In my last blog entry I introduced the notion that optimal decision making wasn’t ‘on the radar’ for many clients in Australasia, and laid out a couple of ideas why. I too once focussed on
Monte Carlo simulation rather than decision evaluation, but last year the most obscure event changed that.
Call me a nerd of you will, but I like modelling problems in Excel. There is skill involved in setting up a problem such that the model assumptions aren’t too gross, and an art to making the model elegant. This elegance can be very important to optimisation problems, but more on that later. My first homemade optimisation problem was generated by motorcycle racing! MotoGP, to be precise. A friendly tipping competition with friends was formed at the start of the 2009 season with the following structure:
- Entrants played the role of Team Manager.
- Team Managers had a fixed budget to spend on riders.
- Either a few good riders could be purchased, or many lesser riders, or something in between.
- The team that had accumulated the most points at the end of the season was the winner and received kudos!
Although the future results could not be known of course so I set up and ran the optimisation with Evolver after the event to see what the optimal team selection would have been. Historical data could have been used to discover the type of rider mix that tended to be optimal and thus make an informed decision for this competition. The risk in having only a few riders was that any misfortune would have a big negative impact on the points won, whereas a team consisting of many (cheaper) riders was less likely to suffer such a fate. This downside scenario will be modelled into the 2010 MotoGP Team Manager predictive, optimised model (currently in production)!
What has this to do with the corporate world? Replace “team” with portfolio and “riders” with “assets”, “shares” or “projects” and you have a classic portfolio optimisation model. I hadn’t created this model with business applications in mind but I realised that was precisely what I was doing. An instant later I realised just how useful
Evolver would be in many decision scenarios even though it doesn’t incorporate uncertainty (
RISKOptimizer does).
In the next instalment I will further explore some practical applications for Evolver and you’ll see just how universally appropriate it can be.
»
Making Optimal Choices, Part 1 Rishi PrabhakarTrainer/Consultant
Risk analysis and decision-making tools are relevant to most organisations, in most industries around the world. This is demonstrated by the speaker line-up at this year's European User Conference, an event at which we believe it is important to bring together customers from a wide range of market sectors.
We are holding '
New Approaches to Risk and Decision Analysis' at the Institute of Directors in central London on 14th and 15th April 2010. As with previous years, the programme aims to provide everyone attending with practical advice to enhance the decision-making capabilities of their organisation. Customer presentations, which offer insight into a wide variety of business applications of risk and decision analysis, include:
- CapGemini: Faldo's folly or Monty's Carlo – The Ryder Cup and Monte Carlo simulation
- DTU Transport: New approaches to transport project assessment; reference scenario forecasting and quantitative risk analysis
- Georg-August University Research: Benefits from weather derivatives in agriculture: a portfolio optimisation using RISKOptimizer
- Graz University of Technology: Calculation of construction costs for building projects – application of the Monte Carlo method
- Halcrow: Risk-based water distribution rehabilitation planning – impact modelling and estimation
- Pricewaterhouse Coopers: PricewaterhouseCoopers and Palisade: an overview
- Noven: Use of Monte Carlo simulations for risk management in pharmaceuticals
- SLR Consulting: Risk sharing in waste management projects - @RISK and sensitivity analysis
- Statoil: Put more science into cost risk analysis
- Unilever: Succeeding in DecisionTools Suite 5 rollout – Unilever's story
We will also look at the recently-launched language versions of @RISK and DecisionTools Suite, which are now available in French, German, Spanish, Portuguese and Japanese. Software training sessions will provide delegates with practical knowledge to ensure they can optimise their use of the tools and implement business best practise and methodologies.
With over 100 delegates from around the world attending, the event is also a good opportunity to network and knowledge-share with risk professionals from around the world.
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Complete programme schedule, more information on each presentation,
and registration details
Something has troubled me for some time regarding the choices being made in risk land. I train and work with many clients whom have adopted
Monte Carlo simulation techniques (via
@RISK for Excel) into the day-to-day running of their businesses. By doing so they (hopefully) now have a good understanding of the exposure they are facing be it in project cost estimation, discounted cash flow analysis or, well, anything really. But this is only one facet of risk and decision assessment, specifically dealing with the descriptive statistical output from a simulation. What of the decision evaluation component? Why aren’t more of my customers analysing the decisions they make, or better yet actually optimising them? I have a few ideas why.
If you’re in business you have to make decisions. Big ones, little ones, yes/no, multiple state and continuous value decisions. Decisions that impact other decisions in simple or complex dependency structures. But are you making the best decisions possible? I’m sure important decisions aren’t being made completely randomly (I hope!) but I see many companies who rely completely upon qualitative techniques for their decision making (experience, gut feel, etc.) which of course means optimality is no more than a hoped for outcome rather than something that is actually being worked towards.
Firstly the decision model must be identified and then quantified, and this can be a difficult task. There is a level of modelling aptitude necessary for effective modelling that goes beyond merely knowing Excel and its functions, and into the construction of logical mathematical descriptions of possibly complicated processes. Relevant decisions need to be identified and the impact of those decisions combined into a formula that can be mathematically optimised. A critical component to all this is the knowledge that spreadsheet models can actually be optimised, and that in cases where Excel’s Solver fails there are Palisade products (
Evolver and
RISKOptimzer) that can perform optimisations under virtually any circumstance.
I too used to focus on Monte Carlo simulation rather than decision evaluation, and this was mainly a product of the clients I was dealing with almost exclusively when I first worked for Palisade. In my next blog I’ll tell you why that changed and also get a little more into the nuts and bolts of optimisation.
Rishi PrabhakarTrainer/Consultant
Allan Roth, who writes a blog for CBS Money Watch called
"The Irrational Investor," recently asked his readers a rhetorical question: Is Financial Monte Carlo Simulation Dead? Since rhetorical questions demand an answer in less time than it takes the questioner to draw breath, Roth obliged.
While expressing sympathy for the investors who were victims of poor risk assessment and forecasting when the financial markets shook themselves down to rubble in 2008, Roth is taking a very politely defensive swing at one of the many critics of risk analysis who have turned up the volume since then--one Jim Otar of
Otar Retirement Solutions and the author of
Unveiling the Retirement Myth.
Roth is an experienced user of Monte Carlo software who knows the pitfalls of overoptimistic assumptions. He says he finds 99 percent of the Monte Carlo models he's see over the years to be inadequate because of this flaw. Jim Otar, for his part, finds other flaws as well: in the generation of randomness and trends and in the sequence of returns. Otar's modeling method does not rely on randomness but on a century's worth of historical data.
Our two worthy opponents put their models up against one another in a match that crunched identical inputs. Their models produced very, very similar results, apparently satisfying each analyst as to the superiority of his method. But while Roth said nice things about Otar and his model, he pointed out the limitations of relying on historical information alone. In other words, he doesn't concede.
For any kind of retirement planning models, he says, the cure to flaws is conservative input. Then he giddily sends his readers to one of those rudimentary online Monte Carlo calculators that investment firms love to offer their clients.
Rumors of this death are greatly exaggerated.
Why is it that most of the high profile projects managed by the government in the UK all ultimately become beset by problems? A number of projects jump to mind – the Millennium Dome, Wembley Stadium and currently the NHS IT. All three have been plagued by developmental delays and financial mismanagement.
Recently, yet another worthy, but ambitious project has been announced – the North-South high speed rail line to connect London to Scotland. One wonders if the government undertakes detailed quantitative project risk analysis for its infrastructure initiatives?
A good example to highlight in this context is ENGCOMP, a Saskatchewan-based engineering consulting firm that has worked with the Canadian Department of National Defence (DND) to help define budgets for the fourth phase of construction of its Fleet Maintenance Facility at Canadian Forces Base Esquimalt in Victoria, British Columbia. Using
@RISK, a Monte Carlo simulation tool, ENGCOMP helped the DND define and secure budget approval from the Federal Government’s Treasury Board. The consultancy firm was able to estimate the impact of the variability and uncertainties pertaining to risks, costs and scheduling. This assessment enabled it to estimate the project risk budget or the risk reserve and schedule contingency, which were both factored in when defining the total project cost of the infrastructure project.
The fact is, in the world of business, risk is inherent and unavoidable. Whilst one cannot completely control risk, one can certainly help reduce uncertainty, greatly increasing the chances of project success. For instance, a key finding of the project risk analysis conducted by ENGCOMP was that, taking into account all the risk and uncertainties on the project, there is an 85 per cent chance that the Fleet Maintenance Facility project will be completed in January 2014. A fairly positive result for the DND, given the scale and complexity of this project in question.
Craig FerriEMEA Managing Director of Risk & Decision Analysis
New DecisionTools Suite 5.5.1 is a maintenance update that has been fully translated into
Spanish,
German,
French,
Portuguese and
Japanese. It features simulation of password-protected worksheets in @RISK as well as an integrated RISKOptimizer toolbar. In addition, you can now also launch any DecisionTools program from within any other program already running. If you still have @RISK 5.0 or DecisionTools Suite 5.0, version 5.5.1 offers @RISK simulations that run 2 to 20 times faster than before, new scatter plots from scenario analysis, a freehand distribution artist, an Excel-style Insert Function dialog with graphs, and much more.
@RISK 5.5.1 and DecisionTools Suite 5.5.1 are free for current maintenance holders. If you don't have maintenance, contact Palisade to get up to date:
US/Canada607-277-8000, sales@palisade.com
Europe+44 1895 425050, sales@palisade-europe.com
Latin America 607-277-8000 x318, ventas@palisade.com
Brasil607-277-8000 x318, vendas@palisade.com
Asia-Pacific+61 2 9929 9799, sales@palisade.com.au
»
Get your update»
Read What's New in @RISK 5.5.1 and DecisionTools Suite 5.5.1
Longtime user of Palisade's Monte Carlo software and other decision analysis tools, Willy Aspinall uses these tools to beat back some heavy-duty varieties of uncertainty. How long will it be before a volcano actually blows its top as opposed to gurgles over its rim? What factors should transportation officials focus on to reduce the likelihood of airline disasters? What are the acceptable limits of air pollution? What exactly will the climate be like for our grandchildren?
Aspinall is often called upon to provide expert testimony on these kinds of life-and-death questions, and he has recently called attention to one of the problems with expert testimony, including his own: In which expert should you place your confidence? In an opinion piece in this January's
Nature--a magazine that is an icon of scientific validity--Aspinall describes the benefits of using a method called "expert elicitation" to balance the opinions of a group of experts. The method, developed by
Roger Cooke of Resources for the Future, attempts to quantify and then pool the uncertainties to arrive at what Cooke calls a "rational consensus."
When experts disagree, Cooke has pointed out, any attempt to impose agreement will "promote confusion between consensus and certainty." In order to get around this problem, Aspinall points out in his article, the goal of risk analysis should be to "quantify uncertainty, not to remove it from the decision process." His ongoing risk assessment of volcanic activity on the island of Monserrat in the West Indies is the longest running application of Cooke's "expert elicitation" method. For details about how the elicitation and the pooling of opinion works, I recommend taking a look at the January 2010 issue of
Nature.
Why attend? This one-day forum is a great way to find out how others in the Healthcare Industry are using our software, as well as to learn new approaches to the problems Healthcare professionals face every day. We will have six software training sessions, and six real-world case studies presented by industry experts covering risk and decision analysis from all angles specific to the Healthcare sector.
You will also see how new versions of @RISK, PrecisionTree, RISKOptimizer, TopRank, NeuralTools, StatTools, and other Palisade software tools work together to give you the most complete picture possible in your situation.
Who should attend? Professionals in risk and financial analysis in: Care Equipment & Services, Pharmaceuticals, Biotechnology & Life Sciences, Hospital Care & Management, or related services
How much? For a limited time, the cost for attending the Health Risk Analysis Forum is has been discounted $100.
$295 covers all sessions, continental breakfast, lunch and a cocktail networking reception. Attendees will also receive a welcome package that includes a 15% discount on their next software purchase.
Please contact Jameson Romeo-Hall at
jromeo-hall@palisade.com if you are interested in attending.
Location The Westin Gaslamp Quarter 910 Broadway Circle
San Diego, CA 92101
(619) 239-2200
Book your room at a discounted rate (subject to availability.)
In the last two blogs I have challenged the idea that simulation results can be boiled down to a single statistic with any positive benefit. The context of a statistic is incredibly important, which is another reason why many statistics and charts/tables should be reported on, not simply one figure. And here’s a compelling reason why.
Consider two competing, similarly-sized projects, of which a company can only pursue one. Now let’s say this company would like to take on the project that has the “least risk”. If they are only familiar with generating the P90 for the total project cost they will be forced to select the project with the lowest P90. But what if the key drivers for exceeding the P90 are easier to mitigate in one project compared to the other? Perhaps the project with the lower P90 also has a higher P95 or P99 – this means the catastrophic failure is actually greater despite a lower P90 and is the mathematical equivalent of “when things go bad, they go really bad”. Not all P90s are created equally! Such an adverse outcome might sink a smaller company where a larger one could wear the loss. The context of the company running the analysis also impacts the context of the analysis itself.
So you can see not only do simulations generate results with which informed decisions can only be made if approached holistically, but if the language used is restrictive this outcome will never be achieved. Risk analyses are a necessary part of business because most of us wish to minimise the chance that something bad will happen, quite simply. Even if a manager tells you they “want the P90” what they are really asking is “tell me about the risk we’re facing”. The answer to this fundamental question is not found in a single figure taken from a simulation, but in a range of charts and tables which require correct interpretation.
More so,
Monte Carlo simulation itself is only one piece of the risk and decision assessment pie. Decision modelling and optimisation, predictive modelling and statistical analyses should also form part of the quantitative approach to uncertainty. There is life beyond just risk simulation software, and I intend on exploring that in future blogs.
»
Part 1 »
Part 2 Rishi PrabhakarTrainer/Consultant
This Thursday, 11 March 2010 at 11am ET, Dr. Jose A. Briones, SpyroTek Performance Solutions, will present a free live webcast entitled, Use of
@RISK for Probabilistic Decision Analysis of a Manufacturing Forecast in an Environment of High Uncertainty
Profitability projections in a manufacturing environment are directly tied to how the sales forecast fits with the capability of the operation. When a company has a large portfolio of products with very different operational production rates, the manufacturing capacity of the plant will be significantly impacted by the product mix to be produced. This in turn will have a radical effect on the output of the plant and the allocation of the fixed cost of production. In this case we present an example where a company is trying to decide how best to balance the sales of certain families of products to maximize revenue, maintain a diverse product line, and properly price each individual product based on the impact to the manufacturing schedule and fixed cost allocation.
»
Register now for this FREE live webcast»
View archived webcasts
The
UK Met Office is not going to ‘live down’ its weather forecast of a ‘
barbeque Summer and a mild Winter’ for 2009, anytime soon. There was ample rain through the Summer, the Cumbrian region saw severe flooding in November and now the nation is gripped by sub-zero temperatures not experienced for more than 30 years.
The inaccurate weather forecast is not a criticism of the Met Office. Forces of nature cannot be controlled, but these severe weather conditions do highlight the need for a more risk-led approach to public service planning. As we are seeing, the lack of planning to combat the current Arctic conditions engulfing the nation has thrown the country in turmoil, not to mention the substantial losses incurred by businesses.
Global Warming is now often touted as the reason for such vagaries in weather, which according to environmentalists is set to intensify in the coming years. There is a very strong case for the government to undertake a scientific, risk-led approach to assess the potential effects of extreme weather, so that the required planning and realistic fund allocation can be made to deal with unforeseen weather situations.
For instance,
Halcrow Group Ltd, specialising in providing planning, design and management services for infrastructure development, works very closely with the UK Environment Agency on its Flood Defense programme.
It conducts risk analysis on several of the Agency’s projects, using Palisade’s @RISK. Through flood risk management, the
UK’s Environment Agency can reduce the probability of flooding from rivers and the sea through the management of land, river systems, and flood and coastal defenses. This also works to helps to reduce the damage floods can do through effective land use planning, flood warning and emergency responses.
There is now a dire need to extend this risk analysis-based approach beyond just flood defense, so that pre-emptive actions can be taken to reduce the adverse impact of extreme weather on the nation.
Craig FerriEMEA Managing Director of Risk & Decision Analysis
Where I left off last time was lamenting the use of Monte Carlo simulation to create a single value (statistic etc.) from a model. It might still not be clear why this is anathema to me, so here goes.
A simulation is not a number. It’s not one possible (future) outcome – that’s a scenario.
Monte Carlo simulation is a methodology for understanding one’s exposure to outcomes not situated close to the central tendency of the process/project in question. Note the plural “outcomes”. Risk analysis, when done properly, should let you know essentially all possible outcomes and how likely they are for your model. Output from a simulation can include a plot of means (over time), or P5s, or P95s, or the mean ± one standard deviation or any number of statistics. But that’s not plotting a simulation! Let’s not give a minimalist graph too much credit.
Such statements also perpetuate the idea that simulation is only used for creating means (or other centrally tending statistics) and ignores the wealth of information available.
Risk simulation software exists to help you do risk analysis which must include not only several statistics but also sensitivity information. It is all too easy to turn a risk assessment into a hunt for a regularly asked for percentile (such as the P90) and there ends the task. I see this a lot, especially in project cost estimation where the pressure both from management and regulatory bodies is to accurately estimate some large percentile. Once found there is usually scant further risk analysis.
Nothing good ensues. When risk analyses are run “to get ‘the’ number” they become simply another box to tick in a process and ultimately any benefits (perceived or actual) will be forgotten and lost to the ages. The notion of context is also lost. No single number by itself really means anything, or at least shouldn’t mean anything to a decision maker. I have often heard phrases like “the model returned/gave $1.2m” followed by an audience nodding in agreement. Huh? Which statistic are you talking about there, and how about reporting a few other numbers around it to place that $1.2m somewhere meaningful?
In the next installment I will look further into this issue of context and hopefully prove the necessity of an holistic approach to understanding and reporting simulation results.
»
Part 1 Rishi Prabhakar Trainer/Consultant
Both the Conservative Party and the Labour Government have indicated that they will raise the state pensions age of men and women to help reduce the UK’s national debt. In addition, more and more employers in the private sector are closing good pension schemes. The
Association of Consulting Actuaries’ (ACA) recent survey on pension trends has revealed that
59% of employers are set to review pensions ahead of 2012 and 24% of employers will consider pension benefit reductions when they have to auto-enroll all employees into a scheme.
With taxes on business and individuals likely to rise over the next few years, it is difficult to see anything other than a deteriorating climate for pension savings unless there is a radical change of approach, says the ACA. It has proposed a standing Pension Commission that will challenge the legal and regulatory hurdles standing in the way of sensible long-term pension designs.
Perhaps, a more in-depth risk analysis may help the ACA make a stronger case to the government. As a related example, in the US, the
Society of Actuaries and the
Casualty Actuary Society, sponsored a research project with the Illinois State University to develop a model for projecting economic indices such as interest rates, equity price levels, inflation rates, unemployment rates, and real estate price levels. The model was created using
Palisade’s @RISK and Microsoft Excel. In fact, @RISK’s built-in probability distribution functions, correlation matrices, and simulation results were essential to the study.
The UK ‘pensions’ landscape is set to undergo tremendous change, which will impact each and every one of us. Using scientific, risk analysis techniques, actuarial industry bodies can develop a strong argument and lobby the government so that informed policy decisions are made that are right for both the financial health of the nation and its citizens.
Craig FerriEMEA Managing Director of Risk & Decision Analysis
I read an interesting article on the causes of the
Global Financial Crisis by John B. Taylor. Although the topic is interesting enough already, especially for a member of a risk analysis-specialising company, something else caught my eye. I have observed in training workshops, onsite consulting and now academic papers a phenomenon regarding probabilistic modelling. Many of those using the methods don’t understand what they should actually be getting from the methodology. There is an intellectual leap from the deterministic to the probabilistic that sometimes does not get made. This limits the usefulness of Monte Carlo simulation, and the value of performing such statistical analyses.
Back to the article which spurred me to write this blog in the first place. Or rather, the graph. Yes a single graph of housing starts vs. time (and its brief description) leapt out at me. One of the lines on the graph was claimed to show model simulations of housing starts using the actual interest rate, compared to the interest rate ‘predicted’ by the Taylor Rule and a third line showing actual data.
So what’s the problem?
The problem is that simulation techniques should not be used to create a single value. The single ‘simulation’ line implies a single modelled/returned value for each time period. This is deterministic modelling. There may be a particular scenario that has been modelled, but it certainly isn’t a simulation that is being represented by that single line. Simulations produce thousands of data, observed values and their associated percentiles as well central moments (mean, variance etc.). Not just one value (sorry Value at Risk – that includes you too) that can be plotted as a single line. I would guess that if a simulation were run as I understand the term then the line in the chart was probably constructed using the simulated means. But I shouldn’t be guessing.
This is far from the only time I’ve seen simulation results reduced to a single entity. I have heard from clients in the past “the simulation gave $X” with little to no context around it, and this is supposed to both mean something to me and to their customers and help to make better decisions under uncertainty…
In the next blog I will explore this idea further and discuss the sorts of results that should be gleaned from a simulation. In particular, why narrowing simulation results down to a single number is counterproductive to healthy business practices.
Rishi Prabhakar Trainer/Consultant
The latest
Business in Britain survey from
Lloyds TSB Commercial shows that the UK's commercial enterprises are regaining confidence. The six monthly report charts the performance of 1,732 UK companies and their views on prospects for the coming year. Its most recent business confidence shows that expectations for both sales and orders have started to recover. The balance of firms anticipating an upturn in sales has climbed to 21% - from just 1% six months ago. And hopes for orders are also looking brighter. The balance expecting order levels to rise over the coming six months has climbed to 23%, from just 6% in the last survey.
But companies planning major new business drives for 2010 would do well to follow the example of
Thales UK, which uses @RISK to enable it to assess commercial feasibility of potential new business wins. @RISK's in-depth risk analysis ensures the leading provider of mission-critical electronic information systems for aerospace, defence and security markets around the world, is fully informed when making business-critical decisions.
Thales operates in a highly competitive environment, with technologically advanced countries presenting tough opposition when it tenders for contracts. It must continually develop highly sophisticated equipment that is robust and failsafe to meet the stringent demands of its customers. Bringing products of this calibre to market is costly in terms of time and resource, so for every competitive new business opportunity, Thales must be confident that it has a reasonable chance of success.
Using Monte Carlo analysis to show all potential scenarios and the likelihood that each will occur,
@RISK enables Thales to calculate the competitiveness of complex markets, measure probabilities for project costs, quantify rate of return, and even account for the effects of cumulative business, thereby providing decision-makers with the most complete picture possible. From this risk analysis, Thales can make an informed decision on the commercial viability of the potential new business offered.
Craig Ferri EMEA Managing Director of Risk & Decision Analysis
Merck's Art Misyan, currently Director, Financial Evaluation and Analysis at the company and a longtime practitioner of risk analysis and decision evaluation, has offered some cogent comment in response to my blog about the calculating the opportunity costs of risk analysis in making decisions under uncertainty:
"In the
Vail Daily News comment, they refer to the cost of being the second entrant. The impact of losing your innovative advantage can be somewhat quantified in a sales forecast, for example: if our launch is delayed, or if we are no longer the first entrant, then there is an EPS impact of $X.
For day-to-day risk management activities, quantifying opportunity costs is more challenging. Sometimes the best decision is the one you didn't make, and other times it costs you either in ongoing transaction costs, deal premiums, etc. For example, transaction costs can rise if the markets become more illiquid over the course of a trading day (say you're trying to trade Far East currency, but now it's late in the day Eastern Standard Time). Or, if you are executing a large-sized deal but don't place the order until late in the day - and the trade has to happen. So, hypothetically, you could calculate the impact of transaction costs, based upon average deal size and bid/offer spread at a time of day.
As a finance representative on the deal team, you are trying to help management arrive at quick decisions with the best available information, while understanding the potential risks. You don't want to be the "speed bump" in the process (again, very difficult to quantify). As part of the economic analyses, we summarize as many risks as possible, as well as a list of potential events that could impact our assessment. After management has reached a decision, we will revisit the numbers if or when these events occur over the course of the due diligence process."
Words from the wise to the wise.
By now we've become accustomed to the marvels of neural network technology and, in fact, inured to the advances it brought in statistical analysis with its computational simulations of nerve cells. Its many everyday applications--especially in online retailing--seem kind of ho-hum, and we'd be put out if for some reason they weren't in use. Wasn't it only four or five short years ago that neural nets themselves were big news?
Last week there was more
big news about neural networks: a French research team's announcement of an "organic" transistor that mimics a brain's synapse. Neural network computing is based on computational stand-ins for biological neurons, and linking these neurons with electronic synapses currently requires at least seven transistors. One new "organic" transistor can take the place of those.
The key here is nano. Tiny. Tinier than tiny. The new transistors are made of nanoparticles of gold and pentacene on a plastic substrate. The resulting connector is called a nanoparticle organic memory field-effect transistor: a NOMFET.
Not only will the NOMFETs accelerate the performance of neural network circuits, but because the human brain uses 10 to the fourth times as many synapses as neurons, the space saving NOMFETs will help make possible a generation of computers inspired by the human brain.
The rise of the NOMFET may also make possible another kind of advance, one that I find a little scary to contemplate. Because its built on plastic, the NOMFET could potentially be used to link a computer with living tissue. Get back, Frankenstein.
Palisade Training services show you how to apply @RISK and the DecisionTools Suite to real-life problems, maximizing your software investment. All seminars include free step-by-step books and multimedia training CDs that include dozens of example models.
North America
- March 1-2, 2010, Houston, TX
Monte Carlo Simulation for the Oil and Gas Industry using @RISK - 3-4 March 2010, Dayton/Versailles, OH
Decision-Making and Quantitative Risk Analysis using @RISK - 10-11 March 2010, Jersey City, NJ
Decision-Making and Quantitative Risk Analysis using @RISK - 23-24 March 2010, Denver, CO
Decision-Making and Quantitative Risk Analysis using @RISK - 23-25 March 2010, Denver, CO
Decision-Making & Quantitative Risk Analysis using the DecisionTools Suite
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