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Carol Novello is the author of "Mutual Rescue: How Adopting a Homeless Animal Can Save You, Too"

Carol Novello is the author of "Mutual Rescue: How Adopting a Homeless Animal Can Save You, Too"

Won the award at the SSON's 2019 North American Shared Services Conference.

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Rita McGrath, professor at Columbia Business School, says the need for organizations to adopt digital business models is more important than ever. Change is accelerating as startups tackle incumbents. And suddenly the coronavirus crisis is forcing the hand of many companies that have put off digital transformations. She explains how established firms can avoid bet-the-farm moves and instead take small steps and quickly target their experiments. McGrath is the coauthor of the HBR article "Discovery-Driven Digital Transformation."

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• The storied investment bank is seeing leadership shakeups under CEO David Solomon and a slew of partner departures. 
• Goldman has been moving away from high-risk businesses like trading and is making pushes into more stable areas like consumer lending, wealth management, and transaction banking. 
• There have been big cultural changes, too. Solomon is looking to create a more transparent workplace, while new tech execs are taking cues from Silicon Valley heavy-hitters. 
• At Business Insider, we are closely tracking the latest developments at Goldman. You can read all of our Goldman coverage on BI Prime.

Storied Wall Street bank Goldman Sachs is going through some massive changes under CEO David Solomon.

It's taken big steps involving transparency and inclusion to change up its culture. It has seen a slew of partner departures — many in the securities division. And it's making big pushes into businesses like wealth management and transaction banking.  

The latest people moves

• Goldman Sachs just hired Kurt Hoffman, an expert in distressed situations and bankruptcy, to join a trading unit known for some of the bank's most lucrative deals
• Goldman Sachs' top tech exec explains how a fresh slew of senior hires are transforming the bank's approach to building products
• Read the full memo Goldman Sachs just sent naming 4 execs to lead its private-equity investments across the merchant-banking division

Culture and talent

• Read the full memo Goldman Sachs just sent to staff announcing its new head of regulatory affairs. The former White House counsel will be tasked with helping clean up the bank's 1MDB drama.
• Goldman Sachs just hired 2 senior recruiting execs focused on luring top talent from other firms —and it's a huge departure from the firm's traditional promote-from-within mentality
• Read the full memo David Solomon just sent to 38,000 Goldman Sachs employees explaining why he's moving his management team out of stuffy offices and into open seating
• Goldman Sachs CEO David Solomon and his management team are ditching their stuffy offices and moving to an open floor plan closer to the people so they can feel the buzz of New York headquarters
• Goldman Sachs just unveiled a new gender pronouns initiative as part of a broader inclusion push at the Wall Street firm
• Read the memo Goldman Sachs just sent to its employees unveiling a new pronouns initiative

Coronavirus response

• Inside a 38,000-person remote work rollout at Goldman Sachs: sleepless nights, assembly lines, and an Amazon-like hub on a Manhattan trading floor
• How a massive New York hospital secured 130,000 N95 masks from China with help from a senior partner at Goldman Sachs, private jets, and a call to Warren Buffett
• Goldman Sachs CEO David Solomon just sent a firm-wide voicemail about the coronavirus crisis. Here's what he told employees.
• Goldman Sachs and Bank of America just updated their WFH policies — again. Here's what they're telling employees about the latest steps aimed at combating the spread of coronavirus.
• Read the full memo Goldman Sachs top brass just sent detailing the firm's coronavirus contingency plans, including separating employees into 'blue' and 'white' teams to alternate working from the office and home

Consumer push, transaction banking, wealth management

• Goldman Sachs just announced its first partnership for transaction banking as it looks to build a new $1 billion business moving money around the world
• Goldman Sachs is sending much less mail to potential Marcus customers. A senior exec lays out the reason why.
• A Goldman Sachs exec explains why the bank isn't sweating concerns over the Apple Card's profitability
• A Wall Street firm crunched the numbers around how much Apple will make from its new credit card with Goldman Sachs
• Here's why Goldman Sachs just did its biggest deal in nearly 20 years as part of a pivot to less wealthy clients
• Goldman Sachs execs are opening up about their plans for Marcus, and they think it can do to banking what iTunes did to the music industry
• Goldman Sachs' partnership with Apple could move it a step closer to being 'a bank branch in your pocket'
• Human resources is the next battleground for Wall Street wealth advisers as Morgan Stanley and Goldman Sachs jockey over new turf
• Goldman Sachs has a novel method for predicting the next economic slump, and it's at the heart of its hot new business

Technology

• JPMorgan and Goldman Sachs are finally beginning to embrace fintech startups. Here's how they test the waters before committing to working with them.
• We talked to the execs behind Bloomberg's new data partnership with Goldman Sachs. Here's why they think it's a sign of Wall Street's future.
• Goldman Sachs is putting its own Marquee app on Amazon's cloud in a pitch to lure more fintech developers
• Goldman Sachs is embracing open-source code and its chief data officer says it's part of a "new world" of software
• Read the memo the new Goldman tech chief sent to the firm's 9,000-plus engineers where he urges them to ditch presentations in favor of Amazon's famous narratives
• A new Goldman Sachs tech exec hired from Amazon is taking a page from the Jeff Bezos playbook by urging engineers to ditch PowerPoint and write memos
• Goldman Sachs' new CTO shares his strategy for attracting outside developers to work more closely with the bank, giving a glimpse into the future of how Wall Street will work
• A Verizon executive is joining Goldman Sachs as chief technology officer as the Wall Street bank reshuffles its ranks
• Marty Chavez is retiring from Goldman Sachs. We chatted with him about the bank's tech transformation, why now is the right time for him to step down, and what he's planning next.
• Goldman Sachs tech guru Marty Chavez is retiring from the bank
• Goldman Sachs' CEO just warned that the bank's big tech bets might not pay off as quickly as people hope
• Goldman Sachs is scrapping a homegrown email app it once touted — and it's a sign the bank is moving away from building tech in house
• Goldman Sachs is exploring plans to create a Netflix for data, and it marks a new frontier for Wall Street
• Goldman Sachs' internal idea factory hatched a plan for the Google of Wall Street, and it's now looking for the next big thing to disrupt the bank
• Goldman Sachs' big bet on the future of Wall Street had a rocky start. Here's the inside story of the bank's struggle to grow its next business and an exclusive look at its plans

Trading

• Bank of America is shaking up its global markets division and poached a Goldman Sachs exec to fill a key new role
• Goldman Sachs' massive quant business now rivals AQR and Two Sigma. We talked to the bank's top quant about asset growth, finding data sources, and why critics of computerized trading are wrong.
• Goldman Sachs' CEO tells us the bank is winning over quant clients. That helped it outpace rivals like JPMorgan last quarter.
• Goldman Sachs is cutting about 5% of sales and trading staff after senior equities leaders delivered a tough town-hall talk
• Goldman Sachs is moving away from a tool championed by its former CFO as it pushes its traders to see clients where they once saw quick wins
• Goldman Sachs is shuffling its top stock trading executives as the business tries to claw back market share from Morgan Stanley and JPMorgan
• Goldman Sachs's bond trading unit is still trying to find its way — and it represents a key challenge for new CEO David Solomon

Alternatives

• Read the full memo Goldman Sachs just sent naming 4 execs to lead its private-equity investments across the merchant-banking division
• Goldman Sachs is making targeted hires for a 'storefront' for alternative investments that's modeled after firms like KKR and Blackstone
• Goldman Sachs' push into private equity is ruffling feathers at Blackstone — and it might be a sign of big client skirmishes to come
• Goldman Sachs execs are jockeying for control of the firm's lucrative private investing units after a plan to merge it — and the stakes couldn't be higher
• Meet the Goldman Sachs execs tasked with building the firms' new Blackstone-esque private-investing unit — and pumping up the bank's flagging stock price
• 'It's good to be Rich': Meet the Goldman Sachs banker who has built a private investing empire that goes head-to-head with Blackstone — and you've probably never heard of him
• Goldman Sachs is considering a shakeup of its alternative investing units as part of a plan to simplify the bank's strategy

Deals

• Goldman Sachs is assembling a team of senior bankers focused on middle-market private equity. Here are the key hires and the playbook they'll use to land new clients.
• Goldman Sachs unloaded some of its WeWork shares before its investment bankers pitched investors on what it once considered a $60 billion-plus IPO
• Goldman Sachs just revealed it sold part of its Uber stake to SoftBank and it helped boost a $4.5 billion business
• A senior Goldman Sachs fintech banker was about to join JPMorgan — but then got lured back —and it's another sign of the fierce battle for M&A talent
• Goldman just promoted a star tech banker close to Tesla and Microsoft to co-head one of its most profitable businesses, as incoming CEO Solomon makes his mark
• Goldman Sachs just announced a shakeup of its leadership — and it signals the rise of bankers over traders
• A tug-of-war between Goldman Sachs and JPMorgan over a top banker highlights Wall Street's $1 trillion battleground

Investor day 2020

• Inside Goldman Sachs' first investor day, where avocado toast and crab apples were served with tech talk, 3-year plans, and a surprising trading mea culpa
• Goldman Sachs just revealed a new wealth brand at its first-ever investor day. It shows how the bank is trying to reshape its strategy — and image.
• Goldman Sachs just unveiled hundreds of slides laying out the future of the company. Here are the 10 crucial slides that show how it plans to transform into a bank for everyone.
• Goldman Sachs is rethinking how it makes private-equity bets with its own money – and one analyst thinks that shift will be a big driver of its stock price

Careers 

• Goldman Sachs is now hiring high-school graduates for roles in Salt Lake City, one of the company's 'high value' locations
• Goldman Sachs has lost at least 54 partners since David Solomon became CEO. We're keeping a running list — and compiling details from insiders about how the exits are being celebrated.
• Read the full memo Goldman Sachs' top brass just sent to staff announcing 2 heads of the bank's private-investing arm are out as it's gearing up to raise billions
• 2 coheads of Goldman Sachs' private-investing business are retiring, in a blow to David Solomon's fundraising plans
• A Goldman Sachs partner who just resigned is leaving behind a job overseeing $2 billion for a London VC with a leading stake in neobank Revolut
• Read the memo announcing the departure of Adam Korn, the Goldman Sachs exec who was 'instrumental in building and championing' innovations like the bank's Marquee platform
• Another Goldman Sachs partner is out. HR chief Dane Holmes is the latest key player to leave the Wall Street bank in a matter of days.
• Goldman Sachs is offering buyouts to encourage partners to leave as CEO David Solomon works to shrink one of the most elite clubs on Wall Street
• Goldman Sachs is making renewable energy a big priority based on its hiring strategy. It's a sign that its ideas incubator is working.
• The David Solomon era at Goldman Sachs kicked off with 43 words Lloyd Blankfein would never say
• Goldman Sachs CEO David Solomon shares his best leadership advice
• Goldman Sachs is shaking up the way it stocks one of the most elite clubs on Wall Street — and it shows how banks are back to making money again
• Goldman Sachs' 1MDB problems are eating into employee morale, and insiders worry the firm will use its legal woes as an excuse to scrimp on bonuses
• Goldman Sachs is about to move dozens of jobs out of pricey New York to Utah as Wall Street turns to cheaper cities

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See Also:

• Goldman Sachs just hired Kurt Hoffman, an expert in distressed situations and bankruptcy, to join a trading unit known for some of the bank's most lucrative deals
• With retailers like J. Crew and Neiman Marcus floundering, top restructuring bankers are seeing a surge in work. Here's how firms like Lazard, Evercore, and Moelis are staffing up.
• A startup that uses AI to scan Wall Street chats is flagging more people for cursing and complaining — and it could be a sign of bigger compliance issues while people work from home

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The consumer has spoken. Forrester Research asked 5,000 of them, "What created the biggest pain when you contacted a business for customer service?" They answered lack and consistency of agent knowledge, followed by the difficulty of finding relevant answers on company websites. So, what is driving this dissatisfaction?

Margaret Parker, MD, MCCM, speaks with Christina L. Cifra, MD. Dr. Cifra is a Pediatric Intensivist and an Assistant Professor in the Department of Pediatrics at the University of Iowa Carver College of Medicine in Iowa City, Iowa.

Divi’s new scroll effects are made for you to easily take your web design experience to the next level. Of course, you can apply it to elements within your section directly, but you can choose to add motion to underlying elements too. Going for an underlying approach allows you to keep content static while having […]

The post How to Use Transformed Motion Shapes as Backgrounds with Divi appeared first on Elegant Themes Blog.

Preset (Everyday) + transform + exposure + graduated filter + radial filter. If shots like this take more than 2 minutes to edit, it’s probably not worth editing. ⏱
—
Boxing Day will be the last day to get my Lightroom presets discounted, which leaves you only 3 more days! Get on it! ???? (at Toronto, Ontario)

Recently, I walked you through how to create a simple landing page that used a couple different CSS animation techniques. “Animation” is a loose term, in web design usually referring to anything that involves movement. CSS transitions are one tool we are given to manipulate elements on state changes or mouse events, and when combines […]

The post Easy CSS Animation With Transition & Transforms appeared first on Web Designer Wall.

I wish I had found Alix Kates Shulman’s memoir "To Love What Is: A Marriage Transformed" in the first month of my husband’s severe TBI, and yet I may not have absorbed it the way I did reading it fifteen years post-injury.

We prove a continuity result for the shearlet transform when restricted to the space of smooth and rapidly decreasing functions with all vanishing moments. We define the dual shearlet transform, called here the shearlet synthesis operator, and we prove its continuity on the space of smooth and rapidly decreasing functions over $mathbb{R}^2 imesmathbb{R} imesmathbb{R}^ imes$. Then, we use these continuity results to extend the shearlet transform to the space of Lizorkin distributions, and we prove its consistency with the classical definition for test functions.

We use the classical Fourier analysis to introduce analytic families of weighted differential operators on the unit sphere. These operators are polynomial functions of the usual Beltrami-Laplace operator. New inversion formulas are obtained for totally geodesic Funk transforms on the sphere and the correpsonding lambda-cosine transforms.

We develop a distributional framework for the shearlet transform $mathcal{S}_{psi}colonmathcal{S}_0(mathbb{R}^2) omathcal{S}(mathbb{S})$ and the shearlet synthesis operator $mathcal{S}^t_{psi}colonmathcal{S}(mathbb{S}) omathcal{S}_0(mathbb{R}^2)$, where $mathcal{S}_0(mathbb{R}^2)$ is the Lizorkin test function space and $mathcal{S}(mathbb{S})$ is the space of highly localized test functions on the standard shearlet group $mathbb{S}$. These spaces and their duals $mathcal{S}_0^prime (mathbb R^2),, mathcal{S}^prime (mathbb{S})$ are called Lizorkin type spaces of test functions and distributions. We analyze the continuity properties of these transforms when the admissible vector $psi$ belongs to $mathcal{S}_0(mathbb{R}^2)$. Then, we define the shearlet transform and the shearlet synthesis operator of Lizorkin type distributions as transpose mappings of the shearlet synthesis operator and the shearlet transform, respectively. They yield continuous mappings from $mathcal{S}_0^prime (mathbb R^2)$ to $mathcal{S}^prime (mathbb{S})$ and from $mathcal{S}^prime (mathbb S)$ to $mathcal{S}_0^prime (mathbb{R}^2)$. Furthermore, we show the consistency of our definition with the shearlet transform defined by direct evaluation of a distribution on the shearlets. The same can be done for the shearlet synthesis operator. Finally, we give a reconstruction formula for Lizorkin type distributions, from which follows that the action of such generalized functions can be written as an absolutely convergent integral over the standard shearlet group.

In the present paper by the Fourier transform we show that every linear differential equations of $n$-th order has a solution in $L^1(Bbb{R})$ which is infinitely differentiable in $Bbb{R} setminus {0}$. Moreover the Hyers-Ulam stability of such equations on $L^1(Bbb{R})$ is investigated.

Large transformer-based language models have been shown to be very effective in many classification tasks. However, their computational complexity prevents their use in applications requiring the classification of a large set of candidates. While previous works have investigated approaches to reduce model size, relatively little attention has been paid to techniques to improve batch throughput during inference. In this paper, we introduce the Cascade Transformer, a simple yet effective technique to adapt transformer-based models into a cascade of rankers. Each ranker is used to prune a subset of candidates in a batch, thus dramatically increasing throughput at inference time. Partial encodings from the transformer model are shared among rerankers, providing further speed-up. When compared to a state-of-the-art transformer model, our approach reduces computation by 37% with almost no impact on accuracy, as measured on two English Question Answering datasets.

The quantum Fourier transform brings efficiency in many respects, especially usage of resource, for most operations on quantum computers. In this study, the existing QFT-based and non-QFT-based quantum arithmetic operations are examined. The capabilities of QFT-based addition and multiplication are improved with some modifications. The proposed operations are compared with the nearest quantum arithmetic operations. Furthermore, novel QFT-based subtraction and division operations are presented. The proposed arithmetic operations can perform non-modular operations on all signed numbers without any limitation by using less resources. In addition, novel quantum circuits of two's complement, absolute value and comparison operations are also presented by using the proposed QFT based addition and subtraction operations.

Representation learning is a critical ingredient for natural language processing systems. Recent Transformer language models like BERT learn powerful textual representations, but these models are targeted towards token- and sentence-level training objectives and do not leverage information on inter-document relatedness, which limits their document-level representation power. For applications on scientific documents, such as classification and recommendation, the embeddings power strong performance on end tasks. We propose SPECTER, a new method to generate document-level embedding of scientific documents based on pretraining a Transformer language model on a powerful signal of document-level relatedness: the citation graph. Unlike existing pretrained language models, SPECTER can be easily applied to downstream applications without task-specific fine-tuning. Additionally, to encourage further research on document-level models, we introduce SciDocs, a new evaluation benchmark consisting of seven document-level tasks ranging from citation prediction, to document classification and recommendation. We show that SPECTER outperforms a variety of competitive baselines on the benchmark.

In this paper we revisit the deterministic version of the Sparse Fourier Transform problem, which asks to read only a few entries of $x in mathbb{C}^n$ and design a recovery algorithm such that the output of the algorithm approximates $hat x$, the Discrete Fourier Transform (DFT) of $x$. The randomized case has been well-understood, while the main work in the deterministic case is that of Merhi et al.@ (J Fourier Anal Appl 2018), which obtains $O(k^2 log^{-1}k cdot log^{5.5}n)$ samples and a similar runtime with the $ell_2/ell_1$ guarantee. We focus on the stronger $ell_{infty}/ell_1$ guarantee and the closely related problem of incoherent matrices. We list our contributions as follows.

1. We find a deterministic collection of $O(k^2 log n)$ samples for the $ell_infty/ell_1$ recovery in time $O(nk log^2 n)$, and a deterministic collection of $O(k^2 log^2 n)$ samples for the $ell_infty/ell_1$ sparse recovery in time $O(k^2 log^3n)$.

2. We give new deterministic constructions of incoherent matrices that are row-sampled submatrices of the DFT matrix, via a derandomization of Bernstein's inequality and bounds on exponential sums considered in analytic number theory. Our first construction matches a previous randomized construction of Nelson, Nguyen and Woodruff (RANDOM'12), where there was no constraint on the form of the incoherent matrix.

Our algorithms are nearly sample-optimal, since a lower bound of $Omega(k^2 + k log n)$ is known, even for the case where the sensing matrix can be arbitrarily designed. A similar lower bound of $Omega(k^2 log n/ log k)$ is known for incoherent matrices.

Sparse models require less memory for storage and enable a faster inference by reducing the necessary number of FLOPs. This is relevant both for time-critical and on-device computations using neural networks. The stabilized lottery ticket hypothesis states that networks can be pruned after none or few training iterations, using a mask computed based on the unpruned converged model. On the transformer architecture and the WMT 2014 English-to-German and English-to-French tasks, we show that stabilized lottery ticket pruning performs similar to magnitude pruning for sparsity levels of up to 85%, and propose a new combination of pruning techniques that outperforms all other techniques for even higher levels of sparsity. Furthermore, we confirm that the parameter's initial sign and not its specific value is the primary factor for successful training, and show that magnitude pruning cannot be used to find winning lottery tickets.

Software Defined Networking is currently revolutionizing computer networking by decoupling the network control (control plane) from the forwarding functions (data plane) enabling the network control to become directly programmable and the underlying infrastructure to be abstracted for applications and network services. Next to the well-known OpenFlow protocol, the XML-based NETCONF protocol is also an important means for exchanging configuration information from a management platform and is nowadays even part of OpenFlow. In combination with NETCONF, YANG is the corresponding protocol that defines the associated data structures supporting virtually all network configuration protocols. YANG itself is a semantically rich language, which -- in order to facilitate familiarization with the relevant subject -- is often visualized to involve other experts or developers and to support them by their daily work (writing applications which make use of YANG). In order to support this process, this paper presents an novel approach to optimize and simplify YANG data models to assist further discussions with the management and implementations (especially of interfaces) to reduce complexity. Therefore, we have defined a bidirectional mapping of YANG to UML and developed a tool that renders the created UML diagrams. This combines the benefits to use the formal language YANG with automatically maintained UML diagrams to involve other experts or developers, closing the gap between technically improved data models and their human readability.

Efficient computation of complex multiplication results and very efficient fast Fourier transforms (FFTs) are provided. A parallel array VLIW digital signal processor is employed along with specialized complex multiplication instructions and communication operations between the processing elements which are overlapped with computation to provide very high performance operation. Successive iterations of a loop of tightly packed VLIWs are used allowing the complex multiplication pipeline hardware to be efficiently used. In addition, efficient techniques for supporting combined multiply accumulate operations are described.

A recursive type-IV discrete cosine transform system includes a first permutation device, a recursive type-III discrete cosine/sine transform device, a cosine/sine factor generation device, a recursive type-II discrete cosine/sine transform device, a second permutation device. The first permutation device performs two-dimensional order permutation operation on N digital signals for generating N two-dimensional first temporal signals. The recursive type-III discrete cosine/sine transform device repeats a type-III discrete cosine/sine transform for generating second temporal signals. The cosine/sine factor generation device sequentially performs cosine/sine factor multiplication and corresponding addition operations for generating third temporal signals. The recursive type-II discrete cosine/sine transform device repeats a type-II discrete cosine/sine transform for generating fourth temporal signals. The second permutation device performs a one-dimensional order permutation operation for generating N one-dimensional output signals. The N one-dimensional output signals are obtained by performing a type-IV discrete cosine transform on the N digital input signals.

A system (200) and a method (100) of operating a computing device to perform memoization are disclosed. The method includes determining whether a result of a function is stored in a cache and, if so, retrieving the result from the cache and, if not, calculating the result and storing it in the cache. The method (100) includes transforming (104) by the computing device at least one selected from the input parameters and the output parameters of the function, the transforming being based on an analysis of the function and its input arguments to establish whether or not there is a possible relationship reflecting redundancy among the input parameters and output parameters of the function. The transforming may include at least one of: use of symmetry, scaling, linear shift, interchanging of variables, inversion, polynomial and/or trigonometric transformations, spectral or logical transformations, fuzzy transformations, and systematic arrangement of parameters.

Techniques for automatically partitioning a multi-platform data transform flow graph to one or more target output platforms are provided. The techniques include performing type inference on a transform graph, wherein the transform graph comprises one or more data transforms, automatically partitioning the transform graph to one or more target output platforms based on one or more policies, performing an optimization of the partitioned transform graph, and generating code, from the partitioned transform graph, for each set of the one or more data transforms based on the one or more target output platforms.

A method for designing a transformer in an integrated circuit includes receiving one or more desired characteristics of the transformer from user input and iteratively determining a design solution for the transformer through one or more simulations and modifications using a rule-set. The method combines the one or more desired characteristics with other preset characteristics of the transformer or the integrated circuit. A first model of the transformer is defined with typical load impedances and simulated having the combined characteristics to determine performance. Results of the simulation are processed to calculate performance with the load impedances specified by the user. The results are further processed to obtain a mathematical model that includes tuning capacitors. The first and subsequent models are modified by drawing on a rule-set of expert knowledge relating to general dependency of at least one design criterion, such as a physical, geometrical or performance characteristic, with another design criterion.

A method and apparatus for partitioning of the input design into repeating patterns called template cores for the application of reticle enhancement methods, design verification for manufacturability and design corrections for optical and process effects is accomplished by hierarchy analysis to extract cell overlap information. Also hierarchy analysis is performed to extract hierarchy statistics. Finally template core candidates are identified. This allows to the design to be made amenable for design corrections or other analyses or modifications that are able to leverage the hierarchy of the design since the cell hierarchy could otherwise be very deep or cells could have significant overlap with each other.

A data transform method and a data transformer. The method includes: importing a data transform rule; acquiring from the data transform rule a source data definition, a destination data definition and a data transform rule definition; predicting resource energy consumption parameters of a data transform node server according to the source data definition, the destination data definition and the data transform rule definition; and deploying a resource energy consumption optimization policy of the data transform node server according to the predicted resource energy consumption parameters of the data transform node server.

The invention relates to an optical resonator, laser apparatus and a method of generating a laser beam inside an optical resonator. The optical resonator (100) includes an optical cavity (102) and an optical element (104.1, 104.2) at either end thereof, operable to sustain a light beam (108) therein, characterized in that each optical element (104.1, 104.2) is a phase-only optical element operable to alter a mode of the beam (108) as it propagates along the length of the optical resonator (100), such that in use the beam (108) at one end of the optical resonator (100) has a Gaussian profile while the beam (108) at the other end of the optical resonator (100) has a non-Gaussian profile.

An optical element includes at least two stacked birefringent layers having respective local optical axes that are rotated by respective twist angles over respective thicknesses of the at least two layers, and are aligned along respective interfaces between the at least two layers. The respective twist angles and/or the respective thicknesses are different. The at least two stacked birefringent layers may be liquid crystal polymer optical retarder layers. Related devices and fabrication methods are also discussed.