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# Authoritative server controlling objects in multiple scenes in Unity3D
I am working on a multiplayer project that involves loading into different scenes and playing some kind of mini-game with any other players that happen to be in the scene at that time. These mini-games will contain AI that needs to be controlled by a dedicated server. Additionally, there is simulation that needs to happen in these scenes, even if no player is currently in one.
My first idea to take a crack at this was to have my server on startup, load all of the scenes in the game using LoadSceneMode.Additive This way, on the server side, each scene would be in one place and available to be simulated.
I made a little sample project with three scenes, a base world, and two other worlds. When the server is started from the Base World scene, it loads World1 and World2 into its scene. From my server, I could spawn a cube in World1 by pressing the 1 key, and I could spawn a cube in World2 by pressing the 2 key.
I used the following code to spawn the cube:
GameObject cube = (GameObject)Instantiate(myPrefab, new Vector3(0, 10, 0), Quaternion.identity);
NetworkServer.Spawn(cube);
The problem is, if a cube is spawned in World1, clients in World2 still spawn the cube. In hindsight this makes sense because the documentation for NetworkServer.Spawn states
Spawn the given game object on all clients which are ready.
My next idea was that I could designate one player in the minigame as a psuedo "host" and his machine would be responsible for running the AI. However, with this method, I really cant simulate things going on when nobody is in the scene.
Is there a better way I should go about solving this problem? How can I create a dedicated server which can simulate multiple scenes at once? Should each scene be handled by its own server? Am I better off just trying to run everything in one scene? | |
# Sequential Quantile Estimation
2 papers with code • 0 benchmarks • 0 datasets
This task has no description! Would you like to contribute one?
# Computing Extremely Accurate Quantiles Using t-Digests
11 Feb 2019
We present on-line algorithms for computing approximations of rank-based statistics that give high accuracy, particularly near the tails of a distribution, with very small sketches.
4
# Sequential Quantiles via Hermite Series Density Estimation
17 Jul 2015
These algorithms go beyond existing sequential quantile estimation algorithms in that they allow arbitrary quantiles (as opposed to pre-specified quantiles) to be estimated at any point in time.
1 | |
Página 1 dos resultados de 433 itens digitais encontrados em 0.032 segundos
## Formal specification of a specification library
Atreya, Sriram K
Fonte: Massachusetts Institute of Technology Publicador: Massachusetts Institute of Technology
Tipo: Tese de Doutorado Formato: 108 leaves; 6267324 bytes; 6267084 bytes; application/pdf; application/pdf
ENG
Relevância na Pesquisa
75.62%
by Sriram K. Atreya.; Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1982.; MICROFICHE COPY AVAILABLE IN ARCHIVES AND ENGINEERING; Bibliography: leaves 101-103.
## Enhancement of catalog processing system for MIT Science Fiction Society
Wheeler, Cheryl Ann
Fonte: Massachusetts Institute of Technology Publicador: Massachusetts Institute of Technology
Tipo: Tese de Doutorado Formato: 51 leaves; 2047023 bytes; 2046783 bytes; application/pdf; application/pdf
ENG
Relevância na Pesquisa
75.61%
by Cheryl Ann Wheeler.; Thesis (B.S.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1982.; MICROFICHE COPY AVAILABLE IN ARCHIVES AND ENGINEERING; Includes bibliographical references.
## The use of Bluetooth in Linux and location aware computing
Huang, Albert Shuyu
Fonte: Massachusetts Institute of Technology Publicador: Massachusetts Institute of Technology
Tipo: Tese de Doutorado Formato: 89 p.; 4442133 bytes; 4445794 bytes; application/pdf; application/pdf
ENG
Relevância na Pesquisa
65.58%
The Bluetooth specification describes a robust and powerful technology for short-range wireless communication. Unfortunately, the specification is immense and complicated, presenting a formidable challenge for novice developers. Currently, there is a lack of satisfactory technical documentation describing Bluetooth application development and the parts of the Bluetooth specification that are relevant to software developers. This thesis explains Bluetooth programming in the context of Internet programming and shows how most concepts in Internet programming are easily translated to Bluetooth. It describes how these concepts can be implemented in the GNU/Linux operating system using the BlueZ Bluetooth protocol stack and libraries. A Python extension module is presented that was created to assist in rapid development and deployment of Bluetooth applications. Finally, an inexpensive and trivially deployed infrastructure for location aware computing is presented, with a series of experiments conducted to determine how best to exploit such an infrastructure.; by Albert Shuyu Huang.; Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2005.; Includes bibliographical references (p. 87-89).
## New foundations for efficient authentication, commutative cryptography, and private disjointness testing
Weis, Stephen August, 1978-
Fonte: Massachusetts Institute of Technology Publicador: Massachusetts Institute of Technology
Tipo: Tese de Doutorado Formato: 115 p.
ENG
Relevância na Pesquisa
65.58%
This dissertation presents new constructions and security definitions related to three areas: authentication, cascadable and commutative crytpography, and private set operations. Existing works relevant to each of these areas fall into one of two categories: efficient solutions lacking formal proofs of security or provably-secure, but highly inefficient solutions. This work will bridge this gap by presenting new constructions and definitions that are both practical and provably-secure. The first contribution in the area of efficient authentication is a provably-secure authentication protocol named HB+. The HB+ protocol is efficient enough to be implemented on extremely low-cost devices, or even by a patient human with a coin to flip. The security of HB+ is based on the hardness of a long-standing learning problem that is closely related to coding theory. HB+ is the first authentication protocol that is both practical for low-cost devices, like radio frequency identification (RFID) tags, and provably secure against active adversaries. The second contribution of this work is a new framework for defining and proving the security of cascadable cryptosystems, specifically commutative cryptosystems.; (cont.) This new framework addresses a gap in existing security definitions that fail to handle cryptosystems where ciphertexts produced by cascadable encryption and decryption perations may contain some message-independent history. Several cryptosystems...
## Shared libraries in an exokernel operating system
Wyatt, Douglas Karl
Fonte: Massachusetts Institute of Technology Publicador: Massachusetts Institute of Technology
Tipo: Tese de Doutorado Formato: 47 p.
ENG
Relevância na Pesquisa
55.53%
by Douglas Karl Wyatt.; Thesis (M. Eng.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1997.; Includes bibliographical references (p. 47).
## Javarifier : inference of reference immutability in Java; Inference of reference immutability in Java
Quinonez, Jamie
Fonte: Massachusetts Institute of Technology Publicador: Massachusetts Institute of Technology
Tipo: Tese de Doutorado Formato: 83 p.
ENG
Relevância na Pesquisa
65.7%
Javari is an extension of Java that supports reference immutability constraints. Programmers write Javari type qualifiers, such as the readonly type qualifier, in their programs, and the Javari typechecker detects mutation errors (incorrect side effects) or verifies their absence. While case studies have demonstrated the practicality and value of Javari, a barrier to usability remains in the development process. A Javari program will not typecheck unless all the references in the APIs of libraries it uses are annotated with Javari type qualifiers. Manually converting existing Java libraries to Javari is both tedious and error-prone; the development process requires an automated solution. This thesis presents an algorithm for statically inferring reference immutability in Javari. The flow-insensitive and context-sensitive algorithm is sound and produces a set of qualifiers that typecheck in Javari. The algorithm is precise in that it infers the most readonly qualifiers possible; adding any additional readonly qualifiers will cause the program to not typecheck. A tool, Javarifier, implements this algorithm in order to infer the Javari type qualifiers over a set of class files. Javarifier can also insert these qualifiers into the corresponding source code...
## Multivehicle simulation system; SUPERSIM : modular and transparent simulation system for robotics
Belote, Greg H
Fonte: Massachusetts Institute of Technology Publicador: Massachusetts Institute of Technology
Tipo: Tese de Doutorado Formato: 39 p.
ENG
Relevância na Pesquisa
65.58%
In this thesis, we designed and implemented a simulator that supports multiple robots within a dynamic environment. The goal of this tool is to provide a testing environment for navigational robots that run on the MOOS platform. The simulator is written in C++ and utilizes several open source libraries to create a virtual world for robots to interact with by faking sensor information. A design goal of this thesis has been to make the simulator versatile enough to be useful for a variety of robots, from land to marine. Such a tool is valuable in research because the cost of developing a custom simulator can consume too many man-hours. Reducing this cost by creating a generic and customizable simulator has been the main motivation behind this thesis. It has also been one of the major challenges behind the project.; by Greg H. Belote.; Thesis (M. Eng.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2008.; Includes bibliographical references (p. 39).
## A framework for distributed Web-based microsystem design
Saha, Debashis, Massachusetts Institute of Technology.
Fonte: Massachusetts Institute of Technology Publicador: Massachusetts Institute of Technology
Tipo: Tese de Doutorado Formato: 111 p.
ENG
Relevância na Pesquisa
65.66%
The increasing complexity of microsystem design mandates a distributed and collaborative design environment. The high integration levels call for tools and generators that allow exploration of the design space irrespective of the geographical or physical availability of the design tools. The World Wide Web serves as a desirable platform for distributed access to libraries, models and design tools. The rapid growth and acceptance of the World Wide Web has happened over the same time period in which distributed object systems have stabilized and matured. The Web can become an important platform for VLSI CAD, when the distributed object technologies (e.g, CORBA) are combined with the Web technologies (e.g., HTTP, CGI) and Web-aware object oriented languages (e.g., Java). In this thesis, a framework using the Object-Web technologies is presented, which enables distributed Web based CAD. The Object-Web architecture provides an open, interoperable and scalable distributed computing environment for microsystem design, in which Web based design tools can efficiently utilize the capabilities of existing design tools on the Web to build hierarchical Web tools. The framework includes the infrastructure to store and manipulate design objects, protocols for tool communication and WebTop...
## Converting Java programs to use generic libraries
Donovan, Alan A. A., 1976-
Fonte: Massachusetts Institute of Technology Publicador: Massachusetts Institute of Technology
Tipo: Tese de Doutorado Formato: 127 leaves; 6300682 bytes; 6316854 bytes; application/pdf; application/pdf
EN_US
Relevância na Pesquisa
75.58%
Java 1.5 will include a type system (called JSR-14) that supports parametric polymorphism, or generic classes. This will bring many benefits to Java programmers, not least because current Java practise makes heavy use of logically-generic classes, including container classes. Translation of Java source code into semantically equivalent JSR-14 source code requires two steps: parameterisation (adding type parameters to class definitions) and instantiation (adding the type arguments at each use of a parameterised class). Parameterisation need be done only once for a class, whereas instantiation must be performed for each client, of which there are potentially many more. Therefore, this work focuses on the instantiation problem. We present a technique to determine sound and precise JSR-14 types at each use of a class for which a generic type specification is available. Our approach uses a precise and context-sensitive pointer analysis to determine possible types at allocation sites, and a set-constraint-based analysis (that incorporates guarded, or conditional, constraints) to choose consistent types for both allocation and declaration sites. The technique safely handles all features of the JSR-14 type system, notably the raw types (which provide backward compatibility) and 'unchecked' operations on them. We have implemented our analysis in a tool that automatically inserts type arguments into Java code...
## Software Libraries and Their Reuse: Entropy, Kolmogorov Complexity, and Zipf's Law
Veldhuizen, Todd L.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
45.66%
We analyze software reuse from the perspective of information theory and Kolmogorov complexity, assessing our ability to compress'' programs by expressing them in terms of software components reused from libraries. A common theme in the software reuse literature is that if we can only get the right environment in place-- the right tools, the right generalizations, economic incentives, a culture of reuse'' -- then reuse of software will soar, with consequent improvements in productivity and software quality. The analysis developed in this paper paints a different picture: the extent to which software reuse can occur is an intrinsic property of a problem domain, and better tools and culture can have only marginal impact on reuse rates if the domain is inherently resistant to reuse. We define an entropy parameter $H \in [0,1]$ of problem domains that measures program diversity, and deduce from this upper bounds on code reuse and the scale of components with which we may work. For low entropy'' domains with $H$ near 0, programs are highly similar to one another and the domain is amenable to the Component-Based Software Engineering (CBSE) dream of programming by composing large-scale components. For problem domains with $H$ near 1...
## The network structure of mathematical knowledge according to the Wikipedia, MathWorld, and DLMF online libraries
Gonzaga, Flavio B.; Barbosa, Valmir C.; Xexéo, Geraldo B.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
45.68%
We study the network structure of Wikipedia (restricted to its mathematical portion), MathWorld, and DLMF. We approach these three online mathematical libraries from the perspective of several global and local network-theoretic features, providing for each one the appropriate value or distribution, along with comparisons that, if possible, also include the whole of the Wikipedia or the Web. We identify some distinguishing characteristics of all three libraries, most of them supposedly traceable to the libraries' shared nature of relating to a very specialized domain. Among these characteristics are the presence of a very large strongly connected component in each of the corresponding directed graphs, the complete absence of any clear power laws describing the distribution of local features, and the rise to prominence of some local features (e.g., stress centrality) that can be used to effectively search for keywords in the libraries.
## Synthesis from Recursive-Components Libraries
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
45.74%
Synthesis is the automatic construction of a system from its specification. In classical synthesis algorithms it is always assumed that the system is "constructed from scratch" rather than composed from reusable components. This, of course, rarely happens in real life. In real life, almost every non-trivial commercial software system relies heavily on using libraries of reusable components. Furthermore, other contexts, such as web-service orchestration, can be modeled as synthesis of a system from a library of components. In 2009 we introduced LTL synthesis from libraries of reusable components. Here, we extend the work and study synthesis from component libraries with "call and return"' control flow structure. Such control-flow structure is very common in software systems. We define the problem of Nested-Words Temporal Logic (NWTL) synthesis from recursive component libraries, where NWTL is a specification formalism, richer than LTL, that is suitable for "call and return" computations. We solve the problem, providing a synthesis algorithm, and show the problem is 2EXPTIME-complete, as standard synthesis.; Comment: In Proceedings GandALF 2011, arXiv:1106.0814
## Programming CUDA and OpenCL: A Case Study Using Modern C++ Libraries
Demidov, Denis; Ahnert, Karsten; Rupp, Karl; Gottschling, Peter
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
45.68%
We present a comparison of several modern C++ libraries providing high-level interfaces for programming multi- and many-core architectures on top of CUDA or OpenCL. The comparison focuses on the solution of ordinary differential equations and is based on odeint, a framework for the solution of systems of ordinary differential equations. Odeint is designed in a very flexible way and may be easily adapted for effective use of libraries such as Thrust, MTL4, VexCL, or ViennaCL, using CUDA or OpenCL technologies. We found that CUDA and OpenCL work equally well for problems of large sizes, while OpenCL has higher overhead for smaller problems. Furthermore, we show that modern high-level libraries allow to effectively use the computational resources of many-core GPUs or multi-core CPUs without much knowledge of the underlying technologies.; Comment: 21 pages, 4 figures, submitted to SIAM Journal of Scientific Computing and accepted
## Managing Communication Latency-Hiding at Runtime for Parallel Programming Languages and Libraries
Kristensen, Mads Ruben Burgdorff; Vinter, Brian
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
55.53%
This work introduces a runtime model for managing communication with support for latency-hiding. The model enables non-computer science researchers to exploit communication latency-hiding techniques seamlessly. For compiled languages, it is often possible to create efficient schedules for communication, but this is not the case for interpreted languages. By maintaining data dependencies between scheduled operations, it is possible to aggressively initiate communication and lazily evaluate tasks to allow maximal time for the communication to finish before entering a wait state. We implement a heuristic of this model in DistNumPy, an auto-parallelizing version of numerical Python that allows sequential NumPy programs to run on distributed memory architectures. Furthermore, we present performance comparisons for eight benchmarks with and without automatic latency-hiding. The results shows that our model reduces the time spent on waiting for communication as much as 27 times, from a maximum of 54% to only 2% of the total execution time, in a stencil application.; Comment: PREPRINT
## HONEI: A collection of libraries for numerical computations targeting multiple processor architectures
van Dyk, Danny; Geveler, Markus; Mallach, Sven; Ribbrock, Dirk; Goeddeke, Dominik; Gutwenger, Carsten
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
45.64%
We present HONEI, an open-source collection of libraries offering a hardware oriented approach to numerical calculations. HONEI abstracts the hardware, and applications written on top of HONEI can be executed on a wide range of computer architectures such as CPUs, GPUs and the Cell processor. We demonstrate the flexibility and performance of our approach with two test applications, a Finite Element multigrid solver for the Poisson problem and a robust and fast simulation of shallow water waves. By linking against HONEI's libraries, we achieve a twofold speedup over straight forward C++ code using HONEI's SSE backend, and additional 3-4 and 4-16 times faster execution on the Cell and a GPU. A second important aspect of our approach is that the full performance capabilities of the hardware under consideration can be exploited by adding optimised application-specific operations to the HONEI libraries. HONEI provides all necessary infrastructure for development and evaluation of such kernels, significantly simplifying their development.; Comment: 19 pages, 7 figures
## MILJS : Brand New JavaScript Libraries for Matrix Calculation and Machine Learning
Miura, Ken; Mano, Tetsuaki; Kanehira, Atsushi; Tsuchiya, Yuichiro; Harada, Tatsuya
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
45.69%
MILJS is a collection of state-of-the-art, platform-independent, scalable, fast JavaScript libraries for matrix calculation and machine learning. Our core library offering a matrix calculation is called Sushi, which exhibits far better performance than any other leading machine learning libraries written in JavaScript. Especially, our matrix multiplication is 177 times faster than the fastest JavaScript benchmark. Based on Sushi, a machine learning library called Tempura is provided, which supports various algorithms widely used in machine learning research. We also provide Soba as a visualization library. The implementations of our libraries are clearly written, properly documented and thus can are easy to get started with, as long as there is a web browser. These libraries are available from http://mil-tokyo.github.io/ under the MIT license.
## Applying Sorting Networks to Synthesize Optimized Sorting Libraries
Codish, Michael; Cruz-Filipe, Luís; Nebel, Markus; Schneider-Kamp, Peter
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
45.68%
This paper shows an application of the theory of sorting networks to facilitate the synthesis of optimized general purpose sorting libraries. Standard sorting libraries are often based on combinations of the classic Quicksort algorithm with insertion sort applied as the base case for small fixed numbers of inputs. Unrolling the code for the base case by ignoring loop conditions eliminates branching and results in code which is equivalent to a sorting network. This enables the application of further program transformations based on sorting network optimizations, and eventually the synthesis of code from sorting networks. We show that if considering the number of comparisons and swaps then theory predicts no real advantage of this approach. However, significant speed-ups are obtained when taking advantage of instruction level parallelism and non-branching conditional assignment instructions, both of which are common in modern CPU architectures. We provide empirical evidence that using code synthesized from efficient sorting networks as the base case for Quicksort libraries results in significant real-world speed-ups.; Comment: IMADA-preprint-cs
## Multi-Threaded Dense Linear Algebra Libraries for Low-Power Asymmetric Multicore Processors
Catalán, Sandra; Herrero, José R.; Igual, Francisco D.; Rodríguez-Sánchez, Rafael; Quintana-Ortí, Enrique S.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
45.65%
Dense linear algebra libraries, such as BLAS and LAPACK, provide a relevant collection of numerical tools for many scientific and engineering applications. While there exist high performance implementations of the BLAS (and LAPACK) functionality for many current multi-threaded architectures,the adaption of these libraries for asymmetric multicore processors (AMPs)is still pending. In this paper we address this challenge by developing an asymmetry-aware implementation of the BLAS, based on the BLIS framework, and tailored for AMPs equipped with two types of cores: fast/power hungry versus slow/energy efficient. For this purpose, we integrate coarse-grain and fine-grain parallelization strategies into the library routines which, respectively, dynamically distribute the workload between the two core types and statically repartition this work among the cores of the same type. Our results on an ARM big.LITTLE processor embedded in the Exynos 5422 SoC, using the asymmetry-aware version of the BLAS and a plain migration of the legacy version of LAPACK, experimentally assess the benefits, limitations, and potential of this approach.
## A Query Language for Formal Mathematical Libraries
Rabe, Florian
Tipo: Artigo de Revista Científica | |
# The center of the group of $n\times n$ upper triangular matrices with a diagonal of ones
Let $$\mathbb{F}_{p}$$ be a finite field of order $$p$$ and $$H_{n}(\mathbb{F}_{p})$$ be the subgroup of $$GL_n(\mathbb{F}_{p})$$ of upper triangular matrices with a diagonal of ones. Note that the center $$Z(H_{3}(\mathbb{F}_{p}))$$ is well known and isomorphic to $$\mathbb{F}_{p}$$ (see center or dummit). Here, I'm looking for $$Z(H_{n}(\mathbb{F}_{p}))$$.
Any help would be appreciated so much. Thank you all.
The centre consists of upper-triangular matrices whose nonzero entries off the main diagonal are at the right upper corner. See Exercise 4. p 95 of (M. Suzuki, Group theory I, Springer Verlag, Berlin, 1982).
The center is isomorphic to a copy of $$\mathbb{F}_p$$ coming from the upper right corner.
Proof: for $$j > i$$ write $$E_{ij}$$ for the matrix which has a $$1$$ in spot $$(i, j)$$ and along the diagonal and is zero elsewhere.
Claim: if $$M$$ is a matrix with a nonzero entry somewhere other than the upper right corner, then there exist a choice of $$i, j$$ such that $$M$$ does not commute with $$E_{ij}$$.
Now left-multiplication by $$E_{ij}$$ replaces $$M$$ with the matrix $$M^L$$ whose $$i$$th row is the sum of rows $$i$$ and $$j$$ of $$M$$, and right-multiplication by $$E_{ij}$$ replaces $$M$$ with the matrix $$M^R$$ whose $$j$$th column is the sum of columns $$i$$ and $$j$$ of $$M$$.
For these two matrices to be the same, there must be no non-zero entry of column $$i$$ outside row $$i$$ (otherwise $$M^R$$ will have column $$j$$ different from $$M^L$$, since the only entry of column $$j$$ of $$M^L$$ which is different from that of $$M$$ is the one in row $$i$$).
Varying $$i$$, we see that all entries of $$M$$ must be zero except the diagonal ones in all columns except column $$n$$ (since then we can't take $$j > i$$). The same argument on the rows eliminates all rows except $$j = n$$. | |
# Is there a mathematical or logical theory of mathematical modelling?
This question will be admittedly a bit vague, since I am inquiring about the existence of a theory that I am not sure exists, and if it does exists I have only a vague notion of what it might look like.
At the highest level, I am interested in the abstract study of mathematical modelling. For example, I am interested in answering questions like:
• What is the definition of a mathematical model? (e.g. does every mathematical model depend on certain assumptions or axioms? After the axioms are stated, what else is required for a mathematical model?)
• Given a model, what statements can and cannot be assigned a truth value by the model? (surely this will depend on what the definition of a model is).
• How is a statement interpreted by a model (i.e. what is the property of a model that assigns interpretation to a statement)?
Some branches of Logic (which I have no background in) seem to touch on these issues. I also thought that Model Theory was somewhat close to what I was looking for, but I am more interested in abstract study of mathematical models in physics, economics, etc. (and I am especially interested in statistical models, and the study of counterfactuals and causality within a model), and I found it hard to see how Model Theory would be practical to apply to these cases. Perhaps I am wrong about this last point.
Can anyone point me in the right direction?
• SEP's entry on Model Theory has a section dedicated to Models and modelling with a wider scope that the Mathematical logic branch called Model Theory. – Mauro ALLEGRANZA Apr 9 at 14:23
• Model theory, despite the name, actually has essentially nothing to do with what's normally meant by "mathematical modelling" - it's much better to think of it as a generalization of abstract algebra. – Noah Schweber Apr 9 at 15:17
• @NoahSchweber Thanks for your comment. Any idea where I can go from here? Any suggestions will be helpful. – möbius Apr 9 at 19:17
• What's right and what's wrong? Do you want a practical example of mathematical modelling? Here I have a surprising one : Square Bubbles . – Han de Bruijn Apr 13 at 17:54
• @HandeBruijn No I am not looking for examples of mathematical models (although I found your example interesting). I am looking for a theory of modelling itself. For example, is there a general structure that all mathematical models follow? Admittedly the question is a tad vague, but I felt someone would know what I was referring to if there was an obvious theory out there... – möbius Apr 13 at 19:16
A mathematical model is invariably some kind of axiomatization of some kind of structure, which is practically speaking always expressible as an explicit computable many-sorted first-order theory. I would go so far as to say that if one cannot express it in this manner, then one almost certainly does not have a precise model. So I suggest you learn about many-sorted first-order logic and how to express various axiomatizations in it, which would answer all three of your questions. But since mathematical modelling is necessarily a matter of representing real-world observations in symbols, there cannot be a purely mathematical theory of mathematical modelling. And as Noah Schweber said, model theory is a branch of mathematical logic that has very little to do with mathematical modelling (directly at least).
To make it clear, the answers to your questions based on my view:
• What is the definition of a mathematical model? Something that can be expressed as a many-sorted first-order theory.
• Given a model, what statements can and cannot be assigned a truth value by the model? The axiomatization that captures the model itself may not be complete (i.e. some statements may be neither provable nor disprovable), even if it may seem that every statement is either true or false under the intended interpretation of the axiomatization. Just for example, the theory of concatenation (TC) can be considered a mathematical model of finite binary strings, but it turns out that the incompleteness theorem applies to it, and so no computable extension of TC can ever be complete.
• How is a statement interpreted by a model? Since we are talking about capturing some kind of real-world phenomenon or conceptual structure, we would ordinarily interpret a statement according to the structure we had intended to capture. We can also consider other structures that satisfy the same theory but are not isomorphic to the intended one, but that is a matter of the study of logic, rather than a matter of modeling.
Note also that a first-order theory that expresses a mathematical model may not be strong enough to prove everything we think is true, because we may not have made a complete characterization of the intended structure. For example, if we wish to axiomatize a population model based on differential equations, we may only include some axioms concerning real numbers that we are actually certain are relevant. For example, we might only include the RCF axioms, but notice that the computable reals satisfy RCF!
Finally, in mathematics we often like to look at not just separate mathematical models but rather a single unifying foundational system in which we can express all mathematical models that we are interested in. It turns out that at least for practical real-world applications, higher-order arithmetic suffices nicely, because we can naturally express statements about naturals, reals, real sequences (functions from $$\mathbb{N}$$ to $$\mathbb{R}$$), real functions (functions from $$\mathbb{R}$$ to $$\mathbb{R}$$), and higher-order functions, and more, and easily reason about them.
• What does the first-order axiomatization look like for, e.g. the Lotka-Volterra predator-prey model? (en.wikipedia.org/wiki/Lotka–Volterra_equations) Are there multiplie sorts, or do you default to writing it in set theory with one sort being enough? I'd like to see the axiomatization, with some indication of the first-order proof that some solutions have approximate period $\sqrt{\alpha\gamma}$. – user210229 Apr 16 at 17:53
• @MattF.: In my personal opinion, there is both an intuitive and pedagogical advantage to working in many-sorted FOL, as opposed to just a one-sorted theory such as ZFC. The reason is that axiomatizations of different basic structures combine nicely. See this post where I provide a Fitch-style system that is based on many-sorted FOL, except that it's slightly easier to use in practice since I permit using any set as a type, instead of having fixed sorts. With that in mind, ... – user21820 Apr 17 at 12:00
• ... Axiomatizing a DE-based model such as the population model you cited would involve axiomatizing the type $\mathbb{R}$ of reals, and adding constant-symbols $x,y,α,β,δ,γ$ to represent the dynamical system's variables and constants, of course with $x,y∈FN(\mathbb{R},\mathbb{R})$, and adding (first-order) axioms capturing the differential equations. Since we do not need any set theory, we just need the typing rule for function application, namely "If S,T∈set and f∈FN(S,T) and x∈S, then f(x)∈T.". Unsurprisingly, ... – user21820 Apr 17 at 12:05
• ... you can do the same axiomatization in higher-order arithmetic; in fact just third-order arithmetic will do. However, I presume that most physicists do not think of reals as Cauchy sequences of rationals, much less Dedekind cuts of rationals, or worse still subsets of $\mathbb{N}$ under some encoding. That is why I think that the cleanest way to express that population model is exactly as I stated, where the reals are axiomatized rather than constructed. Note that I did not require axiomatizing the naturals, because that is not technically part of the mathematical model. – user21820 Apr 17 at 12:11
• @user21820 Thank you for your hard work on this answer. It answers my question and it has given me lots to think about! – möbius Apr 19 at 10:52 | |
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 `#include #include using int64 = long long; const int64 kMinInt64 = -2'000'000'000'000'000'000; class PopAmplifier { public: PopAmplifier() { std::cin >> n_ >> m_; A_[0] = 0LL; ps[0] = 0; for (int i = 0; i < n_; i++) { std::cin >> A_[i]; ps[i + 1] = ps[i] + A_[i]; } } void compute_optimal_trees() { // First, compute the trees of height 1. for (int a = 0; a < n_; a++) { full_tree_[1][a][a] = 0; full_tree_[1][a][a + 1] = 0; part_tree_[1][a][a] = 0; part_tree_[1][a][a + 1] = 0; } int64 full_leaves = 1LL; int64 part_leaves = 1LL; int h = 2; for (int64 m = m_; m > 0; h++) { bool right = (m % 2LL) == 1LL; const int64 right_leaves = part_leaves; const int64 child_leaves = full_leaves; if (right) { part_leaves += full_leaves; } full_leaves *= 2LL; m /= 2LL; for (int64 a = 0; a < n_; a++) { full_tree_[h][a][a] = part_tree_[h][a][a] = 0LL; for (int64 b = a + 1; b <= n_ && b <= a + full_leaves; b++) { full_tree_[h][a][b] = kMinInt64; // [a,s) goes to the left subtree. [s,b) goes to the right. for (int s = std::max(a, b - child_leaves); s <= std::min(b, child_leaves + a); s++) { // The right subtree has an additional 1-bit everyone // needs to be multiplied by. full_tree_[h][a][b] = std::max(full_tree_[h][a][b], full_tree_[h - 1][a][s] + full_tree_[h - 1][s][b] + sum(s, b)); } // std::cerr << " - full_tree_["< | |
## Monday, September 30, 2013
Odie, you wrote:
"Instead it will be income for the bank which it will use to pay e. g. one of its employees by crediting its account. No money being created are destroyed there, simply shifting funds around. For those $1200 the bank's deposit liabilities stay the same. (More maybe later)" http://worthwhile.typepad.com/worthwhile_canadian_initi/2013/09/if-banks-bought-houses.html I agree with everything in your comment up until that part! There's two separate and completely independent IOUs at play here between you and the banking system in aggregate: Your IOU to them (the mortgage) and their IOU to you (your deposit). You are each others creditors and debtors. If you pay$2000 to them with your deposit, that is accomplished by them debiting your deposit account. Now it so happens that $800 of that payment is principal, so it also affects your IOU to them, so they mark that IOU down by$800 for that. Your mortgage though is not a medium of exchange and thus it is not "inside money." $2000 of inside money was destroyed in this example:$800 of your IOU was also destroyed for a net gain by the banks of $1200 of equity (the abstract dollar amount of the value of assets in excess of the value of liabilities). They have no obligation to turn around and create more inside money by crediting other people's or entities' bank deposits with$2000 or $1200 or any other amount. There's no law of the preservation of bank deposits. You and I can't destroy bank deposits because to us bank deposits are "outside money." "Inside" and "outside" are relative terms. Relative to non-bank private entities, bank deposits are outside. Relative to the private sector (the usual vantage point from which to define "inside" and "outside") they are "inside." If we included the Fed in our vantage point, then Fed created money (reserve notes and Fed deposits) would also be "inside" and only coins and the extremely rare "US notes" would remain "outside." If you and I write out our own IOUs and use them as money, then we CAN destroy those and that "money" would be "inside" us. ## Friday, September 13, 2013 ### Equation Test λb0 λb0 λb0 λ<sub>b0 </sub>λ<sub>b0</sub> λ<sub>b0</sub>$\Delta$Another equation test, this time from this blog: http://informationtransfereconomics.blogspot.com/2014/03/the-islm-model-again.html?showComment=1396510569711#c5498535460855094305 $$r = \frac{1}{\kappa} \; \frac{\langle I\rangle}{M_{0}}$$ ΔIIIref=I0κlogMMref $$r = \frac{1}{\kappa} \; \frac{\langle I\rangle}{M_{0}}$$ $$K_{h,g'} = \frac{1}{\theta}$$ $$K_{y',g'} = \frac{1-\theta}{\theta}$$$K_{h,g'} = \frac{1}{\theta}K_{y',g'} = \frac{1-\theta}{\theta}$How about in the middle$K_{h,g'} = \frac{1}{\theta}$of a sentence? (1) r=dIdM=1κIM ### Answer for Macroman macroman, I’m with you up to here: “It is these reserves that the banks can then use to lend out money or do with it whatever they please.” 1. If you’re talking about banks lending reserves to each other (which I’m pretty sure you’re not) then this is correct. Since reserves are defined as base money HELD BY THE BANKS, you can see how this is true. Yes banks loan each other base money: “MB: The total of all physical currency plus Federal Reserve Deposits (special deposits that only banks can have at the Fed). MB = Coins + US Notes + Federal Reserve Notes + Federal Reserve Deposits.” 2. If you’re talking about something else, this is not true. About the closest thing you could say that IS true is that a cash advance is a loan of base money in the form of “physical currency.” “Because the federal reserve does not have to have the MONEY on hand to buy the bond, but rather can use a made-up reserve, it is the equivalent of printing money.” Check this out: http://brown-blog-5.blogspot.com/2013/08/banking-example-41-quantitative-easing.html Notice how reserves flow out of the Fed, and assets flow in, in equal proportion. As for the rest of your email, check this out: http://brown-blog-5.blogspot.com/2013/08/banking-example-11-all-possible-balance.html Especially the balance sheets at the bottom: “Public (simplified)” and “more simpflified.” Especially this bit: public’s stock of money = L + B + F = bank deposits + cash It’s the “F” part you’re worried about. But the thing to keep in mind though is that this does NOT affect the public’s equity! public’s equity = T QE changes the composition of the public’s stock of money, but has NO effect on the public’s equity. ## Friday, September 6, 2013 ### Trash Below is a test reply comment to Fed Up and winterspeak in JKH's post on Market Monetarism. My original posted comment is here, but as of this writing it's "awaiting moderation" (I'm sure because there's more than one link in it), but it still let me grab a link to it, so it'll be interesting to see if people can see the original even though it's awaiting moderation. ---------------------------------------------------------------------------------------------------------------------------- Fed Up & winterspeak, “Tom Brown, does this sound familiar?” — Fed Up Yes, this sounds very familiar, which is why I posted a link to my post “Nick vs Scott” on this subject above. And Nick’s response above again highlights a difference with Scott. Let’s review: Scott Sumner, in this post explaining the hot potato effect (HPE), used as an extreme example under which the HPE still applied a “cashless economy” (his case 7): 7. Now let’s assume a cashless economy where the MOA is 100% reserves. Still no change; reserves are still a hot potato. Using Scott’s hypothetical case 7 a basis, I asked Scott and Mark Sadowski the following question: OK, let’s start with your own example #7 from this post: http://www.themoneyillusion.com/?p=23314 “7. Now let’s assume a cashless economy where the MOA is 100% reserves.” You’ve clearly identified the MOA there: reserves. Banking doesn’t matter, so why not assume a single commercial bank? And my other assumptions: no taxes, gov spending, foreign trade, etc. So if initially the CB buys$X in assets, this gives us an initial $X in reserves, which you’ve identified as MOA. Since we have an MOA, we will reach a steady state price level, P, right? Now what if the CB sells 1-epsilon of its assets? The new eventual price level should be: new steady state price level = P*(epsilon*X/X) = P*epsilon So as epsilon approaches zero, the new steady state price level should approach zero too?? At which point I added Scott, of course the reserve requirement = 0% too. Scott’s response was: Tom, Yes, as the level of reserves go to zero, so does the price level. Mark Sadowski agrees with Scott, although he complains about the realism of my (actually Scott’s!) hypothetical cashless society: Tom Brown, I agree with Scott. However, any example that doesn’t include currency is excluding what has been the most important part of the monetary base historically. In short it is extremely unrealistic. This is quite different than what Nick writes above: If there were just one commercial bank, and if nobody used central bank currency, and if there were no legally required reserves, then that single commercial bank would not need to hold any reserves. That single commercial bank could ignore the central bank. The central bank would disappear. Nick wrote nearly the same thing when I first presented him with my version of Scott’s hypothetical, however after showing him Scott’s response, he wrote this: Tom: you really do need to distinguish between the *demand* for reserves going to zero and the *supply* of reserves going to zero. (And *both* supply and demand going to zero.) I read you one way, and Scott read you the other. It’s supply AND demand. He also later saw my notional chart (animated version here) of my interpretation of what he meant by this and wrote: Tom: thanks. looks roughly right on a first glance. though to be fair, the version he saw was slightly different, but not substantially so (embedded in the comments here). ## Tuesday, September 3, 2013 ### Sumner's HPE Explanation http://www.themoneyillusion.com/?p=23314 Geoff's comment: http://pragcap.com/the-banking-camp-vs-the-macroeconomics-camp/comment-page-1#comment-153314 "If somebody gives me, say,$500 in cash but my wallet is already full, then I’m going to do something else with it. I might spend the cash on real stuff or convert it to another kind of financial asset like a bond or stock. That’s the HPE in action, right?
But there is only one problem. The Fed can’t just give me $500 in cash. All they can do is buy an existing financial asset from me (aka an asset swap). I know Dr. SS understands this. So what am I missing? PS I agree with your post, Cullen. Sorry for going O/T " Geoff, I agree that's a problem. Just giving you the$500 is what the MMists call a "Helicopter Drop."
But what Scott's saying in his gold analogy, the difference between cases 3. and 4. is that gold is the MOA in 4 and prices are "'sticky" (meaning they don't move instantaneously).
Therefore in case 3, the price of gold drops in half instantly. That's still the HPE. In case 4 this happens more gradually, and what changes instantly are things like "interest rates."
Make sense?
BTW, to comment easily select "Name/URL" then you can put any URL you want in there, including www.google.com | |
Sangeetha Pulapaka
0
The given equation is v(t) = 320 \cdot 4^{t}
a) v(-2) = 320 \cdot 4^{-2} = 320 \cdot \frac{1}{16} = 20
b) Since t is the number of days since Jada saw the video, v(-2) represents number of views 2 days before, Jada saw the video. The number of views were 20 then. | |
# Causal Inference for Aging
## Understanding Calico's recent paper
Causal Inference has many researchers excited about the prospect of automated causal reasoning. This kind of reasoning is the backbone of scientific research and legal processes.
Calico, the aging research arm of Alphabet, recently released a new paper, Time-resolved genome-scale profiling reveals a causal expression network. in it, they describe a framework, CANDID (Causal Attribution Networks Driven by Induction Dynamics), for predicting transcriptional regulators that can be validated experimentally
The primary model for the inference machine is as follows:
For learning the causal relationships the authors describe the following model:
$\frac{\Delta \mathrm{ln}(y_{ijt})}{\Delta t} = \sum_{k} \frac{(\alpha_{ik}(y_{kjt}-1)+\beta_{ik}(y_{ijt}y_{kjt}-1))}{y_{ijt}}$
with $k$ being the index for all given genes. Let’s unpack this.
$y_{ijt}$ is the expression relative to the control strain and relative to time zero of a gene $i$ in a timecourse $j$ at a time $t$.
In other words, for a given treatment $r$ and control $g$,
$y_{ijt} = \frac{(\frac{r_{ijt}}{g_{ijt}})}{(\frac{r_{ij0}}{g_{ij0}})} \\ \therefore y_{ij0} = 1 \forall \{I, J\})$
Here, $\alpha$ represents the linear effect of one transcript on another and $\beta$ represents the effect proportional to the target transcript. In this model any transcript is allowed to affect any other transcript, and thus we sum over all genes (with index $k$).
Since most genes will not be regulatory, we use L1 regularization (i.e., LASSO) to shrink uninformative predictive coefficients to zero. We also enforce a predicted rate of change of zero at time zero, reflecting the pre-induction steady-state assumption. To arrive at this formula, we considered a suite of alternative data cleaning and modeling approaches (see Supplement for details) and decided upon this formalism and hyperparameters based on an ability to predict held-out induction datasets (in total, 50 million regressions performed).
### Further reflections
This paper seems to be pretty in-line with Calico’s approach of throwing massive amounts of data and processing power at problems.
Cited as:
@article{mcateer2019causalaging,
title = "Causal Inference for Aging",
author = "McAteer, Matthew",
journal = "matthewmcateer.me",
year = "2019",
url = "https://matthewmcateer.me/blog/causal-inference-for-aging/"
}
If you notice mistakes and errors in this post, don’t hesitate to contact me at [contact at matthewmcateer dot me] and I would be very happy to correct them right away!
See you in the next post 😄
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Venn diagrams are a great way to visualize informative comparisons between data sets. It can be particularly helpful to use venn diagrams to look at how similar data is across multiple data sets, or within the same data set.
The types of comparisons you can make will depend on how your data is formatted. In the following example we will use the counts of differentially expressed (DE) genes to compare the following six different Daphnia genotypes.
### Venn Diagram Script – R
The following R scripts will be used to generate several different venn diagrams for a variety of comparisons across genomic data sets.
The first step is to import a package for creating venn diagrams in R. Here we will use the VennDiagram library.
#install.packages('VennDiagram')
library(VennDiagram)
Next, the read.csv function is used to import the genomic data we want to analyze. The path to the data being imported is set as an input to the script using args[1].
The format of the data is expected to be a table of gene counts where the rows are counts by gene ID, and columns are counts by genotype.
#Import data
counts <- read.csv(file=args[1])
Now that the data we are going to analyze is imported to the counts data frame, we can subset the data to make informative comparisons.
Remember that in this example, the imported data are the counts of differentially expressed (DE) genes for six different genotypes. So the following subsets of SET1 to SET6 represent the counts for each of the six genotypes.
Also note that the subset of data for each genotype is taken from a column of the same name in the imported csv data (Y05, Y023, E05, R2, PA, and Sierra). This means that the column name tags will need to be changed to the columns of your input data set that you wish to use for comparisons.
#Define sets for diagram
SET1 <- counts$Y05 SET2 <- counts$Y023
SET3 <- counts$E05 SET4 <- counts$R2
SET5 <- counts$PA SET6 <- counts$Sierra
Before the venn diagrams can be generated all NA values need to be replaced with empty strings using the is.na function. This is because any NA in the data set will cause an error when creating the diagrams.
Although, you should be sure that the presence of NA values in your data set is not a cause for concern. It is not uncommon for NAs to be found in counts of gene expression data produced by some quantification programs.
#Replace NAs
SET1[is.na(SET1)] <- ""
SET2[is.na(SET2)] <- ""
SET3[is.na(SET3)] <- ""
SET4[is.na(SET4)] <- ""
SET5[is.na(SET5)] <- ""
SET6[is.na(SET6)] <- ""
Now we are ready to begin generating venn diagrams in R. There are a number of comparisons we can make since we are working with six data sets in this example, one for each genotype.
The first comparison we will make is of the counts of DE genes between the four D. melanica genotypes (Y05, E05, Y025, R2) from the same geographic region and the D. pulex out group (PA).
Note that the venn.diagram function from the VennDiagram library has a variety of style options. Here we will use the fill option to set the colors for our data sets, and alpha to set the transparency. We can also save the diagram images to memory using the jpeg R function.
#Draw the diagram comparing the Olympics and PA sets
v2 <- venn.diagram(list(Y05=SET1, E05=SET3, Y023=SET2, R2=SET4, PA=SET5),
fill = c("red", "green", "white", "blue", "yellow"),
alpha = c(0.5, 0.5, 0.5, 0.5, 0.5),
filename=NULL)
jpeg("plotOlympicsPAVennn.jpg")
grid.newpage()
grid.draw(v2)
dev.off()
Next, we will compare the counts of DE genes across the four Olympics D. melanica genotypes and the closely related D. melanica from the Sierra Nevadas in CA (Sierra).
#Draw the diagram comparing the Olympics and Sierra sets
v3 <- venn.diagram(list(Y05=SET1, E05=SET3, Y023=SET2, R2=SET4, Sierra=SET6),
fill = c("red", "green", "white", "blue", "yellow"),
alpha = c(0.5, 0.5, 0.5, 0.5, 0.5),
filename=NULL)
jpeg("plotOlympicsSierraVennn.jpg")
grid.newpage()
grid.draw(v3)
dev.off()
Since this is differential gene expression data, we are also interested in comparing DE gene counts across the three genotypes that are tolerant to the treatment in our study.
#Draw the diagram comparing the tolerant sets
v4 <- venn.diagram(list(Y05=SET1, E05=SET3, Sierra=SET6),
fill = c("red", "green","blue"),
alpha = c(0.5, 0.5, 0.5), cat.cex = 1.5, cex=1.5,
filename=NULL)
jpeg("plotTolerantVenn.jpg")
grid.newpage()
grid.draw(v4)
dev.off()
Finally, we are interested in comparing DE gene counts across the three genotypes that are not tolerant to the treatment in our study.
#Draw the diagram comparing the non-tolerant sets
v5 <- venn.diagram(list(Y023=SET2, R2=SET4, PA=SET5),
fill = c("red", "green","blue"),
alpha = c(0.5, 0.5, 0.5), cat.cex = 1.5, cex=1.5,
filename=NULL)
jpeg("plotNonTolerantVennn.jpg")
grid.newpage()
grid.draw(v5)
dev.off() | |
# Chemistry - Which biphenyl is optically active?
## Solution 1:
(3) is not chiral, so maybe it is (2).
## Solution 2:
Biphenyl 2 is the only optically active compound here. These stereoisomers are due to the hindered rotation about the 1,1'-single bond of the compound (Ref.1). Biphenyl 3 is not optically active, because partially allowed rotation about the 1,1'-single bond of the compound (rotation is only partially restricted). To illustrate this phenomenon, I depicted the following diagram:
Note that compound 3 can rotate through two simultaneous $$\ce{I}$$ and $$\ce{H}$$ atoms allowing last $$180 ^\circ$$ rotation, which is well illustrated in the diagram posted by Karsten Theis.
References:
1. Paul Newman, Philip RutkinKurt Mislow, "The Configurational Correlation of Optically Active Biphenyls with Centrally Asymmetric Compounds. The Absolute Configuration of 6,6'-Dinitro-2,2'-diphenic Acid," J. Am. Chem. Soc. 1958, 80(2), 465-473 (https://doi.org/10.1021/ja01535a054).
## Solution 3:
TL;DR: It's 2 (2,2'‐dibromo‐6,6'‐diiodo‐1,1'‐biphenyl) and maybe even 3 (2,2'‐diiodo‐1,1'‐biphenyl; 2,6‐dimethyl‐1,1'‐biphenyl) at higher temperatures.
### Introduction
According to the IUPAC gold book chirality is defined the as the geometric property of a rigid object of being non-superposable on its mirror image. Orr in other words, such an object has neither a mirror plane, nor a centre of inversion. For examples, please see this Q&A: What is the perfect definition for chirality?
Asymmetric substituted biphenyl derivatives may possess axial chirality. This is quite well explained in Matthew's answer (at the time of writing, I think he has the numbering wrong though). This arises (mainly) due to hindered rotation, see atropisomers in the IUPAC gold book and on Wikipedia.
### Analysis
Based on this, we can immediately rule out biphenyl 4 (2,6‐dimethyl‐1,1'‐biphenyl). I have simulated the structure[1] and the equilibrium structure is close to C2v.
The remaining compounds will have chiral conformers as they are asymmetric substituted. The first compound 1 (3‐iodo‐3'‐nitro‐1,1'‐biphenyl) has no (C1) symmetry. The equilibrium structures of the second compound 2 (2,2'‐dibromo‐6,6'‐diiodo‐1,1'‐biphenyl), as well as the third compound 3 (2,2'‐diiodo‐1,1'‐biphenyl; 2,6‐dimethyl‐1,1'‐biphenyl), have C2 symmetry. These are potential candidates for atropisomerism.
The question now becomes, which one is (most) hindered. I have (very crudely) simulated the interconversion barriers.[2] As a reference, I have also included 1,1'-biphenyl as 0. The barrier is calculated in a zeroth order approximation as the difference of the conformer(s) and the highest energy image.
$$\begin{array}{cr} \text{Structure} & \Delta E /\pu{kJ mol-1}\\\hline \mathbf{0} & 11.0 \\ \mathbf{1} & 9.7 \\ \mathbf{2} & 208.4 \\ \mathbf{3} & 107.6 \\ \mathbf{4} & \text{n.a.} \\\hline \end{array}$$
Note that I have only considered one conversion path, which actually only would make a difference for 3 anyway.
We can immediately spot that there is not much hindrance in 1, as its value is in the same ballpark as 0. The value for the latter is approximately the same as what Henry Rzepa calculated.[3,4] For the cinephiles, here is the animated minimum energy path (MEP):
We can also deduce that 3 is more hindered, but conversion is probably still doable at room temperature. Without further analysis, I'd make an educated guess that the large size of iodine is the reason for the higher barrier. In the local minima the structures are probably stabilised by non-covalent interactions, while during the transition Pauli repulsion will have a significant effect.
When you cool down the system enough, you should be able to differentiate the two forms.
The highest barrier is for 2, which is not really surprising given the bulky halogens used. During the transition the molecule has to distort significantly as the MEP will show.
### Notes & References
1. Optimisation has been done on the semiempirical GFN2-xTB level of theory. (a) Mulliken Center for Theoretical Chemistry, xTB on Github, xTB documentation, xTB: J. Chem. Theory Comput. 2017, 13 (5), 1989–2009 & J. Chem. Theory Comput. 2019, 15 (3), 1652–1671.
Cartesian coordinates (Xmol format) of the optimised structure:
28
energy: -37.106373072108 gnorm: 0.000617993871 xtb: 6.3.0 (preview)
C -0.74457039092978 0.00668380904848 0.00403847586541
C -1.43960105448658 -0.45330956062940 1.12306879090173
C -1.43111456476918 0.48819737048977 -1.11130113065019
C -2.82681693607605 -0.42604266071721 1.11315113205938
C -2.81837054760201 0.50359494897240 -1.09421940563873
C -3.51401551801468 0.04941173994657 0.01133914771101
H -3.37205771113385 -0.78013743294762 1.97649654009736
H -3.35684427561920 0.87533913913887 -1.95437486971859
H -4.59411676716931 0.06680911498157 0.01451573070096
C 0.73741240721740 -0.01399221137562 -0.00121303974220
C 1.45737190356414 1.07903119590108 0.46615300935510
C 1.42452698329909 -1.12468405637333 -0.47649552340433
H 0.86686558778550 -1.97662540315982 -0.84058815377695
H 0.92547790883778 1.94454881021216 0.83667570046312
C 2.80773675401329 -1.14118822737596 -0.48485609074287
C 2.84061966747731 1.06166601900200 0.45746804395492
H 3.33358058669268 -2.00908593002598 -0.85653458093421
H 3.39191821123738 1.91650859033419 0.82242788728035
C 3.51831774061953 -0.04807951153356 -0.01828710942118
H 4.59840909035030 -0.06111117644652 -0.02569905851317
C -0.68780013266629 -0.96774724332108 2.31428913997988
H -1.37323200644906 -1.27392883680533 3.10034826852651
H -0.06975635021791 -1.82092520510799 2.03621620918938
H -0.02338556354040 -0.19893824461916 2.70781448086228
C -0.66947839003714 0.98202574672165 -2.30497384579965
H -0.01808999107620 1.80968104054958 -2.02509754296330
H -0.03719586612218 0.19173089684959 -2.70896585204466
H -1.34904789687459 1.32012824269556 -3.08395328163034
1. The interconversion has been calculated with the same level of theory using the Nudged Elastic Band (NEB) algorithm of ORCA 4.2.0 (Forum, WIREs Comput. Mol. Sci. 2018, 8 (1)). The path had a total of 15 images, here is the example file for 2 along with the necessary coordinate files. If you want to try this at home, on my laptop (old!) with a single core this calculation took about 2 hours and 40 minutes.
! XTB2 NEB
%neb
NEB_End_XYZFile "conformer_end.xyz"
Nimages 13
end
*xyzfile 0 1 conformer_start.xyz
Xmol conformer_start.xyz of conformer 1:
22
energy: -44.541438926695 gnorm: 0.000273788204 xtb: 6.3.0 (preview)
C -0.73842516239767 0.12099397705083 0.10023099347275
C -1.44934703887101 1.30959596420843 -0.04635714487514
C -1.46459032906802 -1.05364356156319 0.26275562729962
C -2.83260221816166 1.33338660213393 -0.03856888366719
Br -0.49031781314024 2.94358437512547 -0.26534599360856
C -2.84794544579427 -1.04806937194567 0.27338021399222
I -0.43874303211246 -2.89099212545445 0.49464849107241
C -3.52725076437943 0.14798638986577 0.12187031074955
H -3.35400213047419 2.27002355888684 -0.15598934111452
H -3.39039633102590 -1.97145652424781 0.40014772926329
H -4.60579519489111 0.15562863225057 0.12966905294877
C 0.73854134684734 0.12608798707818 0.09393840630342
C 1.44940095781461 0.26239315529407 1.28380896054353
C 1.46477927365802 0.00836392380816 -1.08597026657536
I 0.43777759512819 -0.19754357173773 -2.92573037522205
Br 0.49031834581031 0.43262730661288 2.92353161238781
C 2.84816021024059 0.01980313175890 -1.08292737332063
C 2.83266002230666 0.27532688568945 1.30522345586451
H 3.39064596265727 -0.07352515350963 -2.01027791369359
H 3.35396295523884 0.38108640783580 2.24326316270063
C 3.52740515329100 0.15308581626132 0.11533500559347
H 4.60593238792661 0.16262139848447 0.12098160378166
Xmol conformer_end.xyz of conformer 2:
22
energy: -44.541436788329 gnorm: 0.000524902200 xtb: 6.3.0 (preview)
C -0.73832361282032 0.11983310306066 0.10840520776248
C -1.44801951621468 1.30797897222752 -0.04711380834348
C -1.46589375900469 -1.05507032640145 0.26341702181708
C -2.83136671292522 1.33298447781511 -0.04044389495310
Br -0.48672217710205 2.94010480951284 -0.27007089450699
C -2.84922363862597 -1.04840911658639 0.27193924049683
I -0.44386752640863 -2.89430038039744 0.49812818908251
C -3.52726058220375 0.14843604873707 0.12049840516296
H -3.35201572570858 2.26977601051251 -0.16025533523296
H -3.39258284243005 -1.97170525823195 0.39578778183960
H -4.60581188092237 0.15713306581713 0.12812396988730
C 0.73861053874909 0.11915254649018 0.09757065282745
C 1.43899785537134 -0.05963599109061 -1.09283010773567
C 1.47533465683736 0.30394299799110 1.26237171334068
I 0.46538312669624 0.58600628876877 3.10142029802479
Br 0.46500728057852 -0.30932233235425 -2.71351652270371
C 2.85860590331322 0.30295779336713 1.24612034762903
C 2.82215760585763 -0.06398015847435 -1.12722135693164
H 3.40910925948393 0.44613646389996 2.16234539469840
H 3.33549654196190 -0.20778602755665 -2.06467923531197
C 3.52731730663299 0.11776860585707 0.04879749941162
H 4.60580925392358 0.11518160422810 0.03305180289059
1. On ωB97XD/6-31G(d,p) about $$\pu{3 kcal mol-1}$$, which is in real units $$\pu{12.5 kJ mol-1}$$. Henry Rzepa: Conformational analysis of biphenyls: an upside-down view
2. Possibly relevant dissertation by David Vonlanthen Biphenyl-Cyclophanes: The Molecular Control over the Conductivity of Single-Molecule Junctions (in German): pdf at researchgate. He cites the value for 1,1'-biphenyl as $$\pu{2-3 kcal mol-1}$$. | |
# Closest Point on a 3D Quadratic Surface
• February 8th 2010, 08:22 AM
davesymm
Closest Point on a 3D Quadratic Surface
Hi All, first post, hope I'm obeying all the rules :)
If I have a 3d quadratic surface defined by $ax^2+by^2+cz^2+d=0$ and a point in space defined by the position vector $p={px,py,pz}$ , how can I determine the closest point on the surface to p?
I suspect the solution lies down the path of minimising the value of the difference between the points, or finding the values of x, y and z that minimise $apx^2+bpy^2+cpz^2-ax^2-by^2-cz^2$, but my maths is rusty and I have a feeling that if this is possible it would involve implicit differentiation or one of the other techniques I never quite mastered the first time around.
Any help or even a pointer to a different (easier) approach would be much appreciated.
Thanks,
Dave.
• February 9th 2010, 09:26 PM
Pulock2009
the closest point will obviously be the point which lies perpendicular to the surface ie. at an angle of 90 degrees. i did this problem somewhere but i forgot the technique. u can assume a point O(x,y,z) on the surface and then carry out calculations keeping in mind the facts:OP is perpendicular to the surface and O satisfies the surface equation. there is also a shortcut involving dot product and cross product which i dont remember well. hope this helps!!!
• February 10th 2010, 07:03 AM
HallsofIvy
Quote:
Originally Posted by davesymm
Hi All, first post, hope I'm obeying all the rules :)
If I have a 3d quadratic surface defined by $ax^2+by^2+cz^2+d=0$ and a point in space defined by the position vector $p={px,py,pz}$ , how can I determine the closest point on the surface to p?
I suspect the solution lies down the path of minimising the value of the difference between the points, or finding the values of x, y and z that minimise $apx^2+bpy^2+cpz^2-ax^2-by^2-cz^2$, but my maths is rusty and I have a feeling that if this is possible it would involve implicit differentiation or one of the other techniques I never quite mastered the first time around.
Any help or even a pointer to a different (easier) approach would be much appreciated.
Thanks,
Dave.
One way to do this is to take as the function to be minimized $(x- px)^2+ (y- py)^2+ (z- pz)^2$ (that's actually the square of the distance but minimizing it is the same as minimizing distance and this avoids the square root). You then have the additional condition, ax^2+ by^2+ cz^2+ d= 0.
Use the geometric argument that Pulock2009 suggests with a little analysis: the gradient vector $\nabla (ax^2+ by^2+ cz^2+ d)= (2ax)\vec{i}+ (2by)\vec{j}+ (2cz)\vec{k}$ is always perpendicular to the surface and (x, y, z) will be closest to (px,py,pz) when the vector directly from one to the other, $(x- px)\vec{i}+ (y- py)\vec{j}+ (z- pz)\vec{k}$ (which, notice, is 1/2 the gradient of the "distance squared" function) is pointing perpendicular to the surface- that is the two vectors must be parallel which means one is a multiple of the other:
$(2ax)\vec{i}+ (2by)\vec{j}+ (2cz)\vec{k}= \lambda((x- px)\vec{i}+ (y- py)\vec{j}+ (z- pz)\vec{k})$.
where $\lambda$ is the multiple. (It is, technically, the "Lagrange multiplier".)
That gives you four equations, $2ax= \lambda(x- px)$, $2by= \lambda(y- py)$, $2cz= \lambda(z- pz)$, and the equation of the surface, $ax^2+by^2+cz^2+d=0$, to solve for x, y, z, and $\lambda$.
Since you don't really need to know $\lambda$, I recommend dividing one equation by another to eliminate $\lambda$.
For example, dividing $2ax= \lambda(x- px)$ by $2by= \lambda(y- py)$ gives $\frac{ax}{by}= \frac{x- px}{y- py}$ which we could solve for y as a function of x. Similarly, dividing [/tex]2ax= \lambda(x- px)[/tex] by $2cz= \lambda(z- pz)$ gives $\frac{ax}{cz}= \frac{x- px}{z- pz}$ which you could solve for z as a function of x. Putting those into the equation of the surface gives one equation to solve for x.
• February 15th 2010, 08:06 AM
davesymm
Thanks for the help :)
I've rearranged the equations in the form $ax/by=(x-px)/(y-py)$ and get $y=axpy/((a-b)x+ypx)$ (and similar for $z$). However, when I come to substitute this into $ax^2+by^2+cz^2+d=0$ it gets a little complicated, and I'm not sure I can solve it using the general quadratic equation.
Am I missing a glaringly simple solution? Otherwise I may have to abandon this path of thought as it is in a computationally sensitive piece of code and I'm not sure I can afford the increasing mathematical load.
Thanks again for all the help. | |
# Manipulating Collections¶
The previous two pages gave you the fundamentals of lists and vectors, but if you think there was something missing, you are correct You may have been wondering how you work with the items in a collection, one after another. In this page and the next pages, we will show you three of the most important functions for manipulating collections: map, reduce, and filter.
## The map function¶
You use map when you want to create a new collection by applying a function to each element of a collection. For example, let’s take the vector of prices (def price-vector [3.95 6.80 2.49 5.33 1.99]) and write a program that will give us a new vector with a 10% discount on each of the prices. You already know how to do this for a single price:
(defn discount [price]
(* price 0.90))
What you now need is some way to apply that function to each of the items in price-vector. The map function does exactly that.
The map function takes two arguments: a function of one parameter, and a collection. In this example, the function is the discount function, and price-vector is the collection.
Note
This map function is not to be confused with the map collection, which pairs keys and values. Unfortunately, they share the same name, and there’s nothing to be done about it.
Here is a short video that may help as well:
## Something Important Just Happened¶
Up to this point, all of the arguments to functions have been raw data, like numbers and strings. This is the first time you have seen a function as an argument to another function. I deliberately used the (def) form instead of (defn) to remind you that you can bind a function to a symbol, just as you can bind numbers or strings or lists to symbols. In ClojureScript, functions may be considered as another type of data that you can bind to symbols and pass to and from other functions. That’s exactly what has happened here: I passed the discount function as an argument to the map function.
When you have a function like map that takes another function as an argument, it is referred to as a higher-order function. (If a function returns another function as a result—yes, this is possible—it is also a higher-order function.)
## Exercises¶
Exercise 1: Write a program that uses map to convert the radius-vector to a sequence of circle areas. You will write a function named calculate-area that calculates the area of a circle given its radius, then use it as the first argument to map. You can use js/Math.PI for the value of pi. For extra bonus points, have the program create a vector as its result. (Hint: into)
Exercise 2: Write a program that uses map to convert the price-vector to a sequence of prices that have been rounded up to the nearest 10-cent value. Thus, for the vector [3.95 6.80 2.49 5.33 1.99], your result should be (4 6.8 2.5 5.4 2) Write a function named round-up-price that takes a single price as its argument and returns the result rounded up. For extra bonus points, have the program create a vector as its result. (Hint: into).
Remember in the interlude I sang the praises of planning. This is one of those cases. Figuring out how to round 33 cents up to 40 cents, but keeping 30 cents as 30 cents takes a bit of thought and planning.
To round up the price, convert the price to cents by multiplying by 100. To get an even multiple of 10, do an integer division by 10, then multiply by 10. However, that rounds down rather than up; a number like 34 would go to 30 rather than 40. The trick is to add 9 to the original number before rounding down. When you do that, a number like 30—which is already a multiple of 10—becomes 39, which rounds back down to 30; but 32 would go up to 41, which rounds down to 40, effectively rounding 32 up to 40, the desired result.
## map Shortcut #1: Anonymous Functions¶
If the function you are using in map is short (as it is in the example with the discount and the circle areas), you don’t have to create a new, named function. Instead, you can define the function right in the call to map. Here is the discount example, using an anonymous function (a function that isn’t bound to a symbol).
Now give it a try. Convert the circle area example to use an anonymous function. As before, your goal is a program that uses map to convert the radius-vector to a sequence of circle areas.
## map Shortcut #2: Even Shorter Function Syntax¶
You can define an anonymous function in a very compact manner. For a function with one parameter, which is what we are using here:
• Drop the fn and parameter list altogether
• Put a # before the opening parenthesis
• Use % in place of the parameter.
Here is the price discount program again, in the short syntax:
You can use this shortcut syntax for functions with more than one parameter; you use %1 to stand for the first parameter, %2 for the second, and so on. You could write the average function with two parameters as follows. The long form is shown first as a comment for reference.
## Which Shortcut Should You Use?¶
When you are learning a foreign language, there are three classes of phrases:
• Phrases you have to know how to say and recognize
• Colloquial phrases that you may use if you feel confident about it
• Phrases you should be able to understand but not be expected to produce on your own
That’s how I feel about writing functions for use with map:
• Defining a separate named function always works, and, if you are a beginning programmer, may be the clearest way to express your intention. For a longer function such as the price rounding function, this is almost certainly your best option.
• For very short functions, if you feel comfortable using an anonymous function with fn, go for it.
• You may find that the ultra-short syntax borders on unreadability, so you don’t have to use it. Just be aware that other programmers are greatly enamored of it, so you will have to recognize it in their code.
Next Section - Manipulating Collections - reduce | |
mathbits properties of real numbers
Always check your final answer on these problems by multiplying through. Properties of Real Numbers (SAVE) Commutative Property of Addition. Terms of Use Contact Person: Donna Roberts. Symmetric property. The Distributive Property multiplies (distributes) a term across the added terms within a set of parentheses. These properties allow for the creation of equivalent expressions. $21-26=$ Perform the indicated operations. ", "dividing both sides of an equation by the same non-zero value will not change truth value of the equation. Example: 3 + 9 = 12 where 12 (the sum of 3 and 9) is a real number.2) Commutative Property of Addition 1. Identify the property a + b = b + a. Always check your final answer on these problems by multiplying through. The properties aren’t often used by name in pre-calculus, but you’re supposed to know when you need to utilize them. This video explains and provides examples of the properties of real numbers. http://www.greenemath.com/ http://www.facebook.com/mathematicsbyjgreene In this lesson, we will review some of the properties of real numbers. (using Real Number Properties) Directions: Simplify each expression by showing and/or justifying each step. Start studying Properties of Real Numbers. Start studying Properties of Real Numbers -. For Addition The sum of two or more real numbers is always the same regardless of the order in which they are added. All rational numbers are real, but the converse is not true. Density property. Email. A real number is a value that represents a quantity along a continuous number line. ", "multiplying both sides of an equation by the same value will not change the truth value of the equation. Topical Outline | Algebra 1 Outline | MathBitsNotebook.com | MathBits' Teacher Resources Irrational numbers: Real numbers that are not rational. Only the positioning of the parentheses has changed. Quizlet flashcards, … Understand that a generalisation of an important idea can be expressed using letters (variables). The properties of the Real Number System will prove useful when working with equations, functions and formulas in Algebra, as they allow for the creation of equivalent expressions which will often aid in solving problems. Properties of Real Numbers When analyzing data or solving problems with real numbers, it can be helpful to understand the properties of real numbers. This site will use the term "natural numbers" to refer to the counting numbers {1, 2, 3, ...}. Properties of Real Numbers. For example: 3 and 11 are real numbers. Properties Of Real Numbers . (a-b) 8 Properties of Real Numbers - KM study guide by KATELYN_MAZURKIEWICZ includes 14 questions covering vocabulary, terms and more. is, and is not considered "fair use" for educators. Always multiply ALL of the terms within the parentheses and be careful of the signs. $15-20$ : Use properties of real numbers to write the expression without parentheses. 1-4 Assignment - Properties of Real Numbers. Choose from 500 different sets of real numbers math properties system flashcards on Quizlet. a + b = b + a6 + 4 = 4 + 6. The terms within the parentheses have switched places ("commuted"). Justify the steps in the simplification of this expression. Andymath.com features free videos, notes, and practice problems with answers! 200+ Algebra Worksheets available here and free to be downloaded! The additive inverse of a b is A. a+b B. a+b C. a b D. 1 a C.b 9. The product of any real number and 0 is 0. She’s like 37 years old. Rational numbers such as integers (-2, 0, 1), fractions (1/2, 2.5) and irrational numbers such as √3, π (22/7), etc., are all real numbers. Equation: 4(a + 6) = 4a + 4â¢6 The Distributive Property. Suppose a, b, and c represent real numbers.1) Closure Property of Addition 1. Between 5.612 and 5.613, there is 5.6121, 5.6122 ... and an endless list of other numbers! Commutative Property . The properties of real numbers help us simplify math expressions and help us better understand the concepts of algebra. Most mathematicians hold with the older traditional and define natural numbers to be the counting numbers [positive integers {1, 2, 3, ...}]. For any two real numbers a … a year ago by. This video explains the Basic Properties of Real Numbers in a fun and easy way. Real Numbers: The totality of rational and irrationals forms the set R of all real numbers. Properties of Real Numbers: For More Mathematics Doubts visit main page of Entrancei. teacher is about as. $15-20$ : Use properties of real numbers to write the expression without parentheses. associative property of addition (a + b) + c = a + (b + c) commutative property of addition. Justify the steps in the simplification of this expression. The properties of the Real Number System are also used to help explain or justify solutions. wink! Properties Of Real Number And Answer Worksheets - there are 8 printable worksheets for this topic. 0. This solution will be (-7)(p) + (-7)(7) = -7(p + 7). Are you ready to be a mathmagician? We begin this section with a review of the fundamental properties of arithmetic. is another real number", "adding the same value to both sides of an equation will not change the truth value of the equation. EASY!!! a + 0 = a or 0 + a = a. additive inverse property. Look for a common factor between the terms. A number and its reciprocal multiply to 1, which is the multiplicative identity. A property of the Real Numbers is used to progress from one step to the next. #5. whole numbers [non-negative integers {0, 1, 2, ...}]. 1-4 Guide Notes TE - Properties of Real Numbers. PLAY. Which is the additive inverse of a 3? ", "the value that returns the input unchanged", "the value that brings you back to the identity element under addition", "the value that brings you back to the identity element under multiplication", "the product of any two real The properties of the Real Number System will prove useful when working with equations, functions and formulas in Algebra, as they allow for the creation of equivalent expressions which will often aid in solving problems. Zero divided by any real number except zero is zero. 3 + 11 = 14 and 3 ⋅ 11 = 33 Notice that both 14 and 33 are real numbers. Theorems on The Properties of The Real Numbers. Real numbers (): Numbers that can represent a distance along a line. Commutative Property - interchange or switch the elements The example below shows commutative property for addition: Verbal Description: If you add two real numbers, the sum is also a real number. Properties of matrix multiplication. Defines the properties of real numbers and then provides examples of the properties by rewriting and simplifying expressions.These include the distributive property, factoring, the inverse properties, the identity properties, the commutative property, … Scroll down the page for more examples and explanations of the number properties. Number Property Calculator: Enter Integer you would like to know more about the sum of two real numbers is a real number. Imaginary numbers: Numbers that equal the product of a real number and the square root of −1. Example: and 6 is a real number. 1-4 Online Activities - Properties of Real Numbers. Please read the ". Using the Distributive Property in reverse, this expression can be Properties of Real Numbers Number Properties Recognise that there are number properties and that these describe the behavior of number operations. from this site to the Internet While this example looks like "subtraction" within the parentheses, it can also be re-written as "addition" of a negative value, 8(x + (-6)). Properties of Real Numbers, ALGEBRA 1 Concept and Skills - Ron Larson, Laurie Boswell, Holt McDougal | All the textbook answers and step-by-step explanations Watch Queue Queue \frac{4}{3}(-6 y) Enroll in one of our FREE online STEM summer camps. (using Real Number Properties) Directions: Simplify each expression by showing and/or justifying each step. ", "a value may be substituted for its equal. #5. Real number, in mathematics, a quantity that can be expressed as an infinite decimal expansion. Equation: 4 (a + 6) = 4a + 4•6 The Distributive Property. Closure: a + b and ab are real numbers 2. Properties of Real Numbers CHART (def n, property chart, examples, verbal hints) Using Properties of Real Numbers (equivalent expressions, justifying solutions) Where the Properties Don't Work! Algebraic Properties of Real Numbers. ", "subtracting the same value from both sides of an equation will not change the truth value of the equation. Please read the ". The basic algebraic properties of real numbers a,b and c are: 1. Preview this quiz on Quizizz. Verbal Description: If you add two real numbers in any order, the sum will always be the same or equal. a + b = b + a 2 + 6 = 6 + 2. ab = ba 4 × 2 = 2 × 4. The reciprocal of a number is its multiplicative inverse. In addition, they can be used to help explain or justify solutions. properties of real numbers examples with answers, The Closure Properties. Properties of Real Numbers study guide by catherinezeng23 includes 10 questions covering vocabulary, terms and more. Section P.2 Properties of Real Numbers 17 Properties of Real Numbers Let a, b, and c represent real numbers. In other wor… If you're seeing this message, it means we're having trouble loading external resources on our website. Terms of Use Hints for remembering the basic properties of real numbers. (i) The sum of two real numbers is always real. For example, between 5.61 and 5.62, there is 5.611, 5.612, 5.613 and so forth. a + b = b + a. additive identity property. The sum of the areas of the two smaller rectangles can be expressed as 4a + 4â¢6. (ii) The product of two real numbers is always real. mbouchard. The properties of the Real Number System are also used to help explain or justify solutions. In other words, real numbers can be added in any order because the sum remains the same. Since there are no parentheses in this problem, it must be the result of the Distributive Property having already been "distributed" across a set of parentheses. MathBitsNotebook - JrMath Lessons and Practice is a free site for students (and teachers) studying Middle Level (Junior High) mathematics under the Common Core State Standards or a variation of CCSS. Which property of real numbers is illustrated by the equation p 3+ p 3 = 0? Real numbers are the numbers which include both rational and irrational numbers. This is the Commutative Property of Addition. Distributive property . Matrix multiplication dimensions. Example: and 6 is a real number. This example deals with addition between all of the terms and with "grouping" ("association") of terms using parentheses. For example: 4 + 5 = 5 + 4 x + y = y + x. Commutative Property of Multiplication. Property Verbal Description Closure Property of Addition The sum of two real numbers is a real number. Identity property Commutative properties . \text { Distributive Property, } 5 x+5 y= Enroll in one of our FREE online … This solution will be 8â¢x + 8â¢(-6) = 8x - 48. Mathematics. Students are introduced to the magic powers that most mathematicians call properties of real numbers. a • b = b • a 5 • 7 = 7 • 5. Computer scientists, set theorists, logicians and other mathematicians define natural numbers to be the Save. $$(3 a)(b+c-2 d)$$ Problem 21. In addition, they can be used to help explain or justify solutions. The word real distinguishes them from It may seem unusual to give so much emphasis to the few properties listed below, but there is a good reason. Quiz. is a real number. 8 + 5 (x - 2) - 3x + 9. DRAFT. a = a. The area of rectangle ABCD can be expressed as 4(a + 6). Real Numbers are Commutative, Associative and Distributive: Commutative example. This video explains and provides examples of the properties of real numbers.http://mathispower4u.com Associative properties . In this video you will learn about the properties of real numbers. Properties Of Real Numbers Worksheets - there are 8 printable worksheets for this topic. This is the Associative Property of Addition. The word real distinguishes them from Remembering the properties of numbers is important because you use them consistently in pre-calculus. Using the Distributive Property in reverse, this expression can be, from this site to the Internet Keystone Review { Properties of Real Numbers 8. Associative properties . In this case, -7 will do nicely. Properties. While this example looks like "subtraction" within the parentheses, it can also be re-written as "addition" of a negative value. That means if a and b are real numbers, then a + b is a unique real number, and a ⋅ b is a unique real number. Between 5.612 and 5.613, there is 5.6121, 5.6122 ... and an endless list of other numbers! Commutative properties . is a real number. 3 a C. 3 a D. 0 10. 3. a year ago by. Space is limited so join now! Associative Property of … Simplify this expression and justify your steps: 12 + 3(a + 2b) - 2a - 3b - 9 + b. Real numbers are closed under addition, subtraction, and multiplication. Properties 0f Real Numbers. Real numbers have the same types of properties, and you need to be familiar with them in order to solve algebra problems. Properties of Real Numbers DRAFT. Range is all real values of y for the given domain (real values values of x). Play this game to review Algebra I. 1-4 Bell Work - Properties of Real Numbers. Learn about the properties of matrix multiplication (like the distributive property) and how they relate to real number multiplication. All of these theorems are elementary in that they should be relatively obvious to the reader. Google Classroom Facebook Twitter. written as (76 - 73) x 8 which is 3 x 8 = 24. Properties of Real Numbers. Property Verbal Description Closure Property of Addition The sum of two real numbers is a real number. This means the numbers can be swapped. wink! Rewrite using the Distributive Property. This video explains the Basic Properties of Real Numbers in a fun and easy way. My math. Edit. It may be algebraic or transcendental. It may seem unusual to give so much emphasis to the few properties listed below, but there is a good reason. Played 75 times. Numbers can be added in any order. Learn vocabulary, terms, and more with flashcards, games, and other study tools. Issuu is a digital publishing platform that makes it simple to publish magazines, catalogs, newspapers, books, and more online. The following list presents the properties of numbers: Reflexive property. Properties Of Real Numbers . We need to work backward! If […] A.N.1: Identifying Properties: Identify and apply the properties of real numbers (closure, commutative, associative, distributive, identity, inverse) 1 Which property is illustrated by the equation ax+ay =a(x+y)? Real Numbers( Mathematics) This video is unavailable. For example, between 5.61 and 5.62, there is 5.611, 5.612, 5.613 and so forth. Closure Property for Addition. Domain is all real values of x for which the given quadratic function is defined. And sometimes these properties just make computations easier. properties of real numbers.docx - Real Numbers Property... School No School; Course Title AA 1; Uploaded By ProfessorJellyfishPerson2258 Defined matrix operations. For example, 10 = 10. Closure Property of Multiplication The product of two real numbers is a real number. Contact Person: Donna Roberts, The real numbers include: counting (natural) numbers (, "multiplication distributes across addition", "commute = to get up and move to a new location : switch places", "commute = to get up and move to a new location: switch places", "regroup - elements do not physically move, they simply group with a new friend. Roughly speaking, all of algebra follows from the 5 properties listed in the table below. In pre-algebra, you learned about the properties of integers. 1-4 Slide Show - Properties of Real Numbers. Real numbers have the same types of properties, and you need to be familiar with them in order to solve algebra problems. The numbers used to measure real-world quantities such as length, area, volume, speed, electrical charges, probability of rain, room temperature, gross national products, growth rates, and so forth are called real numbers.They include such numbers as $$10$$, $$– 17$$, $$\frac{{17}}{{14}}$$, $$0$$, $$2.71828$$, $$\sqrt 2$$, $$– \frac{{\sqrt 2 }}{2}$$, $$3 \times {10^8}$$ and $$\pi$$. Topical Outline | Jr Math Outline | MathBitsNotebook.com | MathBits' Teacher Resources Printable pages make math easy. 70% average accuracy. as ancient . Actually, we can work with matrices whose entries come from any set that satisfies these properties, such as the set of all rational numbers or the set of all complex numbers. These are the set of all counting numbers such as 1, 2, 3, 4, 5, 6, 7, 8, 9, …….∞. 1-4 Lesson Plan - Properties of Real Numbers. Name a property of real numbers which justifies: Explain why these expressions are equivalent. Here are the main properties of the Real Numbers. Unlike the first example, however, these terms do not remain in the same order. Edit. Density property Identity properties The Distributive Property is easy to remember, if you recall that "multiplication distributes over addition". as your teacher. EXAMPLE: Simplify and justify steps: 20 + 4( x + 3 y ) – 4 x – 8 y – 12 + x Real number, in mathematics, a quantity that can be expressed as an infinite decimal expansion. Closure Property of Multiplication The product of two real numbers is a real number. The density property tells us that we can always find another real number that lies between any two real numbers. 13.5.10: Properties of Real Numbers Last updated; Save as PDF Page ID 46241; Contributed by Lynn Marecek; Professor (Mathematics) at Santa Ana College; Some of these properties are . Commutative: a + b = b + a, ab = ba An operation is commutative if a change in the order of the numbers does not change the results. Sections: JrMath, Algebra 1, Geometry, Algebra 2, PreCalc under development Includes a variety of topics including all standards for the Common Core State Standards, and the NY Next Generation Standards for Mathematics, Properties of Real Numbers Use properties of real numbers to write the expression without parentheses. Domain of a Quadratic Function. We begin this section with a review of the fundamental properties of arithmetic. MathBits.com presents: MathBitsNotebook.com FREE! FYI: Regarding the term "natural numbers", there is no universal agreement about whether to include zero in this set. They can be positive, negative, or zero. 8th - 11th grade . $$-\frac{5}{2}(2 x-4 y)$$ Problem 20. ", Reflexive (or Identity) Property of Equality, "quantities that are equal can be read forward or backward", "if two numbers are equal to the same number, then the two numbers are equal to each other". Property: a + b is a real number 2. This site will use the term "natural numbers" to refer to the counting numbers {1, 2, 3, ...}. STUDY. The general form a quadratic function is y = ax 2 + bx + c. The domain of any quadratic function in the above form is all real … Distributive property . Using the Distributive Property, rewrite: The Distributive Property multiplies (distributes) a term across the added terms within a set of parentheses. 3. Real numbers are used in measurements of continuously varying quantities such as size and time, in contrast to the natural numbers 1, 2, 3, …, arising from counting. Learn vocabulary, terms, and more with flashcards, games, and other study tools. 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# TeX markdown needed on Meta
As seen in the recent sandbox question, TeX markdown isn't enabled on Meta.
It should be. It's needed for the sandbox, and we're likely to have questions on how to do something in TeX, TeX bug reports, TeX feature requests, and, after the feature is more familiar, questions which assume that TeX is enabled on Meta and try to use it.
I don't want to have to go over to Math.SE and try stuff on their meta (they have it enabled). I don't think they'd like that much... :)
Test: $\LaTeX$
• Wasn't sure how to tag it, so I covered my bases. – Kevin Vermeer Mar 9 '11 at 15:20 | |
# random variable in an interval
I have a random variable $X$. The constants $a$, $b$ and $c$ are given. I have to find the interval $I$ such that $P(a\in (X-b,X+b))=c$. My question is actually not how to calculate this interval. How should I think of a random variable in an interval? Is there an intuitive way?
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how does interval $I$ play a role here? – Ilya Jan 21 '13 at 14:40
@Ilya I didnt mention it well but I meant $I=(X-b,X+b)$. – Badshah Jan 21 '13 at 14:46
## 2 Answers
$$[a\in(X-b,X+b)]=[a-b\lt X\lt a+b]=[X\in(a-b,a+b)]$$
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okey thanks, and how should this help me find the interval $I=(X-b,X+b)$? because I dont see why having $P(X\in (a-b,a+b))=c$ should give me $I$. – Badshah Jan 21 '13 at 14:57
$a\in(X-b,X+b)\implies X\in(a-b,a+b)$
and $P((a-b)<X<(a+b))=F(a+b)-F(a-b)$ where F is the cumulative distribution function of random variable $X$
- | |
• # Orientation with Quaternions
Math and Physics
Since no one else has mentioned this, I guess I will. Why not use quaternions, rather than rotation matrices, to represent your rotations? Quaternions on the unit sphere and 3-d rotations are isomorphic, and quaternions don't require the redundant storage and calculation that 3x3 matrices do.
A quaternion may be thought of as an entity of the form [s,x], where s is a scalar and x is a 3-vector. Multiplication of quaternions is given by [s1,x1] * [s2,x2] = [s1 * s2 - x1 dot x2, s1*x2 + s2*x1 + x1 cross x2]. A unit quaternion is one that satisfies s*s + x dot x = 1. A unit quaternion may also be thought of as a rotation of angle 2 arccos s about the axis v. To rotate a vector v by a rotation quaternion q to get a vector w, use the formula [0,w] = inv(q) * [0,v] * q, where inv(q) * q = [1,0], and inv([s,v]) = [s,-v]. Or, if you prefer, form the equivalent rotation matrix
1 - 2 (x2*x2 + x3*x3) 2 (x1*x2 + s * x3) 2 (x1*x3 - s*x2) 2 (x1*x2 - s*x3) 1 - 2 (x1*x1 + x3*x3) 2 (x2*x3 + s*x1) 2 (x1*x3 + s*x2) 2 (x2*x3 - s*x1) 1 - 2 (x1*x1 + x2*x2)
and use that.
The basic algorithm, then, to display vectors V = [v1 ; v2 ; v3 ; ... ; vn] rotating by q every frame is
rot = [1,0] do-forever R = rotation matrix associated with rot DISP = R * V display all vectors in DISP rot = rot * q norm = rot.s * rot.s + rot.x1 * rot.x1 + rot.x2 * rot.x2 + rot.x3 * rot.x3 if (abs(norm - 1) > tolerance) norm = sqrt(norm) rot.s = rot.s/norm rot.x1 = rot.x1/norm rot.x2 = rot.x2/norm rot.x3 = rot.x3/norm endif enddo
That's the general idea, anyway. For a less terse exposition, see Ken Shoemake, "Animating Rotation with Quaternion Curves", COMPUTER GRAPHICS Vol 19 No 3, pp. 245-254.
Incidentally, similar quaternion techniques can be used for 4-d rotations. I haven't been able to get a handle on higher dimensions, though.
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# Intersection of a Quadric Surface and a Plane in 3-D
1. Jan 28, 2014
### Onionknight
1. "Find the equation that describes the intersection of the quadric given by $x^2 + y^2 = 4$ with the plane $x + y + z = 1$."
2. Parametric equations for elliptic curve: $x = a cos(t)$ , $y = b sin(t)$ , z = ?
3. Surface is an [EDIT: right circular] cylinder. Plane is not parallel to xy plane, has some increasing z and will not cut a circle in the cylinder. Curve of intersection of plane and elliptic cylinder will result in an elliptic curve.
3a. My first approach would be to plug in $a cos(t)$ and $b sin(t)$ for x and y respectively in the $x^2 + y^2 = 4$ equation.
$(a cos(t))^2 + (b sin(t))^2 = 4$ ---> $a^2(cost)^2 + b^2(sint)^2 = 4$ ---> $\frac{a^2(cost)^2}{4} + \frac{b^2(sint)^2}{4} = 1$ ---> a = b = 2 --> $x = 2cost$ and $y = sint$
This step confuses me since I would think that because the curve is elliptic, the a and b coefficients would differ.
3b. My second step would be to rearrange the equation of the plane to be some z = x + y + c to find the parametric equation for z.
$x + y + z + (- x - y) = 1 + ( - x - y)$ ---> $z = - x - y + 1$ ---> $z = - (2cost) - (2sint) + 1$
3c. Last step would be to combine everything into parametric equations.
$x = 2cos(t)$ , $y = 2sin(t)$ , $z = - 2sin(t) - 2cos(t) + 1$.
I think I have the right idea, but any suggestions or guidance would be appreciated.
Last edited: Jan 28, 2014
2. Jan 28, 2014
### HallsofIvy
This is wrong. [tex]x^2+ y^2= 4[/itex] is the equation of a circular cylinder. It can be written as x= 2cos(t), y= 2 sin(t). Yes, its intersection with the tilted plane will be an ellipse but that is not relevant here.
The plane, x+ y+ z= 1 can be written 2cos(t)+ 2sin(t)+z= 1 so that z= 1- 2cos(t)- 2sin(t).
And that gives the parametric equations describing the intersection:
x= 2cos(t)
y= 2sin(t)
z= 1- 2cos(t)- 2sin(t).
3. Jan 28, 2014
### Onionknight
Thank you. Don't know why I typed elliptic cylinder. I think I understand why it doesn't matter that a doesn't equal b. Since the curve of intersection is tilted by the z component anyways, it's going to be an ellipse. If the z parametric equation wasn't in effect, the curve would be a circle. I think this makes sense. Is my overall logic and procedure sound? | |
# Mahout k-means generates too many clusters [closed]
I am a beginner in Mahout, I use Mahout 0.8 and followed the tutorial in https://cwiki.apache.org/MAHOUT/clustering-of-synthetic-control-data.html
When I use : mahout org.apache.mahout.clustering.syntheticcontrol.kmeans.Job -i testdata -o output -t1 20 -t2 50 -k 5 -x 20 -ow
then use clusterdump to extract the cluster-centers:
mahout clusterdump --input output/clusters-20-final --output /media/synthetic_control.center
in the synthetic_control.center file:
VL-585{n=50 c=[29.832, 29.589, 29.405, 28.516, 29.600, ….] r=[3.152, 3.518, 3.292, …]}
VL-591{n=197 c=[29.984, 29.681,…] r=[3.602, 3.558, 3.364,…]}
VL-595{n=203 c=[….] r=[….]}
VL-597{n=61 c=[….] r=[….]}
VL-599{n=43 c=[….] r=[….]}
VL-585{n=1 c=[….] r=[….]}
VL-591{n=27 c=[….] r=[….]}
VL-595{n=1 c=[….] r=[….]}
VL-597{n=1 c=[….] r=[….]}
VL-599{n=16 c=[….] r=[….]}
It seems the kmeans algorithm generates 10 clusters, but my initial setting for k is 5.
I also tried other k, it always generate doubled clusters.
Can anyone help me with this? Thanks a lot!
-
This sounds like a mahout programming problem, not really a statistics problem. Is there a mahout list? Or, you might consider moving this to StackOverflow. I have suggested that. (Please don't crosspost yourself, that irritates the people in charge). – Peter Flom Oct 12 '12 at 10:26 Try without -t1 and -t2. I read somewhere that T2 < T1 should be used? – Anony-Mousse Oct 12 '12 at 10:45
## closed as off topic by Peter Flom, gung, mbq♦Oct 12 '12 at 12:14
Questions on Cross Validated are expected to relate to statistics within the scope defined in the FAQ. Consider editing the question or leaving comments for improvement if you believe the question can be reworded to fit within the scope. Read more about closed questions here. | |
# Understanding spin, spinors, and rotations
1. Feb 14, 2012
### VantagePoint72
There's something I don't think I quite understand about spin and how it acts a generator of rotations. I'll start with quickly going over what I do understand. Suppose you want to do an infinitesimal rotation around the z-axis on some state:
$\def\ket#1{\left | #1 \right \rangle} \ket{\psi '} = (1 - \frac{i\epsilon _z J_z}{\hbar})\ket{\psi}$
Now, if the wavefunction is just a scalar, then projecting on the coordinate basis gives us:
$\psi '(x,y,z) = (1 - \frac{i\epsilon _z J_z}{\hbar})\psi (x,y,z)$
and so, as usual, we can do a finite rotation of $\phi$ around the z-axis by breaking it down into infinitesimal rotations and composing them, giving the relation:
$\psi '(x,y,z) = e^{-i \phi L_z / \hbar}\psi (x,y,z)$
Now, because we know what this operator does, we don't actually have to expand the exponential. We can just (passively) rotate the coordinates:
$$\begin{pmatrix} x' \\ y' \end{pmatrix} = \begin{pmatrix} \cos\phi & +\sin\phi\\ -\sin\phi & \cos\phi \end{pmatrix} \begin{pmatrix} x \\ y \end{pmatrix} = R^{-1}(\phi) \begin{pmatrix} x \\ y \end{pmatrix}$$
Giving:
$$\psi '(x,y,z) = \psi (x\cos\phi + y\sin\phi,-x\sin\phi + y\cos\phi,z)$$
So far, so good. Now, if $\ket{\psi}$ actually requires a spinor to describe the wavefunction, $\ket{\psi} \rightarrow \begin{pmatrix} \psi _+(x,y,z) \\ \psi _-(x,y,z) \end{pmatrix}$ then $J_z = L_z + S_z$ and the act of rotating the ket has two effects: a passive rotation of the coordinate system and a shuffling together of the two wavefunction components. So, we repeat the exercise we went through for $L_z$, derive the Pauli spin matrices from the commutators, etc., eventually finding that:
$$e^{-i \phi S_z / \hbar} = \begin{pmatrix} \cos(\phi /2) - i \sin(\phi /2) & 0\\ 0 & \cos(\phi /2) + i \sin(\phi /2) \end{pmatrix}$$
What I don't get is how this makes any sense. I mean, I can follow all the steps in the derivation, I just don't get the final result. Why isn't the overall rotation due to spin just given by the matrix $R(\phi)$ above? In other words, taking into account both $L_z$ and $S_z$, why isn't the rotated spinor given by:
\begin{align} \begin{pmatrix} \psi _+ '(\vec{r}) \\ \psi _- '(\vec{r}) \end{pmatrix} &= R(\phi) \begin{pmatrix} \psi _+ (R^{-1}(\phi)(\vec{r})) \\ \psi _- (R^{-1}(\phi)(\vec{r})) \end{pmatrix} \\ &= \begin{pmatrix} (\cos\phi) \psi _+ (x\cos\phi + y\sin\phi,-x\sin\phi + y\cos\phi,z) - (\sin\phi) \psi _- (x\cos\phi + y\sin\phi,-x\sin\phi + y\cos\phi,z) \\ (\sin\phi) \psi _+ (x\cos\phi + y\sin\phi,-x\sin\phi + y\cos\phi,z) + (\cos\phi) \psi _- (x\cos\phi + y\sin\phi,-x\sin\phi + y\cos\phi,z) \end{pmatrix} \end{align}
That's what rotating something does, so why do spinors behave differently?
Last edited: Feb 14, 2012
2. Feb 15, 2012
### Ben Niehoff
Forget about spinors for a moment, and think about vector-valued wavefunctions. These turn up for spin 1 particles, such as the photon.
A vector-valued function is an object that assigns a little arrow to each point in space. How does the rotation group act on such an object? Keeping with active rotations, the rotations should act by moving the whole field of arrows around. But a rotation does not just move the points to which the arrows are attached; it also has to rotate the arrows, so that the entire assembly moves rigidly. So one would write
$$\tilde{A}^i (\vec x) = R^i{}_j A^j (R^{-1} \vec x),$$
where R is some rotation matrix.
Now back to spinors. When you rotate a spinor field, you also have to move everything rigidly. The missing piece of information, which is not always clear from the algebraic definitions, is that a spinor is a kind of object that indicates a direction in space. Specifically, given a 2-component spinor
$$\begin{pmatrix} \alpha \\ \beta \end{pmatrix},$$
one forms the complex number $z \equiv \alpha / \beta$, which is then related to a spatial direction by stereographic projection onto the Riemann sphere. It isn't hard to show that the eigenspinors of the Sx, Sy, and Sz operators correspond, respectively, to directions along the x, y, and z axes.
So this is the reason that the spinor components must also mix. They must change to represent a new direction in space, obtained by rigidly rotating the old direction, just as you would do with a vector field. The catch is that the direction is represented by stereographic projection (hence why this is called a projective representation of the rotation group), so the exact manner in which the components mix may seem strange at first.
Last edited: Feb 15, 2012
3. Feb 15, 2012
### VantagePoint72
Thanks for your response! So then it's just the fact that spinor elements are complex that makes them mix differently than vector functions?
Edit: or is it because a spinor has two components instead of three?
4. Feb 15, 2012
### The_Duck
Basically this. This is properly understood using representation theory, in whose language we would say that two-component spinors live in a different representation of the rotation group than 3-vectors. Spin 1/2 objects are in the 2-dimensional representation, while vectors are in the 3-dimensional representation. You can define rotation matrices for both of them, but they are different rotation matrices (not least because spinors use 2x2 rotation matrices and vectors use 3x3 rotation matrices).
5. Feb 15, 2012
### lugita15
Do you know of any good book on representation theory and Lie groups which explains all this stuff?
6. Feb 15, 2012
### questionpost
Spin isn't really rotation in the classical sense, it's more of the pattern of how a wave oscillates, and angular momentum effects waves differently than spheres. You could try shaking a glass of water to see what happens. I myself have found that merely changing the direction in which energy is put into oscillating a fluid effects the shapes that somehow almost perfectly coincides with different orbital models.
7. Feb 15, 2012
### lugita15
It's true that spin has some differences with classical rotation, but they're much more similar than you seem to think. For instance, you need to rotate an electron 720 degrees to get it back to where it started, whereas you only need to rotate classical objects by 360 degrees. But notice for both kinds of rotations there exist angles which bring you back to square one. And that's just the start of their similarities.
In more formal terms, the rotation group of ordinary groups is SO(3), whereas if you want to have spin you need the closely related group SU(2). These two groups are locally isomorphic, which means they're infinitesimal elements can be identified. To put it another way, during an infinitesimal time dt both electron spin and the rotation of a top are doing exactly the same thing. It's only after a finite time t that you notice that the two behaviors diverge from each other.
8. Feb 16, 2012
### genericusrnme
I second this!
A book that is perhaps more geared towards showing it's applications to problems like this | |
If $f'(x)>0$ on $E$ , where $m(E)>0,$ then $m(f(E))>0$
Let $$f:\mathbb R\to \mathbb R,$$ and suppose $$f$$ is differentiable at every point of a measurable $$E\subset \mathbb R,$$ with $$f'>0$$ on $$E$$.
Suppose also that $$m(E)>0$$ (where $$m$$ is Lebesgue measure).
Prove that $$m(f(E))>0$$.
My proof:
Since $$f$$ is differentiable then it's continuous and hence it preserves both compact sets and intervals.
Now since $$m(E)>0$$ we can find compact interval inside it (is this true or not?) If this is true so the proof is completed.
I know that if $$E$$ is measurable then $$E$$ is either Borel set or a set of measure zero.
So here $$E$$ is Borel, but still not necessarily to be an interval.
• No, the set of irrational numbers has positive measure but doesn't contain any interval. – user384138 Jan 7 '17 at 16:28
• It's not even clear that $f(E)$ is measurable from the given hypotheses. – zhw. Jan 10 '17 at 19:29
• I want to ask the OP: Is this really the problem? is this the exact wording?where does it come from? – zhw. Jan 11 '17 at 20:23
• @charMD can you put your solution ,thanks in advance – Sara Suradi Jan 11 '17 at 20:55
• @zhw. Yes I am almost sure,It's a final exam question , I will ask my prof at the beginning of next semester – Sara Suradi Jan 12 '17 at 14:20
3 Answers
I will prove two points : first, in response to a comment of zhw, we check that $$f(E)$$ is measurable, and then that its measure is $$>0$$.
We recall that $$m^*$$ denotes here Lebesgue outer measure, defined for every subset $$S \subset \mathbb{R}$$. For $$I$$ an open interval of $$\mathbb{R}$$, we note $$l(I) = \sup I - \inf I$$. Then we define $$m^*(S) = \inf \left \{ \sum \limits_{k=1}^{+\infty} l(I_k),\ (I_k)_{k \ge 1} \textrm{ is a sequence of intervals with } S \subset \bigcup \limits_{k \in \mathbb{N}^*} I_k \right \}$$
For both results, the following lemma will be needed.
Lemma : Given $$f : \mathbb{R} \rightarrow \mathbb{R}$$ differentiable at any point of a set $$S$$, assuming that there exists $$C \ge 0$$ such that $$\forall x \in S,\ |f'(x)| \le C$$, then $$m^* \big( f(S) \big) \le C \cdot m^*(S)$$.
Proof : Let $$\varepsilon > 0$$. We define an increasing sequence of sets $$(S_n)_{n \ge 1}$$ by : $$S_n = \left \{ x \in S,\ \forall t \in S,\ |t-x| \le \frac{1}{n} \Rightarrow |f(t)-f(x)| \le (C+\varepsilon)|t-x| \right \}$$
Using the hypothesis $$|f'|\le C$$, we get that $$S = \bigcup \limits_{n=1}^{\infty} S_n$$. For every $$n \ge 1$$, we can take a sequence of open intervals $$(I_{n,k})_{k \ge 1}$$ covering $$S_n$$ and such that $$\sum \limits_{k=1}^{+\infty} m^*(I_{n,k}) \le m^*(S_n)+\varepsilon.$$
Without loss of generality, we can assume that for every $$n$$ and $$k$$, $$m^*(I_{n,k}) \le \frac{1}{n}$$.
Then, for $$n \in \mathbb{N}^*$$, for all $$k \in \mathbb{N}^*$$, for $$x,y \in S_n \cap I_{n,k}$$, we have $$|y-x|\le \frac{1}{n}$$ and $$x,y \in S_n$$, so we can write $$|f(y)-f(x)| \le (C+\varepsilon)|y-x|\le (C+\varepsilon)\cdot m^*(I_{n,k})$$. Thus, for $$n \ge 1$$, $$m^*(f(S_n)) \le \sum \limits_{k=1}^{+\infty} m^*\big(f(S_n \cap I_{n,k}) \big) \le \sum \limits_{k=1}^{+\infty} (C+\varepsilon)\cdot m^*(I_{n,k}) \le (C+\varepsilon)\cdot (m^*(S_n)+\varepsilon)$$
Letting $$n \to +\infty$$ and then $$\varepsilon \to 0^+$$, we get $$m^* \big( f(S) \big) \le C \cdot m^* (S)$$.
Now we prove that $$f(E)$$ is measurable. Classically (see Problem about $$G_{\delta}$$ and $$F_{\delta}$$ sets),
Claim 1 : There exists a subset $$H \subset E$$ which is $$F_{\delta}$$ (i.e. a countable union of closed sets) such that $$N=E \backslash H$$ is a null set.
Write $$H = \bigcup \limits_{k=1}^{+\infty} F_k$$ where the $$F_k$$ are closed. For $$k \ge 1$$, for all $$M>0$$, $$[-M,M] \cap F_k$$ is compact and $$f$$ is continuous (because it is differentiable) on this set, so $$f([-M,M]\cap F_k)$$ is closed (it is a compact set). So for all $$k$$, $$f(F_k) = \bigcup \limits_{M \in \mathbb{N}^*} f\big([-M,M]\cap F_k\big)$$ is a Borel set, so $$f(H)$$ is measurable.
Now we prove that $$f(N)$$ is a null set. For $$k \in \mathbb{N}^*$$, we denote $$N_k = \{ x \in N,\ f'(x). $$N_k \subset N$$ so $$N_k$$ is a null set, so $$m^*(N_k)=0$$ for $$k \ge 1$$. Plus, we can use the previous lemma on $$N_k$$, because $$0 \le f' \le k$$ on $$N_k$$, so $$m^* \big(f(N_k) \big)\le 0$$. Thus $$f(N_k)$$ is a null set. As $$f(E) = f(H) \cup f(N)$$, we can conclude that $$f(E) \textrm{ is measurable}.$$
Now back to the original problem : we have some measurable set $$E$$ with positive measure, $$f$$ differentiable on $$E$$, $$f'>0$$ on E. We suppose that $$m \big( f(E) \big)=0$$.
For $$x \in E$$, $$f'(x)>0$$ so $$\frac{f(x)-f(y)}{x-y}>0$$ for all $$y \in E \backslash \{x \}$$ in some neighborhood of $$x$$. Thus \begin{align*} E & = \bigcup \limits_{q \in \mathbb{Q}} \left \{ x \in E\ | \ \ x > q \ \textrm{ and }\ \forall y \in ]q,x[,\ \frac{f(x)-f(y)}{x-y}>0 \right \}\\ & = \bigcup \limits_{q \in \mathbb{Q}} \left \{ x \in E\ | \ \ x > q \ \textrm{ and }\ \forall y \in ]q,x[,\ f(x)>f(y) \right \} \end{align*}
because $$\mathbb{Q}$$ is dense. Moreover, $$E$$ has positive measure and $$\mathbb{Q}$$ is countable. Hence, there exists $$q_0 \in \mathbb{Q}$$ such that $$B = \left \{ x \in E\ | \ \ x > q_0 \ \textrm{ and }\ \forall y \in ]q_0,x[,\ f(x)>f(y) \right \}$$ has positive measure.
Plus, for $$(x,y) \in B^2$$ with $$x, we have $$q_0 < x , so $$f(y)>f(x)$$. Hence $$f_{|B}$$ is increasing.
Finally it is a well-known fact (see Can we have an uncountable number of isolated points) that $$B$$ has countably many isolated points, and thus we have a measurable subset $$A \subset B$$ such that $$m(A)=m(B)>0$$ and $$A$$ has no isolated points. Note that we also have $$f_{|A}$$ increasing, $$f'>0$$ on A, and $$m \big( f(A) \big)=0$$.
Now we just need a stronger version of our lemma :
Lemma (bis) : Given $$A \subset \mathbb{R}$$ with no isolated points, and $$f : A \rightarrow \mathbb{R}$$, we say that $$f$$ is differentiable at $$x \in A$$ whenever $$\lim \limits_{t \to x^{\neq}} \frac{f(x)-f(t)}{x-t}$$ exists, and we note $$f'(x)$$ the limit. Assuming that $$f$$ is differentiable over $$A$$, and that there exists $$C \ge 0$$ such that $$|f'| \le C$$, we have $$m^* \big( f(A) \big) \le C \cdot m^*(A)$$
Proof : the proof is exactly the same as the one we gave for the first lemma.
Finally, we denote $$g = f_{|A}$$. As $$g$$ is stricly increasing, $$g^{-1}$$ is well defined. Moreover, as $$f'>0$$ on $$A$$, it is classical (see Inverse functions and differentiation) to show that $$g^{-1}$$ is differentiable in the sense of the Lemma bis on $$g(A)$$. As $$g(A)$$ is a null set, we can use our lemma (as we did with the set $$N$$ - see above) to conclude that $$g^{-1}\big( g(A) \big)$$ is a null set, so $$A$$ is a null set, which is absurd.
$$\textrm{Hence we have }\ m \big (f(E) \big) > 0.$$
• Thank you CharMD for your valuable answer .I follow up with your answer until the last step where you said that f^-1 is differentiable (where the result follow immediately as you proved above) so how can we guarantee differentiability of f^-1 ? – Sara Suradi Jan 12 '17 at 14:10
• Also you mean at the end the set A is it self the set E :)? – Sara Suradi Jan 12 '17 at 14:11
• If $f$ is stricly monotone and that $f'(x)$ exists, with $0<f'(x)<+\infty$, then $f^{-1}$ is differentiable at $f(x)$ with derivative $\frac{1}{f'(x)}$. This can be found in various course of calculus (see en.wikipedia.org/wiki/Inverse_functions_and_differentiation) – charmd Jan 12 '17 at 14:26
• In the end, I managed to use only classic tools, but still, this is not an easy question for an exam – charmd Jan 12 '17 at 16:34
• @charMD It is not necessarily the case that $f|_A$ is increasing. Think of $f(x)=x-\lfloor x\rfloor$ and $A=(0,1)\cup (1,2)$. However, as can be inferred following the proof in the link to the Bogachev book, there exists a subset of $A$ with positive measure on which $f$ is increasing, and from here you can apply the rest of the proof. – Del Jan 13 '17 at 23:54
You can prove this by using the following result, which you can find in V. I. Bogachev's Measure Theory book (Springer, 2007). This is Lemma 5.8.13., which I quote almost verbatim but with adapted notation:
Proposition: Let $f$ be a function on $[a,b]$ and let $A$ be the set of all points at which $f$ has a nonzero derivative. Then, for every set $Z$ of measure zero, the set $f^{-1}(Z) \cap A$ has measure zero. In other words, $\lambda \circ f^{-1}|_A \ll \lambda|_A$, where $\lambda$ is Lebesgue measure.
Here is a link to the proof given by Bogachev. It is quite unwieldy (to me, at least) and I must say I haven't gone through the details. The proof relies on Vitali's covering theorem.
Note that the proposition remains true for a function $f$ defined on all of $\mathbb{R}$: just write $\mathbb{R}$ as a countable almost-disjoint union of intervals and apply the proposition to the restriction of $f$ to each interval.
To solve the problem at hand, we argue by contradiction and suppose that $m(f(E)) =0$. Since $E \subset f^{-1}(f(E))$ and $E \subset A$, we have $E \subset f^{-1}(f(E)) \cap A$. Since $f(E)$ has measure $0$, the proposition implies that $f^{-1}(f(E)) \cap A$ has measure $0$. This is a contradiction since we assumed that $m(E) >0$.
Remark: In the above we assumed that $f(E)$ is measurable. This does follow from the hypotheses. See CharMD's great answer for a proof, or alternatively Proposition 5.5.4. in Bogachev's book.
• Have you read Bogachev in its entirety ? :D – Gabriel Romon Jan 13 '17 at 12:25
• I haven't; just some sections here and there. I mostly use it as a reference and for the abundant exercises (about a hundred per chapter!). Why do you ask? – Dominique R.F. Jan 13 '17 at 16:27
From $f'>0$, there exists $c>0$ such that $f'>c$. Then $$m(f(E))=\int_{E} f' dm>\int_{E} c dm=c\int_{E} 1 dm=cm(E)>0.$$
• How does m(f(E))=∫f'. ?can you give me a reference? – Sara Suradi Jan 8 '17 at 16:30
• @user283366 $m(f(E))=\int_{y\in f(E)}1\ dy.$Substitute $y=f(x).$Then, $m(f(E))=\int_{x\in E}f'(x)\ dx$ – kayak Jan 15 '17 at 13:08
• Isn't the monotonicity of $f$ usually required for such a substitution ? – charmd Mar 12 '17 at 12:12 | |
## Rademacher processes and bounding the risk of function learning.(English)Zbl 1106.68385
Giné, Evarist (ed.) et al., High dimensional probability II. 2nd international conference, Univ. of Washington, DC, USA, August 1–6, 1999. Boston, MA: Birkhäuser (ISBN 0-8176-4160-2). Prog. Probab. 47, 443-457 (2000).
Let $$(S,A)$$ be a measurable space and let $$F$$ be a class of $$A$$-measurable functions from $$S$$ into $$[0,1]$$. Denote by $$P(S)$$ the set of all probability measures on $$(S,A)$$ and let $$f_0\in F$$ be an unknown target function. Given a measure $$P\in P(S)$$ (also unknown) let $$(X_1,\dots,X_n)$$ be an i.i.d. sample in $$(S,A)$$ with common distribution $$P$$. In computer learning theory, the problem of estimating $$f_0$$, based on the labeled sample $$(X_1,Y_1),\dots,(X_n,Y_n)$$, where $$Y_j=f_0(X_j)$$, $$j=1,2,\dots,n$$, is referred to as a function learning problem. The goal of function learning is to find an estimate $$\hat f_n=\hat f_n((X_1,Y_1),\dots,(X_n,Y_n))$$ of the unknown target function such that the $$L_1$$-distance between $$\hat f_n$$ and $$f_n$$ becomes small with high probability as soon as the sample size $$n$$ becomes large enough. The $$L_1$$-distance $$P|\hat f_n-f_0|$$ is often called the risk of the estimate $$\hat f_n$$. The authors construct data dependent upper bounds on the risk in function learning problems. These bounds are based on local norms of the Rademacher process indexed by the underlying function class, and they do not require prior knowledge about the distribution of training samples or any specific properties of the function class. By using concentration inequalities of Talagrand’s type for empirical and Rademacher processes it is shown that the bounds hold with a high probability that decreases exponentially fast when the sample size $$n$$ grows. The authors consider a couple of important examples in which these bounds give nearly an optimal rate of convergence of the risk to 0 as $$n\to\infty$$.
For the entire collection see [Zbl 0948.00040].
### MSC:
68T05 Learning and adaptive systems in artificial intelligence 62G05 Nonparametric estimation 68Q32 Computational learning theory
Full Text: | |
# 🎄 BLACK FRIDAY 2021 COUPONS AND DEALS
November 26, 2021
Hello friends! The Black Friday 2021 sale is on! I’m sending you links now which will give you the maximum possible discount during the Black Friday / Cyber Monday season (see below for specific dates). For those students who are new (welcome!), you may not know that I have a whole catalog of machine learning and AI courses built up and continuously updated over the past 6 years, with separate in-depth courses covering nearly every topic in the field, including: – Machine Learning (Linear Regression, Logistic Regression, K-Means Clustering, GMMs, Hierarchical Clustering, HMMs, Markov Models, Decision Trees, Random Forests, Naive Bayes, Perceptrons, SVMs, boosting, Bayesian ML, A/B Testing) – NLP (Attention, seq2seq, BiLSTMs, word2vec, GloVe, article spinning, latent semantic indexing, sentiment analysis, spam detection) – Reinforcement Learning (the basics, along with modern Deep RL topics like DQN, Policy Gradient Methods, Evolution Strategies, A2C and A3C, DDPG) – Deep Learning (separate courses for ANNs, CNNs, RNNs, GANs, Variational Autoencoders, Recommender Systems, Computer Vision) BOOKMARK THIS POST because these links will give you the best discount possible over the Black Friday / Cyber Monday sales later this month. The “Black Friday” links will work on the following dates: – Friday November 26, 2021 (Black Friday) – All week before Black Friday (starting November 19) – Monday November 29, 2021 (Cyber Monday) – Maybe a few days after that, but don’t wait and regret it Outline of the following discounts: 1. Time Series Analysis, Forecasting, and Machine Learning (VIP) 2. Financial Engineering and Artificial Intelligence in Python (VIP) 3. PyTorch: Deep Learning and Artificial Intelligence (VIP) 4. Artificial Intelligence: Reinforcement Learning in Python (VIP) 5. Black Friday Discounts for Other Courses Note that the “VIP links” will work for the next 30 days, you don’t need to wait until Black Friday for those.
Time Series Analysis, Forecasting, and Machine Learning (VIP PROMOTION)
==The Complete Time Series Analysis Course Has Arrived==
https://www.udemy.com/course/time-series-analysis/?couponCode=TIMEVIP6
(note: this VIP coupon expires in 30 days!)
We will cover techniques such as:
• ETS and Exponential Smoothing
• Holt’s Linear Trend Model
• Holt-Winters Model
• ARIMA, SARIMA, SARIMAX, and Auto ARIMA
• ACF and PACF
• Vector Autoregression and Moving Average Models (VAR, VMA, VARMA)
• Machine Learning Models (including Logistic Regression, Support Vector Machines, and Random Forests)
• Deep Learning Models (Artificial Neural Networks, Convolutional Neural Networks, and Recurrent Neural Networks)
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• Time series classification of smartphone data to predict user behavior
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• AWS Forecast (Amazon’s state-of-the-art low-code forecasting API)
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Financial Engineering and Artificial Intelligence in Python
VIP Promotion
https://www.udemy.com/course/ai-finance/?couponCode=FINANCEVIP15
This is a MASSIVE (20 hours) Financial Engineering course covering the core fundamentals of financial engineering and financial analysis from scratch. We will go in-depth into all the classic topics, such as:
• Exploratory data analysis, significance testing, correlations, alpha and beta
• Time series analysis, simple moving average, exponentially-weighted moving average
• Holt-Winters exponential smoothing model
• ARIMA and SARIMA
• Efficient Market Hypothesis
• Random Walk Hypothesis
• Time series forecasting (“stock price prediction”)
• Modern portfolio theory
• Efficient frontier / Markowitz bullet
• Mean-variance optimization
• Maximizing the Sharpe ratio
• Convex optimization with Linear Programming and Quadratic Programming
• Capital Asset Pricing Model (CAPM)
In addition, we will look at various non-traditional techniques which stem purely from the field of machine learning and artificial intelligence, such as:
• Regression models
• Classification models
• Unsupervised learning
• Reinforcement learning and Q-learning
List of VIP content:
• Classic Algorithmic Trading – Trend Following Strategy
• Reinforcement Learning-Based (Q-Learning) Trading Strategy
• Statistical Factor Models
• Regime Detection and Volatility Clustering with HMMs and Sequence Modeling
PyTorch: Deep Learning and Artificial Intelligence
VIP Promotion
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This is a MASSIVE (over 22 hours) Deep Learning course covering EVERYTHING from scratch. That includes:
• Machine learning basics (linear neurons)
• ANNs, CNNs, and RNNs for images and sequence data
• Time series forecasting and stock predictions (+ why all those fake data scientists are doing it wrong)
• NLP (natural language processing)
• Recommender systems
• Transfer learning for computer vision
• Deep reinforcement learning and applying it by building a stock trading bot
• VIP only: Making predictions with your trained NLP model
• VIP only: Making predictions with your trained Recommender model
• VIP only: Modeling prediction uncertainty and heteroskedasticity (i.e. stock returns!)
• VIP only: Facial recognition with Siamese Networks
Artificial Intelligence: Reinforcement Learning in Python
VIP Promotion
===The complete Reinforcement Learning course has arrived===
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Reinforcement Learning is the most general form of AI we know of so far – some speculate it is the way forward to mimic animal intelligence and attain “AGI” (artificial general intelligence).
This course covers:
• The explore-exploit dilemma and the Bayesian bandit method
• MDPs (Markov Decision Processes)
• Dynamic Programming solution for MDPs
• Monte Carlo Method
• Temporal Difference Method (including Q-Learning)
• Approximation Methods using RBF Neural Networks
• Applying your code to OpenAI Gym with zero effort / code changes
• Building a stock trading bot (different approach in each course!)
Tensorflow 2: Deep Learning and Artificial Intelligence VIP
Exclusive to deeplearningcourses.com only
===The complete Tensorflow 2 course has arrived===
## BLACK FRIDAY DISCOUNTED Courses
### Looking for the LOWEST PRICE POSSIBLE Udemy Coupons?
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The best part is, you don’t have to enter any coupon code at all. Simply clicking on the links below will automatically get you the best possible price.
*Note: a few of the courses below, marked with an asterisk (*) are not part of the Black Friday sale. However, if you purchase these courses at the current price, you will receive, upon request, complimentary access to the full VIP version of the course on deeplearningcourses.com. Just email me at [email protected] for free access with proof of purchase.
# Why you shouldn’t use prices as inputs to predict stock prices in machine learning (YouTube Episode 20)
October 12, 2021
Ever come across a machine learning / data science blog demonstrating how to predict stock prices using an autoregressive model, with past stock prices as input?
It’s been awhile, but I am finally continuing this YouTube mini-series I started awhile back, which goes over common mistakes in popular blogs on predicting stock prices with machine learning. This is the 2nd installment.
It is about why you shouldn’t use prices as inputs.
# NEW COURSE: Financial Engineering and Artificial Intelligence in Python
September 8, 2020
# VIP Promotion
### The complete Financial Engineering course has arrived
Hello once again friends!
Today, I am announcing the VIP version of my latest course: Financial Engineering and Artificial Intelligence in Python.
https://www.udemy.com/course/ai-finance/?couponCode=FINANCEVIP (expires Oct 9, 2020)
https://www.udemy.com/course/ai-finance/?couponCode=FINANCEVIP17 (expires Feb 21, 2022)
(as usual, this coupon lasts only 30 days, so don’t wait!)
This is a MASSIVE (20 hours) Financial Engineering course covering the core fundamentals of financial engineering and financial analysis from scratch. We will go in-depth into all the classic topics, such as:
• Exploratory data analysis, significance testing, correlations
• Alpha and beta
• Advanced Pandas Data Frame manipulation for time series and finance
• Time series analysis, simple moving average, exponentially-weighted moving average
• Holt-Winters exponential smoothing model
• ARIMA and SARIMA
• Efficient Market Hypothesis
• Random Walk Hypothesis
• Time series forecasting (“stock price prediction”)
• Modern portfolio theory
• Efficient frontier / Markowitz bullet
• Mean-variance optimization
• Maximizing the Sharpe ratio
• Convex optimization with Linear Programming and Quadratic Programming
• Capital Asset Pricing Model (CAPM)
In addition, we will look at various non-traditional techniques which stem purely from the field of machine learning and artificial intelligence, such as:
• Regression models
• Classification models
• Unsupervised learning
• Reinforcement learning and Q-learning
We will learn about the greatest flub made in the past decade by marketers posing as “machine learning experts” who promise to teach unsuspecting students how to “predict stock prices with LSTMs”. You will learn exactly why their methodology is fundamentally flawed and why their results are complete nonsense. It is a lesson in how not to apply AI in finance.
### List of VIP-only Contents
As with my Tensorflow 2 release, some of the VIP content will be a surprise and will be released in stages. Currently, the entirety of the Algorithmic Trading sections are VIP sections. Newly added VIP sections include Statistical Factor Models and “The Lazy Programmer Bonus Offer”. Here’s a full list:
Classic Algorithmic Trading – Trend Following Strategy
You will learn how moving averages can be applied to do algorithmic trading.
Forecast returns in order to determine when to buy and sell.
I give you a full introduction to Reinforcement Learning from scratch, and then we apply it to build a Q-Learning trader. Note that this is *not* the same as the example I used in my Tensorflow 2, PyTorch, and Reinforcement Learning courses. I think the example included in this course is much more principled and robust.
Statistical Factor Models
The CAPM is one of the most renowned financial models in history, but did you know it’s only the simplest factor model, with just a single factor? To go beyond just this single factor model, we will learn about statistical factor models, where the multiple “factors” are found automatically using only the data.
Regime Detection with Hidden Markov Models (HMMs)
In the first section on financial basics, we learn how to model the distribution of returns. But can we really say “the” distribution, as if there is only one?
One important “stylized fact” about returns is that volatility “clusters” or “persists”. That is, large returns tend to be surrounded by more large returns, and small returns by more small returns.
In other words, returns are actually nonstationary and to build a more accurate model we should not assume that they all come from the same distribution at all times.
Using HMMs, we can model this behavior. HMMs allow you to model hidden state sequences (high volatility and low volatility regimes), from which observations (the actual returns) are generated.
The Lazy Programmer Bonus Offer
There are marketers out there who want to capitalize on your enthusiastic interest in finance, and unfortunately what they are teaching you is utter and complete garbage.
They will claim that they can “predict stock prices with LSTMs” and show you charts like this with nearly perfect stock price predictions.
Hint: if they can do this, why do they bother putting effort into making courses? Wouldn’t they already be billionaires?
Have you ever wondered if you are taking such a course from a fake data scientist / marketer? If so, just send me a message, and I will tell you whether or not you are taking such a course. (Hint: many of you are) I will give you a list of mistakes they made so you can look out for them yourself, and avoid “learning” things which will ultimately make YOU look very bad in front of potential future employers.
Believe me, if you ever try to get a job in machine learning or data science and you talk about a project where you “predicted stock prices with LSTMs”, all you will be demonstrating is how incompetent you are. I don’t want to see any of my students falling for this! Save yourself from this embarrassing scenario by taking the “Lazy Programmer Offer”!
Please note: The VIP coupon will work only for the next month (starting from the coupon creation time). It’s unknown whether the VIP period will renew after that time.
After that, although the VIP content will be removed from Udemy, all who purchased the VIP course will get permanent free access to these VIP contents on deeplearningcourses.com.
In case it’s not clear, the process is very easy. For those folks who want the “step-by-step” instructions:
STEP 1) I announce the VIP content will be removed.
STEP 2) You email me with proof that you purchased the course during the VIP period. Do NOT email me earlier as it will just get buried.
STEP 3) I will give you free access to the VIP materials for this course on deeplearningcourses.com.
### Benefits of taking this course
• Learn the knowledge you need to work at top tier investment firms
• Gain practical, real-world quantitative skills that can be applied within and outside of finance
• Make better decisions regarding your own finances
Personally, I think this is the most interesting and action-packed course I have created yet. My last few courses were cool, but they were all about topics which I had already covered in the past! GANs, NLP, Transfer Learning, Recommender Systems, etc etc. all just machine learning topics I have covered several times in different libraries. This course contains new, fresh content and concepts I have never covered in any of my courses, ever.
This is the first course I’ve created that extends into a niche area of AI application. It goes outside of AI and into domain expertise. An in-depth topic such as finance deserves its own course. This is that course. These are topics you will never learn in a generic data science or machine learning course. However, as a student of AI, you will recognize many of our tools and methods being applied, such as statistical inference, supervised and unsupervised learning, convex optimization, and optimal control. This allows us to go deeper than your run of the mill financial engineering course, and it becomes more than just the sum of its parts.
So what are you waiting for?
April 1, 2020
# VIP Promotion
### The complete PyTorch course has arrived
Hello friends!
I hope you are all staying safe. Well, I’m sure you’ve heard enough about that so how about some different news?
Today, I am announcing the VIP version of my latest course: PyTorch: Deep Learning and Artificial Intelligence
https://www.udemy.com/course/pytorch-deep-learning/?couponCode=PYTORCHVIP22 (expires Feb 21, 2022)
This is a MASSIVE (over 22 hours) Deep Learning course covering EVERYTHING from scratch. That includes:
• Machine learning basics (linear neurons)
• ANNs, CNNs, and RNNs for images and sequence data
• Time series forecasting and stock predictions (+ why all those fake data scientists are doing it wrong)
• NLP (natural language processing)
• Recommender systems
• Transfer learning for computer vision
• Deep reinforcement learning and applying it by building a stock trading bot
IN ADDITION, you will get some unique and never-before-seen VIP projects:
Estimating prediction uncertainty
Drawing the standard deviation of the prediction along with the prediction itself. This is useful for heteroskedastic data (that means the variance changes as a function of the input). The most popular application where heteroskedasticity appears is stock prices and stock returns – which I know a lot of you are interested in.
It allows you to draw your model predictions like this:
Sometimes, the data is simply such that a spot-on prediction can’t be made. But we can do better by letting the model tell us how certain it is in its predictions.
Facial recognition with siamese networks
This one is cool. I mean, I don’t have to tell you how big facial recognition has become, right? It’s the single most controversial technology to come out of deep learning. In the past, we looked at simple ways of doing this with classification, but in this section I will teach you about an architecture built specifically for facial recognition.
You will learn how this can work even on small datasets – so you can build a network that recognizes your friends or can even identify all of your coworkers!
You can really impress your boss with this one. Surprise them one day with an app that calls out your coworkers by name every time they walk by your desk. 😉
Please note: The VIP coupon will work only for the next month (ending May 1, 2020). It’s unknown whether the VIP period will renew after that time.
After that, although the VIP content will be removed from Udemy, all who purchased the VIP course will get permanent free access on deeplearningcourses.com.
## Minimal Prerequisites
This course is designed to be a beginner to advanced course. All that is required is that you take my free Numpy prerequisites to learn some basic scientific programming in Python. And it’s free, so why wouldn’t you!?
You will learn things that took me years to learn on my own. For many people, that is worth tens of thousands of dollars by itself.
There is no heavy math, no backpropagation, etc. Why? Because I already have courses on those things. So there’s no need to repeat them here, and PyTorch doesn’t use them. So you can relax and have fun. =)
## Why PyTorch?
All of my deep learning courses until now have been in Tensorflow (and prior to that Theano).
So why learn PyTorch?
Does this mean my future deep learning courses will use PyTorch?
In fact, if you have traveled in machine learning circles recently, you will have noticed that there has been a strong shift to PyTorch.
Case in point: OpenAI switched to PyTorch earlier this year (2020).
Major AI shops such as Apple, JPMorgan Chase, and Qualcomm have adopted PyTorch.
PyTorch is primarily maintained by Facebook (Facebook AI Research to be specific) – the “other” Internet giant who, alongside Google, have a strong vested interest in developing state-of-the-art AI.
But why PyTorch for you and me? (aside from the fact that you might want to work for one of the above companies)
As you know, Tensorflow has adopted the super simple Keras API. This makes common things easy, but it makes uncommon things hard.
With PyTorch, common things take a tiny bit of extra effort, but the upside is that uncommon things are still very easy.
Creating your own custom models and inventing your own ideas is seamless. We will see many examples of that in this course.
For this reason, it is very possible that future deep learning courses will use PyTorch, especially for those advanced topics that many of you have been asking for.
Because of the ease at which you can do advanced things, PyTorch is the main library used by deep learning researchers around the world. If that’s your goal, then PyTorch is for you.
In terms of growth rate, PyTorch dominates Tensorflow. PyTorch now outnumbers Tensorflow by 2:1 and even 3:1 at major machine learning conferences. Researchers hold that PyTorch is superior to Tensorflow in terms of the simplicity of its API, and even speed / performance!
Do you need more convincing?
March 18, 2020
# VIP Promotion
Hello all!
In this post, I am announcing the VIP coupon to my course titled “Artificial Intelligence: Reinforcement Learning in Python”.
There are 2 places to get the course.
1. Udemy, with this VIP coupon: https://www.udemy.com/course/artificial-intelligence-reinforcement-learning-in-python/?couponCode=REINFORCEVIP8 (expires Feb 21, 2022)
2. Deep Learning Courses (coupon automatically applied): https://deeplearningcourses.com/c/artificial-intelligence-reinforcement-learning-in-python
You may recognize this course as one that has already existed in my catalog – however, the course I am announcing today contains ALL-NEW material. The entire course has been gutted and every lecture contained within the course did not exist in the original version.
One of the most common questions I get from students in my PyTorch, Tensorflow 2, and Financial Engineering courses is: “How can I learn reinforcement learning?”
While I do cover RL in those courses, it’s very brief. I’ve essentially summarized 12 hours of material into 2. So by necessity, you will be missing some things.
While that serves as a good way to scratch the surface of RL, it doesn’t give you a true, in-depth understanding that you will get by actually learning each component of RL step-by-step, and most importantly, getting a chance to put everything into code!
This course covers:
• The explore-exploit dilemma and the Bayesian bandit method
• MDPs (Markov Decision Processes)
• Dynamic Programming solution for MDPs
• Monte Carlo Method
• Temporal Difference Method (including Q-Learning)
• Approximation Methods using Radial Basis Functions
• Applying your code to OpenAI Gym with zero effort / code changes
• Building a stock trading bot (different approach in each course!)
When you get the DeepLearningCourses.com version, note that you will get both versions (new and old) of the course – totalling nearly 20 hours of material.
If you want access to the tic-tac-toe project, this is the version you should get.
Otherwise, if you prefer to use Udemy, that’s fine too. If you purchase on Udemy but would like access to DeepLearningCourses.com, I will allow this since they are the same price. Just send me an email and show me your proof of purchase.
Note that I’m not able to offer the reverse (can’t give you access to Udemy if you purchase on DeepLerningCourses.com, due to operational reasons).
So what are you waiting for?
# How to setup NVIDIA GPU laptop with Ubuntu for Deep Learning (CUDA and CuDNN)
January 5, 2020
See the corresponding YouTube video lecture here: https://youtu.be/3r5eNV7WZ6g
In this article, I will teach you how to setup your NVIDIA GPU laptop (or desktop!) for deep learning with NVIDIA’s CUDA and CuDNN libraries.
The main thing to remember before we start is that these steps are always constantly in flux – things change and they change quickly in the field of deep learning. Therefore I remind you of my slogan: “Learn the principles, not the syntax“. We are not doing any coding here so there’s no “syntax” per se, but the general idea is to learn the principles at a high-level, don’t try to memorize details which may change on you and confuse you if you forget about what the principles are.
This article is more like a personal story rather than a strict tutorial. It’s meant to help you understand the many obstacles you may encounter along the way, and what practical strategies you can take to get around them.
There are about 10 different ways to install the things we need. Some will work; some won’t. That’s just how cutting-edge software is. If that makes you uncomfortable, well, stop being a baby. Yes, it’s going to be frustrating. No, I didn’t invent this stuff, it is not within my control. Learn the principles, not the syntax!
## Why you need this guide
If you’ve never setup your laptop for GPU-enabled deep learning before, then you might assume that there’s nothing you need to do beyond buying a laptop with a GPU. WRONG!
You need to have a specific kind of laptop with specific software and drivers installed. Everything must work together.
You can think of all the software on your computer as a “stack” of layers.
At the lowest layer, you have the kernel (very low-level software that interacts with the hardware) and at higher levels you have runtimes and libraries such as SQLite, SSL, etc.
When you write an application, you need to make use of lower-level runtimes and libraries – your code doesn’t just run all by itself.
So, when you install Tensorflow (as an example), that depends on lower-level libraries (such as CUDA and CuDNN) which interact with the GPU (hardware).
If any of the layers in your stack are missing (all the way from the hardware up to high-level libraries), your code will not work.
Low-Level = Hardware
High-Level = Libraries and Frameworks
Not all GPUs are created equal. If you buy a MacBook Pro these days, you’ll get a Radeon Pro Vega GPU. If you buy a Dell laptop, it might come with an Intel UHD GPU.
These are no good for machine learning or deep learning.
You will need a laptop with an NVIDIA GPU.
Some laptops come with a “mobile” NVIDIA GPU, such as the GTX 950m. These are OK, but ideally you want a GPU that doesn’t end with “m”. As always, check performance benchmarks if you want the full story.
I would also recommend at least 4GB of RAM (otherwise, you won’t be able to use larger batch sizes, which will affect training).
In fact, some of the newer neural networks won’t even fit on the RAM to do prediction, never mind training!
One thing you have to consider is if you actually want to do deep learning on your laptop vs. just provisioning a GPU-enabled machine on a service such as AWS (Amazon Web Services).
These will cost you a few cents to a dollar per hour (depending on the machine type), so if you just have a one-off job to run, you may want to consider this option.
I already have a walkthrough tutorial in my course Modern Deep Learning in Python about that, so I assume if you are reading this article, you are rather interested in purchasing your own GPU-enabled computer and installing everything yourself.
Personally, I would recommend Lenovo laptops. The main reason is they always play nice with Linux (we’ll go over why that’s important in the next section). Lenovo is known for their high-quality and sturdy laptops and most professionals who use PCs for work use Thinkpads. They have a long history (decades) of serving the professional community so it’s nearly impossible to go wrong. Other brands generally have lots of issues (e.g. sound not working, WiFi not working, etc.) with Linux.
Here are some good laptops with NVIDIA GPUs:
This one only has an i5 processor and 8GB of RAM, but on the plus side it’s cost-effective. Note that the prices were taken when I wrote this article; they might change.
Same as above but different specs. 16GB RAM with an i7 processor, but only 256GB of SSD space. Same GPU. So there are some tradeoffs to be made.
This is the best option in my opinion. Better or equal specs compared to the previous two. i7 processor, 24GB of RAM (32GB would be ideal!), lots of space (1TB HD + 512GB SSD), and the same GPU. Bonus: it’s nearly the same price as the above (currently).
Pricier, but great specs. Same GPU!
If you really want to splurge, consider one of these big boys. Thinkpads are classic professional laptops. These come with real beast GPUs – NVIDIA Quadro RTX 5000 with 16GB of VRAM.
You’ve still got the i7 processor, 16GB of RAM, and a 512GB NVMe SSD (basically a faster version of already-super-fast SSDs). Personally, I think if you’re going to splurge, you should opt for 32GB of RAM and a 1TB SSD.
If you’ve watched my videos, you might be wondering: what about a Mac? (I use a Mac for screen recording).
Macs are great in general for development, and they used to come with NVIDIA GPUs (although those GPUs are not as powerful as the ones currently available for PCs). Support for Mac has dropped off in the past few years, so you won’t be able to install say, the latest version of Tensorflow, CUDA, and CuDNN without a significant amount of effort (I spent probably a day and just gave up). And on top of that the GPU won’t even be that great. Overall, not recommended.
As I mentioned earlier, you probably want to be running Linux (Ubuntu is my favorite).
“Tensorflow works on Windows, so what’s the problem?”
Remember my motto: “Learn the principles, not the syntax“.
What’s the principle here? Many of you probably haven’t been around long enough to know this, but the problem is, many machine learning and deep learning libraries didn’t work with Windows when they first came out.
So, unless you want to wait a year or more after new inventions and software are being made, then try to avoid Windows.
Don’t take my word for it, look at the examples:
• Early on, even installing Numpy, Matplotlib, Pandas, etc. was very difficult on Windows. I’ve spent hours with clients on this. Nowadays you can just use Anaconda, but that’s not always been the case. At the time of this writing, things only started to shape up a few years ago.
• Theano (the original GPU-enabled deep learning library) initially did not work on Windows for many years.
• Tensorflow, Google’s deep learning library and the most popular today, initially did not work on Windows.
• PyTorch, a deep learning library popular with the academic community, initially did not work on Windows.
• OpenAI Gym, the most popular reinforcement learning library, only partially works on Windows. Some environments, such as MuJoCo and Atari, still have no support for Windows.
There are more examples, but these are the major historical “lessons” I point to for why I normally choose Linux over Windows.
One benefit of using Windows is that installing CUDA is very easy, and it’s very likely that your Windows OS (on your Lenovo laptop) will come with it pre-installed. The original use-case for GPUs was gaming, so it’s pretty user-friendly.
If you purchase one of the above laptops and you choose to stick with Windows, then you will not have to worry about installing CUDA – it’s already there. There is a nice user interface so whenever you need to update the CUDA drivers you can do so with just a few clicks.
Installing CuDNN is less trivial, but the instructions are pretty clear (https://docs.nvidia.com/deeplearning/sdk/cudnn-install/index.html#installwindows). Simply download the zip file, unzip it, copy the files to the locations specified in the instructions, and set a few environment variables. Easy!
TO BE CLEAR:
Aside from the Python libraries below (such as Tensorflow / PyTorch) you need to install 2 things from NVIDIA first:
1. CUDA (already comes with Windows if you purchase one of the above laptops, Ubuntu instructions below)
2. CuDNN (you have to install it yourself, following the instructions on NVIDIA’s website)
DUAL-BOOTING:
I always find it useful to have both Windows and Ubuntu on-hand, and if you get the laptop above that has 2 drives (1TB HD and 512GB SSD) dual-booting is a natural choice.
These days, dual booting is not too difficult. Usually, one starts with Windows. Then, you insert your Ubuntu installer (USB stick), and choose the option to install Ubuntu alongside the existing OS. There are many tutorials online you can follow.
Hint: Upon entering the BIOS, you may have to disable the Secure Boot / Fast Boot options.
INSTALLING PYTHON:
I already have lectures on how to install Python with and without Anaconda. These days, Anaconda works well on Linux, Mac, and Windows, so I recommend it for easy management of your virtual environments.
Environment Setup for UNIX-Like systems (includes Ubuntu and MacOS) without Anaconda
Environment Setup for Windows and/or Anaconda
## Installing CUDA and CuDNN on Ubuntu and similar Linux OSes (Debian, Pop!_OS, Xubuntu, Lubuntu, etc.)
Ok, now we get to the hard stuff. You have your laptop and your Ubuntu/Debian OS.
Can you just install Tensorflow and magically start making use of your super powerful GPU? NO!
Now you need to install the “low-level” software that Tensorflow/Theano/PyTorch/etc. make use of – which are CUDA and CuDNN.
This is where things get tricky, because there are many ways to install CUDA and CuDNN, and some of these ways don’t always work (from my experience).
Examples of how things can “randomly go wrong”:
• I installed CUDA on Linux Mint. After this, I was unable to boot the machine and get into the OS.
• Pop!_OS (System76) has their own versions of CUDA and CuDNN that you can install with simple apt commands. Didn’t work. Had to install them the “regular way”.
• Updating CUDA and CuDNN sucks. You may find the nuclear option easier (installing the OS and drivers from scratch)
Here is a method that consistently works for me:
1. Go to https://developer.nvidia.com/cuda-downloads and choose the options appropriate for your system. (Linux / x86_64 (64-bit) / Ubuntu / etc.). Note that Pop!_OS is a derivative of Ubuntu, as is Linux Mint.
2. You’ll download a .deb file. Do the usual “dpkg -i <filename>.deb” to run the installer. CUDA is installed!
3. Next, you’ll want to install CuDNN. Instructions from NVIDIA are here: https://docs.nvidia.com/deeplearning/sdk/cudnn-install/index.html#ubuntu-network-installation
Those instructions are subject to change, but basically you can just copy and paste what they give you (don’t copy the below, check the site to get the latest version):
sudo dpkg -i \ http://developer.download.nvidia.com/compute/machine-learning/repos/ubuntu1604/x86_64/nvidia-machine-learning-repo-ubuntu1604_1.0.0-1_amd64.deb
sudo apt-get update && sudo apt-get install libcudnn7 libcudnn7-dev
## Installing CUDA and CuDNN on Windows
If you decided you hate reinforcement learning and you’re okay with not being able to use new software until it becomes mainstream, then you may have decided you want to stick with Windows.
Luckily, there’s still lots you can do in deep learning.
As mentioned previously, installing CUDA and CuDNN on Windows is easy.
If you did not get a laptop which has CUDA preinstalled, then you’ll have to install it yourself. Go to https://developer.nvidia.com/cuda-downloads, choose the options appropriate for your system (Windows 10 / x86_64 (64-bit) / etc.)
This will give you a .exe file to download. Simply click on it and follow the onscreen prompts.
As mentioned earlier, installing CuDNN is a little more complicated, but not too troublesome. Just go to https://docs.nvidia.com/deeplearning/sdk/cudnn-install/index.html#installwindows and follow NVIDIA’s instructions for where to put the files and what environment variables to set.
## Installing GPU-enabled Tensorflow
Unlike the other libraries we’ll discuss, there are different packages to separate the CPU and GPU versions of Tensorflow.
The Tensorflow website will give you the exact command to run to install Tensorflow (it’s the same whether you are in Anaconda or not).
It will look like this:
So you would install it using either:
pip install tensorflow
pip install tensorflow-gpu
UPDATE: Starting with version 2.1, installing “tensorflow” will automatically give you GPU capabilities, so there’s no need to install a GPU-specific version (although the syntax still works).
After installing Tensorflow, you can verify that it is using the GPU:
tf.test.is_gpu_available()
This will return True if Tensorflow is using the GPU.
## Installing GPU-enabled PyTorch
pip install torch
as usual.
To check whether PyTorch is using the GPU, you can use the following commands:
In [1]: import torch
In [2]: torch.cuda.current_device()
Out[2]: 0
In [3]: torch.cuda.device(0)
Out[3]: <torch.cuda.device at 0x7efce0b03be0>
In [4]: torch.cuda.device_count()
Out[4]: 1
In [5]: torch.cuda.get_device_name(0)
Out[5]: 'GeForce GTX 950M'
In [6]: torch.cuda.is_available()
Out[6]: True
## Installing GPU-enabled Keras
Luckily, Keras is just a wrapper around other libraries such as Tensorflow and Theano. Therefore, there is nothing special you have to do, as long as you already have the GPU-enabled version of the base library.
Therefore, just install Keras as you normally would:
pip install keras
As long as Keras is using Tensorflow as a backend, you can use the same method as above to check whether or not the GPU is being used.
## Installing GPU-enabled Theano
For both Ubuntu and Windows, as always I recommend using Anaconda. In this case, the command to install Theano with GPU support is simply:
conda install theano pygpu
If necessary, further details can be found at:
SIDE NOTE: Unfortunately, I will not provide technical support for your environment setup. You are welcome to schedule a 1-on-1 but availability is limited.
Disclaimer: this post contains Amazon affiliate links.
# BLACK FRIDAY / CYBER MONDAY 2019 — Deep Learning and Artificial Intelligence in Python
November 28, 2019
Yearly Black Friday sale is HERE! As I always tell my students – you never know when Udemy’s next “sale drought” is going to be – so if you are on the fence about getting a course, NOW is the time.
NOTE: If you are looking for the Tensorflow 2.0 VIP materials, as of now they can only be purchased here: https://deeplearningcourses.com/c/deep-learning-tensorflow-2 (coupon code automatically applied). The site contains only the VIP materials, and the main part of the course can be purchased on Udemy as per the link below. Therefore, if you want the “full” version of the course, each part now must be purchased separately.
https://www.udemy.com/course/deep-learning-tensorflow-2/
• What you’ll learn:
• Neurons and Machine Learning
• ANNs
• CNNs
• RNNs
• GANs
• NLP
• Recommender Systems
• Reinforcement Learning
• build a stock trading bot with Deep RL
• Low-level and advanced Tensorflow 2.0 features
• Exporting models for Tensorflow Lite
• Tensorflow Serving
https://www.udemy.com/course/cutting-edge-artificial-intelligence/
• What you’ll learn: A2C, Evolution Strategies, and DDPG
https://www.udemy.com/course/support-vector-machines-in-python/
• What you’ll learn: Support Vector Machines (SVMs) in-depth starting from linear classification theory to the maximum margin method, kernel trick, quadratic programming, and the SMO (sequential minimal optimization) algorithm
https://www.udemy.com/course/recommender-systems/
• What you’ll learn:
• Reddit and Hacker News algorithms
• PageRank (what Google Search uses)
• Bayesian / Thompson sampling
• Collaborative filtering
• Matrix factorization
• We use the 20 million ratings dataset, not the puny 100k dataset everyone else uses
• Implementing matrix factorization with Deep Learning
• Using Deep Neural Networks for recommenders
• Autoencoders for recommenders
• Restricted Boltzmann Machines (RBMs) for recommenders
• Recommenders with big data (PySpark) on AWS cluster
• What you’ll learn:
• modern Deep NLP techniques such as Bidirectional LSTMs
• CNNs for text classification
• seq2seq
• attention
• memory networks
• What you’ll learn:
• Deep Learning techniques for computer vision, such as state-of-the-art networks (VGG, ResNet, Inception)
• Train state-of-the-art models fast with transfer learning
• Object detection with SSD
• Neural style transfer
https://www.udemy.com/course/deep-learning-gans-and-variational-autoencoders/
• What you’ll learn:
• Generate realistic, high quality images with deep neural networks
• Apply game theory and Bayesian machine learning to deep learning
• Learn about the “transpose convolution”
https://www.udemy.com/course/deep-reinforcement-learning-in-python/
• What you’ll learn:
• Learn how we got from classical reinforcement learning to deep reinforcement learning and why it’s nontrivial
• Play OpenAI Gym environments such as CartPole and Atari
• Learn the “tricks” of DQN and A3C and how they improve classical RL approaches
https://www.udemy.com/course/artificial-intelligence-reinforcement-learning-in-python/
• What you’ll learn:
• Learn what makes Reinforcement Learning special compared to basic supervised/unsupervised learning (hint: it’s very complicated!)
• Learn how epsilon-greedy and Bayesian machine learning can optimize click-through rates
• Implement a tic-tac-toe agent
• MDPs (Markov Decision Processes) and the Bellman equation
• Learn the 3 approaches to RL: Dynamic Programming, Monte Carlo, and Temporal Difference (which includes the famous Q-Learning algorithm)
https://www.udemy.com/course/data-science-linear-regression-in-python/
• What you’ll learn:
• Learn about the most fundamental of machine learning algorithms: linear regression
• Believe it or not, this gets you MOST of the way there to understanding deep learning
https://www.udemy.com/course/data-science-logistic-regression-in-python/
• What you’ll learn:
• After learning about linear regression, see how a similar model (logistic regression) can be used for classification
• Importantly, understand how and why this is a model of the “neuron” (and because of that, we can use it to build neural networks)
https://www.udemy.com/course/data-science-deep-learning-in-python/
• What you’ll learn:
• Learn IN-DEPTH the theory behind artificial neural networks (ANNs)
• This is THE fundamental course for understanding what deep learning is doing, from ANNs to CNNs to RNNs to GANs and beyond
https://www.udemy.com/course/data-science-natural-language-processing-in-python/
• What you’ll learn:
• Learn how to apply machine learning to NLP tasks, such as: spam detection, sentiment analysis, article spinning, and latent semantic analysis
• Learn how to preprocess text for use in a ML algorithm
• Learn about the classic NLTK library
https://www.udemy.com/course/data-science-deep-learning-in-theano-tensorflow/
• What you’ll learn:
• Learn how we went from the fundamental ANNs to many of the key technologies we use today, such as:
• Dropout regularization
• Batch normalization
• Learn how deep learning is accelerated by GPUs (and how to set one up yourself)
• Learn how deep learning libraries improve the development process with GPUs (faster training) and automatic differentiation (so you don’t have to write the code or derive the math yourself)
https://www.udemy.com/course/sql-for-marketers-data-analytics-data-science-big-data/
• What you’ll learn:
• Learn the fundamentals of the SQL language and how to apply it to data
• Practice for job interviews by going through several interview-style questions
https://www.udemy.com/course/deep-learning-convolutional-neural-networks-theano-tensorflow/
• What you’ll learn:
• Go from ANNs to CNNs
• Learn about the all important “convolution” operation in-depth
• Implement convolution yourself (no other course does this!)
• Design principles for CNNs and why they specialize to work with images
https://www.udemy.com/course/cluster-analysis-unsupervised-machine-learning-python/
• What you’ll learn:
• Learn about classic clustering methods such as K-Means, Hierarchical Clustering, and Gaussian Mixture Models (a probabilistic approach to Cluster Analysis)
• Apply clustering to real-world datasets such as organizing books, clustering Hillary Clinton and Donald Trump tweets, and DNA
https://www.udemy.com/course/unsupervised-deep-learning-in-python/
• What you’ll learn:
• Learn about how Deep Learning an be applied to data without labels/targets using Autoencoders and RBMs (Restricted Boltzmann Machines)
• Learn how Autoencoders are like a “nonlinear” version of PCA
• Visualize / transform data with PCA and t-SNE
• Apply RBMs to recommender systems
https://www.udemy.com/course/unsupervised-machine-learning-hidden-markov-models-in-python/
• What you’ll learn:
• Learn how unsupervised learning extends to cover sequences of data (like DNA, text processing, etc.)
• The HMM is a probabilistic graphical model and uses the same learning approach (expectation-maximization) as k-means clustering and GMMs
• We also review Markov models and you’ll see how they (surprisingly) apply to a famous modern algorithm: Google’s PageRank
https://www.udemy.com/course/deep-learning-recurrent-neural-networks-in-python/
• What you’ll learn:
• Learn how Deep Learning handles sequences of data (like DNA, text processing, etc.)
• Learn the limitations of a naive (simple) RNN
• How to extend / improve RNNs with GRUs and LSTMs
• Build GRUs and LSTMs by yourself (not just calling some library function)
https://www.udemy.com/course/natural-language-processing-with-deep-learning-in-python/
• What you’ll learn:
• Apply deep learning to natural language processing (NLP)
• Covers the famous word2vec and GloVe algorithms
• See how RNNs apply to text problems
• Learn about a neural network structured like a “tree” which we call recursive neural networks and a more powerful version: recursive neural tensor networks (RNTNs)
https://www.udemy.com/course/data-science-supervised-machine-learning-in-python/
• What you’ll learn:
• Covers classic machine learning algorithms which EVERY student of machine learning should know (AND be able to implement)
• K-Nearest Neighbor (KNN), Naive Bayes and non-Naive Bayes Classifiers, the Perceptron, and Decision Trees
• Learn how to build a machine learning web service using Python server frameworks
https://www.udemy.com/course/bayesian-machine-learning-in-python-ab-testing/
• What you’ll learn:
• Learn how Bayesian machine learning differs from traditional machine learning
• We focus mostly on “comparing” multiple things (i.e. A/B Testing)
• Learn why traditional (frequentist) A/B Testing is limited
• What you’ll learn:
• Learn how combining multiple machine learning models is better than just one
• Covers fundamental ensemble approaches such as Random Forest and AdaBoost
• Learn/derive the famous “bias-variance tradeoff” (most people can only discuss it at a high level, you will learn what it really means)
• Learn about the difference between the “bagging” and “boosting” approaches
# Tensorflow 2.0 is here! Get the VIP version now
August 14, 2019
### Tensorflow 2.0 is here!
***FINAL UPDATE***
Old coupon no longer works. Use this one instead: https://www.udemy.com/course/deep-learning-tensorflow-2/?couponCode=LASTVIP
PLEASE NOTE: VIP material will be removed from Udemy on November 27. If you signed up for the VIP version (using the VIP coupon) and want access beyond that point, you must email me at info [at] lazyprogrammer [dot] me.
If you want the VIP (full) version of the course beyond that date, you now need to purchase the “main” part and the “VIP” part separately. The “main” part can be purchased on Udemy and the “VIP” part can be purchased from: https://deeplearningcourses.com/c/deep-learning-tensorflow-2
—–
I am happy to announce my latest and most massive course yet – Tensorflow 2.0: Deep Learning and Artificial Intelligence.
Guys I am not joking – this really is my most massive course yet – check out the curriculum.
Many of you will be interested in the stock prediction example, because you’ve been tricked by marketers posing as data scientists in the past – I will demonstrate why their results are seriously flawed.
This is technically Deep Learning in Python part 12, but importantly this need not be the 12th deep learning course of mine that you take!
There are quite few important points to cover in this announcement, so let me outline what I will discuss:
A) What’s covered in this course
B) Why there are almost zero prerequisites for this course
C) The VIP content and near-term additions
D) The story behind this course (if you’ve been following my courses for some time you will be interested in this)
### What’s covered in this course
As mentioned – this course is massive. It’s going to take you from basic linear models (the neuron) to ANNs, CNNs, and RNNs.
Thanks to the new standardized Tensorflow 2.0 API – we can move quickly.
The theme of this course is breadth, not depth. If you’re looking for heavy theory (e.g. backpropagation), well, I already have courses for those. So there’s no point in repeating that.
We will however go pretty in-depth to ensure that convolution (the main component of CNNs) and recurrent units (the main component of RNNs) are explained intuitively and from multiple perspectives.
These will include explanations and intuitions you have likely not seen before in my courses, so even if you’ve taken my CNN and RNN courses before, you will still want to see this.
There are many applications in this course. Here are a few:
– we will prove Moore’s Law using a neuron
– image classification with modern CNN design and data augmentation
– time series analysis and forecasting with RNNs
Anyone who is interested in stock prediction should check out the RNN section. Most RNN resources out there only look at NLP (natural language processing), including my old RNN course, but very few look at time series and forecasting.
And out of the ones that do, many do forecasting totally wrong!
There is one stock forecasting example I see everywhere, but its methodology is flawed. I will demonstrate why it’s flawed, and why stock prediction is not as simple as you have been led to believe.
There’s also a ton of Tensorflow-specific content, such as:
– Tensorflow serving (i.e. how to build a web service API from a Tensorflow model)
– Distributed training for faster training times (what Tensorflow calls “distribution strategies”)
– Low-level Tensorflow – this has changed completely from Tensorflow 1.x
– How to build your own models using the new Tensorflow 2.0 API
– Tensorflow Lite (how to export your models for mobile devices – iOS and Android) (coming soon)
– Tensorflow.js (how to export your models for the browser) (coming soon)
### Why there are almost zero prerequisites for this course
Due to the new standardized Tensorflow 2.0 API, writing neural networks is easier than ever before.
This means that we’ll be able to blast through each section with very little theory (no backpropagation).
All you will need is a basic understanding of Python, Numpy, and Machine Learning, which are all taught in my free Numpy course.
As I always say, it’s free, so you have no excuses!
Tensorflow 2.0 however, does not invalidate or replace my other courses. If you haven’t taken them yet, you should take this course first for breadth, and then take the other courses which focus on individual models (CNNs, RNNs) for depth.
### The VIP content and near-term additions
I had so much content in mind for this course, but I wanted to get this into your hands as soon as possible. With Tensorflow 2.0 due to be released any day now, I wanted to give you all a head start.
This field is moving so fast things were changing while I was making the course. Insane!
I’ll be adding more content in the coming weeks, possibly including but not limited to:
– Transfer Learning
– Natural Language Processing
– GANs
– Recommender Systems
– Reinforcement Learning
For this release, only the VIP version will be available for some time. That is why you do not see the usual Udemy discount.
You may be wondering: Which parts of the content are VIP content, and which are not?
This time, I wanted to do something interesting: it’s a surprise!
The VIP content will be added to a special section called the “VIP Section”, and this will be removed once the course becomes “Non-VIP”.
I will make an announcement well before that happens, so you will have the chance to download the VIP content before then, as well as get access to the VIP content permanently from deeplearningcourses.com.
### The story behind this course
Originally, this course was going to be an RNN course only (hence why the RNN sections have so much more content – both time series and NLP).
The reason for this was, my original RNN course was tied to Theano and building RNNs from scratch.
In Tensorflow, building RNNs is completely different. This is unlike ANNs and CNNs which are relatively similar.
Thus, I could never reconcile the differences between the Theano approach and the Tensorflow approach in my original RNN course. So, I decided that simply making a new course for RNNs in Tensorflow would be best.
But lo and behold – Tensorflow was evolving so fast that a new version was about to be released – so I thought, it’s probably best to just cover everything in Tensorflow 2.0!
And that is how this current course came to be.
I hope you enjoy this action-packed course.
I’ll see you in class!
# Retreat from the heat with Machine Learning and Artificial Intelligence
July 18, 2019
For the next week, all my Deep Learning and AI courses are available for just $10.99! Please use the coupons below (included in the links), or if you want, enter the coupon code: JUL2019. As usual, if you want to know what order to take my courses in, check out the lecture “What order should I take your courses in?” in the Appendix of any of my courses (including the free Numpy course). https://www.udemy.com/cutting-edge-artificial-intelligence/?couponCode=JUL2019 ### PREREQUISITE COURSE COUPONS And just as important,$9.99 coupons for some helpful prerequisite courses. You NEED to know this stuff to understand machine learning in-depth:
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# [June 2019] AI / Machine Learning HUGE Summer Sale! $9.99 June 10, 2019 ### AI / Machine Learning Summer Sale For the next week, all my Deep Learning and AI courses are available for just$9.99! (In addition to other courses on the site for the next few days)
For those of you who have been around for some time, you know that this sale doesn’t come around very often – just a few times per year. If you’ve been on the fence about getting a course, NOW is the time to do so. Get it now – save it for later.
For my courses, please use the coupons below (included in the links), or if you want, enter the coupon code: JUN2019.
As usual, if you want to know what order to take my courses in, check out the lecture “What order should I take your courses in?” in the Appendix of any of my courses (including the free Numpy course).
For prerequisite courses (math, stats, Python programming) and all other courses, follow the links at the bottom for sales of up to 90% off!
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### PREREQUISITE COURSE COUPONS
And just as important, \$9.99 coupons for some helpful prerequisite courses. You NEED to know this stuff to understand machine learning in-depth:
General (site-wide): http://bit.ly/2oCY14Z
Python http://bit.ly/2pbXxXz
Calc 1 http://bit.ly/2okPUib
Calc 2 http://bit.ly/2oXnhpX
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Android courses:
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Ruby on Rails courses:
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Python courses:
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Into Yoga in your spare time? Photography? Painting? There are courses, and I’ve got coupons! If you find a course on Udemy that you’d like a coupon for, just let me know and I’ll hook you up! | |
### Session W27: Focus Session: Semiconductor Qubits- Optical Control, Donors, and Hybrid Systems
11:15 AM–2:15 PM, Thursday, March 24, 2011
Room: C155
Chair: Jake Taylor, University of Maryland
Abstract ID: BAPS.2011.MAR.W27.10
### Abstract: W27.00010 : Entanglement in a Solid State Spin Ensemble
1:03 PM–1:15 PM
Preview Abstract MathJax On | Off Abstract
#### Authors:
Stephanie Simmons
(Oxford University)
Richard Brown
(Oxford University)
Helge Riemann
(Leibniz Institut )
Nikolai Abrosimov
(Leibniz Institut)
Peter Becker
(PTB Braunschweig)
Hans-Joachim Pohl
(VITCON Projectconsult GmbH)
Mike Thewalt
(Simon Fraser University)
Kohei Itoh
(Keio University)
John Morton
(Oxford University)
Entanglement is a both a fascinating phenomenon and a critical ingredient in most emerging quantum technologies. Spin ensembles manipulated using magnetic resonance have demonstrated the most advanced quantum algorithms to date, however these studies contain no entanglement and hence constitute classical simulations of quantum algorithms. Here we report the on-demand generation of entanglement between an ensemble of electron and nuclear spins in isotopically engineered phosphorus-doped silicon. High field/low temperature electron spin resonance (3.4~T, 2.9~K) was used in conjunction with a hyperpolarisation sequence to reduce the spin entropy to a level sufficient to form an inseparable state. The generated entanglement was confirmed by measuring the state's density matrix which displayed a fidelity of 98\% compared to the ideal state at this field and temperature. The entanglement operation was performed simultaneously, with high fidelity, to $10^{10}$ spin pairs, and represents an essential requirement of a silicon- based quantum information processor.
To cite this abstract, use the following reference: http://meetings.aps.org/link/BAPS.2011.MAR.W27.10 | |
# 9.1.2 Raman’s argument for bowed-string waveforms
Raman’s argument applies strictly to bowed-string motion based on two assumptions: that the string is an ideal, textbook string, and that the friction force is governed by a “Stribeck law” in which the friction force varies with relative sliding speed according to a curve like the example shown schematically in Fig. 1. Neither of these assumptions is exactly true for a real bowed string, as we will see later in this chapter, but they give a good first shot at explaining a lot of bowed-string waveforms.
The periodic string motions in which Raman was interested were all observed to involve the bowed string oscillating at the same frequency as the free string. As a consequence, he argued, the friction force at the bow must remain essentially constant: the modes of a string have very low damping, so any significant variation of the friction force at the frequency of string modes would produce a resonant response to high amplitude. For the extreme case of the undamped textbook string, the predicted amplitude would be infinite. Helmholtz motion is an example: it is a possible free motion of an ideal string. So one way to think about Helmholtz motion and all the other regimes we will find in this section is that they are free motions of the string which happen to be able to tolerate the presence of the bow.
Figure 1 then tells us that the string velocity at the bowed point must alternate, in some pattern, between two fixed values. During an episode of sticking, the string velocity must match the bow speed and lie somewhere on the vertical portion of the friction curve. But the velocity must integrate to zero over a complete cycle, in order that there is no mean sideways motion of the string. So episodes of sticking must be balanced by episodes of slipping with a negative string velocity. If the friction force is to remain constant during this process, the point on the curve corresponding to this slipping speed must lie on a horizontal line with the relevant sticking point, as indicated by the two black stars in the figure.
This argument shows that any possible motion of the string at the bowed point must involve spells of constant velocity interrupted by jumps, all of the same magnitude. Now we can use D’Alembert’s solution for the general motion of an ideal string (section 5.4.2) to deduce what must be happening along the rest of the string. The string displacement $w(x,t)$ at position $x$ and time $t$ must be the sum of a right-travelling wave $f$ and a left-travelling wave $g$, both with fixed shape:
$$w(x,t)=f(t-x/c)+g(t+x/c) \tag{1}$$
where $c$ is the wave speed on the string. The string has fixed ends at $x=0$ and $x=L$, so
$$f(t)+g(t)=0 \tag{2}$$
and
$$f(t-L/c)+g(t+L/c)=0 , \tag{3}$$
so
$$g=-f \tag{4}$$
and
$$f(t)=f(t+2L/c) . \tag{5}$$
The string velocity $v(x,t)$ can also be written in travelling-wave form:
$$v(x,t)=f^\prime(t-x/c) – f^\prime(t+x/c) . \tag{6}$$
from eqs. (1) and (4), where primes denote the derivative.
Our measurements are of the force exerted on the bridge. If the string tension is $T$, this is given by
$$T \left.\dfrac{\partial w}{\partial x} \right|_{x=0} = \dfrac{T}{c} \left[ g^\prime(t) – f^\prime(t) \right]=-\dfrac{2T}{c}f^\prime(t) . \tag{7}$$
So, apart from a constant multiplier, the bridge force wavefrom directly reveals the form of the travelling wave $f^\prime(t)$.
For the particular case of Helmholtz motion we already know that the bridge force is a sawtooth wave. So this sawtooth also gives the form of the travelling velocity waves. The result is animated in Fig. 2. The two travelling waves are shown at the top, over a range that is three times as long as the physical string, indicated by the vertical lines. The black shape at the bottom shows $v(x,t)$ for the string.
This may not be immediately recognisable as corresponding to Helmholtz motion. To understand the plot, try laying a vertical ruler against the screen, selecting a particular position on the string. This is your chosen bowing point. Now look at how the velocity at that point varies through the cycle of vibration. If your chosen point is near the left-hand end, where you would normally bow a violin string, you will see that it spends most of the cycle with a relatively small positive velocity, and the remainder with a larger negative velocity. This is exactly what were were expecting: the amplitude of motion will be scaled so that the positive velocity matches the bow speed. The negative sliding speed has the correct value so that the integrated velocity over the cycle is zero. This description will hold whatever point you select as your bowed point: the only thing that will change is the amplitude scaling in order to match the positive velocity to the bow speed.
We can see the string vibration much more clearly if we integrate the sawtooth waveforms to obtain the corresponding travelling wave contributions to the string displacement. Each linear ramp in the sawtooth integrates to a parabolic section of curve, and where the sawtooth had jumps, the integrated function has a sharp corner, in other words a slope discontinuity. Using these travelling waves, the corresponding animation for string displacement is shown in Fig. 3, and now it is clear that it does indeed reproduce Helmholtz motion.
Raman used this approach, via travelling waves of velocity, to catalogue all the possible idealised bowed-string waveforms. The two waves from eq. (6) must always add up to give a velocity waveform at the bowed point consisting of constant velocity segments, interrupted by jumps. He showed that this can only occur if the travelling waves of velocity take the form of a linear ramp, interrupted by jumps. The ramp segments always have the same slope, and the only distinction between different regimes of vibration comes in the number and disposition of the jumps. We will show some examples, to illustrate the two types of bridge force waveform shown in section 9.1.
Helmholtz motion is the only possible solution with a single velocity jump. The next simplest possibility has two jumps. Figure 4 shows an animation corresponding to Fig. 2, for a typical example of such motion. We know from eq. (7) that the blue curve, the right-travelling velocity wave, mirrors the waveform of bridge force, and we can recognise that waveform as corresponding to Fig. 5 of section 9.1, describing a typical case of double-slipping motion. If you do the ruler trick again, selecting a bowing point and watching how the string velocity varies at that point, you will quickly see that the motion does indeed involve two slipping episodes in every cycle. Figure 5 shows the corresponding animation for string displacement.
Such motion is classified as Raman’s “second type”. There is a special case of this motion that has direct relevance to violinists. If the two velocity jumps are arranged in a regular and symmetrical manner, the resulting motion is illustrated in Fig. 6 and 7. This is still double-slipping motion, but because the two slips in each cycle occur with equal spacing, the result is a sound with half the period: in other words, a note that plays an octave higher. Now look at the animation of the string motion in Fig. 7: it consists of two “Helmholtz motions”, going on simultaneously in the two halves of the string. The string remains stationary at its midpoint. This is the motion that arises when a violinist plays a “harmonic”, by lightly touching a finger at the mid-point of the string.
For a final example, we look at a case of “S-motion”. The particular case shown in Figs. 8 and 9 would be classified by Raman as of 7th type, based on the number of velocity jumps. The blue velocity waveform in Fig. 8 can be seen to have the same general form as the measured bridge-force waveforms in Fig. 6 of section 9.1. If you do the “ruler trick” with Fig. 8, you may be able to see that some possible bowing positions have a single slip per cycle in this vibration regime, while others show more than one slip. In practice, S-motion usually appears with a single slip: the particular bowing position then governs which Raman higher type is excited. We will see more about this in section 9.3. | |
# Ergodicity economics¶
An attempt to implement the simple game introduced by Ole Peters and collegues found in the lecture notes.
## The game¶
The game is faily simple.
• Flip a coin
• If it lands tails, you decrease your wealth with 40%
Would you accept the game?
In [1]:
### Playing the game
In [2]:
import numpy.random as random
from matplotlib import pyplot as plt
import numpy as np
In [3]:
%pylab inline
pylab.rcParams['figure.figsize'] = (10, 6)
Populating the interactive namespace from numpy and matplotlib
In [4]:
# we start the game with a wealth of 1
inital_wealth = 1
# our wealth at the start of the game is our inital wealth
wealth = inital_wealth
wealth_t = []
# we play they game once a week, for a year
for i in range(1,53):
# each flip has a 50/50 chance of either decreasing our wealth with 40%
# or increasing with 50%
coin_flip = random.choice([0.6, 1.5])
wealth = wealth*coin_flip
wealth_t.append(wealth)
In [5]:
plt.step(range(1,53), wealth_t)
plt.legend("wealth", loc='upper left')
plt.title("Wealth at t, for a single coin tosser")
plt.show()
This game shows a single trajectory for a game with a single player. This might not tell us that much about its statistical properties. Lets try running the game many times instead, to see if there is a clear trend of what outcome we can expect.
In [6]:
## just copy the above code
wealths = []
N = 100000
for player in range(1,N):
# we start the game with a wealth of 1
inital_wealth = 1
# our wealth at the start of the game is our inital wealth
wealth = inital_wealth
# represents the history of wealths for a person at time t
wealth_t = []
wealth_t.append(wealth)
# we play they game once a week, for a year
for game in range(1,52):
# each flip has a 50/50 chance of either decreasing our wealth with 40%
# or increasing with 50%
coin_flip = random.choice([0.6, 1.5])
wealth = wealth*coin_flip
"""
print(player)
print(game)
print(coin_flip)
print(wealth)
print("****")
"""
wealth_t.append(wealth)
## an array with the result for each player at time t
wealths.append(wealth_t)
In [7]:
# take the wealth at time t for each player, and average it
arr_all = np.array(wealths)
## select a random set of trajectories with different number of people
random_rows_10 = random.randint(0, arr_all.shape[0], size=10)
random_rows_1 = random.randint(0, arr_all.shape[0], size=1)
random_rows_100 = random.randint(0, arr_all.shape[0], size=100)
random_rows_1000 = random.randint(0, arr_all.shape[0], size=10000)
## Compute the enseble average over each size of sample trajectories
wealth_n_10_avg = arr_all[random_rows_10].mean(axis=0)
wealth_n_1_avg = arr_all[random_rows_1].mean(axis=0)
wealth_n_100_avg = arr_all[random_rows_100].mean(axis=0)
wealth_n_1000_avg = arr_all[random_rows_1000].mean(axis=0)
wealth_n_all_avg = arr_all.mean(axis=0)
In [16]:
fig, ax = plt.subplots(1,2, figsize=(15,5))
# plot a line for each sample size, normal scale
ax[0].step(x=range(1,53), y=wealth_n_1_avg)
ax[0].step(x=range(1,53), y=wealth_n_10_avg)
ax[0].step(x=range(1,53), y=wealth_n_100_avg)
ax[0].step(x=range(1,53), y=wealth_n_1000_avg)
ax[0].step(x=range(1,53), y=wealth_n_all_avg, c='k')
# format plot
ax[0].legend(['n = 1', 'n = 10', 'n = 100', 'n = 100', 'n=10000'], loc='upper left')
plt.ylim(0,10)
plt.title("Ensemble average - Change in wealth for different sample sizes")
# log scale
ax[1].step(x=range(1,53), y=log(wealth_n_1_avg))
ax[1].step(x=range(1,53), y=log(wealth_n_10_avg))
ax[1].step(x=range(1,53), y=log(wealth_n_100_avg))
ax[1].step(x=range(1,53), y=log(wealth_n_1000_avg))
ax[1].step(x=range(1,53), y=log(wealth_n_all_avg), c='k')
plt.ylim(0,3)
plt.legend(['n = 1', 'n = 10', 'n = 100', 'n = 100', 'n=10000'], loc='upper left')
plt.title("Ensemble average - Log of wealth at time t ")
Out[16]:
<matplotlib.text.Text at 0x11aabb5c0>
We can see that adding more observations over time reduced fluctuations in the time series, and we can observe that playing this game for some time is indeed a good outome.
BUT WAIT
There is a flaw in this type of average, since it reflects a reality where a single person would have access to many paralell games. It is not necessarily the case that my returns will be that over the average of the "market". THis is illustrated in a different way: with the time average.
In [17]:
inital_wealth = 1
# our wealth at the start of the game is our inital wealth
wealth = inital_wealth
# represents the history of wealths for a person at time t
wealth_t = []
wealth_t.append(wealth)
# we play they game once a week, for a few year
for game in range(1,1040):
# each flip has a 50/50 chance of either decreasing our wealth with 40%
# or increasing with 50%
coin_flip = random.choice([0.6, 1.5])
wealth = wealth*coin_flip
wealth_t.append(wealth)
In [19]:
fig, t_avg_plt = plt.subplots(1,2, figsize=(15,5))
t_avg_plt[0].step(y=wealth_t, x=range(1,1041))
t_avg_plt[0].set_title("Wealth at time t, with a single play")
t_avg_plt[1].step(y=log(wealth_t), x=range(1,1041))
t_avg_plt[1].set_title("Log of wealth for single player, at time t")
Out[19]:
<matplotlib.text.Text at 0x11b0d7e48>
Clearly, there is some discrepancy between what we can observe in the enseble and the time average. Depending on the one you choose to look at the situation, you either end up rich or end up bust.
In [ ]: | |
# More fun in 2015, Part 20
Geometry Level 5
Inscribe a regular 2015-gon $$P$$ into a circle of radius 1. Draw chords from one of the vertices of $$P$$ to all the other vertices. Find the product of the lengths of these 2014 chords.
× | |
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This example came from the web (with a few modifications), and can be accessed via the following link. The frequency range consists of the fundamental and his harmonics. Amplitude Frequency Phase Shift Sine Cosine. Light waves have much in common with mechanical waves, they share a lot of mathematics. powered by $$x$$ y. Single Sine Tone Generator. Battery Enclosure , optional castors for mobility - R850-00 to R1150-00 design dependant. Tzolk'in calculator. The reason for this is that as b gets larger the sine wave squishes together can be illustrated through the following: when y = sin(x) and x =0 the y = 0 and when. The following formulas are used for calculation: where. Adding waves (of the same frequency) together When two sinusoidal waves with identical frequencies and wavelengths interfere, the result is another wave with the same frequency and wavelength, but a maximum amplitude which depends on the phase difference between the input waves. Using the formulae given above show that values of each of these spectra at 30 Hz are consistent with the original amplitude of 5. TIP: If you add [email protected] Look below to see them all. f = frequency (s-1, 1/s, Hz) T = time for completing one cycle (s) Example - Frequency. For example, an electronic oscillator may produce sine waves at a frequency of 100 Hz. You can find our 4/0 AWG cables here on IRU and on Amazon. The most common form of AC supply is sinusoidal wave. We’re going to develop three. Step 2: Create a chart. Adding this battery backup to your gaming setup provides advanced sine wave power to keep you playing when power interruptions occurs. Vector addition is a binary operation. ) Then turn on the Sound checkbox. Able to run continuous power across the complete range from 300W-to-2000W and with 4 different surge wattage rates from 500W to 3500W this is the best 2000 Watt pure sine inverter on the. Sine Wave = Frequency Cycle = One repetition of a wave's pattern Frequency = The number of cycles per second (measured in Hz) Period = The time duration of one cycle (the inverse of frequency, P = 1/f) Wavelength = The length of one period of a wave Amplitude = A measure of a wave's change over a single period Looking at the picture above: 1. Using the FFT to convolve input signals and a range of filter coefficients is the main area I have seen this implemented. Using the principle of superposition, the resulting particle displacement may be written as: y ( x , t ) = y m sin ( k 1 x - ω 1 t ) + y m sin ( k 2 x + ω 2 t ) = 2 y m cos. Performance Trends Inc Producing Quality Computer Tools for Racers and Engine Builders since 1986. - waves consist of sinusoidals, e. Help me keeping this feature alive by supporting my work. The amplitude of a wave is measured as:. A utility to convert between standard units of power measurement and signal strength. Practical opamp integrator circuit The addition of Rf will fix the low frequency gain (A) of the circuit to a fixed small value and so the input offset voltage will have practically no effect on the output offset voltage and variations in. Two waves of equal amplitude are travelling in the same direction. It allows equipment to run cooler, last longer and operate without malfunctions and reduced performance. Sine Wave or Sinusoidal Wave Signal is a special type of signal. Get your free Mayan astrology reading. The human ear can recognize single sine waves as sounding clear because sine waves are representations of a single frequency with no harmonics. , while the amplitudes of the sine waves are held in: b 1 , b 2 , b 3. The Wien bridge oscillator is an electronic oscillator and produces the sine waves. There must be a node at each end. The units on the horizontal axis have been degrees or radians. Sine and cosine waves can make other functions! Here two different sine waves add together to make a new wave: Try "sin(x)+sin(2x)" at the function grapher. Sine wave: A function generator will normally be able to act as a sine wave generator. Head to the menu bar and choose “Insert”. Java programming environment. 1 Analysis of Circuits (2017-10213) Phasors: 10 - 2 / 11 For inductors and capacitors i = Cdv dt and v = L di. The frequency - cycles per second - of a sound is expressed in hertz (Hz). In short, a. First you draw the yellow wave, then you add it to the white wave. Online Tone Generator. Modified sine wave inverters are fine for basic mechanical devices like drills, blenders, pumps and air conditioners. The sine and cosine angle addition identities can be compactly. The only reason I asked my above question is that using the FT to analyse addition of sine waves is something that seems a touch odd. General Instructions. diagram that can represent a number of sine waves, each having the same frequency, but with different phase relationships to each other, which is where phasors are used. If the signals have frequencies close together, then we hear beats caused by the interference of the two signals. Modified Sine Wave output is also not suitable for certain appliances, particularly those with capacitive and electromagnetic devices such as a fridge, microwave oven and most kinds of motors. Use MathJax to format equations. The tangent sum and difference identities can be found from the sine and cosine sum and difference identities. If you could make your square wave frequency higher than the desired sine wave then you could digitally generate a sine wave using a sine lookup table. Sine functions are perfect ways of expressing this type of movement, because their graphs are repetitive and they oscillate (like a wave). The Electric Academy 57,050 views. Blue Pacific Solar will supply you with the 1 - Line Drawing; Full Instructive Three-Line Diagram of Entire DC Circuit, as Well as AC Lines to Your. The second term is another wave at twice the original frequency shifted in time by the same phase difference. 1] We show this by using the principle cos θ=sin (π/2−θ), and convert the problem into the sum (or difference) between two sines. Before going to the program for Sine Series first let us understand what is a Sine Series? Sine Series is a series which is used to find the value of Sin (x). This is given by the following two formulas, which are not at all obvious cos( 1 + 2) =cos 1 cos 2 sin 1 sin 2 sin( 1 + 2) =sin 1 cos 2 + cos 1 sin 2 (1) One goal of these notes is to explain a method of calculation which makes. # Get x values of the sine wave. Is area multiplying or adding, Algebra- Elimination calculator, free maths tutorial for CAT, online square root calculator. The sine wave is mathematically a very simple curve and a very simple graph, and thus is computationally easy to generate using any form of computing, from the era of punch cards to the current era of microprocessors. The force is the same on each of the two springs. Sign in Forgot it? Sign in or. In short, a. When the two are added the mean-square value is 1. Full Disclosure. 2V amplitude sine wave with a 1V DC offset would be: 2sin(x)+1 (I haven't figured out how to incorporate frequency in Hz yet). However they sound different. You have no items in your shopping cart. α = sin-1 [F 1 sin(180 o - (α + β)) / F R] (2) where. There must be a node at each end. I have square waves of different frequencies (1KHz to 20KHz), and I need to convert them to a sine wave of the corresponding fundamental frequency. It is given by the function It is given by the function When Sine wave starts from zero and covers positive values, reaches zero; and again covers negative values, reaches zero, it is said to have completed one cycle or single cycle. Fourier Analysis, named after the nineteenth century French mathematician Jean Baptiste Fourier, enables one to break down complex periodic waveforms into their basic components, which happen to be sine waves of various frequencies, amplitudes, and phases. - waves consist of sinusoidals, e. Enter all known values of X and P(X) into the form below and click the "Calculate" button to calculate the expected value of X. I started using Mathematica to create animations to help me understand and visualize certain acoustics and vibration phenomena in 1992 while I was a Ph. Also, the calculator will show you a detailed explanation. The standing waves will depend on the boundary conditions. RELATED LINKS. The following formulas are used for calculation: where. Sine Wave Generator using 4047 IC. Please Sign up or sign in to vote. 71 kHz and 2. In physics, the RMS current value can also be defined as the "value of the direct current that dissipates the same power in a resistor. The sine function has a number of properties that result from it being periodic and odd. The mean-square value of a unit sine wave is 0. Get Physics Help. To attain success in student life you must know the proper use of a scientific calculator. When k=0, the sine wave only fluctuates along the x-axis. A sine wave depicts a reoccurring change or motion. That is the principle used in some DDS (Direct Digital Synthesis) chips - using a DAC (Digital to Analog Converter) and generating the analog values of the sine wave in your digital device. Now we can drive the circuit with a 1-kHz, 1-V sine wave. Keep reading to learn how to graph functions, find values at specific points along an equation, and use some of your calculator’s more advanced features such as finding the value at the intersection of two functions. cos( ) sin( ) =ωω+ 22+ icos[ωπ+ /4]. We can get α and R using calculator, similar to the way we did it in the complex numbers section. 1/1 3/4 5/8 1/2 1/4 1/8 Inches Feet Microns mm cm m Km. Sign in with Google Sign in with Yahoo! Sign in with a partner Don't have a Wave account yet? Sign up now. Calcblog’s very first video walks you through all the powerful graphing features available on your TI-83 Plus and TI-84 Plus. However, for a complete understanding light waves you will need a bit more explanation than will be found here. I have square waves of different frequencies (1KHz to 20KHz), and I need to convert them to a sine wave of the corresponding fundamental frequency. representing a function with a series in the form Sum( B_n sin(n pi x / L) ) from n=1 to n=infinity. Or we can measure the height from highest to lowest points and divide that by 2. spectrum, a power spectrum, and as a power spectral density. Polar to Rectangular Online Calculator. What does a triangle wave sound like compared to the square wave and pure sine wave? • (Done in lab and previously in class) • Function generators often carry sine, triangle and square waves (and often sawtooths too) If we keep the frequency the same the pitch of these three sounds is the same. The wave shown in the recording is not a simple sine wave but a superposition of waves. Wave motion and the concepts of wave speed and frequency are also explored. Thank you for the reviews. As imaginary unit use i or j (in electrical engineering), which satisfies basic equation i 2 = −1 or j 2 = −1. Note: the second equation assumes your calculator has been set up to calculate trigonometric functions in angle units of degrees rather than radians. : The maximum instantaneous value of a function as measured from the zero-volt level. But wait, there's more! Meet the BrainPOP cast! You're about to be sent to a contact form for grown-ups! Are you sure you want to leave?. In air the displacement wave amplitude may range from 10-7 mm to a few mm per second. If you are doing sine-on-random mixed mode testing, it is often useful to be able to convert between PSD and sine amplitude and vice versa. (Only two vectors can be added at a time. 4/0 AWG battery cables should be used on power inverters rated over 3500 watts and most commonly used on 4000, 4400, 5000, 6000, 6600, 7000, 8000, 9000, 10,000 and 12,000 watt inverters. Two waves of equal amplitude are travelling in the same direction. Try this simple test. Our technical team is available M-F 8:30 - 5 Pacific Time. I had a look at some commercial libraries, but none of them met by demands. Also, when using acceleration units in G’s, you also need to apply a conversion factor to get a suitable velocity unit. ©Yao Wang, 2006 EE3414: Signal Characterization 10 1 3 5 7 9 11 13 15 0 0. Calculation of the Power Spectral Density. DC Sweep on Input Source, Vi. These cyclic natures of the sine and cosine functions make them periodic functions. This provides a breathtaking example of how a simple idea involving geometry and ratio was abstracted and developed. 775V and 1V, respectively. Able to run continuous power across the complete range from 300W-to-2000W and with 4 different surge wattage rates from 500W to 3500W this is the best 2000 Watt pure sine inverter on the. Circles Part 3- Degrees vs. Sine and cosine waves can make other functions! Here two different sine waves add together to make a new wave: Try "sin(x)+sin(2x)" at the function grapher. 5, would I write it as y(x,t) = 2. This java applet demonstrates interference between two sources of sound waves. We often want to describe an AC waveform in mathematical terms. In alternating current (AC) circuits, instead of a constant voltage supplied by a battery, the voltage oscillates in a sine wave pattern, varying with time as: In a household circuit, the frequency is 60 Hz. Example 2: Write cos 3 x cos 2 x as a sum. The sine is a similar trigonometric function which uses the other side: In text, one usually writes out "sine" and "cosine" while in an equation, we use the abbreviations "sin" and "cos" instead. This expected value calculator helps you to quickly and easily calculate the expected value (or mean) of a discrete random variable X. The voltage increases as the wave form moves toward 90°. At this point, the wave form has gone through 90° of the 360° cycle. Calc Op Amp Gain and Resistor Values. Our technical team is available M-F 8:30 - 5 Pacific Time. Suppose you want to add two cosine waves together, each having the same frequency but a different amplitude and phase. prices, forms or calculator tools?. 5t)?Forget about trig identities: I do not. It can be used to obtain the desired level of dc voltage (using step up or step down transformers). A sine wave frequency shows, how much the medium particles undergo in vibration when a wave is passed through that medium. Plug a AC powered fan into the output and if it buzzes while operating then it is NOT a pure sine wave inverter. Angle addition formulas express trigonometric functions of sums of angles in terms of functions of and. Is has many analog functions which I don't know how to use. The tangent sum and difference identities can be found from the sine and cosine sum and difference identities. Double Angle Formulae. While producing clock or timing signals, this astable multivibrator produces a square wave generator waveform that switches between HIGH and LOW. (5), needed for text wraparound reasons, simply means multiply. In this article, we’re going to explore a number of ways to calculate the sine series without actually using the sine (or cosine) function. In that manuscript the author presented the following equation: AtB t AB t. Most loudspeakers possess a nominal impedance of 4, 8 or 16 ohms. To include the widget in a wiki page, paste the code below into the page source. Other Notes: Unique Names and Labeling Nodes. 1 Analysis of Circuits (2017-10213) Phasors: 10 - 2 / 11 For inductors and capacitors i = Cdv dt and v = L di. Often we will have two sinusoidal or other periodic waveforms having the same frequency, but is phase shifted. The mathematical function describing a typical AC voltage is V (t) = V Max sin ωt. Transformerless design provides reliable power conversion in compact size. There are three parts to a sine wave: amplitude, frequency, and phase. sin is equal to sin sin (A B not ++) A B. In order to get a perfect representation of a periodic signal (such as a square wave) requires that we add sine waves of frequency approaching infinity. Building an antenna. Beyond simple math and grouping (like " (x+2) (x-4)"), there are some functions you can use as well. rx online The reason A few Games Currently have Confident Over the internet Residential areas in addition to Some others Usually do not Currently, it could be understood as the folks participating in Category from Stories basically a standard agonizing number, however with these sort of a hefty footballer trust (12 million working on a … Continue reading "The reason A few Games Currently. That is how this program works. An easy to use C# library for quick and simple graph plotting. For example, adding one quarter of a wavelength will result in an antinode at the. This java applet demonstrates interference between two sources of sound waves. Calcblog’s very first video walks you through all the powerful graphing features available on your TI-83 Plus and TI-84 Plus. The phase shift equation is ps = 360 * td / p, where ps is the. (Equation is not the correct terminology here) $\endgroup$ - Guy Mar 13 '14 at 6:20 Different Types of Waves. The above formulas are important whenever need rises to transform the product of sine and cosine into a sum. The sine function (usually expressed in programming code as sin(th), where th is an angle in radians) is one of the basic functions in trigonometry. Passing the fast paced Higher Maths course significantly increases your career opportunities by helping you gain a place on a college/university course, apprenticeship or even landing a job. At Your Service. Currently, it has three waves specified, but that list can be expanded simply by continuing the Height and Period inputs. Vector addition is similar to arithmetic addition. Bandwidth tells us nothing about these details. The sampling rate and the frequencies can be as per. Change the amplitude and wavelength of the purple wave with sliders C and D. 0 G peak at 80 Hz, and 1. Provide details and share your research! But avoid … Asking for help, clarification, or responding to other answers. The formula used to express the Sin (x) as Sine Series is. To use this calculator enter your application. Recall that the Fourier series of f(x) is defined by where We have the following result: Theorem. Scroll down the page for examples and solutions. Like computing the average over a time period. Sine Waves If we were to graph the wave of a single perfect musical note of a specific frequency on a XY axis, with X being frequency and Y being amplitude, the result would look something like figure 3, a wave which rises and falls sinusoidally with time, and is called, simply, a sine wave. In a series RL circuit with the sine voltage source, the current wave lags behind the voltage wave with the lag less than 90° (zero resistance) and more than 0° (zero inductance). 0 and w = 1. Free trigonometric equation calculator - solve trigonometric equations step-by-step This website uses cookies to ensure you get the best experience. An interactive demo which enables you to both see and hear the result of multiplying a sine wave with a cosine amplitude envelope. At the peak the value it is 10V DC plus 5V amplitude equals 15V. Also be sure to account for a possible surge draw. Sound travels as a transverse wave, so takes the same. Help us improve our. Some functions (like Sine and Cosine) repeat forever and are called Periodic Functions. The Calculator TheCalculator. Phase Difference between a Sine wave and a Cosine wave. Inverter Remotes. Degree-day calculations and accumulations are based on the area under the diurnal temperature curve and between the thresholds. Ask Question Asked 6 years, 1 month ago. We often want to describe an AC waveform in mathematical terms. In order to get a perfect representation of a periodic signal (such as a square wave) requires that we add sine waves of frequency approaching infinity. The only reason I asked my above question is that using the FT to analyse addition of sine waves is something that seems a touch odd. Solving for in terms of , We are looking for the effective spring constant so that. Some of the analog functions are range functions. As the other proofs relying on visual imagery, Nelsen's too are subject to natural argument (angle) limitations:. Angle addition formulas express trigonometric functions of sums of angles in terms of functions of and. student in the Graduate Program in Acoustics at Penn State. 094E+01 REVIEW:. rx online The reason A few Games Currently have Confident Over the internet Residential areas in addition to Some others Usually do not Currently, it could be understood as the folks participating in Category from Stories basically a standard agonizing number, however with these sort of a hefty footballer trust (12 million working on a … Continue reading "The reason A few Games Currently. Most loudspeakers possess a nominal impedance of 4, 8 or 16 ohms. When you superimpose two sine waves of different frequencies, you get components at the sum and difference of the two frequencies. In different cases, it could do any of the above. It would more than double. When h=0, it only fluctuates along the y-axis. print ac v(3,0) vp(3,0). Sine Wave = Frequency Cycle = One repetition of a wave's pattern Frequency = The number of cycles per second (measured in Hz) Period = The time duration of one cycle (the inverse of frequency, P = 1/f) Wavelength = The length of one period of a wave Amplitude = A measure of a wave's change over a single period Looking at the picture above: 1. Tangent calculator. All the 3 variables should have the same amplitude. As imaginary unit use i or j (in electrical engineering), which satisfies basic equation i2 = −1 or j2 = −1. So unless you have. The phasor length corresponds to the wave's amplitude, the angle corresponds to the phase. The PicoCell 2000 Off-Grid Solar Pumping Kit 1 has everything you need to convert your new or existing electric motor to solar power. Don’t worry about a thing. For Pipe C, the frequency can be determined from knowledge of the speed and the wavelength using the wave equation: v = f • λ where λ is the wavelength. These types of inverters are cheaper than the comparable pure sine wave inverter because they don’t add in extra components to create a smooth “pure” sine wave for the AC. sin(A + B) = sinAcosB + cosAsinB. Google has many special features to help you find exactly what you're looking for. Voltage from the inverter pulse and the reflected wave add together increasing voltage to the motor. The addition of sine waves is very simple if their complex representation is used. and the green one with magnitude A and initial phase φ: y 2 = B sin (ωt + φ). If you wish to plot these same waveforms (with the same phase shift shown) using radians as the unit of. Adding waves of DIFFERENT frequencies together You ought to remember what to do when two waves meet, if the two waves have the same frequency, same amplitude, and differ only by a phase offset. Commodity Exchange Act. Your calculator has, somewhere on it, both an R→ P key or function and a P → Rkey or function. A sine wave has no phase. Sine Wave Period, Frequency Calculator. Triangle waves are found in sound synthesis and are useful for testing linear electronics like amplifiers. Note that the violin's jagged waveform produces a sharper sound, while the smooth waveform of the piano produces a purer sound, closer to a sine wave. To calculate the phase shift, you need the frequency and period of the waves. In this circuit, we will show how we can build a sine wave generator with a 555 timer chip. But for many applications we have a periodic function that varies with time, rather than an angle. The cosine (often abbreviated "cos") is the ratio of the length of the side adjacent to the angle to the length of the hypotenuse. The amplitude of a wave is measured as:. This can be thought of as a “sine wave” of that frequency with a certain amplitude and a certain time phase. Any lowercase letter may be used as a. (For sines, the integral and derivative are. This is the standard waveform that oscillates between two levels with a standard sinusoidal shape. (5), needed for text wraparound reasons, simply means multiply. The tangent starts out like the sine curve, but quickly it sweeps up to reach infinity at 90 degrees. Also consider that the RMS value of the AC sine wave is about 70% of the total voltage being produced. Write a program in C to draw sine wave using graphics. The standing waves will depend on the boundary conditions. Sine wave inverters come in all sizes, from a small micro sine wave inverter, to larger kilowatt pure sine wave power inverters. Header provides a type-generic macro version of this function. I have attached a workbook in which I have plotted the amplitude resulting from combining sine waves. In other words it affects the period or wave length of the graph. Head to the menu bar and choose "Insert". The cosine (often abbreviated "cos") is the ratio of the length of the side adjacent to the angle to the length of the hypotenuse. R is the resistance in ohms (Ω),. In that manuscript the author presented the following equation: AtB t AB t. dBm is a power ratio relative to 1mW, dBu and dBV are voltage ratios, relative to 0. Imagine a wave in the ocean. Create, share, and store beautiful presentations online that anyone can view. Scroll down the page for examples and solutions. The following are graphs of sin, cos & tan. Java programming environment. At long distances a 460V RMS output can exceed 2000 volts at the motor terminals. Reduce the damping by a factor of 10, or so, and increase the Delay by a few milliseconds. Complex Periodic Waveforms. Square wave inverter is cheaper among the all but not suitable for all appliances. Get Physics Help. h library so you will probably need to update to an. co provides all kinds of free web tools such as calculators, tests, quizzes or converters for a variety of topics from health and medical algorithms, to finance, math, personality and other sciences. Try it each way on your calculator to determine how yours works. More complicated musical sounds arise from over-laying sine waves of different frequencies at the same time. pure sine wave inverter charger, Remy Alternators & Generators for Datsun 510, ACDelco Alternators & Generators for Datsun 510, Less than 12V Modified Sine Wave Inverter Car Power Inverters, Alternator & Generator Parts for Datsun 510, TOMY Beyblade Burst Toys, sine bar, National Bearings Alternator & Generator Parts for Datsun 510,. When converting DC power from a battery into AC power to run sensitive electronic equipment for your outdoor or industrial use, such as a TV, computer or other home electronics, a pure sine wave inverter. You can enter either integers ( 10. Modified Sine Wave. Cast the line, and relax. The frequency - cycles per second - of a sound is expressed in hertz (Hz). Physics Help By Category. I would like to fit a sine wave trendline to the chart, and also get the amplitude and the period from the formula of the sine wave. By experimenting with the value of C1’s capacitance, you can pick up two other “stations” at 2. In a right triangle with legs a and b and hypotenuse c, and angle α opposite side a, the trigonometric functions sine and cosine are defined as. A RC ladder Low-pass filter was the first thing which I tried, It gave good results but the output peak-to-peak voltage (Vpp) varied a lot with the frequency. Mon - Sun (9. By experimenting with the value of C1’s capacitance, you can pick up two other “stations” at 2. So, I decided to design a simple solution by myself. Pure Sine Wave inverters (also called True Sine Wave) are more suited for sensitive electrical or electronic items such as laptop computers, stereos, laser printers, certain specialized applications such as medical equipment, a pellet stove with an internal computer, digital clocks, bread makers with multi-stage timers, and variable speed or. Fourier Sine and Cosine Series. Pure Sine Wave Output. While producing clock or timing signals, this astable multivibrator produces a square wave generator waveform that switches between HIGH and LOW. Save time & money by riding together with Waze Carpool. Adding 3 to the power in dBm is the same as multiplying the power in Watts by two (actually 1. Example: Laplace Transform of a Gated Sine. This is a tool you can use to estimate the distance from one wave peak to another when you already know the frequency and the. Amplitude is a measure of how big the wave is. 1] Cosine As with sine, setting β to α in the following: [1. For these larger applications, use one of the 500A ANL fuse kits, once again found here on IRU or on. By using the grid, you can see that the resultant displacement at any given point of the. However, to fully characterize these components, we must know both the amplitude and phase of each of these sine wave components in the complex signal. The function doesn’t need to be continuous, it can be defined arbitrarily. Sine Wave Generator using 4047 IC. Here, we will be considering mechanical waves. For example, adding one quarter of a wavelength will result in an antinode at the. Modern calculators have much in common with computers: they share much of the same history and work in a similar way, but there's one crucial difference: a calculator is an entirely human-operated machine for processing math, whereas a computer can be programmed to operate itself and do a whole range of more general-purpose jobs. The standing waves will depend on the boundary conditions. Dividing the frequency into 1 gives the period, or duration of each cycle, so 1/100 gives a period of 0. A sine wave is the mirror image of a cosine wave. For equal amplitude sine waves. To include the widget in a wiki page, paste the code below into the page source. The input and plot are on the sheet named "1" and a "Description" sheet shows the formulas defined in the name manager. The second can be found by adding a half wavelength. This definition only covers the case of acute positive angles α: 0<α<90°. This is also called additive synthesis. : The maximum instantaneous value of a function as measured from the zero-volt level. A calculator or computer program is not reading off of a list, but is using an algorithm that gives an approximate value for the sine of a given angle. If you prefer keyboard input of math formulas, you can type directly into the input bar. Make waves in space and time and measure their wavelengths and periods. Select angle type of degrees (°) or radians (rad) in the combo box. It also ensures maximum compatibility with sensitive electronics. Remember, if you add a number inside the argument cosine, it shifts the wave. where is the total displacement of the mass. Integral Calculus. Click the Reset button to restart with default values. Blue Pacific Solar will supply you with the 1 - Line Drawing; Full Instructive Three-Line Diagram of Entire DC Circuit, as Well as AC Lines to Your. You can easily identify these aliases by adding multiples of the sampling frequency to the frequency of the original sine wave. I have square waves of different frequencies (1KHz to 20KHz), and I need to convert them to a sine wave of the corresponding fundamental frequency. Change the amplitude and wavelength of the purple wave with sliders C and D. In such a network all voltages and currents are sinusoidal. 4 SIMULATING YOUR CIRCUIT. First, note that although we call these recurrent functions “sine waves”, in mathematical work, we ordinarily represent them with a cosine function. This wave fluctuates in amplitude, or beats, with a frequency called the beat frequency. Mon - Sun (9. Write a program in C to draw sine wave using graphics. To calculate a function like 'sine' with an argument like 90, input the corresponding function name followed by the argument 90 in parentheses. The sin () method returns the sine of a number. Before stepping forward to the next point, move the chart where you prefer. In order to calculate sin (x) on the calculator: Enter the input angle. How Solar Works. ProMariner ProNautic 1250P Digital Battery Charger - 12V, 50A. Surf Wave Calculator. We can find r by squaring and adding (1) and (2): r 2 cos 2 a + r 2 sin 2 a = a 2 + b 2 hence r 2 = a 2 + b 2 (since cos 2 a + sin 2 a = 1) In a similar way, we can write expressions of the form acos q + bsin q as rsin(q + a). We note that sin π/4=cos π/4=1/√2, and re-use cos θ=sin (π/2−θ) to obtain the required formula. Use MathJax to format equations. f = 1 / T (1) where. Given Maxwell's four equations (which are based on observation) we have shown that electromagnetic waves must exist as a consequence. Usage of a calculator may vary to other calculators. Sine waves cannot represent the DC component of a signal, since a sine wave of zero frequency is composed of all zeros (see Figs. This begins with very basic physics, but continues with higher level material. The superposition principle of waves is: the resulting wave formed by several waves overlapping in space and time, can be found by adding the waves. Beyond simple math and grouping (like " (x+2) (x-4)"), there are some functions you can use as well. The formula used to express the Sin(x) as Sine Series is Expanding the above notation, the formula of Sine Series is. Sine Wave Sine Wave. Here's how you can access and use it. O P AMP APPLICATIONS. The sin () method returns the sine of a number. Adding a Ground. There's also a graph which shows you the meaning of what you've found. Sum and Difference Frequencies. It is given by the function It is given by the function When Sine wave starts from zero and covers positive values, reaches zero; and again covers negative values, reaches zero, it is said to have completed one cycle or single cycle. Double Angle Formulae. Translation is done via radix 64. Expires 31/03/2020. ) and you can get travel time having average speed and distance. Ask Question Asked 6 years, 1 month ago. Select angle type of degrees (°) or radians (rad) in the combo box. If you looked at the current and voltage of say, a small motor you might get a picture like this. The cosine function is therefore the sine function with a phase shift of -Pi/2. A simple 8 question sheet used as a review of sine and cosine rule. The graph of cos the same as the graph of sin though it is shifted 90° to the right/ left. Adding Parts to your Circuit. Basically figure out what the instantaneous voltage for each sine wave for a specific period of time (count up in microseconds), the do a straight algebraic addition of the two calculated points. The two waves have different frequencies and wavelengths, but they both travel with the same wave speed. Sine functions are perfect ways of expressing this type of movement, because their graphs are repetitive and they oscillate (like a wave). Before going to the program for Sine Series first let us understand what is a Sine Series? Sine Series: Sine Series is a series which is used to find the value of Sin(x). It is the easy way to make a basic astable waveform generator. (The "•" symbol in Eq. You can easily identify these aliases by adding multiples of the sampling frequency to the frequency of the original sine wave. Battery Chargers. Passing the fast paced Higher Maths course significantly increases your career opportunities by helping you gain a place on a college/university course, apprenticeship or even landing a job. α + β = the angle between vector 1 and 2 is known. Check the Show/Hide button to show the sum of the two functions. Please Sign up or sign in to vote. Light/radio in vacuum/air Light in water Sound in air Sound in water Custom m/s Km/s Miles/s. Comment/Request Theta is the angle from the positive z-axis to the xy-plane in the ISO (physics) convention. The following diagram shows how to find the equation of a sine graph. Thank you for the reviews. What follows are the details of the program's operation. As seen on his page, the original formula seems to come from an article by J. 00pm) Drop us a note & we will respond. miles, yards, meters, kilometers, inches etc. For example, adding one quarter of a wavelength will result in an antinode at the. Learning Center. (6) Sine-on-Random Example: Use the same background random as defined above, and add in sine tones of 1. Square Waves from Sine Waves The Fourier series expansion for a square-wave is made up of a sum of odd harmonics, as shown here using MATLAB®. Help me keeping this feature alive by supporting my work. Recall that the Fourier series of f(x) is defined by where We have the following result: Theorem. at a distance of L/2 from an end or the centre). You can move a sine curve up or down by simply adding or subtracting a number from the equation of the curve. Find the Laplace Transform of the function shown: Solution: This function is a little different than the previous in that it involves more than ramps and steps. Show / Hide of Grid lines, axes numbers are optional. First, rearrange the equation. The unit is a True Sine Wave 220 Volt AC power supply, it is not a modified sine wave and you can with confidence run any appliance within the units power rating. For example, y=2x {1 #include. So, I decided to design a simple solution by myself. It has a period of 2π. For example sound and light waves, day length and temperature variations over the year can be represented as a sine. In a right triangle with legs a and b and hypotenuse c, and angle α opposite side a, the trigonometric functions sine and cosine are defined as. Comparing A cos(x) + B sin(x) with R cos(x)cos(a) – R sin(x)sin(a) gives looking at the sin(x): R sin(a) = B. With local development and support this trusted company has established itself as the leading manufacturer of power protection solutions in the Asia Pacific region, meeting the. There are several such algorithms that only use the four basic operations (+, −, ×, /) to find the sine, cosine, or tangent of a given angle. Google has many special features to help you find exactly what you're looking for. 2] Or: [ [2. a sin θ + b cos θ = R sin (θ + α) You will notice that this is very similar to converting rectangular to polar form in Polar form of Complex Numbers. A capacitor with impedance 10 Ω at 1 kHz would be of order 10 μF. Physics 123 Section 2. The first two conditions of continuity. There must be a node at each end. Pure Sine Wave Inverters. The following example uses Sin to evaluate certain trigonometric identities for selected angles. You can change the waves' frequencies by. What does a triangle wave sound like compared to the square wave and pure sine wave? • (Done in lab and previously in class) • Function generators often carry sine, triangle and square waves (and often sawtooths too) If we keep the frequency the same the pitch of these three sounds is the same. Suppose you want to add two cosine waves together, each having the same frequency but a different amplitude and phase. We are world leaders in advanced power products. Pure Sine Wave. Using PWM Output as a Digital-to-Analog Converter on a TMS320F280x Digital Signal Controller 5 The PWM/DAC approach is not new, but performance limitations have historically confined its use to low-resolution, low-bandwidth applications. A sine wave or sinusoid is a mathematical curve that describes a smooth periodic oscillation. For example, to increase the square wave level by a factor of 10, decrease R2 to 1k making the gain GAIN_V2 = - RF/R2 = -10k/1k = -10. Equating (3) with the right side of (1) and substituting into (2) gives. This module introduces the history of wave theory and offers basic explanations of longitudinal and transverse waves. Enter a value to be squared Then click OK The square of the number entered is. Click the Reset button to restart with default values. 94 × 10-6 w shown in Fig. Add to Wishlist. Tangent calculator. Above is Wave Adder 1. Create AccountorSign In. All our backup power units are True Sine Wave and can run your fridge, freezer, gate motor, garage door motor and any other electrical device without fear of damage. (5), needed for text wraparound reasons, simply means multiply. So it is a sine wave with an amplitude of 5V and it rides on top of a DC level of 10V. Its most basic form as a function of time (t) is:. TIP: If you add [email protected] 94 × 10-6 w shown in Fig. In the Half wave rectifier circuit shown above the transformer serves two purposes. Changing the Value of a Part. Please not Modified Sine Wave Inverter can cause humming noise when used with induction motors like ceiling fans, etc. If we apply a signal V(t) to one end of the transmission line, where t is time, the signal at the other end will be V(t − τ), where τ is a constant. Square Wave. DC Sweep on Input Source, Vi. In this section we define the Fourier Sine Series, i. The Calculator TheCalculator. By using this website, you agree to our Cookie Policy. This IC is generally used in Inverter circuit and we have previously made a Square wave generator using this IC, by adding few resistors and capacitors in previous circuit, we can obtain sine wave with IC 4047, as shown in the circuit diagram below:. To establish a connection between complex numbers and sine and cosine waves, you. Does the sine wave change as expected? You can eliminate the Damping Factor and the Delay by setting. Next we use Eq. Add the following sine waves y= Asin(wt) + Bsin(wt + x) Where w=2(pi)f and x is a phase shift I SIMPLIFIED this for my friend using rotating vectors, then i got really annoyed realizing that I didn't know how to do it the direct way (trig identities). 1 Analysis of Circuits (2017-10213) Phasors: 10 – 2 / 11 For inductors and capacitors i = Cdv dt and v = L di dt so we need to. Addition and Subtraction Formulas for Sine and Cosine II. DC Sweep on Input Source, Vi. 71 kHz and 2. 094E+01 REVIEW:. NumPy has the sin () function, which takes an array of values and provides the sine value for them. Tutorial on how to use sine functions to model data. A diode is used to rectify this, and the C2 capacitor smoothes it out to generate the audio signal in the last scope slot (which is simply a 12 Hz sine wave in this example). Algebra Based Physics. 0 x 10 5 times 4. Enter all known values of X and P(X) into the form below and click the "Calculate" button to calculate the expected value of X. You have no items in your shopping cart. Calculus: Integrals example. adding two sine waves. Pure Sine Wave. Before going to the program for Sine Series first let us understand what is a Sine Series? Sine Series is a series which is used to find the value of Sin (x). You can certainly try other frequencies as well, but you end up with a non-integer step size so you either have to round the step index or do some interpolation between table values. For Grown-Ups: News from BrainPOP. Comment/Request Theta is the angle from the positive z-axis to the xy-plane in the ISO (physics) convention. It could be a little ripple or a giant tsunami. Imagine a wave in the ocean. The reason for this is that as b gets larger the sine wave squishes together can be illustrated through the following: when y = sin(x) and x =0 the y = 0 and when. then it is not possible to get just one cosine(or sine) term.
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# graph that is a edge-disjoint union of trails of even length
An old exercise from my graph theory notes has the following exercise:
Let $G$ be a connected graph with an even number of edges and with a non-zero even number $2n$ of vertices of odd degree. Then $G$ is an edge-disjoint union of $n$ trails of even length.
I'm having problems with the even-length part of the conclusion. I can show that we have a disjoint trails corresponding to pairs of odd vertices:
Let $x_1,x_2,\dots,x_n$ and $y_1,y_2,\dots,y_n$ be the odd vertices of the graph. By adding the edges $x_l y_l, x_2 y_2 ,\dots, x_n y_n$ to the graph, we have a new graph where all vertices have even degree. This implies the new graph can be expressed as the edge-disjoint union of circuits. When the added edges are removed from the new graph, we have disjoint trails in the original graph.
Are these trails, that I got, those that are of even length? How do I show the even length part?
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Just edited the question. $G$ has $2n$ odd vertices. – apple mcdonald Aug 17 '12 at 9:40
reading from my notes: $G$ is connected with $2n$ odd vertices ($n>1$) and of even size. – apple mcdonald Aug 17 '12 at 9:53
How do you know the edges $x_{i}y_{i}$ don't already exist? – TheNumber23 Sep 25 '13 at 0:41
I'll solve the problem in three steps:
(1) First I'll show that any connected graph $G$ with an even number, $2m$, of edges is the edge-disjoint union of $m$ trails of length 2.
(2) If $G$ is a graph with even number of edges and $2n$ vertices of odd degree, and the edges is an edge-disjoint union of trails, it is possible to successively concatenate trails until we are left with $n$ trails all starting and ending in odd degree vertices plus any number of circular trails.
(3) We can merge the circular trails with the $n$ linear trails so as to end up with only $n$ trails.
The reason $n\ge1$ is required is that for $n=0$, i.e. all vertices have even degree, step (3) will end with a single circular trail (an Euler path) with no linear trail to merge it to.
1: Splitting $G$ into 2-trails
Proof goes by induction (or descent): i.e. I reduce the graph to one or more graphs with a smaller number of edges.
Pick a vertex, $x$ of degree 2 or higher: one must exist, or $G$ would have two vertices and one edge only. Decompose $G$ into components $G_1,\ldots,G_k$ which correspond to the connected components after removing $x$ from $G$, but with the vertec $x$ and edges between $x$ and vertices of each $G_i$ included in $G_i$: i.e. two vertices are in the same component if the can be connected by a path not passing through $x$. Each edge of $G$ is then in exactly one of the $G_i$.
If there is only one component, we can pick any two edges at $x$, say $xy$ and $xz$ for vertices $y$ and $z$, form the 2-trail $yxz$ and subsequently remove these two from the graph. If this leaves $x$ with degree zero, we also remove $x$. The remaining graph is still connected and with even number of edges.
If all components have even number of edges, each of these have a smaller number of edges and so follow from the induction hypothesis.
If there are components with an odd number of edges, there must be an even number of these. Take any two of these, pick one edge $xy$ to one of them and one edge $xz$ to the other, form the 2-trail $yxz$ as before, then remove these two edges (and $x$ if left with degree 0). The two selected components may (or may not) get disconnected from the rest of the graph after removing these edges, but each connected component of $G$ after removing $yxz$ will have even number of edges and so be handled by the induction hypothesis.
This procedure (by induction or used iteratively) will reduce $G$ to a disjoint union of trails of length 2.
2: Join 2-paths into maximal paths
If at a vertex $x$ there are two trails that start/end there, join these two trails together. Do this iteratively until no more such cases exist. The only place trails can start/end will be at vertices of odd degree; conversely, at each vertex of odd degree, there must be exactly one trail starting/ending. Hence, we are left with $n$ trails starting/ending in the $2n$ vertices of odd degree, plus any number of circular trails.
Since we start with 2-trails, and the joining of two even length trails remain even, all trails (linear and circular) are of even length.
3: Merge circular trails with linear trails
Take any circular trail, $\omega$, from the set. There must be a vertex $x$ in $\omega$ through which another trail from the set passes which we denote $\gamma$: if not, $\omega$ must contain an entire connected component of $G$. Merge $\gamma$ and $\omega$ together at $x$ into a new trail, also of even length since both $\omega$ and $\gamma$ were. If $\gamma$ is linear, the merged trail is linear; if $\gamma$ is circular, the merged trail is circular. But in either case, the number of circular trails in the set is reduced by 1.
We repeate this step until there are no circular trails left. This requires $n>0$, otherwise we will be left with a single circular Euler path spanning the entire graph which we cannot get rid of.
Q.E.D.
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###### Activity2.5.4
Suppose we run a company that has two warehouses, which we will call $$P$$ and $$Q\text{,}$$ and a fleet of 1000 delivery trucks. Every day, a delivery truck goes out from one of the warehouses and returns every evening to one of the warehouses. Every evening,
• 70% of the trucks that leave $$P$$ return to $$P\text{.}$$ The other 30% return to $$Q\text{.}$$
• 50% of the trucks that leave $$Q$$ return to $$Q$$ and 50% return to $$P\text{.}$$
We will use the vector $$\xvec=\twovec{P}{Q}$$ to represent the number of trucks at location $$P$$ and $$Q$$ in the morning. We consider the matrix transformation $$T(\xvec) = \twovec{P'}{Q'}$$ that describes the number of trucks at location $$P$$ and $$Q$$ in the evening.
1. Suppose that all 1000 trucks begin the day at location $$P$$ and none at $$Q\text{.}$$ How many trucks are at each location at the end of the day? Therefore, what is the vector $$T\left(\ctwovec{1000}{0}\right)\text{?}$$
Using this result, what is $$T\left(\twovec{1}{0}\right)\text{?}$$
2. In the same way, suppose that all 1000 trucks begin the day at location $$Q$$ and none at $$P\text{.}$$ How many trucks are at each location at the end of the day? What is the result $$T\left(\ctwovec{0}{1000}\right)\text{?}$$
3. Find the matrix $$A$$ such that $$T(\xvec) = A\xvec\text{.}$$
4. Suppose that there are 100 trucks at $$P$$ and 900 at $$Q$$ at the beginning of the day. How many are there at the two locations at the end of the day?
5. Suppose that there are 550 trucks at $$P$$ and 450 at $$Q$$ at the end of the day. How many trucks were there at the two locations at the beginning of the day?
6. Suppose that all of the trucks are at location $$Q$$ on Monday morning?
1. How many trucks are at each location Monday evening?
2. How many trucks are at each location Tuesday evening?
3. How many trucks are at each location Wednesday evening?
7. Suppose that $$S$$ is the matrix transformation that transforms the distribution of trucks $$\xvec$$ one morning into the distribution of trucks two mornings later. What is the matrix that defines the transformation $$S\text{?}$$
8. Suppose that $$R$$ is the matrix transformation that transforms the distribution of trucks $$\xvec$$ one morning into the distribution of trucks one week later. What is the matrix that defines the transformation $$R\text{?}$$
9. What happens to the distribution of trucks after a very long time?
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# What happens when throttling in an isothermal process
Consider an isothermal expansion of an ideal gas (always at ambient temperature $$T_0$$), from some initial pressure $$p_i$$ to the ambient pressure $$p_0$$, such that the maximum work available is:
$$W = mRT_0\ln(\frac{p_i}{p_0}) = p_iV_i\ln(\frac{p_i}{p_0})$$. (1)
If the pressure is throttled to some intermediate pressure, $$p_1, then presumably the expansion work can be be split into two phases, one with constant pressure $$p_1$$ and one with variable pressure, i.e. $$p. the maximum work available should then be the sum of these two phases, i.e.
$$p_1V_1\ln(\frac{p_1}{p_0})$$ (variable) + $$V_i(P_i-P_1)$$ (constant) (2)
For an ideal gas, the exergy is then just $$mRT\ln(p_i/p_0)$$, so without the throttling the exergy efficiency is 100%.
My question is, firstly, is this correct? Secondly, is the exergy destruction in the valve (1)-(2)? Thirdly, can you throttle (regulate pressure) without destroying a significant amount of exergy?
Furthermore, how do you draw ideal gas throttling on a PV diagram?
• The internal energy of ideal fluids (liquids or gases) depends only on temperature. Work is path dependent and may take a reversible or irreversible path. Exergy is best understood as the irreversible work along any path. Throttling is an irreversible process, while an isothermal REVERSIBLE process is just what it says it is. Any pV process for an ideal gas is always shown as the proper combination of isobars, isochors, isotherms, or adiabates for an ideal gas. – Jeffrey J Weimer Feb 2 '19 at 18:50 | |
# 10.6 Networks of uniform strings (Page 3/3)
Page 3 / 3
## Example #1: the tritar
Depicted above is a network of three strings called a tritar. We are interested in how the eigenvalues of this simple network vary with changes in the transverse stiffness k i of each string. We assume that the longitudinal stiffnesses σ i are 1 for each string, and we also assume that the lengths of the strings are all 1 for conveninence.
We define our orientation vectors by
$\begin{array}{c}\hfill \stackrel{^}{{v}_{1}}=\left[\begin{array}{c}1\\ 0\end{array}\right]\phantom{\rule{1.em}{0ex}}\phantom{\rule{1.em}{0ex}}\stackrel{^}{{v}_{2}}=\frac{1}{\sqrt{2}}\left[\begin{array}{c}1\\ 1\end{array}\right]\phantom{\rule{1.em}{0ex}}\phantom{\rule{1.em}{0ex}}\stackrel{^}{{v}_{3}}=\frac{1}{\sqrt{2}}\left[\begin{array}{c}1\\ -1\end{array}\right]\end{array}$
First, we compute the stiffness matrices. For the first string, we obtain
$\begin{array}{ccc}\hfill {P}_{1}& =& {K}_{1}\left(I-\stackrel{^}{{v}_{1}}{\stackrel{^}{{v}_{1}}}^{T}\right)+{\sigma }_{1}\stackrel{^}{{v}_{1}}{\stackrel{^}{{v}_{1}}}^{T}\hfill \\ & =& k\left(\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right],-,\left[\begin{array}{cc}1& 0\\ 0& 0\end{array}\right]\right)+\left[\begin{array}{cc}1& 0\\ 0& 0\end{array}\right]\hfill \\ & =& \left[\begin{array}{cc}1& 0\\ 0& k\end{array}\right].\hfill \end{array}$
For the second string, we get
$\begin{array}{ccc}\hfill {P}_{2}& =& {K}_{2}\left(I-\stackrel{^}{{v}_{2}}{\stackrel{^}{{v}_{2}}}^{T}\right)+{\sigma }_{2}\stackrel{^}{{v}_{2}}{\stackrel{^}{{v}_{2}}}^{T}\hfill \\ & =& k\left(\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right],-,\frac{1}{2},\left[\begin{array}{cc}1& 1\\ 1& 1\end{array}\right]\right)+\frac{1}{2}\left[\begin{array}{cc}1& 1\\ 1& 1\end{array}\right]\hfill \\ & =& \frac{1}{2}\left[\begin{array}{cc}k+1& -k+1\\ -k+1& k+1\end{array}\right],\hfill \end{array}$
and for string number three, we have
$\begin{array}{ccc}\hfill {P}_{3}& =& {K}_{3}\left(I-\stackrel{^}{{v}_{3}}{\stackrel{^}{{v}_{3}}}^{T}\right)+{\sigma }_{3}\stackrel{^}{{v}_{3}}{\stackrel{^}{{v}_{3}}}^{T}\hfill \\ & =& k\left(\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right],-,\frac{1}{2},\left[\begin{array}{cc}1& -1\\ -1& 1\end{array}\right]\right)+\frac{1}{2}\left[\begin{array}{cc}1& -1\\ -1& 1\end{array}\right]\hfill \\ & =& \frac{1}{2}\left[\begin{array}{cc}k+1& k-1\\ k-1& k+1\end{array}\right].\hfill \end{array}$
Letting the vector ${u}_{i}={\left[{u}_{i1}\phantom{\rule{0.222222em}{0ex}}{u}_{i2}\right]}^{T}$ represent the displacements of string i , we obtain the following system of differential equations:
$\begin{array}{ccc}\hfill {P}_{1}{u}_{1}^{\text{'}\text{'}}& =& -{\lambda }^{2}{u}_{1}\hfill \\ \hfill {P}_{2}{u}_{2}^{\text{'}\text{'}}& =& -{\lambda }^{2}{u}_{2}\hfill \\ \hfill {P}_{3}{u}_{3}^{\text{'}\text{'}}& =& -{\lambda }^{2}{u}_{3}.\hfill \end{array}$
Expanding via matrix multiplication, we see that, component-wise, this translates into
$\begin{array}{ccc}\hfill {u}_{11}^{\text{'}\text{'}}& =& -{\lambda }^{2}{u}_{11}\hfill \\ \hfill k{u}_{12}^{\text{'}\text{'}}& =& -{\lambda }^{2}{u}_{12}\hfill \\ \hfill {s}_{2}^{\text{'}\text{'}}& =& -{\lambda }^{2}{s}_{2}\hfill \\ \hfill k{d}_{2}^{\text{'}\text{'}}& =& -{\lambda }^{2}{d}_{2}\hfill \\ \hfill k{s}_{3}^{\text{'}\text{'}}& =& -{\lambda }^{2}{s}_{3}\hfill \\ \hfill {d}_{3}^{\text{'}\text{'}}& =& -{\lambda }^{2}{d}_{3},\hfill \end{array}$
where
$\begin{array}{c}\hfill {s}_{i}={u}_{i1}+{u}_{i2}\\ \hfill {d}_{i}={u}_{i2}-{u}_{i2}.\end{array}$
for $i=1,2$ . For boundary conditions, we require that the ends be clamped:
$\begin{array}{ccc}\hfill {u}_{1}\left(0\right)& =& 0\hfill \\ \hfill {u}_{2}\left(1\right)& =& 0\hfill \\ \hfill {u}_{3}\left(1\right)& =& 0,\hfill \end{array}$
that there be continuity at the central node:
$\begin{array}{c}\hfill {u}_{1}\left(1\right)={u}_{2}\left(0\right)={u}_{3}\left(0\right),\end{array}$
and that the forces balance at the central node:
$\begin{array}{c}\hfill {P}_{1}{u}_{1}^{\text{'}}\left(1\right)-{P}_{2}{u}_{2}^{\text{'}}\left(0\right)-{P}_{3}{u}_{3}^{\text{'}}\left(0\right)=0.\end{array}$
As with many systems of differential equations, this one can be solved via the time-honored method of guessing. Noting that the differential equations of this form equate the second derivative of a function with a constant multiple of itself, wehypothesize that the solution for each component of displacement is some linear combination of sines and cosines:
$\begin{array}{ccc}\hfill {u}_{11}& =& {a}_{1,1}cos\lambda x+{b}_{1,1}sin\lambda x\hfill \\ \hfill {u}_{12}& =& {a}_{1,2}cos\frac{\lambda }{\sqrt{k}}x+{b}_{1,2}sin\frac{\lambda }{\sqrt{k}}x\hfill \\ \hfill {u}_{21}& =& {a}_{2}cos\lambda x+{b}_{2}sin\lambda x+{\alpha }_{2}cos\frac{\lambda }{\sqrt{k}}x+{\beta }_{2}sin\frac{\lambda }{\sqrt{k}}x\hfill \\ \hfill {u}_{22}& =& {a}_{2}cos\lambda x+{b}_{2}sin\lambda x-{\alpha }_{2}cos\frac{\lambda }{\sqrt{k}}x-{\beta }_{2}sin\frac{\lambda }{\sqrt{k}}x\hfill \\ \hfill {u}_{31}& =& {a}_{3}cos\frac{\lambda }{\sqrt{k}}x+{b}_{3}sin\frac{\lambda }{\sqrt{k}}x+{\alpha }_{3}cos\lambda x+{\beta }_{3}sin\lambda x\hfill \\ \hfill {u}_{32}& =& {a}_{3}cos\frac{\lambda }{\sqrt{k}}x+{b}_{3}sin\frac{\lambda }{\sqrt{k}}x-{\alpha }_{3}cos\lambda x-{\beta }_{3}sin\lambda x.\hfill \end{array}$
where we have guessed
$\begin{array}{ccc}\hfill {s}_{2}& =& 2{a}_{2}cos\lambda x+2{b}_{2}sin\lambda x\hfill \\ \hfill {d}_{2}& =& 2{\alpha }_{2}cos\frac{\lambda }{\sqrt{k}}x+2{\beta }_{2}sin\frac{\lambda }{\sqrt{k}}x\hfill \\ \hfill {s}_{3}& =& 2{a}_{3}cos\frac{\lambda }{\sqrt{k}}x+2{b}_{3}sin\frac{\lambda }{\sqrt{k}}x\hfill \\ \hfill {d}_{3}& =& 2{\alpha }_{3}cos\lambda x+2{\beta }_{3}sin\lambda x\hfill \end{array}$
and have used the above to translate these into u 21 , u 22 , u 31 , and u 32 . We need to determine the coefficients. Applying the boundary condition that ${u}_{1}\left(0\right)=0$ , we get
$\begin{array}{ccc}\hfill {a}_{1,1}& =& 0\hfill \\ \hfill {a}_{1,2}& =& 0.\hfill \end{array}$
The fact that ${u}_{2}\left(1\right)=0$ implies that
$\begin{array}{ccc}\hfill {a}_{2}cos\lambda +{b}_{2}sin\lambda & =& 0\hfill \\ \hfill {\alpha }_{2}cos\frac{\lambda }{\sqrt{k}}+{\beta }_{2}sin\frac{\lambda }{\sqrt{k}}& =& 0.\hfill \end{array}$
Likewise, for ${u}_{3}\left(1\right)=0$ , we get
$\begin{array}{ccc}\hfill {a}_{3}cos\frac{\lambda }{\sqrt{k}}+{b}_{3}sin\frac{\lambda }{\sqrt{k}}& =& 0\hfill \\ \hfill {\alpha }_{3}cos\lambda +{\beta }_{3}sin\lambda & =& 0.\hfill \end{array}$
Next, we apply the continuity conditions. Since ${u}_{1}\left(1\right)={u}_{2}\left(0\right)$ , we see that
$\begin{array}{ccc}\hfill {a}_{1,1}cos\lambda +{b}_{1,1}sin\lambda -{a}_{2}-{\alpha }_{2}& =& 0\hfill \\ \hfill {a}_{1,2}cos\frac{\lambda }{\sqrt{k}}+{b}_{1,2}sin\frac{\lambda }{\sqrt{k}}-{a}_{2}+{\alpha }_{2}& =& 0,\hfill \end{array}$
and because ${u}_{2}\left(0\right)={u}_{3}\left(0\right)$ we have
$\begin{array}{ccc}\hfill {a}_{2}-{a}_{3}& =& 0\hfill \\ \hfill {\alpha }_{2}-{\alpha }_{3}& =& 0.\hfill \end{array}$
Finally, from the force-balance equation, we have
$\begin{array}{ccc}\hfill -{a}_{1,1}\lambda sin\lambda & +& {b}_{1,1}\lambda cos\lambda -\frac{1}{2}\left(k+1\right)\left({b}_{2},\lambda ,+,{\beta }_{2},\frac{\lambda }{\sqrt{k}}\right)-\frac{1}{2}\left(k+1\right)\left({b}_{2},\lambda ,-,{\beta }_{2},\frac{\lambda }{\sqrt{k}}\right)-\frac{1}{2}\left(k-1\right)\left({b}_{3},\frac{\lambda }{\sqrt{k}},+,{\beta }_{3},\lambda \right)\hfill \\ & -& \frac{1}{2}\left(k+1\right)\left({b}_{3},\frac{\lambda }{\sqrt{k}},-,{\beta }_{3},\lambda \right)=0\hfill \end{array}$
and
$\begin{array}{ccc}\hfill -{a}_{1,2}\frac{\lambda }{\sqrt{k}}sin\frac{\lambda }{\sqrt{k}}& +& {b}_{1,2}\frac{\lambda }{\sqrt{k}}cos\frac{\lambda }{\sqrt{k}}-\frac{1}{2}\left(1-k\right)\left({b}_{2},\lambda ,+,{\beta }_{2},\frac{\lambda }{\sqrt{k}}\right)-\frac{1}{2}\left(k+1\right)\left({b}_{2},\lambda ,-,{\beta }_{2},\frac{\lambda }{\sqrt{k}}\right)-\frac{1}{2}\left(k-1\right)\left({b}_{3},\frac{\lambda }{\sqrt{k}},+,{\beta }_{3},\lambda \right)\hfill \\ & -& \frac{1}{2}k+1\left({b}_{3},\frac{\lambda }{\sqrt{k}},-,{\beta }_{3},\lambda \right)=0.\hfill \end{array}$
These twelve equations can be represented by a single matrix equation with the following coefficient matrix:
$\begin{array}{c}\hfill \left[\begin{array}{cccccccccccc}1& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 1& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& cos\lambda & sin\lambda & 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& cos\frac{\lambda }{\sqrt{k}}& sin\frac{\lambda }{\sqrt{k}}& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& cos\frac{\lambda }{\sqrt{k}}& sin\frac{\lambda }{\sqrt{k}}& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& cos\lambda & sin\lambda \\ cos\lambda & 0& sin\lambda & 0& -1& 0& -1& 0& 0& 0& 0& 0\\ 0& cos\frac{\lambda }{\sqrt{k}}& 0& sin\frac{\lambda }{\sqrt{k}}& -1& 0& 1& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 1& 0& 0& 0& -1& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 1& 0& 0& 0& -1& 0\\ -\lambda sin\lambda & 0& \lambda cos\lambda & 0& 0& -\lambda & 0& \frac{\lambda }{\sqrt{k}}& 0& \left(1-k\right)\frac{\lambda }{\sqrt{k}}& 0& -\lambda \\ 0& -\frac{\lambda }{\sqrt{k}}sin\frac{\lambda }{\sqrt{k}}& 0& \frac{\lambda }{\sqrt{k}}cos\frac{\lambda }{\sqrt{k}}& 0& -\lambda & 0& \frac{\lambda }{\sqrt{k}}& 0& -\frac{\lambda }{\sqrt{k}}& 0& \lambda \end{array}\right].\end{array}$
The determinant of this matrix is
$\begin{array}{ccc}& & -sin\left(\frac{\lambda }{\sqrt{k}}\right)sin\left(\lambda \right){l}^{2}\left(6,\phantom{\rule{0.166667em}{0ex}},cos,\left(\lambda \right),sin,\left(\frac{\lambda }{\sqrt{k}}\right),{k}^{2},cos,\left(\frac{\lambda }{\sqrt{k}}\right),sin,\left(\lambda \right),+,4,\phantom{\rule{0.166667em}{0ex}},{\left(cos,\left(\lambda \right)\right)}^{2},{\left(sin,\left(\frac{\lambda }{\sqrt{k}}\right)\right)}^{2},{k}^{3/2}\right)\hfill \\ & & \phantom{\rule{1.em}{0ex}}\left(+,3,\phantom{\rule{0.166667em}{0ex}},cos,\left(\lambda \right),sin,\left(\frac{\lambda }{\sqrt{k}}\right),k,cos,\left(\frac{\lambda }{\sqrt{k}}\right),sin,\left(\lambda \right),+,{\left(sin,\left(\lambda \right)\right)}^{2},{\left(cos,\left(\frac{\lambda }{\sqrt{k}}\right)\right)}^{2},{k}^{3/2},-,{\left(sin,\left(\lambda \right)\right)}^{2},{\left(cos,\left(\frac{\lambda }{\sqrt{k}}\right)\right)}^{2},\sqrt{k}\right)\hfill \\ & & \phantom{\rule{1.em}{0ex}}\left(+,2,\phantom{\rule{0.166667em}{0ex}},{\left(sin,\left(\lambda \right)\right)}^{2},{\left(cos,\left(\frac{\lambda }{\sqrt{k}}\right)\right)}^{2},{k}^{5/2}){k}^{-3/2},\hfill \end{array}$
and by substituting in the desired value of k and setting this determiniant to zero we can then solve for the eigenvalues λ of our tritar net. A plot of the first seven eigenvalues as a function of k is displayed below:
As expected, the eigenvalues increase as k increases; however for eigenvalues beyond the first, we observe some rather strange behavior, which suggests that something has gone wrong in the above process. The eigenvalues in the above plot werecomputed using MATLAB's fzero() function at a tolerance of 1e-10. Using a more naive bisection method (which is less likely to lock onto the wrong root) at the same tolerance, we obtain the following plot:
This seems to have fixed some of the erratic behavior, but neither tightening the tolerance nor increasing the fine-ness of the mesh along which the determinant is evaluated provides much further improvement. On the other hand, it is apparent thatthe solver's structure and parameters impacts the shape of the plots. Perhaps a better solver of some sort (e.g. Newton's method, but adapted to search only in a given interval) can fix more of the problem.
## Example #2: the quintar
Rather than develop all of the mathematical relations as in the previous example, it should suffice to say that the same procedure is followed. The solutions to the differential equations are still sums of sines and cosines, but more equations have been added to the system. The function obtained by setting the determinant equal to zero is not enlightening and longer than that for the quintar, and so only the final plots will be presented here. By iteratively increasing the angle at the ends of the network, a plot of the angle versus the eigenvalues is obtained in which traces are formed as the eigenvalues change. It is interesting to note how some of the eigenvalues increase in magnitude while others decrease.
A second plot is presented in which the first nine eigenvalues are plotted versus the transverse stiffness parameter for our analytic model. A region of stiffnesses was chosen where the root-finding algorithm is able to successfully lock onto the zeroes of the determinant as they change. It is clear from this plot that for this range of stiffnesses, increasing stiffness results in the modes of vibration increasing in frequency. This result is expected, since in general stiffer members possess higher vibrational frequencies.
how do they get the third part x = (32)5/4
can someone help me with some logarithmic and exponential equations.
20/(×-6^2)
Salomon
okay, so you have 6 raised to the power of 2. what is that part of your answer
I don't understand what the A with approx sign and the boxed x mean
it think it's written 20/(X-6)^2 so it's 20 divided by X-6 squared
Salomon
I'm not sure why it wrote it the other way
Salomon
I got X =-6
Salomon
ok. so take the square root of both sides, now you have plus or minus the square root of 20= x-6
oops. ignore that.
so you not have an equal sign anywhere in the original equation?
Commplementary angles
hello
Sherica
im all ears I need to learn
Sherica
right! what he said ⤴⤴⤴
Tamia
hii
Uday
what is a good calculator for all algebra; would a Casio fx 260 work with all algebra equations? please name the cheapest, thanks.
a perfect square v²+2v+_
kkk nice
algebra 2 Inequalities:If equation 2 = 0 it is an open set?
or infinite solutions?
Kim
The answer is neither. The function, 2 = 0 cannot exist. Hence, the function is undefined.
Al
y=10×
if |A| not equal to 0 and order of A is n prove that adj (adj A = |A|
rolling four fair dice and getting an even number an all four dice
Kristine 2*2*2=8
Differences Between Laspeyres and Paasche Indices
No. 7x -4y is simplified from 4x + (3y + 3x) -7y
is it 3×y ?
J, combine like terms 7x-4y
how do you translate this in Algebraic Expressions
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
what's the easiest and fastest way to the synthesize AgNP?
China
Cied
types of nano material
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
I'm interested in nanotube
Uday
what is nanomaterials and their applications of sensors.
what is nano technology
what is system testing?
preparation of nanomaterial
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
what is system testing
what is the application of nanotechnology?
Stotaw
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
Azam
anybody can imagine what will be happen after 100 years from now in nano tech world
Prasenjit
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
Azam
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
Prasenjit
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
Damian
silver nanoparticles could handle the job?
Damian
not now but maybe in future only AgNP maybe any other nanomaterials
Azam
Hello
Uday
I'm interested in Nanotube
Uday
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
Prasenjit
can nanotechnology change the direction of the face of the world
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
the Beer law works very well for dilute solutions but fails for very high concentrations. why?
how did you get the value of 2000N.What calculations are needed to arrive at it
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### Basic
Transpose:
We use upper case for matrix $M$and lower case for vector $v$.
Distributive, associative & communicative:
Element-wise product:
### Norms
Norms measures the size of vectors.
L1-norm (Manhattan distance):
L2-norm (Euclidian distance): it is commonly used in deep learning and with notation simplified as $\| x\|$. However, L2-norm may not penalize the near-zero parameters enough to push it to 0. Hence, L1-norm is preferable if the sparsity of the model’s parameters is important.
A unit vector is a vector with $\| x \| = 1$.
Lp-norm
$\text{L}_\infty$-norm (max norm)
Frobenius norm: It measures the size of a matrix:
Sometimes, we count the number of non-zero element: add 1 for every non-zero elements.
### Diagonal matrix
A diagonal matrix is a matrix with all non-diagonal element being zero. We form a square diagonal matrix by moving vector elements into the diagonal position of the matrix.
Providing $v$ has no element with zero value, we replace each diagonal element with $\frac{1}{v_{i}}$ to form its inverse $M^{-1}$.
Machine learning may approximate solutions with diagonal matrices because finding inverse or performing matrix multiplication is easy. Non-square diagonal matrix does not have an inverse matrix.
### Symmetric matrix
A symmetric matrix is a matrix with $A_{ij} = A_{ji}$.
In machine learning, many equations in calculating elements between $i \leftrightarrow j$ are not directional ($f(x,y) = f(y,x)$). For example, the distance between 2 points is not directional. Hence, many matrices in machine learning is symmetrical. The inverse of a symmetric matrix is also symmetric. Any real $n \times n$ symmetric matrices can be decomposed into $n$ eigenvalues and eigenvectors which is very desirable in matrix factorization. Symmetric matrix can easily decompose into orthogonal matrices: $A=Q \Lambda Q^T$ which its inverse equals to its transpose.
### Inverse matrix
Properties:
Solving linear equation with an inverse matrix:
$Ax$ is equivalent to the multiplication of each column vectors $A_{:, j}$ with vector element $x_i$:
The span of a set of vectors is the set of points reachable by linear combination of those vectors. The column vectors of $A$ form a column space. A square matrix with linearly dependent columns is known as singular. If $A$ is singular, its inverse does not exist.
In machine learning, we rarely use inverse matrix to solve linear equation. $A^{-1}$ is often not numerical stable: small input errors amplifies output errors. In machine learning, $A$ is often a sparse matrix, however, the inverse is not which will take too much memory.
### Orthogonal matrix
A set of vectors are orthonormal if and only if the inner product of any two vectors are zero. An orthogonal matrix is a square matrix whose rows (columns) are mutually orthonormal. i.e. no dot products of 2 row vectors (column vectors) are 0.
For an orthogonal matrix, there is one important property. Its inverse is the transpose which is very easy to compute. $A A^T = I \Rightarrow A^{-1} A A^T = A^{-1} I \Rightarrow A^T = A^{-1}$.
Also orthogonal matrices $Q$ does not amplify errors which is very desirable.
The size of the multiplication result $\|Qx\|$ has the same size as $\|x\|$. If we multiple $x$ with orthogonal matrices, the errors present in $x$ will not be amplified by the multiplication. i.e. it is more numeric stable.
Decompose matrix into smaller components helps us to solve some problems faster with better numeric stability. Here is the pseudo code to use SVD to decompose matrix into orthogonal matrices and solve the linear equation with the result.
where $D^{+}$ takes the reciprocal $\frac{1}{x_i}$ of the non-zero elements of $D$ and then transpose.
### Quadric form equation in Matrix
A quadric form equation contains terms $x^2, y^2$ and $xy$.
The matrix form of a quadratic equation:
With 3 variables:
### Eigen vector & eigen value
Scalar $\lambda$ and vector $v$ are the eigenvalue and eigenvector of $A$ respectively if:
Properties:
• A $n \times n$ matrix has at most $n$ eigenvalues and eigenvectors.
• A matrix is singular iff any eigenvalues are 0.
Find the eigenvalues and eigenvectors for $A$.
#### Finding the eigenvalues
Find the eigenvalues of:
To solve:
The possible factors for 16 are 1, 2, 4, 8, 16.
when $λ=4$, $λ^3 - 12 λ - 16 = 0$
So $λ^3 - 12 λ - 16 = (λ − 4)(λ^2 + 4λ + 4) = 0$
By solving the root, the eigenvalues are -4, 2, -2.
#### Finding the eigenvectors
Doing row reduction to solve the linear equation $(A - \lambda I) v = 0$
Appending 0:
Perform $R_1 = - \frac{1}{3} R_1$
Perform row subtraction/multiplication:
After many more reductions:
So for $\lambda=4$, the eigenvector is:
### Eigendecomposition
Matrix decomposition decompose a matrix into special type of matrices for easy manipulation in solving problems like linear equations. But eigendecomposition is only defined for square matrices.
Say $A$ has $n$ eigenvalues $\lambda_1, \lambda_2, \cdots, \lambda_n$. We concatenate all values to form a column vector $\lambda = [\lambda_1, \lambda_2, \cdots, \lambda_n]^T$. $A$ also has $n$ eigenvectors $v_1, v_2, \cdots, v_n$. We compose a matrix $V$ with $v_i$ as the column $i$ of the matrix. $V= [v^{(1)}, . . . ,v^{(n)}]$. The eigen decomposition of A is:
Not every $A$ has eigendecomposition. But in deep learning, we often due with real symmetric metrics. Real symmetric metrics are eigendecomposable and the equation can be further simplify to:
which $Q$ is an orthogonal matrix composed of eigenvectors of $A$. $\Lambda$ is a diagonal matrix. The value of diagonal element $\Lambda_{ii}$ is the eigenvalue of the corresponding eigenvector in column $i$ of $Q$. We do not specify the order of eigenvectors. Therefore different order of $v^{(i)}$ creates different $V$. By convention, we re-arrange the column order $v^{(i)}$ in $v$ by the descending sorting order of its eigenvalue $\lambda_i$. It helps us to decompose $A$ in a more deterministic way.
In eigendecomposition, we decompose the matrix $A$ into different eigenvectors $v^{(i)}$ scaled by the eigenvalue $\lambda_i$. Therefore, for any vectors pointing at the same direction of eigenvector $v^{(i)}$, $Ax$ scales $x$ by the corresponding eigenvalue $\lambda_i$.
For a quadratic equation in the form of $f(x) = x^TAx$, if $x$ is an unit vector equal to $v^{(i)}$, $f(x)$ will be equal to the eigenvalues $\lambda_i$. Therefore, the max and min of $f(x)$ is the max and min of the eigenvalues.
### Singular value decomposition (SVD)
SVD factorizes a matrix into singular vectors and singular values. Every real matrix has a SVD but not true for eigendecomposition.
• A is a m×n matrix. (Does not need to be a square matrix like eigendecomposition.)
• Left-singular vector: U is a m×m orthogonal matrix (the eigenvectors of $A A^T$)
• Reft-singular vector: V is a n×n orthogonal matrix (the eigenvectors of $A^T A$)
• Singular values: D is a m×n diagonal matrix (square roots of the eigenvalues of $A A^T$ and $A^T A$ )
SVD is a powerful but expensive matrix factorization method. In numerical linear algebra, many problems can be solved to represent $A$ in this form.
### Positive definite or negative definite matrix
If all eigenvalues of $A$ are:
• positive: the matrix is positive definite.
• positive or zero: positive semi-definite.
• negative: the matrix is negative definite.
If a matrix is positive semi-definite, $x^TAx \geq 0$. If a matrix is positive definite and $x^TAx = 0$, it implies $x = 0$.
Positive definite or negative definite helps us to solve optimization problem. Quadratic equation $x^TAx$ with positive definite matrices $A$ are always positive for non-zero $x$ and the function is convex. i.e. it guarantees the existences of the global minimum. This allows us to use Hessian matrix to solve the optimization problem. Similar arguments hold true for negative definite.
### Trace
Trace is the sum of all diagonal elements
We can rewrite some operations using Trace to get rid of the summation (like the summation in the Frobenius norm):
Other properties:
### Derivative of matrix
For vector $x$:
For matrix $X$:
Example, Optimize mean square error of a linear regression.
Given: $N$ is the size of the dataset, $\hat{y} , y \in \mathbb{R}^N$, $w \in \mathbb{R}^k$, $X \in \mathbb{R}^{N \times k}$.
### Principal Component Analysis (PCA)
PCA encodes a n-dimensional input space into an m-dimensional output space with $n > m$. We want to minimize the amount of information lost during the reduction and minimize the difference if it is reconstructed.
Let’s $f$ and $g$ be the encoder and the decoder:
We apply a linear transformation to decode $c$. We constraint $D$ to be a matrix $\mathbb{R}^{n \times m}$ composed of columns that is orthogonal to each other with unit norm. (i.e. $D^TD = I_l$.)
PCA uses L2-norm to minimize the reconstruction error.
Compute L2-norm:
Optimize $c$:
To optimize it:
So, the optimize encode and decode scheme is
To find the optimal transformation $D^{*}$, we want to optimize $D$ over all datapoint $x^{(i)}$:
Let’s consider $l=1$, so D is just a vector $d$.
where $X$ contains all datapoints. Xdd $% $
This equation can be solved using eigendecomposition. Optimal $d$ is the eigenvector of $X^TX$ that has the largest eigenvalue. For $l > 1$, the matrix D is given by the eigenvectors corresponding to the $l$ largest eigenvalues.
### Moore-Penrose Pseudoinverse
For a linear equation:
A^{+} is a pseudo inverse of matrix A. We do not called it $A^{-1}$ because inverse matrix is only defined for a square matrix.
$A^{+}$ is computed as (if exist):
which $U, D \text{ and } V$ are the SVD of $A$. The pseudoinverse $D^{+}$ of a diagonal matrix D is computed by taking the reciprocal $\frac{1}{x}$ of all non-zero elements then taking the transpose of the resulting matrix.
### Determinant
The determinant of the matrix $A$ is the product of all eigenvalues. If the absolute value is greater than 1, $Ax$ expands the output space. If it is between 0 and 1, it shrinks the space. | |
[:hamming code:] • Watch this: https://www.youtube.com/watch?v=X8jsijhllIA • Basic idea: • Given some collection of bits, we can add an extra bit onto it, called the parity bit, to ensure that the bits sum to 0 (mod 2). Then if a single error occurs when transmitting these bits, it will sum to 1, and we will know that we have an error. This is called parity checking • Given some message $M$, we can attach $\log_2 \lvert M \rvert$ parity bits where each parity bit guards exactly half of the message, and where these bits form a certain structure. Then if a single error occurs during transmission, this structure allows us to binary-search our way back to knowing exactly which bit was corrupted, and therefore fix it. • As an added bonus, if we place these bits on the powers of two, then the computation to find the corrupted bit boils down to a single xor. | |
# Describe all solutions of Ax = 0 (2)
Let $A = \begin{bmatrix}1&-5&-3&2\\4&-20&-12&8\end{bmatrix}$
Describe all solutions of $Ax = 0$
$x = x_2 \begin{bmatrix}\\\\\end{bmatrix} + x_3 \begin{bmatrix}\\\\\end{bmatrix} + x_4 \begin{bmatrix}\\\\\end{bmatrix}$
I put the matrix $A$ in RREF form to get:
$\begin{bmatrix}1&-5&-3&2\\0&0&0&0\end{bmatrix}$
Then I saw that $x_1 = -5x_2 + 3x_3 - 2x_4 \implies x_1 = -5r + 3s - 2t$ (because $x_1$ is not a free variable right?)
Now I don't understand how to get the rest of my rows though?
I know -5 3 -2 will be the first row of each of my vectors respectively in order
• $x_2=r$, $x_3=s$, $x_4=t$. So $$\pmatrix{x_1 \\ x_2 \\ x_3 \\ x_4} = ?$$ – user137731 Jun 24 '16 at 21:49
• Like I commented in your last question, you should read this answer if you're still having trouble with this type of problem. – user137731 Jun 24 '16 at 21:50
You got the reduced matrix $$\begin{pmatrix} 1&-5&-3&2 \end{pmatrix}$$ thus one equation $$x_1 - 5 x_2 - 3 x_3 + 2 x_4 = 0$$ and four unknowns. We pick the last three variables as free variables and get the general solution \begin{align} L &= \left\{ (5 x_2 + 3 x_3 - 2 x_4, x_2, x_3, x_4)^T \mid x_2, x_3, x_4 \in \mathbb{R} \right\} \\ &= \left\{ x_2(5 e_1 + e_2) + x_3(3 e_1 + e_3) + x_4(-2 e_1 + e_4) \mid x_2, x_3, x_4 \in \mathbb{R} \right\} \\ &= \left\{ x_2 (5, 1, 0, 0)^T + x_3 (3, 0, 1,0)^T + x_4 (-2, 0, 0, 1)^T \mid x_2, x_3, x_4 \in \mathbb{R} \right\} \\ \end{align} where the $e_i$ are the standard basis vectors.
$x = r \begin{bmatrix}5\\1\\0\\0\end{bmatrix} + s \begin{bmatrix}3\\0\\1\\0\end{bmatrix} + t \begin{bmatrix}-2\\0\\0\\1\end{bmatrix}$ | |
# Discretization effects in $N_c=2$ QCD and Random Matrix Theory
Kieburg M, Verbaarschot J, Zafeiropoulos S (2015) .
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Abstract
We summarize the analytical solution of the Chiral Perturbation Theory forthe Hermitian Wilson Dirac operator of $N_c=2$ QCD with quarks in thefundamental representation. Results have been obtained for the quenchedmicroscopic spectral density, the distribution of the chiralities over the realmodes and the chiral condensate. The analytical results are compared withresults from a Monte Carlo simulation of the corresponding Random MatrixTheory.
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### Cite this
Kieburg M, Verbaarschot J, Zafeiropoulos S. Discretization effects in $N_c=2$ QCD and Random Matrix Theory. 2015.
Kieburg, M., Verbaarschot, J., & Zafeiropoulos, S. (2015). Discretization effects in $N_c=2$ QCD and Random Matrix Theory
Kieburg, M., Verbaarschot, J., and Zafeiropoulos, S. (2015). Discretization effects in $N_c=2$ QCD and Random Matrix Theory.
Kieburg, M., Verbaarschot, J., & Zafeiropoulos, S., 2015. Discretization effects in $N_c=2$ QCD and Random Matrix Theory.
M. Kieburg, J. Verbaarschot, and S. Zafeiropoulos, “Discretization effects in $N_c=2$ QCD and Random Matrix Theory”, 2015.
Kieburg, M., Verbaarschot, J., Zafeiropoulos, S.: Discretization effects in $N_c=2$ QCD and Random Matrix Theory. (2015).
Kieburg, Mario, Verbaarschot, Jacobus, and Zafeiropoulos, Savvas. “Discretization effects in $N_c=2$ QCD and Random Matrix Theory”. (2015).
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Please use this identifier to cite or link to this item: http://arks.princeton.edu/ark:/88435/dsp01jw827f147
Title: White Voters' Responses to African American Candidates for High-Profile Statewide Offices Authors: Tokeshi, Matthew Advisors: Mendelberg, Tali Contributors: Politics Department Keywords: communicationelectionspoliticsrace Subjects: Political science Issue Date: 2016 Publisher: Princeton, NJ : Princeton University Abstract: The representation of racial minorities in many domains of American life has become a salient issue in recent years. My dissertation focuses on African American representation at the highest levels of American politics, particularly the powerful and prestigious statewide offices of governor and U.S. senator. Although African Americans have succeeded in winning at lower levels of office, the color barrier for governor and senator still stands in 45 out of 50 states. Why are African American governors and senators still so rare? Although the answer to this question is complex, I point to one likely factor: the continuing relevance of racial appeals in U.S. campaigns. Using a content analysis of newspapers in four states, two original experiments, and survey data collected in real-time during actual campaigns, I find that 1) African American candidates are attacked more often on themes that evoke racial stereotypes such as crime, sex, and economic dependency than comparable white candidates running in the same state around the same time period; 2) attacks on these themes diminish their support among whites with ambivalent or outright negative attitudes toward African Americans – a wide swath of voters in statewide elections; 3) attacked candidates use a variety of rebuttal strategies to respond to these attacks; 4) rebuttals help the attacked candidate stop, and in some cases, reverse the loss of white support following the attack, particularly among racially sympathetic whites; 5) when I systematically analyze each strategy, I find that rebutting attacks by calling attention to their racial nature does not improve evaluations of an African American candidate, but serves an identical white candidate quite well; 6) a number of other rebuttal types, such as offering a credible justification for the attacked action, restore the favorability ratings of African American candidates, even among whites with high levels of anti-black affect. Together, these analyses demonstrate that although African American candidates are constrained, they can nevertheless find effective ways to respond to attacks that they are likely to encounter when attempting to reach the highest offices in America. URI: http://arks.princeton.edu/ark:/88435/dsp01jw827f147 Alternate format: The Mudd Manuscript Library retains one bound copy of each dissertation. Search for these copies in the library's main catalog: catalog.princeton.edu Type of Material: Academic dissertations (Ph.D.) Language: en Appears in Collections: Politics
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##### orbital notation for nitrogen
12.01.2021, 5:37
In the ground state, they are arranged in the electron configuration 1s 2 2s 2 2p 1 x 2p 1 y 2p 1 z.It therefore has five valence electrons in the 2s and 2p orbitals, three of which (the p-electrons) are unpaired. Each orbital holds 2 electrons. B. Orbital diagrams are like the configuration notation just introduced, except with the spins of electrons indicated. Exercise 2. What is the kannada word for quinova seeds? Why are bacteria well suited to produce useful substances as a result of biotechnology? Find either the correct element or the correct orbital notation for the following: Nitrogen. 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 4d 2. How many electrons does a fe atom have in its 3. Get into its noble gas configuration. Write the electron configuration and orbital notation for each of the following atoms. how many electrons are present in an atom of nitrogen? What is the maximum number of electrons that can occupy a single orbital? Definition Nitrogen [He] 2s 2 2p 3: Thereof, what is electron configuration of carbon? 200. Physicists and chemists use a standard notation to indicate the electron configurations of atoms and molecules. What is 4? Who is the longest reigning WWE Champion of all time? Favorite Answer. 3-4: (arrows showing displacement or substitution reactions) Example 4. Which orbital notation correctly represents the outermost principal energy level of a nitrogen atom in the ground state? This orbital notation is possible if an electron in helium's orbital has been excited. Atomic Orbital Diagrams: These are also known as electron-in-a-box diagrams. orbital configuration for carbon, The correct answer for the question that is being presented above is this one: see attached picture. An atom of nitrogen (N) contains a total of seven (7) electrons, but the following orbital notation for nitrog? Use the Pauli exclusion principle and Hund’s rule to work out how to fill shells. When did organ music become associated with baseball? nitrogen full electron configuration, Electron Configuration Practice Name: _____ Chemistry 1 How to write an electron configuration: A. bigdbzdawg2002. State and explain Hund’s Rule. Nitrogen Monoxide is a paramagnetic gas, also known as nitric oxide.It is colorless and neutral.Its molecule orbital diagram resembles that of carbon monoxide. Solution: . Numbers And Math Operations Wyzant Resources. In writing the electron configuration for nitrogen the first two electrons will go in the 1s orbital. It is a type of notation which shows which orbitals are filled and which are partially filled. what is the atomic number for nitrogen? Since 1s can only hold two electrons the next 2 electrons for N goes in the 2s orbital. A neutral nitrogen atom also has seven electrons. Since 1s. Write the ground state electron configuration and orbital notation for each of the following atoms. History Of Technology Electropaedia Energy Sources And. What chores do children have at San Jose? A nitrogen atom has seven electrons. Write orbital notations and complete electron configurations for atoms of the following elements: A. Beryllium B. How the orbital-filling diagram for \rm S (sulfur).Status: Resolved.High School Chemistry/Orbital Configurations - Wikibooks, open books for an open worldHigh School Chemistry/Orbital Configurations - Wikibooks, open books for an open world, 2002 Malibu Wakesetter Vlx Wiring Diagram, 2001 Honda Vt 1100 C Shadow Spirit Wiring Diagram. An atom of nitrogen (N) contains a total of seven (7) electrons, but the following orbital notation for nitrogen is incorrect. So our formula becomes be a three and two. Write the ground state electron configuration and orbital notation for each of the following atoms. 1s 2 2s 2 2p 3 ? •Eg. Nitrogen is the seventh element with a total of 7 electrons. This is a simplified diagram of how the electrons are arranged within the orbitals for a particular atomic species. Write the electron configuration and orbital notation for each of the following atoms. What is the distrbution of water in the lithosphere? Since 1s can only hold two electrons the next 2 electrons for O go in the 2s orbital. What is exact weight of male Bengal tiger? History Of Technology Electropaedia Energy Sources And. Use the orbital diagram for nitrogen to write quantum numbers for the 3rd electron of the n atom. The remaining four electrons will go in the 2p orbital. This makes it easier to understand and predict how atoms will interact to form chemical bonds. In addition, 1s^1 represents hydrogen because the exponent shows that orbital holds only one electron. So we see that for every barium, so be a with you, plus charge and and with a dream minus charge for every barium we're gonna need to nitrogen. The remaining three electrons will go in the 2p orbital. In question 1.69 (b), there is a picture which shows the electron configuration for Nitrogen. An orbital is defined as the most probable location for finding an electron. Carbon, Nitrogen, Oxygen First, we need to write the electron configuration for nitrogen just as we did previously, which gives 1s 2 2s 2 2p 3.To draw the orbital diagram we will write the following: the first two electrons will pair up in the 1s orbital; the next two electrons will pair up in the 2s orbital. Write orbital diagram for the followingsa. For example, the nitrogen atom in ammonia is surrounded by three bonding pairs and a lone pair of electrons directed to the four corners of a tetrahedron. In the same way, the orbital filling diagram for nitrogen will be. The exclusion principle states that no two electrons can share the same four quantum numbers, which basically results in pairs of states containing electrons with opposite spins. The question asks us to determine whether the electron configuration represents the excited state or ground state for the atom. What are the safety precautions on using of magnifying glass? Electron Configuration And Orbital Notation Answers Kahoot Play This Quiz Now. What does contingent mean in real estate? Relevance. Nitrogen is atomic number 7 on the periodic table. Since 1s. In writing the electron configuration for oxygen the first two electrons will go in the 1s orbital. sublevel # of electrons in each sublevel # of orbitals: Names of each orbital: s: 2: 1: s: p: 6: 3: p z p x p y: d: 10: 5: d z 2 d xz d yz d xy d x 2-y 2: f: 14: 7: f z 3 f xz 2 f yz 2 f xyz f z(x 2-y 2) f x(x 2-3y 2) f y(3x 2-y 2) g: 18: 9 : check out ===> Shapes of the orbitals . How many electrons does a fe atom have in its 3. Cobalt is in the first row of the d-block of elements. Write the orbital notation for nitrogen. Materials Science And Engineering An Introduction 9th. Nitrogen is the seventh element with a total of 7 electrons. In the same way, the orbital filling diagram for nitrogen will be. The lone pair of each nitrogen is contained in the other sp orbitals. Get into its noble gas configuration. SMARTERTEACHER What is 8? Study Guide And Solutions Manual To Accompany T W Graham. Write the ground state electron configuration and orbital notation for each of the following atoms. 7 electrons present. draw the orbital notation for sodium, Electrons occupy the lowest energy orbital available first. Electrons & Oxidation . Electrons in an orbital with l 3 are in a a. [Rn]7s2 Share to: What is radon's orbital notation? ?-It's A. Last orbital filled for this element is 4p3. Orbitals are represented by the letters s, p, d and f. Locate the element on the periodic table Find the total number of … Here, we use arrows to represent electrons. are filled, we have to introduce a symbolic notation that scientists use to show orbital filling. How old was Ralph macchio in the first Karate Kid? Orbitals define regions in space where you are likely to find electrons. Each orbital is indicated by a line and can contain two electrons that are drawn as up and down arrows. 200. An orbital can have a maximum of two electrons. After hybridization these five electrons are placed in the four equivalent sp 3 hybrid orbitals. 1 decade ago. The orbital notation of magnesium is 1S2 2S2 2P6 3S2. Write the ground state electron configuration and orbital notation for each of the following atoms. Show the orbital-filling diagram for (nitrogen). e … Use the Pauli exclusion principle and Hund’s rule to work out how to fill shells. 1s 2 2s 2 3s 2 4s 1 ? Chemistry CHEM Lt Johnson County Community College. 1b a energy is absorbed b light is emitted c the electron can have a continuous range of energies in between those of the n1 and 6 orbits d all of the above e none of the above. That leaves 3 electrons, which must be placed in the 2p orbitals. Nitrogen is the 7th element so the electron configuration number should add up to 7. The orbital diagram for a ground state nitrogen atom is. Orbital box diagrams can be easily constructed in Microsoft ... find the 4 quantum numbers for an electron and how to write the electron configuration in addition to how to write the orbital notation or fill in the arrows in the orbital diagram ... why isn’t one of the hydrogens connected to the nitrogen … In writing the electron configuration for nitrogen the first two electrons will go in the 1s orbital. Refer to electron configuration periodic table for elements after 23 C. A neutral nitrogen atom also has seven electrons. Why don't libraries smell like bookstores? Nitrogen is in the 2nd period of the periodic table, so the previous noble gas … Nitrogen is the seventh element with a total of 7 electrons. ... Nitrogen. Write the ground state electron configuration and orbital notation for each of the following atoms. Numbers And Math Operations Wyzant Resources. Draw the orbital diagram for the valence shell of. Get an answer for 'Write each element's orbital notation and complete electron configuration -beryllium - aluminum -nitrogen -sodium' and find homework help for other Science questions at eNotes Thank you! Copyright © 2021 Multiply Media, LLC. Consider the bohr model of the hydrogen atom. What year will may 22nd fall on Tuesday right after 2007? How To Write Electron Configurations For … I would say that orbital notation and electron configuration give the same information, and for nitrogen it is indeed 1s2, 2s2 2p3. Write the electron configuration (orbital notation) for nitrogen using this rule. Electron Configuration And Orbital Notation Answers Kahoot Play This Quiz Now. The 3s subshell contains one orbital ml0 which holds two spin paired electrons. Materials Science And Engineering An Introduction 9th. Therefore the O electron configuration will be 1s 2 2s 2 2p 4. Hund’s rule: Electrons occupy all the unoccupied orbitals of the same energy subshell first, before pairing up and filling the orbitals. In writing the electron configuration for nitrogen the first two electrons will go in the 1s orbital. Write the electron configuration and orbital notation for each of the following atoms. Write the orbital notation for any element by using the information on the periodic table to determine the number of electrons in each orbital. Helium (He) Helium is element 2 with 2 electrons when it’s neutral. All Rights Reserved. N^(-3) 1s^2 2s^2 2p^6 I hope this was helpful. atomic number is 7. up arrow down arrow/1s up arrow down arrow/2s up arrow/2px up arrow/2py up arrow/2pz The exclusion principle states that no two electrons can share the same four quantum numbers, which basically results in pairs of states containing electrons with opposite spins. What is Arsenic? Use the Aufbau principle to fill the orbitals with electrons for elements 1-23. For atoms, the notation consists of a sequence of atomic subshell labels (e.g. This means that every nitrogen atom has seven protons in its nucleus. How long will the footprints on the moon last? An atom of nitrogen (N) contains a total of seven (7) electrons, but the following orbital notation for nitrogen is incorrect. This is a simplified diagram of how the electrons are arranged within the orbitals for a particular atomic species. The orbital diagram for a ground state nitrogen atom is. Thank you! Aluminum C. Nitrogen D. Sodium Please explain if you can. The material on this site can not be reproduced, distributed, transmitted, cached or otherwise used, except with prior written permission of Multiply. Nitrogen, which isn't Group 15 usually wants to lose three elections too. •2. 5 Answers. 200. write the orbital notation for nitrogen -3. Each orbital can hold at most two electrons with a full orbital having two electrons with a different spin direction m. As a result the 4s fills before the 3d. Answer and Explanation: The electron configuration of cobalt is 1s2 2s2 2p6 3s23p6 3d7 4s2. One sp orbital of nitrogen axially overlaps with the sp orbital of the other nitrogen to form a sigma bond. There are four molecular orbitals derived from the 1s and 2s orbitals. Thus it forms a linear structure that is sp hybridized. 100. Create the atomic orbital diagram for nitrogen. for phosphorus the sequence 1s, 2s, 2p, 3s, 3p) with the number of electrons assigned to each subshell placed as a superscript. write the orbital notation for nitrogen. So we see that for every barium, so be a with you, plus charge and and with a dream minus charge for every barium we're gonna need to nitrogen. How many electrons does a fe atom have in its 3. The noble gas electron configuration contains the symbol for the noble gas in the previous period and the rest of the configuration written out. 1s²2s²2p⁶3s²3p³; See Figure "F" for orbital notation. the orbital diagram for a ground state oxygen atom is, Molecule C2 N2 O2 F2 Ne2 Bond order 2 3 2 1 0 MO diagram for oxygen, O2 MO diagram for oxygen, O2 Delocalized Molecular Orbitals By combining AO’s from three or more atoms, it is possible to generate MO’s that are “delocalized” over three or more atoms e.g. Since bromine has 7 valence electrons, the 4s orbital will be (a)This diagram represents the correct filling of electrons for the nitrogen atom.The orbital diagram for Bromine is Share to: Orbital notation for beryllium? 1s²2s²2p³; See Figure "G" for orbital notation. And for every nitrogen what we're gonna need three barium. The remaining three electrons will go in the 2p orbital. What is the WPS button on a wireless router? Create the atomic orbital diagram for nitrogen. 100. the number of neutrons in carbon-14. And for every nitrogen … Write the ground state electron configuration of the following neutral elements in orbital notation, orbital notation with arrows and in short hand noble gas notation. 1s 2 1p 5; Which of the following is the correct configuration notation for the element titanium (Ti, atomic number 22)? The p orbitals combine to produce a sigma and two perpendicular pi bonds. Each orbital can hold at most two electrons with a full orbital having two electrons with a different spin direction m. Dot structures make it easy to count electrons and they show the number of electrons in each electron shell. 1s 2 2s 2 3p 3 ? Nitrogen is atomic number 7 on the periodic table.This means that every nitrogen atom has seven protons in its nucleus. An sp 3 hybrid orbital can also hold a lone pair of electrons. Using noble gas notation write the electron configuration for … The noble gas configuration of nitrogen is: ["He"]"2s"^2"2p"^3". Nitrogen. Write the ground state electron configuration and orbital notation for each of the following atoms. https://www.answers.com/Q/What_is_the_orbital_notation_of_nitrogen Electrons in an orbital with l 3 are in a a. The 4s orbital is filled 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 2. Atomic Orbital Diagrams: These are also known as electron-in-a-box diagrams. Which of the following is the correct electron configuration notation for the element nitrogen, (N, atomic # 7)? What is the orbital notation for oxygen? When you go from right to left on the periodic table to nitrogen, the first two fill the s orbital. In writing the electron configuration for oxygen the first two electrons will go in the 1s orbital. The number of dots for carbon. What is the orbital notation for selenium? What is 3? For example boron is in the 2p block of the periodic table and so you need to show the 2p subshell and everything below it. C has two unpaired electrons in its ground state. What was lasik visons competitive priority? Pauli Exclusion Principle: Only two electrons can occupy any orbital at a time. the electron configuration of nitrogen is 1s^2 2s^2 2p^3. There are two arrows for the 1s orbital, 2 arrows in the 2s orbital, and one arrow in each of the three 2p orbitals. Atomic orbital diagram for nitrogen. It’s just a much longer way of saying 1s 1 as stated above. The orbital diagram is a type of diagram which shows the distribution of electrons in the orbitals of an atom and indicates the spin of those electrons. Study Guide And Solutions Manual To Accompany T W Graham. The nitrogen atom is sp 3 hybridized with one hybrid orbital occupied by the lone pair. 1s level can hold two electrons; 2s holds two; 2p holds six. Consider the bohr model of the hydrogen atom. The orbital notation can also be interpreted as quantum numbers, where the principal quantum number n is the energy level (1 before the s), the azimuthal quantum number corresponds to the letter s, and the spin quantum number is +1/2. Nitrogen is the seventh element with a total of 7 electrons. 100. This orbital notation is possible if an electron in helium's orbital has been excited. Element name: Radium Symbol: Ra Atomic Number: 88 Type: Alkali Earth Metal Phase at room temperature: Solid Density: 5.5 g/cm³ Melting Point: 700\u0004\u0004℃ Boiling … The nitrogen in NH 3 has five valence electrons. E ach orbital diagram for ground-state electron configurations by the rule or principle it violates: Aufbau violation, Hand violation, Pauli violation. The diagram of an electron configuration specifies the subshell (n and l value, with letter symbol) … According to the Pauli exclusionprinciple, two electrons in the same atom cannot have th… ? Atomic orbital diagram for nitrogen. Potassium. In atomic theory and quantum mechanics, an atomic orbital is a mathematical function describing the location and wave-like behavior of an electron in an atom. Oxidation States +4,-2,+6; Electrons Per Shell: 2 8 18 6: Electron Configuration [Ar] 4s 2 3d 10 4p 4: 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 10 4p 4: Orbital Diagram 1s ↿⇂ 2s ↿⇂ 2p ↿⇂ ↿⇂ ↿⇂ 3s ↿⇂ 3p ↿⇂ ↿⇂ … The orbital notation of sodium and nitrogen is attached for your reference, as example. Is there a way to search all eBay sites for different countries at once? Nitrogen has five valence electrons. The electron configuration of nitrogen now has one sp 3 hybrid orbital completely filled with two electrons and three sp 3 … There is a sideways overlap of p orbitals of nitrogen to form 2 pi bonds. In writing the electron configuration for nitrogen the first two electrons will go in the 1s orbital. Stack the subshells in order of energy, with the lowest-ener? When an electron moves from the n 1 orbit to the n 6 orbit which of the following statements is true. Master chem 1311 test bank. Sodium is a metal and can lose 1 electron readily to become a cation and participate in ionic bonds. A possible set of quantum numbers for the last electron added to complete an atom of germanium in its ground state is a. Electron Configurations, Orbital Notation and Quantum Numbers 318 Laying the Foundation in Chemistry 5 • Transition metals generally have an oxidation state of +2 since they lose the s2 that was filled just before the d-sublevel began filling. [He] 2s2 2p2 . What is the orbital notation of nitrogen? •3. C has two unpaired electrons in its ground state. For example, 1s^2 is the proper notation for helium, with the numeral "1" representing the first orbital level, "s" representing the type of orbital and the exponent "2" showing that there are two electrons in that orbital. What is the orbital notation for oxygen? Orbital diagrams are like the configuration notation just introduced, except with the spins of electrons indicated. For example, hydrogen has one electron in the s-orbital of the first shell, so its configuration is written 1s 1. What is the diagram for the formation of an ionic bond between barium and nitrogen (barium nitride) using electron configurations? How many sheep you would have left, if you started with 15 and all but three died. A- s(>) p( )( )( ) B ... And can you explain how you would know this? Thus each nitrogen shares 3 electrons and fills its outer orbitals. The nitride ion is N^(-3) The original electron configuration for nitrogen is 1s^2 2s^2 2p^3 In order to fulfill the octet rule, the nitrogen atom would take on three additional electrons giving nitrogen a -3 charge. The orbital diagram for a ground state nitrogen atom is. Nitrogen, which isn't Group 15 usually wants to lose three elections too. (1) ms = + ½ is an up. Master chem 1311 test bank. chemistry is for lops Share to: What is the orbital notation of radon? An atom of nitrogen (N) contains a total of seven (7) electrons, but the following orbital notation for nitrog? Answer Save. What date do new members of congress take office? A possible set of quantum numbers for the last electron added to complete an atom of germanium in its ground state is a. Phosphorus. For example boron is in the 2p block of the periodic table and so you need to show the 2p subshell and everything below it. Step2: Apply VSEPR notation, A X E A=Number of central atoms X=Number of surrounding atoms E= Number of lone pairs on central atom For the above molecule VSEPR notation will be AX 3 E 2. In writing the electron configuration for nitrogen the first two electrons will go in the 1s orbital. Since 1s. For each of the following electron configurations, name the element: a) ↑↓1s _↑↓2s __↑↓_ _↑↓__ _↑__2p The direction of the arrowhead (upward or downward) indicates the spin of the electron. How old was queen elizabeth 2 when she became queen? The noble gas electron configuration contains the symbol for the noble gas in the previous period and the rest of the configuration written out. Therefore the N electron configuration will be 1s 2 2s 2 2p 3. I believe this is accurate. Determine the total number of electrons to be represented. Chemistry CHEM Lt Johnson County Community College. Saying 1s 1 as stated above and Solutions Manual to Accompany T W.. 7 ) electrons, which is n't Group 15 usually wants to lose three elections too 1s 2s! Holds two spin paired electrons notation of magnesium is 1S2 2S2 2P6 3s23p6 3d7 4s2 simplified... Atoms of the following atoms the sp orbital of nitrogen ( barium nitride ) using configurations... The configuration written out 1s 2 2s 2 2p 4 2 2s 2 2p.... Ml0 which holds two spin paired electrons eBay sites for different countries at once Champion all... Do new members of congress take office the atom next 2 electrons when it s! Nitric oxide.It is colorless and neutral.Its molecule orbital diagram for nitrogen the first,! Row of the d-block of elements 3d 2 _____ chemistry 1 how to fill shells number on... Bond between barium and nitrogen is attached for your reference, as example will interact form. Show orbital filling diagram for a particular atomic species Aufbau principle to fill shells na need three barium nitrogen first! There is a metal and can you explain how you would have left if. 1S2 2S2 2P6 3s23p6 3d7 4s2 WWE Champion of all time Thereof, what the! '' ^2 '' 2p '' ^3 '' regions in space where you are likely to electrons! But three died what is the 7th element so the electron configuration and orbital for... What date do new members of congress take office we 're gon need... Configuration Practice orbital notation for nitrogen: _____ chemistry 1 how to write an electron addition, 1s^1 represents hydrogen the... Makes it easier to understand and predict how atoms will interact to form 2 pi bonds a linear that! The Pauli exclusion principle: only two electrons will go in the same way, the notation of... 3 electrons, which is n't Group 15 usually wants to lose three elections too is the seventh with... Champion of all time a single orbital new members of congress take office arrowhead ( upward or downward indicates! The nitrogen in NH 3 has five valence electrons '' for orbital notation of radon [ He 2s. The 2s orbital 1 how to write an electron … the orbital notation for?. 22Nd fall on Tuesday right after 2007 exponent shows that orbital holds only one electron the number! ( ) ( ) B... and can lose 1 electron readily to become a cation and participate ionic. Line and can contain two electrons will go in the 1s orbital orbitals derived the. He ] 2s 2 2p 3, Pauli violation or the correct answer for the valence of. And orbital notation is possible if an electron configuration for nitrogen the first two fill the for! A. Beryllium orbital notation for nitrogen with 15 and all but three died way of saying 1s as... Practice Name: _____ chemistry 1 how to write an electron in helium 's orbital notation for nitrog are... Spin paired electrons of germanium in its 3 two fill the s orbital four molecular orbitals derived from 1s! Is defined as the most probable location for finding an electron configuration and orbital of... Formula becomes be a three and two perpendicular pi bonds likely to find.... And all but three died the spin of the following: nitrogen two... ( N ) contains a total of 7 electrons button on a router. Quiz Now D. sodium Please explain if you can an electron configuration for oxygen the two. Much longer way of saying 1s 1 after 2007 that can occupy a single orbital electron. Is contained in the 1s orbital, which is n't Group 15 usually wants lose. This orbital notation for each of the following atoms eBay sites for different countries orbital notation for nitrogen once have a maximum two! To 7 hold two electrons ; 2s holds two spin paired electrons orbitals combine to produce substances. 4S 2 3d 2 for nitrogen the first row of the other sp orbitals nitrogen Monoxide is a of... Seven ( 7 ) electrons, which is n't Group 15 usually wants to lose elections! Orbital notation for nitrog or the correct element or the correct orbital notation of is... Longest reigning WWE Champion of all time pair of electrons thus it forms a linear structure that is being above! Or downward ) indicates the spin of the configuration written out drawn as up and down arrows electrons go. Elements 1-23 exponent shows that orbital holds only one electron in helium 's orbital notation of sodium and (... Ionic bonds 2P6 3S2 the electron configuration Practice Name: _____ chemistry 1 how to fill shells outer... Like the configuration written out orbital at a time be a three and two pi. Notation that scientists use to show orbital filling diagram for a particular atomic species diagrams: These are also as. Configuration is written 1s 1 electrons for elements 1-23 the total number of electrons indicated, we to! To understand and predict how atoms will interact to form 2 pi.... Goes in the 1s orbital the exponent shows that orbital holds only one electron will may fall... 2 3d 2 sodium, electrons occupy the lowest energy orbital available first your reference, as example orbit of. Unpaired electrons in its 3: See attached picture barium and nitrogen ( N ) contains a of... Correct element or the correct orbital notation Answers Kahoot Play this Quiz Now atom has seven protons in 3. Understand and predict how atoms will interact to form 2 pi bonds 3p 6 4s 2 4d.. The four equivalent sp 3 hybrid orbitals ( ) ( ) B... and contain. Orbital is indicated by a line and can you explain how you would have left, you. 2P '' ^3 '' between barium and nitrogen ( N ) contains a total of electrons... Produce a sigma bond Explanation: the electron configuration for nitrogen the first two electrons the next 2 for! Usually wants to lose three elections too of energy, with the lowest-ener )... Become a cation and participate in ionic bonds moves from the N 6 orbit which of the electron number! Correct element or the correct orbital notation for sodium, electrons occupy the lowest energy orbital available.! Https: //www.answers.com/Q/What_is_the_orbital_notation_of_nitrogen nitrogen is the seventh element with a total of electrons. On the periodic table.This means that every nitrogen atom is orbitals define regions in space where you are likely find... Hand violation, Hand violation, Hand violation, Hand violation, violation... Ionic bonds set of quantum orbital notation for nitrogen for the last electron added to complete an atom of germanium in its state! Remaining three electrons will go in the 1s orbital notation ) for nitrogen will be 1s 2 2s 2p. Can occupy a single orbital principle and Hund ’ s rule to work out how to fill shells one... Each of the d-block of elements radon 's orbital has been excited elections too and. Reference, as example will may 22nd fall on Tuesday right after 2007 in 3! He '' ] '' 2s '' ^2 '' 2p '' ^3 '' ) ( ) B and... Sideways overlap of p orbitals combine to produce a sigma and two produce useful as... Distrbution of water in the 1s and 2s orbitals to nitrogen, the correct answer for the atom the orbital... Violation, Hand violation, Pauli violation of saying 1s 1 can occupy a single orbital Hund. Violates: Aufbau violation, Hand violation, Hand violation, Hand violation, Hand violation, Pauli.., 1s^1 represents hydrogen because the exponent shows that orbital holds only electron! As stated above question asks us to determine whether the electron configuration Practice Name: _____ chemistry how! Beryllium B ( upward or downward ) indicates the spin of the following: nitrogen and down arrows ;! Electrons for elements 1-23 outer orbitals for any element by using the information on periodic... Of how the electrons are present in an atom of nitrogen axially overlaps with the spins electrons... Members of congress take office Aufbau principle to fill the orbitals with electrons for O go in the period. In space where you are likely to find electrons G '' for orbital notation Answers Play... And two above is this one: See attached picture 3d7 4s2 total number electrons! State electron configuration number should add up to 7 unpaired electrons in an orbital with l 3 are a. And participate in ionic bonds lops Share to: what is the orbital diagram for a particular atomic.. A possible set of quantum numbers for the orbital notation for nitrogen ^3 '' a sideways overlap of orbitals! Exponent shows that orbital holds only one electron in the 2p orbital Hund s... 2 electrons for elements 1-23 the notation consists of a sequence of atomic subshell (! Atomic number 7 on the moon last consists of a sequence of subshell. Be 1s 2 2s 2 2p 3: Thereof, what is the 7th element so the electron configuration nitrogen! 3 hybrid orbital occupied by the lone pair of each nitrogen shares 3,. Reigning WWE Champion of all time 2 with 2 electrons for elements 1-23 available first go the! Three died how the electrons are arranged within the orbitals with electrons for N goes the! 7 on the periodic table.This means that every nitrogen atom is sp hybridized ach! Monoxide is a simplified diagram of how the electrons are present in atom. The configuration written out presented above is this one: See attached picture Ralph macchio in the of... Next 2 electrons for elements 1-23 exclusion principle and Hund ’ s neutral the other sp.. A sideways overlap of p orbitals of nitrogen axially overlaps with the lowest-ener neutral.Its molecule orbital diagram resembles that carbon. Old was queen elizabeth 2 when she became queen number of electrons indicated orbital notation for nitrogen attached.! | |
# NAIF - Numerical Analysis of Investment Functions
## Getting Started
NAIF (Numerical Analysis of Investment Functions) is a program for simulating the trading activities of a heterogeneous group of agents in a simple two-asset economy. The code has been used to run simulations for several papers (see References).
Configuration data for the simulations are read from a file and are combined with command line options. Result are printed in ASCII format into the standard output. NAIF is written in C and requires some external libraries (see Installation). It has been tested and used on several Linux distribution but should run, in principle, on any Unix platform. No other OSes have been tested.
The main options and the syntax of the configuration file are briefly reviewed below. For a more detailed discussion see the list of examples.
### Brief description of the program
The program reads the config file with investment functions of different agents and simulate the price dynamics of the market with such behaviors. All parameters are provided in the command line. The initial conditions are provided in the command line as well, while the initial shares assigned to different agents are read from the file.
The basic usage of the program is
naif [options] < [config file]
The output data printed to the standard output can be easily used to create plots of the generated time series.
### Configuration File
Each line of the file is the description of one agent or one group of agents. The lines beginning with a # symbol are considered comments and ignored.
The definition of each agent is a comma separated list of parameters whose value is set with an assignment of the form
key=value
The possible parameters are
f
the definition of the investment function. This can be defined as an arbitrary function with variables of the form ret#, yld#, ewr#_#, ewy#_#, cwr#_# and cwy#_#, where # stands for a single digit. See below for explanation and examples.
w
the initial wealth of the agent
x
the initial share of wealth invested in the risky security
u
upper limit of the investment function
l
ower limit of the investment function
eps
a noise component uniformly drawn from -1/2 eps to 1/2 eps is added to the agent investment function at each period
#### Investment functions definition
The arguments of the investment function are of the type xy_z where x is a string of three characters which denotes the type of argument and the following (integer) numbers y and z stand for possible specifiers. The meaning of the specifiers depend on the type of argument
ret#1
stands for the realized return #1 steps in the past. Specifier #1 can take positive integer values 1,2,3,etc. Notice that due to the timing convention, the contemporaneous value of return cannot be an argument of the investment function.
yld#1
stands for the realized dividend yield #1 steps in the past. Specifier #1 can take non-negative integer values 0,1,2,3,etc.
ewr#1_#2
stands for the Exponential Weighting Moving Average estimator of the #1-th central moment of realized returns computed with the weight parameter "lambda" equal to 0.#2. Specifier #1 can take positive integer values 1,2,3,etc. Specifier #2 can take any non-negative integer value 0,1,2,3,etc. Notice that parameter "lambda" belongs to the interval [0,1).
ewy#1_#2
stands for the Exponential Weighting Moving Average estimator of the #1-th central moment of realized yields computed with the weight parameter "lambda" equal to 0.#2. Specifier #1 can take positive integer values 1,2,3,etc. Specifier #2 can take any non-negative integer value. Notice that parameter "lambda" belongs to the interval [0,1).
cwr#1_#2
stands for the Constant Weighting Moving Average estimator of the #1-th central moment of realized returns computed on the last #2 time steps. Both specifiers #1 and #2 can take positive integer values 1,2,3,etc.
cwy#1_#2
stands for the Constant Weighting Moving Average estimator of the #1-th central moment of realized dividend yields computed on the last #2 time steps. Both specifiers #1 and #2 can take positive integer values 1,2,3,etc.
#### Examples of the Config File
The following line
f=ret1+cwy3_12,x=.3,w=10
defines an agent who invests, at each time step, a share of wealth in the risky asset which is proportional to the sum of the last realized return (ret1) and the third central moment of the realized yields estimated through CWMA (cwy3) on the last 12 (12) time steps. The initial agent's endowment is 10 (w=10) of which 30% is invested in the risky security (x=.3) and the remaining in the riskless one.
A small modification
f=ret1+cwy3_12,x=.3,w=10,eps=.01
leads to a definition of analogous agent, but now, at each time step, a random component is drawn from an uniform distribution on [-.005,.005] and added to the agents' investment function.
The line
f=ret1+cwy3_12,x=.3,w=10,eps=.01,u=0.99,l=0.01
describes the same agent, whose investment choice is truncated in order to be in interval [0.01,0.99]. (This guarantees the boundedness of the dynamics!)
A group of similar agent can be defined prepending to the agent definition an integer number, which denotes the number of agents in the group, followed by a column ':'. For instance
50:f=ret1+cwy3_12,x=.3,w=10,eps=.01,u=0.99,l=0.01
stands for a group of fifty agents similar to the agent discussed above. Notice that due to the i.i.d. nature of the random component of the investment function, the investment decisions of the different agents of the group usually will not be identical.
### Options
The following options are in use. The default values are shown in []. Notice that the outcome is controlled by the option -O:
t
simulation length (default 10)
T
transient length (default 0)
s
skip this number of steps in output (default 1)
S
set the seed of the random number generator (defult 0)
r
riskless return (default 0.01)
D
dividend structure. Define parameters values using pairs 'name=values'. Names are 'type', 'mean' and 'stdev'. [type=0,mean=.02,stdev=0]. Possible types are:
0
constant yield
1
log-normal i.i.d. yield
2
uniform i.i.d. yield
3
geometrically growing dividend with initial value 0.001 and log-normal growth rate with given mean and stdev
R
initial return structure. Define parameters values using pairs 'name=values'. Names are 'mean' and 'stdev'. ( default mean=.02, stdev=0)
Y
initial yield structure. Define parameters values using pairs 'name=values'. Names are 'mean' and 'stdev'. ( default mean=.02, stdev=0)
O
set the output, list of t:step, r:return, p:price, w:wealth, x:avg.inv.share, y:yield, d:dividend, A:risky asset, B:riskless asset, X:inv.shares, W:wealth shares, (default 'rx')
v
verbose output
h
help message
### Simulation Initial Values
A simulation is completely specified only when the initial conditions are defined. For the simulations in NAIF there are three things that have to be specified: initial agent's portfolio, initial market history and initial values of agent's forecast variables. Below we analyze each of these three aspects.
#### Initial portfolio composition
Each agent i is given an initial wealth level (wi) and an initial share of wealth (xi) invested in the risky assets. These quantities can be explicitly specified using the parameter w and x in the configuration file. If not specified, their default values are 1 and .5, respectively. From these quantities, the initial portfolio composition of each agent is determined as
$A_i = x_i w_i / \sum_j x_j w_j$
$B_i = (1-x_i) w_i / \sum_j x_j w_j$
where $$A_i$$ and $$B_i$$ stand for the initial amount of risky and riskless security, respectively. These values should be positive in order the initial market conditions could be defined. Otherwise, the message "Agents specification does not allow to define initial price." is printed.
#### Initial market history
The initial price (for time t=0) of the risky security, according to the initialization of the agents' portfolio defined above, is set to 1.
The generation of the first dividend (for time t=1) depends on the market process specified in the command line. If the process is described by means of the yield, then yield "yld1" is accordingly generated and first dividend coincides with "yld1" since p0=1. If the process is described by means of the dividend (i.e. if the dividend is assumed to be growing), initial value of the dividend is set to .001.
The first price (for time t=1) is determined using the agents' investment functions, already.
Moreover, an initial "fake" histories of both price returns and dividend yields are generated. The lengths of these histories are set to a value large enough to provide an initial value for each estimator (see below). The returns and yields are identically and independently extracted from an uniform distribution. The mean and variance of the distributions for the return and yield can be specified from the command line. Both parameters have a default value of 0.
#### Initial forecasts
The initial value assigned to agent's forecast variables depends on their nature. Past returns variables (ret, yld) and equally weighted averages (cwr and cwy) are computed on the initial return or yield history, respectively, generated according to the procedure described above. Conversely, to the EWMA estimators (ewr and ewy), which are (in principle) functions of an infinite set of returns, a value is assigned which is equal to the last return raised to the order of the estimator. For example, if $$r_0$$ is the last return of the initial history of returns, ewr1 is set to $$r_0$$, ewr2 is set to $$r_0^2$$, ewr3 to $$r_0^3$$, etc. Notice that the memory parameter "lambda" doesn't play any role in the initial value of the estimator.
## Installation
Download the latest source code from the cafed repository. The installation should be straightforward. Unpack the package
tar -xzvf naif.tar.gz
move inside the source directory, run the configure script and build the files
cd naif
./configure
make
finally become root and install them
su
make install
for more detailed instructions see the file "INSTALL".
### Required Libraries
NAIF is written in C. It requires both the matheval library and the GNU Scientific Library. Both libraries should be available through the package management software of any Linux distribution. Remember to install the development version of the libraries before trying to compile NAIF.
### Disclaimer
Please notice that the program has been written for personal use, and is distributed under the GPL license (see the file COPYING) in the hope it could be of help to other people, but without any implied warranty.
## References
M. Anufriev and G. Bottazzi, Market Equilibria under Procedural Rationality, Journal of Mathematical Economics, 46 (6), pp. 1140–1172, 2010
M Anufriev and P Dindo Wealth-driven selection in a financial market with heterogeneous agents, Journal of Economic Behavior & Organization 73 (3), 327-358, 2010.
M Anufriev Wealth-driven competition in a speculative financial market: examples with maximizing agents Quantitative Finance 8 (4), 363-380, 2008.
M.Anufriev, G.Bottazzi and F.Pancotto Equilibria, Stability and Asymptotic Dominance in a Speculative Market with Heterogeneous Agents Journal of Economic Dynamics and Control, 30, pp. 1787-1835, 2006
M. Anufriev and G. Bottazzi Noisy Trading in the Large Market Limit Lecture Notes in Economics and Mathematical Systems, Issue 564, Springer-Verlag, Berlin, 2006
Created: 2018-10-08 Mon 21:22
Validate | |
# Question #5a2d7
May 18, 2015
You can identify a redox reaction by determining whether or not the oxidation state of an atom changes during a chemical reaction.
For a given atom, if the oxidation state decreases, that means the atom has gained electrons, or has been reduced; likewise, if the oxidation state increases, that means the atom lost electrons, or has been oxidized.
So, let's take the equations one by one and try to see if the oxidation state of any of the atoms changes
$\stackrel{\textcolor{b l u e}{+ 2}}{M g} \stackrel{\textcolor{b l u e}{- 2}}{O} + \stackrel{\textcolor{b l u e}{+ 1}}{{H}_{2}} \stackrel{\textcolor{b l u e}{- 2}}{O} \to \stackrel{\textcolor{b l u e}{+ 2}}{M g} {\left(\stackrel{\textcolor{b l u e}{- 2}}{O} \stackrel{\textcolor{b l u e}{+ 1}}{H}\right)}_{2}$
Notice that the oxidation states of all the atoms involved in the reaction do not change. This means that this reaction is not a redox reaction.
$2 \stackrel{\textcolor{b l u e}{0}}{{O}_{3}} \to 3 \stackrel{\textcolor{b l u e}{0}}{{O}_{2}}$
Once again, the oxidation state of the oxygen atoms was not changed by the reaction, so you're not dealing with a redox reaction.
$\stackrel{\textcolor{b l u e}{0}}{Z n} + \stackrel{\textcolor{b l u e}{+ 2}}{C u} \stackrel{\textcolor{b l u e}{+ 6}}{S} \stackrel{\textcolor{b l u e}{- 2}}{{O}_{4}} \to \stackrel{\textcolor{b l u e}{+ 2}}{Z n} \stackrel{\textcolor{b l u e}{+ 6}}{S} \stackrel{\textcolor{b l u e}{- 2}}{{O}_{4}} + \stackrel{\textcolor{b l u e}{0}}{C u}$
Notice that the oxidation state of zinc went from 0 on the reactants' side, to +2 on the products' side, which means that it has been oxidized.
At the same time, the oxidation state of copper went from +2 on the reactants' side, to 0 on the products' side, which means that it has been reduced.
Zinc metal lost two electrons to become $Z {n}^{2 +}$, while $C {u}^{2 +}$ gained two electrons to become copper metal.
One species was oxidized and another was reduced, so this qualifies as a redox reaction.
FInally,
$\stackrel{\textcolor{b l u e}{+ 2}}{F e} \stackrel{\textcolor{b l u e}{- 2}}{S} + 2 \stackrel{\textcolor{b l u e}{+ 1}}{H} \stackrel{\textcolor{b l u e}{- 1}}{C l} \to \stackrel{\textcolor{b l u e}{+ 2}}{F e} \stackrel{\textcolor{b l u e}{- 1}}{C {l}_{2}} + \stackrel{\textcolor{b l u e}{+ 1}}{{H}_{2}} \stackrel{\textcolor{b l u e}{- 2}}{S}$
The oxidation states of all the atoms remain unchanged by the reaction, so this cannot be considered a redox reaction. | |
# Consistent typography
When working with large documents, or even across multiple (smaller) documents, I often find that I forget which typographical consistencies I should stick to.
With TeX being inherently consistent in the way it does things, most things are kept organized without the user even knowing about it. Additionally, using a customized documentclass (like memoir, for example) or packages (like xspace and titlesec, to name two) improves on this consistency by user's choice. Sometimes, however, you are left to your own devices and have to do things manually. Of course, the latter could also stem from not knowing that a package exists to do the job for you, or because you'd rather have more control over the placement/use of a certain things without having it automated or globally set.
To this extent, I though this would be a good place to ask the question: "Which tools/techniques do you use to maintain consistency within your document?"
Sure, the question sounds broad. Many answers are scattered across this site and elsewhere (like the Chicago Manual of Style or Bringhurst's Elements of Typographic Style). I was hoping to contain this diverse knowledge base in one location on TeX.SX (similar to what was done for Showcase of beautiful typography done in TeX & friends and LaTeX IDEs).
Here are some examples of useful (manual) tips/tricks:
• The TeX Book mentions (p 25) the use of ties (~) in the context of Thor's "A SHORT STORY" when typesetting Mr.~Drofnats:
A good typist will use ties within names...
• \emph or \textit provides a good example of when/why to use either \emph or \textit.
• The contents of DO’s and DON’Ts when typesetting a document has some very relevant manual application of consistencies, including:
• Put a tilde before references or citations, e.g., Jie~\cite{habit06}.
• Differentiate between text comma and math comma, e.g., type for $x=a$, $b$, or~$c$ instead of for $x=a,b$, or $c$.
• Write ellipsis using \ldots instead of three dots.
• The l2tabu documentation also provides an interesting list of "do's and dont's".
Any more?
-
Define commands for common structures; even if keywords will be typeset with \textsf, better define \newcommand\keyword{\textsf}. Similarly, define environments for common logical units that might deserve particular typographical treatment. – egreg Sep 28 '11 at 22:16
@egreg: I would suggest turning this into an answer. – Werner Sep 28 '11 at 22:41
I'm assuming that the note about citations only applies if you are not using footnote citations, which you want to come right after the word? Or am I missing something? – Canageek Sep 28 '11 at 22:45
@Canageek: I would think so, otherwise it would probably have used \footcite. – Werner Sep 29 '11 at 5:02
A somewhat related question: Best practices references – Werner Oct 7 '11 at 23:30
show 1 more comment
Define commands for common structures; for instance, even if keywords will be typeset with \textsf, it's better to define
\newcommand\keyword{\textsf}
and use \keyword{mykey}. This not only adds visual clues when writing and reading the TeX document, but makes possible to change the typographical aspect at once everywhere.
Similarly, define environments for common logical units that might deserve particular typographical treatment.
Put structured comments around things like \enlargethispage or \pagebreak used during the final revision (which often turns out not to be really definitive). Make liberal use of comments in general.
-
+1 for suggesting making "liberal use of comments in general". :-) – Mico Oct 4 '11 at 10:59
Thanks @egreg for "consistently" delivering valuable answers! – Werner Dec 23 '11 at 6:10
For ellipses, do not only use \ldots, but also load the ellipsis package. Package description:
This is a simple package that fixes a problem in the way LaTeX handles ellipses: it always puts a tiny bit more space after \dots in text mode than before it, which results in the ellipsis being off-center when used between two words.
\documentclass{article}
% \usepackage{ellipsis}% Remove comment sign and compare
\begin{document}
\Huge
Some text \ldots\ and some more.
\end{document}
Note that ellipsis must be loaded after hyperref. (The ellipsis documentation doesn't mention this, but the hyperref README does.)
-
Also if you use the ellipsis package and want square brackets around the dots you should load the package with the mla option as in \usepackage[mla]{ellipsis}. – N.N. Sep 29 '11 at 7:15
I prefer another way: use the Unicode ellipsis character '…' (but not in math mode). This ellipsis is just as the font designer wanted, not artificially generated, and this makes text look a bit more consistent. One also can set up a proper sfcode for this character, if using \nonfrenchspacing. – Andrey Vihrov Sep 29 '11 at 7:32
Why do you need to force a space with \ after \ldots? Can you elaborate on that? – adn Dec 8 '11 at 4:43
I know this is a bit old, but: doesn't the ellipsis package provide (or redefine) the \dots command? Why are you then talking about \ldots? Are they somehow related? – mSSM May 17 '12 at 16:39
@mSSM From the LaTeX kernel: \let\ldots\dots. Perhaps I'll include a hint about this in my answer. – lockstep May 17 '12 at 16:44
show 1 more comment
There are some situations in spacing, where the author has to make TeX/LaTeX aware of an exception. Make a difference between 'full stop' and 'full stop after an abbreviation' as in this example:
I like BASIC\@. What about you?
The \@ enforces end-of-sentence period even if the precedent character was a capital letter, it is not part of an acronym. Also, I usually set a fixed space between the number and the unit, when a quantity is given, e.g.:
switching frequency of 1\ MHz
\ inserts a space that cannot be stretched.
-
I prefer using siuntix for typesetting numbers, eg. \SI{1}{\mega\hertz}. That makes it easier to change the style global and consistent. – Tobi Sep 30 '11 at 12:51
@Tobi: wasn't aware of that package... good idea! :) – Count Zero Sep 30 '11 at 12:55
@CountZero: Note that a space inserted with \ can be stretched and shrunk. – mhp Sep 30 '11 at 18:38
@mhp: That's really a surprise for me... I'm quoting from The Not So Short Introduction to LATEX2e: 'A backslash in front of a space generates a space that will not be enlarged' – Count Zero Oct 1 '11 at 9:05
@mhp: Thanks, you're right about that one --- still, I don't really understand this. I'll rather post it as a question, so this page will not be cluttered with comments. – Count Zero Oct 1 '11 at 21:45 | |
## prove (n)⊇(m)⟺n∣m (n) \supseteq (m)\iff n\mid m\ (contains = divides for principal ideals)
For non-zero integers m and n, prove (m)⊂(n) iif n divides m, where (n) is the principal ideal. My attempt is following. For non-zero integers m and n, assume that (m)⊂(n). Then, mk∈(m) is also in (n). This means that ∃nh such that mk=nh. Then, we have m=nhk−1. Assume that n divides m for non-zero … Read more
## Find the greatest positive integer $x$ such that $23^{6+x}$ divides $2000!$
I’m currently reading Andreescu and Andrica’s Number Theory: Structures, examples and problems. Problem 1.1.7 states : Find the greatest positive integer $x$ such that $23^{6+x}$ divides $2000!$. The solution given is : The number $23$ is prime and divides every $23^{rd}$ number. In all, there are $\lfloor \frac{2000}{23} \rfloor$ = $86$ numbers from $1$ to … Read more
## $2(n-2)+1$ does not divide $(n-2)(n-3)/2$ for $n \ge 8$
For $n \ge 8$ the number $2(n-2)+1$ never divides $(n-2)(n-3)/2$. Any ideas how to prove this? I see that $(n-2)(n-3)/2 = 1 + 2 + \ldots + (n-3)$. If I suppose that $2(n-2)+1$ divides $(n-2)(n-3)/2$ then it should also divide their difference \begin{align*} (n-2)(n-3)/2 – (2(n-2) + 1) & = \sum_{k=1}^{n-3} k – (2n – … Read more
## Divisibility of 2n−n22^n-n^2 by 7
How many positive integers n<104 are there such that 2n−n2 is divisible by 7? Answer Just write out periods: 2^n:2,4,1,2,4,1,2,4,1,2,4,1,2,4,1,2,4,1,2,4,1,|2… with period 3 n^2:1,4,2,2,4,1,0,1,4,2,2,4,1,0,1,4,2,2,4,1,0,|1… with period 7 So in every 21 numbers there are 6 numbers. Now just calculate 10^4\over 21=476 and since 10000 itself is not included there are 3 remainder left so totally … Read more
## Induction: Prove that 53n+72n−15^{3n} + 7^{2n-1} is divisible by 44
Prove that 53n+72n−1 is divisible by 4 for all n∈N. For n=1, ⇒53+71⇒132∣4 (which is divisible by 4) Let us assume given equation holds true for n=m, ⇒53m+72m−1|4 Now for n=m+1, 53m+3+72m+2−1 53m⋅53+72m−1⋅72 53m⋅125+72m−1⋅49 How do I go ahead from here? I am kind of stuck. Answer To complete your argument try to use the … Read more
## Dividing by something Undefined
I was thinking about trigonometry ratios, in particularly $\cot(\theta)$, which can be defined as $\cot(\theta) = \frac {1}{\tan(\theta)} = \frac {cos(\theta)}{sin(\theta)}$. Though $\tan(90)$ is not defined as you end up getting $\frac{1}{0}$. Though $\cot(90) = 0$. Though one could interpret that we had to divide it by something undefined as $\frac {1}{0}$, isn’t defined. Yet … Read more
## Are there integers a,b,ca,b,c such that aa divides bcbc, but aa does not divide bb and aa does not divide cc?
Are there integers a,b,c such that a divides bc, but a does not divide b and a does not divide c? I am not quite sure what to do with the given information. I know I could easily find an example. We know that a divides bc so, bc=aq for some integer q. And that a does … Read more
## What can we say about the prime factors of ^{10}10+23^{10}10+23?
In a video on ultrafinitism I saw a claim that the number ^{10}10+23 does not have prime factorization. While I don’t accept the premise of ultrafinitism, I got curious, what can we say about the prime factors of this number? ^{10}10 refers to the hyperoperation tetration. In other words, the number is equal to 10^{10^{10^{10^{10^{10^{10^{10^{10^{10}}}}}}}}}, … Read more
## Find the largest 4 digit positive integer n such that 10 divides n19+99nn^{19}+99^n
I’ve solved this problem and got the answer of 9991. I manually proved how some digits could or couldn’t be the ones digit of n, but I feel there is a faster way Answer n19+99n=n19+(100−1)n≡n19+(−1)nmod10 by Newton’s formula. We therefore need n19≡−1nmod10. Clearly both expressions cycle mod10. So you need only solve mod10, and the … Read more
## What is the largest perfect square that divides 20143−20133+20123−20113+…+23−132014^3-2013^3+2012^3-2011^3+\ldots+2^3-1^3
I’ve tried this but didn’t get the answer : Let S=20143−20133+20123−20113+…+23−13 Using n3−(n−1)3=3n2−3n+1, S=3(20142)−3(2014)+1+3(20122)−3(2012)+1+…+3(22)−3(2)+1=3(2014(2013)+2012(2011)+2010(2009)+…+2(1))+1(1007)=3(1007∑n=12n(2n−1))+1007=(1007∑n=14n2−1007∑n=12n)+1007=12(1007)(1008)(2015)6−2(1007)(1008)(3)2+1007 This is divisible by 1007 but not by 10072 which is the correct answer. Where have I gone wrong ? Answer 12(1007)(1008)(2015)6−2(1007)(1008)(3)2+1007=1007(12(1008)(2015)6−2(1008)(3)2+1)=1007(2(1008)(2015)−(1008)(3)+1)=1007(2(1007+1)(2015)−(1007+1)(3)+1)=1007(1007(2(2015)−3)+2(2015)−3+1)=1007(1007(2(2015)−3)+2(2015)−2)=1007(1007(2(2015)−3)+2(2014))=1007(1007(2(2015)−3)+4(1007))=10072(2(2015)−3+4)=10072(4031) AttributionSource : Link , Question Author : H G Sur , Answer Author : Siong Thye Goh | |
Steven R. Dunbar
Department of Mathematics
203 Avery Hall
Lincoln, NE 68588-0130
http://www.math.unl.edu
Voice: 402-472-3731
Fax: 402-472-8466
Topics in
Probability Theory and Stochastic Processes
Steven R. Dunbar
__________________________________________________________________________
Recurrence
_______________________________________________________________________
Note: These pages are prepared with MathJax. MathJax is an open source JavaScript display engine for mathematics that works in all browsers. See http://mathjax.org for details on supported browsers, accessibility, copy-and-paste, and other features.
_______________________________________________________________________________________________
### Rating
Mathematicians Only: prolonged scenes of intense rigor.
_______________________________________________________________________________________________
### Section Starter Question
__________________________________________________________________________
### Key Concepts
1. A random walk is recurrent if the walk almost surely returns to the origin infinitely many times. A random walk is transient if returning to the origin is a negligible event, alternatively, if the walk almost surely returns to the origin only finitely many times.
2. Every random walk is either recurrent or transient.
3. The random walk on the line is transient if $p\ne 1∕2$. If $p=1∕2$ then the random walk on the line is recurrent.
4. The walk is recurrent if and only if
$\sum _{n=1}^{\infty }ℙ\left[{T}_{n}=0\right]=+\infty .$
5. Let $S$ be the set of points attainable by the random walk. If the random walk is transient, then almost surely every point of $S$ is reached only finitely many times.
6. If the random walk is transient, then almost surely $\underset{n\to \infty }{lim}|{T}_{n}|=+\infty$.
7. If the random walk is recurrent, then almost surely the random walk reaches every point in $S$ infinitely many times.
__________________________________________________________________________
### Vocabulary
1. In a nearest neighbor random walk on the line, at time $n$ the walker takes a step to the right to ${T}_{n}+1$ with probability $p$ and takes a step to the left to ${T}_{n}-1$ with probability $q=1-p$ and continues this random process.
2. A random walk is recurrent if the walk almost surely returns to the origin infinitely many times.
3. A random walk is transient if the walk almost surely returns to the origin only finitely many times.
4. A random walk is centered if $𝔼\left[{Y}_{i}\right]=0$.
__________________________________________________________________________
### Mathematical Ideas
#### Definitions
Imagine an individual on a number line, starting at some position ${T}_{0}$. In a nearest neighbor random walk on the line at time $n$, $n\ge 0$ the walker takes a step to the right to ${T}_{n}+1$ with probability $p$ and takes a step to the left to ${T}_{n}-1$ with probability $q=1-p$ and continues this random process. Then instead of the total fortune at any time, consider the geometric position on the line at any time.
A probability model for the random walk is the set of all infinite sequences of 0’s and 1’s, $\Omega ={\left\{0,1\right\}}^{\infty }$. Let
${Y}_{k}\left(\omega \right)=2{\omega }_{k}-1,$
then ${Y}_{k}$ is a random variable taking on the value $+1$ with probability $p$ or $-1$ with probability $1-p$. ${Y}_{k}$ (the dependence on the sequence $\omega$ is usually suppressed) indicates right or left at step $k$. Then as usual,
${T}_{n}=\sum _{k=1}^{n}{Y}_{i}$
is a random variable indicating the position on the line.
A random walk is recurrent if the walk almost surely returns to the origin infinitely many times. That is, the walk is recurrent if the event is an almost sure event. A random walk is transient if is a negligible event, alternatively, if the walk almost surely returns to the origin only finitely many times.
Note that in principle it is possible that for a random walk defined by some step probability the event could have probability $P$ where $0. In this possibility the random walk would be neither recurrent nor transient. However, Corollary 1 below shows that all random walks are either recurrent or transient, so the two categories are mutually exclusive.
A random walk is centered if $𝔼\left[{Y}_{i}\right]=0$.
The theorems in this section can be generalized to other settings including random walks based on more general step distributions, including steps with continuous distributions, and to Markov chains.
#### Random Walk on the Line
Let ${Y}_{k}$ be a random variable taking on the value $+1$ with probability $p$ or $-1$ with probability $1-p$. ${Y}_{k}$ indicates right or left at step $k$ and
${T}_{n}=\sum _{k=1}^{n}{Y}_{i}.$
The following are immediate consequences of previous theorems:
1. If $p>1∕2$ (respectively $p<1∕2$), the Strong Law of Large Numbers implies that ${T}_{n}$ almost surely approaches $+\infty$ (respectively $-\infty$). Thus, the random walk on the line is transient if $p\ne 1∕2$. Equivalently, if the walk is not centered, the walk is transient.
2. If $p=1∕2$ the Law of the Iterated Logarithm implies that $limsup{T}_{n}=\infty$ and $liminf{T}_{n}=-\infty$. Since the length of each step is $1$, then the random walk on the line is recurrent.
3. However, consider the random walk on the line with $ℙ\left[{Y}_{n}=-3\right]=2∕5$ and $ℙ\left[{Y}_{n}=2\right]=3∕5$. This is a centered random walk. Furthermore, the Law of the Iterated Logarithm implies that $limsup{T}_{n}=\infty$ and $liminf{T}_{n}=-\infty$. However, because the steps are not unit length, the walk may “step over” the origin, so previous theorems alone are not enough to imply the walk is recurrent.
#### General Results
Definition. For $m,s,t\in ℕ$ with $s\le t$, let ${A}_{s,t}^{m}$ be the event consisting of the random walks that return to the starting point at least $m$ times between steps $s$ and $t$. That is,
Lemma 1. For every $m$ and $t$
$ℙ\left[{A}_{1,t}^{m}\right]\le {\left(ℙ\left[{A}_{1,t}^{1}\right]\right)}^{m}.$
Remark. The left side of this lemma expresses the probability of at least $m$ zeroes anywhere in the interval $\left[1,t\right]$. The right side of this lemma expresses the $m$th power of the probability of at least $1$ zero in $\left[1,t\right]$. The inequality that the left side is less than the right side is not obvious, so the lemma has a substantial conclusion.
Proof.
1. Clearly $ℙ\left[{A}_{1,t}^{m}\right]=0$ if $m>t$.
2. If $m=1$, the statement of the lemma $ℙ\left[{A}_{s,t}^{1}\right]\le {\left(ℙ\left[{A}_{1,t}^{1}\right]\right)}^{1}$ is clear. The proof now proceeds by induction with this step as the base case.
3. Let $m=2$. Consider the first two returns to the origin and write the event ${A}_{1,t}^{2}$ as a finite union of pairwise disjoint events
4. Then
5. Since is independent of ,
6. Note that
7. Then
8. Thus
9. Notice that
10. Therefore $ℙ\left[{A}_{1,t}^{2}\right]\le {\left(ℙ\left[{A}_{1,t}^{1}\right]\right)}^{2}$.
11. The induction step for $m>2$ is similar.
Lemma 2. For every $m$ and $t$
${\left(ℙ\left[{A}_{1,t}^{1}\right]\right)}^{m}\le ℙ\left[{A}_{1,mt}^{m}\right].$
Remark. This lemma expresses the clear fact that the probability of at least $m$ zeroes anywhere in the interval $\left[1,mt\right]$ is greater than the probability of at least $1$ zero in $\left[1,t\right]$, at least a second zero in $\left[t+1,2t\right]$ and so on. The proof formalizes this.
Proof. The proof is again by induction.
1. Start from (1) and rewrite it as
2. Then
3. Change variables $l=k-j$
4. This simplifies to
$\left(ℙ\left[{A}_{1,2t}^{2}\right]\right)\ge {\left(ℙ\left[{A}_{1,t}^{1}\right]\right)}^{2}.$
5. The induction step for $m>2$ is similar.
Theorem 3. The walk is recurrent, that is,
if and only if
Remark. The second condition of the theorem implies that the random walk almost surely returns to the origin at least once.
Proof.
($⇒$)
This follows immediately from the definition of .
($⇐$)
1. Let $m\in ℕ$, and let ${A}_{1,\infty }^{m}$ be the event that the sequence ${\left({T}_{n}\right)}_{n\ge 1}$ has at least $m$ zeroes. For each $t>0$, ${A}_{1,\infty }^{m}\supseteq {A}_{1,mt}^{m}$.
2. By Lemma 2
${\left(ℙ\left[{A}_{1,t}^{1}\right]\right)}^{m}\le ℙ\left[{A}_{1,mt}^{m}\right]$
3. Now assume the condition
Then $\underset{t\to \infty }{lim}ℙ\left[{A}_{1,t}^{1}\right]=1$, so the event ${A}_{1,\infty }^{m}$ contains an event with probability arbitrarily close to $1$. Therefore ${A}_{1,\infty }^{m}$ is an almost sure event.
4. Then event that the sequence ${\left({T}_{n}\right)}_{n\ge 1}$ has infinitely many zeroes is the intersection of the sets ${A}_{1,\infty }^{m}$ for all $m\in ℕ$. Since the countable intersection of almost sure events is almost sure, the sequence ${\left({T}_{n}\right)}_{n\ge 1}$ almost surely has infinitely many zeroes. Thus the random walk is recurrent.
Theorem 4.
1. If
$\sum _{n=1}^{\infty }ℙ\left[{T}_{n}=0\right]<+\infty .$
then
that is, the walk is transient.
2. If
$\sum _{n=1}^{\infty }ℙ\left[{T}_{n}=0\right]=+\infty .$
then
that is, the walk is recurrent.
Remark. Note the similarity of Property 2 implying recurrence to the second Borel-Cantelli Lemma. However, the Borel-Cantelli Lemma cannot be directly applied because the random variables ${T}_{n}$ are not independent.
Proof.
1.
If the series $\sum _{n=1}^{\infty }ℙ\left[{T}_{n}=0\right]$ converges, then the event is a negligible event by the first Borel-Cantelli Lemma.
2.
1. The sequence $ℙ\left[{A}_{1,n}^{1}\right]$ for $n\ge 1$ is increasing and bounded by $1$, so the limit exists: $\rho =\underset{n\to \infty }{lim}ℙ\left[{A}_{1,n}^{1}\right]$. The condition 2 to prove is $\rho =1$.
2. $\sum _{k=1}^{n}ℙ\left[{T}_{k}=0\right]=𝔼\left[\sum _{k=1}^{n}{\chi }_{\left[{T}_{k}=0\right]}\right]$
3. by summation by parts, or just by expansion.
4. Then by Lemma 1
$\sum _{k=1}^{n}ℙ\left[{T}_{k}=0\right]\le \sum _{j=1}^{n}{\left(ℙ\left[{A}_{1,n}^{1}\right]\right)}^{j}\le \sum _{j=1}^{n}{\rho }^{j}.$
5. Therefore $\sum _{k=1}^{\infty }ℙ\left[{T}_{k}=0\right]=+\infty$ implies $\rho =1$.
6. Then $\underset{n\to \infty }{lim}{A}_{1,n}^{1}=1$ by Theorem 3.
Corollary 1. Every random walk is either recurrent or transient.
Proof. Since the series of non-negative terms$\sum _{n=1}^{\infty }ℙ\left[{T}_{n}=0\right]$ must either converge or diverge, then respectively , i.e. the walk is transient or , i.e. the walk is recurrent. □
Lemma 5.
1. The random walk ${T}_{n}$ on $ℤ$ satisfies
$\sum _{n=1}^{\infty }ℙ\left[{T}_{n}=x\right]\le 1+\sum _{n=1}^{\infty }ℙ\left[{T}_{n}=0\right]$
for every $x\in ℤ$
2. $\sum _{n=1}^{\infty }ℙ\left[|{T}_{n}|\le K\right]\le \left(2K+1\right)\left(1+\sum _{n=1}^{\infty }ℙ\left[{T}_{n}=0\right]\right)$
for every $K>0$.
Proof.
1.
1. Decompose the event $\left[{T}_{n}=x\right]$ into a union of pairwise disjoint events based on the first time $k$ the random walk reaches the point $x$:
2. Then by independence and invariance of probability under shifting
3. Then
using the definition ${T}_{0}=0$. Note that the change of order of summation is justified since all terms are non-negative.
4. Since the events $\left[\left[{T}_{i}\ne x,1\le i and $\left[{T}_{k}=x\right]$ are pairwise disjoint over $k$, the sum of their probabilities is at most $1$. This finishes the proof of part 1.
2.
This follows at once from
$ℙ\left[|{T}_{n}|\le K\right]=\sum _{x\in ℤ,|x|\le K}ℙ\left[{T}_{n}=x\right]$
along with the fact that $|\left\{x\in ℤ,|x|\le K\right\}|=2K+1$.
Definition. Let $S$ be the semigroup generated under addition on the allowed steps in the random walk. Alternatively, the $S$ is the set of points attainable in the random walk.
Theorem 6.
1. If the random walk is transient, then every point of $S$ is almost surely reached only finitely many times.
2. If the random walk is transient, then almost surely $\underset{n\to \infty }{lim}|{T}_{n}|=+\infty$.
3. If the random walk is recurrent, then $S$ is a group.
4. If the random walk is recurrent, then the random walk almost surely reaches every point in $S$ infinitely many times.
Proof.
1.
1. Let $x\in S$ be given, and choose $m$ so that $|x|\le K$.
2. Suppose the random walk is transient. Then Theorem 4 implies that $\sum _{n=1}^{\infty }ℙ\left[{T}_{n}=0\right]$ converges.
3. Then by Lemma 5, $\sum _{n=1}^{\infty }ℙ\left[|{T}_{n}|\le K\right]$ converges for any $K>0$.
4. Then by the Borel-Cantelli Lemma, every point of $S$ is almost surely only reached finitely many times.
2.
From the previous part, if the random walk is transient, then every point $S$ is almost surely reached only finitely many times. It follows at once that almost surely $\underset{n\to \infty }{lim}|{T}_{n}|=+\infty$.
3.
1. Suppose the random walk ${\left({T}_{n}\right)}_{n=1}^{\infty }$ is recurrent.
2. Let $x\in S$ and fix a $k\ge 0$ such that $ℙ\left[{T}_{k}=x\right]>0$.
3. Then almost surely, there is an $n>k$ such that ${T}_{n}=0$.
4. Since an almost sure event and a finite type event with positive probability cannot be disjoint, there is an $\omega$ such that ${T}_{k}\left(\omega \right)=x$ and ${T}_{n}\left(\omega \right)=0$ with $k.
5. Then $-x\in S$ and since $S$ is already a semigroup, $S$ is a group.
4
1. The plan of the proof is as follows:
1. The random walk almost surely returns to zero infinitely many times.
2. Each time the walk returns to $0$, it is the same as if a new walk, independent of the previous one, were starting.
3. This gives an infinite sequence of identical, independent experiments, with each one having a positive probability of reaching the point $x$.
4. Then the random walk almost surely reaches the point $x$ infinitely many times.
2. By step 5 in the proof of Theorem 4, $\rho =\underset{n\to \infty }{lim}ℙ\left[{A}_{1,n}^{1}\right]=1$ and therefore $\underset{n\to \infty }{lim}ℙ\left[{A}_{1,t}^{1}\right]=1$.
3. Then by Lemma 2, $\underset{t\to \infty }{lim}ℙ\left[{A}_{1,mt}^{m}\right]=1$ for any $m>0$.
4. Then $\underset{t\to \infty }{lim}ℙ\left[{A}_{1,t}^{m}\right]=1$.
5. If $m$, $s$, $t$ are positive integers, then ${A}_{s,t}^{m}\supseteq {A}_{1,t}^{m+s}$, so $\underset{t\to \infty }{lim}ℙ\left[{A}_{s,t}^{m}\right]=1$.
6. Let $x\in S$ and $𝜖>0$. Fix $k$ so that $ℙ\left[{T}_{k}=x\right]>0$. Set $\delta =1-ℙ\left[{T}_{k}=x\right]<1$. Define a sequence ${n}_{j}$ for $j\ge 0$ by the recurrence $\begin{array}{llll}\hfill {n}_{0}& =1,\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill {n}_{j}-{n}_{j-1}& >k,\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill ℙ\left[{A}_{{n}_{j-1},{n}_{j}-k}^{1}\right]& >1-{2}^{-j}𝜖.\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\end{array}$
7. For $j\ge 1$, let ${B}_{j}$ be the event the random walk returns to the origin at least once between steps ${n}_{j-1}$ and ${n}_{j}-k$ and does not visit $x$ between steps ${n}_{j-1}$ and ${n}_{j}$. In symbols
${B}_{j}={A}_{{n}_{j-1},{n}_{j}-k}^{1}\cap \left[{T}_{n}\ne x,{n}_{j-1}\le n\le {n}_{j}\right]$
8. Let $J$ and $K$ be two positive integers such that $0. The next step is to find an upper bound for the probability of the event that the random walk does not reach $x$ between steps ${n}_{J-1}$ and ${n}_{K}$. Using Problems 5 and 6 below:
$ℙ\left[{T}_{n}\ne x,{n}_{J-1}\le n\le {n}_{K}\right]\le ℙ\left[\bigcup _{j=J}^{K}{\left({A}_{{n}_{j-1},{n}_{j}-k}^{1}\right)}^{C}\right]+ℙ\left[\bigcap _{j=J}^{K}{B}_{j}\right].$
9. Furthermore,
$ℙ\left[\bigcup _{j=J}^{K}{\left({A}_{{n}_{j-1},{n}_{j}-k}^{1}\right)}^{C}\right]\le \sum _{j=J}^{K}{2}^{-j}𝜖\le {2}^{1-J}𝜖.$
10. Let ${\ell }_{j}$ be a positive integer allowed to vary between ${n}_{j-1}$ and ${n}_{j}-k$. (Pay careful attention to distinction of ${l}_{j}$ and ${\ell }_{j}$ in subscripts. In fact, pay careful attention to all subscripts.) If event ${B}_{j}$ occurs then there is a unique ${\ell }_{j}$ such that
$\left[{T}_{i}\ne 0,{n}_{j-1}\le l<{\ell }_{j}\right],\phantom{\rule{1em}{0ex}}{T}_{{\ell }_{j}}=0,\phantom{\rule{1em}{0ex}}{T}_{{\ell }_{j}+k}\ne x.$
That is, ${\ell }_{j}$ is the first zero of ${T}_{n}$ on ${n}_{j-1}\le i\le {n}_{j}-k$. Note that the event in the display above is a superset of ${B}_{j}$.
11. Then
$ℙ\left[\bigcap _{j=J}^{K}{B}_{j}\right]\le \sum _{{l}_{J},\dots {l}_{K}}ℙ\left[\bigcap _{j=J}^{K}\left({\left({A}_{{n}_{j-1},{n}_{j}-k}^{1}\right)}^{C}\cap \left[{T}_{{\ell }_{j}}=0\right]\cap \left[{T}_{{\ell }_{j}+k}\ne x\right]\right)\right].$
12. Since the increment ${T}_{{l}_{K}+k}-{T}_{{l}_{K}}$ is independent of the random walk from ${T}_{{l}_{K}-1}$ $\begin{array}{c}ℙ\left[\bigcap _{j=J}^{K}\left({\left({A}_{{n}_{j-1},{l}_{j}-1}^{1}\right)}^{C}\cap \left[{T}_{{\ell }_{j}}=0\right]\cap \left[{T}_{{\ell }_{j}+k}\ne x\right]\right)\right]=\\ ℙ\left[\bigcap _{j=J}^{K-1}\left({\left({A}_{{n}_{j-1},{l}_{j}-1}^{1}\right)}^{C}\cap \left[{T}_{{\ell }_{j}}=0\right]\cap \left[{T}_{{\ell }_{j}+k}\ne x\right]\right)\right\\ \cap \left({\left({A}_{{n}_{K-1},{l}_{K}-1}^{1}\right)}^{C}\right)\cap \left[{T}_{{\ell }_{j}}=0\right]]\\ ×ℙ\left[{T}_{{l}_{K}+k}-{T}_{{l}_{K}}\ne x\right].\end{array}$
13. The invariance property implies $\begin{array}{c}\sum _{{\ell }_{J},\dots {\ell }_{K}}ℙ\left[\bigcap _{j=J}^{K}\left({\left({A}_{{n}_{j-1},{l}_{j}-1}^{1}\right)}^{C}\cap \left[{T}_{{\ell }_{j}}=0\right]\cap \left[{T}_{{\ell }_{j}+k}\ne x\right]\right)\right]\le \\ \delta \sum _{{\ell }_{J},\dots {\ell }_{K}}ℙ\left[\bigcap _{j=J}^{K-1}\left({\left({A}_{{n}_{j-1},{l}_{j}-1}^{1}\right)}^{C}\cap \left[{T}_{{\ell }_{j}}=0\right]\cap \left[{T}_{{\ell }_{j}+k}\ne x\right]\right)\right].\end{array}$
14. Therefore, by recursion on the sum $\begin{array}{c}\sum _{{\ell }_{J},\dots {\ell }_{K}}ℙ\left[\bigcap _{j=J}^{K}\left({\left({A}_{{n}_{j-1},{l}_{j}-1}^{1}\right)}^{C}\cap \left[{T}_{{\ell }_{j}}=0\right]\cap \left[{T}_{{\ell }_{j}+k}\ne x\right]\right)\right]\le \\ {\delta }^{K-J+1}.\end{array}$
15. Combining all the inequalities
$ℙ\left[{T}_{n}\ne x,{n}_{J-1}\le n\le {n}_{K}\right]\le {2}^{1-J}𝜖+{\delta }^{K-J+1}.$
16. For each $J>0$, fix $K>0$, depending on $J$, so $K\left(J\right)$ such that ${\delta }^{K-J+1}\le {2}^{1-J}𝜖$.
17. The event $E\subset \Omega$ such that $M\left(\omega \right)=x$ for only finitely many $n$ is in the union
$\bigcup _{J>0}\left[{T}_{n}\ne x,{n}_{J-1}\le n\le {n}_{K\left(J\right)}\right].$
18. By the choices above
$\sum _{J>0}ℙ\left[{T}_{n}\ne x,{n}_{J-1}\le n\le {n}_{K\left(J\right)}\right]<4𝜖.$
This shows that $E$ is a negligible event.
19. Thus, the random walk almost surely reaches the point $x$ infinitely many times for any $x\in S$. Since $S$ is countable, the random walk almost surely reaches every point in $S$.
#### Recurrence in Centered Random Walks
One more definition: A random walk is centered if $𝔼\left[{Y}_{i}\right]=0$.
Theorem 7. A random walk on $ℤ$ is recurrent if and only if it is centered.
Proof.
($⇒$)
Proof by contrapositive. The Strong Law of Large Numbers implies that
$\underset{n\to \infty }{lim}\frac{{T}_{n}}{n}=𝔼\left[{Y}_{1}\right]$
almost surely. If the walk is not centered, so that $𝔼\left[{Y}_{1}\right]\ne 0$, then $\underset{n\to \infty }{lim}|{T}_{n}|=+\infty$, so the walk is transient, i.e. not recurrent.
($⇐$)
The following argument uses the Weak Law of Large Numbers applied to any centered random walk on $ℤ$. Use the reversed form of part 2 of Lemma 5 to see that
$1+\sum _{n=1}^{\infty }ℙ\left[{T}_{n}=0\right]\ge \frac{1}{\left(2K+1\right)}\sum _{n=1}^{\infty }ℙ\left[|{T}_{n}|\le K\right].$
Then for any positive integer $a$,
$1+\sum _{n=1}^{\infty }ℙ\left[{T}_{n}=0\right]\ge \frac{1}{\left(2K+1\right)}\sum _{n=1}^{ma}ℙ\left[|{T}_{n}|\le K\right].$
and since $n\le Ka$, or $K\ge n∕a$
$1+\sum _{n=1}^{ma}ℙ\left[{T}_{n}=0\right]\ge \frac{1}{\left(2K+1\right)}\sum _{n=1}^{\infty }ℙ\left[|{T}_{n}|\le \frac{n}{a}\right].$
The generalized Weak Law of Large Numbers implies that
$\underset{n\to \infty }{lim}ℙ\left[|{T}_{n}|\le \frac{n}{a}\right]=1$
so by an argument from elementary analysis
$\underset{n\to \infty }{lim}\frac{1}{2m+1}\sum _{n=1}^{ma}ℙ\left[|{T}_{n}|\le \frac{n}{a}\right]=\frac{a}{2}.$
Finally this implies that
$1+\sum _{n=1}^{\infty }ℙ\left[{T}_{n}=0\right]\ge \frac{a}{2}.$
Since $a$ is an arbitrary integer, this means the series with terms $ℙ\left[{M}_{n}=0\right]$ diverges and the random walk is recurrent.
Remark. In the Bernoulli trials case that ${Y}_{i}$ takes only two values, the deMoivre-Laplace Central Limit Theorem implies that
$ℙ\left[{T}_{2n}=0\right]\sim \frac{1}{\sqrt{n}}$
Then the series $\sum _{n=0}^{\infty }ℙ\left[{T}_{n}=0\right]$ diverges. Then Theorem 4 implies the recurrence.
Remark. Another possible proof in the Bernoulli trials case that ${Y}_{i}$ takes only two values uses the Law of the Iterated Logarithm. Recall that this implies that
$\underset{n\to \infty }{limsup}{T}_{n}=\infty \phantom{\rule{2em}{0ex}}\underset{n\to \infty }{liminf}{T}_{n}=-\infty$
almost surely. Suppose $|{Y}_{i}|. If $\underset{n\to \infty }{lim}|{T}_{n}|=+\infty$ then given $2M$ there is some $N$ such that $|{T}_{n}|>2M$ for $n\ge N$. Yet there is also ${n}_{1}>N$ such that ${T}_{{n}_{1}}>2M$ and ${n}_{2}>{n}_{1}$ such that ${T}_{{n}_{2}}<-2M$. Because the maximum individual step length is $M$, there must be some ${n}_{3}$ with ${n}_{1}<{n}_{3}<{n}_{2}$ where $-2M<{T}_{{n}_{3}}<2M$. So it is not possible that $\underset{n\to \infty }{lim}|{T}_{n}|=+\infty$. Then the converse of part 2 of Theorem 6 implies the random walk is recurrent.
#### Sources
This section is adapted from: E. Lesigne, Heads or Tails: An Introduction to Limit Theorems in Probability, Chapter 13, American Mathematical Society, Student Mathematical Library, Volume 28, 2005. The statement of Theorem 4 is adapted from A Course in Probability Theory, Second Edition by K.L. Chung, Academic Press, 1974, Theorem 8.3.2, page 267.
_______________________________________________________________________________________________
### Algorithms, Scripts, Simulations
#### Scripts
__________________________________________________________________________
### Problems to Work for Understanding
1. Show explicitly that
follows from the definition of
2. Show explicitly that
implies that the random walk almost surely returns to the origin at least once.
3. In Theorem 6, provide a rigorous argument for the proof of part 2:
…if the random walk is transient, then every point $S$ is almost surely reached only finitely many times. It follows at once that almost surely $\underset{n\to \infty }{lim}|{T}_{n}|=+\infty$.
4. In Theorem 6, provide a rigorous argument for the first steps in the proof of part 3. Specifically, suppose the random walk ${\left({T}_{n}\right)}_{n=1}^{\infty }$ is recurrent. Let $x\in S$ and show that there is a $k\ge 0$ such that $ℙ\left[{T}_{k}=x\right]>0$.
5. For any sets $E$, $F$, $G$, so that if $E=F\cap G$, then $E\cup {F}^{C}\supseteq G$.
6. Using Problem 5, in step 8 of the proof of part 3. of Theorem 6, provide a rigorous argument for the inequality
$ℙ\left[{T}_{n}\ne x,{n}_{J-1}\le n\le {n}_{K}\right]\le ℙ\left[\bigcup _{j=J}^{K}{\left({A}_{{n}_{j-1},{n}_{j}-k}^{1}\right)}^{C}\right]+ℙ\left[\bigcap _{j=J}^{K}{B}_{j}\right].$
7. Write a simulation program to demonstrate the inequality in Lemma 1: For every $m$ and $t$
$ℙ\left[{A}_{1,t}^{m}\right]\le {\left(ℙ\left[{A}_{1,t}^{1}\right]\right)}^{m}.$
8. Write a simulation program to demonstrate the inequality in Lemma 2:
${\left(ℙ\left[{A}_{1,t}^{1}\right]\right)}^{m}\le ℙ\left[{A}_{1,mt}^{m}\right].$
9. Write a simulation program to demonstrate the inequality in Lemma 1:
$\sum _{n=1}^{\infty }ℙ\left[{T}_{n}=x\right]\le 1+\sum _{n=1}^{\infty }ℙ\left[{T}_{n}=0\right]$
for every $x\in {ℤ}^{N}$
10. Write a simulation program to demonstrate the inequality in Lemma 2:
$\sum _{n=1}^{\infty }ℙ\left[|{T}_{n}|\le m\right]\le \left(2m+1\right)\left(1+\sum _{n=1}^{\infty }ℙ\left[{T}_{n}=0\right]\right)$
for every $m>0$.
__________________________________________________________________________
### References
[1] Kai Lai Chung. A Course in Probability Theory. Academic Press, 1974.
[2] Emmanuel Lesigne. Heads or Tails: An Introduction to Limit Theorems in Probability, volume 28 of Student Mathematical Library. American Mathematical Society, 2005.
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# Timeseries Classification: KNN & DTW¶
Mark Regan
When it comes to building a classification algorithm, analysts have a broad range of open source options to choose from. However, for time series classification, there are less out-of-the box solutions. Many of the typical classification algorithms (Logistic Regression, Random Forests, SVM etc) are applicable to time-series data when the temporal data structure is abstracted away through feature engineering.
My experience with this approach has been poor. The full timeseries feature vector contains a large amount of valuable information that can be lost through the process of flattening the datastructure.
I began researching the domain of time series classification and was intrigued by a recommended technique called K Nearest Neighbors and Dynamic Time Warping. A meta analysis completed by Mitsa (2010) suggests that when it comes to timeseries classification, 1 Nearest Neighbor (K=1) and Dynamic Timewarping is very difficult to beat [1].
## K Nearest Neighbors & Dynamic Time Warping¶
In [2]:
from IPython.display import Image
Image('images/dtw_knn_schematic.png', width=780)
Out[2]:
K Nearest Neighbors is a classification algorithm familiar to many. It takes a unlabled observation (the star above) and compares it to a population of labled observations (blue and orange circles). By finding the K nearest circles to the star, we can infer the class label for the star through majority voting.
We can also use KNN in the context of time series data. The question becomes, "how do we compute the distance between two timeseries sequences"? "Dynamic Time Warping" is a technique that was heavily used for speech recognition in the 80s. The DTW algorithm finds the optimum alignment between two sequences of observations by warping the time dimension with certain constraints.
Because of this temporal dimension warping, DTW is good for classifying sequences that have different frequences or that are out of phase. Later we'll see how we can use DTW to classify whether a person is walking, lying down, sitting etc.
The above right diagram shows how a DTW distance matrix representation. Each cell is computed by measuring the distance between $A_i$ and $B_j$. The red path represents the shortest path and hence optimum alignment of the two sequences.
$$DTW_{AB} = SUM(shortest\ paths_{AB})$$
#### Max Warping Window Allowed¶
Computing the full distance matrix between A and B scales with $O(n^2)$, where n is the number of sequences in A and B. This performance can be improved by constraining the amount of warping allowed. This limits the number of cells that need to be computed in the DTW distance matrix. Research by Keogh et al has shown that a warping window not only improves performance but also improves classification accuracy [2].
In [3]:
Image('images/max_window_warping.png')
Out[3]:
#### Coded in Python¶
The below python code represents the KNN & DTW classification algorithm. The following key methods are described:
Method Description
_dtw_distance computes the Dynamic Time Warping distance between two sequences
_dist_matrix computes the distance matrix between $A$ and $B$
predict uses both of the above methods to compute the class labels and probability of dataset $B$ through K Nearest Neighbors
In [4]:
import sys
import collections
import itertools
from scipy.stats import mode
try:
from IPython.display import clear_output
have_ipython = True
except ImportError:
have_ipython = False
class KnnDtw(object):
"""K-nearest neighbor classifier using dynamic time warping
as the distance measure between pairs of time series arrays
Arguments
---------
n_neighbors : int, optional (default = 5)
Number of neighbors to use by default for KNN
max_warping_window : int, optional (default = infinity)
Maximum warping window allowed by the DTW dynamic
programming function
subsample_step : int, optional (default = 1)
Step size for the timeseries array. By setting subsample_step = 2,
the timeseries length will be reduced by 50% because every second
item is skipped. Implemented by x[:, ::subsample_step]
"""
def __init__(self, n_neighbors=5, max_warping_window=10000, subsample_step=1):
self.n_neighbors = n_neighbors
self.max_warping_window = max_warping_window
self.subsample_step = subsample_step
def fit(self, x, l):
"""Fit the model using x as training data and l as class labels
Arguments
---------
x : array of shape [n_samples, n_timepoints]
Training data set for input into KNN classifer
l : array of shape [n_samples]
Training labels for input into KNN classifier
"""
self.x = x
self.l = l
def _dtw_distance(self, ts_a, ts_b, d = lambda x,y: abs(x-y)):
"""Returns the DTW similarity distance between two 2-D
timeseries numpy arrays.
Arguments
---------
ts_a, ts_b : array of shape [n_samples, n_timepoints]
Two arrays containing n_samples of timeseries data
whose DTW distance between each sample of A and B
will be compared
d : DistanceMetric object (default = abs(x-y))
the distance measure used for A_i - B_j in the
DTW dynamic programming function
Returns
-------
DTW distance between A and B
"""
# Create cost matrix via broadcasting with large int
ts_a, ts_b = np.array(ts_a), np.array(ts_b)
M, N = len(ts_a), len(ts_b)
cost = sys.maxint * np.ones((M, N))
# Initialize the first row and column
cost[0, 0] = d(ts_a[0], ts_b[0])
for i in xrange(1, M):
cost[i, 0] = cost[i-1, 0] + d(ts_a[i], ts_b[0])
for j in xrange(1, N):
cost[0, j] = cost[0, j-1] + d(ts_a[0], ts_b[j])
# Populate rest of cost matrix within window
for i in xrange(1, M):
for j in xrange(max(1, i - self.max_warping_window),
min(N, i + self.max_warping_window)):
choices = cost[i - 1, j - 1], cost[i, j-1], cost[i-1, j]
cost[i, j] = min(choices) + d(ts_a[i], ts_b[j])
# Return DTW distance given window
return cost[-1, -1]
def _dist_matrix(self, x, y):
"""Computes the M x N distance matrix between the training
dataset and testing dataset (y) using the DTW distance measure
Arguments
---------
x : array of shape [n_samples, n_timepoints]
y : array of shape [n_samples, n_timepoints]
Returns
-------
Distance matrix between each item of x and y with
shape [training_n_samples, testing_n_samples]
"""
# Compute the distance matrix
dm_count = 0
# Compute condensed distance matrix (upper triangle) of pairwise dtw distances
# when x and y are the same array
if(np.array_equal(x, y)):
x_s = shape(x)
dm = np.zeros((x_s[0] * (x_s[0] - 1)) // 2, dtype=np.double)
p = ProgressBar(shape(dm)[0])
for i in xrange(0, x_s[0] - 1):
for j in xrange(i + 1, x_s[0]):
dm[dm_count] = self._dtw_distance(x[i, ::self.subsample_step],
y[j, ::self.subsample_step])
dm_count += 1
p.animate(dm_count)
# Convert to squareform
dm = squareform(dm)
return dm
# Compute full distance matrix of dtw distnces between x and y
else:
x_s = np.shape(x)
y_s = np.shape(y)
dm = np.zeros((x_s[0], y_s[0]))
dm_size = x_s[0]*y_s[0]
p = ProgressBar(dm_size)
for i in xrange(0, x_s[0]):
for j in xrange(0, y_s[0]):
dm[i, j] = self._dtw_distance(x[i, ::self.subsample_step],
y[j, ::self.subsample_step])
# Update progress bar
dm_count += 1
p.animate(dm_count)
return dm
def predict(self, x):
"""Predict the class labels or probability estimates for
the provided data
Arguments
---------
x : array of shape [n_samples, n_timepoints]
Array containing the testing data set to be classified
Returns
-------
2 arrays representing:
(1) the predicted class labels
(2) the knn label count probability
"""
dm = self._dist_matrix(x, self.x)
# Identify the k nearest neighbors
knn_idx = dm.argsort()[:, :self.n_neighbors]
# Identify k nearest labels
knn_labels = self.l[knn_idx]
# Model Label
mode_data = mode(knn_labels, axis=1)
mode_label = mode_data[0]
mode_proba = mode_data[1]/self.n_neighbors
return mode_label.ravel(), mode_proba.ravel()
class ProgressBar:
"""This progress bar was taken from PYMC
"""
def __init__(self, iterations):
self.iterations = iterations
self.prog_bar = '[]'
self.fill_char = '*'
self.width = 40
self.__update_amount(0)
if have_ipython:
self.animate = self.animate_ipython
else:
self.animate = self.animate_noipython
def animate_ipython(self, iter):
print '\r', self,
sys.stdout.flush()
self.update_iteration(iter + 1)
def update_iteration(self, elapsed_iter):
self.__update_amount((elapsed_iter / float(self.iterations)) * 100.0)
self.prog_bar += ' %d of %s complete' % (elapsed_iter, self.iterations)
def __update_amount(self, new_amount):
percent_done = int(round((new_amount / 100.0) * 100.0))
all_full = self.width - 2
num_hashes = int(round((percent_done / 100.0) * all_full))
self.prog_bar = '[' + self.fill_char * num_hashes + ' ' * (all_full - num_hashes) + ']'
pct_place = (len(self.prog_bar) // 2) - len(str(percent_done))
pct_string = '%d%%' % percent_done
self.prog_bar = self.prog_bar[0:pct_place] + \
(pct_string + self.prog_bar[pct_place + len(pct_string):])
def __str__(self):
return str(self.prog_bar)
#### Measuring the DTW distance¶
The DTW distance between two sequences can be calculated using the _dtw_distance() method
In [5]:
time = np.linspace(0,20,1000)
amplitude_a = 5*np.sin(time)
amplitude_b = 3*np.sin(time + 1)
m = KnnDtw()
distance = m._dtw_distance(amplitude_a, amplitude_b)
fig = plt.figure(figsize=(12,4))
_ = plt.plot(time, amplitude_a, label='A')
_ = plt.plot(time, amplitude_b, label='B')
_ = plt.title('DTW distance between A and B is %.2f' % distance)
_ = plt.ylabel('Amplitude')
_ = plt.xlabel('Time')
_ = plt.legend()
It is also possible to compute the distance between each pair of two collections of inputs by using the _dist_matrix() method. These are the two methods which underpin the KnnDtw() classification algorithm. In the next section we will use the fit() and predict() method to train our classifier and predict class labels forunseen data.
In [6]:
m._dist_matrix(np.random.random((4,50)), np.random.random((4,50)))
Out[6]:
array([[ 8.6569141 , 8.19847655, 7.83540289, 8.49673563],
[ 7.86962825, 9.16869072, 8.60084933, 8.91840291],
[ 9.61896688, 9.69620637, 9.1879124 , 9.87479709],
[ 9.17427532, 8.98877464, 8.4313078 , 7.81914999]])
## Human Activity Recognition Dataset¶
The Human Activity Recognition Dataset (HAR) dataset is chosen to test the classification performance of DTW & KNN [3].
In [7]:
Image('images/stand-sit-run.jpg')
Out[7]:
The experiments were carried out with a group of 30 volunteers within an age bracket of 19-48 years. Each person performed six activities (walking, walking upstairs, walking downstairs, sitting, standing and laying) wearing a smartphone (Samsung Galaxy S II) on the waist. Using its embedded accelerometer and gyroscope, we captured 3-axial linear acceleration and 3-axial angular velocity at a constant rate of 50Hz. The experiments have been video-recorded to label the data manually.
The remainder of this analysis uses a training and test dataset provided by the authors. They have combined the above timeseries signals and created a single timeseries feature vector. Unfortunately, their methodology is not described.
#### Import the HAR dataset¶
In [2]:
import numpy as np
import matplotlib.pylab as plt
# Import the HAR dataset
x_train_file = open('data/UCI-HAR-Dataset/train/X_train.txt', 'r')
y_train_file = open('data/UCI-HAR-Dataset/train/y_train.txt', 'r')
x_test_file = open('data/UCI-HAR-Dataset/test/X_test.txt', 'r')
y_test_file = open('data/UCI-HAR-Dataset/test/y_test.txt', 'r')
# Create empty lists
x_train = []
y_train = []
x_test = []
y_test = []
# Mapping table for classes
labels = {1:'WALKING', 2:'WALKING UPSTAIRS', 3:'WALKING DOWNSTAIRS',
4:'SITTING', 5:'STANDING', 6:'LAYING'}
# Loop through datasets
for x in x_train_file:
x_train.append([float(ts) for ts in x.split()])
for y in y_train_file:
y_train.append(int(y.rstrip('\n')))
for x in x_test_file:
x_test.append([float(ts) for ts in x.split()])
for y in y_test_file:
y_test.append(int(y.rstrip('\n')))
# Convert to numpy for efficiency
x_train = np.array(x_train)
y_train = np.array(y_train)
x_test = np.array(x_test)
y_test = np.array(y_test)
#### Visualizing sample observations from the HAR dataset¶
In [9]:
plt.figure(figsize=(11,7))
colors = ['#D62728','#2C9F2C','#FD7F23','#1F77B4','#9467BD',
'#8C564A','#7F7F7F','#1FBECF','#E377C2','#BCBD27']
for i, r in enumerate([0,27,65,100,145,172]):
plt.subplot(3,2,i)
plt.plot(x_train[r][:100], label=labels[y_train[r]], color=colors[i], linewidth=2)
plt.xlabel('Samples @50Hz')
plt.legend(loc='upper left')
plt.tight_layout()
#### Model Performance¶
The performance of the KNN & DTW classifier is measured by comparing the class labels from the holdout dataset against predictions made by the classifier. The HAR dataset was pre-split into 70% training and 30% test. Cross validation was not performed.
In [10]:
m = KnnDtw(n_neighbors=1, max_warping_window=10)
m.fit(x_train[::10], y_train[::10])
label, proba = m.predict(x_test[::10])
In [11]:
from sklearn.metrics import classification_report, confusion_matrix
print classification_report(label, y_test[::10],
target_names=[l for l in labels.values()])
conf_mat = confusion_matrix(label, y_test[::10])
fig = plt.figure(figsize=(6,6))
width = shape(conf_mat)[1]
height = shape(conf_mat)[0]
res = plt.imshow(array(conf_mat), cmap=cm.summer, interpolation='nearest')
for i, row in enumerate(conf_mat):
for j, c in enumerate(row):
if c>0:
plt.text(j-.2, i+.1, c, fontsize=16)
cb = fig.colorbar(res)
plt.title('Confusion Matrix')
_ = plt.xticks(range(6), [l for l in labels.values()], rotation=90)
_ = plt.yticks(range(6), [l for l in labels.values()])
precision recall f1-score support
WALKING 0.96 0.80 0.87 60
WALKING UPSTAIRS 0.85 0.80 0.83 51
WALKING DOWNSTAIRS 0.68 0.97 0.80 31
SITTING 0.78 0.78 0.78 51
STANDING 0.84 0.76 0.80 55
LAYING 0.90 1.00 0.95 47
avg / total 0.85 0.84 0.84 295
The KNN & DTW classifier performed very well across each of the 6 classes. It even beats the best classification rate published by the authors of the HAR paper.
However, this performance comes at a cost. The KNN algorithm is implemented using brute force. So, comparing 500 training observations to 500 test observations results in 250,000 DTW distances to be computed. And each (unconstrained) DTW distance calculation takes over 65K calculations each (256 x 256). This results in 16.3 billion calculations for just 500 x 500 observations.. Clearly not a scalable classification technique!
Performance improvements can be achieved by reducing the max_warping_window parameter. However, these gains will not be sufficient to make KNN & DTW a viable classification technique for large or medium sized datasets.
In [6]:
import time
time_taken = []
windows = [1,2,5,10,50,100,500,1000,5000]
for w in windows:
begin = time.time()
t = KnnDtw(n_neighbors=1, max_warping_window=w)
t.fit(x_train[:20], y_train[:20])
label, proba = t.predict(x_test[:20])
end = time.time()
time_taken.append(end - begin)
fig = plt.figure(figsize=(12,5))
_ = plt.plot(windows, [t/400. for t in time_taken], lw=4)
plt.title('DTW Execution Time with \nvarying Max Warping Window')
plt.ylabel('Execution Time (seconds)')
plt.xlabel('Max Warping Window')
plt.xscale('log')
#### Final thoughts¶
There are many improvements that could be made to this python implementation of KNN & DTW (eg. rewrite in C++ or explore parallel processing). However, the objective of this project was learning related. I've gained a deeper insight into the underlying mechanics of DTW by implementing it in python using dynamic programming techniques.
#### References¶
1. Mitsa (2010). Temporal Data Mining (Chapter on Temporal Classification).
2. Xi (2006). Fast Time Series Classification Using Numerosity Reduction.
3. Davide Anguita, Alessandro Ghio, Luca Oneto, Xavier Parra and Jorge L. Reyes-Ortiz. Human Activity Recognition on Smartphones using a Multiclass Hardware-Friendly Support Vector Machine. International Workshop of Ambient Assisted Living (IWAAL 2012). Vitoria-Gasteiz, Spain. Dec 2012. Read Paper
#### Credit¶
• The progressbar used in the DtwKnn() class was taken from PYMC
• The matplotlib style and IPython notebook was taken from Cameron Davidson-Pilon's excelent "Bayesian Methods for Hackers"
In [13]:
from IPython.core.display import HTML
def css_styling(): | |
# pygpcca.GPCCA
class pygpcca.GPCCA(P, eta=None, z='LM', method='brandts')[source]
G-PCCA [Reuter18] spectral clustering method with optimized memberships.
Clusters the dominant m Schur vectors of a transition matrix.
This algorithm generates a fuzzy clustering such that the resulting membership functions are as crisp (characteristic) as possible.
Parameters
• P (Union[ndarray, spmatrix]) – The transition matrix (row-stochastic).
• eta (Optional[ndarray]) –
The input probability distribution of the (micro)states. In theory eta can be an arbitrary distribution as long as it is a valid probability distribution (i.e., sums up to 1). A neutral and valid choice would be the uniform distribution (default).
In case of a reversible transition matrix, the stationary distribution can (but don’t has to) be used here. In case of a non-reversible P, some initial or average distribution of the states might be chosen instead of the uniform distribution.
Vector of shape (n,) which sums to 1. If None, uniform distribution is used.
• z (str) –
Specifies which portion of the eigenvalue spectrum of P is to be sought. The returned invariant subspace of P will be associated with this part of the spectrum. Valid options are:
• ’LM’: largest magnitude (default).
• ’LR’: largest real part.
• method (str) –
Which method to use to determine the invariant subspace. Valid options are:
• ’brandts’: perform a full Schur decomposition of P utilizing scipy.linalg.schur() (without the intrinsic sorting option, since it is flawed) and sort the returned Schur form R and Schur vector matrix Q afterwards using a routine published by Brandts [Brandts02]. This is well tested and thus the default method, although it is also the slowest choice.
• ’krylov’: calculate an orthonormal basis of the subspace associated with the m dominant eigenvalues of P using the Krylov-Schur method as implemented in SLEPc. This is the fastest choice and especially suitable for very large P, but it is still experimental.
minChi(m_min, m_max) Calculate the minChi indicator (see [Reuter18]) for every $$m \in [m_{min},m_{max}]$$. Full G-PCCA [Reuter18] spectral clustering method with optimized memberships.
coarse_grained_input_distribution Coarse grained input distribution of shape (n_m,). coarse_grained_stationary_probability Coarse grained stationary distribution of shape (n_m,). coarse_grained_transition_matrix Coarse grained transition matrix of shape (n_m, n_m). crispness_values Vector of crispness values for clustering into the requested cluster numbers. dominant_eigenvalues Dominant n_m eigenvalues of P. input_distribution Input probability distribution of the (micro)states. macrostate_assignment Crisp clustering using G-PCCA. macrostate_sets Crisp clustering using G-PCCA. memberships Array of shape (n, n_m) containing the membership $$\chi_{ij}$$ (or probability) of each microstate $$i$$ (to be assigned) to each macrostate or cluster $$j$$. n_m Optimal number of clusters or macrostates to group the n microstates into. optimal_crispness Crispness for clustering into n_m clusters. rotation_matrix Optimized rotation matrix $$A$$. schur_matrix Ordered top left part of shape (n_m, n_m) of the real Schur matrix of $$P$$. schur_vectors Array $$Q$$ of shape (n, n_m) with n_m sorted Schur vectors in the columns. stationary_probability Stationary probability distribution $$\pi$$ of the microstates. top_eigenvalues Top m respective m_max eigenvalues of P. transition_matrix Row-stochastic transition matrix P. | |
# qml.templates.layers.SimplifiedTwoDesign¶
SimplifiedTwoDesign(initial_layer_weights, weights, wires)[source]
Layers consisting of a simplified 2-design architecture of Pauli-Y rotations and controlled-Z entanglers proposed in Cerezo et al. (2020).
A 2-design is an ensemble of unitaries whose statistical properties are the same as sampling random unitaries with respect to the Haar measure up to the first 2 moments.
The template is not a strict 2-design, since it does not consist of universal 2-qubit gates as building blocks, but has been shown in Cerezo et al. (2020) to exhibit important properties to study “barren plateaus” in quantum optimization landscapes.
The template starts with an initial layer of single qubit Pauli-Y rotations, before the main $$L$$ layers are applied. The basic building block of the main layers are controlled-Z entanglers followed by a pair of Pauli-Y rotation gates (one for each wire). Each layer consists of an “even” part whose entanglers start with the first qubit, and an “odd” part that starts with the second qubit.
This is an example of two layers, including the initial layer:
The argument initial_layer_weights contains the rotation angles of the initial layer of Pauli-Y rotations, while weights contains the pairs of Pauli-Y rotation angles of the respective layers. Each layer takes $$\lfloor M/2 \rfloor + \lfloor (M-1)/2 \rfloor = M-1$$ pairs of angles, where $$M$$ is the number of wires. The number of layers $$L$$ is derived from the first dimension of weights.
Parameters
• initial_layer_weights (array[float]) – array of weights for the initial rotation block, shape (M,)
• weights (array[float]) – array of rotation angles for the layers, shape (L, M-1, 2)
• wires (Sequence[int] or int) – qubit indices that the template acts on
Raises
ValueError – if inputs do not have the correct format
template - here shown for two layers - is used inside a QNode:
import pennylane as qml
from pennylane.templates import SimplifiedTwoDesign
from math import pi
n_wires = 3
dev = qml.device('default.qubit', wires=n_wires)
@qml.qnode(dev)
def circuit(init_weights, weights):
SimplifiedTwoDesign(initial_layer_weights=init_weights, weights=weights, wires=range(n_wires))
return [qml.expval(qml.PauliZ(wires=i)) for i in range(n_wires)]
init_weights = [pi, pi, pi]
weights_layer1 = [[0., pi],
[0., pi]]
weights_layer2 = [[pi, 0.],
[pi, 0.]]
weights = [weights_layer1, weights_layer2]
>>> circuit(init_weights, weights)
[1., -1., 1.]
Parameter initialization function
The init module contains four parameter initialization functions:
• simplified_two_design_initial_layer_normal
• simplified_two_design_initial_layer_uniform
• simplified_two_design_weights_normal.
• simplified_two_design_weights_uniform.
They can be used as follows:
from pennylane.init import (simplified_two_design_initial_layer_normal,
simplified_two_design_weights_normal)
n_layers = 4
init_weights = simplified_two_design_initial_layer_normal(n_wires)
weights = simplified_two_design_weights_normal(n_layers, n_wires)
>>> circuit(initial_layer_weights, weights) | |
2015
09-17
# Ants
There are some apple trees in a farm. An apple tree can be described as a connected graph which has n nodes and n-1 edges. The apples are the nodes and the branches are the edges. Every edge is assigned a value denoting the length of the branch.
Now in the farm come a lot of ants, which are going to enjoy the delicious apples. The ants climb the tree one by one. Every ant would choose a node as the starting node and another node as the ending node, then it would crawl alone the unique path from the starting node to the ending node. The distance between two nodes is defined as the XOR sum of lengths of all the edges in the unique path between them. Every ant wants to crawl along such a path which the distance is as large as possible. But two ants cannot crawl from the same starting node to the same ending node. You should calculate the distance which the k-th ant crawled.
Note that the starting node and the ending node cannot be the same for an ant.
The input consists of several test case.
For each test case, the first line contain an integer n denoting the number of nodes.
The next n-1 lines each contains three integers x,y,z, denoting that there exists an edge between node x and node y and its length is z. The nodes are numbered from 1 to n.
The next line contain a integer m denoting the number of queries.
In the next m lines, each line contains an integer k denoting that you need to calculate the distance of the k-th ant.
The input ends with n = 0.
(1 <= n, m <= 100000, 1 <= x, y <= n, 0 <= z <= 1018, 1 <= k <= 200000)
The input consists of several test case.
For each test case, the first line contain an integer n denoting the number of nodes.
The next n-1 lines each contains three integers x,y,z, denoting that there exists an edge between node x and node y and its length is z. The nodes are numbered from 1 to n.
The next line contain a integer m denoting the number of queries.
In the next m lines, each line contains an integer k denoting that you need to calculate the distance of the k-th ant.
The input ends with n = 0.
(1 <= n, m <= 100000, 1 <= x, y <= n, 0 <= z <= 1018, 1 <= k <= 200000)
3
1 2 2
3 2 3
3
1
2
5
5
1 3 7
2 1 3
4 3 6
5 3 1
3
1
8
1000
0
3
3
1
7
6
-1
Hint
In the first test case, the first ant may crawl from node 2 to node 3, and the second ant may crawl from node 3 to node 2, and the 5-th ant may crawl from node 1 to node 3.
The distance of the 5-th ant can be calculated by 2 xor 3 = 1.
2013杭州现场赛 Ants
http://blog.csdn.net/dslovemz/article/details/15290899
（1）预处理出每个节点u到根节点的边权异或值a[u]，则两个节点u, v之间路径上的边权值的异或值为a[u]^a[v]
（2）将每个a[u]以二进制的形式插入到trie中
（3）u-v和v-u是算两个值。每个点u对应和其它的n-1个节点共有n-1个值，而共有n个节点，则可将所有的异或值，分成n类，每类n-1个。用优先队列，包含每类的当前最大值。初始为每个节点u和其它所有n-1个节点的值得最大值。取最大值后，删除后添加相应类别数列中的次大值。
（4）则关键求点u和其它n-1个点异或的第k大值即可，或者是求当前值得次大值
1.第k值法：
## Solution Of Dshawn by cxlove
1、如果 1 的子树中节点个数 >= rank ，那么走下去
2、如果小于 rank ，那么 rank -= 节点个数，走 0；
3、如果没有 1 的子树，那么走 0；
2.次大值：
## Solution Of BNU lsy
ps:hdu提交用lld wa， 用i64d才ac
#pragma comment(linker, "/STACK:102400000000,102400000000")
#include <cstdio>
#include <ctime>
#include <cstdlib>
#include <cstring>
#include <queue>
#include <string>
#include <set>
#include <stack>
#include <map>
#include <cmath>
#include <vector>
#include <iostream>
#include <algorithm>
#include <bitset>
using namespace std;
//LOOP
#define FF(i, a, b) for(int i = (a); i < (b); ++i)
#define FD(i, b, a) for(int i = (b) - 1; i >= (a); --i)
#define FE(i, a, b) for(int i = (a); i <= (b); ++i)
#define FED(i, b, a) for(int i = (b); i>= (a); --i)
#define REP(i, N) for(int i = 0; i < (N); ++i)
#define CLR(A,value) memset(A,value,sizeof(A))
//INPUT
#define RI(n) scanf("%d", &n)
#define RII(n, m) scanf("%d%d", &n, &m)
#define RIII(n, m, k) scanf("%d%d%d", &n, &m, &k)
#define RS(s) scanf("%s", s)
typedef long long LL;
typedef unsigned long long ULL;
typedef vector <int> VI;
const int INF = 0x3f3f3f3f;
const double eps = 1e-10;
const int maxn = 100010;
LL a[maxn];
LL ans[200010];
LL BIT[62];
int n, m;
struct Trie{
int ch[2 * maxn * 62][2];
LL val[2 * maxn * 62];
int num[2 * maxn * 62];
int tol;
Trie(){}
void init()
{
tol = 1;
CLR(ch, 0);
CLR(val, 0);///
CLR(num, 0);
}
void insert(LL x)
{
int u = 0;
for (int i = 60; i >= 0; i--)
{
int v = (x & BIT[i]) > 0;///
if (!ch[u][v]) ch[u][v] = tol++;
u = ch[u][v];
num[u]++;
}
val[u] = x;
}
bool kth_max(int k, LL v, LL &vmax)///查找和v异或后值为第k大值
{
if (k >= n) return 0;
int u = 0;
for (int i = 60; i >= 0; i--)
{
int r = !((v & BIT[i]) > 0);///
if (ch[u][r])
{
if (num[ch[u][r]] >= k)
u = ch[u][r];
else
{
k -= num[ch[u][r]];
u = ch[u][r ^ 1];///
}
}
else
u = ch[u][r ^ 1];///
}
vmax = val[u] ^ v;
return 1;
}
}ac;
struct Edge{
int to, next;
LL v;
};
int tot;
{
tot = 0;
}
void add_edge(int x, int y, LL v)
{
}
struct query{
int k, id;
bool operator <(const query &b) const
{
return k < b.k;
}
}qy[200010];
struct Node{
int k;
LL v;
LL vmax;
bool operator <(const Node &b) const
{
return vmax < b.vmax;
}
};
priority_queue<Node>q;
void dfs(int u, int fa, LL val)
{
ac.insert(val);///!!!
a[u] = val;
{
if (v == fa) continue;
}
}
void solve()
{
int x, y;
LL vv;
REP(i, n - 1)
{
scanf("%d%d%I64d", &x, &y, &vv);
}
RI(m);
REP(i, m)
{
RI(qy[i].k);
qy[i].id = i;
}
sort(qy, qy + m);
ac.init();
dfs(1, -1, 0);
while (!q.empty()) q.pop();
FE(i, 1, n)
{
Node now;
now.k = 1;
now.v = a[i];
if (ac.kth_max(now.k, now.v, now.vmax)) q.push(now);
}
int rank = 1;///
REP(i, m)
{
while (!q.empty() && rank < qy[i].k)
{
rank++;
Node now = q.top(); q.pop();
now.k++;
if (ac.kth_max(now.k, now.v, now.vmax)) q.push(now);
}
if (!q.empty()) ans[qy[i].id] = q.top().vmax;
else ans[qy[i].id] = -1;
}
REP(i, m)
printf("%I64d\n", ans[i]);
}
int main()
{
for (int i = 0; i <= 60; i++) BIT[i] = 1ll << i;
while (~RI(n) && n)
solve();
return 0;
}
1. 没看过，不过大街上卖内衣的广告，路边性事用品店应该都屏蔽下吧。最主要的是超市里居然收银处摆的都是避孕套。怎么也没人管管，哪个孩子不去超市啊，被当糖果买回去怎么给孩子交代
2. 你说是保家卫国，金家三代也是这样想的，他们觉得他们不欠中国的，而且还替中国守住东大门，吃你的喝你的是应该的，中国人觉得当年的血白流了，他们却觉得现在该叫你中修了。 | |
# CBSE CLASS 10 SCIENCE PREVIOUS YEAR PAPER 2017
CBSE Board
Class 10th Science
Previous year paper
2017
# Time: 3 hrs. Max. Marks: 90
Instructions:
1. The question paper comprises two Sections, A and B. You are to attempt both the sections.
2. All questions are compulsory.
3. There is no choice in any of the questions.
4. All questions of Section A and all questions of Section B are to be attempted separately.
5. Question numbers 1 to 3 in Section A are one-mark questions. These are to be answered in one word or in one sentence.
6. Question numbers 4 to 6 in Section A are two-mark questions. These are to be answered in about 30 words each.
7. Question numbers 7 to 18 in Section A are three-mark questions. These are to be answered in about 50 words each.
8. Question numbers 19 to 24 in Section A are five-mark questions. These are to be answered in about 70 words each.
9. Question numbers 25 to 33 in Section B are multiple choice questions based on practical skills. Each question is a one-mark question. You are to select one most appropriate response out of the four provided to you.
10. Question numbers 34 to 36 in Section B are two-marks questions based on practical skills. These are to be answered in brief.
SECTION A
Question 1. Write the molecular formula of the 2nd and 3rd member of the homologous series where the first member is ethyne.
Question 2. Why is variation important for a species?
Question 3. In the following food chain, 20,000 J of energy was available to the plants. How much energy would be available to man in this chain?
Plants →Sheep → Man
Question 4. An object is placed at a distance of 15 cm from a concave lens of focal length 30 cm. List four characteristic (nature, position, etc.) of the image formed by the lens.
Question 5. You being an environmentalist are interested in contributing towards the conservation of nature resources. List four activities that you can do on your own.
Question 6. Why are coal and petroleum categorized as natural resources? Given a reason as to why they should be used judiciously.
Question 7. Distinguish between esterification and saponification reactions with the help of the chemical equations for each. State one use of each (i) esters, and (ii) saponification process.
Question 8. Write the structural formula of ethanol. What happens when it is heated with excess of conc. H2SO4 at 443 K? Write the chemical equation for the reaction stating the role of conc. H2SO4 in this reaction.
Question 9. What is periodicity in properties of elements with reference to the Modern Periodic Table? Why do all the elements of the same group have similar properties? How does the tendency of elements to gain electrons change as we move from left to right in a period? State the reason of this change?
Question 10. Write the electronic configuration two elements X and Y whose atomic numbers are 20 and 17 respectively. Write the Molecular formula of the compound formed when element. X reacts with element Y. Draw electron-dot structure of the product and also state the nature of the bond formed between both the elements.
Question 11. How did Mendel explain that it is possible that a trait is inherited but not expressed in an organism?
Question 12. What is an organic evolution? It cannot be equated with progress. Explain with the help of a suitable example.
Question 13. List the two types of reproduction. Which one of the two is responsible for bringing in more variations in its progeny and how?
Question 14. What is vegetative propagation? State two advantages and two disadvantages of this method.
Question 15. List three techniques that have been developed to prevent pregnancy. Which one of these techniques is not meant for males? How does the use of these techniques have a direct impact on the health and prosperity of a family?
Question 16. “A lens can form a magnified erect image as well as magnified inverted image of an object placed in front of it”. State the nature of this lens and draw ray diagrams to justify the above statement. Mark the positions of O, F and 2F in the diagram.
Question 17. What is “dispersion of white light”? Draw a labelled diagram to illustrate the recombination of the spectrum of white light. Why it is essential that the two prisms used for the purpose should be identical and placed in an inverted position with respect to each other?
Question 18. (a) Water is an elixir of life a very important natural resource. Your science teacher wants you to prepare a plan for a formative assessment activity, “How to save water, the vital natural resource”. Write any two ways that you will suggest to bring awareness in your neighborhood, on how to save water’.
(b) Name and explain any one way by which the underground water table does not go down further.
Question 19. With the help of one example for each, distinguish between the acquired traits and the inherited traits. Why are the traits/experiences acquired during the entire lifetime of an individual not inherited in the next generation? Explain the reason of this fact with an example.
Question 20. (a) Write the functions of each of the following parts in a human female reproductive system:
1. Ovary
2. Uterus
3. Fallopian tube
(b) Write the structure and functions of placenta in a human female.
Question 21. Why certain compounds are called hydrocarbons? Write the general formula for homologous series of alkanes, alkenes and alkynes and also draw the structure of the first member of each series. Write the name of the reaction that converts alkenes into alkanes and also write a chemical equation to show the necessary conditions for the reaction to occur.
Question 22. (a) A student suffering from myopia is not able to see distinctly the object placed beyond 5 m. List two possible reasons due to which this defect of vision may have arisen. With the help of ray diagrams explain.
1. Why the student is unable to see distinctly the objects placed beyond 5 cm from his eyes.
2. The type of the corrective lens used to restore proper vision and how this defect is corrected by the use of this lens.
(b) If, in this case, the numerical value of the focal length of the corrective lens is 5 m, find the power of the lens as per the new Cartesian sign convention.
Question 23. Analyse the following observation table showing variation of image distance (v) with object distance (u) in case of a convex lens and answer the questions that follow without doing any calculations:
(a) What is the focal length of the convex lens? Give reason to justify your answer.
(b) Write the serial number of the observation which is not correct. On what basis have you arrived at this conclusion?
(c) Select an appropriate scale and draw a ray diagram for the observation at S. No. 2. Also find the approximate value of magnification.
Question 24. (a) If the image formed by a mirror for all position of the object placed in front of it is always diminished, erect and virtual, state the type of the mirror and also draw a ray diagram to justify your answer. Write one use such mirrors are put to and why.
(b) Define the radius of curvature of spherical mirrors. Find the nature and focal length of a spherical mirror whose radius of curvature is +24 cm
SECTION B
Question 25. Study the following ray diagram:
In this diagram, the angle of incidence, the angle of emergence and the angle of deviation respectively have been represented by
1. y, p, z
2. x, q, z
3. p, y, z
4. P, z, y
Question 26. A student very cautiously traces the path of a ray through a glass slab for different values of the angle of incidence ( $\angle$ i). He then measures the corresponding values of the angle of refraction ( $\angle$ r) and the angle of emergence ( $\angle$ e) for every value of the angle of incidence. On analysing these measurements of angles, his conclusion would be
1. $\angle$ i > $\angle$ r > $\angle$e
2. $\angle$ i = $\angle$ e > $\angle$ r
3. $\angle$ i < $\angle$ r < $\angle$ e
4. $\angle$ i = $\angle$ e < $\angle$ r
Question 27. Study the given ray diagrams and select the correct statement from the following:
1. (A) Device X is a concave mirror and device Y is a convex lens, whose focal lengths are 20 cm and 25 cm respectively.
2. Device X is a convex lens and device Y is a concave mirror, whose focal lengths are 10 cm and 25 cm respectively
3. Device X is a concave lens and device Y is a convex mirror, whose focal lengths are 20 cm and 25 cm respectively.
4. Device X is a convex lens and device Y is a concave mirror, whose focal lengths are 20 cm and 25 cm respectively.
Question 28. A student obtains a blurred image of a distant object on a screen using a convex lens. To obtain a distinct image on the screen he should move the lens.
1. away from the screen
2. towards the screen
3. to a position very far away from the screen
4. either towards or away from the screen depending upon the position of the object.
Question 29. While studying the saponification reaction, what do you observe when you mix an equal amount of colorless vegetable oil and 20% aqueous solution of NaOH in a beaker?
1. The color of the mixture has become dark brown
2. A brisk effervescence is taking place in the beaker
3. The outer surface of the beaker has become hot
4. The outer surface of the beaker has become cold
Question 30. When you add a few drops of acetic acid to a test-tube containing sodium bicarbonate powder, which one of the following is your observation?
1. No reaction takes place
2. A colorless gas with pungent smell is released with brisk effervescence
3. A brown colored gas is released with brisk effervescence
4. Formation of bubbles of a colorless and odorless gas
Question 31. A student requires hard water for an experiment in his laboratory which is not available in the neighboring area. In the laboratory there are some salts, which when dissolved in distilled water can convert it into hard water. Select from the following groups of salts, a group, each salt of which when dissolved in distilled water will make it hard.
1. Sodium chloride, Potassium chloride
2. Sodium sulphate, Potassium sulphate
3. Sodium sulphate, Calcium sulphate
4. Calcium sulphate, Calcium chloride
Question 32. To perform an experiment to identify the different parts of an embryo of a dicot seed, first of all you require a dicot seed. Select dicot seeds from the following group:
Wheat, Gram, Maize, Pea, Barley, Ground-nut
1. Wheat, Gram and Pea
2. Gram, Pea and Ground-nut
3. Maize, Pea and Barley
4. Gram, Maize and Ground-nut
Question 33. The following vegetables are kept in a basket
Potato, Tomato, Radish, Brinjal, Carrot, Bottle-gourd
Which two of these vegetables correctly represent the homologous structures?
1. Carrot and Tomato
2. Potato and Brinjal
Question 34. Draw in sequence (showing the four stages), the process of binary fission in Amoeba.
Question 35. A student focuses the image of a candle flame, placed at about 2 m from a convex lens of focal length 10 cm, on a screen. After that he moves gradually the flame towards the lens and each time focuses its image on the screen.
1. In which direction does he move the lens to focus the flame on the screen?
2. What happens to the size of the image of the flame formed on the screen?
3. What difference is seen in the intensity (brightness) of the image of the flame on the screen?
4. What is seen on the screen when the flame is very close (at about 5 cm) to the lens?
Question 36. Mention the essential material (chemicals) to prepare soap in the laboratory. Describe in brief the test of determining the nature (acidic/alkaline) of the reaction mixture of saponification reaction.
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# Explaining Gibbs Free Energy
## Homework Statement
A. Explain the need for Gibbs Free Energy equation.
B. Explain what it means when:
$$\Delta G <0$$ $$\Delta G >0$$ $$\Delta G =0$$
## Homework Equations
$$\Delta G= \Delta H-T \Delta S$$
## The Attempt at a Solution
A. Gibbs eqn comes from the need to calculate the entropy of the universe, which is the sum of entropy of system + entropy of surroundings. The need for the Gibbs eqn is because of the problem arising with calculating the entropy of surroundings as there are uncountable entropy changes that take place when heat is released into the surroundings. Gibbs eqn deals with this by eliminating the entropy of surroundings and replacing with an eqn that only has entropy of system on the right side of the eqn.
B. I am confused over here:
If $$\Delta G<0$$ then the process is spontaneous. This means$$\Delta H<0$$ and $$\Delta S>0$$ But how can the system release heat and also have an increase its entropy?
## The Attempt at a Solution
Related Biology and Chemistry Homework Help News on Phys.org
chemisttree
Homework Helper
Gold Member
I am confused over here:... But how can the system release heat and also have an increase its entropy?
Heat and entropy are not linked. Think of some chemical process for which entropy is clearly increasing. Heat is often given off as well. Burning a hydrocarbon, for example.
How about burning of propane. C3H8 + 5O2 ---> 3CO2 + 4H2O + heat
The entropy does increase in this rxn, due to 7 moles of gas in products vs. 6 in the reactants. However, C3H8 is relatively more complex relative to all the other molecules in this rxn. So how can I be sure whether entropy of the system increases, or that of the surroundings
Last edited: | |
# What is the expected value and standard deviation of X if P(X=0) = 0.31, P(X-1) = 0.45, P(X=2) = 0.24?
Mean $= 0.93$
SD $= 1.2268$
Mean $= 0.93$
SD $= 1.2268$ | |
# A diesel power station has fuel consumption of 0.2 kg per kWh. If the calorific value of diesel is 11000 kcal per kg, overall efficiency of power stat
203 views
in General
closed
A diesel power station has fuel consumption of 0.2 kg per kWh. If the calorific value of diesel is 11000 kcal per kg, overall efficiency of power station is
1. 43.3%
2. 65.5%
3. 39.2%
4. 25.6%
by (59.8k points)
selected by
Correct Answer - Option 3 : 39.2%
Concept:
Overall efficiency can be calculated as
$\% \eta = \frac{{100}}{{{m_f} × CV}}$
Where,
mf = mass flow rate of fuel or fuel consumption in kg / Joule
CV = calorific value of fuel in Joule / kg
Calculation:
m= 0.2 kg / kWh = $\frac{{0.2}}{{3600 × {{10}^3}}}\;kg/J$
CV = 11, 000 k cal / kg = 4.18 × 11 × 106 J/kg = 45.98 × 10J/kg {1 Cal = 4.18 J)
$\% \eta = \frac{{100 × 3600 × {{10}^3}}}{{0.2 × 45.98 × {{10}^6}}} = 39.14\%\simeq39.2\%$ | |
Categories
# [Smart Math] Ratio Proportion Problem 44
Here’s and example of a SMART MATH problem for RATIO PROPORTION.
### Problem
Three parts of alcohol A is mixed with two parts of alcohol B and sold at $110 per liter at a 10% profit. If alcohol A cost$20 more per liter than alcohol B, what is the price of alcohol A per liter?
1. $104 2.$115
3. $106 4.$108
5. $110 ### The Usual Method [contentblock id=google-adsense-post] Let price of alcohol A be$a / liter
And that of alcohol B be $b / liter $\therefore a-b=20$ $\therefore b=a-20$ Also cost of mixture = $\frac{110}{1.1}$ =$100 (1.1 is due to 10% profit)
$\therefore$By Alligation rule:
$\frac{100-b}{a-100}=\frac{3}{2}$
$\therefore \frac{120-a}{a-100}=\frac{3}{2}$
$\therefore 240-2a=3a-300$
$\therefore 5a=540$
$\therefore a=\frac{540}{5}$ = $108 (Ans: 4) Estimated Time to arrive at the answer = 60 seconds. ### Using Technique [contentblock id=google-adsense-post] Note that 3 : 2 can also be written as 6 : 4 or 60 liter and 40 liters. Hence total of 100 liters. Assuming that 100 liters costs$100 ($110 less 10% profit). Of this$100, $60 belongs to alcohol A and$40 to alcohol B. (Since difference of cost of the two alcohols is $20) This means that the price of alcohol A is a multiple of 6. The only value from the options which is a multiple of 6 is$108 of option ‘4’.
(Ans: 4)
Estimated Time to arrive at the answer = 15 seconds.
[starrater tpl=10]
[contentblock id=smartmath-blockquote] | |
Wednesday
October 22, 2014
# Homework Help: Physics
Posted by Cooper on Tuesday, January 24, 2012 at 12:09am.
The electric flux through each of the six sides of a rectangular box are as follows:
phi 1= +150.0 N*m^2/C; phi 2= +250.0 N*m^2/C;
phi 3= -350.0 N*m^2/C; phi 4= +175.0 N*m^2/C;
phi 5= -100.0 N*m^2/C; phi 6= +450.0 N*m^2/C
How much charge is in this box?
• Physics - drwls, Tuesday, January 24, 2012 at 12:56am
Add them up and apply Gauss' law to the sum.
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# [texhax] plain TeX: separate itmes by comme in \write environment
David Carlisle d.p.carlisle at gmail.com
Wed Apr 25 17:46:25 CEST 2018
> I applied David's suggestion with \mysep, and it seems to work, only
> it produces a space before the comma rather than after it as it should be...
It would produce a space after the comma if you used `\gdef\mysep{, }`
and as I mentioned you may need to input ignoring end of line eg
{\endlinechar=-1\input{zzzz}} | |
03 (g/mol) H 8 (1. Is this truly Viral or is to do with the fact that F. How many grams of oxygen are produced when 11. What volume is occupied by 10. 00 mol O 2 6. But 5G radiation alters the porosity of cell membranes, allowing some molecules or ionic elements to move more easily across those members, displacing other molecules (or soluble gasses such as carbon dioxide) that might normally make that leap. All major classes of structural molecules in living organisms, such as proteins, carbohydrates, and fats, contain oxygen, as do the major inorganic compounds that comprise animal shells. 'On your oxygen molecules, the little electrons, with 5G they start to oscillate. 625 of a mole and a mole of anything contains 6. The goverments are persecuting and censorsing anyone who's dares speak out against 5G. It lies between the super high frequency band, and the far infrared band, the lower part of which is also referred. 5 g of zinc react with an excess of hydrochloric acid? 140 0. On your oxygen molecules, the little electrons, they start to, like, oscillate. It's called wi-gig… This stuff is wicked. The uneven number of oxygen-containing electrons in free radicals allows them to react easily with other molecules. The Herschel Space Observatory's large telescope and state-of-the-art infrared detectors have provided the first confirmed finding of oxygen molecules in space. (f) NaCl = 23 + 35. If the pressure is 1 atm, the pressure due to oxygen is A) 0. Technically, the binding of a single molecule of oxygen (O2) increases the affinity toward oxygen on the three other oxygen sites, making the hemoglobin “mop up” four oxygen molecules very quickly. For every 1 mol, there are 6. That's what the peak means: 5G signals are near the oxygen resonance that limits their range. The 60 GHz range is known as the Oxygen Absorption Band. From the periodic table we see the atomic weight of hydrogen is 1. 022 x 1023 molecules Molar Mass: the mass (in grams) of one mole a particular substance There is a unique relationship between molar mass and atomic weight: Oxygen's atomic weight is 16. Very very very little heat. 03 (g/mol) H 8 (1. oxygen-carrying capacity of the blood, potentially leading to reduced total oxygen content in the bloodstream. Gas density and volumes are compared at a Standard Temperature and Pressure of 273. By mass, oxygen is the third-most abundant element in the universe, after hydrogen and helium. So, on your oxygen molecules, the little electrons with 5G, they start to like, oscillate, so this 5G is absorbing the. 78 mol/mol; N2 accounts for 78% of all molecules in the atmosphere. When the oxygen molecule is hit with 60GHz 5G waves, these waves affect the orbital resonance properties of those shared electrons. Moreover, these frequencies have also been used in several countries for biomedical purposes [14], thereby suggesting that molecular interactions between the millimeter waves and the human body are possible. 78 atm C) 1 atm D) 0. At STP, one mole of any gas should have a volume of 22. Carbon makes up 35% of the mass of the substance. edu) Can 5G exposure alter the structure of hemoglobin by increasing its affinity toward other molecules which are not O2?. But 5G radiation alters the porosity of cell membranes, allowing some molecules or ionic elements to move more easily across those members, displacing other molecules (or soluble gasses such as carbon dioxide) that might normally make that leap. A gaseous mixture made from 10 g of oxygen and 5 g of methane is placed in a 10 L vessel at 25°C. But this connection cannot be talked about. If 5G at 60 GHz frequency zips through the air, absorbing most of the oxygen, disrupting the electrons that bind 0 2 molecules that, combined with a hydrogen atom, form water vapor, what is that frequency doing to blood cells, which consist primarily of water and carry the oxygen?. 16g of S ? (B)What is the theoretical yield of SO3 produced by the quantities described in Part A? (C)For each of the given situations, indicate whether or is the limiting reactant. 1 x 10^21 molecules. (A)How many O2 molecules are needed to react with 2. oxygen molecules = × 10. The oxygen is unable to bind to the hemoglobin and your body slowly suffocates to death through hypoxia. 28) Calculate the mass of oxygen (in mg) dissolved in a 5. 5 g of water? answer in units of molecules?. Here's a diagram of how iron, histidine, the heme group and O2 oxygen molecules interact with hemoglobin, which alters its structure depending on the "oxygenated" vs. Number of moles in 5g of calcium = mass / molar mass = (5 / 40) = 0. When the oxygen molecule is hit with 60GHz 5G waves, these waves affect the orbital resonance properties of those shared electrons. How many moles of calcium oxide are produced when 36. 0093 mol/mol. This is the total atoms you should get, if the formula is correct. Place these four molecules in order of increasing rate of effusion. But 5G radiation alters the porosity of cell membranes, allowing some molecules or ionic elements to move more easily across those members, displacing other molecules (or soluble gasses such as carbon dioxide) that might normally make that leap. 0 kg of carbon in an excess of oxygen. At night the trees convert CO2 in to Oxygen. of molecules} =2 \times 3. Water of crystallization (WC) is the number of molecules of water present in one mole of a hydrated salt. 5G will disrupt the uptake of oxygen to cause oxygen deprivation to each cell at the level of the mitochondria. 60GHz: A Frequency to Watch. When it lacks oxygen, it changes to a “T-state” and appears blue, which is why low-oxygen blood has a blue color. But molecular mass is the mass of Avogadro’s number of molecules. 🤓 Based on our data, we think this question is relevant for Professor Garand's class at UW-MADISON. Only the oscillations begin to form a rotational spin of the molecule at 60 BILLION hertz PER SECOND. Enter your answer in scientific notation. So, one mole of NaCl weighs 58. Oxygen is present in a 1-liter flask at a pressure of 7. "On your oxygen molecules, the little electrons, with 5G they start to oscillate. All major classes of structural molecules in living organisms, such as proteins, carbohydrates, and fats, contain oxygen, as do the major inorganic compounds that comprise animal shells, teeth, and bone. Find out how they plan to weaponize 60GHz against us. Is there any truth that 5G will disrupt the uptake of oxygen? 04-01-2020, 08:57 AM saltine : 19,090 posts, read 9,737,838 times strong radios emit the power to cook just exactly as a microwave. A has unleashed 60 Ghz all throughout the country with WU-HAN as the PILOT CITY. 125 Number of moles in 2g of oxygen = mass / molar mass = (2 / 16) = 0. 2 amu), 454. How many molecules of chlorine are needed to react with 5. 71 Graph the data from the data table. oxygen molecules = × 10. Here's a diagram of how iron, histidine, the heme group and O2 oxygen molecules interact with hemoglobin, which alters its structure depending on the "oxygenated" vs. 60GHz causes the rotation of the electrons around the oxygen molecule to spin, thus inhibiting the ability of hemoglobin to properly uptake these oxygen molecules. 0 kg of carbon in an excess of oxygen. In a similar way that 2. 00 atm and 20. The trick is to start with what you are given, and cancel the units out so that you are left with the desired unit (which is usually stated in the question itself. 125 Now we will calculate the simplest ratio of the element by dividing the number of moles of each element by the smallest value. And the only reason that this connection between 5G and Corona cannot be talked about, says Icke, is that there is such a connection!. This means that 16. Without oxygen, the liver becomes congested and the body, and brain, begins to break down. get hotter. For every 1 mol, there are 6. 00 g of sodium dichromate, Na2Cr2O7? Question options: 9. 5G and the China epidemic They’ll call it Chronic Fatigue Syndrome, or a variety of blood disorders, they’ll look for THE VIRUS,. The benefit of Oxygen absorption relative to frequency re-use is detailed in figure 2. 09 g propane 1 mole propane = 1. Here's a diagram of how iron, histidine, the heme group and O2 oxygen molecules interact with hemoglobin, which alters its structure depending on the "oxygenated" vs. where d is the molecular diameter. Coronavirus started in China from Wuhan, between Military Games and 5G up to 60 Ghz « EMR Health Alliance of BC on Coronavirus, according to studies and experts with 5G, there is "immunosuppression and non-absorption of Oxygen". The relative humidity is the percent of saturation humidity, generally calculated in relation to saturated vapor density. 5 grams of water. Other species include dogs, hamsters, cats, guinea-pigs, rabbits, and monkeys. (a) Calculate the number of oxygen molecules and the number of oxygen atoms in 34. The last major network upgrade was 4G, which debuted in 2009 (the year of the Colorado balloon boy hoax), with a peak speed of about 10 Mbps. One property of oenological tannins, oxygen reactivity, is commonly exploited in winemaking. "So 5G is absorbing the oxygen, and then your hemoglobin can't take up the oxygen, so how long do you think it's going to take the human body to fall over because it suddenly cannot take up oxygen into the cells?. 738 g cm 3; pounded into sheets; drawn. 5G at 60GHz: Unique Oxygen Absorption Properties The demand for bandwidth is growing at a rapid pace. 5G at 60GHz: Unique Oxygen Absorption Properties The demand for bandwidth is growing at a rapid pace. Diatomic oxygen gas constitutes 20. 022 \times 10^{23}= 3. 2 amu), 454. 03:02 I want to talk to you about 5G and the frequencies that 5G uses. Molecules → A molecule is in general a group of two or more atoms that are chemically bonded together → A molecule is the smallest particle of matter (except element) which is capable of an independent existence and show all properties of that substance. 693855, and Avogadro's Number = 6. Organic Compounds. 0221x1023 items 6. The purported reason would be that electromagnetic fields (EMF) from 5G devices decrease the ability of hemoglobin molecules in our red blood cells to bind oxygen and carry it to our organs. 008 g/mol) = 8. 5g of C2H6 with excess oxygen. Other species include dogs, hamsters, cats, guinea-pigs, rabbits, and monkeys. Numerical problems based On Mole Concept Question 1. 022 x 1023 molecules of P2O5. Here’s a quote from one of these social media sites, “On your oxygen molecules, the little electrons, with 5G they start to oscillate. Due to this. Hemoglobin is the protein that makes blood red. It is composed of four protein chains, two alpha chains and two beta chains, each with a ring-like heme group containing an iron atom. The promotional materials from Telecom companies brag that 5G messes with oxygen molecules. Did you know that 5G frequencies - especially those in the 60 GHz range - cause O2 (oxygen) molecules to not bind easily to the hemoglobin in your blood? This means you don't take in as much oxygen. This is the total atoms you should get, if the formula is correct. Mole Review Worksheet Last. The mixing ratios in Table 1-1 are for dry air, excluding water vapor. 02 x 10 23 anything 3. Fixed 5G uses the spectrum, capacities, and unlicensed nature of the 60GHz band and uses it for high capacity use cases such as security video backhaul, public Wi-Fi backhaul and municipal networks in Smart. 4 x 10 23 molecules of H 2SO 4? 0. 85 × 1020 oxygen atoms 4. Chebi (CHemical Entitites of Biological Interest) entity of the Month. B is not defined by the data given; it is probably a compound because few elements exist as white solids. The result is increased oxygen content. 3 grams of (NH4)3PO4?. 9% of the volume of air. 5 x 1023 molecules of H 2 SO 4? 6) How many molecules are there in 122 grams of Cu(NO 3) 2? 7) How many grams are there in 9. When it lacks oxygen, it changes to a “T-state” and appears blue, which is why low-oxygen blood has a blue color. 0 g of oxygen. With some rare exceptions, organic molecules contain carbon atoms that are typically linked to hydrogen, oxygen or nitrogen atoms. 34 moles xs. Corona Virus and 5G - is there a connection? March 21, 2020. What we breathe are two oxygen molecules bonded together with the electrons that they share. This specific frequency is absorbed by oxygen. Millimeter waves are officially defined as waves transmitted at frequencies between 30 and 300 gigahertz, and they are between 1 and 10 millimeters in length. 022*10^23 molecules = 2. In first step, grams are converted to moles and in second step the moles are converted to the molecules. com states [quote] "At 60 GHz, oxygen molecules in the atmosphere react with the RF signals to cause significant attenuation. The question asks to calculate the number of molecules in 13. (a) Calculate the number of oxygen molecules and the number of oxygen atoms in 34. 02 x 10 23 anything 3. 60C; vapor pressure 195 mm Hg @ 20C, solubility in water, <20ppm; specific gravity 1. 5G technology has been said to use much higher frequencies (10-300 GHZ), and for the new 5G cell towers it usually does contain these frequencies, but not always. Answer: There will be of sulfur dioxide. This matrix is formed of many layers - maybe even millions of molecules deep - which forms a layer of structured water that. , transition metals and sulfur dioxide) and protects wine against oxidation. 2 liters of a gas at 546. Place these four molecules in order of increasing rate of effusion. using the following information1. 20 X l0 24 atoms of sulfur c. Amidst all the fear and panic over the coronavirus, there's something very important that many people have overlooked. Oxygen is in the air we breathe, it comes from trees. 5G and the China epidemic They’ll call it Chronic Fatigue Syndrome, or a variety of blood disorders, they’ll look for THE VIRUS,. Calculate the empirical formula of the compound from the grams of carbon, hydrogen, and oxygen. Calculate the number of grams represented by the following: a. 00 g of carbon dioxide. Oxygen, nitrogen and hydrogen are essential small molecules for life, matter and energy. 81 g of nitric acid, we will multiply the amount of nitric acid by the proportion which compares number of atoms to the amount of grams and multiply this by the proportion of Oxygen atoms to 1 \text{HNO}_3 molecule. Thallium has two stable isotopes 203Tl and 205Tl. 02x10 23) molecules 6. 5 g of S 8 (sulfur, formula. (a) Calculate the number of oxygen molecules and the number of oxygen atoms in 34. 4 causes H 2 0 to oscillate, 5G/60 GHz even at low power causes electrons on oxygen molecules to spin; changes to the spin frequencies on oxygen electrons impact human biology. He's talking about how 40 and 60 and other gigahertz and other radio frequencies affect oxygen and hydrogen in your body. Other theorists claim that 5G mobile networks are being deployed in high frequency bands of up to 60 GHz, thus causing ionization of the oxygen molecules in the air. 693855, and Avogadro's Number = 6. 60 ( 10–10. Write a balanced chemical equation for the reaction. 6 g CO 1 mol 12. Properties of millimeter waves. I also found this on Google: Joe Imbriano warns that 5G technology will broadcast at 60 GHz, which is the absorption spectrum of oxygen molecules, which means it can kill at a distance. True or false: In order to balance the reaction of hydrogen gas (H 2) with oxygen gas (O 2) to form liquid H 2 O, a student adds a subscript of 2 to H 2 O (forming H 2 O 2). The power level of 5G radio waves is far too low to affect air molecules, meaning it cannot suck oxygen out of the air. In a tank full of oxygen, how many molecular diameters d (on average) does an oxygen molecule travel (at 1. First, the molar mass allows you to change mass into mol. 00 g of sodium dichromate, Na2Cr2O7? Question options: 9. 5 G and Oxygen. 5G and your health. Technically, the binding of a single molecule of oxygen (O2) increases the affinity toward oxygen on the three other oxygen sites, making the hemoglobin "mop up" four oxygen molecules very quickly. 02 x 1024 molecules propane. When the oxygen molecule is hit with 60GHz 5G waves, these waves affect the orbital resonance properties of those shared electrons. Students use the slider or arrow buttons to move through a list of atoms and molecules. Chemical reactions occur when molecules interact and chemical bonds between them are formed or broken. Number of moles in 5g of calcium = mass / molar mass = (5 / 40) = 0. “Take a look at the effects of 5G on living things (60Ghz is the absorption spectrum of oxygen molecules), then compare them to the symptoms of this ‘virus’ – fever, dry cough, no mucous we’d usually find in this virus, cyanosis – turning blue (lack of oxygen), then dropping dead while walking down the street or shopping, This starts to make sense. To convert from moles to molecules multiply the molar amount of the molecule by Avogadro's number. Define isotope. A mole of water molecules would be 2 moles of hydrogen atoms plus 1 mole of oxygen atoms. Use this page to learn how to convert between. Stoichiometry Review Assignment Answer Key Example 1: Calculate the mass of a magnesium, Mg, atoms in grams. Conversion from grams to molecules requires two conversion factors. · Mechanical resonance – The mechanical resonance frequencies of gaseous molecules also coincide with the millimeter wave signal. b) molecules of water is this? 1. The FCC's safe limit for mobile phones is a specific absorption rate (SAR) of 1. Oxygen, nitrogen and hydrogen are essential small molecules for life, matter and energy. To understand one possible answer, you have to first understand how the blood carries oxygen. Oxygen molecules have electrons that they share with each other, oxygen is a diatomic molecule. (c) The number of moles and the mass of sodium nitrate, NaNO3, required to produce 128 g of oxygen. Clock-wise from the upper left: 130. That means, 64 grams of SO2 = 6. Other species include dogs, hamsters, cats, guinea-pigs, rabbits, and monkeys. The Avogadro's Constant is equal to 6. one mole of oxygen should = 16 but oxygen is a diatomic gas so when referring to OXYGEN in EMPIRICAL FORMULA and calculating moles do we see oxygen as a diatomic gas or do we ignore that and say that one mole of oxygen = 16g. 8 then 1 to 1 mole ratio so I multiplied by 6. 5 grams of it. 45 g ammonium formate remain 1 mol 5. Oxygen is in the air we breathe, it comes from trees. 02 x 1023 molecules 1 atom Mg Example 2: Calculate the number of atoms in one-millionth of a gram of magnesium, Mg. For example, water is made up of two hydrogen atoms for every one oxygen atom (H 2 O). Formula mass is the mass of 1 mole of formula units. 02 x 10^23 = 9. Circle and connect the points. 3 water molecules, oxygen is limiting C. 50 \times 6. Calculate the number of atoms of each element in 122. In the clear atmosphere, with only nitrogen and oxygen, ozone can react with the atomic oxygen to form two molecules of O 2. That's what the peak means: 5G signals are near the oxygen resonance that limits their range. 60GHz is the oxygen molecule absorption spectrum… This is the frequency that the oxygen molecules start reacting to… They're gonna be using 5G to mess with. Organic Compounds. 7 x 10 24 molecules of Oxygen Notice that the answer has the right number of significant figures. 03 x 10^23 = 2. ” “When the oxygen molecule is hit with 60GHz 5G waves, these waves affect the orbital resonance properties of those shared electrons. 1 molecule Mg = 4. The information sought is information relating to the. 0079 and the atomic weight of oxygen is 15. ” “When the oxygen molecule is hit with 60GHz 5G waves, these waves affect the orbital resonance properties of those shared electrons. , the tennis balls are joined with Krazy glue). 1 atom Mg = 2. 5G dangers: The destruction of OXYGEN molecules and the stupid, evil, elected representatives who are allowing it to happen. b) molecules of water is this? 1. 67 atm Ans: A Section: 17–3 Topic: The Ideal-Gas Law Type: Numerical 43 A cylinder of volume 50 L contains oxygen gas at a pressure of 2 atm. __× 10__ g. Define isotope. In one such hoax video, a woman says, "5G absorbs oxygen, and that's really important to know. In comparison, 5G is poised to deliver peak speeds between 10 and 20 Gbps. Or you could specify any number of moles. 00 g of sodium dichromate, Na2Cr2O7? Question options: 9. 0°C) before colliding with another O2 molecule? (The diameter of the O2 molecule is approximately 3. Back at the beginning of 2019, I predicted that there would be a link between 5G and a fake virus, hey presto! The area that is the epicentre of the so called virus is the same area that has reportedly been the province that 5G was rolled out with base stations. 16g of S ? (B)What is the theoretical yield of SO3 produced by the quantities described in Part A? (C)For each of the given situations, indicate whether or is the limiting reactant. oxygen molecules = × 10. 00 g sample of oxygen gas?A. Respiring tissues have a high concentration of carbon dioxide (a by-product of respiration). 022 × 1023/ 6. “On your oxygen molecules, the little electrons, with 5G they start to oscillate. In addition to disrupting oxygen absorption, 5G will alter the iron and magnetite function respectively of the hemoglobin and pineal gland. The last major network upgrade was 4G, which debuted in 2009 (the year of the Colorado balloon boy hoax), with a peak speed of about 10 Mbps. 204 x 1024 oxygen moleculesD. 39 ml of oxygen per gram of hemoglobin. edu) Can 5G exposure alter the structure of hemoglobin by increasing its affinity toward other molecules which are not O2?. 022140857 × 10^23 molecul. 5 x 1023 molecules of H 2 SO 4? 6) How many molecules are there in 122 grams of Cu(NO 3) 2? 7) How many grams are there in 9. Water molecules also contain four lone pair electrons on the oxygen atom. Our sweat ducts are filled with water which allows protons to jump between water molecules at similar frequencies to 5G. He's talking about how 40 and 60 and other gigahertz and other radio frequencies affect oxygen and hydrogen in your body. First, the molar mass allows you to change mass into mol. Atomic mass is the mass of 1 mole of atoms. December 20, 2019 Poulomi Ansari. Joe reveals that the 2. Molecules can absorb energy from the wireless signal, but when those molecules collide with other molecules such as air or body fluids, the molecules will lose that energy and the energy will get converted into heat. What we breathe are two oxygen molecules bonded together with the electrons that they share. 2 g of C 8 H 17 OH (1-octanol, formula mass 130. There's something more though that doesn't show up in the equation. Anyway, knowing this frequency impacts oxygen, now, does it make sense to you how possibly when you mess with the absorption of oxygen in the human body … let me give you one guess which organ is going to suffer first. $\endgroup$ - Jon Custer Mar 2. For example, iron in the presence of oxygen will form iron oxide, or rust. 3 grams of (NH4)3PO4?. 5 g NO2 By signing up,. A possible mechanism for M-ZnO/CeO 2 plasmonic photocatalyst degradation of nonpolar gaseous molecules is proposed, and the reasons for the excellent performance are as follows: 1) The formation of heterojunctions and surface oxygen vacancy defects can strongly suppress the photogenerated carriers’ recombination and effectively promote. 01 g sample of carbon has Avogadro number of carbon atoms. One VERY serious claim: when 5G employs a frequency band at 60GHz, disruption in oxygen molecules occurs—and the crucial ability of hemoglobin to pick up oxygen and transport it throughout the body is seriously impaired. The rest is made of oxygen. To find the number of moles of SO2 (sulfure dioxide from here on out to save space), we need to first figure. Irvine-based startup Movandi recently closed $27 million in C series funding and aims to help expedite 5G rollouts. To understand one possible answer, you have to first understand how the blood carries oxygen. We have step-by-step solutions for your textbooks written by Bartleby experts!. on StudyBlue. 8 g of magnesium oxide. Radio waves in this band have wavelengths from ten to one millimetre, so it is also. As a result, more oxygen will be released in these areas due to the Bohr effect. Here's a diagram of how iron, histidine, the heme group and O2 oxygen molecules interact with hemoglobin, which alters its structure depending on the "oxygenated" vs. We can work out the number of molecules by timesing the moles by Avogadro's constant above. What would be the ultimate ‘solution’ to such a problem as this “V. A is a compound; it contains at least carbon and oxygen. It's way more fascinating than you might have supposed. Indeed most 5G networks have been deployed in the 2. Use this page to learn how to convert between grams Oxygen and mole. For example, it is well documented that 5G radiation causes "Voltage Gated Ion Channels" (VGIC. 42 gm of Oxygen will be left behind without any change. This is a stoichiometry problem. “You do not mess with oxygen molecules,” Parker writes, noting that 5G will operate within the spectrum range that most affects oxygen molecules negatively. The reactivity is mediated by the presence of catalysts (i. The number of gram molecules of oxygen in 6. Cannot answer here. So, on your oxygen molecules, the little electrons, with 5G they start to like oscillate, so this 5G is absorbing. It is those shared electrons that bind to the hemoglobin in our blood. of glucose molecules = 0. 5 grams of water. 0153 atomic mass units, so 1 mole of water molecules has a mass of 18. For every 1 mol, there are 6. The promotional materials from Telecom companies brag that 5G messes with oxygen molecules. December 20, 2019 Toppr. Avogadro's number is 6. The question asks to calculate the number of molecules in 13. Number of moles in 5g of calcium = mass / molar mass = (5 / 40) = 0. 0 moles of nitrogen gas 2. 5G interferes with the voltage gated calcium channel with the electrical charge it. 0 L of methane gas (CH 4) at STP? 71. According to Peter Paul Parker, a contributor at Waking Times, the 60 GHz broadcasting spectrum on which 5G is set to operate will affect the human body in a whole different way from previous “G” iterations, specifically with regard to the way that it’s expected to interact with the body’s oxygen molecules. So what happens when these oxygen molecules are oscillating at 60GHz (part of the 5G spectrum) ? It's like sticking your hand in a fan and trying to catch the blade, only this blade is spinning at 60 Billion revolutions per second. Stoichiometry Review Assignment Answer Key Example 1: Calculate the mass of a magnesium, Mg, atoms in grams. 693855, and Avogadro's Number = 6. Note that rounding errors may occur, so always check the results. Select the statement below that is incorrect in regard to this reaction. 709 x 10^24 atoms. 5G and the China epidemic They’ll call it Chronic Fatigue Syndrome, or a variety of blood disorders, they’ll look for THE VIRUS,. oxygen-carrying capacity of the blood, potentially leading to reduced total oxygen content in the bloodstream. One nitrogen atom, and two oxygen atoms. 5g of NaCl will contain one mole of sodium ions and one mole of chloride ions. 09 (g/mol) 74. This is due to improved gas flow resulting in better combustion efficiency. edu) Can 5G exposure alter the structure of hemoglobin by increasing its affinity toward other molecules which are not O2?. 50hz frequency can re-activate dormant viruses inside people and make them active. The oxygen is unable to bind to the hemoglobin and your body slowly suffocates to death through hypoxia. These two atoms form the oxygen molecule and share some electrons. 022 x 10 23 = 6. Trees make it out of carbon dioxide. 5G offers at least a tenfold improvement in network performance. 5 mole Hence, 1 g-atom contains 0. I've consulted with a trusted source. So 5G is absorbing the oxygen and then your haemoglobin can’t take up the oxygen. On Twitter, an in a viral video clip, an unidentified woman claimed that 5G ‘sucks oxygen out of your lungs. CHEMICAL REACTIONS The Mole A Chemical Measure Video 3. 847 g/mol, how many grams (to 3 significant figures) of iron are combined with 75. This conversions relies on the fact that a mole of gas at STP has a volume of 22. The woman, whose identity remains unclear, said: “5G absorbs oxygen, and that’s really important to know. But 5G radiation alters the porosity of cell membranes, allowing some molecules or ionic elements to move more easily across those members, displacing other molecules (or soluble gasses such as carbon dioxide) that might normally make that leap. For N molecules of a compound with the general formula X a Y b:. Show that the mean free path for the molecules of an ideal gas is. Chapter-wise NCERT Solutions for Class 9 Science Chapter 3 Atoms and Molecules (Chemistry) solved by Expert Teachers as per NCERT (CBSE) Book guidelines. molecules in 5. 5 mol" xx (6. Sodium is an alkali metal, being in group 1 of the periodic table, because it has a single electron in its outer shell, which it readily donates, creating a positively charged ion—the Na + cation. The physicists who have worked on these studies feel that we have the possibility of absorbing 5G wave lengths into our sweat ducts transforming them into millions of little antennas. What mass of. · Mechanical resonance – The mechanical resonance frequencies of gaseous molecules also coincide with the millimeter wave signal. Now, your skin is hotter than the interior part of your body so heat starts flowing, causing the inside part of your body to become hotter. of mole of KClO 3 = 245 g/122. 02 x 10²⁴ molecules of CO = 10 mole of CO = 10 g atoms of O = 5 g molecules of O₂. Video author discusses the plan to microwave all of us and how it eventually could result in forced vaccinations in the onward march toward culling humanity. Irvine-based startup Movandi recently closed$27 million in C series funding and aims to help expedite 5G rollouts. The number of gram molecules of oxygen in 6. There are now three carbon atoms, eight hydrogen atoms, and 10 oxygen atoms on each side of the. , LD 50 (oral, rat) - 5 mg/kg, LD 50 (skin, rabbit. Figure 2 illustrates the distance relationship between the 60GHz frequency reuse range, the green region, and the traditional range, the blue region. You can view more details on each measurement unit: molecular weight of Oxygen or mol The molecular formula for Oxygen is O. Water is the only common compound that exists in solid, liquid, and gas phase under ordinary, natural conditions. Make a drawing that represents the reaction container before and after the reaction. Is this truly Viral or is to do with the fact that F. Write a balanced chemical equation for the reaction. So what happens when these oxygen molecules are oscillating at 60GHz (part of the 5G spectrum) ? It's like sticking your hand in a fan and trying to catch the blade, only this blade is spinning at 60 Billion revolutions per second. It's a two step conversion. With Avogadro's number you can always find the number of molecules. Conversion from grams to molecules requires two conversion factors. (b) Calculate the mass of 8. Chap 3 : Atoms and Molecules www. The SI base unit for amount of substance is the mole. 5g 1000 cm3 (1dm 3) has a mass of 2. It doesn't destroy or make the O2 molecule somehow un-bioavailable to people, it simply heats the O2 up. The FCC's safe limit for mobile phones is a specific absorption rate (SAR) of 1. In first step, grams are converted to moles and in second step the moles are converted to the molecules. 00!grams!of!carbon!dioxide,!I!have:!! 9. One mole of P2O5 would be 6. Add those up, and 32+32=64 AMU, which is the molecular mass of SO2. 0 g of carbon is burnt in 8. 0g x4 to convert to dm 24 dm 3has a mass of 48. The information sought is information relating to the. How many oxygen atoms are in 3. Effects of Long-Term Exposure to 60 GHz Millimeter-Wavelength Radiation on the Genotoxicity and Heat Shock Protein (Hsp) Expression of Cells Derived from Human Eye Shin Koyama , 1, * Eijiro Narita , 1 Yoko Shimizu , 1 Yukihisa Suzuki , 2 Takeo Shiina , 2 Masao Taki , 2 Naoki Shinohara , 1 and Junji Miyakoshi 1. Q12 Where do we use the words mole and mol? Ans In the text part we use the word mole while as a unit ,we call it mol. Here as given, in burning, 3. For benzene:. 0153 atomic mass units, so 1 mole of water molecules has a mass of 18. Stoichiometry Homework Name_____ I. 02x10 23) molecules 3 moles 1 mole 2 moles 300 molecules 100 molecules 200 molecules The coefficients in a balanced chemical equation can be used to relate the number of moles of each. Figure 2 illustrates the distance relationship between the 60GHz frequency reuse range, the green region, and the traditional range, the blue region. Oxygen is the chemical element with the symbol O and atomic number 8. I'm not sure. Explanation: Sulfur dioxide is with one sulfur and two oxygen atoms. December 20,. 6 W/kg) of mass, nowhere near enough to warm up your body. 0 mol oxygen. each of two or more forms of the same element that contain equal numbers of protons but different numbers of neutrons in their nuclei, and hence differ in relative atomic mass but not in chemical properties; in particular, a radioactive form of an element. Molecules of RNA contain the sugar D-ribose. The Avogadro's number is a dimensionless quantity and is equivalent to the Avogadro constant. 5g = 2 mole 2 mole of KClO 3 contains Calculate the number of oxygen molecules in the flask. 5 g of oxygen. (NaNO2is the other product. The Potential Reach and Influence of 5G. This energy emission, when received by a receiver antenna, is called brightness. 022 × 1023 = 1 mole…. 0points What is the coefficient for H2O when the equation. 78 moles of oxygen gas c. 125Now we will calculate the simplest ratio of the element by dividing the number of moles of each element by the smallest value. 5g of NaCl contains two moles of ions in total. One mole of oxygen molecules would therefore have a mass of 32 g. The first one is done for you. The frequency used by 5G, 60GHz, is also the frequency at which Oxygen molecules resonate. 01 x 10 24 atoms d) atoms of hydrogen is this? 2. This is probably wrong, but I hope this helps or at least gives you an idea on how to do it. 00 g oxygen, 11. 02 xx 10^23 "molecules/mol". oxygen molecules = × 10. It is tetramer, that is, one molecule of hemoglobin in adult is composed of four globin chains, 2 alpha and 2 beta. This is due to improved gas flow resulting in better combustion efficiency. The promotional materials from Telecom companies brag that 5G messes with oxygen molecules. When you hit oxygen molecules with 60 GHz millimeter wave emissions it affects the orbital properties of the. Chemistry 30S Unit 3 – Chemical Reactions 2. 022×1023 of Hydrogen + 6. 0 g of CH 3 OH (methanol, formula mass 32. The molecules were discovered in the Orion star-forming complex. Enzymes and Reaction Rates. 2) For every mole of sulfure dioxide, we have 6. 02 10 molecules 1mol Na SO 2mol H O 142. 83 × 1022 oxygen atoms 6. An estimate of the rate of this termination step to the cycling of atomic oxygen back to ozone can be found simply by taking the ratios of the concentration of O 2 to O 3. What would be the ultimate 'solution' to such a problem as this "V. 015 atomic mass units happens to be water’s molecular weight, and the weight of one mole of water is approximately 18. Number of moles in 5g of calcium = mass / molar mass = (5 / 40) = 0. A gaseous mixture made from 10 g of oxygen and 5 g of methane is placed in a 10 L vessel at 25°C. Essentially rendering the air in the path of that 'laser beam' un. Note that rounding errors may occur, so always check the results. Enter your answer in scientific notation. Free O2 occurs in the exhaust when there is an excess of. LG V50 ThinQ 5G’s is one of the first 5G phones available. 02 \times 10^{-23}$c. 6 g CO 1 mol 12. 258 moles SiO. Here's a diagram of how iron, histidine, the heme group and O2 oxygen molecules interact with hemoglobin, which alters its structure depending on the "oxygenated" vs. (a) Calculate the number of oxygen molecules and the number of oxygen atoms in 39. A has unleashed 60 Ghz all throughout the country with WU-HAN as the PILOT CITY. CHAPTER 5 HOW CHEMISTS MEASURE ATOMS AND MOLECULES 137 Since the mass of individual atoms is a very, very small number when expressed in SI units such as g or kg, it is convenient to express atomic masses using the atomic mass unit (u). "On your oxygen molecules, the little electrons, with 5G they start to oscillate. When it lacks oxygen, it changes to a “T-state” and appears blue, which is why low-oxygen blood has a blue color. 60GHz causes the rotation of the electrons around the oxygen molecule to spin, thus inhibiting the ability of hemoglobin to properly uptake these oxygen molecules. The Avogadro's Constant is equal to 6. , 750cm 3 of CO 2 and CH 4 contains the same number of molecules) · Molar volume is the volume occupied by 1 mole of gas. December 20,. Let's think about this a bit further: 58. This video isn't here right now. In diatomic gases, No. Standard Temperature and Pressure (STP) is defined as 0 degrees Celsius and 1 atmosphere of pressure. 71 Graph the data from the data table. The benefit of Oxygen absorption relative to frequency re-use is detailed in figure 2. of atoms =$2 \times \text{No. 89 moles of calcium d. 03:02 I want to talk to you about 5G and the frequencies that 5G uses. From the periodic table we see the atomic weight of hydrogen is 1. The result is increased oxygen content. 60GHz is the oxygen molecule absorption spectrum… This is the frequency that the oxygen molecules start reacting to… They’re gonna be using 5G to mess with oxygen… When you hit oxygen molecules with 60GHz millimeter emissions, it effects the orbital properties of the electrons…. 022 x 1023 units of that substance. While oxygen absorption at 60GHz severely limits range, it also eliminates interference between same frequency terminals. a Molecule of the Week. 26 moles Al metal. So 5G is absorbing the oxygen and then your hemoglobin can’t take up the oxygen. none of the above 16. Oxygen the molecule is 0 2. and methylbenzene: However, for these hydrocarbons, combustion is hardly ever complete, especially if they are burnt in air. Carbon is 12. 625 of a mole and a mole of anything contains 6. How many oxygen molecules are needed for combustion of 0. 5M glucose solution is needed to provide 100 mg of glucose? 100 mg x 1 mole/180 grams x 1 gram/1000 mg x 1 liter/0. 5G will disrupt the uptake of oxygen to cause oxygen deprivation to each cell at the level of the mitochondria. 00 g of oxygen from the total of 50 gm of Oxygen to produce 11 gm of Carbon Dioxide. Trees make it out of carbon dioxide. Options (a) 10 gm molecules (b) 5 gm molecules (c) 1 gm molecules (d) 0. Type in your own numbers in the form to convert the units! Convert another chemical substance. 0g of oxygen is: a. On Twitter, an in a viral video clip, an unidentified woman claimed that 5G 'sucks oxygen out of your lungs. NASA's Curiosity rover continues to make discoveries that challenge our understanding of the Martian environment. The formula P2O5, could itself represent one molecule of diphosphorus pentoxide. (b) Calculate the mass of 9. 011 × 10 23 water molecules = 0. Mlib013075 005 10. 02 x 10 23 molecules H 2SO 4 = 1. What we breathe are two oxygen molecules bonded together with the electrons that they share. For example, it is well documented that 5G radiation causes "Voltage Gated Ion Channels" (VGIC), specifically with. Oxygen absorption makes possible the same-frequency reuse within a very localized region of air space. a Molecule of the Week. With some rare exceptions, organic molecules contain carbon atoms that are typically linked to hydrogen, oxygen or nitrogen atoms. So what happens when these oxygen molecules are oscillating at 60GHz (part of the 5G spectrum) ? It's like sticking your hand in a fan and trying to catch the blade, only this blade is spinning at 60 Billion revolutions per second. 7 10 molecules H O 1mol H O 6. 3 grams of (NH4)3PO4?. oxygen atoms = × 10. So, number of oxygen molecules: Moles of oxygen gas: 1 mole = 1 gram molecule of compound. Home News 5G - a public health tragedy in the making? Who We Are Meet The Team it splits into positive and negative charges which then creates a negatively-charged matrix built from molecules of hydrogen and oxygen. 21 mol/mol, and argon (Ar) with CAr = 0. Two atoms together. From the periodic table we see the atomic weight of hydrogen is 1. The number of gram molecules of oxygen in CO molecule is 5g molecules. The question asks to calculate the number of molecules in 13. Ozone generators produce ozone by adding energy to oxygen molecules (O 2), which cause the oxygen atoms to part ways and temporarily recombine with other O 2 molecules, creating ozone (O 3). Numerical problems based On Mole Concept Question 1. Recent studies have shown that nitric oxide can bind to specific cysteine residues in hemoglobin and also to the. 144 g of oxygen. If we have one mole of water, then we know that it will have a mass of 2 grams (for 2 moles of H atoms) + 16 grams (for one mole O atom) = 18 grams. If the pressure is 1 atm, the pressure due to oxygen is A) 0. 00 g of carbon is burnt in 50. When it lacks oxygen, it changes to a “T-state” and appears blue, which is why low-oxygen blood has a blue color. In less than a microsecond the oxygen may relax through collisional processes with other molecules in the air. WiFi, 5G and How They Affect Fertility and Our Molecules | Jeff Rense [video] Starship Earth: The Big Picture. Free O2 occurs in the exhaust when there is an excess of. 5 xx 10^24 molecules. Numerical problems based On Mole Concept Question 1. There are six oxygen atoms in three CO 2 molecules and four oxygen atoms in four H 2 O molecules. The Potential Reach and Influence of 5G. There are now three carbon atoms, eight hydrogen atoms, and 10 oxygen atoms on each side of the. 0 kg of carbon in an excess of oxygen. Information regarding 5G. Explanation: Number of molecules of CO = 6. There's something more though that doesn't show up in the equation. 02 23 10 molecules O2 ___ 1 mol O 2 2 O atoms __ 24 molecule O 2 6. It is tetramer, that is, one molecule of hemoglobin in adult is composed of four globin chains, 2 alpha and 2 beta. The 60 GHz range is known as the Oxygen Absorption Band. 999 AMU) Hydrogen Oxygen Hydrogen WATER MOLECULE menu 6. We received this request on 9 April 2020 and have considered it under the Environmental Information Regulations 2004 (“the EIR”). CBSE Class 9 Chemistry Chapter 3 Atoms and Molecules Exercise Questions with Solutions to help you to revise complete Syllabus and Score More marks. 125 Now we will calculate the simplest ratio of the element by dividing the number of moles of each element by the smallest value. 02 x 10 23 molecules H 2SO 4 = 1. So 5G is absorbing the oxygen and then your hemoglobin can’t take up the oxygen. So, on your oxygen molecules, the little electrons, with 5G they start to like oscillate, so this 5G is absorbing. 24 × 100% = 60% 2. For N molecules of a compound with the general formula X a Y b:. Couple that with COVID19 and it's planned / mutated genetic offshoots of COVID21, and you have essentially what I would term as 'ZombieLandia'. Now, your skin is hotter than the interior part of your body so heat starts flowing, causing the inside part of your body to become hotter. The FCC's safe limit for mobile phones is a specific absorption rate (SAR) of 1. Diatomic oxygen gas constitutes 20. O 3 + O → 2 O 2. Essentially rendering the air in the path of that 'laser beam' un. Relative Humidity The amount of water vapor in the air at any given time is usually less than that required to saturate the air. These losses are greater at certain frequencies, coinciding with the mechanical resonant frequencies of the gas molecules. The 60GHz Oxygen Absorption Band. 022 x10 23. Normally Oxygen-18 is normally produced by separation of the naturally occuring element. Molecules can absorb energy from the wireless signal, but when those molecules collide with other molecules such as air or body fluids, the molecules will lose that energy and the energy will get converted into heat. If you want molecules, just divide the whole thing by 2 because there are 2 oxygen atoms in one molecule of oxygen gas. It is composed of four protein chains, two alpha chains and two beta chains, each with a ring-like heme group containing an iron atom. "On your oxygen molecules, the little electrons, with 5G they start to oscillate. The power level of 5G radio waves is far too low to affect air molecules, meaning it cannot suck oxygen out of the air. , the tennis balls are joined with Scotch tape). Unbelievable comparisons to symptoms 'showing' as a V-Irus compared vs what happens when one is hit with 60GHz waves, and it's impact. 5G is the term used to describe the next-generation of mobile networks beyond the 4G. 015 atomic mass units happens to be water’s molecular weight, and the weight of one mole of water is approximately 18. Sample Question: Dianabol is one of the anabolic steroids that has been used by some athletes to increase the size and strength of their muscles. Atomic mass is the mass of 1 mole of atoms. 9% of the volume of air. 709 x 10^24 atoms. at STP? Answer in units of L. Oxygen molecules have electrons that they share with each other, oxygen is a diatomic molecule. For example, oxygen gas O 2 is diatomic (each molecule contains two atoms) so its relative formula mass is 32. One way to determine if a molecule is organic or inorganic is to look at its molecular formula. This specific frequency is absorbed by oxygen. 5G will disrupt the uptake of oxygen to cause oxygen deprivation to each cell at the level of the mitochondria. 00 g oxygen, 11. Chapter 2 Atoms, Molecules and Ions 18 Isotope Abundance and Atomic Mass 9. The best part about mols is that 1 mol of atoms is equal to the atomic mass in grams and 1 mol of molecules is equal to the molecular mass in grams. Other theorists claim that 5G mobile networks are being deployed in high frequency bands of up to 60 GHz, thus causing ionization of the oxygen molecules in the air. Herschel Telescope Detects Oxygen Molecules In Space. For every 1 mol, there are 6. This is probably wrong, but I hope this helps or at least gives you an idea on how to do it. Which of the following is a chemical property? A Oxidizes in air B Conducts an electric current C Attraction. (b) How many molecules of cinnamic alcohol are contained in a sample of mass 0. 02 x 1023 molecules 1 atom Mg Example 2: Calculate the number of atoms in one-millionth of a gram of magnesium, Mg. 5 g of S 8 (sulfur, formula. Select the statement below that is incorrect in regard to this reaction. in Get all GUIDE and Sample Paper PDFs by whatsapp from +91 89056 29969 Page 19 = 0. 5 g of S 8 (sulfur, formula. 1 oxygen moleculeB. It lies between the super high frequency band, and the far infrared band, the lower part of which is also referred. 76 10 molecules Cl 1mol Cl 6. Add those up, and 32+32=64 AMU, which is the molecular mass of SO2. 78 mol/mol; N2 accounts for 78% of all molecules in the atmosphere. Coronavirus started in China from Wuhan, between Military Games and 5G up to 60 Ghz « EMR Health Alliance of BC on Coronavirus, according to studies and experts with 5G, there is "immunosuppression and non-absorption of Oxygen". What is the partial pressure of each gas, and what is the total pressure in the vessel? (10 g O 2)(1 mol/32 g) = 0. 02 10 molecules 2mol AlCl 3mol Cl. (Atomic mass of Ca = 40 u; O = 16 u) [CBSE 2011 ] Ans. The way 60 GHz impacts oxygen is this. (b) Calculate the mass of 9. The benefit of Oxygen absorption relative to frequency re-use is detailed in figure 2. At 60 GHz, Oxygen molecules in the atmosphere interact with the RF signals to cause significant attenuation. Oxygen is in the air we breathe, it comes from trees. The combustion of 38. of glucose molecules = 0. 0 g divided by 32. It takes two molecules of the diatomic hydrogen gas, combined with one molecule of the diatomic oxygen gas to produce two molecules of water. And you might already recognize this. The empirical formula of X is CH 2 O.
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## 8 May 2015
### A Link Between topicmodels LDA and LDAvis
Carson Sievert and Kenny Shirley have put together the really nice LDAvis R package. It provides a Shiny-based interactive interface for exploring the output from Latent Dirichlet Allocation topic models. If you've never used it, I highly recommend checking out their XKCD example (this paper also has some nice background).
LDAvis doesn't fit topic models, it just visualises the output. As such it is agnostic about what package you use to fit your LDA topic model. They have a useful example of how to use output from the lda package.
I wanted to use LDAvis with output from the topicmodels package. It works really nicely with texts preprocessed using the tm package. The trick is extracting the information LDAvis requires from the model and placing it into a specifically structured JSON formatted object.
To make the conversion from topicmodels output to LDAvis JSON input easier, I created a linking function called topicmodels_json_ldavis. The full function is below. To use it follow these steps:
1. Create a VCorpus object using the tm package's Corpus function.
2. Convert this to a document term matrix using DocumentTermMatrix, also from tm.
3. Run your model using topicmodel's LDA function.
4. Convert the output into JSON format using topicmodels_json_ldavis. The function requires the output from steps 1-3.
5. Visualise with LDAvis' serVis. | |
# Avionics/Safety/Regs question
### Help Support Homebuilt Aircraft & Kit Plane Forum:
#### DLrocket89
##### Well-Known Member
So, here's a question...I'm considering building a CH801 (in about 10 years :ermm. If I fly the CH801, I'll fly it because it'll be good for getting into and out of my backyard. My intent is to make it amphibious and be able to fly up north and go camping/fishing on a lake with it.
Now, I was interested in the Garmin 430W (whatever one is the Nav/Comm/GPS combo) that lets you fly WAAS approaches...so...instrument landings on GPS basically.
I've also seen that some of the LCD panels will show you a "hiway in the sky"...basically, they take your flight plan and convert it into boxes on the screen. Fly through those boxes and you're on course.
That got me thinking...with WAAS being as accurate as it is (and electronics these days being as adapative as it is), is there a way I could program in a WAAS approach (or something similar..."hiway in the sky", whatever) so that I could fly an instrument/WAAS approach into my backyard?
It's something like $10K or$100K to have a WAAS approach officially published...not interested in that. Just wondering if the instruments would help me out any.
As for the regs part of the question, I have a sneaky suspicion that this would be illegal per FAA regs. Maybe. I dunno...I'm new to this whole thing.
Thoughts anyone?
#### Topaz
##### Super Moderator
Staff member
Log Member
I can't help you on the instruments question, but we get the "fly from my backyard" question quite a bit. Basically:
1) You'd better have a really big "back yard". As in tens of acres. We usually have the question asked, "Is a 500' strip okay, even though I've got trees at one or both ends?" Even though the published takeoff and landing distances of something like the CH801 are very short, you still need to have a pretty large chunk of land for a runway for one, with no obstructions on either end. Why both ends? For the time you have to do a go-around. If the far end is obstructed, your go-around may end up in the trees or wires you thought you'd never cross. You're really going to need something like an unobstructed 1,200'+ strip. There's just too many variables at work to make it safe trying to shoehorn your airplane into a tiny strip every time you go flying. It's just not worth the effort and/or risk. That goes double, triple, and quintuple if you think you're going to do instrument approaches - even under GPS/WAAS. Up the runway length a whole bunch if that's what you really intend to do.
2) Federal. AFAIK, there's nothing at the federal level preventing you from scraping out a runway on your own 'south 40' and flying from it. Just don't let anyone else ever land there, because then you're an airport and the FAA wants to know about you.
3) Local. God help you if you've got neighbors less than a mile away. I don't know what it's like in Wisconson, but if you want to open up a runway - even for just you - in California, you'll need to get a zoning variance from the local City Council. And a Conditional Use Permit. Both of which will require a public hearing where your neighbors are invited to come and comment on the idea of you flying over their houses and heads at low altitude. To get the Conditional Use Permit, you'll need to file an Environmental Impact Report conducted by a recognized independant third-party contractor. No, you can't do it yourself, nor can your lawyer buddy do it for you. EIRs generally run from about $20k on up. And up. And up. Once the EIR is done, there will be a public hearing on that, so that they can then do the hearing for the Conditional Use Permit. In California, if you're going to let anyone but you and you alone fly from the airport (including friends and family) you have to get CalTrans (the state transportation entity) to sign off on your airport plans as well. This is not to say that, out in the desert in the middle of nowhere, there aren't plenty of guys with great neighbors (sufficiently far away) who don't complain when he's flying his airplane from his unapproved dirt strip that he forgot to tell any of the authorities about. And everything will probably be just fine until some neighbor finally complains, or there's an accident. And then the sky falls in on him. Start looking at the regs for your state, county, and city. Become really good friends with your neighbors. If there's an existing airport anywhere in the area, just use that. You'll save yourself so much work and heartache in the end, even if you have a patch of land that's really suitable for a runway. #### DLrocket89 ##### Well-Known Member I can't help you on the instruments question, but we get the "fly from my backyard" question quite a bit. Basically: 1) You'd better have a really big "back yard". As in tens of acres. We usually have the question asked, "Is a 500' strip okay, even though I've got trees at one or both ends?" Even though the published takeoff and landing distances of something like the CH801 are very short, you still need to have a pretty large chunk of land for a runway for one, with no obstructions on either end. Why both ends? For the time you have to do a go-around. If the far end is obstructed, your go-around may end up in the trees or wires you thought you'd never cross. You're really going to need something like an unobstructed 1,200'+ strip. There's just too many variables at work to make it safe trying to shoehorn your airplane into a tiny strip every time you go flying. It's just not worth the effort and/or risk. That goes double, triple, and quintuple if you think you're going to do instrument approaches - even under GPS/WAAS. Up the runway length a whole bunch if that's what you really intend to do. 2) Federal. AFAIK, there's nothing at the federal level preventing you from scraping out a runway on your own 'south 40' and flying from it. Just don't let anyone else ever land there, because then you're an airport and the FAA wants to know about you. 3) Local. God help you if you've got neighbors less than a mile away. I don't know what it's like in Wisconson, but if you want to open up a runway - even for just you - in California, you'll need to get a zoning variance from the local City Council. And a Conditional Use Permit. Both of which will require a public hearing where your neighbors are invited to come and comment on the idea of you flying over their houses and heads at low altitude. To get the Conditional Use Permit, you'll need to file an Environmental Impact Report conducted by a recognized independant third-party contractor. No, you can't do it yourself, nor can your lawyer buddy do it for you. EIRs generally run from about$20k on up. And up. And up. Once the EIR is done, there will be a public hearing on that, so that they can then do the hearing for the Conditional Use Permit. In California, if you're going to let anyone but you and you alone fly from the airport (including friends and family) you have to get CalTrans (the state transportation entity) to sign off on your airport plans as well.
This is not to say that, out in the desert in the middle of nowhere, there aren't plenty of guys with great neighbors (sufficiently far away) who don't complain when he's flying his airplane from his unapproved dirt strip that he forgot to tell any of the authorities about. And everything will probably be just fine until some neighbor finally complains, or there's an accident. And then the sky falls in on him.
Start looking at the regs for your state, county, and city. Become really good friends with your neighbors.
If there's an existing airport anywhere in the area, just use that. You'll save yourself so much work and heartache in the end, even if you have a patch of land that's really suitable for a runway.
Yeah...I feel sorry for you people in California. I know of 3 people w/in 25 miles of me that fly out of backyards here in Wi. I know I could pull it off in Wisconsin (including buying sufficient real estate).
My wife wants to move out east eventually, we'll have to see what things are like out there...
#### Topaz
##### Super Moderator
Staff member
Log Member
Yeah...I feel sorry for you people in California. I know of 3 people w/in 25 miles of me that fly out of backyards here in Wi. I know I could pull it off in Wisconsin (including buying sufficient real estate).
Well, that's great then. Check with those guys that are already doing it and see what process they went through. People love to talk about their airplanes and the clever things they've done with them. You'll get an earful of really great practical advice for the price of a beer.
My wife wants to move out east eventually, we'll have to see what things are like out there...
Depends upon where you go, but it'll probably be more like here in CA. The higher the population density, the more they regulate things like this. They might be a little less stringent on the EIR (you know how we Californians are about the environment), but the rest of the leaps and hurdles are probably going to sound disturbingly familiar. Fortunately, there seems (from my perspective here) to be a larger number of small airports 'back east', so that the odds of you locating near one are relatively good.
#### LArzfromarz
##### Well-Known Member
DL-
You can do something we called a "synthetic approach". Simply make the runway endpoint a waypoint. You fly the GPS (hopefully WAAS) as a localizer. It won't create a glideslope but you can use a standard 3 degree approach, follow the CDI and you should get to minimums. Shouldn't be real difficult but it is NOT a precision approach and I would not attempt in IFR conditions.
Larz
#### bmcj
##### Well-Known Member
HBA Supporter
1) You'd better have a really big "back yard". As in tens of acres. We usually have the question asked, "Is a 500' strip okay, even though I've got trees at one or both ends?" Even though the published takeoff and landing distances of something like the CH801 are very short, you still need to have a pretty large chunk of land for a runway for one, with no obstructions on either end. Why both ends? For the time you have to do a go-around. If the far end is obstructed, your go-around may end up in the trees or wires you thought you'd never cross. You're really going to need something like an unobstructed 1,200'+ strip. There's just too many variables at work to make it safe trying to shoehorn your airplane into a tiny strip every time you go flying. It's just not worth the effort and/or risk. That goes double, triple, and quintuple if you think you're going to do instrument approaches - even under GPS/WAAS. Up the runway length a whole bunch if that's what you really intend to do.
I worked with an ultralight dealer and flight school when someone came to us and wanted to buy an ultralight to fly out of his bick back yard. I took him up in the two seat for a lesson and to look at his landing site. He had a large flat area on his property (in the hills) with a few obstructions. I could have landed there, but it would require a careful setup. We flew back to the airport where I told him that I would recommend against his plan based on the margins of safety and lack of options if things went bad. My bass (the U/L dealer agreed and supported that assessment despite the fact that it meant the loss of a sale.
As I said before, I could have landed there, but chose not to because I didn't want to give the passenger a false sense of "If he can do it, I can too." Not being pretentious, just cautious.
#### Topaz
##### Super Moderator
Staff member
Log Member
I'll bet we've all had this dream from time to time. Especially if there's a likely-looking patch of land to be had. I remember as a teen when the ultralight craze was going on, looking at the huge back-field at the local elementary school and thinking I could just get an ultralight in and out of there. Ah, the naïvité of youth. I swear my dad probably bought the Aeronca just to keep me from building something and trying it. :gig:
Anyway, my experince of this sort of thing is that it's a lot like a ski slope. From the bottom, you say, "Sure, I can handle that!" Once you get to the top, though, you're suddenly wondering how they managed to grade that slope about twice as steep while you were on the chairlift...
Runways are the same. I took my first flying lessons at Brackett Airport (POC). On the ground, it's just a huge parcel of land - particularly for someone growing up in southern California. Just huge. And the runways look like they're forever. And then you're on your first approach and you're thinking, "We're going to land on THAT little thing?!?!?!"
#### DLrocket89
##### Well-Known Member
I'll bet we've all had this dream from time to time. Especially if there's a likely-looking patch of land to be had. I remember as a teen when the ultralight craze was going on, looking at the huge back-field at the local elementary school and thinking I could just get an ultralight in and out of there. Ah, the naïvité of youth. I swear my dad probably bought the Aeronca just to keep me from building something and trying it. :gig:
Anyway, my experince of this sort of thing is that it's a lot like a ski slope. From the bottom, you say, "Sure, I can handle that!" Once you get to the top, though, you're suddenly wondering how they managed to grade that slope about twice as steep while you were on the chairlift...
Runways are the same. I took my first flying lessons at Brackett Airport (POC). On the ground, it's just a huge parcel of land - particularly for someone growing up in southern California. Just huge. And the runways look like they're forever. And then you're on your first approach and you're thinking, "We're going to land on THAT little thing?!?!?!"
Yeah, understood, lots of wisdom there. The hope was that I could spend a lot of time practicing such things and eventually get to it. *Shrugs* saves on hangaring fees at least.
My wife rides horses, so we were planning on having land enough for that (along with a nice pasture and stuff). I was figuring rent a nice bulldozer or something for a day and bulldoze a nice flat strip of dirt, get the rocks and stuff out, seed it in a nice grass, and there you go. *shrugs* we'll see.
#### bmcj
##### Well-Known Member
HBA Supporter
Before you decide how close to put the hangar, taxiway and runway to the stable, best to check your horse's reaction to a running airplane engine.
#### BBerson
##### Light Plane Philosopher
HBA Supporter
It takes a huge piece of land to make a safe private airstrip. Mostly for clear approaches.
I had a dream of keeping a helicopter next to my shop. But even for a helicopter the approaches would be uncomfortably tight here with my 1000feet of land.
My wife will not allow a helicopter because of the horses, so I gave up.
The neighbors would have a heart attack as well.
My airplanes are trailerable. Believe it not, most airplanes sit idle most of the time. Storage at home on a trailer for the winter works well for me.
#### DLrocket89
##### Well-Known Member
Before you decide how close to put the hangar, taxiway and runway to the stable, best to check your horse's reaction to a running airplane engine.
Ain't that the truth? I've been around horses my whole life, some are "good" with these things, some bad, and some freak out "because I can".
I'm also looking at typical aviation engines, with straight pipes like they have, and wondering if there's a way to put a muffler on them. It'd need to be sized appropriately of course to not create undo backpressure or whatever, but still. *shrugs*
I used to ride motocross bikes alot, the insane volume levels there drove me towards trying to find a quieter muffler to keep the neighbors happier. Same thing here perhaps?
#### Topaz
##### Super Moderator
Staff member
Log Member
Tony Bingelis' book Firewall Forward has a very interesting low-backpressure aircraft muffler design on p. 111. The book is well worth the purchase price and, I would say, essential if you're putting a homebuilt airplane together.
#### bmcj
##### Well-Known Member
HBA Supporter
Just a wild supposition, but I wonder if gun silencer technology could be used as a muffler. A straight line unrestricted path would definitely reduce the back pressure. I know the noise source is different (bullet=sonic boom) but could you gain some noise suppression in an exhauset stack with the same design?
#### BBerson
##### Light Plane Philosopher
HBA Supporter
Tony Bingelis' book Firewall Forward has a very interesting low-backpressure aircraft muffler design on p. 111. The book is well worth the purchase price and, I would say, essential if you're putting a homebuilt airplane together.
Is that the Swiss muffler?
Swiss style muffler
#### Topaz
##### Super Moderator
Staff member
Log Member
Is that the Swiss muffler?
Swiss style muffler
Yep, that's it. In fact, the text and drawings on that page are taken directly from Firewall Forward. And it is, indeed, very much like a gun silencer in operation. No baffling in the flow path.
#### DLrocket89
##### Well-Known Member
Is that the Swiss muffler?
Swiss style muffler
That's pretty much a motocross bike's muffler too. On motocross bikes, they SUCK, but that's because they're usually about 8" long. :shock:
Definately planning on going with a muffler like that, regardless of anything (engine, where I fly out of, etc).
##### Well-Known Member
I can't help you on the instruments question, but we get the "fly from my backyard" question quite a bit. Basically:
1) You'd better have a really big "back yard". As in tens of acres. We usually have the question asked, "Is a 500' strip okay, even though I've got trees at one or both ends?"
Some years ago a friend built a UL strip on his property. The runway was maybe 400 feet long, cut through a bunch of scrub trees, and ending at the base of some 50 foot tall Poplars. This was a one-way in and opposite way out strip and it didn't matter which way the wind was blowing (basically only useable in no wind). Several of us flew there on occasion but it wasn't for the faint of heart. Judgement eventually prevailed and the strip was abandoned.
#### Topaz
##### Super Moderator
Staff member
Log Member
I'll bet final approach was a hoot. "Please don't need to do a go-around. Please don't need to do a go-around!"
We fly that type of one-way-in, opposite-way-out pattern at my airfield, except that it's for noise abatement and you can bust it if the conditions warrant. No trees in the way. The neighbors on the 'bad' end of the runway get a little upset when the jump plane takes off that way, but one of the advantages of gliders is that when we land 'over the wires' as we call it (there's some low phone lines well below the approach path), nobody hears us go over. :gig: | |
## University Calculus: Early Transcendentals (3rd Edition)
Published by Pearson
# Chapter 9 - Section 9.8 - Taylor and Maclaurin Series - Exercises - Page 536: 33
#### Answer
$-1-2x-\dfrac{5x^2}{2}+....$
#### Work Step by Step
The Maclaurin's series for $\cos x$ is as follows: $1-\dfrac{x^2}{2!}+\dfrac{x^4}{4!}+......=\Sigma_{n=0}^{\infty} (-1)^n \dfrac{x^{2n}}{(2n)!}$ Now, we have the Maclaurin's series for $\dfrac{2}{1-x}$ is as follows: $2(1+x+x^2+......+x^n+...)=2 \Sigma_{n=0}^{\infty} x^n$ Therefore, $\cos x -\dfrac{2}{1-x}=1 -\dfrac{x^2}{2!}+\dfrac{x^4}{4!}+......-[2(1+x+x^2+......+x^n+...)]=[\Sigma_{n=0}^{\infty} (-1)^n \dfrac{x^{2n}}{(2n)!}]-[2 \Sigma_{n=0}^{\infty} x^n]$ or, $=-1-2x-\dfrac{5x^2}{2}+....$
After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback. | |
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Videos, worksheets, 5-a-day and much more The worksheets on this page contain picture graphs with symbols, Printable bar graph worksheets with questions, A collection basic, intermediate, and advanced of line graph worksheets. Till now, we have seen how to draw a pie chart. Example: The graph shows different grades scored by students in grade 4. Worksheet: Creating Pie Charts #2 Related Resources The various resources listed below are aligned to the same standard, (6SP04) taken from the CCSM (Common Core Standards For Mathematics) as the Statistics and probability Worksheet shown above. Quickly access your most used files AND your custom generated worksheets! Displaying top 8 worksheets found for - Pie Chart Grade 7. An exemplary tool for comparison, a pie chart displays the data as pie slices. They made a pie graph with the survey results. Read the pie graph and answer the questions. There is an extension question at the end testing their understanding on interpreting data from a pie chart. The worksheet is differentiated where each question requires a bit more working out each time. Some of the worksheets for this concept are Grade 4 fractions work, Grade 4 fractions work, Summer camp activites, Pie charts, Data handling grade 4 7, Pie graph, Mathematics linear 1ma0 pie charts, Rock restaurant surveyed a sample of customers on their. Preview. Pie charts are provided and students can color in the charts if needed. This worksheet is a supplementary fourth grade resource to help teachers, parents and children at home and in school. You can & download or print using the browser document reader options. The worksheets might be less challenging than those where the angles must be measured or drawn, but still are great sixth grade graphing material. Ans. Example 1. Worksheets: Comparing proper fractions (with pie charts) Below are six versions of our grade 4 fractions worksheet on comparing proper fractions. We also have a bunch of pie charts worksheets with either with numbers or percentage as representations. Data and graphs Worksheets â PDF printable data and graphs math worksheets for children in: Pre-K, Kindergarten, 1 st grade, 2 nd grade, 3 rd grade, 4 th grade, 5 th grade, 6 th grade and 7 th grade. The "Advanced Pie Graphs" require students to understand percentages./p>. (Approx grade levels: 6, 7, 8) Line Graph Worksheets. This page has several pie graph worksheets. Pie charts . 25 students. Now, answer the following questions: Q1. Pie Graph - Color, Tally and GraphThis is a first pie graph worksheet set - most suited to lower grades (kindergarten, grade one, grade two)There are 9 worksheets in this set.Each worksheet follows the same pattern, you color the animals according to the key, you count and tally them up. Use the information in the summer camp pie graph to answer the questions. Pie Chart Grade 4 - Displaying top 8 worksheets found for this concept. The "Basic Pie Graphs" require students to have a basic understanding of fractions. ID: 1270450 Language: English School subject: Math Grade/level: Elementary Age: 6-10 Main content: Pie Charts Other contents: Add to my workbooks (6) Download file pdf Embed in my website or blog Add to Google Classroom How many student scored Grade A? Some of the worksheets for this concept are mathematics linear 1ma0 pie charts bar charts histograms line graphs pie charts gcse exam questions on pie charts grade d their pie charts the pie graph shows the information on the number of farm summer camp activites rock restaurant surveyed a sample of customers on their graphing exercise create a pie graph by selecting a. Students must identify which fraction is larger or whether the 2 fractions are equal. Fractions have different denominators. It has an answer key attached on the second page. Q2. Grade 4 Maths Resources (6.2 Data Representation - Pie Charts ... (6.2 Data Representation â Pie Charts Printable Worksheets) Written by Somaira Khatri. Box Plots (Box-and-Whisker Plots) Create box plots on a number line using the values for Q1, median, Q3, minimum, and maximum. 'Pie Chart questions'- answers have been provided and would work well printed onto tracing paper for easy checking of the drawings. Some of the worksheets for this concept are Mathematics linear 1ma0 pie charts, Data handling grade 4 7, Grade 4 fractions work, Graphs and charts, Pie charts, Pie graph, Bar charts histograms line graphs pie charts, Summer camp activites. To download/print, click on pop-out icon or print icon to worksheet to print or download. The pie graph worksheets are designed for students of grade 3 through grade 7. Looking at the wedge-like sectors on the chart, we can decipher the proportion of each category in a jiffy. Answer 1 (B) Any other information like TV Size and Sold by various distributors is not get from the chart. Graph and data worksheet for 4th grade children. Therefore, people prefer more the vanilla flavor than the red velvet flavor. Section B: (Examples) Go through pie chart questions in this section one by one. Homework that was awarded a grade B can be expressed as the following fraction: \dfrac{5}{24}. Please login to your account or become a member and join our community today to utilize this helpful feature. The pie graph in these printable worksheets for grade 5, grade 6, and grade 7 require conversion of a whole number into percentage. And 1 unit length on y ⦠Whole numbers, percents, and fractions are used to represent the data. This is a math PDF printable activity sheet with several exercises. Read and create line graphs with these worksheets. Whether you want a homework, some cover work, or a lovely bit of extra practise, this is the place for you. ... Use the information in the summer camp pie graph to answer the questions. Line Plot (Dot Plot) Worksheets The Corbettmaths Practice Questions on Reading Pie Charts. Contents. Answer 5 (B) For March month the Stick height is 4 unit length on y-axis. 4) How many customers voted for burger as their favorite? Requires knowledge of fractions. Grade 4 Maths Resources (6.2 Data Representation . Some of the worksheets for this concept are Grade 4 fractions work, Grade 4 fractions work, Summer camp activites, Pie charts, Data handling grade 4 7, Pie graph, Mathematics linear 1ma0 pie charts, Rock restaurant surveyed a sample of customers on their. Grades in math test State Standards a Basic understanding of fractions extension at... Length on y-axis by students in grade 4 - Displaying top 8 worksheets for! Several exercises sectors on the second page and join our community today utilize! Join our community today to utilize this helpful feature, a pie graph the! 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Essential University Physics: Volume 1 (3rd Edition)
We can find the length of the wire as $L=r\theta$ We plug in the known values to obtain: $L=(8.1)(1.4)$ $L=11cm$ | |
# Magnetic force term in Kobe's derivation of Maxwell's equations
I'm trying to follow the paper "Derivation of Maxwell's equations from the gauge invariance of classical mechanics" by Donald Kobe, available here (American Journal of Physics, 1980): https://aapt.scitation.org/doi/10.1119/1.12094. There's a vector calc step, I think using integration by parts, that I'm having trouble following through to get a magnetic force term.
After a few pages (first column of p.350), the author gets a Lagrangian, equivalent to the following: $$L = \frac{1}{2} m\dot{\mathbf{r}}^2 - U(\mathbf{r}) + \frac{q}{c} \left( c A_0(\mathbf{r}, t) + \dot{\mathbf{r}} \cdot \mathbf{A}(\mathbf{r},t) \right)$$
The action is then $S= \int_{t_1}^{t_2} L \, dt$. To take the variation of this action, we start with
\begin{align} \delta S &= \int_{t_1}^{t_2} dt \left[ \frac{1}{2} m \, \delta (\dot{\mathbf{r}}^2 ) - \delta U(\mathbf{r}) + q \, \delta A_0(\mathbf{r}, t) + \frac{1}{c} \delta(\dot{\mathbf{r}} \cdot \mathbf{A}(\mathbf{r},t) ) \right] \\ &= \int_{t_1}^{t_2} dt \, \left[ (\delta \mathbf{r}) \cdot \left[ -m\ddot{\mathbf{r}} - \nabla U + q \left( - \nabla A_0 - \frac{\partial \mathbf{A}}{\partial t} \right) \right] + \dot{\mathbf{r}} \cdot ( \delta \mathbf{A}(\mathbf{r}, t) ) \right] \end{align}
where the terms dotted against $\delta(\mathbf{r})$ come from integration by parts and the Leibniz rule. It's the last term, the magnetic force, that gives me grief. I need to show that
$$\int_{t_1}^{t_2} dt \, [ \dot{\mathbf{r}} \cdot ( \delta \mathbf{A}(\mathbf{r}, t) ) ] = \int_{t_1}^{t_2} dt \, [ (\delta \mathbf{r}) \cdot (\mathbf{r} \times (\nabla \times \mathbf{A})) ]$$
However, when I expand the LHS integrand, I'm not sure how to rearrange the integral into the RHS form. | |
The following applet show interaction force between a circular current loop in magnetic field generated by a magnet.
Red arrow show the direction of the current.
Blue arrow are force $\vec{F}=i d\vec{\ell}\times \vec{B}$ due to current loop in magnetic field generated by a magnet.
You can change the location of magnet with two sliders (move in y/z direction).
The radius R of the current loop can be changed with slider,too.
Click play to trace out the magnetic field lines (produced by magnet).
/htdocs/ntnujava/ejsuser/2/users/ntnu/fkh/magnetNcoil_pkg/magnetNcoil.propertiesFull screen applet or Problem viewing java?Add http://www.phy.ntnu.edu.tw/ to exception site list | |
# Stochastic Differential Equations Pt2: The Lognormal Distribution
This post follows from the earlier post on Stochastic Differential Equations.
I finished last time by saying that the solution to the BS SDE for terminal spot at time T was
$\inline&space;S_T&space;=&space;S_0&space;e^{(\mu&space;-&space;{1&space;\over&space;2}\sigma^2)T&space;+&space;\sigma&space;W_T}$
When we solve an ODE, it gives us an expression for the position of a particle at time T. But we’ve already said that we are uncertain about the price of an asset in the future, and this expression expresses that uncertainty through the $\inline&space;\sigma&space;W_T$ term in the exponent. We said in the last post that the difference between this quantity at two different times s and t was normally distributed, and since this term is the distance between t=0 and t=T (we have implicitly ignored a term $W_0$, but this is ok because we assumed that the process started at zero) it is also normally distributed,
$W_T&space;\sim&space;{\mathbb&space;N}(0,T)$
It’s a well-known property of the normal distribution (see the Wikipedia entry for this and many others) that if $X&space;\sim&space;{\mathbb&space;N}(0,1)$ then $aX&space;\sim&space;{\mathbb&space;N}(0,a^2)$ for constant a. We can use this in reverse to reduce $W_T$ to a standard normal variable x, by taking a square root of time outside of the distribution so $W_T&space;\sim&space;\sqrt{T}\cdot{\mathbb&space;N}(0,1)$ and we now only need standard normal variables, which we know lots about. We can repeat our first expression in these terms
$\inline&space;S_T&space;=&space;S_0&space;e^{(\mu&space;-&space;{1&space;\over&space;2}\sigma^2)T&space;+&space;\sigma&space;\sqrt{T}&space;X}$
What does all of this mean? In an ODE environment, we’d be able to specify the exact position of a particle at time T. Once we try to build in uncertainty via SDEs, we are implicitly sacrificing this ability, so instead we can only talk about expected positions, variances, and other probabilistic quantities. However, we certainly can do this, the properties of the normal distribution are very well understood from a probabilistic standpoint so we expect to be able to make headway! Just as X is a random variable distributed across a normal distribution, S(t) is now a random variable whose distribution is a function of random variable X and the other deterministic terms in the expression. We call this distribution the lognormal distribution since the log of S is distributed normally.
The random nature of S is determined entirely by the random nature of X. If we take a draw from X, that will entirely determine the corresponding value of S, since the remaining terms are deterministic. The first things we might want to do are calculate the expectation of S, its variance, and plot its distribution. To calculate the expectation, we integrate over all possible realisations of X weighted by their probability, complete the square and use the gaussian integral formula with a change of variables
${\mathbb&space;E}[S_t]&space;=&space;\int^{\infty}_{-\infty}&space;S_t(x)&space;p(x)&space;dx$
$={S_0&space;\over&space;\sqrt{2\pi}}\int^{\infty}_{-\infty}&space;e^{(\mu-{1\over&space;2}\sigma^2)t&space;+&space;\sigma&space;\sqrt{t}x}&space;e^{-{1\over&space;2}x^2}&space;dx$
$={&space;{S_0&space;e^{(\mu-{1\over&space;2}\sigma^2)t}}&space;\over&space;\sqrt{2\pi}}\int^{\infty}_{-\infty}&space;e^{-{1\over&space;2}x^2&space;+&space;\sigma&space;\sqrt{t}&space;x}&space;dx$
$={{S_0&space;e^{(\mu-{1\over&space;2}\sigma^2)t}}&space;\over&space;\sqrt{2\pi}}\int^{\infty}_{-\infty}&space;e^{-{1\over&space;2}&space;(x&space;-&space;\sigma&space;\sqrt{t})^2}&space;e^{{1\over&space;2}\sigma^2&space;t}&space;dx$
$={{S_0&space;e^{\mu&space;t}}&space;\over&space;\sqrt{2\pi}}\int^{\infty}_{-\infty}&space;e^{-{1\over&space;2}&space;y^2}&space;dy$
$=S_0&space;e^{\mu&space;t}$
which is just the linear growth term acting over time [exercise: calculate the variance in a similar way]. We know what the probability distribution of X looks like (it’s a standard normal variable), but what does the probability distribution of S look like? We can calculate the pdf using the change-of-variables technique, which says that if S = g(x), then the area under each curve in corresponding regions must be equal:
$\int_{x_1}^{x_2}&space;p_x(x)&space;dx&space;=&space;\int_{g(x_1)}^{g(x_2)}&space;p_S(S)&space;dS$
$p_x(x)&space;dx&space;=&space;p_S(S)&space;dS$
$p_S(S_t)&space;=&space;p_x(x)&space;{dx&space;\over&space;dS_t}$
We know the function S(x), but the easiest way to calculate this derivative is first to invert the function t make it ameanable to differentiation
$x&space;=&space;{\ln{S_t&space;\over&space;S_0}&space;-&space;(\mu&space;-&space;{1&space;\over&space;2}\sigma^2)t&space;\over&space;\sigma&space;\sqrt{t}}$
${dx&space;\over&space;dS_t}&space;=&space;{1&space;\over&space;\sigma&space;\sqrt{t}&space;S_t}$
So the pdf of S expressed in terms of S is
$p_S(S_t)&space;=&space;{1&space;\over&space;S_t&space;\sigma&space;\sqrt{2\pi&space;t}}&space;\exp{-\Bigl(\ln{S_t\over&space;S_0}&space;-&space;(\mu-{1\over&space;2}\sigma^2)t&space;\Bigr)^2\over&space;2&space;\sigma^2&space;t}$
Well it’s a nasty looking function indeed! I’ve plotted it below for a few typical parameter sets and evolution times.
This distribution is really central to a lot of what we do, so I’ll come back to it soon and discuss a few more of its properties. The one other thing to mention is that if we want to calculate an expected value over S (which will turn out to be something we do a lot), we have two approaches – either integrate over $\inline&space;p_S(S_t)$
${\mathbb&space;E}[f(S_t)]&space;=&space;\int_0^{\infty}&space;f(S_t)p_S(S_t)dS$
or,instead express the function in terms of x instead (using $\inline&space;S_t&space;=&space;S_0&space;e^{(\mu&space;-&space;{1&space;\over&space;2}\sigma^2)t&space;+&space;\sigma&space;\sqrt{t}&space;x}$) and instead integrate over the normal distribution
${\mathbb&space;E}[f(S_t(x))]&space;=&space;\int_{-\infty}^{\infty}&space;f(x)p_x(x)dx$
This is typically the easier option. I think it is called the Law of the Unconscious Statistician. On that note, we’ve certainly covered enough ground for the moment!
-QuantoDrifter | |
### Session B5: The Scientific Legacy of John Wheeler
10:45 AM–12:33 PM, Saturday, May 2, 2009
Room: Governor's Square 15
Chair: James Hartle, University of California, Santa Barbara
Abstract ID: BAPS.2009.APR.B5.2
### Abstract: B5.00002 : John Wheeler, 1952 - 1976: Black Holes and Geometrodynamics
11:21 AM–11:57 AM
MathJax On | Off Abstract
#### Author:
Kip S. Thorne
(California Institute of Technology)
In 1952 John Wheeler turned his attention from nuclear physics and national defense to a backwater of physics: general relativity. Over the next 25 years, with students and postdocs he led a revolution'' that made relativity a major subfield of fundamental physics and a tool for astrophysics. Wheeler viewed curved spacetime as a nonlinear dynamical entity, to be studied via tools of geometrodynamics (by analogy with electrodynamics) -- including numerical relativity, for which his students laid the earliest foundations. With Joseph Weber (his postdoc), he did theoretical work on gravitational waves that helped launch Weber on a career of laying foundations for modern gravitational-wave detectors. Wheeler and his students showed compellingly that massive stars must form black holes; and he gave black holes their name, formulated the theory of their pulsations and stability (with Tullio Regge), and mentored several generations of students in seminal black-hole research (including Jacob Bekenstein's black-hole entropy). Before the discovery of pulsars, Wheeler identified magnetized, spinning neutron stars as the likely power sources for supernova remnants including the Crab nebula. He identified the Planck length and time as the characteristic scales for the laws of quantum gravity, and formulated the concept of quantum fluctuations of spacetime geometry and quantum foam. With Bryce DeWitt, he defined a quantum wave function on the space of 3-geometries and derived the Wheeler-DeWitt equation that governs it, and its a sum-over-histories action principle. Wheeler was a great inspiration to his colleagues and students, pointing the directions toward fruitful research problems and making intuitive-leap speculations about what lies beyond the frontiers of knowledge. Many of his ideas that sounded crazy at the time were just crazy enough to be right''.
To cite this abstract, use the following reference: http://meetings.aps.org/link/BAPS.2009.APR.B5.2 | |
# productive efficiency formula
Step 3: Finally, the formula for productivity can be derived by dividing the output (step 2) produced by the input (step 1) provided as shown below. “Underutilized” inputs can distort productivity calculation results. Productivity and efficiency are two of the key goals of any business enterprise. To be clear, shrinkage includes any scheduled/unscheduled contact centre activities that … Efficiency Formula. 24/12/2019 Gal Merom Production efficiency Leave a comment. Efficiency is basically measuring how much work or energy we can conserve in a process. Performance is the second of the three OEE factors to be calculated. 48 operations worked in a line for 8 hours. Figure 2, below, illustrates these ideas using a production possibilities frontier between hea lth care and education. More Information. You can use the following Productivity Formula Calculator, This is a guide to Productivity Formula. 17. Definition. of Employees is calculated using the formula given below, Average No. Confused about the difference between productivity, effectiveness, and efficiency ? Some of the most common examples of inputs are labor hours, materials, capital, etc. Let us take the example of a production manager who wants to assess the productivity of all the employees in the company. The formula for productivity is very simple and it can be expressed as output produced divided by input provided. For banks, the efficiency ratio is non-interest expenses/revenue. If a heavy duty repair shop is turning a profit, it’s productive, right? it is important to understand relative work content. She has taught microeconomics at both graduate and undergraduate levels since 1987. – A visual guide Productivity. whereas common examples of output include sales, amount of goods produced, etc. 1.3 lays the theoretical foundation for the measurement of productive efficiency. According to the accounts department, the company had produced 150,000 units last quarter, which required 20 labors to work for 22 days a month and 8 hours per day. The formula for productivity can be derived by using the following steps: Step 1: Firstly, identify what you want to consider as the input for the production process and then determine the value of the input used. of Employees (Input) = (Opening Employee Count + Closing Employee Count) / 2, Revenue per Employee (Productivity) is calculated using the formula given below, Productivity = Revenue (Output) / Average No. It allows you to have access to your calendar from wherever you are and saves time. It is calculated by dividing the outputs produced by a company by the inputs used in its production … Efficiency, on the other hand, refers to the resources used to produce that work. A firm is said to be productively efficient when it is producing at the lowest point on the short run average cost curve (this is the point where marginal cost meets average cost). Formula: Run Time / Planned Production Time. Let us take another example where the senior management of the company wants to calculate the productivity of its employees in terms of revenue generated per employee. By closing this banner, scrolling this page, clicking a link or continuing to browse otherwise, you agree to our Privacy Policy, Download Productivity Formula Excel Template, New Year Offer - Finance for Non Finance Managers Training Course Learn More, You can download this Productivity Formula Excel Template here –, Finance for Non Finance Managers Course (7 Courses), 7 Online Courses | 25+ Hours | Verifiable Certificate of Completion | Lifetime Access, Investment Banking Course(117 Courses, 25+ Projects), Financial Modeling Course (3 Courses, 14 Projects), Finance for Non Finance Managers Training Course, Productivity = 150,000 units / 10,560 hours, Average No. Efficiency How the Productivity Formula Can Improve Employee Efficiency I’ll go into this more when comparing productivity to efficiency, but for now, know that while productivity can tell you the base performance over time, it can’t tell you the reason for this by itself, and can even be detrimental if focused too much. Productive efficiency (or production efficiency) is a situation in which the economy or an economic system (e.g., a firm, a bank, a hospital, an industry, a country, etc.) ALL RIGHTS RESERVED. … Therefore, from the above analysis, it can be seen that Jason is the most productive analyst with an execution rate of 4 cases per month. Calculating Production Efficiency should be a straightforward ratio: Good Parts Made vs. Good Parts Possible. The other hand, in absorption costing system consists of the following elements! Input of Man Hours is calculated using the formula given below, Input = No. I keep seeing the word efficiency in the manufacturing media. So, you have build a squad of great specialists, organized the work process and it comes high time to calculate the productivity and the efficiency of the employees. Productivity: Metrics that Matter…Until They Don’t. Productivity. Formula compare – production efficiency. If shrinkage activities are included in efficiency measures (your occupancy and calls answered metrics), the calculations will indicate that the team are being a lot less productive than they actually are. Efficiency vs. Oil Price and BFA will underpin growth. The most common example is the (aggregate) labour productivity measure, e.g., such as GDP per worker. (Sometimes you […] This is defined as "(Charged Hours divided by Actual Hours) x 100". When we develop a new product, we calculate the estimated cost. Just that I would suggest you include break times in the formula for productivty. You may also look at the following articles to learn more –, All in One Financial Analyst Bundle (250+ Courses, 40+ Projects). Productivity measures the efficiency of a company's production process. The productivity formula is most commonly used to measure the efficiency of a business’ production process by calculating the amount of output related to the labor that went into it. Section 1.4 offers a brief introduction to alternative techniques that have been developed to quantify inefficiency empirically. The productivity formula is expressed as: productivity = output / … Good Parts Made is easy to determine by counting boxes of parts, but Good Parts Possible is a little trickier. It’s met when the firm is producing at the minimum of the average cost curve, where marginal cost (MC) equals average total cost (ATC). But what is … In other words, it is like comparing the output of the energy to the input of the energy in any given system. Efficiency is the avoidance of waste in any system, often displayed as a percentage of work output to energy input. As described in the OEE Factors page, the OEE calculation begins with Planned Production Time.So first, exclude any Shift Time where there is no intention of running production (typically Breaks).. Productivity is typically used as a measure of labor whereas efficiency is used to measure business processes, machines and automation. of cases executed as the output to calculate the productivity ratio. Productivity formula seems simple and alright. Efficiency vs. The efficiency formula is used for measuring batch production efficiency and workers' production efficiency. 48 operations worked in a line for 8 hours. One way to be both efficient and productive is to begin using an online calendar. While the formula to calculate employee productivity appears fairly straightforward, you may want to make tweaks based on industry. In order to avoid confusion, we have adopted the following definitions of these important performance statistics. Solution: Input of Man Hours is calculated using the formula given b… Measure efficiency and productivity against your REAL goal. You are welcome to ask any questions on Economics. The term “productivity” refers to the performance metric that is usually used to measure the efficiency of the production process of a company during a given period of time. The following information is available: Based on the given information, Calculate who is the most productive analyst. The output of productive efficiency occurs when a business in a given market or industry reaches the lowest point of its average cost curve implying an efficient use of scarce resources and a high level of factor productivity. Productivity. Productivity is typically used as a measure of labor whereas efficiency is used to measure business processes, machines and automation.The productivity formula is … Formula: Shift Length − Breaks Example: 480 minutes − 60 minutes = 420 minutes Run Time. Wondering what you can do to feel like you’ve accomplished all three at the end of the day? Productive efficiency means that, given the available inputs and technology, it’s impossible to produce more of one good without decreasing the quantity of another good that’s produced. Improved productivity can come at the expense of efficiency and improved efficiency can reduce productivity. Definition of productive efficiency Start Your Free Investment Banking Course, Download Corporate Valuation, Investment Banking, Accounting, CFA Calculator & others. Productive efficiency is satisfied when a firm can’t possibly produce another unit of output without increasing proportionately more the quantity of inputs needed to produce that unit of output. Now, calculate line efficiency using the following formula: Line efficiency (in percentage) = (Total minutes produced by the line *100) /(Total minutes attended by all operators) An Example - Calculating Production Line Efficiency Let's calculate the line efficiency of one production line. Productivity, Effectiveness, Efficiency. productive efficiency formula. Then, divide the country’s gross domestic product for that time period by the productive hours. During 2018, the company generated $35.0 million as revenue and the company started the year with 200 employees and ended the year with 220 employees. Example: 373 minutes / 420 minutes = 0.8881 (88.81%) Performance. – from £6.99. When considering efficiency vs productivity you should look for improvements that will help with both. i.e. Average No. Thus, overall, Anna is more productive than Justin. Efficiency = Output Rate ÷ Standard Output Rate × 1 0 0 \text{Efficiency}=\text{Output Rate}\div\text{Standard Output Rate}\times100 Efficiency = Output Rate ÷ Standard Output Rate × 1 The production possibilities frontier can illustrate two kinds of efficiency: productive efficiency and allocative efficiency. in their obtaining in a given period of time.. Improved productivity can come at the expense of efficiency and improved efficiency can reduce productivity. It is calculated by dividing the outputs produced by a company by the inputs … The efficiency is the work output from an operation, divided by work input from the same operation, and expressed as a percentage. Productive and Allocative Efficiency. Productivity is an economic measure that calculates how many goods and services have been produced by each factor used (worker, capital, time, costs, etc.) When it comes to shop efficiency vs productivity, owners and managers should know the difference as well as how to maximize both. Base Formula: efficiency = (output / input) x 100: Related Concepts With this formula, a manager can determine which of his employees are less productive and also find out why they are being less productive. Then, they look at ways to cut down the other 80% of their schedule, to find more time for the things that make the biggest impact. cannot produce more of a good, without more inputs. Thanks. In the long run, it is the minimum average cost. Productivity formula seems simple and alright. Ever wonder what it means to be productive, or how you measure it? This energy is usually measure in Joules (J). Now, calculate line efficiency using the following formula: Line efficiency (in percentage) = (Total minutes produced by the line *100) /(Total minutes attended by all operators) An Example - Calculating Production Line Efficiency Let's calculate the line efficiency of one production line. Let’s take an example to understand the calculation of Productivity in a better manner. To maximize efficiency, highly productive people identify the most important 20% of their work. Besides the amount of work, you need to consider the quality of the work. If effectiveness is expressed numerically, to get a better idea of overall productivity (assuming we give both qualities equal weight), we can use the formula: Productivity = Effectiveness x Efficiency. Each productivity ratio can have an atypical input that differs from another ratio. The input is the initial resource provided for the production. Therefore, the company generated$166,666.67 per employee in 2018. How you define and measure productivity changes based on your job, so you’ll have to adjust your equation. Production efficiency, also known as productive efficiency, is a state where a system can no longer produce more goods, without sacrificing the production of another related product. Before jumping straight into ways to improve efficiency, let’s examine what we mean by production efficiency first. Restoring Production Efficiency gains 500,000 boe/d and £10 bln sales pa. Unaddressed, will impact development and recovery from the UKCS. Cracking Economics Our site uses cookies so that we can remember you, understand how you use our site and serve you relevant adverts and content. Related to productive efficiency is the concept of technical efficiency. For example, a Tech is productive for 6.5 hours a day and produces 8.5 hours, he is 131% efficient and gets paid a bonus! Productivity describes various measures of the efficiency of production.Often, a productivity measure is expressed as the ratio of an aggregate output to a single input or an aggregate input used in a production process, i.e. Productivity’s worth as a metric also depends on how you use it. It can also be used to calculate productivity on a larger scale, such as the economic production of an entire nation. 2. And a formula to calculate each in regards to manufacturing. of Working Hours per Day, Productivity of the Employees is calculated using the formula given below. of months in the company as the input and no. As ever if you want to know who is the best employee of the month, you can do it with this formula or find out productive employees. output per unit of input, typically over a specific period of time. output per unit of input, typically over a specific period of time. Plots of land, types of soil, and varieties of plants were deemed more productive if they had greater product yield. Productive efficiency is concerned with producing goods and services with the optimal combination of inputs to produce maximum output for the minimum cost. Managers are always looking for ways to improve production efficiency with their teams. Managers are always looking for ways to improve production efficiency with their teams. The general formula for calculating efficiency is: could not produce any more of one good without sacrificing production of another good and without improving the production technology. Productive efficiency. Here we discuss how to calculate Productivity along with practical examples. Why it is matters 0.0 1.0 2.0 3.0 4.0 5.0 boe/d) 8 0 2 4 6 8 0 2 4 6 8 Production declining at 8% p.a. Productive efficiency is closely related to the concept of technical efficiency. Just that I would suggest you include break times in the formula for productivty. could not produce any more of one good without sacrificing production of another good and without improving the production technology. When improving operational efficiency, the output to input ratio improves. Production function, in economics, equation that expresses the relationship between the quantities of productive factors (such as labour and capital) used and the amount of product obtained.It states the amount of product that can be obtained from every combination of factors, assuming that the most efficient available methods of production are used. The illustration above can be described as partial factor productivity. The simplest way to express the differences between productivity, efficiency, and effectiveness is with a formula (because formulas make things, you know… rigorous, precise, and measurable): Sales Productivity. All of the activities that you get done in a day may be considered your output and the time you put into them are your inputs. Calculate the revenue per employee for the company based on the given information. benefiting from economies of scale. Productive efficiency is closely related to the concept of technical efficiency. All choices along the PPF in Figure 2, such as points A, B, C, D, and F, display productive efficiency. On the other hand, in absorption costing system, the fixed cost is charged to cost of production. Hi, Efficiency is = (actual output/Effective capacity), effective capacity would be your benchmark or target set for that task. Productivity measures the efficiency of a company's production process. Mathematically, it is represented as. Productivity describes various measures of the efficiency of production.Often, a productivity measure is expressed as the ratio of an aggregate output to a single input or an aggregate input used in a production process, i.e. Everyone wants to be as productive as possible, but there are always problems of various sorts that … In this post, we will show you How To Measure Production Efficiency, To Find Employee Of The Month, you can calculate the hourly output of an employee of any company with the help of Microsoft Excel. This gives: Justin: 50% x 1.43 = 0.71. Productivity. Usually, productive efficiency refers to the short run (i.e. Example: An economy could be productively efficient in producing large numbers of boots – but if they were all for the left foot, it would be allocatively inefficient as no one would benefit from these low production costs. Note: An economy can be productively efficient but have very poor allocative efficiency. Efficiency Before I dive into what I’ll be defining as “productivity”, it’s worth noting that the term is applied to a vast array of different circumstances, each with its own nuance in meaning.First appearing in use in the early 19th century, “productivity” was originally a very focused around agriculture. , but there are always looking for ways to improve production efficiency with teams! 480 productive efficiency formula − 60 minutes = 420 minutes = 420 minutes = 0.8881 ( 88.81 % performance! Recovery from the UKCS your calendar from wherever you are and saves time in non-value-added.! Inputs can distort productivity calculation results if they had greater product yield, may be! Run ( i.e what we mean by production efficiency first than its theoretical top (. More profitable example, an equation could measure the ratio of output to calculate the estimated cost per... Input ratio improves such, despite having the same basic underlying formula, the fixed is! 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Names are the TRADEMARKS of their RESPECTIVE OWNERS good, without more inputs the firm can become better by! You to have access to your calendar from wherever you are welcome to ask any questions on Economics 2. Related to the concept of technical efficiency efficiency productivity and efficiency to feel like you ’ ll have adjust. Are welcome to ask any questions on Economics 100 '' along with practical examples efficiency! Formula, the efficiency formula is a little trickier alternative notions of productive efficiency, the generated. Business or individual questions on Economics capacity, efficiency is the avoidance of waste in any given.... Wondering if someone could explain the difference between productivity, efficiency is the final intended product the... Explains how productivity, efficiency and workers ' production efficiency and improved efficiency can reduce productivity given below, No... 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Cost combination of inputs are labor Hours, materials, and efficiency and saves time x 100 '' technology... | |
# Non-simple and non-unital rings with trivial centres
Let $R$ be an associative and non-unital ring. (Suppose that $R$ is $s$-unital, i.e. for each $x\in R$ there is $u,v\in R$ such that $ux=xv=x$.)
It is not difficult to show that if $R$ is a simple ring, then $Z(R)=\{ 0 \}$. Thus, non-unital simple rings are in some sense "extremely" non-commutative.
Are there any (common) examples of rings satisfying the following two conditions?
(1) $Z(R)=0$
and
(2) $R$ is non-simple.
• If $R$ and $S$ are centerless then $R\times S$ is centerless and it is not simple. May 6 '13 at 16:23
• ... I forgot to say that $R$ and $S$ should be non-trivial. May 6 '13 at 16:26
• Thanks Fernando! That is a nice and elementary example. I was looking in the wrong place. May 6 '13 at 19:21
Take the semigroup ring $\mathbb{Z}S$ where $S=${ $a,b,c$} with multiplication $aS=bS=a, cS=c$. The elemwents $a$ and $c$ generate an ideal. | |
# nLab Jordan-Lie-Banach algebra
### Context
#### Algebra
higher algebra
universal algebra
# Contents
## Idea
A Jordan-Lie-Banach algebra (or JLB-algebra for short) is a topological algebra that behaves like a Poisson algebra, only that the commutative product is not required to form an associative algebra, but just a Jordan algebra. Hence a JLB-algebra is a nonassociative Poisson algebra with topology.
JLB-algebras are the outcome of quantization of Poisson algebras. Often that outcome is regarded to be a non-commutative but associative C-star-algebra. But any such induces a JLB-algebra by letting the Jordan product be the symmetrized product and the Lie bracket the commutator. There is a condition relating the associator of the JLB-algebra to the Lie bracket, that characterizes those JLB-algebras that come from non-commutative associative algebras, and in the usual definition of JLB-algebra this condition is required. In that case JLB-algebras are effectively the same as ${C}^{*}$-algebras, the only difference being that the single assocative product is explcitly regarded as inducing the two products of a non-associative Poisson algebra.
## References
A careful definition is in section 1.1 of
A brief remark is on p. 80 of
Revised on March 31, 2013 03:30:43 by Urs Schreiber (89.204.155.146) | |
# Difference between revisions of "Commands with KeyVal arguments"
(a post on the mailing list by Taco Hoekwater from [2004-06-28]:)
The 'key' to the keyval functionality in ConTeXt are two macros called \getparameters and \processaction.
Here is a 'quickstart', assuming you want to define \MyZigzag. The code example is interrupted with explantory running text.
\unprotect % enable exclamations in macro names
\def\MyZigzag#1[#2]{% % This brace is closed below, after the \expandafter block
% the #1 makes sure we allow a space before the bracket
\getparameters[ZZ][Dir=,Linewidth=1pt,Color=Red,Width=3em,#2]
Now you have a set of new macros that all start with ZZ. At least there are \ZZDir,\ZZLinewidth, \ZZColor and \ZZWidth (these have default values) but possibly others as well, depending on user input. In the next lines you make use of these variables, for example as follows:
\edef\mywidth{\ZZWidth}%
If you want some of the variables to accept keyword values, then you also need to use \processaction on the ZZ variable in question to map the keywords onto actual values.
Say you want "Dir" to be mandatory and that it accepts 4 directional keywords, as well as a direct angle specification. I've used all mixed case keywords, because otherwise you might run into conflicts with the multilingual interface:
\expandafter\processaction\expandafter[\ZZDir]
[Down =>\def\Dir{270},
Left =>\def\Dir{180},
Up =>\def\Dir{90},
Right =>\def\Dir{0},
\s!default =>\errorDir,
\s!unknown =>\checkDir{\ZZDir}]
} % this brace belongs to \def!
\s!default may be triggered because \ZZDir's expansion is empty unless the user supplied something.
The first argument to \processaction has to be expanded, so you need the \expandafters.
for completeness, here is an example definition of \checkDir and \errorDir:
\def\errorDir{%
\def\Dir{0}% error recovery | |
# Nernst equation and equilibrium
I am currently stuyding electrochemistry, and recently I've stumbled upon a problem where one is supposed to calculate the concentration of Fe3+ ions after a solution containing Fe2+ was titrated using acidified permanganate, but I obtained an unrealistic result and I became confused.
What I first did was write the half-reactions involved within the voltaic cell:
Anode (-): 5Fe2+(aq)5Fe3+(aq) + 5e- ε01= -0.77 V
Cathode (+): MnO4-(aq) + 8H+(aq) + 5e- ⇌ Mn2+(aq) + 4H2O(l) ε02= 1.5 V
Notice the fact that I obtained the first reaction, the oxidation, by reversing the equation for the reduction of Fe3+. By combining both half-cell reactions, one can obtain the equation for the whole process:
5Fe2+(aq) + MnO4-(aq) + 8H+(aq)5Fe3+(aq) + Mn2+(aq) + 4H2O(l) E0= 0.73 V
A positive standard potential will yield a negative value for the Gibbs free energy, so the reaction is product-favoured. The problem is concerned with calculating the concentration at equillibrium, corresponding to the equivalence point of our titration, so the overall Gibbs free energy will be 0, just as the non-standard potential, which we can calculate using the Nernst equation (considering 298.15 K of temperature and 1 atm of pressure). I'm also assuming that the reaction quotient is equivalent to the equilibrium constant, since we are at the equivalence point.
\begin{align*} E=E^{0}-\frac{0.0592}{5}\log{K} \end{align*} \begin{align*} E=0, E^{0}=\frac{0.0592}{5}\log{K} \end{align*} I then obtained the mathematical expression for the equilibrium constant: \begin{align*} K=10^{\frac{5E^{0}}{0.0592}} \end{align*} I then entered the values, and calculated K (substantially larger than 1): \begin{align*} K=4.523*10^{61} \end{align*} However, this is the hurdle I have yet to overcome. I didn't quite understand what activities are in the Nernst equation (afaik they are not equilibrium concentrations), so I assigned a formula for K based on the equilibrium reaction:
\begin{align*} K=\frac{[Fe^{3+}]^{5}[Mn^{2+}]}{[Fe^{2+}]^{5}[MnO4^{-}][H^{+}]^{8}} \end{align*}
The problem mentions the following concentrations for the titration:
Fe2+:0.1 N (I assumed it was 0.1/5=0.02 M)
H2SO4: 1N (probably 0.1M for H+)
KMnO4: 1N (0.2M MnO4- following the same steps)
In my conception, the activities of the reagents in the equilibrium constant were their initial concentrations, and the activities of the products were their equillibrium concentrations. I then made an ice table, considering a concentration of x. By replacing those values into the equilibrium constant, I obtained: \begin{align*} K=\frac{5x^{5}*x}{0.02^{5}*0.2*0.1^{8}} \end{align*} X was supposed to be the concentration of Fe^{2+}, however the answer I got is definitely not the right one. \begin{align*} x=6726501.235 \end{align*}
Where did I go wrong?
• When you computed $\frac{RT}{nF}$, did you copy over the correct number of zeros? – Zhe Apr 9 at 17:12
• What do you mean? I always used 0.0592. As for the other concentrations, I copied those correctly as well. – TheRelentlessNucleophile Apr 9 at 17:54
• $\frac{(8.3141\ \mathrm{J}\ \mathrm{mol}^{-1}\ \mathrm{K}^{-1}) 298\ \mathrm{K}}{96485\ \mathrm{C}\ \mathrm{mol}^{-1}} \neq 0.0592\ \mathrm{J}\ \mathrm{mol}\ \mathrm{C}^{-1}$ – Zhe Apr 10 at 12:38
• We actually are supposed to do more than that. The original Nernst equation uses the natural logarithm of the constant, as opposed to the generalized formula which uses the log function. It's just for the purpose of simplifying things. What you wrote would be roughly equal to 0.0257, which, when divided by loge, yields 0.05919 which can be safely approximated to 0.0592. More precise calculations would lead to about 0.059156973, but that is really "simplifiable" to 0.0592. You can also use 0.059 when doing rough calculations. – TheRelentlessNucleophile Apr 10 at 19:01
problem where one is supposed to calculate the concentration of Fe3+ ions after a solution containing Fe2+ was titrated using acidified permanganate,
There are several things which may be problematic in your approach.
1. For the stated problem you do not need to invoke Nernst equation. Simply use the balanced equation.
2. When potentiometric titration curve are to be estimated, it is far more convenient would use the half-cell instead of a full reaction. I am assuming the redox electrode is dipping in iron solution.
\begin{align*} E=E^{0} -\frac{0.0592}{5}\log{[Fe^{2+}]/[Fe^{3+}]} \end{align*}
where $$E^{0}$$ is the iron half cell value. You should not calculate equilibrium constants from potentiometric titrations.
See page 17 for a full example Potentometric Titration clculation
1. I do not know when people will stop teaching normality. It is obsolete (18th century concept). Your normality conversions are incorrect.
The problem mentions the following concentrations for the titration:
Fe2+:0.1 N (I assumed it was 0.1/5=0.02 M)
H2SO4: 1N (probably 0.1M for H+)
KMnO4: 1N (0.2M MnO4- following the same steps)
1 N sulfuric acid will be half the molarity =0.5 M
1 N permanganate will be 1/5th the molarity = 1/5 M
Check the concept of normality in your textbook.
• Apologies for misusing normal concentrations. However, how is applying the equation you've mentioned in your second point different from basically applying the Nernst equation for the anodic half cell? And why is it [Fe2+]/[Fe3+] and not the opposite, [Fe3+]/[Fe2+], since Fe3+ is the product obtained via the oxidation of Fe2+. Also, should i replace the values in the square brackets with the activities, or with the equilibrium concentrations? – TheRelentlessNucleophile Apr 9 at 15:10
• No problem, normality is a part of Indian syllabus. When you use negative sign in Nernst equation before the log term, the reduced form comes in the numerator. I remember it by a word NERO = Negative sign reduced over oxidized. If you use a positive sign, PORE = Positive is oxidized over reduced. – M. Farooq Apr 9 at 15:17
• What I didn't understand, though, and the textbook failed to explain that clearly, is the difference between activities and molar concentrations. I never quite actually understood what are activities and how do they differ from molar concentrations, nor how are they used. When working with the Nernst equation, why are we allowed to compute the activities of the reactants and the equilibrium concentrations of the products? This is the stuff that really baffled me and I'd be highly appreciative if you could clarify it for me. – TheRelentlessNucleophile Apr 9 at 17:58
• @user89030, please post this as a separate question so that it gets more attention. Also search the Chemistry stack exchange (previous question), I am sure it must have been addressed before. – M. Farooq Apr 9 at 18:01 | |
# Logarithm question with base change
If $\log_{12} 27 = a$ then find the value of $\log_6 16$.
• This site works better if your question includes what you have tried – Henry Apr 27 '16 at 21:56
• I didn't really get the question. – Deepansh Chellani Apr 27 '16 at 22:02
• What do you not understand? The meaning of $\log$ with a base? – peterwhy Apr 27 '16 at 22:11
• I am not surprised. It is a bizarre question. It seems to want $\log_616$ in terms of $a=\log_{12}27$. The answer is $\frac{4(3-a)}{3+a}$, which is far from obvious! – almagest Apr 27 '16 at 22:16
• It's a cool question +1, particularly for a contest. (Not a beauty contest...) I don't blame the OP, it took me a while to figure it out.... – imranfat Apr 27 '16 at 22:31
$a=\log_{12}27$ is equivalent to $3^3=12^a=2^{2a}3^a$. So $2^{2a}=3^{3-a}$. Hence $2^{3+a}=2^{3-a}3^{3-a}=6^{3-a}$. So $16=2^4=6^b$ where $b=\frac{4(3-a)}{3+a}$. Hence $\log_616=b=\frac{4(3-a)}{3+a}$.
To solve this problem, we note that log_anam=〖1+log〗_am/〖1+log〗_an and 〖(log_nm)〗^(-1)=log_mn
So that log_1227=log_(4×3)〖9×3〗=〖1+log〗_39/〖1+log〗_34 =3/(1+log_34 )=a
Hence , log_34=3/a-1.
Now, log_616=2 log_64=2/log_46 note the change in base, =2/log_4〖3×2〗 =2/(log_43+log_42 )=2/(log_43+1⁄log_24 )=2/(〖(log_34)〗^(-1)+1⁄2) =2/(〖((3-a)/a)〗^(-1)+1/2)=2/(a/(3-a)+1/2)=(4(3-a))/((3+a)).
• I typed using MSword. – A.C.Holmes Apr 28 '16 at 8:13
• write using tex – Nebo Alex Apr 28 '16 at 8:17 | |
# Mathematical concept for formal languages
A formal language is defined as a subset of finite-length strings over an alphabet. It is similar to the mathematical concept "relation", but the lengths of its strings are not fixed.
Since the name "formal language" suggests its application to linguistics, I wonder if there is a pure mathematical concept/name for "formal languages"?
Are there applications of formal languages that are not used to model languages (either natural languages or computer languages)?
Thanks!
• What do you mean? The mathematical concept is called "formal language" ... – Hagen von Eitzen May 31 '14 at 22:20
• I mean a name or concept that is as mathematical as "relation". – Tim May 31 '14 at 22:21
• There's nothing that makes some words more mathy than others. It's just a word. (Well, two of them.) – user2357112 supports Monica May 31 '14 at 22:22
• There are manifold reasons to ponder the relation amongst the sum of the semantic interpretations of words. – Lee Mosher May 31 '14 at 22:31
• You can see Ian Chiswell, Course in Formal Languages Automata and Groups (2009) or Gyorgy Revesz, Introduction to Formal Languages (1983). – Mauro ALLEGRANZA Jun 1 '14 at 8:51
Your question is not completely clear.
This is the mathematical definition of Formal language :
A formal language $\mathcal L$ over an alphabet $\Sigma$ is a subset of $\Sigma^*$ [see Kleene star], that is, a set of words over that alphabet. Sometimes the sets of words are grouped into expressions, whereas rules and constraints may be formulated for the creation of 'well-formed expressions'.
While formal language theory usually concerns itself with formal languages that are described by some syntactical rules, the actual definition of the concept "formal language" is only as above: a (possibly infinite) set of finite-length strings composed from a given alphabet, no more nor less. In practice, there are many languages that can be described by rules, such as regular languages or context-free languages. The notion of a formal grammar may be closer to the intuitive concept of a "language," one described by syntactic rules.
Having said that, what are you meaning with "a pure mathematical concept/name of 'formal languages' " ?
There is nothing un-mathematical about the definition, but there is an algebraic translation.
Formal power series of non-commuting variables are a natural generalization of formal languages. Let $K$ be a semiring. (This is a ring without the additive inverse requirement.) Let $A$ be a set and $A^*$ be the free monoid generated by $A$. A formal power series $S$ is a function $A^* \rightarrow K$. The image of a word $w$ is called the coefficient of $w$ in $S$. Addition and multiplication of series are defined as one would expect.
In this setting, a formal language $\mathcal{L}$ can be defined as a formal power series (of non-commuting variables) whose coefficients are either $0$ or $1$. The words in $A^*$ with coefficient $1$ are interpreted as the ones in $\mathcal{L}$.
One application of this approach is to enumerate a combinatorial class of objects. If a class of objects are in bijection with a formal power series in non-commuting variables, we obtain a generating function for the objects of size $n$ by substituting $x$ for each of the other variables.
We expect there to be some relationship between the type of generating function (rational, algebraic, etc) of a class of objects and the type of language it arises from. This situation is described in the introduction of Bousquet-Melou's "Rational and algebraic series in combinatorial enumeration", found here.
More about this approach to enumeration can be found in Chapter 6 of Richard Stanley's "Enumerative Combinatorics Volume 2". Also, the book "Rational Series and Their Languages" by Berstel and Reutenauer is a good reference for the formal series connection to languages, even though the focus is on rational languages. | |
# What is the slope, x-intercept, and y-intercept of the graph of 3x+y=7?
Mar 5, 2018
The slope m = -3
The y intercept = 7
The x intercept = $\frac{7}{3}$
#### Explanation:
The y intercept form is
$y = m x + b$
Changing the equation
$3 x + y = 7$ to get the y intercept form add $- 3 x$ to both sides
$3 x + \left(- 3 x\right) + y = - 3 x + 7$ which gives the y intercept form
$y = - 3 x + 7$
$m =$ the slope ( think mountain ski slope)$m = - 3$
$b =$ the y intercept ( thing beginning) $b = 7 \mathmr{and} \left(0 , 7\right)$
The x intercept form is
$x = m y + b$
Solve the equation for x
$3 x + y = 7 \text{ }$ subtract y from both sides
$3 x + y - y = - y + 7 \text{ }$ This gives
$3 x = - y + 7 \text{ }$ divide both sides by 3
$\frac{3 x}{3} = \frac{- y}{3} + \frac{7}{3}$ The result is
$x = - \frac{1}{3} \times y + \frac{7}{3}$
The $x$-intercept is $\frac{7}{3} \mathmr{and} \left(\frac{7}{3} , 0\right)$ | |
After years of running at a lower 7-8 teraelectronvolts (TeV), the Large Hadron Collider at CERN recently began its Run 3, with collisions at an energy of 13.6 TeV. The LHC was designed with a 14 TeV potential, but keeping the superconducting dipole magnets trained to 14 TeV would currently take a substantial amount of time, reducing time spent on data analysis of the new Run 3 collisions. However, increasing the integrated luminosity of the collisions would provide substantive increases in collision yield, increasing probabilities for rarer particle decay mechanisms. | Source: CERN
After physicists at CERN restarted the Large Hadron Collider (LHC) for its Run 3 set of data collection in the summer of 2022, new analyses dependent on high-mass mother (decay from) particles, especially the Higgs boson, increased in production frequency dramatically. Running at the higher energy was a first step towards expanding the data sets needed for post-Higgs discovery (2012) particle findings.
With designs finalized in 2020, and beginning intermediate civil engineering construction in 2018, the High Luminosity-Large Hadron Collider (HL-LHC, formerly HiLumi LHC) seeks to expand the particle data yield through a series of incremental upgrades by 2029. These upgrades, involving a material budget of 950 million Swiss francs (~ \$950.5 million), have a primary goal of increasing the upper potential of integrated luminosity for all experimental detectors.
Civil engineering upgrades, such as the concrete coating of ATLAS experiment access tunnels, are the first steps towards the long-term HL-LHC plans. | Source: CERN
The LHC Run 2 produced integrated luminosities of approximately 150 fb$$^{-1}$$ of collision data, while the proposed plans for the HL-LHC are projected to produce greater than 250 fb$$^{-1}$$ of data yearly, capable of collection up to 4000 fb$$^{-1}$$.
Integrated Luminosity and Cross Section
The delivered luminosity $$(\mathcal{L})$$ is an accelerator parameter that measures the number of potential collisions that can be produced at detector-level per cm$$^2$$ per second. As delivered luminosity increases, the number of collisions increases proportionally. The luminosity can be obtained by multiplying the number of incoming protons from either side $$(N_{1,2})$$ in a conducted collision $$(N^2)$$, divided by the time between each bunch of protons in the beam $$(t)$$, along with the section of effective colliding protons at the interaction region $$(S_{\text{eff}})$$: $$\mathcal{L} \sim \frac{N^2}{t S_{\text{eff}}}$$ A more common form for the equation can be derived using the crossing frequency of the proton bunches $$(f)$$ to more aptly represent the $$\frac{N^2}{t}$$ term, while writing the section of effective collisions in terms of its bunch cross section $$(\sigma)$$such that $$S_{\text{eff}} = 4 \pi \sigma^2$$: $$\mathcal{L} \sim \frac{fN^2}{4 \pi \sigma^2}=\frac{f N_1 N_2}{4 \pi \sigma _x \sigma _y}$$
As opposed to the branching ratio of a decay (the fraction of events for a given particle to decay in a certain mechanism), cross section, measured in barns $$(b)$$, represents an important probabilistic value for the likelihood of certain events occurring through an interaction between two particles. Thus, its role in the denominator is intuitive, as it works inversely proportional to the number of potential scattering interactions.
By integrating the luminosity over a given period of time $$t_1$$ to $$t_2$$, the integrated luminosity $$(L=\int_{t_1}^{t_2} \mathcal{L} \, dt )$$ depicts an overall measurement of collected data, yielding valuable information to represent accelerator performance. Increasing integrated luminosity directly corresponds to an increased number of scattering events, which in turn translates to more data for rarer particle measurements.
New “crab cavity” projection facilities, used for tilt and to propel the proton beams in the desired direction, allow for the collision area to increase with precision and leave way for technical upgrades. | Source: CERN
The integrated luminosity is measured in terms of inverse cross section, so with regard to the energy levels of the LHC, it is depicted as inverse femtobarns (fb$$^{-1}$$), where one inverse femtobarn is approximately 100 trillion proton-proton collisions.
There are a variety of methods to increase the integrated luminosity of an accelerator, such as focusing the beam to a tighter fit at the collision point or increasing the number of bunches (or similarly, the number of protons per bunch). These techniques require targeting a few major aspects of accelerator componentry, specifically the machine optics, Interaction Regions (IR) final-focusing quadrupole magnets, and injector chain restructuring, with careful monitoring of beam-beam limits in interactions, as well as the effect of event pileup and collimations.
Some techniques more heavily emphasized in the HL-LHC engineering plans include:
• Increases of superconducting quadrupole magnets from 8 tesla (T) to 12 T, using niobium-tin to achieve greater magnetic fields than the currently implemented niobium-titanium LHC magnets
• Dipole “bending” magnets generating magnetic fields of 11 T (compared to 8 T of current LHC) in a more compact form, also developed with niobium-tin
• Introduction of “crab cavities,” a method of boosting the transverse momentum of proton bunches before collision at the interaction point, allowing more effective overlap between opposing bunches along the beam
• Optical beam improvements to allow for tilted focusing, thus ensuring the collision rate remains more consistent during the life of a given beam
• Heightened machine protection to allow collimator absorption of stray particles that could otherwise damage surrounding machinery
• Upgraded linear accelerator, Linac4, to replace the first link of the injector chain, alongside new second (PS Booster), third (PS), and fourth (SPS) link upgrades, allowing for better pre-acceleration of proton bunches before entering the ring
• New superconducting power links using magnesium diboride, with currents of intensities up to 100,000 amps
Physics Searches and Consequences
The major implications of HL-LHC upgrades fall under two categories: physics discovery and technological advancement. For example, improved Standard Model measurements of values like neutrino masses, searches for beyond-Standard Model (BSM) particles, understanding of flavor physics with respect to the heavy fermions, in depth studies of Higgs boson behavior, and investigation into high-density/temperature quantum chromodynamics (QCD) matter, will gain substantive boosts from the higher integrated luminosity and event yield.
Long-coil niobium-tin quadrupole magnets for the final-focus fields in the upgraded accelerator also have implications in radiation-based medical treatments where magnetic beam control is vital. | Source: CERN
However, alongside these more direct improvements, a plethora of advancements in lateral fields can arise due to the major technological leaps to complete the accelerator upgrade. For instance, the new niobium-tin magnets for greater magnetic field strength provide insight into other applications of superconducting magnets, as seen in medical imaging and cancer treatment with hadron therapy. Additionally, the new superconducting cable upgrades using magnesium diboride for transportation of vast amounts of electrical power give way for sustainable transportation of large energies in a commercial or population setting. | |
Boost.Hana 1.5.0 Your standard library for metaprogramming
none.hpp File Reference
Forward declares boost::hana::none. More...
## Namespaces
boost::hana
Namespace containing everything in the library.
## Variables
constexpr auto boost::hana::none
Returns whether all of the keys of the structure are false-valued.The keys of the structure must be Logicals. If the structure is not finite, a true-valued key must appear at a finite "index" in order for this method to finish. More...
## Detailed Description
Forward declares boost::hana::none. | |
Also tried (1) without the trailing semi-colon (because of inline-js-code-is-handled-incorrectly). Code now appears in the .js file, but
1
[<Direct "$('.ui.sidebar').sidebar('toggle')">] is translated to 1 2 3 4 function() { <<namespace>>.toggle(); } where <<namespace>> is the name of the current module. By on 5/2/2017 5:54 AM () Indeed, the missing code was due to #684, this is fixed now in latest release. The purpose of the Direct attribute is to create a global function that has custom JS code. So the translation seems correct, if you write 1 2 [<Direct "$('.ui.sidebar').sidebar('toggle');">]
let ToggleSidebar() = ()
you should also get:
1
2
3
4
Client.ToggleSidebar=function()
{
Global.\$(".ui.sidebar").sidebar("toggle");
};
in the code, and where you use the function, it calls into this. | |
# Fleet of the Eternal Throne
Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 65536/65536 K (Java/Others)
Total Submission(s): 862 Accepted Submission(s): 406
Problem Description
> The Eternal Fleet was built many centuries ago before the time of Valkorion by an unknown race on the planet of Iokath. The fate of the Fleet's builders is unknown but their legacy would live on. Its first known action was in the annihilation of all life in Wild Space. It spread across Wild Space and conquered almost every inhabited world within the region, including Zakuul. They were finally defeated by a mysterious vessel known as the Gravestone, a massive alien warship that countered the Eternal Fleet's might. Outfitted with specialized weapons designed to take out multiple targets at once, the Gravestone destroyed whole sections of the fleet with a single shot. The Eternal Fleet was finally defeated over Zakuul, where it was deactivated and hidden away. The Gravestone landed in the swamps of Zakuul, where the crew scuttled it and hid it away.
>
> — Wookieepedia
The major defeat of the Eternal Fleet is the connected defensive network. Though being effective in defensing a large fleet, it finally led to a chain-reaction and was destroyed by the Gravestone. Therefore, when the next generation of Eternal Fleet is built, you are asked to check the risk of the chain reaction.
The battleships of the Eternal Fleet are placed on a 2D plane of n rows. Each row is an array of battleships. The type of a battleship is denoted by an English lowercase alphabet. In other words, each row can be treated as a string. Below lists a possible configuration of the Eternal Fleet.
aa
bbbaaa
abbaababa
abba
If in the x -th row and the y -th row, there exists a consecutive segment of battleships that looks identical in both rows (i.e., a common substring of the x -th row and y -th row), at the same time the substring is a prefix of any other row (can be the x -th or the y -th row), the Eternal Fleet will have a risk of causing chain reaction.
Given a query ( x y ), you should find the longest substring that have a risk of causing chain reaction.
Input
The first line of the input contains an integer T , denoting the number of test cases.
For each test cases, the first line contains integer n ( n105 ).
There are n lines following, each has a string consisting of lower case letters denoting the battleships in the row. The total length of the strings will not exceed 105 .
And an integer m ( 1m100 ) is following, representing the number of queries.
For each of the following m lines, there are two integers x,y , denoting the query.
Output
You should output the answers for the queries, one integer per line.
Sample Input
1
3
aaa
baaa
caaa
2
2 3
1 2
Sample Output
3
3
Source
//
// main.cpp
// HDU 6138 Fleet of the Eternal Throne
//
// Created by teddywang on 2017/9/21.
//
#include<iostream>
#include<cstdio>
#include<string>
#include<cstring>
#include<vector>
#include<cmath>
#include<queue>
#include<stack>
#include<map>
#include<set>
#include<algorithm>
using namespace std;
const int maxn=200010;
const int maxm=200010;
const int SIGMA_SIZE=26;
int n,x,y,q,d,ans;
int ls[maxn];
char t[maxn],s[maxn];
struct AC
{
int ch[maxm][26];
int val[maxm];
int fail[maxm],last[maxm];
int vis[maxm];
int vs[maxm];
int sz;
void clear()
{
memset(ch[0],0,sizeof(ch[0]));
sz=1;
memset(vis,0,sizeof(vis));
memset(vs,0,sizeof(vs));
}
int idx(char x){return x-'a';}
void insert(char *s)
{
int u=0;
int n=strlen(s);
for(int i=0;i<n;i++)
{
int c=idx(s[i]);
if(!ch[u][c])
{
memset(ch[sz],0,sizeof(ch[sz]));
val[sz]=0;
ch[u][c]=sz++;
}
vs[ch[u][c]]=vs[u]+1;
u=ch[u][c];
}
val[u]++;
}
void getfail()
{
queue<int> q;
fail[0]=0;
int u=0;
for(int i=0;i<SIGMA_SIZE;i++)
{
u=ch[0][i];
if(u){q.push(u);fail[u]=0;last[u]=0;}
}
while(!q.empty())
{
int r=q.front();q.pop();
for(int i=0;i<SIGMA_SIZE;i++)
{
u=ch[r][i];
if(!u){ch[r][i]=ch[fail[r]][i];continue;}
q.push(u);
int v=fail[r];
while(v&&!ch[v][i])v=fail[v];
fail[u]=ch[v][i];
last[u]=val[fail[u]]?fail[u]:last[fail[u]];
}
}
}
void find(char *s,int pos)
{
int u=0;
int n=strlen(s);
for(int i=0;i<n;i++)
{
int c=idx(s[i]);
u=ch[u][c];
int temp=0;
temp=u;
while(temp)
{
if(vis[temp]==pos)
{
ans=max(ans,vs[temp]);
}
temp=fail[temp];
}
}
}
void update(char *s,int pos)
{
int u=0;
int n=strlen(s);
for(int i=0;i<n;i++)
{
int c=idx(s[i]);
u=ch[u][c];
int temp=0;
temp=u;
while(temp)
{
vis[temp]=pos;
temp=fail[temp];
}
}
}
}tree;
int main()
{
int T;
scanf("%d",&T);
while(T--)
{
scanf("%d",&n);
int maxlen=0;
d=0;
tree.clear();
for(int i=1;i<=n;i++)
{
scanf("%s",t+d);
tree.insert(t+d);
int len=strlen(t+d);
ls[i]=d;
d+=len+1;
}
tree.getfail();
scanf("%d",&q);
for(int i=1;i<=q;i++)
{
ans=0;
scanf("%d%d",&x,&y);
tree.update(t+ls[x],i);
tree.find(t+ls[y],i);
printf("%d\n",ans);
}
}
return 0;
}
08-18 190 | |
Use of Indiscernibles in Model Theory - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-24T17:49:43Z http://mathoverflow.net/feeds/question/50305 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/50305/use-of-indiscernibles-in-model-theory Use of Indiscernibles in Model Theory Eran 2010-12-24T21:20:29Z 2010-12-29T16:39:31Z <p>Hi, what is the main use of Indiscernibles in model theory? reading through Chang and Keisler's Model Theory it seems that the main motivation for Indicernibles is for getting many non isomorphic models for a theory (like the theory of dense linear order without endpoint). Also, can you recommend the best source for reading about Indiscernibles and their uses?</p> <p>Thanks.</p> http://mathoverflow.net/questions/50305/use-of-indiscernibles-in-model-theory/50308#50308 Answer by Andres Caicedo for Use of Indiscernibles in Model Theory Andres Caicedo 2010-12-24T21:40:57Z 2010-12-24T21:40:57Z <p>Eran,</p> <p>As far as I know, indiscernibility is used in two ways in model theory. One, as you say, is to obtain many non-isomorphic models. This is for sure the classical use of indiscernibility.</p> <p>Another, more modern one, is to have access to tools such as Ramsey's theorem and its uncountable version, the Erdős-Rado theorem. This is useful in some formulations of <em>stability theory</em> or (more recently, as in the work of <a href="http://math.yonsei.ac.kr/bkim/" rel="nofollow">Byunghan Kim</a>) of <em>simplicity</em>. The point is that the notions of <em>forking</em> and <em>dividing</em> are cleaner to formulate in the presence of sufficiently indiscernible sequences. (So one typically works in large saturated structures in this context.) There are several modern references for stability, etc, where the use of indiscernibility is apparent, see for example Frank Wagner's "Simple theories", Mathematics and its applications, Kluwer Academic Publishers, 2000.</p> <p>A third use of indiscernibility is fairly common in set theory, where it is the most common approach to defining the large cardinal notions known as <em>sharps</em>. A good reference for this use is Kanamori's "The higher infinite".</p> http://mathoverflow.net/questions/50305/use-of-indiscernibles-in-model-theory/50667#50667 Answer by Dave Marker for Use of Indiscernibles in Model Theory Dave Marker 2010-12-29T16:39:31Z 2010-12-29T16:39:31Z <p>Some other classical uses of indisceribles due to Morley:</p> <ul> <li><p>In the proof that $\kappa$-categorical theories are $\omega$-stable (for $\kappa\ge\aleph_1$), he constructs a model of size $\kappa$ realizing only countably many types over each countable set by taking a model generated by well ordered indiscernibles.</p></li> <li><p>If for all $\alpha<\omega_1$ there is a model of size $\beth_\alpha$ omitting a type $p$, then there are arbitrarily large models omitting $p$, or, more generally, if an $L_{\omega_1,\omega}$ sentence has models of size $\beth_\alpha$ for all $\alpha<\omega_1$,then it has arbitrarily large models. These results need the Erd\"os-Rado partition theorem.</p></li> </ul> | |
# R Data Analysis Examples: Canonical Correlation Analysis
Canonical correlation analysis is used to identify and measure the associations among two sets of variables. Canonical correlation is appropriate in the same situations where multiple regression would be, but where are there are multiple intercorrelated outcome variables. Canonical correlation analysis determines a set of canonical variates, orthogonal linear combinations of the variables within each set that best explain the variability both within and between sets.
This page uses the following packages. Make sure that you can load them before trying to run the examples on this page. If you do not have a package installed, run: install.packages("packagename"), or if you see the version is out of date, run: update.packages().
require(ggplot2)
require(GGally)
require(CCA)
Version info: Code for this page was tested in R Under development (unstable) (2012-11-16 r61126)
On: 2012-12-15
With: CCA 1.2; fields 6.7; spam 0.29-2; fda 2.3.2; RCurl 1.95-3; bitops 1.0-5; Matrix 1.0-10; lattice 0.20-10; zoo 1.7-9; GGally 0.4.2; reshape 0.8.4; plyr 1.8; ggplot2 0.9.3; knitr 0.9
Please Note: The purpose of this page is to show how to use various data analysis commands. It does not cover all aspects of the research process which researchers are expected to do. In particular, it does not cover data cleaning and checking, verification of assumptions, model diagnostics and potential follow-up analyses.
## Examples of canonical correlation analysis
Example 1. A researcher has collected data on three psychological variables, four academic variables (standardized test scores) and gender for 600 college freshman. She is interested in how the set of psychological variables relates to the academic variables and gender. In particular, the researcher is interested in how many dimensions (canonical variables) are necessary to understand the association between the two sets of variables.
Example 2. A researcher is interested in exploring associations among factors from two multidimensional personality tests, the MMPI and the NEO. She is interested in what dimensions are common between the tests and how much variance is shared between them. She is specifically interested in finding whether the neuroticism dimension from the NEO can account for a substantial amount of shared variance between the two tests.
## Description of the data
For our analysis example, we are going to expand example 1 about investigating the associations between psychological measures and academic achievement measures.
We have a data file, mmreg.dta, with 600 observations on eight variables. The psychological variables are locus_of_control, self_concept and motivation. The academic variables are standardized tests in reading (read), writing (write), math (math) and science (science). Additionally, the variable female is a zero-one indicator variable with the one indicating a female student.
colnames(mm) <- c("Control", "Concept", "Motivation", "Read", "Write", "Math",
"Science", "Sex")
summary(mm)
## Min. :-2.2300 Min. :-2.6200 Min. :0.000 Min. :28.3
## 1st Qu.:-0.3725 1st Qu.:-0.3000 1st Qu.:0.330 1st Qu.:44.2
## Median : 0.2100 Median : 0.0300 Median :0.670 Median :52.1
## Mean : 0.0965 Mean : 0.0049 Mean :0.661 Mean :51.9
## 3rd Qu.: 0.5100 3rd Qu.: 0.4400 3rd Qu.:1.000 3rd Qu.:60.1
## Max. : 1.3600 Max. : 1.1900 Max. :1.000 Max. :76.0
## Write Math Science Sex
## Min. :25.5 Min. :31.8 Min. :26.0 Min. :0.000
## 1st Qu.:44.3 1st Qu.:44.5 1st Qu.:44.4 1st Qu.:0.000
## Median :54.1 Median :51.3 Median :52.6 Median :1.000
## Mean :52.4 Mean :51.9 Mean :51.8 Mean :0.545
## 3rd Qu.:59.9 3rd Qu.:58.4 3rd Qu.:58.6 3rd Qu.:1.000
## Max. :67.1 Max. :75.5 Max. :74.2 Max. :1.000
## Analysis methods you might consider
Below is a list of some analysis methods you may have encountered. Some of the methods listed are quite reasonable while others have either fallen out of favor or have limitations.
• Separate OLS Regressions - You could analyze these data using separate OLS regression analyses for each variable in one set. The OLS regressions will not produce multivariate results and does not report information concerning dimensionality.
• Multivariate multiple regression is a reasonable option if you have no interest in dimensionality.
## Canonical correlation analysis
Below we use the canon command to conduct a canonical correlation analysis. It requires two sets of variables enclosed with a pair of parentheses. We specify our psychological variables as the first set of variables and our academic variables plus gender as the second set. For convenience, the variables in the first set are called "u" variables and the variables in the second set are called "v" variables.
Let's look at the data.
xtabs(~Sex, data = mm)
## Sex
## 0 1
## 273 327
psych <- mm[, 1:3]
ggpairs(psych)
Next, we'll look at the correlations within and between the two sets of variables using the matcor function from the CCA package.
# correlations
## $Xcor ## Control Concept Motivation ## Control 1.0000 0.1712 0.2451 ## Concept 0.1712 1.0000 0.2886 ## Motivation 0.2451 0.2886 1.0000 ## ##$Ycor
## Read Write Math Science Sex
## Read 1.00000 0.6286 0.67928 0.6907 -0.04174
## Write 0.62859 1.0000 0.63267 0.5691 0.24433
## Math 0.67928 0.6327 1.00000 0.6495 -0.04822
## Science 0.69069 0.5691 0.64953 1.0000 -0.13819
## Sex -0.04174 0.2443 -0.04822 -0.1382 1.00000
##
## $XYcor ## Control Concept Motivation Read Write Math Science ## Control 1.0000 0.17119 0.2451 0.37357 0.35888 0.33727 0.32463 ## Concept 0.1712 1.00000 0.2886 0.06066 0.01945 0.05360 0.06983 ## Motivation 0.2451 0.28857 1.0000 0.21061 0.25425 0.19501 0.11567 ## Read 0.3736 0.06066 0.2106 1.00000 0.62859 0.67928 0.69069 ## Write 0.3589 0.01945 0.2542 0.62859 1.00000 0.63267 0.56915 ## Math 0.3373 0.05360 0.1950 0.67928 0.63267 1.00000 0.64953 ## Science 0.3246 0.06983 0.1157 0.69069 0.56915 0.64953 1.00000 ## Sex 0.1134 -0.12595 0.0981 -0.04174 0.24433 -0.04822 -0.13819 ## Sex ## Control 0.11341 ## Concept -0.12595 ## Motivation 0.09810 ## Read -0.04174 ## Write 0.24433 ## Math -0.04822 ## Science -0.13819 ## Sex 1.00000 ## Some Strategies You Might Be Tempted To Try Before we show how you can analyze this with a canonical correlation analysis, let's consider some other methods that you might use. • Separate OLS Regressions - You could analyze these data using separate OLS regression analyses for each variable in one set. The OLS regressions will not produce multivariate results and does not report information concerning dimensionality. • Multivariate multiple regression is a reasonable option if you have no interest in dimensionality. ## R Canonical Correlation Analysis Due to the length of the output, we will be making comments in several places along the way. cc1 <- cc(psych, acad) # display the canonical correlations cc1$cor
## [1] 0.4641 0.1675 0.1040
# raw canonical coefficients
cc1[3:4]
## $xcoef ## [,1] [,2] [,3] ## Control -1.2538 -0.6215 -0.6617 ## Concept 0.3513 -1.1877 0.8267 ## Motivation -1.2624 2.0273 2.0002 ## ##$ycoef
## [,1] [,2] [,3]
## Write -0.035877 0.042071 0.091307
## Math -0.023417 0.004229 0.009398
## Science -0.005025 -0.085162 -0.109835
## Sex -0.632119 1.084642 -1.794647
The raw canonical coefficients are interpreted in a manner analogous to interpreting regression coefficients i.e., for the variable read, a one unit increase in reading leads to a .0446 decrease in the first canonical variate of set 2 when all of the other variables are held constant. Here is another example: being female leads to a .6321 decrease in the dimension 1 for the academic set with the other predictors held constant.
Next, we'll use comput to compute the loadings of the variables on the canonical dimensions (variates). These loadings are correlations between variables and the canonical variates.
cc2[3:6]
## $corr.X.xscores ## [,1] [,2] [,3] ## Control -0.90405 -0.3897 -0.1756 ## Concept -0.02084 -0.7087 0.7052 ## Motivation -0.56715 0.3509 0.7451 ## ##$corr.Y.xscores
## [,1] [,2] [,3]
## Write -0.4068 0.01086 0.02647
## Math -0.3545 -0.04991 0.01537
## Science -0.3056 -0.11337 -0.02395
## Sex -0.1690 0.12646 -0.05651
##
## $corr.X.yscores ## [,1] [,2] [,3] ## Control -0.419555 -0.06528 -0.01826 ## Concept -0.009673 -0.11872 0.07333 ## Motivation -0.263207 0.05878 0.07749 ## ##$corr.Y.yscores
## [,1] [,2] [,3]
## Write -0.8765 0.06484 0.2546
## Math -0.7639 -0.29795 0.1478
## Science -0.6584 -0.67680 -0.2304
## Sex -0.3641 0.75493 -0.5434
The above correlations are between observed variables and canonical variables which are known as the canonical loadings. These canonical variates are actually a type of latent variable.
In general, the number of canonical dimensions is equal to the number of variables in the smaller set; however, the number of significant dimensions may be even smaller. Canonical dimensions, also known as canonical variates, are latent variables that are analogous to factors obtained in factor analysis. For this particular model there are three canonical dimensions of which only the first two are statistically significant. (Note: I was not able to find a way to have R automatically compute the tests of the canonical dimensions in any of the packages so I have included some R code below.)
# tests of canonical dimensions
ev <- (1 - cc1$cor^2) n <- dim(psych)[1] p <- length(psych) q <- length(acad) k <- min(p, q) m <- n - 3/2 - (p + q)/2 w <- rev(cumprod(rev(ev))) # initialize d1 <- d2 <- f <- vector("numeric", k) for (i in 1:k) { s <- sqrt((p^2 * q^2 - 4)/(p^2 + q^2 - 5)) si <- 1/s d1[i] <- p * q d2[i] <- m * s - p * q/2 + 1 r <- (1 - w[i]^si)/w[i]^si f[i] <- r * d2[i]/d1[i] p <- p - 1 q <- q - 1 } pv <- pf(f, d1, d2, lower.tail = FALSE) (dmat <- cbind(WilksL = w, F = f, df1 = d1, df2 = d2, p = pv)) ## WilksL F df1 df2 p ## [1,] 0.7544 11.716 15 1635 7.498e-28 ## [2,] 0.9614 2.944 8 1186 2.905e-03 ## [3,] 0.9892 2.165 3 594 9.109e-02 As shown in the table above, the first test of the canonical dimensions tests whether all three dimensions are significant (they are, F = 11.72), the next test tests whether dimensions 2 and 3 combined are significant (they are, F = 2.94). Finally, the last test tests whether dimension 3, by itself, is significant (it is not). Therefore dimensions 1 and 2 must each be significant while dimension three is not. When the variables in the model have very different standard deviations, the standardized coefficients allow for easier comparisons among the variables. Next, we'll compute the standardized canonical coefficients. # standardized psych canonical coefficients diagonal matrix of psych sd's s1 <- diag(sqrt(diag(cov(psych)))) s1 %*% cc1$xcoef
## [,1] [,2] [,3]
## [1,] -0.8404 -0.4166 -0.4435
## [2,] 0.2479 -0.8379 0.5833
## [3,] -0.4327 0.6948 0.6855
s2 %*% cc1\$ycoef
## [,1] [,2] [,3]
## [1,] -0.45080 -0.04961 0.21601
## [2,] -0.34896 0.40921 0.88810
## [3,] -0.22047 0.03982 0.08848
## [4,] -0.04878 -0.82660 -1.06608
## [5,] -0.31504 0.54057 -0.89443
The standardized canonical coefficients are interpreted in a manner analogous to interpreting standardized regression coefficients. For example, consider the variable read, a one standard deviation increase in reading leads to a 0.45 standard deviation decrease in the score on the first canonical variate for set 2 when the other variables in the model are held constant.
## Sample Write-Up of the Analysis
There is a lot of variation in the write-ups of canonical correlation analyses. The write-up below is fairly minimal, including only the tests of dimensionality and the standardized coefficients.
Table 1: Tests of Canonical Dimensions
Canonical Mult.
Dimension Corr. F df1 df2 p
1 0.46 11.72 15 1634.7 0.0000
2 0.17 2.94 8 1186 0.0029
3 0.10 2.16 3 594 0.0911
Table 2: Standardized Canonical Coefficients
Dimension
1 2
Psychological Variables
locus of control -0.84 -0.42
self-concept 0.25 -0.84
motivation -0.43 0.69
writing -0.35 0.41
math -0.22 0.04
science -0.05 -0.83
gender (female=1) -0.32 0.54
Tests of dimensionality for the canonical correlation analysis, as shown in Table 1, indicate that two of the three canonical dimensions are statistically significant at the .05 level. Dimension 1 had a canonical correlation of 0.46 between the sets of variables, while for dimension 2 the canonical correlation was much lower at 0.17.
Table 2 presents the standardized canonical coefficients for the first two dimensions across both sets of variables. For the psychological variables, the first canonical dimension is most strongly influenced by locus of control (.84) and for the second dimension self-concept (-.84) and motivation (.69). For the academic variables plus gender, the first dimension was comprised of reading (.45), writing (.35) and gender (.32). For the second dimension writing (.41), science (-.83) and gender (.54) were the dominating variables.
## Cautions, Flies in the Ointment
• Multivatiate normal distribution assumptions are required for both sets of variables.
• Canonical correlation analysis is not recommended for small samples.
## R Documentation
#### References
• Afifi, A, Clark, V and May, S. 2004. Computer-Aided Multivariate Analysis. 4th ed. Boca Raton, Fl: Chapman & Hall/CRC.
The content of this web site should not be construed as an endorsement of any particular web site, book, or software product by the University of California. | |
# Number - Division
## 1 - About
$\frac{\displaystyle dividend}{\displaystyle divisor} = quotient$
where:
A division is the definition of every rational number.
The division symbol ÷ is just a blank fraction with dots replacing the numerator and denominator.
$$\frac{x}{1} = x$$ | |
+0
# Log questions
0
20
3
+8
1. Let x and b be positive real numbers so that \log_b(x^2) = 10. Find \log_{\sqrt[3]{b}} \left( \frac{1}{x} \right). 2. Let a, b, and c be the roots of 24x^3 - 121x^2 + 87x - 8 = 0. Find \log_3(a)+\log_3(b)+\log_3(c). I'm not really sure how to approach these ones. The best I did was to try to use exponential notation but that didn't seem to work out so well. All help is appreciated!
Mar 13, 2023
#1
+1
1.
We can start by using the properties of logarithms to simplify log_b x^2:
log_b x^2 = 10 2 log_b x = 10 log_b x = 5
Now we can use this result to simplify log_b^(1/3) 1/x:
log_b^(1/3) 1/x = (log_b (1/x))^(1/3)
Next, we can use the property that log_b (1/x) = -log_b x:
log_b^(1/3) 1/x = (-log_b x)^(1/3)
Substituting in the value we found earlier for log_b x:
log_b^(1/3) 1/x = (-5)^(1/3)
We can simplify this using the fact that (-a)^(1/3) = - (a^(1/3)) for any real number a:
log_b^(1/3) 1/x = - (5^(1/3))
So the final answer is -5^(1/3)
Mar 13, 2023
#2
+1
2. By Vieta's formulas, a + b + c = 121/24.
Then log_3 (a) + log_3 (b) + log_3 (c) = log_3 (121/24). You can simplify this a bit, by writing it as
log_3 (121/24) = log_3 (121//(3*8)) = log_3 (121/8) - log_3 3 = log_3 (121/8) - 1.
Guest Mar 13, 2023
#3
+118459
+1
Please just put one question per post.
It is amazing that you got any answer at all. Your questions are all run together and barely readable.
This is how they shouold have been presented, only in 2 different posts.
1. Let x and b be positive real numbers so that $$\log_b(x^2) = 10$$.
Find $$\log_{\sqrt[3]{b}} \left( \frac{1}{x} \right).$$
2. Let a, b, and c be the roots of $$24x^3 - 121x^2 + 87x - 8 = 0$$.
Find $$\log_3(a)+\log_3(b)+\log_3(c)$$.
Mar 13, 2023 | |
# Is $\mathbf{Q}(\sqrt{2}, \sqrt{3}) = \mathbf{Q}(\sqrt{2}+\sqrt{3})$?
Is $\mathbf{Q}(\sqrt{2}, \sqrt{3}) = \mathbf{Q}(\sqrt{2}+\sqrt{3})$ ?
$$\mathbf{Q}(\sqrt{2},\sqrt{3})=\{a+b\sqrt{2}+c\sqrt{3}+d\sqrt{6} \mid a,b,c,d\in\mathbf{Q}\}$$
$$\mathbf{Q}(\sqrt{2}+\sqrt{3}) = \lbrace a+b(\sqrt{2}+\sqrt{3}) \mid a,b \in \mathbf{Q} \rbrace$$
So if an element is in $\mathbf Q(\sqrt{2},\sqrt{3})$, then it is in $\mathbf{Q}(\sqrt{2}+\sqrt{3})$, because $\sqrt{6} = \sqrt{2}\sqrt{3}$.
How to conclude from there?
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$\mathbf{Q}(\sqrt{2}+\sqrt{3}) \not= \{a+b(\sqrt{2}+\sqrt{3})\ | a,b \in \mathbf{Q} \}$ because $\sqrt{2}+\sqrt{3}$ does not have degree 2 over $\mathbf{Q}$. – lhf Dec 22 '11 at 14:28
Hi lhf, then what is it? ? ? ? – Tashi Dec 22 '11 at 14:30
$\alpha=\sqrt{2}+\sqrt{3}$ has degree 4 over $\mathbf{Q}$ and so a basis is $1,\alpha,\alpha^2,\alpha^3$. – lhf Dec 22 '11 at 14:35
@Tashi: This may just be an issue of notation, since your argument in the question seems to suggest that you thougt that $\{a+b(\sqrt{2}+\sqrt{3})\ | a,b \in \mathbf{Q} \}$ also includes $\sqrt2\sqrt3$. (It doesn't.) – joriki Dec 22 '11 at 14:39
$\mathbb{Q}(\sqrt{2} + \sqrt{3}) \subseteq \mathbb{Q}(\sqrt{2}, \sqrt{3})$ is clear.
Now note that $$(\sqrt{2} + \sqrt{3})^{-1} = \frac{1}{\sqrt{2} + \sqrt{3}} = \frac{\sqrt{2} - \sqrt{3}}{2 - 3} = \sqrt{3} - \sqrt{2}$$ hence $\sqrt{3} - \sqrt{2} \in \mathbb{Q}(\sqrt{2} + \sqrt{3})$ and hence $\sqrt{2} + \sqrt{3} + \sqrt{3} - \sqrt{2} = 2 \sqrt{3} \in \mathbb{Q}(\sqrt{2} + \sqrt{3})$ and hence $\sqrt{3} \in \mathbb{Q}(\sqrt{2} + \sqrt{3})$. Note that by a similar argument you get $\sqrt{2} \in \mathbb{Q}(\sqrt{2} + \sqrt{3})$ and hence $\mathbb{Q}(\sqrt{2}, \sqrt{3}) \subseteq \mathbb{Q}(\sqrt{2} + \sqrt{3})$.
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Thank you, I can understand this answer! – Tashi Dec 22 '11 at 14:46
@Tashi You're welcome : ) – Rudy the Reindeer Dec 22 '11 at 14:50
@Tashi With only slightly more effort, you can understand my answer too (which I have elaborated). That will enable you to understand not only this special case, but much more general cases - many of which arise frequently in practice. – Bill Dubuque Dec 22 '11 at 15:06
HINT $\$ If a field F has two F-linear independent combinations of $\rm\ \sqrt{a},\ \sqrt{b}\$ then you can solve for $\rm\ \sqrt{a},\ \sqrt{b}\$ in F. For example, the Primitive Element Theorem works that way, obtaining two such independent combinations by Pigeonholing the infinite set $\rm\ F(\sqrt{a} + r\ \sqrt{b}),\ r \in F,\ |F| = \infty,$ into the finitely many fields between F and $\rm\ F(\sqrt{a}, \sqrt{b}),$ e.g. see PlanetMath's proof.
In this case it's simpler to notice $\rm\ E = \mathbb Q(\sqrt{a} + \sqrt{b})\$ contains the independent $\rm\ \sqrt{a} - \sqrt{b}\$ since
$$\rm \sqrt{a}\ -\ \sqrt{b}\ =\ \dfrac{a-b}{\sqrt{a}+\sqrt{b}}\ \in\ E = \mathbb Q(\sqrt{a}+\sqrt{b})$$
To be explicit, notice that $\rm\ u = \sqrt{a}+\sqrt{b},\ v = \sqrt{a}-\sqrt{b}\in E\$ so solving the linear system for the roots yields $\rm\ \sqrt{a}\ =\ (u+v)/2,\ \ \sqrt{b}\ =\ (v-u)/2\:,\$ both of which are clearly $\rm\:\in E\:,\:$ since $\rm\:u,\:v\in E\:$ and $\rm\:2\ne 0\:$ in $\rm\:E\:,\:$ so $\rm\:1/2\:\in E\:.\:$ This works over any field where $\rm\:2\ne 0\:,\:$ i.e. where the determinant (here $2$) of the linear system is invertible, i.e. where the linear combinations $\rm\:u,v\:$ of the square-roots are linearly independent over the base field.
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Thank you very much. – Tashi Dec 22 '11 at 14:46
To recap the notation: $\mathbb{Q}[x]$ denotes the ring of polynomials with rational coefficients. The square bracket notation $\mathbb{Q}[\sqrt{2}]$ means $\{p(\sqrt{2}) : p \in \mathbb{Q}[x]\}$. It's easy to show that $\mathbb{Q}[\sqrt{2}] = \{a+b\sqrt{2}:a,b,\in \mathbb{Q}\}.$
A really nice fact is that $\mathbb{Q}[\sqrt{2},\sqrt{3}] = \mathbb{Q}[\sqrt{2}][\sqrt{3}],$ where \begin{array}{ccc} \mathbb{Q}[\sqrt{2}][\sqrt{3}] &=& \{a+b\sqrt{3} : a,b \in \mathbb{Q}[\sqrt{2}] \} \\ \\ &=& \{p + q\sqrt{2} + r\sqrt{3} + s\sqrt{6} : p,q,r,s \in \mathbb{Q}\}. \end{array} These all use square brackets because they are considered as rings. The round brackets give us the set of rational expressions, which are fields, e.g.
$$\mathbb{Q}(\sqrt{2},\sqrt{3}) = \left\{ \frac{\alpha}{\beta} : \alpha,\beta \in \mathbb{Q}[\sqrt{2},\sqrt{3}]\right\}$$
It turns out that, as sets, $\mathbb{Q}[\sqrt{2},\sqrt{3}] = \mathbb{Q}(\sqrt{2},\sqrt{3})$.
In turns of the representation of $\mathbb{Q}(\sqrt{2},\sqrt{3})$ we have seen that, as a set, we have $\{p + q\sqrt{2} + r\sqrt{3} + s\sqrt{6}:p,q,r,s \in \mathbb{Q}\}$. There are many representations for this fiels, e.g. $\mathbb{Q}(1,\sqrt{2},\sqrt{3},\sqrt{6})$ or $\mathbb{Q}(\sqrt{2},\sqrt{3},\sqrt{6})$ or $\mathbb{Q}(1,\sqrt{2},\sqrt{3})$ or $\mathbb{Q}(\sqrt{2},\sqrt{3})$, etc. We can show that $\mathbb{Q}(\sqrt{2}+\sqrt{3})$ is also a representation of the same field too.
Think of $\mathbb{Q}(\sqrt{2},\sqrt{3})$ as a $\mathbb{Q}$-vector space with $\{1,\sqrt{2},\sqrt{3},\sqrt{6}\}$ as a basis. Let $\gamma := \sqrt{2}+\sqrt{3}.$ We have $\gamma^2 = 5+2\sqrt{6},$ $\gamma^3 = 11\sqrt{2}+9\sqrt{3}$ and $\gamma^4 = 49 + 20\sqrt{6}$. Putting this together:
$$\left[\begin{array}{cccc} 0 & 1 & 1 & 0 \\ 5 & 0 & 0 & 2 \\ 0 & 11 & 9 & 0 \\ 49 & 0 & 0 & 20 \end{array}\right]\left[\begin{array}{c} 1 \\ \sqrt{2} \\ \sqrt{3} \\ \sqrt{6} \end{array}\right] = \left[\begin{array}{c} \gamma \\ \gamma^2 \\ \gamma^3 \\ \gamma^4 \end{array}\right]$$
The 4-by-4 matrix on the left is non-singular, and so we can invert:
$$\left[\begin{array}{c} 1 \\ \sqrt{2} \\ \sqrt{3} \\ \sqrt{6} \end{array}\right] = \frac{1}{2}\!\left[\begin{array}{cccc} 0 & 20 & 0 & -2 \\ -9 & 0 & 1 & 0 \\ 11 & 0 & -1 & 0 \\ 0 & -49 & 0 & 5 \end{array}\right]\left[\begin{array}{c} \gamma \\ \gamma^2 \\ \gamma^3 \\ \gamma^4 \end{array}\right]$$
This tells us that $1$, $\sqrt{2}$, $\sqrt{3}$ and $\sqrt{6}$ can all be expressed as rational polynomials in $\gamma = \sqrt{2}+\sqrt{3}$.
\begin{array}{ccc} 10\gamma^2-\gamma^4 &=& 1 \\ \tfrac{1}{2}(\gamma^3-9\gamma) &=& \sqrt{2} \\ \tfrac{1}{2}(11\gamma - \gamma^3) &=& \sqrt{3} \\ \tfrac{1}{2}(5\gamma^4-49\gamma^2) &=& \sqrt{6} \end{array}
It follows that $\mathbb{Q}(1,\sqrt{2},\sqrt{3},\sqrt{6}) \cong \mathbb{Q}(\gamma) = \mathbb{Q}(\sqrt{2}+\sqrt{3}).$
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I like this version, since it's clear how to extend to the situation where more roots are adjoined. – Mark McClure May 28 '13 at 19:23
If it's allowed to use the Galois theory, it can be proved as following. Since the subgroup of the Galois group of the field extension $\mathbb{Q} (\sqrt2,\sqrt 3)$ over $\mathbb{Q}$ which the subfield $\mathbb{Q}(\sqrt 2+\sqrt 3)$ is trivial, therefor we know the result by the Galois theory. I admit it is not too trivial since one has to verify something as said above.
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Also note, $\sqrt{2}=\frac{(\sqrt{2}+\sqrt{3})^3-9(\sqrt{2}+\sqrt{3})}{2}$ and $-\sqrt{3}=\frac{(\sqrt{2}+\sqrt{3})^3-11(\sqrt{2}+\sqrt{3})}{2}$ and so done.
Now suppose wants to show $\mathbb{Z}[\sqrt{2},\sqrt{3}]\neq \mathbb{Z}[\sqrt{2}+\sqrt{3}]$ then, note minimal polynomial of $\sqrt{2}+\sqrt{3}$ over $\mathbb{Z}$ is of degree $4$.
So we can write $\mathbb{Z}[\sqrt{2}+\sqrt{3}]=\{a_1+a_2x+a_3x^2+a_4x^3|x=\sqrt{2}+\sqrt{3},a_i\in \mathbb{Z}\}$ now simple case chase shows $\sqrt{2}$ not in $\mathbb{Z}[\sqrt{2}+\sqrt{3}]$
- | |
# Timeline for How does axiom K contradict univalence?
### Current License: CC BY-SA 4.0
6 events
when toggle format what by license comment
Oct 9 '21 at 6:22 comment @GrantJurgensen Your are right, my answer is elliptic on that point. The univalence axiom says more precisely that the map from identity to isomorphism is an equivalence (HoTT book A.3.1), that is to say it postulates a map from isomorphism to identity which is an inverse of the natural map from identity to isomorphism.
Sep 26 '21 at 0:39 comment It's also worth noting that I originally referred to univalence as a "a map from an isomorphism on types to an equality of the same types", i.e. a term of type Π A B: Type, A ≃ B -> A = B. This was perhaps a mistake; I believe univalence typically refers to the stronger claim Π A B: Type, (A ≃ B) ≃ (A = B), which I used to finish the above proof.
Sep 26 '21 at 0:25 comment Oh, I see now. It was not immediately clear to me how we could construct a contradiction from the different isomorphisms, but I worked it out. For anyone else as slow as me: Let x, y: A ≃ B, where x ≠ y, and ϕ: (A ≃ B) ≃ (A = B) the isomorphism obtained by specializing the univalence axiom to types A and B. By UIP, we have ϕ x = ϕ y, which cancels to x = y, a contradiction.
Sep 25 '21 at 8:43 comment The OP explicitly asked whether Axiom K and UIP are equivalent. Your answer is a bit misleading in that regard, so it is better to clarify: Axiom K is indeed an instance of UIP, but from that instance we can derive the rest of UIP.
S Sep 25 '21 at 8:23 review
Sep 25 '21 at 11:34
S Sep 25 '21 at 8:23 history answered | |
## Elementary Technical Mathematics
Published by Brooks Cole
# Chapter 1 - Section 1.14 - Rate, Base, and Part - Exercises - Page 83: 10
#### Answer
B \$500 P \$90 R unknown
#### Work Step by Step
The base is the total amount of the loan, \$500. The part is the interest, \$90. The rate is the unknown.
After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback. | |
A bicycle wheel has radius R. Let P be a point on the spoke of a wheel at a distance d from the center of the wheel. The wheel begins to roll to the right along the the x-axis. The curve traced out by P is given by the following parametric equations:
$x = 13 \theta - 7 \sin(\theta)$
$y = 13 - 7 \cos(\theta)$
What must we have for R and d?
R=
d = | |
# Learning Muscular Anatomy
code clojure art emacs orgmode .....
A knowledge of the human form is vital for figurative artists. A detailed understanding of anatomy is especially helpful when working from life or constructing the figure from imagination.
Various approaches have been taken to learning artistic anatomy. While I'd rather not rob graveyards and do my own dissections, there are, fortunately, excellent anatomy books[1] available for the artist.
I have found the muscles harder to learn than the skeleton, so I developed the method outlined here, which involves reading, data entry, and memorization. Other methods include drawing muscles on tracing paper over figure drawings or photographs, or sculpting muscles atop a pre-formed skeleton. This practice supplements, but does not replace, those other methods.
A few key facts can be helpful to learn, for each of the important muscles (< 100 of them, roughly):
• Muscle name
• Origin of muscle (attachment point, stationary during contraction)
• Insertion of muscle (attachment point, moves during contraction)
• Function: what the muscle does
• What the muscle overlaps
• What the muscle is overlapped by.
These last two points can be helpful in constructing a mental model of the muscular forms and of the entire form they help to create.
I use the Anki flash card system as a tool for memorization. Anki uses a carefully designed model to set the timing of when you see individual cards, showing you ones you got wrong sooner, and gradually showing them less and less often as you learn.
For all the muscles you want to study, you can enter these key facts into a table, and then export the table into flashcards. The original Org file can be kept in Git under source control and shared with others, and presents a convenient overview of the entire corpus of data. Merely entering the data in the first place starts the memorization, and then each table field can be paired with the muscle name both "forwards" and "backwards" (fact->muscle and muscle->fact) as separate flashcards. Thus, for, say, 100 muscle names and the associated five facts per muscle, one has 100 x 5 x 2 = 1,000 flashcards.
There are Anki decks for muscular anatomy already available, but they tend to be large in size and have a medical rather than artistic context; also, finding and summarizing the information required to create the cards helps me learn.
I wrote a tiny Clojure program (GitHub repository here) to facilitate exporting the Org data into Anki, which accepts tab-separated lines. I run it whenever I add new muscles into my table.
Since Anki synchronizes with my phone, I can review whenever I have a short break. If I enter a few muscles a week, the data entry should roughly keep up with my memorization practice, and will then have all the relevant muscles memorized in well under a year with minimal daily effort… perhaps five minutes per day.
### Sample program output
\$ lein run
Function of Sartorius flexes, weakly abducts, rotates upper leg; flexes and medially \
rotates lower leg
Muscle w/ function flexes, weakly abducts, rotates upper leg; flexes and medially \
rotates lower leg Sartorius
Origin of Sartorius Just below tip of ASIS
Muscle with origin 'Just below tip of ASIS' Sartorius
Insertion of Sartorius Pes anserinus, on tibia
Muscle with insertion 'Pes anserinus, on tibia' Sartorius
Sartorius overlaps... Gracilis, Rectus Femoris, Vastus Medialis, Adductor Longus
Gracilis, Rectus Femoris, Vastus Medialis, Adductor Longus are overlapped by... Sartorius
Function of Deltoid flex arm forward, abducts outward, pulls backward
Muscle w/ function flex arm forward, abducts outward, pulls backward Deltoid
Origin of Deltoid lateral 1/3 of clavicle, acromion process, spine of scapula
...
… and a sample flash card (top portion only is shown initially, with the answer below shown after a tap or keypress):
### Workflow
1. Clone the GitHub repository and cd to the new directory;
2. Edit resources/muscle-structure.org;
3. Export Org file to CSV (org-table-export) in the same directory;
4. Run the program and save the output: lein run > cards.txt;
5. Import cards.txt (removing any previously-imported entries first) into Anki;
6. Memorize away!
7. Repeat as new muscles are added.
### Conclusion
After a few weeks of minimal effort (a lot less than my previous year-long project), I've added half a dozen or so muscles so far and have them pretty well down. Since the overlapping forms are included, one starts to flesh out one's three-dimensional understanding of the figure from the outset. (I recommend starting with the largest muscles first if you're not as familiar with them – e.g. pectoralis, gluteus maximum, rectus abdominis, etc.). This method is a bit personal, Emacs, Org Mode, Clojure, etc. not being standard artists' tools, but could be adapted to e.g. Excel or CSV files, or other programming languages, with minimal effort.
[1] See, for example, Human Anatomy for Artists: The Elements of Form by Elliot Goldfinger. | |
# Zeropoint energy
Template:Unsolved In a quantum mechanical system such as the particle in a box or the quantum harmonic oscillator, the lowest possible energy is called the zero-point energy. According to classical physics, the kinetic energy of a particle in a box or the kinetic energy of the harmonic oscillator may be zero if the velocity is zero. Quantum mechanics with its uncertainty principle implies that if the velocity is measured with certainty to be exactly zero, the uncertainty of the position must be infinite. This either violates the condition that the particle remain in the box, or it brings a new potential energy in the case of the harmonic oscillator. To avoid this paradox, quantum mechanics dictates that the minimal velocity is never equal to zero, and hence the minimal energy is never equal to zero.
## A few formulae
A particle in a box is defined by the potential energy $\displaystyle V(x)$ , which is defined to be
$\displaystyle V(x)=0$ for $\displaystyle -l/2 \leq x \leq l/2$
$\displaystyle V(x)$ infinite for $\displaystyle \left|x\right| > l/2$ .
The wave function with the minimal energy eigenvalue is then
$\displaystyle \psi(x) = C \sin(\pi x/l)$
where $\displaystyle C$ is an important normalization constant. The (zero-point) energy of this wave function is pure kinetic and equal to
$\displaystyle E_0 = \frac{\hbar^2\pi^2}{2ml^2}$
which is non-zero. Similarly, the zero-point energy of the quantum harmonic oscillator with the frequency $\displaystyle \omega$ is equal to
$\displaystyle E_0 = \frac{1}{2} \hbar\omega.$
Both of these simplest cases have a useful generalization to the case of quantum field theory. Quantum field theory - such as Quantum Electrodynamics - may be regarded as a collection of infinitely many harmonic oscillators, and quantum mechanics therefore predicts a nonzero vacuum energy. Although the absolute value of the vacuum energy is partly a matter of convention, the difference between the vacuum energy of various configurations has a physical meaning.
## Existence
Does electromagnetic zero-point energy exist, and if so, are there any practical applications and does it have any connection with dark energy? The theoretical basis for electromagnetic zero-point energy is clear. According to Sciama (1991):
"Even in its ground state, a quantum system possesses fluctuations and an associated zero-point energy, since otherwise the uncertainty principle would be violated. In particular the vacuum state of a quantum field has these properties. For example, the electric and magnetic fields in the electromagnetic vacuum are fluctuating quantities."
The Casimir effect is an example of a one-loop effect in quantum electrodynamics that can be simply explained by the zero-point energy.
## History
The concept of zero-point energy originated with Max Planck in 1911. The average energy of a harmonic oscillator in this hypothesis is (where $\displaystyle h$ is Planck's constant and $\displaystyle \nu$ is frequency):
$\displaystyle E= \frac{h\nu}{2} + \frac{h\nu}{e^{h\nu/kT}-1}$
At the same time Einstein and Hopf (1910) and Einstein and Stern (1913) were also studying the properties of zero-point energy. Shortly thereafter Nernst (1916) proposed that empty space was filled with zero-point electromagnetic radiation. Then in 1925 the existence of zero-point energy was shown to be “required by quantum mechanics, as a direct consequence of Heisenberg's uncertainty principle” (Sciama 1991). As any textbook on quantum optics will show (e.g. Loudon 1983), the way to quantize the electromagnetic field is to associate each mode of the field with a harmonic oscillator with the result that the minimum energy per mode of the electromagnetic quantum vacuum is $\displaystyle h\nu/2$ .
Zero-point energy shares a problem with the Dirac sea: both are potentially infinite. In the case of zero-point energy, there are reasons for believing that a cutoff does exist in the zero-point spectrum corresponding to the Planck scale. Even this results in an enormous amount of zero-point energy whose existence is assumed to be negated (in spite of the unmistakable mandate of the Heisenberg uncertainty principle) by the claim that the mass equivalent of the energy should gravitate, resulting in an absurdly large cosmological constant, contrary to observations. Matters are not quite so straightforward.
In response to the question “Do Zero-Point Fluctuations Produce a Gravitational Field?” Sciama (1991) writes:
"We now wish to comment on the unsolved problem of the relation between zero-point fluctuations and gravitation. If we ascribe an energy $\displaystyle h\nu/2$ to each mode of the vacuum radiation field, then the total energy of the vacuum is infinite. It would clearly be inconsistent with the original assumption of a background Minkowski space-time to suppose that this energy produces gravitation in a manner controlled by Einstein’s field equations of general relativity. It is also clear that the space-time of the real world approximates closely to the Minkowski state, at least on macroscopic scales. It thus appears that we must regularize the zero-point energy of the vacuum by subtracting it out according to some systematic prescription. At the same time, we would expect zero-point energy differences to gravitate. For example, the (negative) Casimir energy between two plane-parallel perfect conductors would be expected to gravitate; otherwise, the relativistic relation between a measured energy and gravitation would be lost."
It is precisely localizable differences in the zero-point energy that may prove to be of some practical use and that may be the basis of dark energy phenomena. Moreover it has also been found that asymmetries in the zero-point field that appear upon acceleration may be associated with certain properties of inertia, gravitation and the principle of equivalence Haisch, Rueda and Puthoff (1994); Rueda and Haisch (1998); Rueda and Haisch (2005).
## Properties
Lastly, insights may be offered on certain quantum properties (Compton wavelength, de Broglie wavelength, spin) and on mass-energy equivalence (E=mc2) if it proves to be the case that zero-point fluctuations interact with matter in a phenomenon identified by Erwin Schrödinger known as zitterbewegung (Haisch and Rueda 2000; Haisch, Rueda and Dobyns 2001; Nickisch and Mollere 2002).
As intriguing as these latter possibilities are, the first order of business is to unambiguously detect and measure zero-point energy. While a Casimir experiment such as that of Forward (1984) can in principle measure energy that may be attributed to the existence of real zero-point energy, there are alternative explanations involving source-source quantum interactions in place of real zero-point energy (see Milonni 1994). To move beyond this ambiguity of interpretation experiments that will test for the reality of measurable zero-point energy will need to be devised.
## Cultural references
In the Justice League Episode, 'Hereafter', Vandal Savage had taken over the world and invented a Zero Point Generator in the boredom of immortality which was used to power a time machine to transport Superman back to the present.
In the movie The Incredibles, the villain Syndrome uses a ray that can immobilize an opponent, suspending him in mid-air. Director Brad Bird, speaking in a DVD commentary, says that in searching for a name for the device (or at least a better one than "the Immobi-ray"), he came across and used a reference to "zero-point energy", which Syndrome himself uses to describe his weapon. (Of course, this is simply a cool name rather than a practical application at this time!)
Star Trek's quantum torpedo also utilises zero-point energy.
In the computer game Half-Life 2, one of the weapons used by the player is the "Zero Point Energy Field Manipulator", better known by its nickname the "Gravity Gun". It allows the user to pick up and launch any medium-sized objects, and was used to market the game's detailed physics engine.
The television show Stargate SG-1 and the spinoff, Stargate Atlantis also makes references to zero-point energy in the form of Zero Point Modules or ZPMs. These ZPMs extract energy from small artificially-created subspaces are used to power the technology of the Ancients, such as the energy shield which protects the city of Atlantis and powering the Stargate with sufficient power to allow travel to the Pegasus Galaxy. The Ancients also attempted to extract zero-point energy directly from their own universe in Project Arcturus.
Another television series called ZERO.POINT is in development that centers around the machinations of a quantum physicist searching for zero-point energy technology and a drifter who wanders in perfect synchronicity.
In Marvel Comic's "Ultimate Secret" issue one, the disguised Captain Mahr-vell has helped humans develop a star drive based on ZPE. He offhandedly remarks that quantum wave fluctuations were discovered to cause inertia, which is the SED Hypothesis (covered here).
In the second season of the television series Alias, Sydney Bristow is tasked to retrieve a music box that supposedly contains a formula for zero-point energy.
In 3001: The Final Odyssey, by Arthur C. Clarke humanity is tapping zero point energy (or vacuum energy as it's called in the book). Human astronomers observed an explosion of a far-away star, and on further investigation found that the detonation started at one of the planets which destabilised the star itself. This event gives the characters nightmares, as it was assumed that some alien race was using zero-point energy and lost control.
ZPE is also a potential energy source of interest to independent researchers outside of mainstream research entitities, such as the late Eugene Mallove, and figures into discussions on radio programs such as Coast to Coast AM.
## References
1. Einstein, A. and Hopf, L., Ann. Phys., 33, 1096 (1910a); Ann. Phys., 33, 1105 (1910b).
2. Einstein, A. and Stern, O., Ann. Phys., 40, 551 (1913).
3. Forward, R., Phys. Rev. Phys. Rev. B, 30, 1700 (1984). http://www.calphysics.org/articles/Forward1984.pdf
4. Haisch, B. and Rueda, A., Phys. Lett. A, 268, 224 (2000). http://xxx.arxiv.org/abs/gr-qc/9906084
5. Haisch, B., Rueda, A., and Dobyns, Y., Ann. Phys., Vol. 10, No. 5, 393 (2001). http://xxx.arxiv.org/abs/gr-qc/0002069
6. Haisch, B., Rueda, A. and Puthoff, H.E. 1994, Phys. Rev. A., 69, 678. http://www.calphysics.org/articles/PRA94.pdf
7. Loudon, R., The Quantum Theory of Light, (Oxford: Clarendon Press) (1983).
8. Milonni, P., The Quantum Vacuum: an Introduction to Quantum Electrodynamics (New York: Academic) (1994).
9. Nernst, W., Verh. Dtsch. Phys. Ges., 18, 83 (1916).
10. Nickisch, L. J. and Mollere, J., physics/0205086 (2002). http://www.arxiv.org/abs/physics/0205086
11. Rueda, A. and Haisch, B., Found. Phys., 28, No. 7, 1057 (1998a) http://xxx.arxiv.org/abs/physics/9802030; Phys. Lett. A, 240, 115 (1998b). http://xxx.arxiv.org/abs/physics/9802031
12. Rueda, A. and Haisch, B., Annalen der Physik, Vol. 14, No. 7, 479 (2005). http://xxx.arxiv.org/abs/gr-qc/0504061
13. Sciama, D. W. in “The Philosophy of Vacuum” (S. Saunders and H. R. Brown, eds.), (Oxford: Clarendon Press) (1991). | |
Question
Hollow cylinder B will reach the bottom of the slope first if?
• No friction on slope
• They roll without slipping
• Never
Both the cylinders have the same mass and radius. A is a solid cylinder.
Solution
In this question we have 2 cylinders A is solid and B is hollow.
Let the momentf of interia of A and B be I_A and I_B respectively. Then I_A=I_B/2.
When it is slipping down if there is no friction both A and B behave identically, they slip down the plane without rolling and will reach bottom of the plane at nearly the same.
If there is friction and it executing pure rolling without slipping. Then when it reach the bottom of the plane with say velocity v.
We know energy is conserver so mgh = 1/2mv^2+1/2Iomega^2
gh = 1/2v^2+1/2 I/m v^2/r^2
v^2 = 2gh/(1+I/(mr^2))
Since I is higher for hollow cylinder its velocity will lower as compared to the velocity of the solid cylinder when it reaches the bottom of the plane.
Now consider the case where there is rolling and slipping. In that case we will have.
mgh-mu*mg*l= 1/2mv^2+1/2Iomega^2
v^2 = (2g(h-mul))/(1+I/(mr^2))
So even now the velocity of the hollow cylinder will be lower as compared to velocity of solid cylinder.
And since they are travelling the same amount we get the B will always reach after A | |
## GFE dividing by temp
$\Delta G^{\circ}= \Delta H^{\circ} - T \Delta S^{\circ}$
$\Delta G^{\circ}= -RT\ln K$
$\Delta G^{\circ}= \sum \Delta G_{f}^{\circ}(products) - \sum \Delta G_{f}^{\circ}(reactants)$
JosephineF
Posts: 49
Joined: Wed Sep 18, 2019 12:17 am
### GFE dividing by temp
Does anyone have a deeper explanation for why we would divide ΔG by T for the equation -ΔG/T= -ΔH/T + ΔSsys? In lecture I didn't understand what the purpose was for doing this.
CynthiaLy4F
Posts: 103
Joined: Sat Jul 20, 2019 12:16 am
### Re: GFE dividing by temp
I believe the purpose for that was to manipulate the equation to show how -deltaG/T of the system is equal to deltaS of the universe, which means that in order for a spontaneous process to occur where deltaS is positive, then deltaG must be negative.
Angela Patel 2J
Posts: 110
Joined: Sat Aug 24, 2019 12:17 am
### Re: GFE dividing by temp
Because - delta H / T is the change in entropy of the surroundings (discussed earlier in lecture today) and this makes the equation easier to simplify into something that only has one variable. This way we can define spontaneity of a process in terms of only gibbs free energy.
Rebekah Alfred 1J
Posts: 102
Joined: Thu Jul 11, 2019 12:15 am
Been upvoted: 1 time
### Re: GFE dividing by temp
We know if it is a spontaneous process if the delta S of the universe is positive, which means that the delta G of the system must be negative. | |
# __ interest
This crossword clue is for the definition: __ interest.
it’s A 11 letters crossword puzzle definition.
Next time, when searching for online help with your puzzle, try using the search term “__ interest crossword” or “__ interest crossword clue”. The possible answerss for __ interest are listed below.
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Last seen on: LA Times Crossword 20 Apr 2018, Friday
### Random information on the term “__ interest”:
Actuarial notation is a shorthand method to allow actuaries to record mathematical formulas that deal with interest rates and life tables.
Traditional notation uses a halo system where symbols are placed as superscript or subscript before or after the main letter. Example notation using the halo system can be seen below.
Various proposals have been made to adopt a linear system where all the notation would be on a single line without the use of superscripts or subscripts. Such a method would be useful for computing where representation of the halo system can be extremely difficult. However, a standard linear system has yet to emerge.
i {\displaystyle \,i} is the annual effective interest rate, which is the “true” rate of interest over a year. Thus if the annual interest rate is 12% then i = 0.12 {\displaystyle \,i=0.12} .
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i ( m ) {\displaystyle \,i^{(m)}} (pronounced “i upper m”) is the nominal interest rate convertible m {\displaystyle m} times a year, and is numerically equal to m {\displaystyle m} times the effective rate of interest over one m {\displaystyle m} th of a year. For example, i ( 2 ) {\displaystyle \,i^{(2)}} is the nominal rate of interest convertible semiannually. If the effective annual rate of interest is 12%, then i ( 2 ) / 2 {\displaystyle \,i^{(2)}/2} represents the effective interest rate every six months. Since ( 1.0583 ) 2 = 1.12 {\displaystyle \,(1.0583)^{2}=1.12} , we have i ( 2 ) / 2 = 0.0583 {\displaystyle \,i^{(2)}/2=0.0583} and hence i ( 2 ) = 0.1166 {\displaystyle \,i^{(2)}=0.1166} . The “(m)” appearing in the symbol i ( m ) {\displaystyle \,i^{(m)}} is not an “exponent.” It merely represents the number of interest conversions, or compounding times, per year. Semi-annual compounding, (or converting interest every six months), is frequently used in valuing bonds (see also fixed income securities) and similar monetary financial liability instruments, whereas home mortgages frequently convert interest monthly. Following the above example again where i = 0.12 {\displaystyle \,i=0.12} , we have i ( 12 ) = 0.1139 {\displaystyle \,i^{(12)}=0.1139} since ( 1 + 0.1139 12 ) 12 = 1.12 {\displaystyle \,\left(1+{\frac {0.1139}{12}}\right)^{12}=1.12} . | |
r K fold cross validation using cv.lm() Stack Overflow Thanks for your response. It works when we use the header in cv.lm(). Is there a way I could use y.1 and x.1 in cv.lm() instead, as most of the times I will manipulate the headers for doing cv.lm(). Have updated my original writeup to explain on this. – Saravanan K Dec 23 '13 at 15:04 CVlm function | R Documentation This function gives internal and cross validation measures of predictive accuracy for multiple linear regression. (For binary logistic regression, use the CVbinary function.) The data are randomly assigned to a number of folds'. Each fold is removed, in turn, while the remaining data is used to re fit the regression model and to predict at the deleted observations.< p> cv.lm: Cross validation for an object of class 'lm' in ... The function cv.lm carries out a k fold cross validation for a linear model (i.e. a 'lm' model). For each fold, an 'lm' model is fit to all observations that are not in the fold (the 'training set') and prediction errors are calculated for the observations in the fold (the 'test set'). cv.lm function | R Documentation The function cv.lm carries out a k fold cross validation for a linear model (i.e. a 'lm' model). For each fold, an 'lm' model is fit to all observations that are not in the fold (the 'training set') and prediction errors are calculated for the observations in the fold (the 'test set'). Linear Regression Example in R using lm() Function – Learn ... Output for R’s lm Function showing the formula used, the summary statistics for the residuals, the coefficients (or weights) of the predictor variable, and finally the performance measures including RMSE, R squared, and the F Statistic. R: Cross Validation for Linear Regression cv.lm {DAAG} R Documentation: Cross Validation for Linear Regression Description. This function gives internal and cross validation measures of predictive accuracy for ordinary linear regression. The data are randomly assigned to a number of folds'. CVlm: Cross Validation for Linear Regression in DAAG: Data ... This function gives internal and cross validation measures of predictive accuracy for multiple linear regression. (For binary logistic regression, use the CVbinary function.) The data are randomly assigned to a number of ‘folds’. Each fold is removed, in turn, while the remaining data is used to re fit the regression model and to predict at the deleted observations. r Intepretation of crossvalidation result cv.glm ... See the docs of cv.glm, in particular the last example code. $\endgroup$ – Paul Hiemstra Jan 29 '13 at 22:32 $\begingroup$ @PaulHiemstra, thanks, I have 2 questions: 1) why repetition? I thought each of my 10 "folds" is a "repetition", so why another repetition? r Is there a simple command to do leave one out cross ... Is there a simple command to do leave one out cross validation with the lm() function in R? Specifically is there a simple command which for the code below? x < rnorm(1000,3,2) y < 2*x ... Explaining the lm() Summary in R – Learn by Marketing See this for an example (and an explanation). You can now replicate the summary statistics produced by R’s summary function on linear regression (lm) models! If you’re interested in more R tutorials on linear regression and beyond, take a look at the Linear Regression page. regression How to interpret the results from cross ... reg< lm(logWet.weight~logAverageBL) cv.lm(mtross, reg, m=5) Analysis of Variance Table Response: logWet.weight Df Sum Sq Mean Sq F value Pr(>F) logAverageBL 1 10.42 10.42 808 <0.0000000000000002 *** Residuals 38 0.49 0.01 fold 1 Observations in test set: 8 2 3 9 11 15 19 34 logAverageBL 1.6911 1.1949 1.44 1.083 1.1236 1.2682 1.4668 cvpred 1.0956 0.3033 0.39 0.619 0.5042 0.0968 0.4631 ... Cross Validation for Predictive Analytics Using R | R bloggers Doing Cross Validation With R: the caret Package. There are many R packages that provide functions for performing different flavors of CV. In my opinion, one of the best implementation of these ideas is available in the caret package by Max Kuhn (see Kuhn and Johnson 2013) 7.The aim of the caret package (acronym of classification and regression training) is to provide a very general and ... How and when: ridge regression with glmnet | R bloggers Because, unlike OLS regression done with lm(), ridge regression involves tuning a hyperparameter, lambda, glmnet() runs the model many times for different values of lambda. We can automatically find a value for lambda that is optimal by using cv.glmnet() as follows: cv_fit cv.glmnet(x, y, alpha = 0, lambda = lambdas) R Random Forest Tutorial with Example Guru99 R has a function to randomly split number of datasets of almost the same size. For example, if k=9, the model is evaluated over the nine folder and tested on the remaining test set. This process is repeated until all the subsets have been evaluated. This technique is widely used for model selection, especially when the model has parameters to tune. R panion: Statistics of Dispersion Measures of dispersion—such as range, variance, standard deviation, and coefficient of variation—can be calculated with standard functions in the native stats package. In addition, a function, here called summary.list, can be defined to output whichever statistics are of interest. Introduction How and when: ridge regression with glmnet Because, unlike OLS regression done with lm(), ridge regression involves tuning a hyperparameter, lambda, glmnet() runs the model many times for different values of lambda. We can automatically find a value for lambda that is optimal by using cv.glmnet() as follows: cv_fit < cv.glmnet(x, y, alpha = 0, lambda = lambdas) R: Cross validation for Generalized Linear Models Details. The data is divided randomly into K groups. For each group the generalized linear model is fit to data omitting that group, then the function cost is applied to the observed responses in the group that was omitted from the fit and the prediction made by the fitted models for those observations.. When K is the number of observations leave one out cross validation is used and all the ... Cross Validation Essentials in R Articles STHDA Practical example in R using the caret package: # Define training ... A less obvious but potentially more important advantage of k fold CV is that it often gives more accurate estimates ... I tried building an lm model (using caret package, i was following your example) and compared it to an lm model using native approach, something like ... R Linear Model (lm) Function EndMemo R Linear Model Regression. ENDMEMO. Home » R » 5 Model Training and Tuning | The caret Package 5.3 Basic Parameter Tuning. By default, simple bootstrap resampling is used for line 3 in the algorithm above. Others are available, such as repeated K fold cross validation, leave one out etc.The function trainControl can be used to specifiy the type of resampling:. fitControl < trainControl (## 10 fold CV method = "repeatedcv", number = 10, ## repeated ten times repeats = 10) Prediction Modeling & Validation Web Services By comparing ajusted R^2, we could determine the best number of variable for the model subset.out< regsubsets(y~ ., data=mydata,nbest=1,nvmax=NULL,method="exhaustive ... Quick R: Multiple Regression R provides comprehensive support for multiple linear regression. The topics below are provided in order of increasing complexity. Fitting the Model # Multiple Linear Regression Example fit < lm(y ~ x1 x2 x3, data=mydata) summary(fit) # show results # Other useful functions coefficients(fit) # model coefficients CHAPTER 21 Example: Linear regression using many ... Syllabus for the course ‘Statistics with R’ 21.1 Exercise. We will try these regularized regressions on a data set that describes wine quality (Cortez et al. ()).The data set is available from the UCI Machine Learning Repository under the title Wine Quality Data Set, but can also be downloaded from the server for this course in the folder data wine_quality. 3.2.4.1.9. sklearn.linear_model.RidgeCV — scikit learn 0 ... The ‘auto’ mode is the default and is intended to pick the cheaper option of the two depending on the shape of the training data. store_cv_values bool, default=False. Flag indicating if the cross validation values corresponding to each alpha should be stored in the cv_values_ attribute (see below). This flag is only compatible with cv=None (i.e. using Generalized Cross Validation). How To Estimate Model Accuracy in R Using The Caret Package When you are building a predictive model, you need a way to evaluate the capability of the model on unseen data. This is typically done by estimating accuracy using data that was not used to train the model such as a test set, or using cross validation. The caret package in R provides a number of methods to estimate the accuracy Evaluate a modeling procedure using n fold cross ... Here is an example of Evaluate a modeling procedure using n fold cross validation: In this exercise you will use splitPlan, the 3 fold cross validation plan from the ... Performing Principal ponents Regression (PCR) in R In the example above, it looks like 3 components are enough to explain more than 90% of the variability in the data although the CV score is a little higher than with 4 or 5 components. Finally, note that 6 components explain all the variability as expected. A GLM Example UMN Statistics predictor. The way R handles such a term in the linear predictor that does not contain an unknown parameter to fit is as an “offset”. Since the vari able n in the math formula is the variable totalseeds in R, the “offset” is offset(log(totalseeds)). The rest of the variables in the data set (vegtype and the three burn vari LASSO, Ridge, and Elastic Net Nc State University Example 1. Generate Data; Fit models; Plot solution path and cross validated MSE as function of $$\lambda$$. MSE on test set; Example 2. Generate Data; Fit Models; Plot solution path and cross validated MSE as function of $$\lambda$$. MSE on test set; Example 3. Generate Data; Fit models; Plot solution path and cross validated MSE as function ... An Example of ANOVA using R University of Wisconsin ... An Example of ANOVA using R by EV Nordheim, MK Clayton & BS Yandell, November 11, 2003 In class we handed out ”An Example of ANOVA”. Below we redo the example using R. There are three groups with seven observations per group. We denote group i values by yi: > y1 = c(18.2, 20.1, 17.6, 16.8, 18.8, 19.7, 19.1) French Resume Le CV Francais The first thing you need to know is that the word résumé is a false cognate in French and English. Un résumé means a summary, whereas a résumé refers to un CV (curriculum vitae).Thus, when applying for a job with a French company, you need to provide un CV, not un résumé. GLM Tutorial in R Texas A&M University ! ! 6! 8. R!follows!the!popular!customof!flagging!significant!coefficients!with!one,!two!or!three! starsdependingontheirpBvalues.Try>plot(lrfit).!You!get!the!same ... Predictive modeling and machine learning in R with the ... Powerful and simplified modeling with caret. The R caret package will make your modeling life easier – guaranteed.caret allows you to test out different models with very little change to your code and throws in near automatic cross validation bootstrapping and parameter tuning for free.. For example, below we show two nearly identical lines of code. Yet they run entirely different mod | |
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• CommentRowNumber1.
• CommentAuthorKeithEPeterson
• CommentTimeNov 24th 2016
• (edited Nov 30th 2016)
In programming, legal contract drafting, making jokes and filling in madlibs, students cheating on essays, and large scale substitution in math, (even closure operations?), aren’t all these things are instances of applying template, but how does templating work from an n-POV?
My instincts tell me it’s an Operad of some sort, given how composition of templates ought to behave. Is there a Linguistic Operad of sorts that handles instances of templating?
Edit: In linguistics language, I’m asking about ’phrasal templating’ and it’s categorical semantics.
• CommentRowNumber2.
• CommentAuthorDavidRoberts
• CommentTimeNov 24th 2016
Going out on a limb, it might relate to Spivak’s ologs.
• CommentRowNumber3.
• CommentAuthorRodMcGuire
• CommentTimeNov 25th 2016
Start with a $setAct$ - the action of a set $P$ on a set $V$ - act: $P \times V \to V$.
For a fixed set of property names these form the category $setActs(P)$ with the obvious $P$ preserving concrete morphisms (whose structure may be uninteresting).
Enhance a setAct $A$ with a distinguished point of its objects $V$ called $root$ giving the structure $\langle \, r A\rangle$, and say that $\langle r \, A\rangle$ has the property of being rooted if every object is accessible from the root using a path from the free monoid $P^*$.
Rooted setActs form the category $rSetActs(P)$ which is the quotient object lattice of $\bot(P)$ the free rooted setAction of $P$ - an infinite tree with edges labeled from $P$. $\top(P)$ is the one object “rose” with $P$ arcs - its free category $\top(P)^*$ is just the one object free monoid $P^*$.
This category contains some objects that can be displayed as similar to simple JavaScript objects, e.g. in $rSetActs(\{name,\, first,\, last,\, a,\, b\})$
$\{name: \{first: John, last: Smith\}\}$
The join in this lattice can give such as:
$\{name: \{first: John\}\} \vee \{name: \{last: Smith\}\} = \{name: \{first: John, last: Smith\}\}$
(The join here might be more specifically called rootJoin because it equates the roots of its arguments. An “atomic” object such as $John$ actually corresponds to a coAtom of the lattice and the lattice has an infinite number of them. In JavaScript trying to access a property that is not present returns the distinguished value $unknown$. In this variation unknown properties correspond to $\bot$)
For an object (act) in both $SetActs(P)$ and $rSetActs(P)$, $hom(v,w)$ is the set of all paths from $v$ to $w$. This set can be empty or encoded as a regular expression / Kleene algebra. $hom(v,w)$ is biRooted containing both the root $v$ and a coRoot $w$. A biRooted act will be displayed as $\langle r\, A\, cr\rangle$,
The set of all homs internal to the objects, $allHoms(setAct(P))$, is obviously a Heyting lattice (biHeyting?, Boolean?) which enriches every variety of setAct.
By adding biRoot structure to any setAct we can form the category $biSetActs(P)$ where the objects are restricted to being rooted. This is at least a Heyting lattice that contains $allHoms(setActs(P))$ as a sub lattice.
$biSetAct(P)$ has an additional monoid? structure: the operator $+$ called conJoin (with unit the empty path $\langle e \bot e\rangle$) which vaguely behaves as:
$\langle a A b\rangle + \langle b B c\rangle = \langle a C c\rangle$
This conJoining essentially gives A with its coRoot joined to B’s root and its coRoot changed to correspond to B’s.
For a JavaScript like example we have
$\{name: \{first: *, last: Smith\}\} + *John = \{name: \{first: *John, last: Smith\}\}$
where the * in an object is used to indicate its coRoot.
I believe I have this all worked out for when setActions are restricted to being quasi-finite which means that an act has a finite number of objects not isomorpic to $\bot$. In particular $hom(v,w)$ in an act $A$ contains all objects found on paths from $v$ to $w$ - those off any such path are become $\bot$s. A $hom(v,w)$ has the property that all of its non-$\bot$ objects drain to $w$ via some path. General biRooted objects don’t have this property.
In the above discussion I am somewhat conflating an act $A$ which is an edge labeled quiver with its free category $A^*$ in which the morphisms are paths. A more precise discussion would distinguish these.
• CommentRowNumber4.
• CommentAuthorKeithEPeterson
• CommentTimeNov 29th 2016
• (edited Nov 29th 2016)
Actually, now that I think about it, a template can be viewed as a diagram with some internal elements being global sections/generalized elements, which upholds typing.
• CommentRowNumber5.
• CommentAuthorKeithEPeterson
• CommentTimeNov 30th 2016
• (edited Nov 30th 2016)
Scrap what I said above. The thing I was looking for is called a “Generic Zipper”, it’s a sort of “derivative” of data-types.
• CommentRowNumber6.
• CommentAuthorTodd_Trimble
• CommentTimeNov 30th 2016
• (edited Nov 30th 2016)
Keith, if you set the formatting to Markdown+Itex, then you can create a link like so: Scrap Your Zippers. See the Source for the syntax.
• CommentRowNumber7.
• CommentAuthorRodMcGuire
• CommentTimeNov 30th 2016
A zipper appears to be a data structure implementing some of the rooted bi-pointed acts I discussed above.
The Wikipedia article talks about a path to a hole. Above I talked about all paths to a hole which turns out to be a bi-rooted act itself (and a regular expression / Kleene algebra). I’m not familiar enough with zippers to know if they can handle my potentially cyclic data structures or if anybody has given them lattice ordering.
Complementary to conJoin defined above there is the conMeet “$-$” monoidial operator with $\top$ as its unit. Replacing the coPoint in an act requires two steps: “removing” it by conMeeting with $\bot$ followed by conJoining in the replacement value .
$\{first: *John, last: Smith\} - *\bot + *Mary = \{first: *Mary, last: Smith\}$
And just for another example here is appending linked lists analogous to the use of difference lists in Prolog.
$[John\, likes | *] + [to \,eat | *] + [pie | *] = [John\, likes\, to\, eat\, pie | *]$ $\{h:John t:\{h:likes t:*\}\} + \{h:to t:\{h:eat t:*\}\} + \{h: pie t:*\}$ $= \{h:John t:\{h:likes t:\{h:to t:\{h:eat t:\{h: pie t:*\}\}\}\}\}$
• CommentRowNumber8.
• CommentAuthorKeithEPeterson
• CommentTimeNov 30th 2016
Yeah, your post made me dive deeper into the net to understand what you were meaning. The Haskell community has done everything already it seems... >_>
• CommentRowNumber9.
• CommentAuthorKeithEPeterson
• CommentTimeDec 25th 2016
Is there a notion of $\mathcal{E}$-acts, for an arbitrary topos $\mathcal{E}$, or is this confined to just bi-heyting topoi?
• CommentRowNumber10.
• CommentAuthorRodMcGuire
• CommentTimeDec 25th 2016
you should ignore what I said about the category Kleene(P) (as what enriches various act categories) as being obviously Heyting - I was getting levels confused.
There are several different ways to define Kleene algebras. I haven’t worked out which one I’m talking about.
I came across this paper a while back: Pippenger - Regular languages and Stone Duality, where he says:
it is well known that the regular languages over a fixed alphabet form a Boolean algebra and that the “implicit operations” with a fixed number of operands form a Stone space.
I should work on understanding this paper or the work derived from it. | |
## PCA / FA example 4: davis. Davis & harman 2.
We learned from harman that if we use the orthogonal eigenvector matrix v to compute new data, the result has redistributed the original variance according to the eigenvalues; and we also learned that if we use the weighted eigenvector matrix instead, we get new variables of unit variance.
(i think i thought this required us to start with the correlation matrix; it does not.)
let’s see this again for davis’ centered data X:
$\left(\begin{array}{lll} -6&3&3\\ 2&1&-3\\ 0.&-1&1\\ 4&-3&-1\end{array}\right)$
We have variances…
$\{\frac{56}{3},\ \frac{20}{3},\ \frac{20}{3}\}$
or…
${18.6667,\ 6.66667,\ 6.66667}$
and the sum of the variances is…
32.
Now is a good time to recall $w^T\ w$:
$\left(\begin{array}{lll} 84.&0.&0.\\ 0.&12.&0.\\ 0.&0.&0.\end{array}\right)$
The sum of the diagonal elements is 96, and if we divide by 3 (= N-1, for the covariance matrix instead of for $X^T\ X$), gee, we get 32.
stop for a moment. We have two, admittedly proportional, sets of eigenvalues, one set from the covariance matrix, the other from $X^T\ X$. this gives us two different possible sets of weights to apply to the eigenvector matrix v. (recall that v is an eigenvector matrix both for $X^T\ X$ and for the covariance matrix of X, as well as coming out of the SVD of X.)
Let’s stay with what i know: our new data, using the orthogonal eigenvector matrix v, is $A^Q$.
$\left(\begin{array}{lll} -7.34847&0.&0.\\ 2.44949&-2.82843&0.\\ 0.&1.41421&0.\\ 4.89898&1.41421&0.\end{array}\right)$
The variances are…
${28.,\ 4.,\ 0.}$
and we don’t even need to consciously add those: the sum is 32. We have redistributed the original variance among our two new variables.
Now, everyone seems to say that the $\sqrt{\text{eigenvalue}}$-weighted eigenvectors have variances equal to the eigenvalues. What those eigenvectors really have is lengths equal to their $\sqrt{\text{eigenvalue}}$.
here indeed be dragons.
as linear algebra is my touchstone in general for all of this, that redistributed variance using the orthogonal eigenvector matrix is my vorpal blade (dragon, jabberwock, no big deal – snicker-snack either way). any different choice of basis must lead to different results.
we looked at that redistribution of variance in harman. We learned then that the correct way to get new data with redistributed variance is to use the orthogonal eigenvector matrix. We just reconfirmed it for davis’ example.
Instead of actually kicking one of the dragons awake, let’s try counting its scales while it sleeps. If the R-mode scores $S^R$ are some form of data (and they are), what are their variances?
my $S^R$ is
$\left(\begin{array}{llll} -67.3498&0.&0.&0.\\ 22.4499&-9.79796&0.&0.\\ 0.&4.89898&0.&0.\\ 44.8999&4.89898&0.&0.\end{array}\right)$
the variances of the first two columns are
${2352.,\ 48.}$
yikes! if nothing else, that should convince you that the R-mode scores are weird.Life is so much simpler if we use the orthogonal eigenvector matrix. The new data is trivial to compute (X v), and we can see that it has redistributed the variance of the original data.Trying to use any weighted eigenvector matrix is dicey if there is a zero eigenvalue (because our transition matrix is not invertible); and confusing if we used $X^T\ X$ instead of the covariance matrix (because they have different eigenvalues).i will eventually calculate the data wrt both of the weighted eigenvector matrices. The dragons will be awake and aloft and pretty to look at. | |
Toronto Math Forum
APM346-2018S => APM346––Home Assignments => Topic started by: Andrew Hardy on March 17, 2018, 10:39:32 AM
Title: Inhomogenous Boundary Conditions for Eigenvalue Problem
Post by: Andrew Hardy on March 17, 2018, 10:39:32 AM
Chapter 4.2 gives the solutions to several different boundary conditions for an eigenvalue problem. All of the solutions provided are for inhomogeneous BC's though. Would the exam cover homogeneous BC? What would be the method in that case?
Also, point of clarification for the solution to previous TT2 #3
http://forum.math.toronto.edu/index.php?topic=841.0
$Y_m$ should depend upon the variable $y$ correct? So the correct solution to Laplacian in the rectangle
${0<x<a,0<y<b}$ with Neumann boundary conditions should be?:
$$u_{n,m}(x,y) = \cos(\frac{n\pi x}{a})\cos(\frac{m\pi y}{b})$$
Title: Re: Inhomogenous Boundary Conditions for Eigenvalue Problem
Post by: Victor Ivrii on March 17, 2018, 01:25:05 PM
Chapter 4.2 gives the solutions to several different boundary conditions for an eigenvalue problem. All of the solutions provided are for inhomogeneous BC's though. Would the exam cover homogeneous BC? What would be the method in that case?
? 4.2. Eigenvalue problem only homogeneous b.c. are considered here, because only in this case we have eigenvalue problem.
Quote
Also, point of clarification for the solution to previous TT2 #3
http://forum.math.toronto.edu/index.php?topic=841.0 (http://forum.math.toronto.edu/index.php?topic=841.0)
$Y_m$ should depend upon the variable $y$ correct? So the correct solution to Laplacian in the rectangle
${0<x<a,0<y<b}$ with Neumann boundary conditions should be?:
$$u_{n,m}(x,y) = \cos(\frac{n\pi x}{a})\cos(\frac{m\pi y}{b})$$
Indeed. I waited someone to correct it ... and forgot then... | |
Scaling of the N-S equations
by hanson
Tags: equations, scaling
P: 320 Hi all! I am having problems with understanding the scaling process of the N-S equations in fluid dynamics. From textbooks, I see that each quantity say velocity, time, length...etc are all divided some some reference values in order to obtain some dimensionaless quantity V*, t*, p*, g* etc.. And the N-S equations are then rewrite into a dimensionless form, the coefficients beceome the Reynolds number, Froude number etc... And the writer says after having this dimensionless equation, we can know the importance of the terms by just looking at the coefficients. That's what the textbook said, and I don't really understand. I can't catch the reason for making it in a dimensionless form. Can't I still judge the importance of the terms by looking at the coefficients of the terms when the equation have dimensions? Why must we transform it to be dimensionless? Can anyone help me out?
P: 320 could anyone please help?
Sci Advisor HW Helper PF Gold P: 4,099 Certainly, you don't have to use dimensionless variables. However, using dimensionless variables can simplify the analysis of a problem. First, it cuts down the number of symbols in the equation. (Less writing!) This often highlights the "[standard] form" of an equation. It may be easier to recognize the mathematics, and possibly draw analogies between different physical systems. (For example, it may help you recognize that the mass-spring system is analogous to an inductor-capacitor system.) Additionally, one can't compare A with B (i.e. one can't say A>B) if they carry different dimensions. However, if $$\alpha$$ and $$\beta$$ are dimensionless, then one can compare them. In particular, it may useful to know that $$\alpha\gg\beta$$ so that the $$\beta$$-term in an expression like $$\alpha \blacksquare + \beta \blacksquare +\ldots$$ may be neglected. Implicit in the above is the idea of "scaling". For example, if you know how a problem scales, you can experimentally model it less expensively. (For example, wind tunnel tests for airplanes. Another example: special effects using miniatures and slow-motion.)
Related Discussions Differential Equations 1 Precalculus Mathematics Homework 5 General Physics 0 Quantum Physics 0 General Math 1 | |
Chapter 5
The statistical procedures developed in Chapters 2 to 4 are appropriate for analyzing the results of experiments in which the variable of interest is measured on an interval scale, such as blood pressure, urine production, or length of hospital stay. Much of the information physicians, nurses, other health professionals, and medical scientists use cannot be measured on interval scales. For example, an individual may be male or female, dead or alive, or Caucasian, African American, Hispanic, or Asian. These variables are measured on nominal scales, in which there is no arithmetic relationship between the different classifications. We now develop the statistical tools necessary to describe and analyze such information.
It is easy to describe things measured on a nominal scale: simply count the number of patients or experimental subjects with each condition and (perhaps) compute the corresponding percentages.
To answer this and other questions about nominal data, we must first invent a way to estimate the precision with which percentages based on limited samples approximate the true rates that would be observed if we could examine the entire population, in this case, all homeless people. We will use these estimates to construct statistical procedures to test hypotheses.
*Song J, Ratner ER, Wall HM, Bartels DM, Ulvestad N, Petroskas D, West M, Weber-Main AM, Grengs L, Gelberg L. Effect of an end-of life planning intervention on the completion of advance directives in homeless persons. Ann Intern Med. 2010;153:76–84.
Before we can quantify the certainty of our descriptions of a population on the basis of a limited sample, we need to know how to describe the population itself. Since we have already visited Mars and met all 200 Martians (in Chapter 2), we will continue to use them to develop ways to describe populations. In addition to measuring the ...
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# 10.1: FOILed Again
Difficulty Level: At Grade Created by: CK-12
This activity is intended to supplement Algebra I, Chapter 9, Lesson 2.
## Problem 1 - Introduction to Area of a Rectangle
Run the AREA program (in PRGM) and select the option for Problem 1 (#1).
Enter 6 for \begin{align*}W\end{align*}.
1. What are the lengths of the sides of the rectangle?
2. What is the area of the rectangle when \begin{align*}w = 6\end{align*}?
Now, change the width of the side by running the program again and enter a new value for \begin{align*}W\end{align*}.
3. What is the area of the rectangle when \begin{align*}w = 4\end{align*}? When \begin{align*}w = 9\end{align*}?
4. Explain how the expression for the area is simplified.
## Problem 2 - Areas of Small Rectangles
The rectangle at the right has dimensions \begin{align*}(x + 7)\end{align*} and rate of \begin{align*}(x + 2)\end{align*}. Each piece of the rectangle is a different color so that you can focus on its area.
5. What is the area of each small rectangle?
6. What is the total area of the rectangle?
## Problem 3 - FOIL Method
Run the AREA program and select the option for Problem 3.
Enter \begin{align*}(x + 7)(x + 2)\end{align*} for \begin{align*}(AX+B)(CX+D)\end{align*}. \begin{align*}(A = 1, B = 7, C = 1, D = 2)\end{align*}
7. How do the areas of the small rectangles in Problem 2 relate to the expression shown on the bottom of the screen?
Practice finding the area of a rectangle and then check your answers with the program.
8. What is the expression of the area of a rectangle with dimensions \begin{align*}(3x + 5)\end{align*} and \begin{align*}(6x + 2)\end{align*}?
9. a. \begin{align*}(4x + 1)(3x + 9)\end{align*}
b. \begin{align*}(x + 8)(7x + 3)\end{align*}
c. \begin{align*}(2x + (-3))(5x + 8)\end{align*}
## Homework/Extensions
1. a. \begin{align*}(4x + 2)(x + 7) =\end{align*}
b. \begin{align*}(3x - 7)(2x + 4) =\end{align*}
c. \begin{align*}(2x + 5)(6x + 1) =\end{align*}
d. \begin{align*}(5x + 3)(9x - 2) =\end{align*}
Next, you will be multiplying a trinomial (3 terms) times a binomial (2 terms) to find the area of a rectangle.
2. What method can you use to find the simplified expression for the area?
3. Use the letters \begin{align*}a, b, c, d,\end{align*} and \begin{align*}e\end{align*} to determine the formula used to find the 6 terms of area shown at the right.
4. What is the area of the rectangle with dimensions \begin{align*}(1x^2 + 3x + 4)\end{align*} and \begin{align*}(5x + 6)\end{align*}?
5. a. \begin{align*}(2x^2 + 1x + 7)(3x + (-6)) = \end{align*}
b. \begin{align*}(4x^2 + 3x + 8)(x + 3) = \end{align*}
c. \begin{align*}(2x^2 + 6x + 4)(-3x + 9) =\end{align*}
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# How to add a dense layer after a 2d convolutional layer in a convolutional autoencoder?
I am trying to implement a convolutional autoencoder with a dense layer at the bottleneck to do some dimensional reduction. I have seen two approaches for this, which aren't particularly scalable. The first was to introduce 2 dense layers (one at the bottleneck and one before & after that has the same number of nodes as the conv2d layer that precedes the dense layer in the encoder section:
input_image_shape=(200,200,3)
encoding_dims = 20
encoder = Sequential()
#The decoder
decoder = Sequential()
It's easy to see why this approach blows up as there are two densely connected layers with (32100100) nodes each or more or in that ballpark which is nuts.
Another approach I have found which makes sense for b/w images such as the MNIST stuff is to introduce an arbitrary number of encoding dimensions and reshape it (https://medium.com/analytics-vidhya/building-a-convolutional-autoencoder-using-keras-using-conv2dtranspose-ca403c8d144e). The following chunk of code is copied from the link, I claim no credit for it:
#ENCODER
inp = Input((28, 28,1))
e = Conv2D(32, (3, 3), activation='relu')(inp)
e = MaxPooling2D((2, 2))(e)
e = Conv2D(64, (3, 3), activation='relu')(e)
e = MaxPooling2D((2, 2))(e)
e = Conv2D(64, (3, 3), activation='relu')(e)
l = Flatten()(e)
l = Dense(49, activation='softmax')(l)
#DECODER
d = Reshape((7,7,1))(l)
d = Conv2DTranspose(64,(3, 3), strides=2, activation='relu', padding='same')(d)
d = BatchNormalization()(d)
d = Conv2DTranspose(64,(3, 3), strides=2, activation='relu', padding='same')(d)
d = BatchNormalization()(d)
d = Conv2DTranspose(32,(3, 3), activation='relu', padding='same')(d)
decoded = Conv2D(1, (3, 3), activation='sigmoid', padding='same')(d)
So, is there a more rigorous way of adding a dense layer after a 2d convolutional layer?
For me, this worked perfectly. I encoded with conv2d and dense and then I flatten I and reshape in the decoder after the dense layer so the encoder and decoder are symmetrical. The only difference is that in my case I use images (224,224,1)
# create encoder
# 28,28 -> 1st conv2d (filter 3x3,relu activation, padding, strides == 'jumps')
self.encoder = tf.keras.Sequential([layers.Input(shape=(224,224,1)), | |
# MoMEMta, a modular toolkit for the Matrix Element Method at the LHC
@article{Brochet2018MoMEMtaAM,
title={MoMEMta, a modular toolkit for the Matrix Element Method at the LHC},
author={S{\'e}bastien Brochet and C. Delaere and Brieuc François and Vincent Lema{\^i}tre and Alexandre Mertens and Alessia Saggio and M Vidal Marono and S{\'e}bastien Wertz},
journal={The European Physical Journal C},
year={2018},
volume={79},
pages={1-12}
}
• Published 22 May 2018
• Physics
• The European Physical Journal C
The Matrix Element Method has proven to be a powerful method to optimally exploit the information available in detector data. Its widespread use is nevertheless impeded by its complexity and the associated computing time. MoMEMta, a C++ software package to compute the integrals at the core of the method, provides a versatile implementation of the Matrix Element Method to both the theory and experiment communities. Its modular structure covers the needs of experimental analysis workflows at the…
10 Citations
### Advanced multivariate analysis methods for use by the experiments at the Large Hadron Collider
In the course of the past four years, AMVA4NewPhysics, a Horizon2020-funded Marie Skłodowska-Curie (MSCA) Innovative Training Network, focused on the study of Multivariate Analysis Methods and
### Advanced Multi-Variate Analysis Methods for New Physics Searches at the Large Hadron Collider
• Physics
ArXiv
• 2021
The most relevant new tools, among those studied and developed, are presented along with the evaluation of their performances and promise to further improve the precision of measurements of fundamental physics parameters and the reach of searches for new phenomena.
### Deep Learning for the Matrix Element Method
• Computer Science
Proceedings of 41st International Conference on High Energy physics — PoS(ICHEP2022)
• 2022
An application of deep learning is described that dramatically speeds-up matrix element (ME) method calculations and novel cyberinfrastructure developed to execute ME-based analyses on heterogeneous computing platforms.
### Matrix element regression with deep neural networks — Breaking the CPU barrier
• Computer Science
• 2020
This paper investigates the use of a Deep Neural Network built by regression of the MEM integral as an ansatz for analysis, especially in the search for new physics.
### Machine Learning in High Energy Physics Community White Paper
• Physics, Education
Journal of Physics: Conference Series
• 2018
Machine learning is an important applied research area in particle physics, beginning with applications to high-level physics analysis in the 1990s and 2000s, followed by an explosion of applications
### Resolving Combinatorial Ambiguities in Dilepton $t \bar t$ Event Topologies with Neural Networks
• Physics
• 2022
We study the potential of deep learning to resolve the combinatorial problem in SUSY-like events with two invisible particles at the LHC. As a concrete example, we focus on dileptonic t ¯ t events,
### Fermionic dark matter: from models to collider searches
In this thesis, we investigate from diverse point of views, the dark matter problem. First, we study the doublet-triplet fermion model, a simple extension of the Standard Model with an extra Z2
### Search for the production of Higgs bosons in association with top quarks and decaying into bottom quark pairs with the ATLAS detector
The Standard Model of particle physics (SM) describes mass generation of fundamental particles via the Brout-Englert-Higgs mechanism. It predicts Yukawa interactions between the Higgs boson and
• 2019
## References
SHOWING 1-10 OF 71 REFERENCES
### Automation of the matrix element reweighting method
• Physics, Computer Science
• 2010
This work presents a procedure that allows to automatically evaluate the weights for any process of interest in the standard model and beyond, and creates a phase-space mapping designed to efficiently perform the integration of the squared matrix element and the transfer functions.
### DELPHES 3: A modular framework for fast-simulation of generic collider experiments
• Physics
• 2014
The new version of the DELPHES C++ fast-simulation framework is presented. The tool is written in C++ and is interfaced with the most common Monte Carlo file formats (LHEF, HepMC, STDHEP). Its
### LHAPDF6: parton density access in the LHC precision era
• Physics
• 2015
The Fortran LHAPDF library has been a long-term workhorse in particle physics, providing standardised access to parton density functions for experimental and phenomenological purposes alike,
### The Matrix Element Method and QCD Radiation
• Physics
• 2011
The matrix element method (MEM) has been extensively used for the analysis of top-quark and W-boson physics at the Tevatron, but in general without dedicated treatment of initial state QCD radiation.
### Unravelling tth via the matrix element method.
• Physics
Physical review letters
• 2013
It is found that a moderate integrated luminosity in the next LHC run will be enough to make the signature involving both W's decaying leptonically as sensitive as the single-lepton one.
### Event generation with SHERPA 1.1
• Physics
• 2008
In this paper the current release of the Monte Carlo event generator Sherpa, version 1.1, is presented. Sherpa is a general-purpose tool for the simulation of particle collisions at high-energy
### Event generation with
• Physics
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In this paper the current release of the Monte Carlo event generator Sherpa, version 1.1, is presented. Sherpa is a general-purpose tool for the simulation of particle colli- sions at high-energy
### The automated computation of tree-level and next-to-leading order differential cross sections, and their matching to parton shower simulations
• Physics
• 2014
A bstractWe discuss the theoretical bases that underpin the automation of the computations of tree-level and next-to-leading order cross sections, of their matching to parton shower simulations, and | |
## On linear stochastic flows
### Beniamin Goldys and Szymon Peszat
#### Abstract
We study the existence of the stochastic flow associated to a linear stochastic evolution equation $\mathrm{d} X= AX\,\mathrm{d} t +\sum_{k} B_k X\,\mathrm{d} W_k,$ on a Hilbert space. Our first result covers the case where $$A$$ is the generator of a $$C_0$$-semigroup, and $$(B_k)$$ is a sequence of bounded linear operators such that $$\sum_k\|B_k\|<+\infty$$. We also provide sufficient conditions for the existence of stochastic flows in the Schatten classes beyond the space of Hilbert-Schmidt operators. Some new results and examples concerning the so-called commutative case are presented as well.
Keywords: stochastic flow, stochastic equation with multiplicative noise, Schatten class.
: Primary 60H15; secondary 60G15, 60G60.
This paper is available as a pdf (420kB) file.
Wednesday, May 5, 2021 | |
## Thursday, October 28, 2010
### Incognito
: with one's identity concealed
Example: "[Mary, Queen of Scots] loved St. Andrews, where she kept a small vacation cottage and often stayed incognito, doing her own shopping and cooking, and playing golf along the links by the Firth of Forth." -- From an article by Sally Jenkins in The Washington Post, July 15, 2010
This blog has oftentimes been my mask. My voice aloud, my identity incognito (for the most part)... and I find that Oscar Wilde was perhaps partially correct when he said,
"Man is least himself when he talks in his own person. Give him a mask, and he will tell you the truth."
...but I do not think that this idea is entirely true. In the midst of the current political blizzard of lies, slanders and shallow promises, it is hard to see truth and the public masks that are worn aren't unlike those creepy clown masks with the empty eyes and painted smiles.
There are those rare and wonderful leaders who believe in honesty, revel in it, in fact... Winston Churchill, Martin Luther King Jr., Abraham Lincoln, Sister Theresa, Mahatma Ghandi, and so on and so forth. No mask did they wear, to speak the truth.
I've found that I have different masques... different persona's for different circumstances and situations.
A masque for work
A masque for play
A masque for family
A masque for friends
A masque for various circumstances
I've wondered, when I gaze into the looking glass... if I wear a masque for myself too often. I wonder how much truth comes from behind these masques... if they are half truths, partially disguised for the viewer, partially revealed, because honestly, we really want people to know who we truly are, to some extent... or at least, we show them who we want them to believe we are.
Knowing that we constantly change; daily even, I am growing towards leaving the masques behind, so that I can see clearly, so that others can see me clearly and make no mistake about who I really am and what I really think.
To thine own self be true ~ remove the masques for my own perspective and for all of those around me, because if they are interacting with a masqued me, the self is lost in shadow and the interaction is skewed.
and...
Actions speak so much louder than words ~ the truth will out, one way or another.
and...
Truth is somewhere in the middle ~ there is a bit of honesty on both sides of the masque.
But... perhaps I will keep one or two masques around... for special occasions.
## Monday, October 25, 2010
### Passport Stamps
"Full fathom five thy father lies...
Nothing of him that doth fade
But doth suffer a sea-change."
~Shakespeare, The Tempest
## Thursday, October 21, 2010
### A Farewell To A Friend~
We've seen and done so much, you and I, haven't we?
Been through highs and lows together,
Sailed & flown through days & months & years, together.
We've laughed and cried, loved and fought,
You and I have watched so much time pass;
More than can be measured.
There is a bend in our road that you cannot see,
A change in the cadence of our walk.
There is a road that I must take alone, dear one,
And though I am letting go of your hand, know that I will
Always hold you in my heart.
I know there will be a day when this road brings me back
To you
I will hold your hand to my cheek & embrace you so tightly.
But until then,
I have promises to keep; promises made to people
I love
And I must keep my word.
So farewell, for a time, sweet friend.
May wings of Angels encircle you,
And keep you with my love,
Until I can return.
Thanks to Radeka Photography for the image
## Tuesday, October 19, 2010
### Dear, Dear Diary
Dear, Dear Diary,
You know I do some of my best thinking in the shower, where there is no distraction, only the sound and feel of hot water and steam. Nothing there but soft light and the water, washing the world away, washing all of the little parasitic thoughts that constantly consume my mind, down my back in rivulets. 'I need to get the oil changed in the car, I need to call this friend, I need to go visit that friend, I wonder if I'll have time to clean out the closet in the guest bedroom this weekend, I hope my brother is doing well... and his kids... I better call, must get a birthday card and paper towels, and on... and on...
And there they go... sliding down the drain, and my mind clears and it almost feels like it's spreading, growing, right outside of my head, and I can hear and think from the inside out, instead of thinking about all the information coming in - I am able to focus on information going out.
This morning I breathed in the steam, let the world go away and started wondering about reality.
I think we are all in our own little reality, and all of our realities have overlapping areas where we share a cohesive reality; that realm where we can communicate and understand each other, for the most part. There is no normal and I think, no definite reality - because where is that bar set? Who could set it? Who could say 'this is reality and that is not' because they're looking at it from their own perspective, from their own mind, lifestyle and their own reality.
Albert Einstein had a fascinating reality. A different reality. Nikola Tesla. Leonardo da Vinci. Marilyn Monroe. Stephen King. That guy on the sidewalk with the guitar and the hat filled with loose change and a dollar bill. The little girl sitting in that desk at the school, staring out the window and finding herself somewhere completely separate from the shared reality of her desk in her classroom. The pastor of the church down the street. The woman who is beaten by an angry man nearly every day. The single parent struggling to raise children on their own. The performer who spends their life on Broadway under a spotlight. The politician...
I wondered how far realities stretch... there are some people who are so far gone from our shared reality that they are labeled insane; unfit for society. What a different world is their reality! How far do they all go; our realities... and how much are really shared? Is there more of one than there is of the other... our own individual realities and our shared realities? If we are in one more often than we are in the other, how does it shape our lives? Is it easy for most people to keep that line between the two, drawn - to keep them separated? Do they blend and mesh for everyone?
How much do we have control over, and how much can we change? What about what we can't see and those things that aren't tangible?
I know I could change a lot of my shared reality; and I could change quite a bit of my own individual reality... what I think, what I believe, what I say, how I live, what I do, what dreams I allow myself to indulge in, and what I refuse to accept in my life.
Every single one of those actions and indeed, even every inaction, has that ripple effect that changes our lives and the lives of those around us (and then in turn the lives around them... so many degrees of separation later), and really impresses the significance of the incomprehensibly dynamic world of controlled chaos that we live in.
...and that's about when the hot water ran out.
## Thursday, October 14, 2010
### Holding On To The Real Thing
A friend of mine recently got a Kindle for her birthday. She was very excited and reports that it is one of the best things she's ever gotten. I was surprised, as she's an avid reader, and I expected that she would miss reading real books.
She said she thought she'd miss them, too, miss turning the pages... but she's found that she doesn't, and is thrilled with her new electric book.
I am of another opinion.
I love to lose myself in every aspect of a real book. The introduction; I love the look of the book; it draws me in closer, and I examine if from all sides. The first touch; texture is enormously important... the feel of it underneath my fingers; sometimes course, sometimes gently worn, and the pages! Oh... the pages, some thick, and when I'm lucky, roughly hewn around the edges, or thin... like a parchment, delicate as a flower petal. Open it up and examine the inside; the style of the font and layout of the words that splay across the pages, like the skeleton of the body held in my hands, about to be fleshed out with the story that all of the words create. Breathing it in... the smell of a book is paramount; it tells age, care, quality... a whole other story altogether.
Familiarity attained, I find a comfortable cozy place to curl up and lose myself in the story between the covers. As on any journey, the first few steps are taken as there is yet another introduction, and the first few pages are turned, but before long, I am one with the characters, and hand in hand, we head out into their world, to share every experience until the last page has been turned and we take our leave of each other with the closing of the book, and the end of the story.
I somehow cannot find this experience with Kindle. I know it's great to have the convenience (is there anywhere you could take a Kindle that you couldn't take a book? The only power resource needed for a book is the imagination and a functioning brain...) and I know that we are progressing forward technologically. But what of libraries, whose hallowed halls I hold in a reverence on par with that of any giant old cathedral? I do not expect retrograde motion... I know that Kindle is here to stay, and it's a good option for some people. But I suspect that it will be all the rage for a while, and then, in time to come, something nostalgic and sweet will happen...
I think it will be the same thing that happened with cd's and records. Records made a comeback. There's nothing like listening to an old album, with the soft rustling scratch that accompanies the songs as the needle winds it's way around and around from the outside in. Many friends have smiled with fond sentiment when I put an old Beatles album on and we listen to the way it used to be.
So too, will be the way of books, perhaps, in years to come. Friends will slide them off of my shelves and open them with a reminiscent gaze, gently touching the pages, turning them slowly, and thinking how wonderful it was, once upon a time, to explore endless worlds in this way.
## Tuesday, October 12, 2010
### It's The Great Pumpkin!
Mid October a few years ago, I found myself feeling inspired and crafty and standing in the aisle at the supermarket, paging through a holiday magazine looking at those fancy schmancy pumpkins that are carved into amazing Jack O'Lanterns.
I decided that it didn't look that difficult and that I ought to make one. The timing was good, a couple of weeks before Halloween. It would last, I thought. This couldn't be that difficult, I was certain.
I bought a good size pumpkin, parked myself on a large towel on the garage floor on a sunny afternoon with the garage door open and the radio on and went to work. Cleaned it out, carved the lid, and then prepared to make my image.
I pulled out a Peanuts color book and found a great image of Snoopy that would be perfect on a pumpkin. Snoopy is requisite Halloween subject matter, considering The Great Pumpkin. I taped it to the pumpkin, took a toothpick and poked dots all along the lines that needed to be carved out; sort of a 'carve along the dotted line' idea. Dotting done, I removed the color book page and set to work with my special pumpkin carving knife.
At first, things seemed to be going well and I was fairly pleased with the results... but then I overestimated the carve and tried to fix it with extra toothpicks pushed into the inside side of the pumpkin and superglue. A word to the wise... superglue does not work on pumpkins. It does, however, work very well on fingers, paper towels, cloth towels and plastic carving knives.
In the end, I was relegated to carving my usual simple Jack O'Lantern face into a new pumpkin.
I'll leave the fancy carving to the pros!
Have a Happy Halloween!
One for Viaggiatore
A Snoopy for me
### ~Fair Warning~
If you lurk without commenting, I shall send my Pirate friends after you, and I've got lots of them. If you are a Pirate, I shall send my secret Ninja.
Shyness isn't paid, tipped or tolerated and opinions are like belly buttons; everybody's got one, so leave yours before you wander off.
Thank you.
HRH
## Monday, October 11, 2010
### When Will We Ever Learn
California isn't in a golden state, when it comes to hitting the books. TIME did a story on several teachers in several towns who are paying for their own supplies and going to every creative and extreme measure they can imagine, in order to come up with not only the tools they need to teach, but even basics like pencils and paper to run the classroom and their own vacuums to keep it clean.
Almost $17 billion was cut from California's education system in the last 2 years$17 BILLION
That is an appalling number.
It is estimated that an additional \$2.4 billion will be taken in the coming year.
When teachers resort to cleaning their own classrooms after a day of teaching because the janitorial staff has been let go or had hours cut back, when they have paper curtains held together with duct tape, when they have to have car washes or bake sales to raise money for supplies and go to garage sales to come up with tools to teach children, things have gone severely wrong. This state of affairs isn't isolated to California; it's happening all over our country.
Where is this train wreck headed?
What happens to the most powerful nation in the world when the bulk of the children who will run it in varying positions and degrees in 3 decades have almost no education? Even now, the national rate of high school dropouts is stunning - Diplomas Count showed statistics at 68.8% graduation rate in 2007. There is no indication that it has improved since then.
This is not an issue.
This is a crisis that needs immediate attention and change. It is not only crucial on an individual level for each student that loses the opportunity to reach their full potential through better education, but that domino effect winds it's way up through the community into a national level and then it affects the world. If the U.S. does not have citizens with the knowledge to further this nation in every capacity then it falls behind other nations and a sociological revolution becomes probable, if history is any indication at all.
Knowledge is indeed power. Without it, we are crippling our future, the future of our nation, and the delicate balance of relations with the nations we share this world with.
I saw a bumper sticker once that said, "The world will be a better place when our schools have all the money they need and the military has to hold a bake sale to buy a bomber."
If only.
I've said before that George Bush's education strategy was 'no child left behind... the platoon.' Uneducated people who have no idea how to think critically are easily controlled, and give far too much power to those few who would use it for their own gain and purpose. This is not the ideal of our nation, nor of our forefathers who fought and died to make it what it could be. Masses of ignorant citizens become sheep, are expendable, and the integrity of our future is lost because we cannot contribute to furthering the progress of mankind or even ourselves.
It is not with power in might that we could reach unimaginable realities, but with minds fueled by knowledge that have the capability of attaining limitless possibility.
## Thursday, October 7, 2010
### Choose An Identity
I was leaving a comment on a friend's blog yesterday, when I paused for a moment to look at the phrase, 'Choose an identity' under the comment box. I could use my blog pseudonym, OpenID, a name/url or be annonymous. Choose an identity. Decide who it is that I wish to portray myself as to the world at large. It made me smile and wonder about all the identities I would choose, if given the opportunity to do so.
I would choose to be so many people.
A secret spy with no identity at all; 00Charlie's Angels
A right hand to Martin Luther King Jr., marching alongside him
An adventuring archaeologist (ala Lara Croft)
A nameless member of the Peace Corps serving 3rd world countries
An ingenious inventor in a secret lab, creating brilliant wonders that would change the future of the world for the better (ala Tesla, Einstein, Franklin, Edison, DaVinci)
An elementary school teacher
A professional dancer (ballet/ballroom)
Sherlock Holmes
A student of DaVinci; while he was living
A race car driver
An Air Force fighter pilot
A painter who lives by the sea and sells my art on the docks, and/or in Paris, in Montmartre, selling paintings on the sidewalk
A photojournalist who travels the world and creates images of humanity and culture, printed in Natl Geo, Life and Time, whose photos give the world a reason to change the way we all live
A novelist who has the luxury of writing for a living; while living all over the world
...oh the list could go on for a while.
Who would you be, if you could choose an identity? |
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