Theano is a Python library and optimizing compiler for manipulating and evaluating mathematical expressions, especially matrix-valued ones. In Theano, computations are expressed using a NumPy-esque syntax and compiled to run efficiently on either CPU or GPU architectures. == History == Theano is an open source project primarily developed by the Montreal Institute for Learning Algorithms (MILA) at the Université de Montréal. The name of the software references the ancient philosopher Theano, long associated with the development of the golden mean. On 28 September 2017, Pascal Lamblin posted a message from Yoshua Bengio, Head of MILA: major development would cease after the 1.0 release due to competing offerings by strong industrial players. Theano 1.0.0 was then released on 15 November 2017. On 17 May 2018, Chris Fonnesbeck wrote on behalf of the PyMC development team that the PyMC developers will officially assume control of Theano maintenance once the MILA development team steps down. On 29 January 2021, they started using the name Aesara for their fork of Theano. On 29 Nov 2022, the PyMC development team announced that the PyMC developers will fork the Aesara project under the name PyTensor. == Sample code == The following code is the original Theano's example. It defines a computational graph with 2 scalars a and b of type double and an operation between them (addition) and then creates a Python function f that does the actual computation. == Examples == === Matrix Multiplication (Dot Product) === The following code demonstrates how to perform matrix multiplication using Theano, which is essential for linear algebra operations in many machine learning tasks. === Gradient Calculation === The following code uses Theano to compute the gradient of a simple operation (like a neuron) with respect to its input. This is useful in training machine learning models (backpropagation). === Building a Simple Neural Network === The following code shows how to start building a simple neural network. This is a very basic neural network with one hidden layer. === Broadcasting in Theano === The following code demonstrates how broadcasting works in Theano. Broadcasting allows operations between arrays of different shapes without needing to explicitly reshape them.
Sports Card Investor
Sports Card Investor is an American sports collectibles media platform and mobile application founded by Geoff Wilson. The platform provides market data, analysis, and editorial content focused on sports trading cards and related collectibles. It operates a website, mobile app, and digital media channels covering developments in the sports card industry. The company posted its first YouTube video in July 2019, shortly before a period of rapid growth in sports card collecting in the early 2020s, which was marked by increased trading volumes and mainstream media attention. == History == Sports Card Investor was founded by Geoff Wilson, an entrepreneur and collector who began publishing sports card–related content online before launching the platform's dedicated app and subscription tools. In February 2020, the company launched Market Movers, the first website and app to chart sports card prices and track card collections. The platform expanded its media presence through partnerships and distribution agreements. In 2023, Yahoo Sports announced a new collectibles coverage initiative that included additional content from Sports Card Investor. In February 2024, the Sports Card Investor studio relocated to CardsHQ in Atlanta, Georgia, and visitors to the facility can watch Sports Card Investor videos being filmed. == Platform and content == The Sports Card Investor app provides users with pricing data, portfolio-tracking tools, and market-trend analysis for trading cards. The company also produces video and editorial content discussing market developments, grading trends, and major card releases. Coverage in industry publications has referenced Sports Card Investor in discussions about shifts in sports card licensing rights and hobby market reactions. == Industry context == The growth of Sports Card Investor coincided with a broader resurgence in trading card markets, including record sales and expanded retail presence. Mainstream outlets have cited the company and its founder in reporting on collectibles investing trends, grading practices, and market volatility. The Sports Card Investor app has attracted over 37,000 reviews on the Apple App Store, reflecting its strong user engagement within the sports card community.
Dominant resource fairness
Dominant resource fairness (DRF) is a rule for fair division. It is particularly useful for dividing computing resources in among users in cloud computing environments, where each user may require a different combination of resources. DRF was presented by Ali Ghodsi, Matei Zaharia, Benjamin Hindman, Andy Konwinski, Scott Shenker and Ion Stoica in 2011. == Motivation == In an environment with a single resource, a widely used criterion is max-min fairness, which aims to maximize the minimum amount of resource given to a user. But in cloud computing, it is required to share different types of resource, such as: memory, CPU, bandwidth and disk-space. Previous fair schedulers, such as in Apache Hadoop, reduced the multi-resource setting to a single-resource setting by defining nodes with a fixed amount of each resource (e.g. 4 CPU, 32 MB memory, etc.), and dividing slots which are fractions of nodes. But this method is inefficient, since not all users need the same ratio of resources. For example, some users need more CPU whereas other users need more memory. As a result, most tasks either under-utilize or over-utilize their resources. DRF solves the problem by maximizing the minimum amount of the dominant resource given to a user (then the second-minimum etc., in a leximin order). The dominant resource may be different for different users. For example, if user A runs CPU-heavy tasks and user B runs memory-heavy tasks, DRF will try to equalize the CPU share given to user A and the memory share given to user B. == Definition == There are m resources. The total capacities of the resources are r1,...,rm. There are n users. Each users runs individual tasks. Each task has a demand-vector (d1,..,dm), representing the amount it needs of each resource. It is implicitly assumed that the utility of a user equals the number of tasks he can perform. For example, if user A runs tasks with demand-vector [1 CPU, 4 GB RAM], and receives 3 CPU and 8 GB RAM, then his utility is 2, since he can perform only 2 tasks. More generally, the utility of a user receiving x1,...,xm resources is minj(xj/dj), that is, the users have Leontief utilities. The demand-vectors are normalized to fractions of the capacities. For example, if the system has 9 CPUs and 18 GB RAM, then the above demand-vector is normalized to [1/9 CPU, 2/9 GB]. For each user, the resource with the highest demand-fraction is called the dominant resource. In the above example, the dominant resource is memory, as 2/9 is the largest fraction. If user B runs a task with demand-vector [3 CPU, 1 GB], which is normalized to [1/3 CPU, 1/18 GB], then his dominant resource is CPU. DRF aims to find the maximum x such that all agents can receive at least x of their dominant resource. In the above example, this maximum x is 2/3: User A gets 3 tasks, which require 3/9 CPU and 2/3 GB. User B gets 2 tasks, which require 2/3 CPU and 1/9 GB. The maximum x can be found by solving a linear program; see Lexicographic max-min optimization. Alternatively, the DRF can be computed sequentially. The algorithm tracks the amount of dominant resource used by each user. At each round, it finds a user with the smallest allocated dominant resource so far, and allocates the next task of this user. Note that this procedure allows the same user to run tasks with different demand vectors. == Properties == DRF has several advantages over other policies for resource allocation. Proportionality: each user receives at least as much resources as they could get in a system in which all resources are partitioned equally among users (the authors call this condition "sharing incentive"). Strategyproofness: a user cannot get a larger allocation by lying about his needs. Strategyproofness is important, as evidence from cloud operators show that users try to manipulate the servers in order to get better allocations. Envy-freeness: no user would prefer the allocation of another user. Pareto efficiency: no other allocation is better for some users and not worse for anyone. Population monotonicity: when a user leaves the system, the allocations of remaining users do not decrease. When there is a single resource that is a bottleneck resource (highly demanded by all users), DRF reduces to max-min fairness. However, DRF violates resource monotonicity: when resources are added to the system, some allocations might decrease. == Extensions == Weighted DRF is an extension of DRF to settings in which different users have different weights (representing their different entitlements). Parkes, Procaccia and Shah formally extend weighted DRF to a setting in which some users do not need all resources (that is, they may have demand 0 to some resource). They prove that the extended version still satisfies proportionality, Pareto-efficiency, envy-freeness, strategyproofness, and even Group strategyproofness. On the other hand, they show that DRF may yield poor utilitarian social welfare, that is, the sum of utilities may be only 1/m of the optimum. However, they prove that any mechanism satisfying one of proportionality, envy-freeness or strategyproofness may suffers from the same low utilitarian welfare. They also extend DRF to the setting in which the users' demands are indivisible (as in fair item allocation). For the indivisible setting, they relax envy-freeness to EF1. They show that strategyproofness is incompatible with PO+EF1 or with PO+proportionality. However, a mechanism called SequentialMinMax satisfies efficiency, proportionality and EF1. Wang, Li and Liang present DRFH - an extension of DRF to a system with several heterogeneous servers. == Implementation == DRF was first implemented in Apache Mesos - a cluster resource manager, and it led to better throughput and fairness than previously used fair-sharing schemes.
Server.com
Server.com is a domain name that was owned by software as a service (SaaS) company Server Corporation. They offered a suite of services from 1996 until 2007. It was the first SaaS site to offer a variety of services and the first to use the term WebApp to describe its services. It was selected as an Incredibly Useful Site by Yahoo! Internet Life magazine. net magazine listed Server.com among the 100 most influential websites of all time. Server.com launched in 1996 offering the first online personal information manager. In 1997, they rolled out the first threaded message board service; the first web based mailing list manager; one of the first online calendar services; and one of the first online form builders. In 2000, Server.com partnered with NBCi and became server.snap.com until 2001. In 2001, Server.com was serving 100 million monthly pageviews. Media Life declared it one of the 20 biggest ad domains on the Web. In 2002, Server.com developed one of the first web-based RSS aggregators. In 2007, all services were moved to YourWebApps.com. The domain name Server.com was sold in 2009 for $770,000.
Focus recovery based on the linear canonical transform
For digital image processing, the Focus recovery from a defocused image is an ill-posed problem since it loses the component of high frequency. Most of the methods for focus recovery are based on depth estimation theory. The Linear canonical transform (LCT) gives a scalable kernel to fit many well-known optical effects. Using LCTs to approximate an optical system for imaging and inverting this system, theoretically permits recovery of a defocused image. == Depth of field and perceptual focus == In photography, depth of field (DOF) means an effective focal length. It is usually used for stressing an object and deemphasizing the background (and/or the foreground). The important measure related to DOF is the lens aperture. Decreasing the diameter of aperture increases focus and lowers resolution and vice versa. == The Huygens–Fresnel principle and DOF == The Huygens–Fresnel principle describes diffraction of wave propagation between two fields. It belongs to Fourier optics rather than geometric optics. The disturbance of diffraction depends on two circumstance parameters, the size of aperture and the interfiled distance. Consider a source field and a destination field, field 1 and field 0, respectively. P1(x1,y1) is the position in the source field, P0(x0,y0) is the position in the destination field. The Huygens–Fresnel principle gives the diffraction formula for two fields U(x0,y0), U(x1,y1) as following: U ( x 0 , y 0 ) = 1 j λ ∫ ∫ U ( x 1 , y 1 ) e j k r 01 r 01 cos θ d x 1 d y 1 {\displaystyle \mathbf {U} (x_{0},y_{0})={\frac {1}{j\lambda }}\int \!\int \mathbf {U} (x_{1},y_{1}){\frac {e^{jkr_{01}}}{r_{01}}}\cos \theta dx_{1}dy_{1}} where θ denotes the angle between r 01 {\displaystyle r_{01}} and z {\displaystyle z} . Replace cos θ by r 01 z {\displaystyle {\frac {r_{01}}{z}}} and r 01 {\displaystyle r_{01}} by [ ( x 0 − x 1 ) 2 + ( y 0 − y 1 ) 2 + z 2 ] 1 / 2 {\displaystyle [(x_{0}-x_{1})^{2}+(y_{0}-y_{1})^{2}+z^{2}]^{1/2}} we get U ( x 0 , y 0 ) = 1 j λ z ∫ ∫ U ( x 1 , y 1 ) exp ( j k z [ 1 + ( x 0 − x 1 z ) 2 + ( y 0 − y 1 z ) 2 ] 1 / 2 ) 1 + ( x 0 − x 1 z ) 2 + ( y 0 − y 1 z ) 2 d x 1 d y 1 {\displaystyle \mathbf {U} (x_{0},y_{0})={\frac {1}{j\lambda z}}\int \!\int \mathbf {U} (x_{1},y_{1}){\frac {\exp(jkz[1+({\frac {x_{0}-x_{1}}{z}})^{2}+({\frac {y_{0}-y_{1}}{z}})^{2}]^{1/2})}{1+({\frac {x_{0}-x_{1}}{z}})^{2}+({\frac {y_{0}-y_{1}}{z}})^{2}}}dx_{1}dy_{1}} The further distance z or the smaller aperture (x1,y1) causes a greater diffraction. A larger DOF can lead to a more effective focused wave distribution. This seems to be a conflict. Here are the notations: Diffraction In a real imaging environment, the depths of objects comparing to the aperture are usually not enough to lead to serious diffraction. However, a long enough depth of the object can truly blurs the image. Effective Focus Small aperture, small blurring radius, few wave information. Loses details in comparing to a large aperture. In conclusion, diffraction explains a micro behavior whereas DOF shows a macro behavior. Both of them are related to aperture size. == Linear canonical transform == As the meaning of "canonical", the linear canonical transform (LCT) is a scalable transform that connects to many important kernels such as the Fresnel transform, Fraunhofer transform and the fractional Fourier transform. It can be easily controlled by its four parameters, a, b, c, d (3 degrees of freedom). The definition: L M ( f ( u ) ) = ∫ L M ( u , u ′ ) f ( u ′ ) d u ′ {\displaystyle L_{M}(f(u))=\int L_{M}(u,u')f(u')du'} where L M ( u , u ′ ) = { 1 b e − j π / 4 e [ j π ( d b u 2 ) − 2 1 b u u ′ + a b u ′ 2 ] , if b ≠ 0 d e j 2 c d u 2 δ ( u ′ − d u ) , if b = 0 {\displaystyle L_{M}(u,u')={\begin{cases}{\sqrt {\frac {1}{b}}}e^{-j\pi /4}e^{[j\pi ({\frac {d}{b}}u^{2})-2{\frac {1}{b}}uu'+{\frac {a}{b}}u'^{2}]},&{\mbox{if }}b\neq 0\\{\sqrt {d}}e^{{\frac {j}{2}}cdu^{2}}\delta (u'-du),&{\mbox{if }}b=0\end{cases}}} Consider a general imaging system with object distance z0, focal length of the thin lens f and an imaging distance z1. The effect of the propagation in freespace acts as nearly a chirp convolution, that is, the formula of diffraction. Besides, the effect of the propagation in thin lens acts as a chirp multiplication. The parameters are all simplified as paraxial approximations while meeting the freespace propagation. It does not consider aperture size. From the properties of the LCT, it is possible to obtain those 4 parameters for this optical system as: [ 1 − z 1 f λ z 0 − λ z 0 z 1 f + λ z 1 − 1 λ f 1 − z 0 f ] {\displaystyle {\begin{bmatrix}1-{\frac {z_{1}}{f}}\quad &\lambda z_{0}-{\frac {\lambda z_{0}z_{1}}{f}}+\lambda z_{1}\\-{\frac {1}{\lambda f}}\quad &1-{\frac {z_{0}}{f}}\end{bmatrix}}} Once the values of z1, z0 and f are known, the LCT can simulate any optical system.
Bottlenose (company)
Bottlenose.com, also known as Bottlenose, is an enterprise trend intelligence company that analyzes big data and business data to detect trends for brands. It helps Fortune 500 enterprises discover, and track emerging trends that affect their brands. The company uses natural language processing, sentiment analysis, statistical algorithms, data mining, and machine learning heuristics to determine trends, and has a search engine that gathers information from social networks. KPMG Capital has invested a "substantial amount" in the company. Bottlenose processed 72 billion messages per day, in real-time, from across social and broadcast media, as of December 2014. == History == The company is based in Los Angeles, CA. Bottlenose is a real-time trend intelligence tool that measures social media campaigns and trends. The company also provides a free version of its Sonar tool that shows real-time trends across social media. In October 2012, the company received $1 million of funding from ff Venture Capital and Prosper Capital. By 2014, the company raised about $7 million in funding. In December 2014, KPMG Capital announced further investment in the company. In February 2015, the company confirmed it had raised $13.4 million in Series B funding led by KPMG Capital. Bottlenose partnered with the nonprofit No Labels during the 2014 State of the Union Address to analyze Twitter conversations for bipartisanship. The company also partnered with media monitoring company Critical Mention to analyze broadcast analytics. The Bottlenose Nerve Center integrated with the Critical Mention API to analyze real-time trends in television and radio broadcasts. In June 2014, Bottlenose updated its trend detection product to Nerve Center 2.0. It creates a newsfeed to show changes in trends and sends alerts when trends occur. It also has "emotion detection," which will display the emotions associated with specific comments on trending topics. In 2016, Bottlenose released its Nerve Center 3.0 platform, which was designed to automate the work of data scientists and lower the cost of artificial intelligence for businesses.
Contrast-to-noise ratio
Contrast-to-noise ratio (CNR) is a measure used to determine image quality. CNR is similar to the metric signal-to-noise ratio (SNR), but subtracts a term before taking the ratio. This is important when there is a significant bias in an image, such as from haze. As can be seen in the picture at right, the intensity is rather high even though the features of the image are washed out by the haze. Thus this image may have a high SNR metric, but will have a low CNR metric. One way to define contrast-to-noise ratio is: C = | S A − S B | σ o {\displaystyle C={\frac {|S_{A}-S_{B}|}{\sigma _{o}}}} where SA and SB are signal intensities for signal producing structures A and B in the region of interest and σo is the standard deviation of the pure image noise.