. Researchers and practitioners will need to stay abreast of these developments to effectively leverage the Q-Factor in their analytical endeavors,
ensuring that they maintain a competitive edge in the rapidly changing landscape of data science. | {"url":"https://statisticseasily.com/glossario/what-is-q-factor/","timestamp":"2024-11-02T11:50:39Z","content_type":"text/html","content_length":"139768","record_id":"<urn:uuid:1bb8f66c-21b7-4659-b18a-8130336057f3>","cc-path":"CC-MAIN-2024-46/segments/1730477027710.33/warc/CC-MAIN-20241102102832-20241102132832-00134.warc.gz"} |
compiling direct x version
05-31-2014, 07:32 PM
Post: #151
Dona12345 Posts: 45
userandroid Joined: Mar 2013
Reputation: 0
RE: compiling direct x version
hi i want to talk with developer if is possible to have buffered rendering in directx mode. i have a asus f9e and the emulator works very well now in the new build, i have only a problem with
buffered rendering that appear black screen ,sorry my not perfect english
06-03-2014, 08:32 AM
Post: #152
raintime Posts: 38
Junior Member Joined: May 2014
Reputation: 0
RE: compiling direct x version
the developer seems lack interest, we must support anyone who wants to continue and contribute for the development of the ppsspp with directx backend support, such a great project, the original
developer should see this
06-07-2014, 08:01 AM
Post: #153
Arborea Posts: 45
Junior Member Joined: May 2014
Reputation: -1
RE: compiling direct x version
(06-03-2014 08:32 AM)raintime Wrote: the developer seems lack interest, we must support anyone who wants to continue and contribute for the development of the ppsspp with directx backend
support, such a great project, the original developer should see this
Directx9 is way outdated only Directx12 backend makes sense at this point.
06-07-2014, 08:15 AM
Post: #154
Bigpet Posts: 456
Senior Member Joined: Nov 2013
Reputation: 23
RE: compiling direct x version
The only reason people are asking for a DirectX backend is so that it works on old devices that only have crappy GPU drivers that don't support OpenGL 2.0 how will DirectX12 help those people?
06-07-2014, 11:09 AM
(This post was last modified: 06-07-2014 11:09 AM by Arborea.)
Post: #155
Arborea Posts: 45
Junior Member Joined: May 2014
Reputation: -1
RE: compiling direct x version
(06-07-2014 08:15 AM)Bigpet Wrote: The only reason people are asking for a DirectX backend is so that it works on old devices that only have crappy GPU drivers that don't support OpenGL 2.0 how
will DirectX12 help those people?
Maybe it wont help those people in particular but can help performance and possibly add more graphical features.
06-07-2014, 12:29 PM
Post: #156
Bigpet Posts: 456
Senior Member Joined: Nov 2013
Reputation: 23
RE: compiling direct x version
So we have will actually help people versus "can help performance and possibly add more graphical features."?
06-07-2014, 12:37 PM
Post: #157
Raimoo Posts: 1,018
Currently Lurking o,o Joined: Nov 2013
Reputation: 20
RE: compiling direct x version
(06-07-2014 11:09 AM)Arborea Wrote:
(06-07-2014 08:15 AM)Bigpet Wrote: The only reason people are asking for a DirectX backend is so that it works on old devices that only have crappy GPU drivers that don't support OpenGL 2.0
how will DirectX12 help those people?
Maybe it wont help those people in particular but can help performance and possibly add more graphical features.
You pretty much get the wrong idea here... the DirectX backend was mend to make PPSSPP playable on device that doesn't support OpenGL2.0. DirectX12 may "can help performance and possibly add more
graphical feature" but if it doesn't works on the device I mention earlier, why do you even bother to have the latest DirectX implemented in PPSSPP then?
o.o Oh Hi XD
P.S: Wanted to go to Japan so badly
Windows 7 Home Basic (32bit)
Intel Atom N2800 (Quad-core) 1.86GHz
Intel Graphic Media Accelerator 3600 series
06-08-2014, 11:23 PM
Post: #158
raintime Posts: 38
Junior Member Joined: May 2014
Reputation: 0
RE: compiling direct x version
that's right ppsspp to work on old devices that doesn't support opengl2.0, just like my laptop opengl 1.4, a lot of people are still using old pc or laptop that's also the reason they wanted the
backend support, the angle port originally created by ced and mod by bigpet runs all psp games on old devices, however a bit of graphics fix should be made, and its perfect just like the latest build
of today
06-09-2014, 12:01 AM
(This post was last modified: 06-09-2014 12:01 AM by Bigpet.)
Post: #159
Bigpet Posts: 456
Senior Member Joined: Nov 2013
Reputation: 23
RE: compiling direct x version
I think you misunderstood. Ced wrote an actual directx backend (that was never completely integrated back into ppsspp)
I just changed the wgl initialization function calls to egl and that automatically made the ANGLE library work (which translates opengl calls to DirectX calls, think of WINE but in the other
What ced did and what I did are completely different things. What he did takes a lot of time and knowledge of DirectX, what I did was just change a few function calls.
06-12-2014, 03:28 AM
Post: #160
raintime Posts: 38
Junior Member Joined: May 2014
Reputation: 0
RE: compiling direct x version
then someone please patch this for the newest ppsspp build, thanks a lot
06-18-2014, 12:25 PM
(This post was last modified: 06-18-2014 12:25 PM by Arborea.)
Post: #161
Arborea Posts: 45
Junior Member Joined: May 2014
Reputation: -1
RE: compiling direct x version
(06-07-2014 12:37 PM)Raimoo Wrote:
(06-07-2014 11:09 AM)Arborea Wrote:
(06-07-2014 08:15 AM)Bigpet Wrote: The only reason people are asking for a DirectX backend is so that it works on old devices that only have crappy GPU drivers that don't support OpenGL
2.0 how will DirectX12 help those people?
Maybe it wont help those people in particular but can help performance and possibly add more graphical features.
You pretty much get the wrong idea here... the DirectX backend was mend to make PPSSPP playable on device that doesn't support OpenGL2.0. DirectX12 may "can help performance and possibly add more
graphical feature" but if it doesn't works on the device I mention earlier, why do you even bother to have the latest DirectX implemented in PPSSPP then?
Thats not a problem DirectX is backwards compatible so Directx12 should work on gpus with lower feature levels but it would be most useful for Windows users with new hardware.
06-22-2014, 05:15 AM
Post: #162
Tabris666 Posts: 54
Member Joined: Jun 2014
Reputation: -3
RE: compiling direct x version
The directX would be interesting but i think the person implied thay he was unable to use ppsspp because it have old gpu i asume he is using windows xp so asume if is posible directx9 because thats
the only directx for windows xp.
now directx12 is not backward compatible (beta tester of windows 8 with direct X 12) in fact the last version of direct X rrendered unusable almost all my games even the directx 11 games so is
unacceptable if is posible the implementation of that version.
i have readed cmments saying if you have opengl 2.0 you can use ppsspp but is imposible i have an old gpu with open gl 2.0 but it have pixel shader 2.0 and appears a warning saying you need a gpu
with pixel shader 3.0 to work" if is posible to make a directx version would be fun to test
06-22-2014, 01:46 PM
(This post was last modified: 06-22-2014 02:58 PM by Arborea.)
Post: #163
Arborea Posts: 45
Junior Member Joined: May 2014
Reputation: -1
RE: compiling direct x version
(06-22-2014 05:15 AM)Tabris666 Wrote: The directX would be interesting but i think the person implied thay he was unable to use ppsspp because it have old gpu i asume he is using windows xp so
asume if is posible directx9 because thats the only directx for windows xp.
now directx12 is not backward compatible (beta tester of windows 8 with direct X 12) in fact the last version of direct X rrendered unusable almost all my games even the directx 11 games so is
unacceptable if is posible the implementation of that version.
i have readed cmments saying if you have opengl 2.0 you can use ppsspp but is imposible i have an old gpu with open gl 2.0 but it have pixel shader 2.0 and appears a warning saying you need a gpu
with pixel shader 3.0 to work" if is posible to make a directx version would be fun to test
You are hard to understand but Dirextx12 isnt available currently and most likely wont available on Windows 8.0 so I dont know what you are talking even if you have early access to SDK or some very
early version DirectX12 it is likely not working properly yet and there are no GPUs currently with full hardware support for Directx12 also Dirext12 require WDDM 2.0 while Windows 8.1 has WDDM 1.3 so
I dont know how can you use Directx12 on Windows 8. Bottom line is Directx is backwards compatible newer versions can play old games which used lower feature levels.
06-23-2014, 02:55 AM
Post: #164
NgJinXiang14 Posts: 116
Monster Hunter Fan Joined: Dec 2013
Reputation: 3
RE: compiling direct x version
Please try to shut up and make a new version ppsspp with directx support for adhoc,dont say directx 12 or bla bla bla.
Sry for bad english im chinese at malaysia
06-23-2014, 07:13 AM
(This post was last modified: 06-23-2014 07:14 AM by Arborea.)
Post: #165
Arborea Posts: 45
Junior Member Joined: May 2014
Reputation: -1
RE: compiling direct x version
(06-23-2014 02:55 AM)NgJinXiang14 Wrote: Please try to shut up and make a new version ppsspp with directx support for adhoc,dont say directx 12 or bla bla bla.
No reason to be arrogant and I will talk about Directx12 if I want to. | {"url":"https://forums.ppsspp.org/showthread.php?tid=2399&page=11","timestamp":"2024-11-05T09:30:37Z","content_type":"application/xhtml+xml","content_length":"77166","record_id":"<urn:uuid:05c5492b-d592-4197-9ce3-b08b1376895b>","cc-path":"CC-MAIN-2024-46/segments/1730477027878.78/warc/CC-MAIN-20241105083140-20241105113140-00576.warc.gz"} |
Constructing a frequency distribution 2022 Best - Superb-Writers
Constructing a frequency distribution 2022 Best
This assignment involves constructing a frequency distribution and creating 2 different visual representations of data collected (pie chart, bar graph, etc).
Constructing a frequency distribution
Answer the questions below about your data adhering to the outlined criteria in complete sentences. Cite any outside sources that are used. Item Description 1 Treat your data just as you would one of
the datasets from the homework. Be sure you include appropriate measures of central tendency and dispersion etc. 2 Construct a frequency distribution using 5 –8 classes. 3 Create 2 different but
appropriate visual representations of your data (pie chart, bar graph, etc). You MUST use Excel to do this. 4 Complete the calculations for the 8 statistics you identified in your worksheet in week
Constructing a frequency distribution
You MUST use Excel to do this. 5 Write a brief paragraph describing the meaning or interpretation for EACH of the statistics. For example, if some of the statistics chosen were the mean, median and
mode, which is the best measure? 6 Construct a 95% Confidence Interval to estimate the population mean/proportion in the claim. 7 Complete the calculations for the 8 statistics
you identified in your What can you conclude from this result regarding the topic? 8 Write up the responses to these questions in an APA paper between 500-1,000 words.
Constructing a frequency distribution
Length/Formatting Instructions Length 500-1,000 Words Font 12 point , Calibri Font, no more than 1″ margins Program/File Type Submit in Word Attachments Should be pasted into the Word document if
possible. Referencing system APA referencing system is necessary in assignments, especially material copied from the Internet. For examples of correct citations, visit the following link: http://
owl.english.purdue.edu/owl/resource/560/01/. https://youtu.be/vKWStqSbdXE
Additional Files | {"url":"https://www.superb-writers.com/constructing-a-frequency-distribution/","timestamp":"2024-11-13T16:02:51Z","content_type":"application/xhtml+xml","content_length":"109960","record_id":"<urn:uuid:cca9ac5f-b122-4ed5-8fff-b9b3293afe28>","cc-path":"CC-MAIN-2024-46/segments/1730477028369.36/warc/CC-MAIN-20241113135544-20241113165544-00755.warc.gz"} |
List Simplification
simplifyDims {Hmisc} R Documentation
List Simplification
Takes a list where each element is a group of rows that have been spanned by a multirow row and combines it into one large matrix.
All rows must have the same number of columns. This is used to format the list for printing.
a matrix that contains all of the spanned rows.
Charles Dupont
See Also
a <- list(a = matrix(1:25, ncol=5), b = matrix(1:10, ncol=5), c = 1:5)
version 5.1-3 | {"url":"https://search.r-project.org/CRAN/refmans/Hmisc/html/simplifyDims.html","timestamp":"2024-11-13T14:20:29Z","content_type":"text/html","content_length":"2343","record_id":"<urn:uuid:b5d80130-4489-47e9-ac23-19e9800b7282>","cc-path":"CC-MAIN-2024-46/segments/1730477028369.36/warc/CC-MAIN-20241113135544-20241113165544-00481.warc.gz"} |
How Many Blocks Are There In 1 Square Meter (1m²) | Guardian Constructors
How Many Blocks Are There In 1 Square Meter (1m²)
For most builders and contractor or clients, the most challenging problem is being able to know how many block there are in 1 square meter.
So If i were to charge a client per square meter in bricklaying, how many blocks actually make a square meter or 1m²?
In order to be able to determine the number if blocks needed for every 1m², we have to be able to calculate the area of the surface area of one block.
How Many Blocks Are there in one Square meter?
Nigerian blocks have length of 1.6 ft. The height is actually 9 inches…
Now let’s convert these to the S.I unit (meters)
1.6 ft = 45.72cm
9 inches = 22.86cm
45.72/100 = 0.4572m
22.86/100 = 0.2286m
What is the Area Of a 9 inch Block?
We simply multiply the length by the height to get the area.
Area = 0.4572 x 0.2286 = 0.1045
1/0.1045 = 9.6 blocks
Therefore, in every 1 square meter, we have a total of 9.5 blocks or 10 blocks but as you know, we would need to leave some space for bonding..
what is the meaning of one square meter?
Mark another 1 meter such that both intersect at the edges. Now close the other edges!
Please try to share with others in order to help them get enlightened too
8 Comments
1. For Australia. Blocks .390 x .190 face area.
Allow for 14 blocks per square metre.
2. 0.2286 x 0.4572 = 0.10451592 your answer is wrong
3. Corrected now.
Thanks for correcting me
4. Thank you so much for this explanation
5. Richard Nwachukwu
Your answer isn't wrong please. . Approximate to four decimal places and your are very correct!
6. Sold block 8inches 600sq ft how many stones
7. thank you very much for taking the time to write and post this online it really helps!
□ 9 blocks for 1square metre. | {"url":"https://guardianconstructors.com/2017/05/how-many-blocks-are-there-in-1-square.html","timestamp":"2024-11-07T04:26:13Z","content_type":"text/html","content_length":"217587","record_id":"<urn:uuid:8d98e26d-09d3-4c8b-842a-847ffafd055a>","cc-path":"CC-MAIN-2024-46/segments/1730477027951.86/warc/CC-MAIN-20241107021136-20241107051136-00517.warc.gz"} |
[Solved] चंद्रावर वातावरण नाही. कारण काय आहे?
चंद्रावर वातावरण नाही. कारण काय आहे?
Answer (Detailed Solution Below)
Option 2 : गुरुत्वाकर्षण शक्ती तुलनेने कमी आहे
ST 1: Theory of Structures - UKPSC AE Civil
3 K Users
20 Questions 40 Marks 20 Mins
कारण गुरुत्वाकर्षण शक्ती तुलनेने कमी आहे. तर, सुटण्याचा वेग कमी आहे आणि वायूंचे गुरुत्वाकर्षण बल कमी आहे.
संकल्पना :
सुटलेला वेग
• हा किमान वेग आहे ज्याने ग्रहाच्या पृष्ठभागावरून वस्तू प्रक्षेपित केली पाहिजे जेणेकरून शरीर अनंतापर्यंत पोहोचेल .
• असे दिले आहे,
\(⇒ v_{e}=\sqrt{\frac{2GM}{R}}\)
जेथे v e = एस्केप वेग, G = गुरुत्वाकर्षण प्रवेग, M = ग्रहाचे वस्तुमान आणि R = ग्रहाची त्रिज्या
दिलेले - चंद्राचे वस्तुमान (Mm ) = 7.4x1022 kg, चंद्राची त्रिज्या (Rm ) = 1.75x106m आणि G = 6.67x10-11 Nm2 /kg2
• त्यामुळे चंद्राचा सुटलेला वेग असा दिला जातो,
\(⇒ v_{e}=\sqrt{\frac{2GM_{m}}{R_{m}}}\)
⇒ v e = 2.38 किमी/सेकंद
• चंद्राचा सुटण्याचा वेग मुळापेक्षा कमी म्हणजे चंद्रावरील वायूच्या रेणूंचा चौरस वेग , त्यामुळे चंद्रावर वातावरण नाही.
Latest UKPSC AE Updates
Last updated on May 31, 2024
-> UKPSC AE Result has been released!
-> UKPSC has released the result of written (objective type) examination.
-> The successful candidates have been declared provisionally successful for the interview.
-> A total of 171 vacancies are available for this post. Boost your exam preparation with UKPSC AE Previous Year Papers. | {"url":"https://testbook.com/question-answer/mr/there-is-no-atmosphere-on-the-moon-it-is-because--61939eb003a25a62cb351cc0","timestamp":"2024-11-03T12:09:01Z","content_type":"text/html","content_length":"211868","record_id":"<urn:uuid:c5d94a4b-20c6-4e8c-b0ed-5acf4bc151ee>","cc-path":"CC-MAIN-2024-46/segments/1730477027776.9/warc/CC-MAIN-20241103114942-20241103144942-00172.warc.gz"} |
Statistical Significance Tests
The means of quantitative measurements from two groups can be compared using Student’s t-test. To compare the means of measurements for more than two levels of a categorical variable, one-way ANOVA
has to be used. Here, we’ll explore the parametric, one-way ANOVA test as well as the non-parametric version of the test, the Kruskal-Wallis test, which compares median values. | {"url":"https://www.datascienceblog.net/categories/statistical-test/","timestamp":"2024-11-08T14:20:22Z","content_type":"text/html","content_length":"49146","record_id":"<urn:uuid:cd6b90eb-b60d-4c22-9a04-7032607d9bb1>","cc-path":"CC-MAIN-2024-46/segments/1730477028067.32/warc/CC-MAIN-20241108133114-20241108163114-00687.warc.gz"} |
Package org.geotools.referencing.crs
Coordinate reference systems
implementation. An explanation for this package is provided in the OpenGIS® javadoc. The remaining discussion on this page is specific to the Geotools implementation.
AbstractCRS is the base class for all coordinate reference systems (CRS). CRS can have an arbitrary number of dimensions. Some are two-dimensional (e.g. GeographicCRS and ProjectedCRS), while some
others are one-dimensional (e.g. VerticalCRS and TemporalCRS). Those simple coordinate systems can be used as building blocks for more complex coordinate reference systems. For example, it is
possible to construct a three-dimensional CRS with (latitude, longitude, time) with an aggregation of GeographicCRS and TemporalCRS. Such aggregations are built with CompoundCRS.
• Class Summary
Class Description
AbstractCRS Abstract coordinate reference system, usually defined by a coordinate system and a datum.
A coordinate reference system that is defined by its coordinate
AbstractDerivedCRS from another coordinate reference system (not by a
DefaultCompoundCRS A coordinate reference system describing the position of points through two or more independent coordinate reference systems.
DefaultDerivedCRS A coordinate reference system that is defined by its coordinate conversion from another coordinate reference system but is not a projected coordinate reference system.
DefaultEngineeringCRS A contextually local coordinate reference system.
DefaultGeocentricCRS A 3D coordinate reference system with the origin at the approximate centre of mass of the earth.
A coordinate reference system based on an ellipsoidal approximation of the geoid; this provides an accurate representation of the geometry of geographic features for a large
DefaultGeographicCRS portion of the earth's surface.
DefaultImageCRS An engineering coordinate reference system applied to locations in images.
DefaultProjectedCRS A 2D coordinate reference system used to approximate the shape of the earth on a planar surface.
DefaultTemporalCRS A 1D coordinate reference system used for the recording of time.
DefaultVerticalCRS A 1D coordinate reference system used for recording heights or depths. | {"url":"https://docs.geotools.org/latest/javadocs/org/geotools/referencing/crs/package-summary.html","timestamp":"2024-11-08T23:41:18Z","content_type":"text/html","content_length":"11852","record_id":"<urn:uuid:d8264ab9-1d2b-4237-8440-ae7558472097>","cc-path":"CC-MAIN-2024-46/segments/1730477028106.80/warc/CC-MAIN-20241108231327-20241109021327-00540.warc.gz"} |
psychology – Pertinent Observations
This morning, when I got back from the gym, my wife and daughter were playing 20 questions, with my wife having just taught my daughter the game.
Given that this was the first time they were playing, they started with guessing “2 digit numbers”. And when I came in, they were asking questions such as “is this number divisible by 6” etc.
To me this was obviously inefficient. “Binary search is $O(log n)$“, I realised in my head, and decided this is a good time to teach my daughter binary search.
So for the next game, I volunteered to guess, and started with “is the number $\ge 55$“? And went on to “is the number $\ge 77$“, and got to the number in my wife’s mind (74) in exactly 7 guesses
(and you might guess that $\lceil log_2 90 \rceil$ (90 is the number of 2 digit numbers) is 7).
And so we moved on. Next, I “kept” 41, and my wife went through a rather random series of guesses (including “is it divisible by 4” fairly early on) to get in 8 tries. By this time I had been feeling
massively proud, of putting to good use my computer science knowledge in real life.
“See, you keep saying that I’m not a good engineer. See how I’m using skills that I learnt in my engineering to do well in this game”, I exclaimed. My wife didn’t react.
It was finally my daughter’s turn to keep a number in mind, and my turn to guess.
“Is the number $\ge 55$?”
“Is the number $\ge 77$?”
“Is the number $\ge 88$?”
My wife started grinning. I ignored it and continued with my “process”, and I got to the right answer (99) in 6 tries. “You are stupid and know nothing”, said my wife. “As soon as she said it’s
greater than 88, I knew it is 99. You might be good at computer science but I’m good at psychology”.
She had a point. And then I started thinking – basically the binary search method works under the assumption that the numbers are all uniformly distributed. Clearly, my wife had some superior
information to me, which made 99 far more probable than any number between 89 and 98. And s0 when the answer to “Is the number $\ge 88$?”turned out to by “yes”, she made an educated guess that it’s
And since I’m used to writing algorithms, and teaching dumb computers to solve problems, I used a process that didn’t make use of any educated guesses! And thus took far many more steps to get to
the answer.
When the numbers don’t follow a uniform distribution, binary search works differently. You don’t start with the middle number – instead, you start with the weighted median of all the numbers! And
then go on to the weighted median of whichever half you end up in. And so on and so forth until you find the number in the counterparty’s mind. That is the most optimal algo.
Then again, how do you figure out what the prior distribution of numbers is? For that, I guess knowing some psychology helps.
Jordan Peterson’s Chapter Eleven
So I read Jordan Peterson’s 12 Rules For Life last month. It took a bit of an effort, and there were a couple of occasions when I did wonder if I should abandon the book. However, my stated aim of
reading at least 50 books this year made me soldier on, and in the end I’m glad I finished it. Especially for Chapter Eleven of the book (Do not bother children when they are skateboarding).
Now, this is a long chapter, and Peterson spends considerable time rambling about various controversies he has got involved in over the last few years – such as his stand on political correctness, or
his stand on environmentalism (in fact, he has an interesting take on the latter – that environmentalism and climate change worries have an adverse impact on mental health of people, so I didn’t mind
reading him on that!).
The chapter is about risk – one thought (which has also been expressed by Nassim Nicholas Taleb in one of his books – which one I can’t remember), is that people have a “natural level of risk”. And
if you, for whatever reason, prevent them from taking that risk, they will find other ways to take risk, perhaps indulging in riskier activities.
And in order to explain why we are fundamentally wired to take risk, Peterson talks about gender, and relationships. He talks about friend-zoning, for example:
Girls aren’t attracted to boys who are their friends, even though they might like them, whatever that means. They are attracted to boys who win status contests with other boys.
And winning these status contests involves taking risk! Peterson goes on about relationships, about the crisis in the United States nowadays where women are more educated than men (on average), and
then choose to remain single rather than “marrying down”.
This is the bit which really caught my attention – the apparent contradiction between the desire for women to do well, and this desire resulting in their not being able to find partners for
themselves. And there are no easy solutions here. The desire for a woman to “marry up” is biological, and nobody can be faulted for being ambitious and wanting to do well for themselves in life.
Now, it is easy to go all ad hominem about this argument, calling Peterson a chauvinist and a traditionalist (as his opponents, mostly on the political left, have done), but the problem he mentions
is real, and as the father of a (rather young) daughter, it hit hard for me – obviously I want her to do really well in life and make a mark professionally; but I also want her to propagate my genes,
and do a good job of that.
I’m hopeful that as the daughter of Marriage Broker Auntie, she’ll be able to sort things out. But them, she may not want to listen to her mother – at least in these matters!
There were other places where the book was really inspirational. Chapter Twelve had a simple message – that there are times when you go through shit, and a way to get through them is to appreciate
the smaller joys of life. In fact, Peterson is at his best when he talks about clinical psychology – which is the topic of his everyday research.
He does a fantastic job in Chapter One as well, and I may not be exaggerating by saying that the chapter was thought-provoking enough to make me analyse how I might have ended up with depression, and
then make a conscious effort to avoid those actions that either betrayed depression, or made me feel more depressed. And that makes me get why people contribute so much to him on Patreon. Some of his
advice can indeed be life changing.
However, I have no plans to pay him anything more than the £9.99 I paid Amazon for the book. And that is partly because the psychology parts of the book are indeed brilliant, he frequently goes on
long rambling thoughts on religion (Christianity in particular, since that is the religion most familiar to him) and philosophy. And in those parts (there’s an especially long sequence between
chapters 7 to 10 of the book), the book gets incredibly laboured and boring.
I recommend you read the book. The clinical psychology parts of it are nothing short of brilliant. There’s a lot of religion and psychology you will need to go through as well, and I hope you find
more insight there than I managed to!
Here are the notes and highlights I made from the book. | {"url":"https://www.noenthuda.com/tag/psychology/","timestamp":"2024-11-03T01:18:35Z","content_type":"text/html","content_length":"87719","record_id":"<urn:uuid:310623bf-2a0a-4f57-9452-7b9a387b2703>","cc-path":"CC-MAIN-2024-46/segments/1730477027768.43/warc/CC-MAIN-20241102231001-20241103021001-00286.warc.gz"} |
Single Hydraulic Cylinder Simulation
This example shows how to use Simulink® to model a hydraulic cylinder. You can apply these concepts to applications where you need to model hydraulic behavior.
Model Analysis and Physics
This schematic diagram shows a model of a hydraulic cylinder. The model directs the pump flow, Q, to supply pressure, p1, from which the laminar flow, q1ex, leaks to exhaust. The control valve for
the piston/cylinder assembly is modeled as turbulent flow through a variable-area orifice. Its flow, q12, leads to intermediate pressure, p2, which undergoes a subsequent pressure drop in the line
connecting it to the actuator cylinder. The cylinder pressure, p3, moves the piston against a spring load, resulting in position x.
At the pump output, the flow is split between leakage and flow to the control valve. The model uses the Equation Set 1 equations to simulate the leakage, q1ex, as laminar flow.
Equation Set 1
The model implements the orifice equation to simulate turbulent flow through the control valve. The sign and absolute value functions accommodate flow in either direction, as shown in Equation Set 2.
Equation Set 2
The fluid within the cylinder pressurizes due to the fluid flow, q12 = q23, minus the compliance of the piston motion. The model implements the fluid flow and flow compressibility using the Equation
Set 3 equations.
Equation Set 3
The model neglects the piston and spring masses because of the large hydraulic forces. The system of equations is incorporated by differentiating this relationship and incorporating the pressure drop
between p2 and p3.
Equation Set 3 models laminar flow from the valve to the actuator. Equation Set 4 gives the force balance at the piston.
Equation Set 4
Run the Simulation
To run the simulation, on the Simulink Toolstrip, click Run.
During simulation, the model logs relevant data to the MATLAB workspace in the Simulink.SimulationOutput object out. Signal logging data is stored in the out object, in a structure called
sldemo_hydcyl_output. Logged signals have a blue badge.
Pump Subsystem
To look under the Pump subsystem mask, right-click the Pump subsystem and select Mask > Look Under Mask. The pump model computes the supply pressure as a function of the pump flow and the load
(output) flow. Qpump is the pump flow data, which is saved in the model workspace. A matrix with column vectors of time points and the corresponding flow rates [T,Q] specifies the flow data. The
model calculates pressure p1, as indicated in Equation Set 1. Because Qout = q12 is a direct function of p1 via the control valve, an algebraic loop is formed. An estimate of the initial value, p10,
enables a more efficient solution.
You can use 'Pump' subsystem mask to access and change the T, Q, p10, and C2 parameters.
Valve/Cylinder/Piston/Spring Assembly Subsystem
To view the Actuator subsystem, right-click the mased Valve/Cylinder/Piston/Spring Assembly subsystem and select Mask > Look Under Mask. A system of differential-algebraic equations models the
cylinder pressurization with the pressure p3, which appears as a derivative in Equation Set 3 and is used as the state (integrator). If the piston mass is neglected, the spring force and piston
position are direct multiples of p3, and the velocity is a direct multiple of the time derivative of p3. The latter relationship forms an algebraic loop around the Beta Gain block. The intermediate
pressure p2 is the sum of p3 and the pressure drop due to the flow from the valve to the cylinder (Equation Set 4). This relationship also imposes an algebraic constraint through the control valve
and the 1/C1 gain.
The control valve subsystem computes the orifice (Equation Set 2). The control valve subsystem uses the upstream and downstream pressures and the variable orifice area as inputs. The Control Valve
Flow subsystem computes the signed square root:
The subsystem implements three nonlinear functions, two of which are discontinuous. In combination, however, y is a continuous function of u.
The model simulation uses the data loaded from the MAT-file sldemo_hydcyl_data.mat. You can change parameter values via the Pump and Cylinder masks.
T = [0 0.04 0.04 0.05 0.05 0.1 ] sec
Q = [0.005 0.005 0 0 0.005 0.005] m^3/sec
Plot Simulation Results
The system initially steps to a pump flow of 0.005 m^3/sec=300 l/min, steps to zero at t=0.04 sec, and then resumes its initial flow rate at t=0.05 sec.
The control valve starts with zero orifice area and ramps to 1e-4 sq.m. during the 0.1 sec simulation time. With the valve closed, all of the pump flow goes to leakage, so the initial pump pressure
increases to p10 = Q/C2 = 1667 kPa.
As the valve opens, pressures p2 and p3 build up while p1 decreases in response to the load increase. When the pump flow cuts off, the spring and piston act like an accumulator, and p3 decreases
continuously. Then, the flow reverses direction, so p2, though relatively close to p3, falls. At the pump itself, all of the back-flow leaks, and p1 drops. The behavior reverses as the flow is
The piston position is directly proportional to p3, where the hydraulic and spring forces balance. Discontinuities in the velocity at 0.04 sec and 0.05 sec indicate negligible mass. The model reaches
a steady state when all of the pump flow again goes to leakage, which is now due to a zero pressure-drop across the control valve when p3 = p2 = p1 = p10.
Related Examples
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• 87659256 contains a backwards run of 4. In 0.33% of 8-digit numbers, there are backwards runs of 4 or longer.
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