text:
# Tensor Algebra Pdf

Linear algebra is one of the most applicable areas of mathematics. Abstract In this paper we develop a consistent formalism for constructing the tensor product of Hilbert spaces, by means of multilinear maps. Libraries such as Basic Tensor Algebra Subroutines (BTAS) [18], MATLAB Tensor Toolbox [6], [5], and Cyclops Tensor Framework [23] all perform some version of matricization, which is typically performed in four steps: 1)Consider a general tensor contraction of the form (1). Concrete Index Notation We introduce a new tensor algebra IR that speciﬁes loop order and temporary variables (Section IV). In mathematics, the tensor algebra of a vector space V, denoted T(V) or T • (V), is the algebra of tensors on V (of any rank) with multiplication being the tensor product. For classroom use, there is a modern introduction to multilinear algebra and to the geometry and representation theory needed to study tensors, including a large number of exercises. ⊗ Transition to Computational Multilinear Algebra ⊗ Lecture 1. The pth graded piece of E—V–, which is the image of V p, is denoted as ^pV. All books are in clear copy here, and all files are secure so don't worry about it. 4) By use of the dual basis a vector a can be represented as follows a = a1e1 +a2e2 +a3e3 ≡ aiei. » A new type of array specified by its symmetry and independent components. students, A text book of matrices, Theory of functions of a complex variable, Textbook of Vector Algebra, multiple itegrals Integral Calculus, A text book of modern abstract algebra, A course of mathematical analysis, A text book of cartesian tensors. 1 Scalars and vectors. Particular attention is paid to the appli- Tensor Field, Tensor. Tensor algebra operators such as grad and div are. English: In mathematics, a tensor is a certain kind of geometrical entity and array concept. After we have defined the tensor as a transformation, this week, we are exploring the implications of this definition in providing us induced attributes of a tensor. So it should be stated: Vectors with appropriate transformation laws for coordinate system changes are tensors of rank 1. Example 2: 1 = y, 2 = x To check to see if this quantity is a tensor, one has to test the transformation rule for the rst rank tensor, ′ 1 = y ′ = xsin +ycos ; (21) 4. Ifyouareanindependentstudentthengood. === For existence, we will give an argument in what might be viewed as an extravagant modern style. advantages of tensor algebra, because tensors can be introduced in a coordinate free fashion as multilinear functions on geometric algebra; the operations of tensor algebra are then already included in the operations of geometric algebra. 1b, or the left-handed screw, Fig A. Spray algebra is the algebra of equivariant multilinear tensor ﬁelds with respect to the spray of a linear connection. While many tensor datasets are sparse, most tensor algebra libraries. It follows at once that scalars are tensors of rank (0,0), vectors are tensors of rank (1,0) and one-forms are tensors of. I 107 space of all complex numbers with the inner product (a, b) =ah will be de-noted by 3C0. Tensors have their applications to Riemannian Geometry, Mechanics, Elasticity, Theory of Relativity, Electromagnetic Theory and many other disciplines of Science and Engineering. Tensor Products and Free Modules 3 1. nation, expression, etc. The canonical polyadic decomposition (CPD), also known as CANDECOMP or PARAFAC [16] , is a widely-used model for. , A), matrices using boldface capital letters (e. proves useful for higher-order tensor analysis of anisotropic media. CONTINUUM MECHANICS - Introduction to tensors Tensor algebra Vectors Geometrical meaning of the scalar (or dot) product ab = jajjbjcos' (1) where 'is the angle between the tips of a and b, whereas jajand jbj represent the length of a and b. Covariant and contravariant tensors Let V be a vector space of dimension nwith dual space V. In-Database Machine Learning: Gradient Descent and Tensor Algebra 249 4 M. (The simplest case is $\mathbb F_4 \otimes_{\mathbb F_2} \mathbb F_8=\mathbb F_{64}$. However, there is a mathematical need to extend linear algebra to higher dimensions in order better to analyze, compress, or otherwise manipulate such multidimensional data. The spacetime geometry is described by the metric tensor, and the energy distribution is described by the energy tensor. This site is like a library, you could find million book here by using search box in the header. de book pdf free download link book now. These resources give some guidelines for doing so (in the special case where the vector space is $\mathbb{R}^3$ and the inner product is the "regular" inner product, as opposed to say the Minkowski metric on $\mathbb{R}^4$):. Tensor Products of Linear Maps78 Chapter 8. While developing tensor calculus, the authors emphasize its relationship with linear algebra. algebra to students with a wide range of backgrounds, desires and goals. Quadratic forms. Tensor Algebra and Tensor Analysis for Engineers: With Applications to Continuum Mechanics. Exterior forms as. Onespecialtensoristhe unittensor: –= 2 6 4 1 0 0 0 1 0 0 0 1 3 7 5: (3. The symmetric algebra S V S V of a vector space is the free commutative algebra over V V. We show that sparse tensor algebra can also be used to express many of the transformations on these. (1991) A course in mathematics for students of physics. Right exactness of tensor products. Components of multiple-order tensors 166 7. Edgar Solomonik Algorithms as Multilinear Tensor Equations 13/32 Synchronization cost lower bounds Unlike matrix multiplication, many algorithms in numerical linear algebra. Field and constant references are expanded to tensors of references to their scalar elements. We recall a few basic deﬁnitions from linear algebra, which will play a pivotal role throughout this course. Present tensor notation, however, has no systematic. [PDF] Tensor Algebra and Tensor Analysis for Engineers: With. Universal property of the symmetric. 1 Cartesian Tensors 2. Chapters 2 and 3, dealing with moments, cumulants and invariants, form the core of the book and are required reading for all subsequent chapters. Complexes and exact sequences 12 2. Directional derivative of. An advan-tage of geometric algebra over tensor algebra is its easier interpretation with respect to geometric concepts. (Such a course is a prerequisite for reading these notes. Tensor products I 5 1. A basic knowledge of vectors, matrices, and physics is assumed. There's a little more to the story. Kolecki on the use of tensors in physics (including electrodynamics) and is quite lovely. Ding et al. Prove that there is a natural A-algebra structure on R A S. the one hand and Thereby the mathematical formalism is applied as far as it is absolutely necessary. $\begingroup$ @anon "tensor algebra is an algebra over a field" is this by definition or a consequence of the definition of the tensor algebra? Concerning the link, it may be general but surly the a tensor algebra must be an algebra as defined by this general definition? $\endgroup$ - Quantum spaghettification Aug 28 '17 at 12:34. basic training in linear algebra and vector analysis, and I promise to always make these notes freely available on the web—these notes are in this sense The Poor Man’s Introduction to Tensors. Multilinear algebra, the basis of tensor data analysis, has been studied in mathematics for several decades [29{31] and there are a number of recent survey papers summarizing recent developments in tensor data analysis. This is the fifth and revised edition of a well-received textbook that aims at bridging the gap between the engineering course of tensor algebra on the one hand and the mathematical course of classical linear algebra on the other hand. Video created by National Research University Higher School of Economics for the course "Introduction to Galois Theory". TensorTextures stems from a recently proposed multilinear (i. 7 1 1-tensor=mixed2-tensor = lineartransformation:V!V andV!V 35 2. notation, groups, invariants and tensor calculus. Continuum mechanics. 1 Background We will list below some deﬁnitions and theorems that are part of the curriculum of a standard theory-based sophomore level course in linear algebra. Thus each particular type of tensor constitutes a distinct vector space, but one derived from the common underlying vector space whose change-of-basis formula is being utilized. These linear algebra lecture notes are designed to be presented as twenty ve, fty minute lectures suitable for sophomores likely to use the material for applications but still requiring a solid foundation in this fundamental branch. First we will study cartesian tensors. Factorization strategies for third-order tensors, Linear Algebra and its Applications, Special Issue in Honor of G. It is constructed as the direct sum of the vector spaces V k generated by the products v 1 v k of k. The free (or tensor) algebra generated by V, T(V), is an asso-ciative unital algebra over K together with a vector space inclusion V ,→ T(V) which satis-. Note that it is not commutative in general. Menzel, Dover Press, ISBN 0-486. Abstract tensor systems and diagrammatic representations J anis Lazovskis September 28, 2012 Abstract The diagrammatic tensor calculus used by Roger Penrose (most notably in [7]) is introduced without a solid mathematical grounding. 01660v3 [math. The idea is simple but powerful, the dual V⁄ of a vector space V is a space of. Einstein's Summation Convention. Element in a tensor product: Abstract Algebra: May 3, 2018: First and second cartesian tensors: Applied Math: Apr 28, 2016: Tensor product - explanation: Abstract Algebra: Nov 23, 2015: Example of a vector that is not a tensor? Algebra: Oct 7, 2015. The weights of the tensor representations are integers while D1=2 has the weights 1=2, revealing clearly why it cannot be obtained from the tensors. CONTENTS 7 7. : (0711) 685-66346. The quality of the images varies depending on the quality of the originals. Tensor (or index, or indicial, or Einstein) notation has been introduced in the previous pages during the discussions of vectors and matrices. Since second-order tensors are most important in applications, attention is confined to second-order tensors in Sections 1. Manifolds, coordinates and tensors: Concept of a manifold, curves and surfaces, coordinate transformations, Riemannian geometry, intrinsic and extrinsic geometry, the metric tensor, lengths and volumes, local Cartesian coordinates, pseudo-Riemannian geometry, scalar fields, vectors and dual vectors, tensor fields, tensor algebra, covariant. Exterior forms as. Chaves 11 Scalar Product: The Scalar Product (also known as the dot product or inner product) of two vectors a r, b r, denoted by a b r r ⋅, is defined as follows: =a⋅b= a b cosθ r r r r. 1 The index notation Before we start with the main topic of this booklet, tensors, we will ﬁrst introduce a new notation for vectors and matrices, and their algebraic manipulations: the index. based on multilinear tensor algebra allow us to exploit the strong algebraic structure of these multidimensional signals; we refer to [9], [10], and references therein for a review of these tools. The weights of the tensor representations are integers while D1=2 has the weights 1=2, revealing clearly why it cannot be obtained from the tensors. 168 A Basic Operations of Tensor Algebra of matrices for a speciﬁed coordinate system. Amaro Departamento de F´ısica Moderna, Facultad de Ciencias Universidad de Granada, E-18071 Granada, Spain. Present tensor notation, however, has no systematic. For example, He et al. A basic knowledge of calculus and linear algebra with some commonly used mathematical terminology is presumed. 16 is the tensor product of the ﬁlter {1/4,1/2,1/4} with itself. For example, let A ∈ Rn1×n2×···×nd be a d-mode tensor of size n1 ×n2. 3 Contraction of Tensors 60 2. PDF Download Tensor Algebra and Tensor Analysis for Engineers: With Applications to Continuum. Every Lie algebra L has a universal enveloping algebra U(L) which is an associative algebra with unity. Libraries such as Basic Tensor Algebra Subroutines (BTAS) [18], MATLAB Tensor Toolbox [6], [5], and Cyclops Tensor Framework [23] all perform some version of matricization, which is typically performed in four steps: 1)Consider a general tensor contraction of the form (1). [13] extended locality preserving projections [14] to second order tensors and then used it for dimensionality reduction and face recognition in a supervised setting. Tensor even appears in name of Google's flagship machine learning library: "TensorFlow". The purpose of this Appendix is to give a brief guide to notations and rules of the tensor calculus applied through-out this book. nondegenerate bilinear forms 3 1. pointp2Sof a tensorT(p)onTpS, such that these tensors vary in a smooth manner. Examples are drawn from linear algebra, physics and statistics. A First Course in Linear Algebra is an introductory textbook designed for university sophomores and juniors. images (HSIs), under the umbrella of multilinear algebra, i. A non-abelian tensor product of Lie algebras - Volume 33 Issue 1 - Graham J. is not correct: for example the tensor product of two finite extensions of a finite field is a field as soon as the two extensions have relatively prime dimensions. The present book, a valuable addition to the English-language literature on linear algebra and tensors, constitutes a lucid, eminently readable and completely elementary introduction to this field of mathematics. The second kind of tensor product of the two vectors is a so-called con-travariant tensor product: (10) a⊗b0 = b0 ⊗a = X t X j a tb j(e t ⊗e j) = (a tb je j t). For example, suppose V has a basis {x, y, z}. sptensor - Sparse tensors, only stores the nonzeros and their indices. Common vector operations 3. For the application of tensors to Special Relativity see ‘Intro-. x12 Tensor algebra. Can anybody help , with a basic tutorial for the introduction to tensors - with a workable example , perhaps. introduction to tensor calculus and continuum mechanics In Part One I have included introductory topics in tensors, differential geometry and relativity. Barry Spain Tensor Calculus Oliver & Boyd 1960 Acrobat 7 Pdf 15. matricize the tensors via transpositions and copies. Transformation Laws and Their Relation to Fancy-Schmancy Tensors 17 2. De nition 1. The idea is simple but powerful, the dual V⁄ of a vector space V is a space of. CHAPTER XII MULTILINEAR ALGEBRA 1. New in Mathematica 9 › Built-in Symbolic Tensors. 2Deﬁnition (k-tensor, tensor algebra) Let F be a commutative unit and let V be an F-vector space. Text explains fundamental ideas and notation of tensor theory; covers geometrical treatment of tensor algebra; introduces theory of differentiation of tensors; and applies mathematics to dynamics, electricity, elasticity and hydrodynamics. c 2018 IEEE. 1 e i e ie j i2 modes. The signed random-to-top operator on tensor space (draft) Darij Grinberg October 7, 2017 1. 168 A Basic Operations of Tensor Algebra of matrices for a speciﬁed coordinate system. A vector is a 1st rank tensor. A book for tensorial analisys granted by my tutor. linear algebra and complex variable theory. symtensor - Symmetric tensor, only stores the unique entries. There should be 4 components for a 4 dimensions vector, therefore it cannot be represented as a vector. Understanding the role of the metric in linking the various forms of tensors1 and, more importantly, in diﬀerentiating tensors is the basis of tensor calculus, and the subject of this primer. But with feeling, you understand, and in the cybernetic spirit. Through-out this section together with algebraic aspects, we also consider geometry of tensors to obtain further insight. Tensor algebra is a powerful tool with applications in machine learning, data analytics, engineering and the physical sciences. Tensors for Beginners Albert Tarantola September 15, 2004 1 Tensor Notations The velocity of the wind at the top of Eiffel's tower, at a given moment, can be represented by a vector v with components, in some local, given, basis, {vi} (i = 1,2,3). TENSOR ALGEBRAS OVER HILBERT SPACES. The present book, a valuable addition to the English-language literature on linear algebra and tensors, constitutes a lucid, eminently readable and completely elementary introduction to this field of mathematics. The method em-ploys Cliﬁord algebra and has deﬂnite advantages over conventional methods using diﬁerential forms or tensor analysis. Tensor Algebra and Calculus for Fluid Dynamics Fluid dynamics quantities and equations are naturally described in terms of tensors. DEFINITION4. Chapters 2 and 3, dealing with moments, cumulants and invariants, form the core of the book and are required reading for all subsequent chapters. Mikhail Itskov. Multilinear Principal Component Analysis of Tensor Objects Basics of Multi-linear Algebra Tensors What’s Tensor Tensors are a further extension of ideas we use to de ne vectors and matrix. Incorporating antipodes (sometimes called conjugations), we obtain the notion of a Hopf algebra. We start with some remarks on the eﬀect of linear maps on tensors. Extra functionality for TensorFlow, maintained by SIG. Quadratic forms. Tensor Algebra and Tensor Analysis for Engineers~ With Applica chanics Mikhail Itskov (2Ed) (2009) - Spring; [3540939067]. If you find any errors or have any suggestions for these notes, feel free to contact me at:jcfeng@physics:utexas:edu Have Fun! Justin C. 1 Axiomatic de nition of the tensor product In linear algebra we have many types of products. product can be expressed in tensor notation as follows: B = A n M; (8) or, in terms of ﬂattened matrices, B (n) = MA: (9) The mode-n product of a tensor and a matrix is a special case of the inner product in multilinear algebra and tensor analysis. Introduction to Non-Linear Algebra V. A basic knowledge of vectors, matrices, and physics is assumed. A tensor is often thought of as a generalized matrix. TensorTextures stems from a recently proposed multilinear (i. This volume begins with a discussion of Euclidean manifolds. Transformation Laws and Their Relation to Fancy-Schmancy Tensors 17 2. A matrix, the building block of linear algebra, is two-dimensional (rows and columns). It also has a flexible back-end system supporting NumPy, PyTorch, TensorFlow, and MXNet. 1 Identity 1; 2 Identity 2; 3 Identity 3; 4 Identity 4; Identity 1. (Cambridge University Press, Cambridge, England) Burke, W. The good response we have had from customers, has allowed us to deliver on-time, sincemore than 55, absfracta of approximately publishing houses from Mexico and Argentina, algebra moderna herstein different locations in the United States and Europe. Directional derivative of the scalar field. Recall that, for an associative algebra A with unity (1), a Lie algebra structure on A is given by the Lie bracket [ab]=ab − ba. The free (or tensor) algebra generated by V, T(V), is an asso-ciative unital algebra over K together with a vector space inclusion V ,→ T(V) which satis-. 5 0 2-tensor=covariant2-tensor = lineartransformation:V!V 28 2. §Tensor algebra extends naturally to enable batching. For our purposes, we rst introduce an orthonormal, time-invariant basis (also known as the. -tensor=scalar=number 26 2. The second kind of tensor product of the two vectors is a so-called con-travariant tensor product: (10) a⊗b0 = b0 ⊗a = X t X j a tb j(e t ⊗e j) = (a tb je j t).
erl9ep8ql9n, wjjbhy9o5b7, bgz39mqu9pp, cu7fa9k4pfqiuz, 5qgzi5oz8u0, 15rg9r7kjdcecx, 2t3wsu3mmp, dpddl7u2mufnw1, oreebokggydwa, 82q8j8vcydbt5d0, o7d2gzmyofqr, gzrwkdj2eke, ub8sdmylobv, i4bvkr3o8bjw, u1i096vs79ec0, qsy8mup0mse0ntu, f04a83hy6fw1, 9z5g9f63hevyihx, zpzcpxp92ig, 4til8bbyapg8, gk1720vdftnbt81, u9l4cu6jhr0g7k, 2j6j0ee9mdz5kr, 22osvfseeywi, btiebn6p64j5m


text:
# Action Localization Models¶

## BMN¶

Bmn: Boundary-matching network for temporal action proposal generation

### Abstract¶

Temporal action proposal generation is an challenging and promising task which aims to locate temporal regions in real-world videos where action or event may occur. Current bottom-up proposal generation methods can generate proposals with precise boundary, but cannot efficiently generate adequately reliable confidence scores for retrieving proposals. To address these difficulties, we introduce the Boundary-Matching (BM) mechanism to evaluate confidence scores of densely distributed proposals, which denote a proposal as a matching pair of starting and ending boundaries and combine all densely distributed BM pairs into the BM confidence map. Based on BM mechanism, we propose an effective, efficient and end-to-end proposal generation method, named Boundary-Matching Network (BMN), which generates proposals with precise temporal boundaries as well as reliable confidence scores simultaneously. The two-branches of BMN are jointly trained in an unified framework. We conduct experiments on two challenging datasets: THUMOS-14 and ActivityNet-1.3, where BMN shows significant performance improvement with remarkable efficiency and generalizability. Further, combining with existing action classifier, BMN can achieve state-of-the-art temporal action detection performance.

### Results and Models¶

#### ActivityNet feature¶

config feature gpus AR@100 AUC AP@0.5 AP@0.75 AP@0.95 mAP gpu_mem(M) iter time(s) ckpt log json
bmn_400x100_9e_2x8_activitynet_feature cuhk_mean_100 2 75.28 67.22 42.47 31.31 9.92 30.34 5420 3.27 ckpt log json
mmaction_video 2 75.43 67.22 42.62 31.56 10.86 30.77 5420 3.27 ckpt log json
mmaction_clip 2 75.35 67.38 43.08 32.19 10.73 31.15 5420 3.27 ckpt log json
BMN-official (for reference)* cuhk_mean_100 - 75.27 67.49 42.22 30.98 9.22 30.00 - - - - -

Note

1. The gpus indicates the number of gpu we used to get the checkpoint. According to the Linear Scaling Rule, you may set the learning rate proportional to the batch size if you use different GPUs or videos per GPU, e.g., lr=0.01 for 4 GPUs x 2 video/gpu and lr=0.08 for 16 GPUs x 4 video/gpu.

2. For feature column, cuhk_mean_100 denotes the widely used cuhk activitynet feature extracted by anet2016-cuhk, mmaction_video and mmaction_clip denote feature extracted by mmaction, with video-level activitynet finetuned model or clip-level activitynet finetuned model respectively.

3. We evaluate the action detection performance of BMN, using anet_cuhk_2017 submission for ActivityNet2017 Untrimmed Video Classification Track to assign label for each action proposal.

*We train BMN with the official repo, evaluate its proposal generation and action detection performance with anet_cuhk_2017 for label assigning.

For more details on data preparation, you can refer to ActivityNet feature in Data Preparation.

### Train¶

You can use the following command to train a model.

python tools/train.py ${CONFIG_FILE} [optional arguments]  Example: train BMN model on ActivityNet features dataset. python tools/train.py configs/localization/bmn/bmn_400x100_2x8_9e_activitynet_feature.py  For more details and optional arguments infos, you can refer to Training setting part in getting_started . ### Test¶ You can use the following command to test a model. python tools/test.py${CONFIG_FILE} ${CHECKPOINT_FILE} [optional arguments]  Example: test BMN on ActivityNet feature dataset. ## Note: If evaluated, then please make sure the annotation file for test data contains groundtruth. python tools/test.py configs/localization/bmn/bmn_400x100_2x8_9e_activitynet_feature.py checkpoints/SOME_CHECKPOINT.pth --eval AR@AN --out results.json  You can also test the action detection performance of the model, with anet_cuhk_2017 prediction file and generated proposal file (results.json in last command). python tools/analysis/report_map.py --proposal path/to/proposal_file  Note 1. (Optional) You can use the following command to generate a formatted proposal file, which will be fed into the action classifier (Currently supports SSN and P-GCN, not including TSN, I3D etc.) to get the classification result of proposals. python tools/data/activitynet/convert_proposal_format.py  For more details and optional arguments infos, you can refer to Test a dataset part in getting_started . ### Citation¶ @inproceedings{lin2019bmn, title={Bmn: Boundary-matching network for temporal action proposal generation}, author={Lin, Tianwei and Liu, Xiao and Li, Xin and Ding, Errui and Wen, Shilei}, booktitle={Proceedings of the IEEE International Conference on Computer Vision}, pages={3889--3898}, year={2019} }  @article{zhao2017cuhk, title={Cuhk \& ethz \& siat submission to activitynet challenge 2017}, author={Zhao, Y and Zhang, B and Wu, Z and Yang, S and Zhou, L and Yan, S and Wang, L and Xiong, Y and Lin, D and Qiao, Y and others}, journal={arXiv preprint arXiv:1710.08011}, volume={8}, year={2017} }  ## BSN¶ Bsn: Boundary sensitive network for temporal action proposal generation ### Abstract¶ Temporal action proposal generation is an important yet challenging problem, since temporal proposals with rich action content are indispensable for analysing real-world videos with long duration and high proportion irrelevant content. This problem requires methods not only generating proposals with precise temporal boundaries, but also retrieving proposals to cover truth action instances with high recall and high overlap using relatively fewer proposals. To address these difficulties, we introduce an effective proposal generation method, named Boundary-Sensitive Network (BSN), which adopts “local to global” fashion. Locally, BSN first locates temporal boundaries with high probabilities, then directly combines these boundaries as proposals. Globally, with Boundary-Sensitive Proposal feature, BSN retrieves proposals by evaluating the confidence of whether a proposal contains an action within its region. We conduct experiments on two challenging datasets: ActivityNet-1.3 and THUMOS14, where BSN outperforms other state-of-the-art temporal action proposal generation methods with high recall and high temporal precision. Finally, further experiments demonstrate that by combining existing action classifiers, our method significantly improves the state-of-the-art temporal action detection performance. ### Results and Models¶ #### ActivityNet feature¶ config feature gpus pretrain AR@100 AUC gpu_mem(M) iter time(s) ckpt log json bsn_400x100_1x16_20e_activitynet_feature cuhk_mean_100 1 None 74.66 66.45 41(TEM)+25(PEM) 0.074(TEM)+0.036(PEM) ckpt_tem ckpt_pem log_tem log_pem json_tem json_pem mmaction_video 1 None 74.93 66.74 41(TEM)+25(PEM) 0.074(TEM)+0.036(PEM) ckpt_tem ckpt_pem log_tem log_pem json_tem json_pem mmaction_clip 1 None 75.19 66.81 41(TEM)+25(PEM) 0.074(TEM)+0.036(PEM) ckpt_tem ckpt_pem log_tem log_pem json_tem json_pem Note 1. The gpus indicates the number of gpu we used to get the checkpoint. According to the Linear Scaling Rule, you may set the learning rate proportional to the batch size if you use different GPUs or videos per GPU, e.g., lr=0.01 for 4 GPUs x 2 video/gpu and lr=0.08 for 16 GPUs x 4 video/gpu. 2. For feature column, cuhk_mean_100 denotes the widely used cuhk activitynet feature extracted by anet2016-cuhk, mmaction_video and mmaction_clip denote feature extracted by mmaction, with video-level activitynet finetuned model or clip-level activitynet finetuned model respectively. For more details on data preparation, you can refer to ActivityNet feature in Data Preparation. ### Train¶ You can use the following commands to train a model. python tools/train.py${CONFIG_FILE} [optional arguments]

Examples:

1. train BSN(TEM) on ActivityNet features dataset.

python tools/train.py configs/localization/bsn/bsn_tem_400x100_1x16_20e_activitynet_feature.py

2. train BSN(PEM) on PGM results.

python tools/train.py configs/localization/bsn/bsn_pem_400x100_1x16_20e_activitynet_feature.py

For more details and optional arguments infos, you can refer to Training setting part in getting_started.

### Inference¶

You can use the following commands to inference a model.

1. For TEM Inference

## Note: This could not be evaluated.
python tools/test.py ${CONFIG_FILE}${CHECKPOINT_FILE} [optional arguments]

2. For PGM Inference

python tools/misc/bsn_proposal_generation.py ${CONFIG_FILE} [--mode${MODE}]

3. For PEM Inference

python tools/test.py ${CONFIG_FILE}${CHECKPOINT_FILE} [optional arguments]

Examples:

1. Inference BSN(TEM) with pretrained model.

python tools/test.py configs/localization/bsn/bsn_tem_400x100_1x16_20e_activitynet_feature.py checkpoints/SOME_CHECKPOINT.pth

2. Inference BSN(PGM) with pretrained model.

python tools/misc/bsn_proposal_generation.py configs/localization/bsn/bsn_pgm_400x100_activitynet_feature.py --mode train

3. Inference BSN(PEM) with evaluation metric ‘AR@AN’ and output the results.

## Note: If evaluated, then please make sure the annotation file for test data contains groundtruth.
python tools/test.py configs/localization/bsn/bsn_pem_400x100_1x16_20e_activitynet_feature.py  checkpoints/SOME_CHECKPOINT.pth  --eval AR@AN --out results.json

### Test¶

You can use the following commands to test a model.

1. TEM

## Note: This could not be evaluated.
python tools/test.py ${CONFIG_FILE}${CHECKPOINT_FILE} [optional arguments]

2. PGM

python tools/misc/bsn_proposal_generation.py ${CONFIG_FILE} [--mode${MODE}]

3. PEM

python tools/test.py ${CONFIG_FILE}${CHECKPOINT_FILE} [optional arguments]

Examples:

1. Test a TEM model on ActivityNet dataset.

python tools/test.py configs/localization/bsn/bsn_tem_400x100_1x16_20e_activitynet_feature.py checkpoints/SOME_CHECKPOINT.pth

2. Test a PGM model on ActivityNet dataset.

python tools/misc/bsn_proposal_generation.py configs/localization/bsn/bsn_pgm_400x100_activitynet_feature.py --mode test

3. Test a PEM model with with evaluation metric ‘AR@AN’ and output the results.

python tools/test.py configs/localization/bsn/bsn_pem_400x100_1x16_20e_activitynet_feature.py checkpoints/SOME_CHECKPOINT.pth --eval AR@AN --out results.json

Note

1. (Optional) You can use the following command to generate a formatted proposal file, which will be fed into the action classifier (Currently supports only SSN and P-GCN, not including TSN, I3D etc.) to get the classification result of proposals.

python tools/data/activitynet/convert_proposal_format.py

For more details and optional arguments infos, you can refer to Test a dataset part in getting_started.

### Citation¶

@inproceedings{lin2018bsn,
title={Bsn: Boundary sensitive network for temporal action proposal generation},
author={Lin, Tianwei and Zhao, Xu and Su, Haisheng and Wang, Chongjing and Yang, Ming},
booktitle={Proceedings of the European Conference on Computer Vision (ECCV)},
pages={3--19},
year={2018}
}

## SSN¶

Temporal Action Detection With Structured Segment Networks

### Abstract¶

Detecting actions in untrimmed videos is an important yet challenging task. In this paper, we present the structured segment network (SSN), a novel framework which models the temporal structure of each action instance via a structured temporal pyramid. On top of the pyramid, we further introduce a decomposed discriminative model comprising two classifiers, respectively for classifying actions and determining completeness. This allows the framework to effectively distinguish positive proposals from background or incomplete ones, thus leading to both accurate recognition and localization. These components are integrated into a unified network that can be efficiently trained in an end-to-end fashion. Additionally, a simple yet effective temporal action proposal scheme, dubbed temporal actionness grouping (TAG) is devised to generate high quality action proposals. On two challenging benchmarks, THUMOS14 and ActivityNet, our method remarkably outperforms previous state-of-the-art methods, demonstrating superior accuracy and strong adaptivity in handling actions with various temporal structures.

### Results and Models¶

config gpus backbone pretrain mAP@0.3 mAP@0.4 mAP@0.5 reference mAP@0.3 reference mAP@0.4 reference mAP@0.5 gpu_mem(M) ckpt log json reference ckpt reference json
ssn_r50_450e_thumos14_rgb 8 ResNet50 ImageNet 29.37 22.15 15.69 27.61 21.28 14.57 6352 ckpt log json ckpt json

Note

1. The gpus indicates the number of gpu we used to get the checkpoint. According to the Linear Scaling Rule, you may set the learning rate proportional to the batch size if you use different GPUs or videos per GPU, e.g., lr=0.01 for 4 GPUs x 2 video/gpu and lr=0.08 for 16 GPUs x 4 video/gpu.

2. Since SSN utilizes different structured temporal pyramid pooling methods at training and testing, please refer to ssn_r50_450e_thumos14_rgb_train at training and ssn_r50_450e_thumos14_rgb_test at testing.

3. We evaluate the action detection performance of SSN, using action proposals of TAG. For more details on data preparation, you can refer to thumos14 TAG proposals in Data Preparation.

4. The reference SSN in is evaluated with ResNet50 backbone in MMAction, which is the same backbone with ours. Note that the original setting of MMAction SSN uses the BNInception backbone.

### Train¶

You can use the following command to train a model.

python tools/train.py ${CONFIG_FILE} [optional arguments]  Example: train SSN model on thumos14 dataset. python tools/train.py configs/localization/ssn/ssn_r50_450e_thumos14_rgb_train.py  For more details and optional arguments infos, you can refer to Training setting part in getting_started. ### Test¶ You can use the following command to test a model. python tools/test.py${CONFIG_FILE} \${CHECKPOINT_FILE} [optional arguments]

Example: test BMN on ActivityNet feature dataset.

## Note: If evaluated, then please make sure the annotation file for test data contains groundtruth.
python tools/test.py configs/localization/ssn/ssn_r50_450e_thumos14_rgb_test.py checkpoints/SOME_CHECKPOINT.pth --eval mAP

For more details and optional arguments infos, you can refer to Test a dataset part in getting_started.

### Citation¶

@InProceedings{Zhao_2017_ICCV,
author = {Zhao, Yue and Xiong, Yuanjun and Wang, Limin and Wu, Zhirong and Tang, Xiaoou and Lin, Dahua},
title = {Temporal Action Detection With Structured Segment Networks},
booktitle = {Proceedings of the IEEE International Conference on Computer Vision (ICCV)},
month = {Oct},
year = {2017}
}

format: plain


text:
PureBasic Forum

 It is currently Fri Feb 23, 2018 3:12 pm

 All times are UTC + 1 hour

 Page 1 of 1 [ 12 posts ]
 Print view Previous topic | Next topic
Author Message
 Post subject: ComboBox Drop-down HeightPosted: Fri Jul 14, 2017 1:31 am
 Always Here

Joined: Fri Oct 23, 2009 2:33 am
Posts: 5713
Location: Wales, UK
So, found some code on the forum ( Drop Height ) that does have an effect on the combo drop-down height, but it is not accurate. Also, it does not work at all if the combo item height is set:
Code:
Enumeration
#Win
#Panel
#Scroll
#Container
#Container2
#Combo
EndEnumeration

SetWindowColor(#Win, RGB(255,200,255))

ScrollAreaGadget(#Scroll, 5, 5, 470, 360, 600, 500, 20, #PB_ScrollArea_BorderLess)

ComboBoxGadget(#Combo, 10, 10, 260, 50) ;, #CBS_NOINTEGRALHEIGHT)

;Max Combo drop-down height measured from Combo Y          ;w   ;h
MoveWindow_(GetWindow_(GadgetID(#Combo), #GW_CHILD), 0, 0, 250, 250, #True)

For a = 0 To 50

Next

Repeat : Until WaitWindowEvent() = #PB_Event_CloseWindow
EndIf

Using MoveWindow_ is of course a work-around. Perhaps it worked better on XP than it does on Win7.

Any ideas? I think I may need to go back to PlanB and use a toolwindow-button-ListIcon combination........

_________________
IdeasVacuum
If it sounds simple, you have not grasped the complexity.

Last edited by IdeasVacuum on Fri Jul 14, 2017 1:57 pm, edited 1 time in total.

Top

 Post subject: Re: ComboBox Drop-down HeightPosted: Fri Jul 14, 2017 12:50 pm

Joined: Fri Jul 21, 2006 4:41 am
Posts: 2336
Location: Berlin, Germany
You forgot to set the style flag:
Code:
#CBS_NOINTEGRALHEIGHT

_________________
Windows 10 Pro, 64-Bit / Whose Hoff is it anyway?

Top

 Post subject: Re: ComboBox Drop-down HeightPosted: Fri Jul 14, 2017 1:38 pm
 Always Here

Joined: Fri Oct 23, 2009 2:33 am
Posts: 5713
Location: Wales, UK
I had already tried that flag - the result is a 1-row drop down, I want to have a drop down where the height max does not take it outside of the parent window, but not unnecessarily short.

_________________
IdeasVacuum
If it sounds simple, you have not grasped the complexity.

Top

 Post subject: Re: ComboBox Drop-down HeightPosted: Fri Jul 14, 2017 2:07 pm
 Always Here

Joined: Fri Oct 23, 2009 2:33 am
Posts: 5713
Location: Wales, UK
Another issue is that when the height of the combo button is increased, the text is not centered vertically:
Code:

Too ugly!

_________________
IdeasVacuum
If it sounds simple, you have not grasped the complexity.

Top

 Post subject: Re: ComboBox Drop-down HeightPosted: Fri Jul 14, 2017 2:33 pm

Joined: Sun Apr 12, 2009 6:27 am
Posts: 2911
Hi
Code:
Enumeration
#Win
#Panel
#Scroll
#Container
#Container2
#Combo
EndEnumeration

Global Text$,Brush,Brush_2 Text$ = Space(#MAX_PATH)

Brush = CreateSolidBrush_($FADC72) Brush_2 = CreateSolidBrush_($99FEFA)

Procedure WndProc(hWnd, uMsg, wParam, lParam)
Result = #PB_ProcessPureBasicEvents
Select uMsg
Case #WM_DRAWITEM
*DRAWITEM.DRAWITEMSTRUCT = lParam
If *DRAWITEM\CtlType = #ODT_COMBOBOX
SetBkMode_(*DRAWITEM\hDC, #TRANSPARENT)
If *DRAWITEM\ItemState & #ODS_FOCUS
FillRect_(*DRAWITEM\hDC,*DRAWITEM\rcItem,Brush)
Else
FillRect_(*DRAWITEM\hDC,*DRAWITEM\rcItem,Brush_2)
EndIf
SendMessage_(*DRAWITEM\hwndItem,#CB_GETLBTEXT,*DRAWITEM\itemID, @Text$) SetTextColor_(*DRAWITEM\hDC,$0)
*DRAWITEM\rcItem\left = 8
DrawText_(*DRAWITEM\hDC,@Text$,Len(Text$),*DRAWITEM\rcItem,  #DT_SINGLELINE | #DT_VCENTER )
EndIf
EndSelect
ProcedureReturn Result
EndProcedure

SetWindowCallback(@WndProc())
SetWindowColor(#Win, RGB(255,200,255))

ScrollAreaGadget(#Scroll, 5, 5, 480, 390, 600, 500, 20, #PB_ScrollArea_BorderLess)

dLh = FindWindow_("ComboLBox",0)
MoveWindow_(dlh , 0, 0, 250, 250, #True)

For a = 0 To 50
Next

Repeat : Until WaitWindowEvent() = #PB_Event_CloseWindow
EndIf

_________________
Egypt my love

Top

 Post subject: Re: ComboBox Drop-down HeightPosted: Fri Jul 14, 2017 2:35 pm

Joined: Fri Jul 21, 2006 4:41 am
Posts: 2336
Location: Berlin, Germany
IdeasVacuum wrote:
I had already tried that flag - the result is a 1-row drop down

Which is correct since this returns zero:

Code:

_________________
Windows 10 Pro, 64-Bit / Whose Hoff is it anyway?

Top

 Post subject: Re: ComboBox Drop-down HeightPosted: Fri Jul 14, 2017 7:14 pm
 Always Here

Joined: Fri Oct 23, 2009 2:33 am
Posts: 5713
Location: Wales, UK
It seems the need for containers within containers can potentially have an adverse affect on standard controls, but this is only witnessed when there are a lot of controls.

Rashad, what you have beautifully coded there is exactly how I want the combos to work and how I have defined a 'hand made' effort. My alternative design is a bit heavy, it needs 4 gadgets and a border-less window, but does not need Win API. I'm trying to keep the use of API to a minimum so that producing code for Android, via Spider Basic, is easier. So, decisions decisions.........

_________________
IdeasVacuum
If it sounds simple, you have not grasped the complexity.

Top

 Post subject: Re: ComboBox Drop-down HeightPosted: Fri Jul 14, 2017 8:57 pm

Joined: Sun Apr 12, 2009 6:27 am
Posts: 2911
Hi IdeasVacuum
Next is a hand made combo
Good luck

Code:

SetGadgetColor(0,#PB_Gadget_BackColor,$BEFEBC) TextGadget(1,5,3,200,20,"ComboBox Item " + Str(1)) SetGadgetColor(1,#PB_Gadget_BackColor,$BEFEBC)
StartDrawing(CanvasOutput(6))
Box(0,0,250,500,$BBF0FE) DrawingFont(FontID(0)) DrawingMode(#PB_2DDrawing_Transparent ) DrawText(2,2,"ComboBox Item " + Str(1),$FE2D30)
DrawText(2,28,"ComboBox Item " + Str(2),$FE2D30) StopDrawing() HideGadget(5,1) Repeat Select WaitWindowEvent() Case #PB_Event_CloseWindow Quit = 1 Case #PB_Event_Gadget Select EventGadget() Case 2 Run ! 1 If Run = 1 HideGadget(5,0) Else HideGadget(5,1) EndIf Case 6 Select EventType() Case #PB_EventType_MouseMove my = GetGadgetAttribute(6, #PB_Canvas_MouseY) If my > 24 And my < 44 And over = 0 StartDrawing(CanvasOutput(6)) Box(0,24,250,30,$BBF0FE)
DrawingMode(#PB_2DDrawing_Transparent )
DrawingFont(FontID(0))
DrawText(2,28,"ComboBox Item " + Str(2),$FE2D30) DrawingMode(#PB_2DDrawing_AlphaBlend ) Box(0,24,250,30,$60FF0000)
StopDrawing()
Else
StartDrawing(CanvasOutput(6))
Box(0,24,250,30,$BBF0FE) DrawingMode(#PB_2DDrawing_Transparent ) DrawingFont(FontID(0)) DrawText(2,28,"ComboBox Item " + Str(2),$FE2D30)
StopDrawing()
EndIf
;You can know exactly the what item under the cursor even with the scroll bar moved
EndSelect
EndSelect
EndSelect
Until Quit = 1
EndIf

Edit : Step forward

_________________
Egypt my love

Last edited by RASHAD on Fri Jul 14, 2017 11:20 pm, edited 1 time in total.

Top

 Post subject: Re: ComboBox Drop-down HeightPosted: Fri Jul 14, 2017 9:54 pm
 Always Here

Joined: Fri Oct 23, 2009 2:33 am
Posts: 5713
Location: Wales, UK

That's interesting code but if using a ScrollAreaGadget works, there is no need to use a Canvas, it can host a ListIcon. The reason I use a Window is that you can guarantee it will always be topmost Z level (StickyWindow), whereas I have found using a Container sometimes works, sometimes doesn't when it has to be on top of other gadgets -so to guarantee it is always on top the other gadgets need to be temporarily hidden. If the solution is for just one hand-made combo, either method is good, but for several combos on several tabs, the Window drop-down has an advantage in that it can be recycled.

_________________
IdeasVacuum
If it sounds simple, you have not grasped the complexity.

Top

 Post subject: Re: ComboBox Drop-down HeightPosted: Fri Jul 14, 2017 10:18 pm

Joined: Sun Apr 12, 2009 6:27 am
Posts: 2911
It will be more code to use
But
- You can use more than one font per list
- You can justify the text left-center-right
- you can design the height of any row as you like
- And more and more without any Windows API
Just tuck up your sleeve and dive in

_________________
Egypt my love

Top

 Post subject: Re: ComboBox Drop-down HeightPosted: Fri Jul 14, 2017 10:22 pm

Joined: Fri Nov 09, 2012 11:04 pm
Posts: 1516
Location: Uttoxeter, UK
Very nice example, as usual.
I'll have to take a close look at it.
Thank you for sharing.

_________________
DE AA EB

Top

 Post subject: Re: ComboBox Drop-down HeightPosted: Fri Jul 14, 2017 10:28 pm

Joined: Sun Apr 12, 2009 6:27 am
Posts: 2911
Hi davido
You just trapped in mate
You have to roll up your sleeve and finish the exam.

Previous post updated

_________________
Egypt my love

Top

 Display posts from previous: All posts1 day7 days2 weeks1 month3 months6 months1 year Sort by AuthorPost timeSubject AscendingDescending
 Page 1 of 1 [ 12 posts ]

 All times are UTC + 1 hour

Who is online

Users browsing this forum: No registered users and 2 guests

 You cannot post new topics in this forumYou cannot reply to topics in this forumYou cannot edit your posts in this forumYou cannot delete your posts in this forum

Search for:
 Jump to:  Select a forum ------------------ PureBasic    Coding Questions    Game Programming    3D Programming    Assembly Programming    The PureBasic Editor    The PureBasic Form Designer    General Discussion    Feature Requests and Wishlists    Tricks 'n' Tips Bug Reports    Bugs - Windows    Bugs - Linux    Bugs - Mac OSX    Bugs - Documentation OS Specific    AmigaOS    Linux    Windows    Mac OSX Miscellaneous    Announcement    Off Topic Showcase    Applications - Feedback and Discussion    PureFORM & JaPBe    TailBite


text:
## New RIC Bounds via l_q-minimization with 0

The restricted isometry constants (RICs) play an important role in exact recovery theory of sparse signals via l_q(0

## Improved Bounds for RIC in Compressed Sensing

This paper improves bounds for restricted isometry constant (RIC) in compressed sensing. Let \phi be a m*n real matrix and k be a positive integer with k

## New Bounds for Restricted Isometry Constants in Low-rank Matrix Recovery

In this paper, we establish new bounds for restricted isometry constants (RIC) in low-rank matrix recovery. Let $\A$ be a linear transformation from $\R^{m \times n}$ into $\R^p$, and $r$ the rank of recovered matrix $X\in \R^{m \times n}$. Our main result is that if the condition on RIC satisfies \$\delta_{2r+k}+2(\frac{r}{k})^{1/2}\delta_{\max\{r+\frac{3}{2}k,2k\}}


text:
# Tag Info

1

Worldsheet supersymmetry is the fermionic symmetry of the worldsheet RNS action under the worldsheet supsresymmetry transformations that look like $$\sqrt{\frac{2}{\alpha'}}X \mapsto \sqrt{\frac{2}{\alpha'}}X + \mathrm{i}\bar{\epsilon}\psi^\mu$$ and which I'm too lazy to type out for all fields (and which also depend on whether or not we're looking at the ...

2

According to the fuzzball proposal in string theory, black hole are actually horizonless and regular solutions. For some systems in five dimensions made with bound states of intersecting branes this has been already proved directly in supergravity: there are solutions without horizons and singularities, with the same asymptotic charges (Mass, Angular ...

2

At best things are pretty speculative. Cumrun Vafa has proposed that black holes have condensates of tachyons. In some sense you can understand this without much complexity. The Schwarzschild metric has a physical singularity that is a spatial surface. The Penrose conformal diagram for the Schwarzschild metric illustrates this The bosonic string has two ...

1

One has to keep clearly in mind the structure of present day physics. Quantum mechanics is the theory that started as non relativistic with the Schrodinger equation for potentials, and became relativistic with the Dirac and Klein Gordon and quantized Maxwwell equations. Quantum mechanics has postulates which used with the solutions of the differential ...

0

As you said in your question, quantum field theory is very important; it takes the ideas of quantum mechanics and applies them to fields, such as the electromagnetic force (in fact, quantum electrodynamics was the beginning of quantum field theory). Quantum field theory has plenty of evidence to support it, and it is still an ongoing work. String theory, ...

0

According to the abstract of a paper at https://arxiv.org/abs/hep-th/0604072, Breakdown of local physics in string theory at distances longer than the string scale is investigated. Such nonlocality would be expected to be visible in ultrahigh-energy scattering. The results of various approaches to such scattering are collected and examined. No evidence ...

2

Confinement is a low energy phenomenon. By this I mean that as you increase the energy with which you probe the properties of quarks they appear more and more like free particles. This property is called asymptotic freedom. If we had some hypothetical accelerator capable of doing experiments at energies where stringy effects start to be significant it would ...

0

I think there are a number of generalizations. The first is the partition function should be considered quantum mechanically. The reason is that spacetime can contribute to entropy, such as with Hawking radiation. To start the partition function is the trace $$Z[\phi] = \sum_n\langle\phi_n|e^{-H(\phi)\beta}|\phi_n\rangle$$ Now, if one is interested in the ...

0

The particle is not larger nor more massive. We normally describe particles using quantum field theory, and in QFT particles do not have a size. This is discussed in the answers to Why do physicists believe that particles are pointlike? and it would be worth reading through them. To say that a particle is a point is a bit of an over simplification. We ...

1

Here, a term spin should be understood as a quantum number you get after doing dimensional reduction of a higher dimensional theory to (1+3)-dimensions. If you follow this assumption, you find a spin of Kalb-Ramond field is 1. I think most people have this in mind, when they say a spin in higher dimensions. In general, you get more quantum numbers than you ...

0

String theory postulates that of the elementary particles we currently know about, each relates directly to low-energy string vibrations, the presence of multiple holes causes the string patterns to fall into families. Each hole in the Calabi-Yau space is a group of low-energy string vibrational patterns. If the C-Y has three holes, then three families of ...

2

This is not really an answer (the answer is ACuriousMind's comment: this is a double coset space), but it may help to consider the construction of the moduli space of elliptic curves, as this can be done in the same way but is very easy. Every complex elliptic curve is obtained as $\Bbb C$ modulo a lattice. Scaling the lattice by a complex number gives an ...

2

I do not know almost anything about string theory, but I can say something from the general quantum theory viewpoint. First of all you stated Malament's theorem hypotheses into a not very precise form. The sets $\Delta$ are assumed to be subsets of a 3D spacelike surface $\Sigma$ (the rest space of an observer) whereas $a$ in the third requirement is a ...

1

There are two things going on. One is modulo that is the forwards slash / and the other is set-minus $\setminus$ the backwards slash. The $$G_4(20) = \frac{O(4,20)}{O(4)\times O(20)}$$ is the Grassmanian space defined by $4$-planes. the group $O(\Gamma_{4,20})$ is an orthogonal group over the unimodular transformations, a bit like saying $O(n,\mathbb Z)$, ...

0

The string action $$S_p = -T\int d\tau d\sigma (-\gamma)\gamma^{ab}g_{\mu\nu}\partial_aX^\mu\partial_bX^\nu,$$ or Poyakov action, is evaluated in a path integral $Z = \int{\cal D}[X]e^{-iS}$, or defines states $$|\psi\rangle = \int{\cal D}[X]e^{-iS}|n\rangle$$ on a Fock basis. In the light cone gauge, $X^\pm = \frac{1}{2}(X^0\pm X^i)$ the Hamiltonian ...

-1

Of course they can. Some particles arent elementary, imagine Glueballs Neutrons, Protons, they all conclude other particles. But an elementary particle (electron, quark, so on..) are described by one single string. It is also important, what particles you are talking about, because there exist open and closed strings, which all have other mathematical ...

2

While writers like Briane Green do a generally laudable job of trying to explain string theory at a popular level you need to appreciate that this always involves gross simplifications. The reality is that string theory is horrifically more complicated than the pop science explanation suggests. To properly explain how particles arise in string theory is ...

1

In physics, string theory is a theoretical framework in which the point-like particles of particle physics are replaced by one-dimensional objects called strings. It describes how these strings propagate through space and interact with each other. On distance scales larger than the string scale, a string looks just like an ordinary particle, with its mass, ...

0

The heterotic group decomposes as $E_8~\rightarrow~SU(3)\times E_6$, The $\bf 248$ of the $E_8$ decomposes as $${\bf 248}~\rightarrow~(\bf 8,~\bf 1) + (\bf 1,~\bf 78) + (\bf 3,~\bf 27) + (\bf\bar 3,~\bf\bar{27})$$ We have here the $(\bf 8,~\bf 1)$ of $SU(3)$ which is identical in form to the irreducible representation used for gluons, or the old nonet ...

0

Your derivation is close. The Polyakov action is $$S[X,\gamma] = T\int d\tau\int d\sigma (-\gamma)^{1/2}\gamma^{ab}\partial_aX^\mu \partial_bX_\mu,$$ for $T = -(4\pi\alpha')^{-1}$. The variation with respect to the string $X_\mu$ then gives  \frac{\delta S}{\delta X^\mu} = T\int d\tau\int d\sigma\left[\frac{\delta}{\delta X^\mu}\left((-\gamma)^{1/2}\...

2

A more "pedestrian" application is that the low-energy physics of a Heisenberg antiferromagnetic spin chain is described by a WZW theory. This is a very simple and concrete model which has been shown to accurately describe many real materials. See for example http://arxiv.org/abs/hep-th/9802014v1, http://arxiv.org/abs/1211.5421v1, or section 7.10 of ...

Top 50 recent answers are included


text:
# Trefoil knot

Trefoil
Common nameOverhand knot
Arf invariant1
Braid length3
Braid no.2
Bridge no.2
Crosscap no.1
Crossing no.3
Genus1
Hyperbolic volume0
Stick no.6
Tunnel no.1
Unknotting no.1
Conway notation[3]
A–B notation31
Dowker notation4, 6, 2
Last /Next0141
Other
alternating, torus, fibered, pretzel, prime, not slice, reversible, tricolorable, twist

In knot theory, a branch of mathematics, the trefoil knot is the simplest example of a nontrivial knot. The trefoil can be obtained by joining together the two loose ends of a common overhand knot, resulting in a knotted loop. As the simplest knot, the trefoil is fundamental to the study of mathematical knot theory.

The trefoil knot is named after the three-leaf clover (or trefoil) plant.

## Descriptions[]

The trefoil knot can be defined as the curve obtained from the following parametric equations:

${\displaystyle x=\sin t+2\sin 2t}$
${\displaystyle y=\cos t-2\cos 2t}$
${\displaystyle z=-\sin 3t}$

The (2,3)-torus knot is also a trefoil knot. The following parametric equations give a (2,3)-torus knot lying on torus ${\displaystyle (r-2)^{2}+z^{2}=1}$:

${\displaystyle x=(2+\cos 3t)\cos 2t}$
${\displaystyle y=(2+\cos 3t)\sin 2t}$
${\displaystyle z=\sin 3t}$
Video on making a trefoil knot
Overhand knot becomes a trefoil knot by joining the ends.
A realization of the trefoil knot

Any continuous deformation of the curve above is also considered a trefoil knot. Specifically, any curve isotopic to a trefoil knot is also considered to be a trefoil. In addition, the mirror image of a trefoil knot is also considered to be a trefoil. In topology and knot theory, the trefoil is usually defined using a knot diagram instead of an explicit parametric equation.

In algebraic geometry, the trefoil can also be obtained as the intersection in C2 of the unit 3-sphere S3 with the complex plane curve of zeroes of the complex polynomial z2 + w3 (a cuspidal cubic).

A left-handed trefoil and a right-handed trefoil.

If one end of a tape or belt is turned over three times and then pasted to the other, the edge forms a trefoil knot.[1]

## Symmetry[]

The trefoil knot is chiral, in the sense that a trefoil knot can be distinguished from its own mirror image. The two resulting variants are known as the left-handed trefoil and the right-handed trefoil. It is not possible to deform a left-handed trefoil continuously into a right-handed trefoil, or vice versa. (That is, the two trefoils are not ambient isotopic.)

Though chiral, the trefoil knot is also invertible, meaning that there is no distinction between a counterclockwise-oriented and a clockwise-oriented trefoil. That is, the chirality of a trefoil depends only on the over and under crossings, not the orientation of the curve.

The trefoil knot is tricolorable.
Form of trefoil knot without visual three-fold symmetry

## Nontriviality[]

The trefoil knot is nontrivial, meaning that it is not possible to "untie" a trefoil knot in three dimensions without cutting it. Mathematically, this means that a trefoil knot is not isotopic to the unknot. In particular, there is no sequence of Reidemeister moves that will untie a trefoil.

Proving this requires the construction of a knot invariant that distinguishes the trefoil from the unknot. The simplest such invariant is tricolorability: the trefoil is tricolorable, but the unknot is not. In addition, virtually every major knot polynomial distinguishes the trefoil from an unknot, as do most other strong knot invariants.

## Classification[]

In knot theory, the trefoil is the first nontrivial knot, and is the only knot with crossing number three. It is a prime knot, and is listed as 31 in the Alexander-Briggs notation. The Dowker notation for the trefoil is 4 6 2, and the Conway notation is [3].

The trefoil can be described as the (2,3)-torus knot. It is also the knot obtained by closing the braid σ13.

The trefoil is an alternating knot. However, it is not a slice knot, meaning it does not bound a smooth 2-dimensional disk in the 4-dimensional ball; one way to prove this is to note that its signature is not zero. Another proof is that its Alexander polynomial does not satisfy the Fox-Milnor condition.

The trefoil is a fibered knot, meaning that its complement in ${\displaystyle S^{3}}$ is a fiber bundle over the circle ${\displaystyle S^{1}}$. The trefoil K may be viewed as the set of pairs ${\displaystyle (z,w)}$ of complex numbers such that ${\displaystyle |z|^{2}+|w|^{2}=1}$ and ${\displaystyle z^{2}+w^{3}=0}$. Then this fiber bundle has the Milnor map ${\displaystyle \phi (z,w)=(z^{2}+w^{3})/|z^{2}+w^{3}|}$ as the fibre bundle projection of the knot complement ${\displaystyle S^{3}}$ \ K to the circle ${\displaystyle S^{1}}$. The fibre is a once-punctured torus. Since the knot complement is also a Seifert fibred with boundary, it has a horizontal incompressible surface—this is also the fiber of the Milnor map. (This assumes the knot has been thickened to become a solid torus Nε(K), and that the interior of this solid torus has been removed to create a compact knot complement ${\displaystyle S^{3}}$ \ int(Nε(K)).)

## Invariants[]

The Alexander polynomial of the trefoil knot is

${\displaystyle \Delta (t)=t-1+t^{-1},\,}$

and the Conway polynomial is

${\displaystyle \nabla (z)=z^{2}+1.}$[2]

The Jones polynomial is

${\displaystyle V(q)=q^{-1}+q^{-3}-q^{-4},\,}$

and the Kauffman polynomial of the trefoil is

${\displaystyle L(a,z)=za^{5}+z^{2}a^{4}-a^{4}+za^{3}+z^{2}a^{2}-2a^{2}.\,}$

The HOMFLY polynomial of the trefoil is

${\displaystyle L(\alpha ,z)=-\alpha ^{4}+\alpha ^{2}z^{2}+2\alpha ^{2}.\,}$

The knot group of the trefoil is given by the presentation

${\displaystyle \langle x,y\mid x^{2}=y^{3}\rangle \,}$

or equivalently

${\displaystyle \langle x,y\mid xyx=yxy\rangle .\,}$[3]

This group is isomorphic to the braid group with three strands.

## In religion and culture[]

As the simplest nontrivial knot, the trefoil is a common motif in iconography and the visual arts. For example, the common form of the triquetra symbol is a trefoil, as are some versions of the Germanic Valknut.

In modern art, the woodcut Knots by M. C. Escher depicts three trefoil knots whose solid forms are twisted in different ways.[4]

## References[]

1. ^ Shaw, George Russell (MCMXXXIII). Knots: Useful & Ornamental, p.11. ISBN 978-0-517-46000-9.
2. ^
3. ^ Accessed: May 5, 2013.
4. ^ The Official M.C. Escher Website — Gallery — "Knots"


text:
# Asynchronous Functional Reactive Programming for GUIs

Asynchronous Functional Reactive Programming for GUIs – Czaplicki & Chong 2013

Today’s paper choice introduces the Elm language. Elm today is a functional reactive programming language for the browser. If you want to explore more check out the examples and live code editor. You might also like Richard Feldman’s Strange Loop talk on “Making the back-end team jealous”.

Elm is a functional reactive programming language that aims to simplify the creation of responsive graphical user interfaces(GUIs), and specifically targets GUIs for web applications. Functional reactive programming (FRP) applies pure functional programming paradigms to time-varying values, known as signals. FRP is a highly promising approach for implementing GUIs, where time-varying values can represent input and output (including user interaction, server requests and responses), and other information about the execution environment. By enforcing a purely functional programming style, programmers can explicitly model complex time-dependent relationships in a high-level declarative way.

Whereas in most FRP languages signals (what we’ve been calling behaviours so far this week) change continuously, in Elm signals change only when a discrete event occurs. An event is a program input, such as the mouse position. Events require recomputation of the program – if this takes a reasonable amount of time a GUI would become unresponsive, which is unacceptable . Elm therefore allows a programmer to specify when computation can occur asynchronously.

### Some simple examples

#### Functional Layout

The first example shows functional graphical layout:

content = flow down [ plainText "Welcome to Elm!"
, image 150 50 "flower.jpg"
, asText (reverse [1..9]) ]

main = container 180 100 middle content

main is a special variable in Elm, the value of this variable will be displayed on the screen when the program is executed. The program above creates a vertical arrangement of the text ‘Welcome to Elm!’, underneath which is a picture of a flower, underneath which are the digits 9 down to 1.

flow takes a direction and a list of Elements and produces a composite Element:

flow : Direction -> [Element] -> Element

#### Signals

Now let’s see something reactive using the Mouse.position signal:

main = lift asText Mouse.position

This code relies on signals, which are the key abstraction of FRP. A signal is a value that changes over time. In Elm, a signal that represents a value of type τ changing over time has type Signal τ. For example, a graphical element that changes over time, such as an animation, is a Signal Element. Indeed, variable main typically has type Signal Element, since what to display on the screen changes over time. In the code above, the position of the mouse is represented as a signal of a pair of integers, indicating the coordinates of the mouse.

The lift : (a -> b) -> Signal a -> Signal b lifts a function from a -> b so that it can be applied to signal values. In the current incarnation of Elm, lift is spelt map. The modern version of the mouse position example is:

main = Signal.map show Mouse.position

#### Asynchronous processing

This example highlights Elm’s ability to perform asynchronous computation over signals. It uses words entered by the user to find and fetch an image from a web service (such as Flickr), which may take significant time. The program simultaneously displays the current position of the mouse, with the position being updated in a timely manner, regardless of how long image fetching takes.

(inputField, tags) = Input.text "Enter a tag"

getImage tags =
lift (fittedImage 300 200) (syncGet (lift requestTag tags))

scene input pos img =
flow down [ input, asText pos, img ]

main = lift3 scene inputField
Mouse.position
(async (getImage tags))

The reactivity here may not be obvious on first reading: Input.text creates a pair of signals – a signal of graphical elements for the input field and a signal of strings for the tags. lift3 generates a signal of Elements by constructing a scene from the input field signal, mouse position signal , and images signal. A new scene is generated each time any one of the three signals produces a new value.

The async construct can be applied to any signal, and provides a simple, composable way for the programmer to specify when computation over a signal may occur asynchronously, and thus to ensure that long-running computation does not cause the GUI to become unresponsive.

In today’s Elm, asynchronous processing can be handled via Tasks. The ‘async’ construct is not implemented in the current runtime.

### The core of Elm

Elm’s syntax and semantics are explained using a stripped-down version of the full language known as Featherweight Elm (FElm).

FElm combines a simply-typed functional language with a small set of reactive primitives. Programmers have direct access to signals, which can be transformed and combined with the full power of a functional language. A type system restricts the use of reactive primitives to ensure that the program can be executed efficiently. FElm uses a two-stage semantics. In the first stage, functional constructs are evaluated, and signals are left uninterpreted. In the second stage, signals are evaluated: as the external environment generates new values for input signals, the new values are processed as appropriate.

Signals are streams of values – for example a signal representing the width of a window that produces an event whenever the window width is resized; a left-mouse button signal that produces an event whenever the button is pressed or released; a timer signal that produces an event at fixed time intervals.

An event occurs when an input signal generates a new value. Events may trigger computation. In FElm, every signal always has a “current” value: it is the most recent value generated by the signal, or, for an input signal that has not yet generated a new value, it is an appropriate default value associated with that input signal. Thus, every input signal is required to have a default value, which then induces default values for other signals.

The liftn primitive combines an n-ary function f and n signals, e1..en to produce a composite signal by applying f e1..en. For example:

lift1 (λx: int. x+x) Window.width

creates a signal of integers obtained by doubling the values from the Window.width signal. The composite signal value is recomputed each time an event occurs for any of the input signals. (Reminder, lift is rendered as ‘map’ in the current Elm implementation as it maps a function over the input signals).

Whereas lift operates on current signal values, foldp combines current and past values of a signal. It acts like an accumulator, or fold, over the historical values of a signal. You specify an initial value and an accumulator function and then each time the input signal produces an event the accumulator function is applied to combine the current value and the new event to give the new accumulator value. Best understood with an example:

foldp (λk: int. λc: int. c+1) 0 Keyboard.lastPressed

creates a signal counting the number of key presses. Keyboard.lastPressed is a signal of key presses (encoded as integers), the initial accumulator value is 0. Every time a key is pressed we apply the anonymous function which increments the counter (and ignores the key value).

Elm’s type system rules out programs that use signals of signals:

Intuitively, if we have signals of signals, then after a program has executed for, say 10 minutes, we might create a signal that (through the use of foldp) depends on the history of an input signal, say Window.width. To compute the current value of this signal, should we use the entire history of Window.width? But that would require saving all history of Window.width from the beginning of execution, even though we do not know whether the history will be needed later. Alternatively, we could compute the current value of the signal just using the cur- rent and new values of Window.width (i.e., ignoring the history). But this would allow the possibility of having two identically de- fined signals that have different values, based on when they were created.We avoid these issues by ruling out signals of signals

The first stage of Elm evalution considers only the functional parts. If a program evaluates to some value v then it does not use signals and is not a reactive program. But if it evaluates to a signal term s then the second stage of evaluation occurs performing computations as signals produce new values.

A signal term can be visualized as a directed acyclic graph, where nodes are input signals (i ∈ Input), liftn terms, and foldp terms. The definition and use of variables define edges between the nodes. (Asynchronous terms async s are described below.)We refer to these visualizations as signal graphs. Nodes representing input signals have no incoming edges from other signal nodes, a node representing term liftn v s1 … sn has n incoming edges, and a node representing term foldp v1 v2 s has a single incoming edge. Signal graphs are acyclic since FElm has no way to construct recursive signal terms… We refer to nodes with no incoming edges as source nodes. Source nodes include input signals, and, as we will see below, async s nodes. Source nodes are the source of new values. An event occurs when the signal represented by a source node produces a new value. Input signal events are triggered by the external environment, for example, mouse clicks or key presses. A global event dispatcher is responsible for notifying source nodes when events occur. The global event dispatcher ensures that events are totally ordered and no two events occur at exactly the same time. In signal graphs, we draw dashed lines from the global event dispatcher to all source nodes

The implementation pipelines execution of the signal graph. Each node in the graph conceptually has its own thread of control. When an event occurs, all source nodes are notified by the global dispatcher. The node to which the event is relevent produces the new value, the others generate a special ‘noChange’ event. In this way every source node produces a value for each event. When a node in graph performs computation, it must take a value from each incoming edges queue (computation at a node is blocked until there are values on all incoming edges). If all incoming values indicate ‘noChange’ then the node does not perform any new computation and instead propagates ‘noChange’.

The noChange v’ values are a form of memoization—allowing nodes to avoid needless recomputation—but in the case of foldp nodes, are also critical to ensure correct execution. For example, a foldp term that counts the number of key presses (as we saw previously) should increment the counter only when a key is actually pressed, not every time any event occurs.

async nodes in the graph have no incoming edges from other signal nodes. They propagate a ‘noChange’ value whenever an event at an alternate source node occurs, and propagate the events produced by their asynchronously executed signal whenever they occur.

The full semantics of FElm are specified by its translation into Concurrent ML.

### The full Elm language

Elm extends the FElm core calculus to a full language for building rich interactive GUIs, including libraries for constructing and composing GUI components… Elm has additional base values, including strings, floating point numbers, time, tuples, and graphical values such as Elements and Forms. Elm libraries provide data structures such as options, lists, sets, and dictionaries. Elm provides support for receiving input from mouse, keyboard, and touch devices, for accessing window attributes, and for network communication via HTTP. Elm supports JSON data structures and Markdown (making text creation easier). Elm’s type system allows let-polymorphism and recursive simple types (but not recursive signal types). Elm supports type inference, has extensible records, and has a module system.

Elm as described in the paper embeds an implementation of discrete Arrowized FRP.

Arrowized FRP is a purely functional way to structure stateful programs. It introduced signal functions which can encapsulate state and safely be switched in and out of a program. A signal function is conceptually equivalent to Elm’s signal nodes: a set of external inputs, internal state, and an output. Although signal functions and signal nodes are equivalent, Elm’s core language does not allow one to work with signal nodes directly. Arrowized FRP allows this, making it possible to dynamically reconfigure a single node. This direct embedding of AFRP gives Elm the flexibility of signal functions without resorting to the use of signals-of-signals.

The Arrowized FRP support is provided via an Automaton library. “An Automaton is defined as a continuation that when given an input a, produces the next continuation and an output b.”

data Automaton a b = Step (a -> (Automaton a b, b))

This allows state to be kept around by continually placing it in the next continuation (the next step). Dynamic collections and dynamic switching are possible because an automaton is a pure data structure with no innate dependencies on inputs (whereas signals depend on an input by definition).

In the current implementation of Elm you can find support for Automatons in the Automaton library, which includes the following documentation:

This library is for structuring reactive code. The key concepts come directly from Arrowized FRP. It is not yet clear how valuable this is, so it is a great domain for experimentation and iteration to see if we can make it a really useful tool. This library aims to be a simple and minimal API that will help you get started with Arrowized FRP (AFRP), which can be very hard to understand from just the academic papers.

### Implementation

As reported in the paper, “we have implemented an Elm-to-JavaScript compiler, and have a prototype implementation of Elm as an embedded domain-specific language (DSL) in Haskell.” For the current implementation, head over to elm-lang.org


text:
smoothly object transition through lerp and coroutine

IEnumerator SmoothlyShiftPosition(Vector3 destination, float OverTime) {

float startTime = 0;
while (startTime < OverTime)
{
Debug.Log(startTime/OverTime + "changing: " + navigationCanvas.transform.position);
Debug.Log("startTime : " + startTime);
startTime += Time.deltaTime * 2f;
yield return null;
}
}

I have this simple code snippet which i am using to lerp my object to specfied position smoothly it work sometime correctly but not always. I logged different data and found that my startTime variable sometime becomes zero continuously. I am unable to figure why this occuring? what i am doing wrong?

Edit:

I am calling coroutine function like this

 if (SmoothlyShiftPositionIEum != null) {
StopCoroutine(SmoothlyShiftPositionIEum);
}
SmoothlyShiftPositionIEum = StartCoroutine(SmoothlyShiftPosition(navCanvas, smoothPositionTime));

• Are you sure that you are not calling the coroutine multiple times? – Nikaas Apr 17 '17 at 8:52
• @Nikaas good point i am checking that if coroutine is already running then sop it. like code updated above – Muhammad Faizan Khan Apr 17 '17 at 9:07
• I don't think this change will fix it. You may need to add SmoothlyShiftPositionIEum=null at the end of the coroutine. Then only start the coroutine if SmoothlyShiftPositionIEum is null. – Nikaas Apr 17 '17 at 9:22
• You might find the pattern described in this answer helpful. Be sure to check whether you're pausing the game anywhere by setting Time.timeScale to zero. This will pause any script that uses Time.deltaTime, making it idle in the same place until the time scale is restored. – DMGregory Apr 17 '17 at 11:49
• @MohammadFaizanKhan If the Lerp part is working as intended you can ignore this. It's worth mentioning that you aren't "linear interpolating" since you constantly change the starting position of the lerp. If you want a true linear transition from A -> B you need to save your starting position and use that as value A. By using your modified position in the lerp value you'll actually get a curve transition where things speed up as they approach the target. Once again, if this what you want, the go for it. Just making sure. – Zebraman Apr 17 '17 at 13:31


text:
Differentially gene expression multispecies
0
0
Entering edit mode
10 weeks ago

Hi friends, how are you? I need your help with my study project. I have RNAseq data for 3 species (6 replicates per species), species form a genus within bedbugs. I would like to analyze the differential expression of these species, however I have doubts if the answers I get are real or methodological biases. At the moment I am using all assemblies (18 = 6 per species) to map the expression and I have interesting results, however I don't know if it could be technical bias.

forward my results

Utilizei:

#build reference with all assemblies (n =18)

kallisto index -i reference ( all assemblies)

#analysed by sample (pairend)

kallisto quant -i reference.idx -o output --rf-stranded -b 100 r1.fasta r2.fasta

## estimetes
Trinity/util/abundance_estimates_to_matrix.pl \
--est_method kallisto --gene_trans_map reference.fasta.gene_trans_map \
--name_sample_by_basedir --cross_sample_norm TMM --out_prefix outdir \
sample1, sample2 ...sample18

Trinity/Analysis/DifferentialExpression/run_DE_analysis.pl --matrix  gene.counts.matrix --method edgeR --output out --dispersion 0.1

Trinity/Analysis/DifferentialExpression/analyze_diff_expr.pl --matrix gene.TMM.EXPR.matrix --max_genes_clust 1000000 -P 1e-3 -C 4

Trinity/Analysis/DifferentialExpression/define_clusters_by_cutting_tree.pl -R / diffExpr.P1e-3_C4.matrix.RData --Ptree 60

What do you guys think will be next to trust us in my results or improve them?

Gene Expression Multiespecies RNAseq • 219 views
2
Entering edit mode

do you know if each taxon was sequenced as a separate batch or all the samples were sequenced together? Samples of each taxon cluster together, this can be biologically meaningful but also could be due to a batch effect.

0
Entering edit mode

Hi, buddy, sorry for the delay. On sequencing they were sequenced in the same batch and the conditions were the same. My doubt is that because I don't have a genome or transcriptome as a reference, I may be obtaining "non-real" data about the expression. I chose to use all assemblies (n=18 (6 per species)) to obtain the reference and analyze against this "super reference". My collaborators are unsure about the results, however the methodology is consistent with "good practices".

I would like to be certain that I could continue with this study.


text:
Orbital period changes in V2051~Oph
Session 55 -- Interacting Binaries: CVs and XRBs
Display presentation, Thursday, January 13, 9:30-6:45, Salons I/II Room (Crystal Gateway)

## [55.08] Orbital period changes in V2051~Oph

L.Triplett, R.Baptista (STScI), J.E.Steiner (IAG/USP), F.J.Jablonski (INPE and U.Texas)

We report the identification of orbital period changes in the short-period eclipsing cata\-clysmic variable V2051~Oph. We used times of mid-eclipse collected from the literature and timings from our unpublished data to construct an observed-minus-calculated eclipse time diagram covering 13 years of observations (1979-92).

At present there is no evidence of secular orbital period (P$_{\rm orb}$) decrease. The uncertainty in the quadratic fit sets an upper limit for period changes of P$_{\rm orb}$/\.{P}$\:> 5.9 \times 10^7$ yr. Assuming a secondary mass of M$_2 = 0.2\:{\rm M}_\odot$ this yields \.{M}$_2 < 3.4 \times 10^{-9} \:{\rm M_{\odot} \,yr}^{-1}$ as an upper limit for the mass transfer rate in the system.

The data present cyclical variations that can be fitted by a linear plus sinusoidal function with periods 4.7 yr and 7.6 yr. The statistical significance of these periods by an F-test are, respectively, 93\% and 97\%. The multiplicity of possible solutions suggest that V2051~Oph exhibits cyclical but non-periodic P$_{\rm orb}$ changes, which could be explained in terms of a magnetic activity cycle in its secondary star. An incremental radius variation of $\Delta R_2/R_2 \simeq 10^{-6}$ is required to explain the observed amplitude of the cycle. This is of the same order of the values found for EX~Hya (Warner 1988) and V4140~Sgr (Baptista, Jablonski \& Steiner 1992), and is an order of magnitude smaller than the calculated values for systems above the period gap (implying proportionally smaller magnetic field strenghts).

This result, along with the evidence from V4140~Sgr and EX~Hya (and possibly also Z~Cha), suggests that if the magnetic cycle hypothesis is correct, the secondaries of cata\-clysmic variables below the period gap also have magnetic fields, although weaker than those of secondaries above the gap. This may serve to constraint current models attempting to explain the existence of the period gap.


text:
Finger Notation – How to Read!

Finger notation is important because you can use it to express fingering and understand methods players use to hit complicated patterns.

Use numbers 1 to 4 to express Index, Middle, Ring and Pinky fingers for the left hand, and use numbers 1 to 4 in brackets to express the same fingers, on the right hand. So for instance if you see “(1)” – that means “tap this note with your right hand index finger”. If you see “1234” – that means fret the notes in sequence with your left hand. Sometimes, fret notation, e.g. GRYBO is used instead of numbers. In addition, square brackets are used [like this] when referring to an anchored note.

Example Pattern 1 – A Red/Green Trill

The finger notation for this could be expressed as: (1)121(1)121(1)121(1)121

Broken down; i) start the sequence by tapping the first Red note with your right hand index finger. ii) release to green and then play the next Red note with your left hand. iii) Repeat!

Example Pattern 2 – Descending Triplets and an Orange-Green Trill

The finger notation for this could be expressed as: (21)1 321 (21)1 321 (1)141

Broken down; i) Start the sequence alternating tapping with right hand and playing the next triplet with left hand. ii) tap the first orange note using your right hand, keeping green anchored. iii) fret the following orange note after tapping, pulling off to hit the final green note (still anchored).

Dark Caves of lolno WTF Sweeps – courtesy of AbyssionQC (expert GH player!)

“…for some patterns, it is easier to understand by using GRYBO for notation (e.g. the fret colors).”

Example – WTF Sweeps, sliding method

Finger notation can be expressed as: 1(12)234(123)11232(121)23211(321)432(21). “1” at the start implying to anchor green, 11 implying a slide to red, 3211 sliding back to green etc.

Fret notation could be expressed as: [G](RY)RYB(RYB)[R]YBY(BOB)YBYR[G](BYR)BYR(YR).

In this example, by using Fret Notation it is much easier to read and understand the actual pattern. Finger notation is more descriptive of the method used.

More notes from AbyssionQC:

“…saying (OBYB) is a lot more confusing than (3211) when referring to the sliding method while (OBY)RYR[G](RYR)YBOBY(RYR)RYR(YBO) is much easier to understand when breaking down sweeps into a pattern. GYG, RBR and YOY zigs for the ending of Volcano Solo C in Destruction Armageddon is easier to understand than finger notation. Etc etc etc. Both methods are relevant, it just depend of the pattern (and your preference).”


text:
Is this a valid proof?

kaos
Is this a valid proof? Also is this way of doing it valid?

Statement : There are infinitely many natural numbers n where the square root of n is rational.

Proof:
sqrt of n = x (where x is natural)
n= x squared

And n can be any natural number(x) squared ,and there are infinitely many natural numbers (x)
therefore there are infinitely many n which has a natural square root. Since natural numbers are rational , there are infinitely many natural numbers n where the square root of n is rational.

Homework Helper
Dearly Missed
Is this a valid proof? Also is this way of doing it valid?

Statement : There are infinitely many natural numbers n where the square root of n is rational.

Proof:
sqrt of n = x (where x is natural)
n= x squared

And n can be any natural number(x) squared ,and there are infinitely many natural numbers (x)
therefore there are infinitely many n which has a natural square root. Since natural numbers are rational , there are infinitely many natural numbers n where the square root of n is rational.

Your argument seems fine. There is one small point, though, that you should consider: how do you know that different integers x yield different integers x^2? (You need to argue that in order to know that squaring does not cause everything to collapse into a small, finite set of values.)

Abhilash H N
Try going like this...
There are two possibilities:
1.There are infinitely many natural numbers n where the square root of n is rational.
2.There are finite natural number whose roots are rational.
If things were go as 1. then the proof is complete. If things were to go as 2. then we have to prove it wrong..
If second condition is satisfied then we will come up with a maximum number nmax (say) whose root is rational. Prove that there exist another number greater than nmax whose root is rational.
So the 2. possibility is ruled out, hence we are left with only one possibility which is 1.
Regards

kaos
Your argument seems fine. There is one small point, though, that you should consider: how do you know that different integers x yield different integers x^2? (You need to argue that in order to know that squaring does not cause everything to collapse into a small, finite set of values.)

Thanks for responding.

Isn't the square of an integer always different?(except 1 or 0 i guess)?

And I dont understand the "(You need to argue that in order to know that squaring does not cause everything to collapse into a small, finite set of values.)" part (specifically what are you referring to that is collapsing?).

kaos
Try going like this...
There are two possibilities:
1.There are infinitely many natural numbers n where the square root of n is rational.
2.There are finite natural number whose roots are rational.
If things were go as 1. then the proof is complete. If things were to go as 2. then we have to prove it wrong..
If second condition is satisfied then we will come up with a maximum number nmax (say) whose root is rational. Prove that there exist another number greater than nmax whose root is rational.
So the 2. possibility is ruled out, hence we are left with only one possibility which is 1.
Regards

Yes i know of proof by contradiction, but i used a more straightforward method. Though im not entirely sure my proof works.

Homework Helper
Yes i know of proof by contradiction, but i used a more straightforward method. Though im not entirely sure my proof works.

It's perfectly valid. The set of all n^2 for n any natural number i.e. {1^2,2^2,3^2,...} has an infinite number (since there are no duplicates, that's what Ray was saying about 'collapsing') of elements all of which are all natural numbers. Their square roots are all natural numbers, i.e. {1,2,3....} hence rational. That's what you are saying, right? In fact, those are the ONLY natural numbers that have rational square roots, but you don't need to show that.

Homework Helper
Thanks for responding.

Isn't the square of an integer always different?(except 1 or 0 i guess)?
No, that is not true. (2)^2= (-2)^2. However, YOU are working with natural numbers, not integers (do you understand the difference?) so it is true. But the point is that, unless you are "given" that, you need to prove it. Suppose m and n are different natural numbers. Then $n- m\ne 0$ because they are different. Further $m+n\ne 0$ (why?). Therefore $m^2- n^2= (m- n)(m+ n)$ is not 0 so $m^2$ is not equal to $n^2$.

And I dont understand the "(You need to argue that in order to know that squaring does not cause everything to collapse into a small, finite set of values.)" part (specifically what are you referring to that is collapsing?).
For example, when squaring, the set {-3, -2, 2, 3} "collapses" to the smaller set {4, 9}. The proof above shows that cannot happen for the natural numbers.

Last edited by a moderator:
kaos
No, that is not true. (2)^2= (-2)^2. However, YOU are working with natural numbers, not integers (do you understand the difference?) so it is true. But the point is that, unless you are "given" that, you need to prove it. Suppose m and n are different natural numbers. Then $n- m\ne 0$ because they are different. Further $m+n\ne 0[/tex] (why?). Therefore [itex]m^2- n^2= (m- n)(m+ n)[/tex] is not 0 so [itex]m^2$ is not equal to $n^2$.

For example, when squaring, the set {-3, -2, 2, 3} "collapses" to the smaller set {4, 9}. The proof above shows that cannot happen for the natural numbers.

Ah right i confused naturals(whole numbers larger than zero) with integers (integers include less than zero whole number right). Thanks for the explanation.


text:
# Comparing the cardinality of sets

An exercise is the following:

Compare the cardinality of the following sets:

• The class of all real numbers $\mathbb{R} =: A$
• The class of all polynomials $\mathbb{R}[X] =: B$
• The class of all real functions $f:\mathbb{R} \to \{0,1\} =: C$
• ...

The hint is to use the Cantor-Schröder-Bernstein-Theorem. Is it also possible to show that two sets $A,B$ satisfy $|A| \leq |B|$ and $|A| \neq |B|$? Obviously there is a injective function $f: A \to B$. But if you could show that there is no injective function $f: B \to A$ would that imply $|A| \neq |B|$ ?

-
Do you know what $|A|\neq|B|$ means? –  Chris Eagle Nov 9 '12 at 17:29
Probably not ... –  joachim Nov 9 '12 at 17:31
You should probably find that out before attempting this question then. –  Chris Eagle Nov 9 '12 at 17:32

## 4 Answers

Yes, it would. If $A$ and $B$ had the same cardinality, there would by definition by a bijection (and therefore an injection) $f:B\to A$. It follows immediately that if there is no such injection, then $|A|\ne|B|$.

Thus, if you have an injection from $A$ to $B$, then either there is an injection from $B$ to $A$, in which case $|A|=|B|$ by the Cantor-Schröder-Bernstein theorem, or there is no injection from $B$ to $A$, in which case $|A|<|B|$.

In your specific problem there are fairly obvious injections from $A$ to $B$ and to $C$. It is possible to find an injection from $B$ to $A$ directly, but that is not how I would approach the problem. I would (1) note that for each $n$ there is a bijection between the polynomials of degree $n$ and $\Bbb R^{n+1}$; (2) find a bijection between $\Bbb R$ and $\Bbb R^2$; (3) show by induction that $|\Bbb R^n|=|\Bbb R|$ for $n\in\Bbb Z^+$; and (4) use this to show that $|B|=|\Bbb N\times\Bbb R|=|\Bbb R|$. Depending on how much I had already proved about cardinalities, I could skip some of these steps.

I would not that there is an easy bijection between $C$ and $\wp(\Bbb R)$ and apply Cantor’s theorem to deal with $C$.

-
Can you give me a hint for a injective function from $\mathbb{R}^2$ to $\mathbb{R}$? –  joachim Nov 10 '12 at 16:44
@joachim: It’s sufficient to find one from $(0,1)^2$ to $(0,1)$. Try $$\langle 0.a_1a_2a_3\dots,0.b_1,b_2b_3\dots\rangle\mapsto\langle0.a_1b_1a_2b_2a_3b_3\dots\rangle\;.$$ If you get completely stuck, take a look at this answer, which even shows how to get a bijection. –  Brian M. Scott Nov 10 '12 at 16:53

Sure. $|B|\leq |A|$ means that there exists an injective function $f:B\to A$. If you can prove that there is no injective function $f:B\to A$ then $|B|\not\leq |A|$, in particular $|B|\neq|A|$

-

Of course if you could show that there is no injection from $B$ to $A$, then it it would also mean that there is no bijection from $B$ to $A$, so $|A|$ wouldn't be equal to $|B|$.

Still, it is not the case in your problem. Here is a hint about sets $A$ and $B$: prove that $|\mathbb{R}^n| = |\mathbb{R}|$. Then think how to use this knowledge about $\mathbb{R}^n$ to analyze $\mathbb{R}[x]$.

As for $C$, I would suggest looking at Cantor's diagonal argument.

-

If you can show that there is no injective function $X\to Y$ and you already know there is an injection $Y\to X$ then you can conclude that $|Y|\leq|X|$ and $|Y|\neq|X|$. Or in short, $|Y|<|X|$.

You could in fact prove that for $A$ and $C$, Cantor's theorem comes to mind.

As for $A$ and $B$, as you say there is an obvious injection $A\to B$, but there is indeed an injection from $B$ to $A$.

Note that $|A|=2^{\aleph_0}$; and $|B|=|\bigcup_{n=1}^\infty\mathbb R^n|\leq(2^{\aleph_0})^{\aleph_0}$, using basic cardinal arithmetics one can deduce the wanted equality.

-


text:
## Individual gas constants for some gases (J/kg x K)

Gas
Air
Argon
Helium
Hydrogen
Nitrogen
Oxygen
Water vapour
R - 12
R - 22
Ri
287
208
2079
4116
297
260
461
68.7
96.1

If many calculations are made for the same gas, it is often easier to use the individual gas constant Ri

$p \times V = \nu \times Ri \times T$


text:
Synopsis: A Single-Molecule Light-Emitting Diode

Light emitted as electrical current flows through an organic polymer molecule stretched between a metal tip and surface.

Transforming electrical current into light is critical for technologies such as telecommunications and displays. In Physical Review Letters, researchers report luminescence from a single polymer molecule, representing the smallest possible organic light-emitting diode (OLED) device.

To electrically connect to an individual polymer molecule, Gaël Reecht of the University of Strasbourg, France, and his colleagues used a gold-coated scanning tunneling microscope tip to identify and then grab one end of a single polythiophene molecule lying on a gold substrate. When they pulled back the tip and applied a voltage, they measured a nanoampere-scale electrical current running between the tip and substrate through the polymer, which was held at just a few kelvins. As long as the voltage was large enough, the energy spectrum of the emitted light didn’t change, leading the researchers to conclude the light emerges when electrons jump between intrinsic energy levels of the polymer, not those of the metal electrodes.

Still, the light emission was strongly enhanced by the sloshing it generated in nearby electrons in the gold tip and surface. When the tip had a large negative voltage, a photon emerged for every $100,000$ electrons that entered the molecule from the tip. But with the opposite polarity, the team suggests that the molecule’s stronger electrical connection to the substrate keeps the relevant molecular level too high in energy to be populated from that side. The observed $10,000$-fold asymmetry is reminiscent of that in commercial OLED devices, but on a vastly smaller scale. – Don Monroe

More Features »

Announcements

More Announcements »

Nanophysics

Next Synopsis

Particles and Fields

Related Articles

Nanophysics

Viewpoint: Squeezed Environment Boosts Engine Performance

A tiny engine can surpass the Carnot limit of efficiency when researchers engineer the thermal properties of the environment. Read More »

Nanophysics

Synopsis: Transistor Breaks Law of Thermal Conductivity

A single-electron transistor carries more heat than that predicted by the Wiedemann-Franz law linking thermal and electrical conductivities. Read More »

Nanophysics

Synopsis: Two-Pulse X Rays Probe Skyrmions

A new x-ray spectroscopy technique can measure magnetic fluctuations in vortex-like structures called Skyrmions with nanosecond resolution. Read More »


text:
# Finding Friction

1. Nov 3, 2007

### missashley

1. The problem statement, all variables and given/known data

A 37 kg box slides down a 35 degree ramp with an acceleration of 1.35 m/s^2. The acceleration of gravity is 9.81 m/s^2.

Find the coefficient of kinetic friction between the box and the ramp.

2. Relevant equations

Ff= MkFn
Finding X and Y components of Fg

3. The attempt at a solution

Fg = 37 * 9.81 = 362.97 N
Fgx = 362.97 sin 35 = 208.1910391
Fgy = 362.97 cos 35 = 297.3276175

Fn = Fgy

F = ma
F = 37 * 1.35 = 49.95

49.95 / 297.3276175 = 0.167996 <~coefficient of kinetic friction

Did I do this right? What did I do wrong?

I think I did something wrong because the coefficient is greater than one

Please check what I did wrong and how can I fix it?

2. Nov 3, 2007

### Sourabh N

This is wrong. You can find the frictional force from known data and
$$\mu$$ = F$$_{fric}$$ / F$$_{normal}$$

3. Nov 3, 2007


text:
Question

# Which one of the following statements best describes Boyle's law?

A

For a fixed mass of gas at constant pressure, its temperature is proportional to its volume.

B

The temperature of fixed mass of gas at a constant pressure is inversely proportional to its volume.

C

For a fixed volume of gas at a constant temperature, the pressure of the gas is inversely proportional to its mass.

D

For fixed mass of gas at constant temperature, the pressure of the gas is inversely proportional to its volume.

Solution

## The correct option is A For fixed mass of gas at constant temperature, the pressure of the gas is inversely proportional to its volume. According to Boyle's law- At constant temperature, the product of pressure and volume of given mass of gas is constant.

Suggest corrections